Methodology for Predicting Channel Migration (2004)

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11 CHAPTER 2 FINDINGS LITERATURE REVIEW Introduction The literature review process resulted in about 1,300 citations relating to the keyword 'meander.' However, initial examination of the titles, keywords and abstracts of the cited literature revealed that a great number of these articles were not directly relevant to this study, in general, and practical prediction of meander migration, in particular. In screening the large number of initial citations, reviewers sought to retain the key articles necessary to underpin a study of meander migration, and target the literature review on acquiring the knowledge contained in those articles for use when evaluating the relative merits of different prediction approaches. In this context, the articles selected in the targeted review covered a range of issues and aspects including: • Fundamental aspects of meandering in rivers and other fluid shear flows • Flow patterns, velocity distributions, and boundary shear stress distributions at bends • Numerical models of flow and sediment processes at bends • Meander planform characteristics • Historical and monitoring studies of meander evolution • Factors affecting rates of meander change • Styles of meander change • Conceptual and empirical models of meander evolution • Numerical models of meander migration • Technical problems related to meander measurement, characterization, and monitoring Articles excluded from the targeted review included those dealing with detailed fluid dynamics, geologic and sedimentary aspects of meandering rivers and their alluvial deposits, and material that was either too highly theoretical to apply in practice or lacked the sound basis in engineering science necessary to make it reliable. In conducting the review, particular attention was paid to careful consideration of the advantages and disadvantages of deterministic, probabilistic, analytical, and empirical approaches to meander migration prediction. Fundamental Aspects of Meandering A meander is defined as "A loop-like bend in a river characterized by a river cliff on the outside of the curve and a gently shelving point bar on the inner side of the bend" (1). Meanders are ubiquitous to the channels of creeks, streams, and rivers spanning several orders of magnitude in scale. In fact, meandering is not confined to rivers (2, 3, 4), but has also been identified in a wide variety of other fluid shear flows including: • Capillary jets and rivulets running down roughened plates • Human blood stream

12 • Water flowing over ice • Ocean currents • Planetary jet stream • Channels carved by molten lava on the Moon • Sub-surface water flows on Mars The propensity for flowing fluids to meander indicates that this behavior is inherent to shear flows and cannot be attributed solely to local non-uniformity of sediment transport or bank erosion, although both are necessary for meandering in alluvial rivers. It is clear that meanders can form almost spontaneously given the right conditions. For example, Davis (5) observed meanders to develop very quickly due to the action of swift flow on the bed of a reservoir following rupture of the dam. While the precise cause of meandering remains undefined, it seems that meandering stems from the influence on the time-averaged flow field of coherent flow structures with dimensions approximating those of the channel cross-section (6). These large eddies induce a sinuous path in the line of the maximum velocity filament and surrounding flow field that is subsequently strengthened by positive feedback between curvature of the flow and skew-induced secondary currents of Prandtl's first kind (7). Provided that the bed material is mobile, asymmetry in the velocity and boundary shear stress distributions rapidly leads to the generation of pools, riffles, and alternate bars (8) though if the channel banks are unerodible, the channel itself may remain straight indefinitely (9). In this respect, bank erosion is a necessary condition for meander initiation, although it is not a cause itself (10). In streams with erodible banks, the sinuous path of maximum velocity filament drives a matching pattern of deformation in the banklines that marks the onset of channel meandering (11, 12, 13). The point at which the channel transitions from straight or sinuous to meandering is open to debate. Leopold and Wolman (14) suggested that a sinuosity 1.5 marks the lower boundary for true meandering, although most later authors agree on a somewhat lower threshold sinuosity of 1.3. While there is still much to be explained about the fundamental causes and mechanisms of meandering, it is clear from the literature that meandering is a natural attribute of most alluvial streams. It follows that meandering behavior should be expected in alluvial streams and must be accounted for in the design, siting, and inspection of highway bridge crossings on alluvial streams. Flow Patterns, Velocity Distributions, and Boundary Shear Stress Distributions at Bends The complex nature of flow at bends caused by curvature effects has been recognized and commented on for over a century (15, 16). Early investigators quickly established that the dominant flow structure at a bend is helical flow generated by the combination of primary and secondary currents. Secondary currents occur in the plane normal to the primary flow direction and appear at bends due to skewing of a portion of the cross-stream vorticity into the long-stream direction (7, 15). The main, skew-induced secondary cell drives fast, near-surface water outwards at a bend and carries slow, near-bed water inwards. During most of the twentieth century, it was believed that helical flow associated with skew-induced secondary circulation occupied the entire cross section at the bend apex (see for example (17, 18)). But in the early

13 1970s, direct measurements of primary and secondary velocities at bends revealed that a small, counter-rotating cell may exist next to the outer bank (19). This 'outer bank cell' interacts with the main, skew-induced circulation to generate elevated velocities and high local boundary shear stresses on the lower bank and the bend adjacent to the outer bank (7, 20). It is the high intensity of flow attack that undercuts the bank and scours the bed at the toe to promote erosion, instability, and rapid bank retreat (21, 22). In turn, it is this rapid retreat of the outer bank that enables active meanders to shift and migrate. Even after the existence of the outer bank cell became widely accepted, the belief persisted that helical flow extended to the inner bank (see for example (23, 24)). However, in the late 1970s and 1980s, theoretical analyses, coupled with detailed measurements of primary and secondary velocities around the inner bank, questioned this belief (25). Theory and measurement indicated that, over the upper part of the point bar, topographic steering of the flow leads to secondary currents directed radially outwards through the whole flow depth (26). It is this outward flow that causes erosion of the outer bank early in the bend (20) and encourages the filament of maximum velocity to cross to the outer bank earlier than is predicted by most analytical models, because the models ignore the convective acceleration terms in simplified versions of equations of motion for curved flows (27). Improved understanding of the flow pattern near the inner bank is also important because it explains why the characteristic cross- profile of the point bar is non-linear. Natural point bars consist of a flat upper surface, which is dominated by outward flow (termed the point bar platform by (25)), separated from a steep lower surface, which is dominated by helical flow (termed the point bar face), and by a sharp depositional edge (termed the point bar crest). Taken together, the results of theoretical and empirical studies performed in the 1970s and 1980s yield a picture of bend flow-morphology interactions that is more complex than originally envisioned, but which is consistent with observed forms and features (Figure 1). Figure 1. Summary diagram for flow pattern and cross-sectional morphology at a bend apex (adapted from (28)).

14 As bends evolve through time, they tend to increase in amplitude and decrease in radius. Tightening of the bend produces significant changes in the flow pattern. In a series of flume and pipe experiments, Bagnold (29) noted that a zone of separation develops at the inner bank downstream of the bend apex, reducing the effective width and concentrating downstream flow against the outer bank around and downstream of the bend exit. He also noted that development of inner bank separation was associated with an increase in the propensity for meanders to migrate downstream while maintaining their shape and occurred for bend radius of curvature to width ratios (Rc/W) of the order of 2 to 3. Bagnold's results indicated that an Rc/W of 2 to 3 corresponds to a minimum in the energy losses generated by the bend, a finding that was subsequently supported on theoretical grounds by Chang (30) who found that the river does least work in turning for Rc/W of approximately 3. Bagnold's laboratory results were also supported by the field measurements of Leeder and Bridges (31) who ascribed inner bank separation to a Froude number effect, although this cannot actually be correct as Bagnold noted the same pattern of separation at bends in closed conduits where Froude number has no meaning as there is no free surface. If the bend becomes very tight, a second zone of separation develops at the outer bank (29). In Bagnold's experiments, this zone had the effect of 'stalling' the spatially organized pattern of helical flow, resulting in intense turbulence and massively increased energy losses. Outer bank separation in tight bends of meandering rivers has also been widely observed (28) and leads to marked changes in the distribution of boundary shear stress and bank retreat. Bank erosion in the zone of separation may produce rapid local retreat upstream of the bend apex that may quickly generate a 'double-headed' bend (32), while in heavily sediment-laden streams deposition of a bar in slackwater areas associated with stalled flow can lead to flow deflection and erosion of the inner bank and potential bend abandonment by chute cutoff (8, 33, 34). In either case, development of separation of flow at the outer bank marks a profound change in the evolution and migration pattern of the bend. Outer bank separation seems to occur at a lower Rc/W than that for inner bank separation, and Markham and Thorne (28) proposed generalized sketches of flow separation at bends on this basis (Figure 2). Figure 2. Generalized sketch of flow patterns and separation at very tight bends.

15 Changes in bend geometry and migration rate may be largely explained by the patterns of flow at bends and the way in which curvature effects first strengthen and later modify velocity and shear stress distributions as the bend evolves. Hey (35) provides a succinct review of bend- flow morphology relations that adequately covers the main phenomena. In long, slightly curved bends curvature effects are weak, but helical flow strengthens as bend amplitude grows and radius shortens. When flow at the inner bank separates, meander evolution switches from growth to downstream migration. If outer bank separation occurs, the bend may divide in two (double heading) or cut off. Thresholds in behavior may be related to Rc/W, which tends to decrease through time as the bend evolves. Rc/W ratios between 20 and 4 characterize bend growth, Rc/W values of 2 to 3 characterize migration, and values less than 2 characterize double heading or abandonment (36). Numerical Models of Flow and Sediment Processes at Bends Many attempts have been made to model flow and sediment processes at bends, and the fundamental approaches that can be adopted have been fully reviewed in papers, texts, and research monographs such as Henderson (18), Parker et al. (37), Elliott (38), and Ikeda and Parker (39). Many models stem from the early work of Engelund (40) who produced a simplified set of equations describing flow at a bend that were amenable to analytical solution. In particular, Engelund's approach was developed and refined by Odgaard (41, 42) to produce a model that could be applied in the context of engineering analysis of meandering rivers. Odgaard's work is particularly significant because he went on to use the implications of his analytical bend-flow model to underpin an empirical model for bank retreat at bends (43, 44). However, Engelund's approximations of the equations of motion for curved flow were heavily criticized by Dietrich et al. (45) because he ignored certain terms for convective accelerations, which turned out to be crucial to generating outward secondary flow near the inner bank. The model of Smith and McLean (27) demonstrated that these terms were not negligible and their omission seriously limited the capability of Engelund's model (or other models derived from it) to represent bend flow properly. However, application of the Smith and McLean model demands very accurate data on water surface topography. It is sensitive to errors of only ± 0.04 inches (± 1 mm) in water-surface elevation, ruling it out as a tool for engineering analysis or design in real alluvial streams. A number of authors have attempted to produce simpler models suitable for engineering applications by modifying more complex models. This approach can be illustrated by the work of Garcia et al. (46) who developed the model of Ikeda et al. (47) specifically to provide "A Tool for Stream Management and Engineering." They combined the 2-dimensional, depth-averaged St. Venant equations for shallow flow with the depth-averaged continuity equation to produce a function that gives the depth-averaged downstream velocity at every point in the channel. Knowledge of the spatial distribution of depth-averaged velocity can be used to drive a morphological model capable of predicting bed scour and the spatial distribution of bank retreat. However, the practical utility of Garcia et al.'s model comes at the price of accepting limiting assumptions that rule out its application to many alluvial rivers. For example, boundary conditions specify a constant channel width maintained by parallel migration of inner and outer banks, a linear, steady-state, cross-stream bed slope, and a bend radius that is large compared to

16 the channel half-width. There are theoretical difficulties too. For instance, sediment continuity is neglected so that an important reality check is eliminated. Cherry et al. (48) evaluated the performance of Garcia et al.'s (46) model in forecasting the behavior of bends at 26 sites selected from the Brice (49) data set on planform shifting of meanders in alluvial streams. They discovered that additional data collection was essential to support application of the computational model, which would limit the applicability of the approach to sites where detailed data either pre-existed due to earlier academic research or could be collected through intensive fieldwork. The results of model application were not encouraging and they concluded that prediction of meander migration based on a computational bend-flow model was not feasible at that time (mid-1990s). (For further discussion, see the section on Evaluation of Analysis Options). Meander Planform Characteristics Meanders are best appreciated and described when viewed from above and there has been a great deal of study directed at defining and analyzing meander planform. It is in terms of planform shape and dimensions that a meander bend is defined. Figure 3 illustrates the most commonly used parameters of bend geometry. Planform studies have attempted to characterize the shape of an individual bend or pair of bends when viewed from above using a variety of mathematical functions. Early investigators examined circular, parabolic, and sine curves (Figure 4) before deciding that a sine-generated curve best resembled an idealized meander (50). Figure 3. Definition of key planform parameters.

17 Figure 4. Simple mathematical functions used to represent meander shape. However, Leopold and Langbein also noted that, unlike the simple geometric shapes they investigated, real meander bends are rarely symmetrical. Much subsequent work [well reviewed by Ferguson (51) and Carson and Lapointe (52)] has failed to produce a function that describes meander form to the general satisfaction of academics. It is recognized that attempts to find a complex function capable of accurately representing idealized planform for a meander are probably futile (53, 54). Carson and Lapointe (52) recommend that sine-generated models of meander shape be discarded but do not suggest an alternative function that should be used. Although Chang (55) reports on flow paths and migration of symmetrical bends, Whitesell et al. (56) concluded that asymmetry is inherent to meander bends. The problem is eloquently captured by Weihaupt (57) who stated: "After working with river meanders for a number of years, one cannot help but believe that a common geometry must underlie all meanders. For any individual meander loop that is examined, it is possible to find one geometric form, which is mathematically definable, that will fit the feature. The difficulty arises when the investigator goes on to the next meander loop in the river, and finds that the geometric shape selected for the previous meander loop does not fit the next one under study. Nevertheless, a new mathematically definable geometric form can be found which will fit the next meander loop. But, of course, this second geometric form will fit neither the first or a third meander loop. The reason for the inability to fit one geometric form to all meander loops is that the size and configuration of individual meander loops appear to be unique to that meander loop. No two meander loops in nature are absolutely identical."

18 In light of this, it seems wise to characterize meander bend geometry by a simple function such as a circular arc, but recognize that the true bend forms in meandering channels will inevitably deviate and scatter around this simple representation. In fact, few natural meanders display a classic or idealized planform in any case, due to non-uniformity in the bed and bank materials (58) or variation in entrance flow conditions (59). For example, studies of the Lower Mississippi by Fisk (58) demonstrated the influence of clay plugs, in-filling cutoff bends, and sand deposits found in abandoned former channel courses on bend form and evolution. Lower Mississippi bend forms and dynamics were further examined by Schumm and Thorne (60), who identified no less than five different effects a clay plug could have on meander form and migration. Schumm et al. (61) expanded on the earlier work by identifying and discussing the nature and causes of variability in the form of the Lower Mississippi between Cairo and Old River. Studies of the planforms of longer, meandering reaches were initially based on mapping, and Dort's (62) investigation of historical changes to the Kansas River and its tributaries between 1857-1868 and 1976 provides an excellent example of what can be achieved. However, analytical work based on historical maps is hampered by uncertainties concerning the accuracy of the maps and the criteria used in representing the banklines of the river. Hooke and Redmond (63) provide a comprehensive review of these issues. Planform studies were given a huge boost when aerial photography began in the 1920s and 1930s, and many investigators have found aerial photographs to be invaluable to the classification of meander form, study of meander processes, and documentation of changes through time. Planform studies using maps and aerial photographs have yielded a number of empirical relationships for reach-scale meander geometry and scale. For example, Leopold and Wolman (14, 64) identified power law relationships between channel width (W), meander wavelength (λ), and bend radius (Rc): 1.1W32.7λ = 1.0912.13Wλ = 0.98 c4.7Rλ = Richards (23) suggested that the exponent in the width-wavelength equation was not significantly different from unity and proposed a simplified version: W34.12λ = Hickin (65) suggested a set of simple meander geometry equations broadly based on his results and those of earlier researchers (for example (66)) that could be used to predict meander response to changes in discharge:

19 10 W λ ≅ 4 R λ c ≅ 2 W Rc ≅ 0.510Qλ ≅ where: λ = meander wavelength W = bankfull width Rc = radius of curvature Q = bankfull discharge Chang and Toebes (67, 68) investigated the effect of discharge on meander bend radius for two areas in the Wabash Basin with contrasting glacial histories and suggested: 2/1 arcm Q24R = (older) Illinoian glaciation 3/1 arcm Q197R = (younger) Wisconsin glaciation Based on their results, Chang and Toebes concluded that the geological history of channel development, as well as the current flow regime, influences equilibrium meander form and they suggested that bend radius better represents meander geometry than wavelength. They also found that average discharge better represented river size than bankfull discharge. Williams (69) compiled a wide range of data to derive a number of empirical relations defining meander planform geometry. Notable examples are: 1.12 m 7.5WL = 2.43 W R c = where: Lm = meander length Rc/W = geometric mean radius of curvature to width ratio for a reach

20 While indicative of a geometry that is common to meanders of very different scales and on rivers of different types, these equations have no basis in theory and are at best "morphological rules of thumb." It is no surprise then that the use of simple morphological relationships outside the area for which they were developed in river engineering and restoration schemes has been criticized by Rinaldi and Johnson (70). Brice of the United States Geological Survey has been a notable proponent of the use of aerial photographs for meander planform analysis, amassing a large collection of historical aerial photographs for over 350 rivers in the continental United States (71). Brice used his collection (49, 72) to develop a classification of meander forms (73) and a method to assess channel stability based on aerial photographs (Figure 5). Brice's classification correctly identifies that sinuous and braided behavior are not mutually exclusive and that rivers close to the meandering-braiding threshold may display elements of both patterns. In this respect, an examination of the Ovens and King Rivers in Australia is instructive (74). These rivers have multi-channel, anastomosing planforms in which individual anabranches adopt meandering planforms. However, the behavior of meanders differs from that in single-thread rivers in that increasing sinuosity leads to avulsion rather than meander migration. Schumm et al.'s (74) findings for sand-bed rivers in Australia were later replicated in North American, gravel-bed rivers. Gottesfeld and Johnson (75) used dendrochronology to date a history of channel change in the Morice River in Canada and found no pattern to the way channels migrated downstream in its "wandering" planform (wandering streams are in transition between braiding and meandering). Monitoring of the Tanana River in Alaska by Neill and Collins (76) showed how meanders in that multi-channel system migrate downstream in a way similar to meanders in single-thread rivers, but with rates and patterns affected by unpredictable internal shifting and switching of sub-channels and bars. Most recently, Jones and Harper (77) found that trends of sinuosity increase in the Rio Grande in Colorado were punctuated by abrupt reductions not due to cutoffs, but due to avulsions. The existence of features in multi-channel systems that appear similar to meanders, but act differently, is a potential source of error when classifying meandering rivers for engineering analysis and prediction (78). This finding indicates that before classifying the degree or type of meandering, an initial screening is required to identify and exclude rivers that are actually multi- threaded (that is braided or anastomosing or wandering) even though they have meandering traits at certain scales or flow stages. A further cautionary note on planform classification arises from the work of Alabyan and Chalor (79) which showed that different classifications may be valid for the same reach depending on the scale at which the channel is analyzed. Their review of extensive Russian literature recognized separate characteristic planforms at the scales of the valley bottom, flood channel, and low-water channel. Clearly, scale dependency must be borne in mind when classifying meander planforms, with the purpose of the exercise guiding the engineer to the appropriate classification scale for that particular application.

21 Figure 5. Brice classification of single-thread rivers based on the degree and character of sinuosity (adapted from (72)).

22 Brice applied his planform analysis and classification techniques to many practical problems: for example those associated with shifting of the Sacramento River (80) and channel response to artificial cutoffs (81). Brice's work is significant because it both founded and established the practical utility of contemporary and historical aerial photographs for meander classification, stability analysis, and migration prediction across the continental United States. Of particular relevance to the study of meander migration was Brice's discovery that the width of actively meandering channels varies systematically with planform position. Active meanders tend to be wider at bends than at crossings, while meandering channels that do not exhibit this trait – termed equiwidth by Brice – are static for long periods. Lewin and Brindle (82) highlighted how a restricted floodplain width or narrow valley can constrict or even confine meanders. This topic was taken up by Richards (23) who used the case of the Afon Elan in Wales to demonstrate how the apparent meandering of this stream is actually caused by its deflection off valley wall bluffs on opposite sides of a relatively narrow floodplain. Richards' work is important in highlighting the existence of "passive meandering," which is displayed by sinuous channels in which meandering is either inherited from a former hydrologic regime or imposed by valley topography. In either case, bends look like those in an actively meandering stream, but differ in that they neither grow nor migrate. Stolum (83) explored the impact of finite valley width on active meandering, concluding that meander behavior is unaffected down to floodplain width 50 times the channel width, although an impact on the stable average sinuosity could be detected for valley widths less than 100 times the channel width. Historical and Monitoring Studies of Meandering Rivers Attempts to relate meander morphology to meander growth and shift, based on long-term monitoring and measurement, have contributed a great deal to our understanding of meandering. A good example is work conducted by Braga and Gervasoni (84), who used a particularly long period of record based on historical maps to chronicle the evolution of the Po River in Italy between 1230 and 1980. Figure 6 shows the planform features and geomorphic surfaces associated with meander morphology and migration identified through geomorphic measurement and monitoring in the field. Historical and long-term field studies have revealed how meanders evolve, even if they only hint at why. It has long been recognized that point bar construction and bank erosion are the principal process drivers responsible for lateral channel migration and meander evolution (14, 29, 31, 85, 86, 87, 88, 89, 90, 91, 92, 93). The broad pattern of scour along the outer bank and deposition along the inner bank can be explained qualitatively by the flow patterns and the related distributions of velocity, sediment transport capacity, and sediment sorting at bends (see discussion of Flow Patterns). Despite this, attempts to quantify and predict the association between the dynamics of water and sediment, the morphology of the bend, and interaction between the hydraulic, sedimentary, and morphological adjustments responsible for bend evolution remain imperfect (see discussion of Numerical Modeling). Hooke (32, 94, 95) presents a good series of reviews of channel changes observed in monitoring studies during the twentieth century.

23 Figure 6. Schematic diagram showing in planform features and geomorphic surfaces associated with meander bends. Hickin and Nanson conducted important studies of bend form and evolution based on historical analysis of the Beatton River in Canada (88, 90, 96, 97, 98, 99). Initially, the history of meander evolution was inferred from scroll bars left on the floodplain. Scroll bars are crescent-shaped ridges observed inside migrating bends and taken to represent the radius of the inner bank at the time the sediments forming the ridge were deposited. Hickin (88) noted that migrating bends maintained a RC/W value of about 2 and that, while the channel seemed to display dynamic stability over long periods, natural cutoffs induced channel changes triggered by renewed meander development in bends adjacent to the cut off bend. Hickin and Nanson (98) carried the analysis further, concluding that the maximum rate of bend migration occurred when RC/W was about 3. It should be noted that the referenced radius was based on scroll bar curvature and pertains to the inner bank radius rather than the more common convention of using the centerline radius to represent the bend curvature. In a later paper, Hicken (96) observed that migration was discontinuous, with individual loops migrating and depositing sediment during a number of distinct migration phases. Hickin found that each phase has an initiation stage, growth period, and abrupt termination stage. Termination was associated with a RC/W of about 2. Nanson (99) broadened the scope of studies of the Beatton River to include consideration of neotectonics (i.e., recent and ongoing surface deformation associated with tectonic processes). He concluded that the valley of the river is tilted to the east and that meanders grew preferentially down-tilt. However, the extended down-tilt bends cut off more frequently, so that the channel was positioned to the western side of the valley.

24 Nanson and Hickin (90) and Hickin and Nanson (100) built on the findings from the Beatton River, adding data from other rivers to produce generalized descriptions of bend migration for engineering applications. The tools developed indicate that the maximum rate of bend migration (made non-dimensional by dividing it by the width) can be expressed as a function of bend curvature, represented by RC/W. • Newly initiated bends have a long radius and grow slowly (initiation stage, RC/W > 10). • As bends develop and tighten, the erosion rate increases rapidly (growth period, 3 < RC/W < 10). • Bends then maintained their shape, while migrating rapidly (migration phase, 2 < RC/W < 3). • If the bend becomes overly tight the erosion rate falls abruptly and the bend is cut off (termination phase, RC/W < 2). Many subsequent studies have reinforced Hickin and Nanson's basic description of the stages of bend development, while also demonstrating that there is wide variation in the relative rates of erosion for a given degree of bend curvature (93, 95, 101, 102, 103, 104, 105, 106, 107). Figure 7 presents a summary compilation of data from several sources (including Hickin and Nanson). It should be noted that the curves shown in Figure 7 represent upper bounds to data clouds rather than best-fit lines. In fact, there is great variability in the rate of erosion for a given RC/W, especially at values around 2 to 3. Figure 7. Erosion rate as a function of bend curvature for data from Hickin and Nanson and other authors (adapted from (32)). Some of the variability may be explained by boundary conditions, such as the erodibility or mass stability of the outer bank of the bend. For example, Biedenharn et al. (104) showed that bends on the Red River in Arkansas that encountered clay plug, backswamp or Pleistocene materials migrated much slower than those eroding banks formed in meander belt sediments.

25 A further source of variability was revealed by observations of channel evolution on the Lower Mississippi River by Larsen and Shen (108). They found that the sinuosity of 55 bends increased progressively over long periods of time. When the sinuosity became large, the bend was cut off, with the life span of a bend being of the order of 600 years. However, the occurrence of a cutoff not only reduced the sinuosity of the cut off bend, it also influenced adjacent bends upstream and downstream. This phenomenon was also observed by Hooke (109) following both neck and chute cutoffs on the meandering River Bollin in England. She showed that in a dynamically meandering stream the effect of a cutoff in one bend is absorbed through local morphological adjustments in adjacent bends. These studies demonstrate that the rate of erosion at a given bend is determined not only by the geometry of that bend, but also the evolution of the bends immediately upstream and downstream (110). Clearly, while the sequence of erosion phases proposed by Hickin and Nanson may be discerned in Figure 7, further variables would have to be added to produce a satisfactory predictive tool with general applicability. A further point that arises from review of historical studies of planform change and shifting is that by no means do all meandering rivers display the degree of lateral activity suggested by Figure 7. For example, Biedenharn et al. (111) found that despite its sinuous course, the planform position of the low gradient Ouchita River in Arkansas and Louisiana has remained stable for 160 years. Similarly, Swanson (112) found that a meander loop in the higher energy Tazlina River in Alaska changed very slowly. The existence of sinuous rivers with stable, nearly static planforms indicates that it cannot be assumed that meanders will grow or migrate significantly on the basis of a single site visit or air photograph. Repeat measurements, long-term monitoring, or comparison of historical aerial photographs are essential to differentiating dynamic from passive or stable meanders. Factors Affecting Rates Of Meander Change As a bend evolves in an initially straight channel, the radius of bend curvature decreases and the rate of migration tends to increase because increased curvature strengthens secondary currents and helical flow so that: • Pool zone is constricted laterally against the outer bank (78) • Point bar expands (23, 24, 78) • Intensity of fluvial attack of the outer bank increases (7) • Stability of the outer bank with respect to mass failure decreases (22) • Bank retreats and debris is removed (113, 114) • Meander migrates through scour along the outer bank, deposition along the inner bank, and renewed constriction (115) Consequently, over the medium- to long-term, the rate of meander bend growth and migration takes place through complex interactions between flow and morphology, depending on multiple factors. Compiling the findings of several studies together (91, 113, 36), important factors influencing meander migration rate include: • Discharge (magnitude and frequency of channel forming flows) • Bed material mobility (ability of curved flow to produce bend scour) • Supply of sediment (availability of sediment to fuel point bar growth)

26 • Bank erodibility (ability of banks to withstand fluvial shear stress) • Bank geotechnics (bank stability with respect to slip failure) • Bank vegetation (through affects on flow erosivity, bank erodibility and bank stability) • Basal clean out (removal of bank failure debris from base of eroding bank) • Human interventions (impacts of river regulation, re-alignment and bank stabilization) Discharge The importance of discharge, and particularly high, formative events, has been established through a large number of flume and field studies. Ackers and Charlton (116) used a large sand flume to show that over time the plan geometry of a meandering channel adjusts to the dominant or bankfull discharge. Field studies by Hughes (117) supported this finding in that major meander adjustments were related to floods with a recurrence interval of 1.5 years (usually taken to represent bankfull discharge). Schumm (118) chronicled river changes resulting from climate induced alterations to runoff in the Murrumbidgee River in Australia, and Daniel (119) related the movement of meanders in Indiana streams to the duration of above-average discharge events. Hooke (120) found most bank erosion to be associated with peak flows. Laczay (121) showed that over a 35- year period migration rates of Hungarian rivers were positively related to periods of increased runoff associated with hydrological variability. Hagerty et al. (122) studied bank erosion along the Ohio River, relating the rate of erosion to discharge, although Odgaard (44) reported similar rates of bank erosion on two different rivers in Iowa. The East Nishnabotna River has a natural regime while the Des Moines River is regulated by Red Rock Reservoir. Despite differences in discharge magnitude and regime, both undergo cutbank erosion in bends at a rate of 10 to 13 feet per year (2 to 4 meters per year). Mobility of Bed Material Nagabhushanaiah (123) suggested that the necessary condition for the origin and formation of meanders in an alluvial stream is the erosion of bed material and deposition of the eroded material downstream. The ability of the river to entrain and transport bed material depends on the relationship between specific stream power and bed material size. Van der Berg (124) compiled a large data set based on the results of previous studies to relate channel planform pattern to stream power and bed grain size. Lewin (125) reported a good relationship between unit stream power at bankfull discharge and channel shifting rate for three rivers in Wales. Often, sediment mobility is highest in the middle reaches of the drainage basin – corresponding to the "transport zone" in the fluvial system (126). For example, in studies of the Rivers Bollin and Dane, Hooke (109) found that meander migration was indeed greatest and cutoffs occurred most frequently in the middle reaches of these gravel-bed rivers. Bed material grain mobility does not vary only through the system, however, and wide fluctuations may occur over relatively short distances, especially due to local variations in channel or valley slope. Nagabhushanaiah (123), Martinson (127), and Hooke (128) all found that the most active meanders were located in the steepest reaches of their study rivers. Schumm et al. (129) investigated local slope variations due to valley floor warping by neotectonic activity. They found clear evidence of morphological deformation caused by neotectonics. The sensitivity of morphology to local slope variability may explain why Hooke (109) reports that there is no simple relationship between reach-averaged stream power and migration rate.

27 The scour resistance of material generally increases with grain size, but for very fine sediment erosion resistance and scour depth may be limited by cohesion. Rhoads and Miller (130) attributed the lack of a morphological response to high flows on a stretch of the low- energy Des Plaines River in Illinois to the presence of fine bed material. Nanson and Hickin (91) used statistical analysis of bank erosion and channel migration in western Canada to show that 70 percent of the variability in migration rates of 18 meandering rivers could be explained by variability in discharge and bed sediment size. On this basis, it appears that while discharge and bed material size are the predominant controls on migration rate, other variables may also be significant. Sediment Supply In a flume study, Ackers and Charlton (131) demonstrated that an increase in sediment load could both trigger the initiation of meanders in a formerly straight channel, and drive an increase in the sinuosity of a meandering channel. Neill (132) likewise noted that an increase in bank erosion rate was associated with elevated levels of bed load. A long-term study of the Oconee River in Georgia by Brook and Luft (133) provides a useful case study of the effects of changes in sediment supply on meander migration. During the 19th and early 20th centuries, land use changes that made the watershed more erodible coupled with higher than usual peak and annual discharges raised sediment concentrations in the river. The channel responded through accelerated meander migration that produced an increase in sinuosity and decreases in wavelength and bend radius. After about 1910, improved soil conservation and runoff management produced decreased sediment concentrations and peak flows. The channel responded by decreasing its sinuosity while increasing meander wavelength and bend radius. This sequence of process-response is by no means unique to the Oconee. For example, Burke (134) chronicles a similar record of meander change triggered by natural processes and human activities on the Kansas River over a 125-year period. Historical records of bend movement over a period of 100 years compiled by Lewin (54) illustrated the influence of sediment transport pattern on bend migration rate, with the spatial distribution of rapid shifting being associated with changes in the local sediment transport pathways. Chang (135) supplied a theoretical explanation for the sensitivity of meandering to sediment supply. He demonstrated how the bedload/discharge ratio for an alluvial channel of constant slope and sediment size varies in response to changing discharge. Following a decrease in discharge, the sediment load supplied from upstream decreases proportionately more than is required to maintain a constant slope. The channel responds by increasing its sinuosity through enhanced meandering, which reduces the slope in line with the reduced sediment supply. Yen and Ho (136) provide further evidence of the importance of sediment movement on bend evolution, especially through its effect on bedforms. Erodibility of Bank Materials The mobility of meanders is affected by the erosion resistance of the material forming the retreating bankline. Rhoads and Miller (130) studied the morphological impacts of sequential flows, including a 100-year flood and several bankfull events, on a 4.5 mile (7.2 km) reach of the

28 Des Plaines River in Illinois. The response of the river was minor and Rhoads and Miller attributed this in part to the high erosion resistance of the cohesive banks. Hasegawa (137) developed a bank erosion coefficient based solely on the bank soil properties. He found that the value of the effective bank erosion coefficient was similar for different rivers, suggesting that it possesses characteristics that are sufficiently universal to justify its use as a basis for predicting bank erosion rates at meander bends. However, Hooke (120) pointed out that erodibility is not a conservative bank property. She discovered that rates of erosion for a given peak flow were much higher if antecedent precipitation had weakened the banks by raising soil moisture levels. Similarly, Lawler (138) discovered that frost action greatly weakens exposed bank soils, significantly reducing their ability to resist subsequent fluvial shearing. In any case, in a later paper Hasegawa distinguishes between bank erosion equations and meander migration equations, concluding that with regard to erodibility coefficients, it is "too early to consider the relations being universal" (139). Thein (140) provides a useful review of bank erosion studies and development of bank erosion models. Bank Geotechnics Chitale (141) attributed progressive recession of the bankline in river meanders to instability of the side slopes. He used a simple slope stability equation for planar slides to relate the limiting height for a vertical river cliff to the geotechnical properties of the bank material: 2 cotc4h φγ= where: h = limiting vertical height of bank c = bank material cohesion γ = specific weight of bank material φ = friction angle of bank material Thorne et al. (142) first recognized that limiting bank height with respect to mass stability could represent a geomorphic threshold capable of influencing the evolution and eventual equilibrium morphology of unstable alluvial streams. Thorne and Osman (113, 114) applied this principle to meandering channels, using a bank stability model developed by Osman and Thorne (143). They demonstrated theoretically the influence of the bank's geotechnical properties on lateral shifting at meander bends. In weakly cohesive banks, the limiting bank height with respect to mass stability affects the equilibrium scour depth, cross-profile, and migration rate. Subsequent empirical work by Thorne (4) on the Red River in Arkansas provided field validation of the conceptual hypothesis that bend geometry and migration are influenced by bank geotechnics.

29 Riparian Vegetation and Land-Use The influence of bank vegetation on meander migration has been recognized since the early 1980s. Hickin (144) suggested that vegetation would directly affect fluvial processes and channel dynamics through five mechanisms: • Resistance to flow • Bank material strength • Providing a nucleus for bar sedimentation • Concave bank bench deposition • Construction and breaching of log jams Gray and MacDonald (145) addressed the first and second effects identified by Hickin. They noted that vegetation increases the effective roughness height for the bank and produces a three-layer flow field next to the bank consisting of: • A viscous sub-layer adjacent to the soil-water interface • A turbulent zone with wake effects extending up to the top of the vegetation stems • A zone outside the vegetation that is free of wake effects Measurements made in the turbulent zone during a significant flood indicated that reduction of velocities and damping of turbulence within the wake zone rendered the near-bank flow non-erosive. They further noted that plant roots reinforced the soil, significantly increasing its shear strength and reducing erosion rates – an effect first noted by Smith (146). The wider influence of root reinforcement by riparian vegetation on spatial patterns of channel instability at the reach-scale was demonstrated in a monitoring study of Little Piney Creek in Missouri by Jacobson and Pugh (147). However, Peterson (148) pointed out that to be effective in reducing flow erosivity and enhancing soil erosion resistance, vegetation must extend to the interface of the water surface and the bank. Similarly, Thorne (22) noted that root reinforcement is only effective if roots cross the most critical potential failure plane, which may be deep within the bank. Hence, bank height relative to the position and rooting depth is important, and the presence of vegetation at the outer bank alone does not guarantee a reduced migration rate. Land-use change that alters the vegetation on and behind the eroding bankline can have a spectacular impact on the rate of meander migration. Migration rates seem to be particularly sensitive to removal of the riparian forest. For example, Beck et al. (149) noted that lateral channel movement along the Genessee River in New York was 130 percent faster through farmland than in forested reaches. Beeson and Doyle's (150) work indicates even stronger effects in that bends without riparian vegetation were nearly five times more likely to undergo detectable erosion during a flood event, and bank erosion was thirty times more prevalent on non-vegetated banks than vegetated ones. More recently, Burckhardt and Todd (151) found that average migration rates for bends with unforested concave banks along streams in Missouri were three times that for bends with forested banks.

30 The results of Murgatroyd and Ternan (152) are often quoted as challenging the generality that land-use change involving deforestation accelerates meander migration. They found that afforestation accelerated bank erosion. Careful reading of Murgatroyd and Ternan's paper indicates that in their study accelerated bank erosion occurred because afforestation led to increased channel width, reduced sinuosity, and formation of mid-channel bars, thereby producing a braided pattern. Hence, afforestation triggered planform metamorphosis rather than acceleration of meander migration, and the general finding that bends migrate faster through areas cleared of riparian forest still holds. Basal Cleanout Sustained retreat of an alluvial stream bank can only occur if near-bank flow in the channel is able to remove the debris produced by bank erosion and failure (22). Where debris removal does not keep pace with retreat of the bank top, a wedge or berm of bank-derived sediment accumulates, buttressing the bank and protecting intact material at the toe from fluvial scouring. Hence, in the medium- and long-term, rates of bank retreat and meander migration depend on the sediment transport capacity of flows near the eroding bank. This was recognized in the early 1980s, when Hickin and Nanson (100) proposed that a constant representing bank erosion resistance was largely a function of the basal sediment size. Jones (153) went further, concluding that the rate of bank retreat is controlled by the rate of basal removal of erosion products. Human Intervention Brice (81) conducted stability assessments of 100 meandering channels affected by engineering realignments and relocations. The typical channel response to a bend cutoff was widening of the new channel and acceleration in the growth rate of adjacent bends. Brice suggested that, as a general rule, the length of channel affected by scour upstream of a cutoff is in the range 10 to 20 times the width. Work on natural cutoffs by Hooke (109) also indicated that these adjustments are completed quickly, with rapid response in 2 to 3 years following a cutoff, and completion of even major adjustments within 6 to 12 years. Bradley and Smith (154) showed how artificial diversion of flow from the St Mary River into the Milk River in 1951 increased the mean discharge downstream and resulted in increased mean meander migration rate from 4.4 ft/year to 7.2 ft/year (1.35 m/year to 2.2 m/year). Conversely, closure of a dam on the Milk River in 1952 significantly reduced peak flows in the reach downstream of the dam resulting in a decrease in migration rate from 5.7 ft/year to 1.5 ft/year (1.75 m/year to 0.45 m/year). Decreases in meander migration rate following dam closure were also observed in a general study of downstream effects of dams by Williams and Wolman (155) and more specifically on the Bighorn River in Wyoming (156), the Brazos River in Texas (157), and the Marias River in Montana (158). However, Whitesell et al. (56) concluded that closure of Denison Dam on the Red River Oklahoma had no significant impact on river planform. A good review of the impact of dams on rivers and meander migration is provided by Friedman et al. (159).

31 Friedkin (11) conducted laboratory experiments to demonstrate the effect of bank revetments on meander geometry, showing how attempts to stabilize the outer bank in a meander led to deeper scour that tended to undermine the revetment. Thorne (4) noted a similar response in the Red River in Arkansas. Overview A considerable body of literature was reviewed to illustrate how a wide range of controls on meander growth and shift will complicate any attempt to generalize behavior from one meander to another. These are summarized In Table 1 and Figure 8. Table 1. Controls on Meander Morphology and Variability of Change. Geology 1 Faults - can change valley slope 2 Uplift - can change valley slope 3 Subsidence - can change valley slope 4 Bedrock outcrops in bed and/or banks - can prevent degradation or meander shift Alluvium 5 Clay plugs - provide local hard points that affect meander shift and growth 6 Fine-grained sediments form floodplain (backswamp deposits - inhibit meander migration) 7 Tributary contribution – different type of sediment and/or increased sediment load. Pattern Change 8 Upstream cutoff - steepens channel, increases sediment delivery downstream, can cause additional cutoffs 9 Downstream cutoff – causes upstream degradation 10 Flow direction change – shifts focus of maximum erosion downstream Human 11 Channelization (modification of reach) 12 Revetments and bank protection 13 Cutoffs (Modification of a bend) 14 Dams and diversions, land use Vegetation 15 Type and density of vegetation

32 a1 b3 b2 b1 c d1 d2 e2e1 f a A fault or uplift steepens valley downstream of fault or axis of uplift (dashed line). b Meanders deformed by encountering bedrock or resistant alluvium. Hatching indicates resistant material. c Uniform relatively stable, high amplitude meander in backswamp alluvium of Mississippi valley. d Change of meander pattern as result of sediment influx from tributary (arrow). Depending on type of sediment load, sinuosity may increase or decrease or river may braid. Dashed lines show expected change. e Effects of cutoff or change of flow orientation on downstream river pattern. Dashed lines show expected change. f Change of flow direction of upstream meander affects shape of downstream meander. Dashed lines show expected change. Figure 8. Controls on river patterns.

33 The effects of most of these variables are shown diagrammatically in Figure 8. Each example is based upon observations made on rivers, and each numbered example of Table 1 is considered as follows: 1 A fault, which crosses the river and steepens it locally, will cause a change of sinuosity (Figure 8-a1) and increase the rate of meander migration. 2 Deformation of a valley floor by uplift will also create two reaches of different morphology and behavior. Upstream of the axis of uplift the channel will be less sinuous and less active than the steeper reach downstream of the axis (Figure 8- a1). 3 Subsidence will reverse the sequence of Figure 8-a1 with the steepest reach located upstream of the axis of uplift. 4, 5 When an alluvial meander encounters resistant sediments or bedrock, the downstream limb of the meander will be fixed in position and the upstream limb will continue to migrate, thereby deforming the meander (Figure 8-b1). A meander increasing in amplitude will develop a flat top, when it encounters resistant material (Figure 8-b2). Finally, a sequence of meanders may be deformed as they shift down valley toward resistant material (Figure 8-b3). 6 A river entering a region of resistant floodplain sediments such as backswamp deposits in the Mississippi Valley will develop characteristic stable bends of relatively high amplitude (Figure 8-c). The farthest downstream bends of the Mississippi River are of this type and they are very different from those upstream. The rate of change is much higher upstream. 7 A tributary that introduces a large sediment load into the channel can have a major impact. The Arkansas River has introduced a large sediment load of sand into the Mississippi River. This has steepened the gradient downstream of the confluence, which increases sinuosity and the rate of meander growth and shift (Figure 8-d1). Introduction of a high sand load can also cause braiding (Figure 8- d2). 8 Meanders can be affected by bend behavior both upstream and downstream. A cutoff upstream can cause incision that increases sediment delivery downstream, which in turn can trigger additional cutoffs or increase meander growth and the migration rate (Figure 8-e1). 9 Downstream cutoffs can cause incision upstream, increased bank erosion, and perhaps increased meander migration (Figure 8-e2). 10 Even a change in shape of a meander can cause a change of flow direction, which affects the downstream pattern (Figure 8-f).

34 11,12,13 Human activities both upstream and downstream can significantly impact a river. Therefore, the highway engineer must consider future work on the river and changes of land use when evaluating meander impacts. 14 Hydrologic changes will affect rates of meander growth and shift. Dam construction and reduced peak discharge reduces the rate of meander migration. 15 Riparian vegetation usually reduces bank erosion and the rate of meander shift, but if the vegetation or its roots are not actually on the bank, they may have no effect (see (147)). Styles of Meander Change The location of maximum bank erosion within a bend changes as the bend evolves and so too does the primary direction of meander movement. The complexity of meander growth, migration and distortion has been described by a number of authors and is codified in a number of styles of change (Figure 9). Figure 9. Styles of change displayed by meander bends (adapted from (24)). Initially, bends tend to grow in a direction that is transverse to the valley axis (31), and this has been referred to as extension (24, 80). This pattern of development occurs because maximum erosion is located close to the bend apex (109).

35 Eventually, because of flow separation at the inner bank downstream end of the point bar, which effectively establishes a minimum resistance to flow, meander activity switches from primarily driving growth, to promoting downstream migration, which is referred to as translation (24, 29, 31). Under these circumstances, the zone of maximum bank erosion is located downstream of the bend apex (109). However, meander bend activity is by no means limited to growth and migration; bends also display changes described in terms of rotation and combinations of extension, translation, and rotation (Figure 9). Hooke (160) synthesized the results of several previous studies to suggest the following styles of meander change: Simple Combined Extension Extension and Rotation Translation Rotation and Extension Rotation Rotation and Translation Enlargement Complex She pointed out that stable reaches, unstable reaches, and reaches with changing channel pattern within a given stream may co-exist, so that there is no single style of meander change that can be applied to describe planform change in the system. As meanders grow by extension, the channel length increases. There is evidence from both conceptual and observational studies that as the channel spacing between crossings increases, a point is reached where flow through very long bends breaks down to produce an intermediate riffle and two minimum curvature points (12, 161). Parker (162) echoed these findings, describing how high amplitude bends tend to double back on themselves and develop intense skewing. As a result, they exhibit slower rates of downstream migration and become vulnerable to neck cutoff by a more rapidly migrating bend upstream. Whiting and Dietrich (163, 164) re-examined large amplitude meander evolution in long bends in detail, illustrating the process and mechanisms responsible for generating complex growth behavior. They found that multiple pools spaced at about 3 to 4 channel widths developed along the outer bank, separated by distinct bars at the inner bank. These bed features cause localized bank erosion that produces bend asymmetry and compound behavior and "double heading." Meander bends eventually cut off when the curvature becomes very tight. This may occur due to stalling of the flow and generation of a zone of flow separation at the outer bank, or as the result of the arrest of the down valley limb of the bend by more erosion-resistant material. Cutoffs occur as a result of chute development (80, 93, 101) or neck closure (58, 126). A chute cutoff is a manifestation of reduced hydraulic slope which causes reduction in sediment- transport capacity of the flows within the upstream portion of the bend and leads to sediment deposition within the channel and reduced hydraulic capacity of the channel (8, 78, 93). Reduced hydraulic capacity in the upstream portion of the bend increases the frequency of flows over the point bar which leads to chute development and eventually bend cutoff (78, 93). A neck cutoff is a manifestation of late-stage bend evolution in a tortuous meandering system with erosion resistant bank materials or meander distortion by plugs or bands of resistant material.

36 Conceptual and Empirical Models of Meander Evolution Conceptual Models of Meander Migration The evolution of a bend through time should be predictable, bearing in mind that channel migration has been shown to be a discontinuous process that is highly dependent on the occurrence of morphogenetically significant hydrological events (71, 88, 90, 91, 93). Numerous geomorphological studies have taken data from different locations and used the data to infer landform development through time (129, 165, 166, 167, 168). Harvey (93), using this location- for-time substitution technique, developed a seven-stage model of bendway evolution for the Sacramento River that related bend shape (reducing radius of curvature through time) to both migration rates (bank erosion) and cutoffs. Hooke (109) has produced a similar model of meander evolution. Bagnold (29), Leeder and Bridge (31), Nanson and Hickin (90, 91), and Harvey (93) have demonstrated that lateral migration rates of meandering rivers can be correlated with the radius of curvature of bends. Migration rates (MR/W) are highest when the radius of curvature to channel width ratio (RC/W) is about 2.5, and they are lower when RC/W is both higher and lower because of the lack of flow convergence and energy loss, respectively. Considerable scatter is apparent in the data, but based on the Beatton River data, Nanson and Hickin (90) showed that at a RC/W ratio of 2.5, the migration rate, expressed as channel widths per year was maximized (about 0.03 channel widths per year), and that lower values of channel migration were correlated with 2 < RC/W > 4. Using multi-variate statistics on a data set derived from 18 rivers in Canada, Nanson and Hickin (91) demonstrated that 70 percent of the volume of erosion of the concave bank could be explained by the size of the river, and the grain size of the sediment at the base of the bank. Keady and Priest (169) observed the downstream migration rate of "free" meanders in alluvial rivers to produce: ( )Sƒ gA V = where: V = migration rate (ft/year) g = gravity (ft/s2) A = meander amplitude (ft) S = free surface slope ƒ = "function of" They showed that migration rate peaked when S x 104 = 1.5. Because meander migration is a discontinuous process dependent on the occurrence of morphogenetically significant flood flows, Harvey (93) evaluated both short- and long-term meander migration rates on the Sacramento River. Short-term rates were calculated for the

37 period between 1981 and 1986 in which two significant floods occurred (1983, 1986). For radius of curvature (Rc) values between 1,250 and 2,750 feet (381 and 838 m) (Rc/W values of 2.5 to 5.5), the migration rates (MR) varied from 32 to 122 feet/year (9.8 to 37.2 m/yr). A least squares regression of the data is: MR = 175.8 - 0.049RC (R2 = 0.69) The progressive development of a meander bend can occur to the point where it cuts off. Recent (within the period of record between 1896 and 1986) and historic cutoffs on the floodplain of the Sacramento River were investigated to evaluate whether cutoffs could be predicted (93). A dimensionless cutoff index, which is defined as the ratio of the Radius of Curvature to the migration distance (Rc/MD), was developed to predict cutoff occurrence. For the coarse-grained meanderbelt section of the Sacramento River, the dimensionless cutoff index is: 1.7<RC/MD<3.7 For the fine-grained meanderbelt section, where the floodplain sediments are more cohesive, the cutoff index is: 2.5<RC/MD<4.3 Hooke (120) related erosion rate to watershed area (a surrogate for discharge or channel width) and showed that the resulting regression relationship could explain 53 percent of the variation in mean erosion rate and 39 percent of the variation in maximum erosion rate. The equations obtained were: Y = 8.67 + 0.114 A Ymax = 2.45 A0.45 where: Y = mean erosion rate (m/year) Ymax = maximum erosion rate (m/year) A = watershed area (km2) Martin et al. (170) studied the migration of bends on the Lower Mississippi River to classify bends into six categories based on their style of evolution. The categories were: • Downstream limb migration • Downstream limb rotation • Mainly upstream limb migration • Upstream limb rotation • Pure translation • Pure expansion

38 Over 60 percent of future meander migrations could have been predicted from the characteristics of each individual bend in the initial channel pattern. Martin et al. (170) found that the most stable meander bend radius to width ratios were in the range 1.0 to 2.8. The close association identified between bend characteristics and future evolution suggests that a predictive approach based on classifying bend types and using this to predict the style of change in the next few years has promise. However, classifying bends in this way requires skill and consistency on the part of the observer and it is by no means certain that relationships between morphological classes and styles of development are transferable between streams. Numerical Models of Meander Migration Nagabhushanaiah (123) was one of the first researchers to develop an equation for meander expansion. He concluded that the origin and development of meanders in an alluvial channel depend on the erosion of bed material and its subsequent deposition downstream. He then used experimental results to calibrate a theoretically-based equation: 5.0 3 s 2 c 2 s w d t)SQQS(76.0 d M ⎥⎦ ⎤⎢⎣ ⎡ −= where: Mw = meander width ds = mean diameter of bed material Q = discharge S = longitudinal bed slope Qc = critical discharge for initiation of bed material movement t = time This equation, like so many other empirical approaches, deals with some but not all of the processes involved in meander growth. For example, no account is taken of the relative erodibility of bank versus bed sediments or the manner in which bend growth alters as the ratio of bend radius to width decreases through time. Nakagawa (171) made the ratio of total bank shear force to total bed shear force (both per unit length downstream) the basis for his equation to predict meander initiation. He concluded that a necessary (but not in itself sufficient) condition for stream meandering was: α<τ τ bb ss p p where: α = 0.2 τs = average bank shear stress τb = average bed stress ps = average bank wetted perimeter of half a channel pb = average bed wetted perimeter of a half channel

39 Chang (172) produced a numerical water and sediment routing model (Fluvial-11) capable of predicting time and spatial variations in the water surface profile, cross-sectional profile, and other variables. In essence, this model could be used to model channel changes in meandering rivers, although it uses very simple representations of bank slopes (planar) and bank erodibility that would limit its applicability to streams with banks formed in uniform, non- cohesive materials. Unfortunately, very few rivers have banks with planar slopes that behave as if they are non-cohesive (22). Hence, even though Chang's model faithfully represents hydraulic processes, bank processes intimately involved in meander migration (such as erosion and mass failure of stratified banks with complex profiles) are inadequately represented. It is these difficulties that led Cunge (173) to conclude, "Existing models should not be taken as representing reality because the complexity of bank characteristics is not properly simulated." The meander model of Odgaard (41) concentrated on the ratio of near-bank, depth- averaged velocity to the section-averaged velocity. This model builds on the theoretical model of Ikeda et al. (47) to predict the increase in near bank scour depth (and related bank retreat) as a function of this velocity ratio. In a companion paper (42), the model is applied by linearization of the flow equations, which renders it inapplicable to bends with large curvatures. The modeling approach of Odgaard (41) has many positive attributes, although its theoretical basis is weak in that it does not account for the convective accelerations now known to be central to control of flow patterns at bends (25). Ikeda et al.'s (47) model also formed the basis for a simulation model for meandering rivers developed by Sun et al. (174). The results of this model demonstrate that meander wavelength is determined mostly by discharge and valley slope and is essentially independent of differences in the erodibilities of sedimentary deposits. This finding is consistent with empirical equations that relate wavelength to bankfull discharge and channel width alone. Sun et al. (174) conclude that at that time numerical simulations were capable of realistically reproducing meander configuration observed in nature. They did not, however, address meander change or migration. Geomorphologists have developed a number of models of channel planform evolution and the floodplain morphology that results from lateral reworking by meanders. Howard (110) provides an excellent review of available methods and presents the latest version of his own model (175). This employs the bend theory of Parker to predict how a meandering reach evolves through time, stressing the importance of changes in upstream and downstream bends on the behavior of each modeled bend. Geomorphic models such as Howard's are able to create planform patterns and bend behaviors that appear similar to those of meandering rivers in general, and they are able to reproduce the changes displayed historically by particular rivers through hind casting. However, they are not able to predict a priori the future evolution of real systems due to lack of information on details of bank material properties that may be encountered by a particular bend. The problem that arises is that an error in prediction for a single bend quickly propagates to bends up and downstream, so that the predicted planform position and pattern diverges from that actually occurring due to the sensitivity of the models to up and downstream feed back effects.

40 The work of Ligeng and Schiara (176) and Levent (177) represent typical examples of attempts to produce engineering equations to predict meander movement. Ligeng and Schiara (176) took the basis for their approach from the hypothesis that meander bend expansion is caused mainly by erosion of the concave bank. Based on this principle they produced a formula relating expansion to outer bank planform concavity: ⎟⎠ ⎞⎜⎝ ⎛≈⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛= W r15.1 W r15.1C 1.1 98.0 where: C = bend concavity r = radius of outer bank at bend W = channel width They concluded that maximum bend expansion occurs when the bend concavity is equal to 0.5 to 0.65. This equation is consistent with historically observed records of bend growth, but adds little to the wider generalizations of Hickin and Nanson regarding the relationship between bend curvature and migration rate. Levent (177) developed a theoretical model for meander bend expansion and amplitude increase based on bed sediment transport and continuity and validated it using experimental data. The resulting equation is: ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛⎟⎠ ⎞⎜⎝ ⎛= dt d n Lhq ybubwh where: qbwh = bed load carried by the whole channel at the meander bend hu = flow depth at meander bend axis L = meander bend length dyb/dt = rate of bend expansion n = constant While such equations are potentially useful in that they have a theoretical basis and are expressed in simple forms, their applicability is limited by the use of input variables that are rarely known in practice (for example, bed load carried at the bend) and by the requirement to calibrate the equation for the river in question to find the appropriate value for constants such as n. In a thorough review of mathematical models of river planform changes, Mosselman (178) discussed the utility of several 2-dimensional, depth averaged models. He concluded that while these models were able to help in understanding how river planforms evolve, none of them had reached the level of being a generally valid and easy to apply software package suitable for routine application.

41 Cherry et al. (48) used historical records of bend movement for 26 study sites selected from the Brice collection to test the utility of Garcia et al.'s (46) analytical model of bend migration. Their findings were not encouraging and they recommended against attempting to apply analytical models to make routine prediction of meander movement. (For further discussion see Evaluation of Analysis Options.) The diversity of processes and forms present in natural, meandering rivers means that, even assuming that the governing equations are fully understood and are correctly formulated mathematically, a single computational model is unlikely to have universal validity. Instead computational models are developed to simulate specific, idealized representations of natural fluvial systems (179). The literature reveals that a wide variety of empirical, analytical, and numerical models of meander migration (47, 174, 180, 181, 182, 183), flow and sediment transfer (25, 163, 164, 184, 185, 186), bend scour (113, 114, 187, 188), sediment sorting (188), and hydraulic geometry (20, 91) have been formulated, and each of these models has their own particular advantages and limitations. Most empirical and analytical models of meander morphology are limited to ultimate or fully-formed meanders. While these models have had success in predicting equilibrium meander forms, they provide no information concerning the rates and mechanisms of adjustment. Meander migration is usually simulated using a functional relationship between bank erosion rate and near-bank flow velocity, using a proportionality coefficient determined by calibration (41, 42, 47, 137, 174, 180, 183). Such models are idealized, non-mechanistic, representations of the bank erosion process. Many existing models are restricted to artificial morphologies tied to idealized representations of the river planform, such as the sine-generated curve. Such representations have in the past proved a useful means of simplifying the governing curved flow equations. However, in simulating real meanders that diverge from these idealized planforms, numerical problems are introduced due to grid distortion. Meandering rivers commonly have asymmetrical bends and non-uniform widths, so models which utilize idealized representations of planform are limited in scope. The applicability of existing modeling approaches is limited because they do not account for all the degrees of freedom involved in channel adjustment. Rivers adjust to changes in control variables through mutual adjustment of channel roughness, planform, width, depth, gradient, and boundary material characteristics (189). However, existing meander models neglect the adjustment of channel width through time (190). This is despite the fact that channel changes are often dominated by width adjustment (189, 191, 192). Thorne and Osman (113, 114) and Darby et al. (193) have shown that neglecting width adjustment in models of river channel morphology seriously biases predictions of bed-level change in rivers with erodible banks. The development of mechanistic width adjustment models therefore remains a research priority (194, 195).

42 Technical Problems Related to Meander Measurement, Characterization, and Monitoring To apply any of the empirical or numerical methods to predict meander movement requires accurate measurements of meander planform. Measuring and characterizing meanders and meander migration are by no means straightforward tasks. For example, Andrle (196) discusses several potential sources of errors in measuring meander wavelength and sinuosity. Downward et al. (197) produced a method for quantifying river channel planform change using GIS to produce vector overlays, area map overlays and historic stability overlays. They point out the advantages of GIS-based approaches, including: • Digitized boundaries provide geometrically stable representations that are easily manipulated • Aids in the correction of planimetric errors • Quantitative analysis of linear and areal displacements • Variety of map products can be produced • Digital GIS statistical outputs can be exported directly into other software Gurnell et al. (198) applied the GIS approach proposed by Downward et al. (197) to a study of subtle changes on a single meander of the Lower River Dee in Wales. They emphasized the importance of using GIS to map channel migration and narrowing at a decadal scale. Unless measurement errors can be kept within acceptable limits then it is impossible to judge whether apparent changes in meander geometry or position are real or the product of measurement error. In this regard the use of GIS technology provides a useful tool for making measurements accurate, precise, objective, and repeatable. Summary The review of the literature on meander growth and migration indicates that while the occurrence, patterns, and sequences of meander growth and migration have been well- documented, it is very difficult to predict the magnitude, direction, and rate at which changes will occur. Relations between bend geometry and controlling variables such as discharge and channel width allow reasonably accurate predictions of equilibrium meander geometry. However, it is much more difficult to predict meander migration and channel sinuosity changes. Geomorphic and engineering equations based on flow theory and empirical observations from historical maps and aerial photographs illustrate general relations, but there remains great variability due to variables unaccounted for in the equations. Experimental and practical studies demonstrate that with additional information on channel morphology and bed and bank sediments the ability to predict meander shift may be greatly improved. It is clear that prior screening of bends to exclude those that display meander-like behavior, although they are part of a multi-channel system, is essential to successful predictions. Also, classification of the type of sinuosity present in single-thread, meandering streams greatly enhances predictive confidence. At the very least, the recognition that bends of equal channel width are relatively stable in contrast to meanders with variable width, should be of significance to the highway engineer. This simple observational criterion could eliminate many rivers from concern.

43 In spite of evidence that the prediction of meander shift using numerical models is possible in principle, many difficulties remain unresolved with this approach. Most models require field calibration that demands unrealistic lead times before predictions can be obtained. Also, the input data required is simply unavailable for most streams, while the models themselves use highly simplified forms of the equations of motion for curved flow that may be challenged theoretically. Few models consider all of the processes known to be involved in meander migration and those that do are impractical for routine use due to their complexity and need for very accurate field data. In any case, sedimentary and geologic controls within the floodplain that cannot be detected in advance may interrupt progressive meander migration and cause deformation of the bend (Table 1 - 4, 5). In addition, changes of the meander pattern itself can complicate the bend behavior (Table 1 - 8, 9, 10) and, finally, human activities can have significant impacts (Table 1, 11, 12, 13, 14). As a result, a river may be composed of reaches of very different morphology, which requires that each meander must be described quantitatively, and predictions made for a single meander may not be transferred directly to another meander. However, this complexity in itself provides valuable information that can be used to improve prediction of meander behavior. The conclusion to be drawn from this literature review is that the only complete model of a river is the river itself. While the past behavior of a meandering reach is not necessarily indicative of its future behavior, at least the historical record integrates the effects of all the relevant variables as they operate in that location. If changes in flow regime, sediment availability, bank materials or human activities are known to have occurred during the period of record, the response of the river in the past can indicate how the river may respond to continued changes in the future. It appears that, provided the planform evolution of the study reach can be accurately chronicled using aerial photographs and GIS techniques, a reliable basis exists for prediction by extrapolation on the basis of meander class and style of change, adjusted where appropriate, to account for changes known to have occurred during the period of record or believed to be likely to occur during the period of prediction. EVALUATION OF ANALYSIS OPTIONS The Johns Hopkins Study A study by Johns Hopkins University (48) for the U.S. Army Corps of Engineers Waterways Experiment Station investigated the use of both empirical and analytical approaches to provide solutions to the problem of predicting meander migration. Two approaches to prediction were evaluated: (1) the use of empirical (statistical) relationships between planform characteristics and controlling variables such as discharge, sediment loads, stream or valley gradient, and (2) the use of flow-based computational meander migration models. This Johns Hopkins study evaluated these two methods for forecasting planform change and bankline migration using data originally assembled and analyzed by Brice (49) to assess stream channel instability problems at bridges for the Federal Highway Administration (FHWA). Of the 350 sites in the Brice collection, 133 of the meandering river sites which included a time series of aerial photography and a nearby stream gage, were used in the Johns Hopkins

44 evaluation of empirical relationships. Brice's data included the following: channel width, meander wavelength, sinuosity, gradient, valley slope, drainage area, erosion rate and some hydrologic data. Measurements of additional meander properties were made for the Johns Hopkins study. Local channel curvature and local bank erosion were measured for a smaller group of 26 sites. These 26 sites were used to evaluate the predictive capabilities of bend-flow meander migration computer models. The computational bend-flow meander migration model used in the study was developed by Garcia et al. (46). Empirical Relationships As pointed out in the Johns Hopkins report (48), the basic strategy of the empirical approach is to find "simple" relationships between easily measured variables and the planform characteristics to be predicted. The Brice data set was used to develop and evaluate several single variable regression relationships. To evaluate the capabilities of computer modeling in predicting meander migration, Johns Hopkins also tested the bend-flow model of Ikeda et al. (47), which attempts to predict analytically the depth-averaged velocity at every point in the channel. The Johns Hopkins study did not report promising results with either approach; however, only single variable regressions based on the supplemental field data available from Brice were evaluated. The study recognized that a meandering river is a complex system involving relations among many variables. The erosion rate for a meander bend is determined by the balance between the erosive forces applied to the channel bank and the resistance to erosion provided by the bank material and bank vegetation. Erosive force is a complex function of discharge, channel cross section geometry, sediment load, bed roughness, presence of bedforms and bars, and the planform geometry. Resistance to erosion is related to the properties of the bank material, the bank geometry (slope, height, shape), the presence of vegetation, and the state of the pore water in the bank (48). Although simplified, single valued correlations between a number of variables were established empirically and expressed as power functions, Johns Hopkins concluded that they did not adequately describe meander behavior. The Johns Hopkins study concluded that "clearly, this multidimensional variability cannot be captured in a simple regression equation," and noted that other than descriptive data on bank material type, the Brice data set does not include parameters to characterize the erodibility of the bank material. Even with this limitation, several useful empirical relationships were developed. Channel width was found to give more precise forecasts of meander spacing and reach-averaged erosion rates than discharge. Channel curvature provided the best empirical forecast of local and bend maximum erosion rates. For 26 study sites, local erosion direction was accurately predicted, on average, for 62 percent of a given meandering reach. Bend-Flow Meander Migration Models In regard to computer modeling, Johns Hopkins points out that a number of authors have developed versions of the bend flow model (41, 42, 46, 137, 149, 180)) and although the models have typically been tested with plots of predicted vs. observed channel form for a limited number

45 of channels, there has been little general testing of these models over a range of hydrologic and geologic conditions. After testing the bend flow model for 26 of the meandering sites in the Brice data set, the Johns Hopkins study concluded that both the accuracy and applicability of the bend-flow meander migration model are limited by a number of simplifying assumptions. Among the most important of these are the use of a single discharge and the assumption of constant channel width, both of which prevent the model from successfully forecasting the spatial and temporal variability that appears to be inherent in the process of bend migration. It was also concluded that much of the discrepancy between the predicted and observed distributions of erosion can be accounted for by the fact that meander migration is modeled as a smooth, continuous process. In reality, erosion occurs predominantly in discrete events, and varies greatly both temporally and spatially along the channel from bend to bend (90). The Johns Hopkins study noted that the identification of local factors that influence the amount of bank erosion that occurs is a subject "that will require further investigation." The faculty co- author of the Johns Hopkins study concluded that "further refinements in bend-flow modeling will not improve our predictive capability until we find a more rational way to wed the flow model to a bank erosion model." In addition to channel and bank characteristics, floodplain characteristics must also be incorporated into an analysis procedure. The floodplain characteristics that should affect meander migration include geologic controls, alluvial deposits and topographic variability. Geologic controls include bedrock outcrops and erosion resistant features along the valley sides. Alluvial deposits frequently include oxbows, meander scrolls and scars, and clay plugs, each with different erodibility characteristics. Topographic variability that should be considered include the cross valley slope of the adjacent floodplain and valley slope. The Federal Emergency Management Agency Evaluation The Federal Emergency Management Agency (FEMA) published a report which evaluates the feasibility of mapping Riverine Erosion Hazard Areas (REHA) (199). This study addresses requirements in the National Flood Insurance Reform Act (NFIRA, September 1994) which requires that FEMA submit a report to Congress that evaluates the technological feasibility of mapping REHAs and assesses the economic impact of erosion and erosion mapping on the National Flood Insurance Program (NFIP). In regard to mapping REHA, FEMA's concern is both channel instability (erosion) induced by natural and human processes and lateral migration. Technological feasibility means that there are methodologies that are scientifically sound and implementable under the NFIP. Scientific soundness means that the methodologies are based on physical or statistical principles and are supported by the scientific community. Implementable means that the approaches can be applied by FEMA as part of a nationwide program under the NFIP and for an acceptable cost. The FEMA project team conducted a search of existing methodologies used to predict riverine erosion, with emphasis on case studies. In general, case studies were categorized as:

46 • Geomorphic methods - relying primarily on historic data and geomorphic investigations; • Engineering methods - relying primarily on predictive equations based on engineering and geomorphic principles, and • Mathematical modeling methods - relying primarily on computer modeling of fluvial processes. A Project Working Group (PWG) of experts in the field of riverine erosion was organized. Their functions were to provide guidance to FEMA on technological feasibility of mapping REHAs, to act as an information source to locate and select case studies, and to review and comment on reports prepared during the study. The PWG included a nationwide mix of individuals from academia; Federal, State, regional, and local government; and the private sector. Riverine Erosion The following observations on riverine erosion are extracted (generally verbatim) from the Executive Summary of the FEMA study (199). Fluvial systems respond to perturbations that may be the result of naturally occurring inputs, such as precipitation, or human intervention in the form of urban development, forestry, mining, flow diversions, flood regulation, navigation, and other activities. Complex physical processes whose mathematical characterization is still imperfect govern the response, although there is reasonable qualitative understanding of the nature of this response. In the context of riverine erosion hazard areas, engineers are mostly concerned with migration of the channel alignment and various forms of erosion and deposition. Numerous factors affect the spatial and temporal response of a stream channel. These factors encompass various aspects of geomorphology and fluid mechanics and include fluid properties, sediment characteristics, discharge, sediment transport, channel geometry, and fluid velocities. The behavior of these variables depends on the time scale under consideration: short-term, long- term, and very long (geologic) term. For example, channel geometry can be considered relatively constant in the short-term of a few weeks but highly variable in the geologic time frame. For most practical applications, engineers are interested in phenomena that take place in the short- and long-term; thus, certain variables can be considered independent. For instance, in the geologic time frame, valley slope is a function of geology and climate; however, short- and long-term channel formation processes occur at a much faster rate, and valley slope can be considered independent in many instances. For short- and long-term analyses, it can be assumed that the discharge regime and sediment supply are the driving variables that act on channel boundaries and vegetation to produce changes in channel cross section, longitudinal profile, and alignment. The FEMA study defines lateral migration as shifting of the streambank alignment due to a combination of vertical erosional and depositional processes (degradation, aggradation, and scour). The most common example is meander migration in the floodplain. Bank retreat due to mass failure is another example.

47 Evaluation of Channel Changes The FEMA study concludes that mathematical representation of fluvial fluid mechanics is difficult due to imperfect knowledge of the complex physical phenomena involved. The many attempts to modeling of fluvial processes have shortcomings largely due to the fact that sediment transport equations commonly overpredict or underpredict sediment loads by orders of magnitude of actual measured sediment transport rates. Some analysis methods are based on the hypothesis that the stream system tends toward a state of dynamic equilibrium in which the channel adjusts to changes in the water and sediment supply regimes. These methods include simple equations called "regime relationships," techniques based on mechanical stability conditions, and complex computer models. These equilibrium-based approaches have difficulties in accounting for ever-changing land use conditions. In addition to fluvial processes, numerous climatic, environmental and geotechnical factors are involved. Hydrodynamically induced erosion and deposition and the occurrence of mass failure of the streambanks drive channel cross sectional changes. Induced effects include changes in roughness, bed material composition, vegetation cover, and planform. Prediction of cross sectional adjustments can only be accomplished for site-specific conditions after the most significant geomorphological factors have been identified. Therefore, any prediction of channel geometry should be based on sound field observations. The FEMA study team evaluated several hundred pieces of literature and after an initial screening, 108 articles and reports were evaluated to compile methods currently in use to predict channel changes. Of this set, 12 case studies were selected for detailed review. In assessing the technical feasibility of mapping REHAs, each case study was analyzed for applicability, limitations, potential for mapping riverine erosion, cost, and regulatory potential. These documents revealed that numerous techniques are currently in use covering geomorphic methods, basic engineering principles, and mathematical modeling. Conclusions from the FEMA Study The FEMA study concluded that the case studies indicate that there are scientifically sound procedures for delineating riverine erosion hazard areas. Various geomorphic, engineering, and modeling procedures can be applied, depending on site-specific conditions. Specialized knowledge and experience are needed to draw conclusions that would lead to delineation of a hazard area. Given a suitable time frame, future erosion could be estimated either extrapolating from historic data or through the use of mathematical models. In both cases, an estimate of the reliability of the prediction needs to be provided. Riverine erosion is a complex physical process that involves interaction of numerous factors: fluvial hydraulics, geotechnical stability, sediment transport, and watershed characteristics, including hydrology and sediment yield, past and future land use, and vegetation among others. The study of riverine erosion is multidisciplinary in nature and requires experienced geomorphologists, hydrologists, hydraulic engineers, geotechnical engineers, photo-

48 interpreters, planners, and mapping specialists. Some of these professions require advanced degrees in their specialties. Valuable input is also needed from local floodplain managers. Modeling is the most complex approach, and its implementation requires considerable expertise and resources (emphasis added). Despite decades of research into the physical processes associated with riverine erosion, knowledge of the subject is still imperfect, and much work remains to be done. Accurate mathematical representation of these processes has not been achieved yet, and available tools produce results surrounded by varying degrees of uncertainty. Nevertheless, there are analytical procedures that can be used to characterize riverine erosion and that, depending on the application, can yield reliable results. For example, because of limitations in data availability and model capabilities, it is extremely difficult to reproduce detailed time variation of stream movement; however, it is entirely feasible to analyze channel history and infer trends in the stream alignment and average migration rates. Data Needs Both the literature review and evaluation of analysis options support an empirical approach to predicting channel migration. It is useful, however, to discuss the data requirements of empirical versus deterministic approaches. For the purposes of this discussion, empirical approaches are assumed to be primarily statistical, while deterministic approaches account directly for the physical processes responsible for, in this case, channel migration. The division between empirical and deterministic approaches is not absolute, but a matter of degree. The selection of dependent and independent variables and the success of a statistical analysis relies on an understanding of the dominant physical processes. Conversely, when the physical processes are extremely complex, as is the case with channel migration, a completely deterministic model may be impossible to develop. Therefore, deterministic models for channel migration must incorporate simplifications of the physical processes and are, to some degree, empirical. An example is the Garcia et al. (46) model presented in the Johns Hopkins (48) report. In this bend-flow meander migration model, an erosion coefficient is calibrated by fitting observed and computed channel planform. The erosion coefficient relates channel migration rates to velocity and channel width, but clearly does not address the physical processes controlling bank retreat. Empirical Approach A statistical approach can be viewed as pure data analysis, meaning that one only needs data and does not need to understand the physical processes in order to perform the analysis. Certainly, the data must be selected carefully to accurately represent the physical processes. Although the process based modeling approach could have been adopted for this project, there remains a significant level of uncertainty related to the processes of channel migration. This level of uncertainty is evident in the use of an erodibility index that is incorporated into several models. It is a lumped parameter involving many different material characteristics and physical processes.

49 Statistical analyses, typically regression, also involve uncertainty for a variety of reasons. (1) Processes are represented by surrogate parameters or lumped parameters such as the erodibility index described above. An example of a surrogate parameter would be the use of width-depth ratio as a measure of bank erodibility because lower width depth ratios indicate relatively higher bank erosion resistance. (2) The data used for development of regression equations must represent the range and variability of data used for its application. If this is not the case, there will be situations where the equation should not be used and, if used, will result in additional potential error due to extrapolation. (3) The data will over represent some conditions and under represent others. This is similar to the second case except that, while the results may be valid for the well represented conditions, there is a bias incorporated into the predictions. (4) The form of the regression equation is unknown. In the data analysis process, various forms of the equation will be reviewed. Some of the processes may be related linearly with channel migration while other may be exponentially related. (5) Statistical requirements may not be satisfied. Standard regression analyses assume that the scatter of observations are normally distributed relative to the prediction. If the normal distribution requirement is not satisfied, there may be bias in the predictions. This can be addressed through other "non-parametric" statistical techniques. Deterministic Approach From a purely deterministic model or process-based approach, the model should be able to simulate the actual migration of a meander. The computational properties of such a model would include: (1) The model would need to simulate the hydraulics and sediment transport processes through time, potentially in a 3-dimensions and simulate both channel and overbank flow conditions. (2) The model would have to simulate erosion processes (grain-by-grain detachment), mass failure processes (bank failure), and account for the subsequent removal of the material that accumulates at the bank toe from the mass failure. (3) The model would have to incorporate the reinforcing strength provided by roots and potentially the surcharge from the mass of trees. (4) The model would have to be able to revise the channel geometry and account for changes in boundary material as migration exposes new materials. (5) The model would have to incorporate varying hydrology (actual flow record) and some aspects of weather because saturation of the bank materials affects the unit weight of the bank material as well as the internal friction angle and cohesion. This purely deterministic model, starting at some historic condition, would simulate flow and sediment transport conditions for a hydrologic and weather record. The model would simulate the erosion and mass wasting of bank material and accretion of the opposing point bar. It would then be able to replicate the actual channel development for the historic period. To predict future channel migration, the model would use representative long-term hydrology and weather conditions. This model would not incorporate empirically derived variables because all the input would be measurable and the model would be applicable to all river types and conditions. The data requirements to develop and apply such a model are extreme. The hydrology and weather data would have to be known for a significant period of record. The model would need to include bed and bank material properties as they vary spatially and temporally. Bank

50 material properties would need to be determined for the various strata comprising the bank. These properties include not only grain size and erodibility, but also mechanical properties such as shear strength, angle of internal friction and cohesion for varying soil moisture and saturation. The mechanical properties of tree roots would also have to be quantified. This model would be so complex that its development is, arguably, impossible. It is as unrealistic as suggesting that one regression equation could be used for all rivers types and that the regression equation would rely on a single independent variable. Some middle ground was necessary to achieve the goals of this project (1) reasonable predictions of meander migration and (2) practical use of the final procedure. That middle ground could be a deterministic model that uses empirically derived variables or a statistical analysis of physically meaningful variables. Making use of the photogrammetric comparison procedures necessary to developing the data base for a statistical analysis could also provide a "model" for predicting future channel position based on observed historic trends. Some level of simplification is needed for each of the properties of the deterministic model outlined above. Hydraulically, a 2-dimensional bend-flow model would appear to be most appropriate, but use of 1-dimensional models simplify the input and data requirements. Simulating a long-term flow record, including low, moderate and extreme flow conditions would also be arduous. Use of a single, channel forming or effective discharge is a common technique to simplify this aspect of the problem. Sediment transport analyses inherently include significant complexity and uncertainty. This process would need to rely on a variety of sediment transport formulae for various size sediments. Finally, the geotechnical investigations required to describe the spatial variability of the bank materials could rival the effort of performing the bend migration simulations. Temporal variability of bank material properties would probably need to be eliminated to reduce computational requirements. These simplifications could be made and the model could still be considered as deterministic, especially if the processes of bank erosion and failure were addressed from a physical standpoint. Mass bank failure is related to the mechanical properties of the bank materials and removal (erosion) of toe support. Removal of toe support occurs either laterally or through channel degradation. Therefore erosion and mass failure need to be addressed as well as sediment transport. From this viewpoint the Garcia et al. (46) model is deterministic in many ways, but not with regard to the processes of bank retreat. In their model the erosion coefficient is calibrated based on observed migration rates. To improve the utility of this approach the erosion coefficient would have to be related to other measurable properties of the bank material and vegetation conditions. There are other models that treat bank retreat in a deterministic manner. Osman and Thorne (143) and Thorne and Osman (114) provide an excellent example of combining hydraulics, sediment transport and bank stability processes that could be extended, with considerable effort, into a more comprehensive migration model. However, the effort required to produce such a migration model would not only exceed the resources available for this project but would result in a product too complex for widespread use. A list of the data required by the Osman and Thorne model includes: channel geometry (average depth, central depth, flow depth at radial distance r, bend radius of curvature, bank height, bank angle, width, channel slope), discharge, bed material median size, largest size and

51 median fall diameter, cohesion, effective cohesion, pore fluid salt concentration in the bank material, sodium absorption ratio of the bank material, dielectric dispersion of the bank material, unit weights of the bed and bank materials, angle and effective angle of internal friction, friction factor and Manning n, bed material porosity and ratio of tension crack depth to bank height. Many of these parameters can be reasonably estimated, but the amount of data required is still much greater than could normally be justified for the purposes of a meander migration estimate. It is also clear that use of this model would require significant expertise in hydraulics, sediment transport, geotechnical engineering and hydraulic modeling. Summary Review of the literature, evaluation of analysis options, and consideration of data needs for empirical and deterministic (physical process mathematical modeling) approaches to predicting meander migration support the finding that empirical approaches are more likely than deterministic approaches to yield a practical methodology that will be useful to practicing engineers. A comparison can be drawn between predicting meander migration and the current practice for predicting scour at bridge piers. The current practice for pier scour is to use empirical equations that relate pier geometry and hydraulics to potential pier scour. Alternatively one could use physical modeling for complex pier shapes or sophisticated 3-dimensional flow and erosion computer modeling. The physical and numerical modeling are, to varying degrees, limited by several factors. These include time, cost, scale effects, and the ability to characterize the erosion properties of some sediments. Numerical and physical modeling are useful tools and expand our knowledge of pier scour, but could not replace the utility of the empirical equations for practical problems. CLASSIFICATION AND SCREENING PROCEDURES Objective The objectives of this project included developing a quantitative screening procedure to identify stable meandering reaches. This information will be significant to both bridge design engineers and bridge inspectors and provide a basis for concentrating design and inspection resources on less stable problem reaches. Classification Concepts Channel classification systems provide engineers with useful information on typical characteristics associated with a given river type and establish a common language as a basis for communication. Classification requires identifying a range of geomorphological channel types that minimizes variability within them and maximizes variability between them (200). Given the complexity of natural systems, inevitably some information is sacrificed in the attempt to simplify a continuum of channel geomorphic characteristics into discrete intervals for classification. Rivers are often categorized as either straight, meandering, or braided. These categories identify the three major alluvial river types. An alluvial river is one that is flowing in a channel

52 that has bed and banks composed of sediment transported by the river. That is, the channel is not confined by bedrock or terraces, but it is flanked by a floodplain. In addition to these three basic river "types," there are also anabranching alluvial rivers and rivers that are termed wandering. Brice (72) illustrates the range of channel types for meandering, braided, and anabranching channels (Figure 10). Figure 10 shows the difference between low sinuosity, straight channels and meandering channels, as well as the difference between bar-braided and island-braided channels. It also demonstrates that the braided river occupies one channel whereas the anabranching channel has multiple channels separated by a vegetated floodplain. On Figure 10 the degree and character of sinuosity portions are related directly to the objectives of this project. The braiding and anabranching processes, while of interest, were not considered in the scope of this project. Classification and Screening A wide range of channel classification approaches (72, 126, 201, 202, 203, 204, 205, 206, 207) were considered as a basis for developing procedures to screen sites that would have a high probability of being stable and to classify sites by meander mode as a means of segmenting the data base. It was concluded that a channel pattern classification originally developed by Brice (72) could be used as a basis for both screening and classification (Figure 10). The "character of sinuosity" portion of this classification provides both a screening and classification procedure. Based on original work by Brice, which was validated and expanded on with sites in the data base developed for this project, sites that have the equiwidth characteristic could be screened into a "stable" class and given a low priority for further analysis. Modifications were made to the Brice classification to support the specific objectives of this project. As shown in Figure 11, nine screening and classification categories can be used to represent the full range of meandering rivers encountered in the field. As noted above, equiwidth rivers, such as A, B1, and G1, can be screened as stable. One class, the "wandering" river shown as F, should be screened as potentially so unstable and unpredictable that further evaluation would not be likely to produce a meaningful result (in terms of predicting meander migration). All other meandering rivers can be classed as one of the remaining five categories, B2, C, D, E, G2, and analyzed by the photogrammetric comparison techniques presented in the Handbook developed for this project. Application of this procedure to 58 Brice sites indicated that all sites fit into one of the categories, without apparent anomalies, and the classification results were replicable. Additional verification of the validity and applicability of this classification and screening procedure was provided by regression analysis (see the next section).

53 Figure 10. Channel pattern classification devised by Brice (after (72)).

54 Figure 11. Modified Brice classification.

55 REGRESSION ANALYSIS Introduction Data from the Brice (72) sites (including data from recent aerial photographs) were used (1) to assess screening and classification procedures, and (2) to establish guidance and limits for predicting meander movement when using photo comparisons. For (1) the data clearly shows that migration rates are related to meander class. Although it was hoped that regression equations could be developed for use in predicting migration when historic aerial photos were not available, statistically significant regression equations were not successfully developed (see Chapter 3 for further discussion). However, for (2), a frequency analysis approach was developed to guide photo comparisons. The rates of bend expansion, extension, and translation (see Figure 9) were computed for each location and each of three time periods. The bankline data are generally from the 1930s, 1960s, and 1990s. Using the first and second, second and third, and first and third time periods resulted in average intervals of 27, 26, and 56 years, respectively. The data were grouped using Figure 11. The A, B1, B2, and C classes, which included 89, 249, 408, and 915 data points (in the Brice data set), respectively, are included. A sites are single phase, equiwidth, incised or deep. B1 sites are single phase, equiwidth. B2 sites are single phase, wider at bends without bars. C sites are single phase, wider at bends with point bars. The classification based screening was intended to identify river types that would exhibit different channel migration characteristics. The A and B1 sites were expected to exhibit such low migration rates that further analysis would be unnecessary (or low priority). B2 and C sites were expected to exhibit much higher rates of movement and were to receive the focus for prediction techniques. The D, E, and G2 sites are not well represented in the Brice data set. Each of the three modes of bend movement are vectors, i.e., they each have a magnitude and direction. Figure 12 depicts the modes of meander movement (positive rates are shown for each mode). The direction for extension is in the bend orientation direction and the direction for translation is in the downstream direction perpendicular to the bend orientation. The bend radius does not have a specific direction. However, if the bend radius is contracting, then the rate of bend radius "expansion" is negative. In order to assess the amount of bank movement, the three vectors measuring migration were combined into a resultant magnitude, termed "apex movement." Apex movement is the movement of the outer bank apex and is computed as the vector sum of the three components of movement at the apex location. Justification of the Classification System Figure 13 shows the rates of apex movement in ft/yr for the four classifications plotted as cumulative percent. As anticipated, the A and B1 sites show low rates of movement as compared to the B2 and C sites. One hundred percent of the Brice A sites have rates of movement less than 2.8 ft/yr (0.85 m/yr) and 90 percent of the B1 sites have rates of movement less than 4.2 ft/yr (1.28 m/yr). These rates are approaching the accuracy of the measurements from aerial photography. The B2 and C site bends show similar rates of movement above the 90 percent level and much greater rates of movement than the A and B1 sites. A significant

56 proportion of the B2 and C bends (40 and 20 percent) show low rates of movement (less than 3 ft/yr). The B2 and C sites also have a significant number of rapidly moving bends. At the 90 percent level the B2 and C bends are moving at a rate of approximately 13 ft/yr (3.96 m/yr) and at the 95 percent level, bends are moving at almost 18 ft/yr (5.49 m/yr). From these statistics, it can be concluded that one in ten C and B2 bends are moving at rates greater than 13 ft/yr (3.96 m/yr) and 1 in 20 are moving at rates greater than 18 ft/yr (5.49 m/yr). (x1,y1) (x2,y2) Translation Extension Rc1 Rc2 Expansion = Rc2 - Rc1 Apex Movement Figure 12. Modes of meander bend movement. These results may be somewhat biased by scale. The average channel widths of the A, B1, B2, and C sites are 89, 212, 321, and 276 feet (27, 64.6, 97.8, 84.1 m) at the crossings and 104, 238, 382, and 346 feet (31.7, 72.5, 116.4, 105.5 m) (at the bend apexes, respectively. Dividing the migration rate by the channel width yields a migration rate in terms of channel widths per year. Figure 14 shows the rates of apex movement in apex widths per year. The A and B1 sites are virtually indistinguishable on a rate expressed in channel apex widths/year. The B2 sites, the widest class, show rates of movement closer to the A and B1 sites. The C sites are not, on average, the widest channels in the data set but do show the greatest rates (in ft/yr). The difference between the C sites and the other classifications is most evident when normalized by the channel width. While Figure 14 still supports the premise that A and B1 sites move less than B2 and C sites, on a normalize basis there is less to distinguish between the first three classes (A, B1 and B2). The mean, standard deviation, 90th percentile, and maximum rates of apex movement for the four classes of Brice data are shown in Table 2. Each of these statistics indicates that the screening and classification approach is justified and that the C and B2 sites have the greatest potential for migration problems. Although the A and B1 sites do migrate and at normalized rates that are not too dissimilar to the B2 sites, these channels are generally smaller and are, therefore, less likely to cause a problem.

57 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 5 10 15 20 25 30 35 40 45 50 Apex Movement (ft/yr) C um ul at iv e Pe rc en t Brice A Sites Brice B1 Sites Brice B2 Sites Brice C Sites Figure 13. Cumulative percentage of Apex Bend Movement in ft/yr. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Apex Movement (Channel Widths/yr) C um ul at iv e Pe rc en t Brice A Sites Brice B1 Sites Brice B2 Sites Brice C Sites Figure 14. Cumulative percentage of Apex Bend Movement in channel widths/yr.

58 Table 2. Apex Movement Statistical Characteristics. ft/year Mean Std. Dev. 90th Percentile Maximum A Sites 1.1 0.6 2.0 2.8 B1 Sites 2.1 1.9 4.1 10.3 B2 Sites 5.6 5.5 12 47 C Sites 8.0 9.4 14 105 Channel Widths/year Mean Std. Dev. 90th Percentile Maximum A Sites 0.012 0.009 0.023 0.048 B1 Sites 0.012 0.009 0.022 0.077 B2 Sites 0.016 0.014 0.032 0.104 C Sites 0.032 0.033 0.065 0.32 Comparison with Other Studies Nanson and Hickin (91) concluded that the greatest rates of bend movement occur for ratios of bend radius of curvature to channel width (Rc/W) of approximately 2.5 (Figure 15). This study supports that conclusion. Figure 16 shows rates of apex movement (presented as channel widths per year) plotted versus Rc/W. The highest potential for erosion appear to occur at Rc/W values between 2 and 4. It appears that, for a specific channel width, the rate of maximum movement is lowest for long radius bends and increases as the radius decreases. The highest rates of movement occur for bends with Rc/W of approximately 3 and decrease rapidly as the bend radius decreases further. It should also be noted that very low rates of movement also occur for the entire range of Rc/W. So although there appears to be higher potential for rapid movement at Rc/W of around 3, this figure does not appear to provide a significant basis for predicting meander movement. Close examination of Figures 15 and 16 indicates that the lowest rates of movement also occur for Rc/W values between 2 and 4. Other studies have found weak correlation between erosion rate and other channel or basin characteristics. For example, the Johns Hopkins study (48) found that a power function produced the highest correlation between median erosion rate and channel width (R2 = 0.37). Based on variety of regression relationships (see Chapter 3 for further discussion), similar results were obtain from the Brice site data assembled for this study. Figure 17 shows the poor correlations obtained using apex movement versus channel apex width. The Johns Hopkins study excluded approximately 20 percent of their sites from the regression due to "no detectable erosion." In this study these sites would primarily be classified as A and B1 channels. All of the Brice data from the B2 and C sites are included in Figure 17.

59 Figure 15. Migration Rate (MR/W) versus Radius of Curvature/Width (91) (see also Figure 7). 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0 2 4 6 8 10 12 14 Rci/Wi A pe x M ov em en t ( C ha nn el W id th s/ ye ar ) Time 1-3 (52 yr. avg.) Time 1-2 (27 yr. avg.) Time 2-3 (25 yr. avg.) Figure 16. Apex Movement versus Radius of Curvature/Width.

60 C Sites y = 0.3965x0.4747 R2 = 0.1193 B2 Sites y = 0.0143x0.9834 R2 = 0.375 C & B2 Sites y = 0.115x0.6669 R2 = 0.1974 0.1 1 10 100 10 100 1000 10000 Channel Width at Apex (ft) A pe x M ov em en t ( ft/ yr ) C Sites B2 Sites Power (C Sites) Power (B2 Sites) Power (C & B2 Sites) Figure 17. Apex Movement versus Channel Width. Migration Prediction One mode of meander migration is radius expansion (Figure 12). Bends can either expand or contract (negative expansion). Figure 18 shows the ratio of bend radius of curvature at the end of a time period to radius of curvature at the beginning of the time period plotted versus initial radius of curvature over width (Rci/Wi, bend tightness). Although there are expanding and contracting bends throughout the range of Rci/Wi, the tighter bends tend to expand and longer bends tend to become tighter by reducing their radius. The data set is dominated by a cluster of data points centered on Rcn/Rci = 1. A value of one indicates that the bend did not change its radius of curvature, a value greater than one indicates and expanding bend and a value less than one indicates a contracting bend. Considering bend tightness (Rci/Wi) and time, the best fit equation for the data in Figure 18 yields an R2 = 0.23, indicating that while there is a trend (which is evident in Figure 18), there is significant scatter around the equation. Attempts to improve the predicted radius by including discharge, unit discharge, slope stream power, unit-stream power, grain size, and percent silt- clay did not yield increased R2. The two other modes of meander migration are translation and extension (Figure 12). These modes may also be positive or negative depending on the direction of movement, but they tend to be positive. Statistically significant relationships for extension and translation were also not forthcoming, at least no more so than shown in Figure 17.

61 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Rci/Wi Rc n/ Rc i Time 1-3 (52 yr. avg.) Time 1-2 (27 yr. avg.) Time 2-3 (25 yr. avg.) Figure 18. Change in Radius of Curvature versus Radius of Curvature/Width (C Sites). Frequency Analysis As an alternative to regression equations, a frequency analysis approach is suggested for predicting extension and translation. Figures 19 and 20 show the cumulative percent of extension and translation in channel widths per year. Rates of translation tend to be greater than rates of extension (bends tend to move "downstream" relative to their orientation). 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Extension (Channel Widths/yr) C um ul at iv e Pe rc en t Brice A Sites Brice B1 Sites Brice B2 Sites Brice C Sites Figure 19. Cumulative percentage of extension in channel widths per year.

62 Using a frequency analysis approach relies on identifying the channel classification and applying a rate based on the frequency occurrence. The rates for the Brice classes and different probabilities are shown in Table 3. The cumulative percent is the probability that a bend will migrate less than the given amount. One hundred minus the cumulative percent is the chance that a bend will migrate more than that amount. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 Translation (Channel Widths/yr) C um ul at iv e P er ce nt Brice A Sites Brice B1 Sites Brice B2 Sites Brice C Sites Figure 20. Cumulative percentage of translation in channel widths per year. Table 3. Rates of Extension and Translation. Extension (channel widths/yr) Translation (channel widths/yr) Cum. % 50 75 90 95 50 75 90 95 A Sites 0.0015 0.008 0.015 0.018 0.0025 0.010 0.015 0.019 B1 Sites 0.004 0.010 0.015 0.026 0.0023 0.009 0.016 0.020 B2 Sites 0.004 0.009 0.016 0.020 0.007 0.016 0.026 0.033 C Sites 0.008 0.018 0.032 0.045 0.015 0.031 0.055 .074 Another way of assessing channel migration is to use the probabilities to predict the length of time for the channel to migrate one channel width. This is shown in Table 4 and is computed as one divided by the vector sum of the extension and translation rates. From Table 4, there is a 25 percent chance that an A site will require less than 78 years to migrate one channel width and a 75 percent probability that it will require more than 78 years. At the other extreme, a C site has a 50 percent chance that it will migrate one channel width (mostly translation) in 59 years and a 25 percent chance that it will migrate one channel width in only 28 years. These results are another clear indication that screening for relatively stable sites and classification are valuable aspects of evaluating channel migration potential.

63 Table 4. Years to Migrate One Channel Width. 50 25 10 5 Percent Chance Years to migrate one channel width A Sites 343 78 47 38 B1 Sites 217 74 46 30 B2 Sites 124 54 33 26 C Sites 59 28 16 7 Figure 21 is an illustration of the frequency analysis approach applied to an A and C site assuming a similar starting condition. For the initial condition both banklines are shown and for a 30 year future condition several potential channel locations (outer bank only) are shown. The radius is approximately 3 times the width so expansion is assumed to be zero. At the 50 percent level the A site shows almost no migration while the C site shows the potential to migrate half the channel width. At the more extreme percentage, there is a 10 percent chance that the A site will migrate half a channel width in 30 years and that the C site will migrate nearly two channel widths. As an alternative to photo comparison or as a check on the results of the photo comparison, this frequency analysis approach provides reasonable results. However, it should only be considered as an alternative to photo comparison when no data is available for the extrapolation technique using photo comparison. A site 30 Years Initial Bankline 50 Percent 75 Percent 90 Percent C site Figure 21. Example movement frequencies.

64 In applying the frequency analysis approach, one could plot the 50 percent migration potential. If this amount would cause a problem for the structure, some countermeasure would be warranted. If this amount of migration potential would not cause a problem, but one of the lower probability amounts of migration would, then, depending on the structure, an action ranging from a constructed countermeasure to monitoring may be warranted. If even the most extreme migration would not cause a problem, then only monitoring may be warranted. Summary The statistical analyses support the following conclusions: • The classification procedure to segment meander data (Figure 11), and screening equiwidth sites (A and B1, classes) as low priority for impact on infrastructure are valid. • The frequency approach (for extension and translation) is intended, primarily, as a back-up approach. The most reliable prediction of channel migration can be made using the photo comparison techniques in the Handbook. • Applying standard regression techniques to predicting meander migration directly did not yield statistically significant relationships. THE HANDBOOK Overview The principal product of this research was a stand-alone Handbook for predicting stream meander migration using aerial photographs and maps. The Handbook deals specifically with the problem of incremental channel shift and provides a methodology for predicting the rate and extent of lateral channel shifting and down valley migration of meanders. The methodology is based, primarily, on the analysis of bend movement using map and aerial photo comparison techniques; but frequency analysis results are provided (see Regression Analysis) to supplement the comparative analysis. The methodology enables practicing engineers to evaluate the potential for adverse impacts due to incremental meander migration over the design life of a bridge or highway river crossing and ascertain the need for countermeasures to protect the bridge from any associated hazards. This section summarizes the content, methodology, and approach of the Handbook. Chapter 3 provides interpretation and appraisal of the Handbook methodologies, results of testing and evaluation by the Research Team, and Beta testing by State DOTs. The Handbook covers the following topics: • Screening and classification of meander sites • Sources of mapping and aerial photographic data • Basic principles and theory of aerial photograph comparison • Manual overlay techniques • Computer assisted techniques • GIS-based measurement and extrapolation techniques

65 • Frequency analysis • Sources of error and limitations • Illustrated examples and applications using manual overlay techniques Chapter 1 provides an introduction to the Handbook and a discussion of a range of potential applications of the techniques described in the Handbook. Chapter 2 describes the basic principles and processes of stream channel meander migration and discusses the potential hazards caused by meander migration as well as by avulsions and cutoffs. Chapter 3 presents a geomorphic classification scheme, modified from the channel pattern classification originally developed by Brice (72), as an approach for both screening and classification. The most common river types (or meander modes) likely to be encountered by hydraulic engineers in the field are addressed by this classification. The screening procedure to identify stable meandering stream reaches ensures that engineering and inspection resources are not allocated to locations where there is little probability of a problem developing. The basic principles of photogrammetry, the types and sources of aerial photography, and the application of aerial photography to meander migration analysis are discussed in Chapter 4. Chapter 5 describes a manual overlay technique that uses historic bankline positions acquired from sequential historic maps and aerial photos to assess historic channel position. By inscribing and tracking the movement of circles of known radius on a bend over time, a prediction can be made on the probable position of the bend at some point in the future. The chapter provides information on using three ways to apply the overlay technique including: (1) a manual method, (2) the use of computer assisted methods, and (3) the use of the ArcView-based Bend Measurement and Channel Migration Predictor tools developed for use with the Handbook. The potential sources of error and limitations associated with the use of historic aerial photographs and maps in conducting a meander migration assessment and prediction are described in Chapter 6. A detailed description of manual, computer assisted, and GIS-based methodologies using map and aerial photo comparison techniques to conduct the overlay and prediction of meander migration over time is provided in Chapter 7. The GIS-based measurement and extrapolation tools are included on CD-ROM at the back of the Handbook. The use of the frequency analysis results to assist in accurately predicting meander migration is described as well. Chapter 8 provides detailed, step-by-step examples of assessing historic meander migration and predicting future meander development using the methodologies described in the previous chapters. Appendix A of the Handbook describes how to download TerraServer images from the Internet for use in the analysis and prediction of meander migration. Methods for delineating the bankline of a channel and determining the radius of a meander bend are provided in Appendix B. Instructions on installing the ArcView–based Data Logger and Channel Migration Predictor tools are provided in Appendix C. Tips for delineating banklines from historic aerial photos that

66 are not georeferenced for use with the Channel Migration Predictor can be found in Appendix D. A glossary of terms used in the Handbook is provided in Appendix F. Application of Photogrammetry to Meander Migration Analysis The most accurate means of measuring changes in channel geometry and lateral position is through repetitive surveys of channel cross sections referenced to fixed monuments. However, this data is rarely available. A relatively simple and accurate method of determining migration rate and direction is through the comparison of sequential historical aerial photography (photos), maps, and topographic surveys. The first major use of photogrammetry in the evaluation of fluvial systems was conducted on the Mississippi River Valley. Fisk (58) used maps, aerial photographs, and ground investigations to document historic and pre-historic Mississippi River channel patterns in the lower Mississippi River Valley. Brice (72) developed his classification system of alluvial rivers by analyzing the planform properties of 200 river reaches from topographic maps and aerial photos in order to correlate aspects of river behavior, such as rate of lateral erosion and depth of scour, with river type. From this, he developed a comprehensive methodology for conducting a stream stability and meander migration assessment using a comparative analysis of aerial photos, maps, and channel surveys (49). Since Fisk’s work, numerous researchers have used photogrammetry to document channel planform changes, erosion and sedimentation patterns, and meander migration rates on a wide variety of streams in geographically diverse regions. For example, Hooke (94, 160) used historic aerial photos and maps to document the lateral mobility of rivers in Devon, England over a 50-year period. Williams (208) used photos taken of the Platte River in Nebraska to document the spectacular reductions in channel width that have resulted from river regulation since 1900. Burkham (209) used surveys, maps, and photographs to document channel changes on the Gila River in Arizona, and Ruhe (210) used maps covering the period 1852-1970 and aerial photos from 1925-1966 to document changes of the Otoe bend on the Missouri River. Using historic maps and aerial photographs, WET (211, 212) conducted a geomorphic analysis of more than 100 miles of the Sacramento River in California. Migration rates for specific bends, a bend evolution model, and a bend cutoff index were developed to identify critical sites requiring bank protection and sites where the potential for cutoffs was high (see Literature Review). Map and Aerial Photography Sources Historical and contemporary aerial photos and maps can be obtained inexpensively from a number of Federal, State, and local agencies. Table 5 lists some of the main sources. The Internet provides numerous sites with links to data resources and sites having searchable data bases pertaining to maps and aerial photography. Often, just typing in a few key words relative to aerial photos or maps for a particular site into a search engine will generate a large number of links to related web sites, which can then be evaluated by the user. It is this ready availability of aerial photography resources that makes the methodologies presented in the Handbook powerful and practical tools for predicting meander migration.

67 Table 5. Sources of Contemporary and Historical Aerial Photographs and Maps. Source Internet Address Comments Microsoft TerraServer – USA terraserver.microsoft.com Free downloads of contemporary digital topographic and aerial photo files. Operated by MSN in conjunction with Compaq and USGS USGS EROS Data Center Sioux Falls, South Dakota Photo Finder: edcwww.cr.usgs.gov/Webglis/ glisbin/finder_main.pl? dataset_name=NAPP Map Finder: edc.usgs.gov/Webglis/glisbin/ finder_main.pl?dataset_name= MAPS_LARGE Operated by the USGS. Interactive data base search for historic and contemporary topographic maps and aerial photos. USDA Farm Service Agency Aerial Photo Field Office (FSA - APFO) Salt Lake City, Utah www.apfo.usda.gov/ filmcatalog.html Operated by the Farm Service Agency. Catalog of historic and contemporary aerial photos for much of the United States. Sources include SCS (NRCS), Forest Service, BLM, Park Service, and other government Agencies. USGS Special Collections Library Denver, Colorado Reston, Virginia library.usgs.gov/specoll.html Field Records Collection is an archive of historic records including maps and aerial photography collected by USGS scientists dating back to 1879. Map Collections includes topographic maps for all states dating back to early 1880s. National Archives and Records Administration (NARA) - Cartographic and Architectural Records Washington D.C. www.nara.gov/publications/ leaflets/gil26.html#aerial2 Archive of historic maps and pre- 1941 aerial photos Western Association of Map Libraries (WAML) San Diego, California www.waml.org/wmlpubs.html References to information on obscure historic maps and where they can be found for reproduction U.S. Army Corps of Engineers www.usace.army.mil Corps Districts often have a wealth of historic photos, maps, and survey data.

68 Extensive topographic map coverage of the United States at a variety of scales can be obtained from the local or regional offices of the U.S. Geological Survey (USGS). In general, both aerial photos and maps are required to perform a comprehensive and relatively accurate meander migration assessment. Since the scale of aerial photography is often approximate, contemporary maps are usually needed to accurately determine the true scale of unrectified aerial photos. Geo-referenced and rectified maps and aerial photos are the most desirable for use in the analysis of meander migration, but often can be expensive to obtain. Presently, aerial photos for the 1990s for most areas of the United States can be obtained from three major sources, the MSN TerraServer World Wide Web site, the USDA Farm Service Agency, and the U.S. Geological Survey (Table 5). A major source of 1990s aerial photos available to the public is the TerraServer Web site operated by Microsoft Corporation. TerraServer, in partnership with the USGS and Compaq, provides free public access to a vast data store of maps and aerial photographs of the United States. Aerial photos and topographic maps at a wide variety of resolutions can be downloaded free of charge from the TerraServer Web site. The advantages of the TerraServer images are that they are rectified, geo-referenced, and are in digital format so that they are easily manipulated by a wide variety of software and can be used in GIS applications. For sites where TerraServer photographic coverage from the 1990s is unavailable, aerial photos can be ordered from the USGS Earth Resources Observation System (EROS) Data Center in Sioux Falls, South Dakota, or from the USDA Farm Service Agency Aerial Photo Field Office (APFO) in Salt Lake City, Utah. Both agencies have World Wide Web sites (Table 5) with searchable catalogs of available contemporary and historic aerial photography. Aerial photographs from the EROS Data Center that were flown in the 1980s and 1990s are usually part of the National Aerial Photography Program (NAPP) or the National High Altitude Photography Program (NHAP) and are at scales of 1:40,000 (1 in = 3,333 ft) or 1:60,000 (1 in = 5,000 ft). Because of the scale of these photos, small objects may be difficult to see, the resolution of enlarged portions may be poor, and measurements made from the photos may be inaccurate. Historic aerial photos ordered from EROS or from APFO range in scale from 1:5,000 to 1:40,000 with most flights having optimal scales of 1:20,000 or 1:24,000. Although both agencies have the ability to enlarge any photo to specification, some resolution is lost with increasing enlargement. Topographic maps in paper or electronic format can be obtained from a variety of sources. Paper copies of topographic maps can be obtained from the USGS or any commercial map supplier. Digital maps (DRGs, DEMs) can be downloaded free from the EROS Web site or purchased from commercial suppliers as well. Most digital maps are geo-referenced and can be loaded directly into GIS-based applications. Portions of geo-referenced topographic maps can be downloaded free from the TerraServer web site and pieced together to form a complete map of a given area or used to fill in gaps. The Handbook cautions that care should be taken when using digital maps and photos because the geo-referenced coordinates and dimensions are usually in metric (SI) units while the contours and spot elevations shown on the maps may be in English units.

69 Map and Aerial Photo Comparison Techniques A large number of geographic features and geomorphic planform characteristics used in the evaluation of meander migration are readily discernible on aerial photographs and topographic maps. Thus, a comparison of many of these features and characteristics over time can be made to determine the rate and extent of historic changes and assess potential future changes. The Handbook deals with assessments using aerial photos, but the same methods can be used when making assessments or measurements from maps. Manual Overlay Techniques An easy and relatively accurate method of determining migration rates and direction is through the comparison of sequential historical aerial photography, maps, and surveys. Accuracy in such an analysis is greatly dependent on the time intervals over which migration is evaluated, the amount and magnitude of internal and external perturbations forced on the system over time, and the number and quality of sequential aerial photos and maps. Major changes in watershed characteristics and hydrologic conditions can have a profound effect on meander migration patterns and rates. An analysis of long-term changes can be useful on a channel that has coverage consisting of data sets (aerial photos, maps, and surveys) that cover multiple time intervals over a long period of time (several tens of years to more than 100 years). Long-term changes can be documented and changing migration rates can be evaluated with regard to changes in watershed characteristics and hydrology over time. If only two or three data sets covering a short time period (several years to a few tens of years) are available, a short-term analysis may be conducted. A short-term analysis covering recent data can provide information on existing migration rates and conditions. Predictions of migration for channels that have been extensively modified or have undergone major adjustments attributable to extensive land use changes will be much less reliable than those made for channels in relatively stable watersheds. The manual overlay technique consists of overlaying channel banklines or centerlines traced from successive historic maps or photos that have been registered to one another on a base map or photo. The first requirement of conducting a simple overlay technique is obtaining the necessary aerial photos and maps for the period of observation. The amount of detail available for analysis increases as the length of time between successive maps or photos decreases. However, a longer period of record for comparison will tend to "average out" anomalies in the record and provide a better basis for predicting meander migration by extrapolation. Abrupt changes in migration rate and major position shifts can often be accounted for by analyzing maps and photos for land use changes, and nearby stream gage records can be examined for extreme flow events. Although most photos come with an optimal scale (e.g., 1:20,000), the scale is not always accurate for the purposes of analysis. The scale problem can be overcome through the use of multiple distance measurements taken between common reference points on a photograph and related base map. Measurements of distance for several reference-point pairs common to both the photo and the map are then averaged to define a relatively accurate approximation of the

70 scale of the photos. Common reference points can include constructed features such as building corners, roads, fence posts and intersections, irrigation channels and canals, or natural features such as isolated rock outcrops, large boulders, trees, drainage intersections, stream confluences, and the irregular boundaries of water bodies. The following relationship is used to determine the scale of the aerial photo relative to the base scale of the base map or photo: ScalePhotoAerialScaleBase BaseonPointsReferenceSameBetweenLength PointsReferencePhotoAerialBetweenLength =× Once the scale of each historic aerial photo is estimated, the photo can be enlarged or reduced to the scale of the base, whether it is another photo or a map. This can be done using a copier with a reduction or enlargement mode or using a flatbed scanner. With photos at a common scale, successive bankline or centerline positions can be determined. Accurate delineation of a bankline on an aerial photo is dependent primarily on vegetation density at the top of the bank. The bank top is most easily defined if stereopairs of photos are available, but individual photos can also be used when evaluated by experienced personnel. A detailed discussion of the methods for delineating a bankline is provided in Appendix B of the Handbook. After the maps and photos have been enlarged or reduced to a common scale, common reference points have been identified, and the banklines or centerlines have been delineated, the banklines or centerlines are then overlain on each other by matching the common reference points. The overlain bankline or centerline positions can then be evaluated with regard to migration distance, rate, and direction over time. Using the information and data obtained from this type of analysis, predictions can then be made on the potential position of the river at some point in the future. A step-by-step example of the application of the overlay prediction technique is presented in Chapter 3. Computer Supported Techniques The availability of powerful computers and photo editing software provides an alternative approach for performing the photo comparison techniques discussed in the previous section. For example, photo comparison and prediction can take advantage of the photo editing capabilities in Microsoft Word or PowerPoint. These features were used to develop the illustrative examples provided in Chapters 7 and 8 of the Handbook. In addition, computer aided design and drawing (CADD) software, such as AutoCAD and Bentley’s MicroStation, and GIS-based software, such as ArcView and ArcInfo, can be used in conjunction with a flatbed scanner and digitizing tablet to perform the photo comparisons with greater precision and accuracy, especially when the maps and photos are geo-referenced. Where digital files of aerial photographs are unavailable, a flatbed scanner can be used to scan aerial photographs to a relatively high resolution. Software that can manipulate a photographic image, such as MicroStation Descartes, can be used to warp a scanned aerial photograph to fit a map or another resolved aerial photo. A digitizing tablet can be used to record the registration points and bankline positions, as well as other features from historical aerial photographs, directly onto a geo-referenced drawing, map, or photo.

71 The photos and banklines can also be geo-referenced and the associated data can be imported into a GIS. For example, for the data collection effort for this project, the bend characteristics and meander migration patterns for more than 1,500 bends on numerous rivers distributed across the continental United States were recorded using a digitizing tablet in conjunction with Bentley’s MicroStation (see discussion of Archive Data Base). The acquired data was used to develop the GIS-based photogrammetric comparison methods to predict the rate and direction of bend migration outlined in the next section. GIS-Based Measurement and Extrapolation Techniques ArcView is a GIS and mapping software package developed by Environmental Systems Research Institute Inc. (ESRI). An ArcView extension, the Data Logger, is a GIS-based, menu- driven circle template methodology that was developed for NCHRP Project 24-16 to streamline the measurement and analysis of bend migration data and aid in predicting channel migration. The Channel Migration Predictor is another ArcView extension that was developed for this project using the extrapolation techniques described in more detail in Chapter 3. Both extensions were developed using ArcView Version 3.2. The Predictor tool uses the data archived by the Data Logger in predicting the probable magnitude and direction of bend migration at some specified time in the future. The Data Logger and the Channel Migration Predictor are ArcView extensions that were created using Avenue, a programming language and development environment that is part of the ArcView software package. Avenue is used to create specialized graphical user interfaces and to run scripts that customize the functionality of ArcView. An ArcView project is a file used to store the work done with ArcView on a particular application, such as recording river bankline data. An ArcView project file contains all the views, tables, charts, themes, and scripts associated with an application. Both the Data Logger and the Channel Migration Predictor consist of a set of ArcView scripts. A script is the component of an ArcView project that contains Avenue code. Just like macros, procedures, or scripts in other programming or scripting languages, ArcView scripts are used to automate tasks and add new capabilities to ArcView. The Data Logger provides users with a quick and easy way to gather and archive river planform data. The physical banklines are represented by one or more ArcView themes. A theme is a set of geographic features in a view. A view is an interactive map that allows the user to display, explore, query and analyze geographic data in ArcView. The bend delineation points for each bend and each historical record are archived in individual themes to provide a graphical record of the user’s interpretation of each bend. For each river bend and each historical record, the Data Logger records various river characteristics (e.g., bend radius, bend centroid, river widths, bend wavelength, etc.). This data is organized by river reach and recorded in a table identified by the reach name. These tables provide a permanent record of several river planform characteristics that can be further studied using the Channel Migration Predictor or various statistical procedures.

72 The Channel Migration Predictor examines a table of river reach data for several bends and two or three historical records per bend and then calculates rates of change in bend radius and bend center position. This rate data allows the Channel Migration Predictor to estimate the location of a bend at user specified times. As discussed above, river reach data tables can be created using the Data Logger. Users can also create tables for input to the Channel Migration Predictor in the form of properly formatted data base files using other means, such as Excel or Avenue. Data logging and prediction require the following steps to be performed at each bend for each historical record: 1. Locate the bankline delineation points on the outside of a river bend. 2. Inscribe an arc of a circle over the demarcation points to describe the radius and orientation of the bend. 3. Estimate the channel widths at the apex of the bend and at the upstream and downstream crossings (ends of the bend). 4. Estimate the wavelength and amplitude of the bend. 5. Use consecutive historical records and the data collected in steps 1-3 to estimate the extension and translation rates for a bend. 6. Use the migration and extension rates to extrapolate and estimate the future bankline locations. Instructions on installing the ArcView-based Data Logger and Channel Migration Predictor are provided in Appendix C of the Handbook. Examples using these tools to conduct planform measurements and meander migration prediction are provided in Chapter 8 of the Handbook. ARCHIVE DATA BASE Overview Another stand-alone deliverable for this project was an archive of the data base compiled on CD-ROM to include all meander site data acquired for this study. With this archive data set, future researchers will have a readily accessible data base in a very useable format for a variety of studies. These studies could include additional empirical analyses and more complex regressions based on the archive data. The Brice data alone is an invaluable resource for future researchers, as it includes the field measurements compiled by the U.S. Army Corps of Engineers Waterways Experiment Station for their study of stable channel design. Although the Panel suggested developing a relational data base for the archive, this effort proved to be beyond the scope and budget available for the following reasons: • Size of the data base with 141 meander sites, containing 1,503 meander bends • Size of the files required to archive base quad sheets, mapping, and photography • Multiple file formats for the data (e.g., MicroStation files, JPEG, TIFF, and Excel files) • For ease of use, files are distributed in different subdirectories; however, this makes developing hyperlinks for related files a complex and time consuming process

73 The Excel spreadsheet format adopted for the data base permits cross-referencing based on data source, meander class, river name, or State. This provides a simple and useable approach to searching the data base. The spread sheets to search the data base by these four categories are shown in Appendix B. The data collection and measurement procedures used to develop the data base are described in detail in Chapter 3. The CDs containing the archived data base compiled for this project were provided to TRB/NCHRP with this report. A paper copy of the data spread sheets was also submitted on acid-free paper for permanent archiving by TRB. Data Base Structure The hierarchy for the distribution of the sites and accompanying data included in the data base is shown in Figure 22. NCHRP Project 24-16 Data Base ª River Classes ª A B1 B2 C D E F G1 G2 Other ª (Individual Rivers) ª Aerial Photos (Date) Data Base Workbook MicroStation Topo Maps ª (Individual Files) Figure 22. Hierarchy for Archive Data Base Figure 23 shows an example of how the directory structure appears on the CDs. As noted above, included under the main directory is an Excel workbook file that includes four spreadsheets that cross-reference each data site by the (1) source of the data, (2) modified stream classification, (3) river name, and (4) state in which the site is located (see Appendix B). A Word document included in the main directory briefly describes each of the file types included in the data base. An ASCII text file is also included that provides the color key for the historic channel position sheets for the various Kansas rivers included in the data base (see Chapter 3, Data Collection). The data for each meander site is compiled in Microsoft Excel workbooks. There are multiple spreadsheets within each of the workbooks. The first spreadsheet, designated General Data, contains the general information compiled by various sources and an aerial photo showing the site limits and the included meander bends (Figure 24). Each meander bend is numbered from upstream to downstream. There are individual spreadsheets, designated by the bend number, which contain detailed historic data for each of the bends of the site (Figure 25). There is also a spreadsheet, designated Discharge Data, that has the mean daily and annual peak discharge data for the gage nearest to the site. Finally, a summary spreadsheet contains all the measured data for all the bends of the site.

74 Figure 23. Example directory for the Archive Data Base. Summary The CD-ROM archives contain the Excel workbooks, MicroStation files, 1990s and historic (where applicable) aerial photos, and the topographic maps for each site in digital file format. The data base includes 141 meander sites containing 1,503 meander bends on 89 rivers in the U.S. The maps and photos are in JPEG format. The files are sorted by stream class and river name with subdirectories for the workbooks, maps, photos, and MicroStation files. Within the archived data base there is a text file that provides a cross-reference between the data source and the stream class and location.

75 Figure 24. General Data spreadsheet containing the existing data and aerial photograph with bend locations for a site on the Brazos River, Texas.

76 Figure 25. Bend spreadsheet containing measured and existing data for a bend on the Brazos River, Texas.