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From page 7... ...
This section is structured as follows: • A listing of available MERRA-2 data tables applicable to pavements • A summary of MERRA-2 data extraction and unit conversions • A selected set of comparisons and final variable selections • A proposed process to integrate selected variables into the LTPP InfoPave Climate Tool 3.1.1 Available MERRA-2 Data Tables and Variables for Pavement Applications The MERRA-2 NASA data tables with hourly data for potential use in pavement applications include the radiation diagnostics (tavg1_2d_rad_Nx) , land surface diagnostics (tavg1_2d_lnd_ Nx)
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From page 8... ...
U.S. Equivalent Units EVLAND Evaporation land kg m–2 s–1 lb ft–2 s–1 EVPTRNS Transpiration energy flux W m–2 BTU ft–2 h–1 LWLAND Net longwave land W m–2 BTU ft–2 h–1 QINFIL Soil water infiltration rate kg m–2 s–1 lb ft–2 s–1 RUNOFF Overland runoff, including throughflow kg m–2 s–1 lb ft–2 s–1 SMLAND Snowmelt flux land kg m–2 s–1 lb ft–2 s–1 SWLAND Net shortwave land W m–2 BTU ft–2 h–1 TSAT Surface temperature of saturated zone K K TSOIL1 Soil temperatures layer 1 K K TSOIL2 Soil temperatures layer 2 K K TSOIL3 Soil temperatures layer 3 K K TSOIL4 Soil temperatures layer 4 K K TSOIL5 Soil temperatures layer 5 K K TSOIL6 Soil temperatures layer 6 K K TUNST Surface temperature of unsaturated zone K K ECHANGE Rate of change of total land energy W m–2 BTU ft–2 h–1 GHLAND Ground heating land W m–2 BTU ft–2 h–1 LHLAND Latent heat flux land W m–2 BTU ft–2 h–1 PRECTOTLAND Total precipitation land; bias corrected kg m–2 s–1 lb ft–2 s–1 SHLAND Sensible heat flux land W m–2 BTU ft–2 h–1 SPLAND Rate of spurious land energy source W m–2 BTU ft–2 h–1 SPSNOW Rate of spurious snow energy W m–2 BTU ft–2 h–1 TPSNOW Surface temperature of snow K K TSURF Surface temperature of land, including snow K K
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From page 9... ...
Units LWGNET Surface net downward longwave flux W m–2 BTU ft–2 h–1 Upwelling longwave flux at top of the atmosphere LWTNET W m–2 BTU ft–2 h–1 (TOA) PRECLS Large scale rainfall kg m–2 s–1 lb ft–2 s–1 or in SWNETSRF Surface net downward shortwave flux W m–2 BTU ft–2 h–1 SWNETTOA TOA net downward shortwave flux W m–2 BTU ft–2 h–1 HFLUX Sensible heat flux from turbulence W m–2 BTU ft–2 h–1 Table 6. List of radiation diagnostics (tavg1_2d_rad_Nx)
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From page 10... ...
Units Surface net downward longwave flux assuming clear LWGNTCLR W m–2 BTU ft–2 h–1 sky Surface net downward longwave flux assuming clear LWGNTCLRCLN W m–2 BTU ft–2 h–1 sky and no aerosol LWTUP Upwelling longwave flux at TOA W m–2 BTU ft–2 h–1 LWTUPCLR Upwelling longwave flux at TOA assuming clear sky W m–2 BTU ft–2 h–1 Upwelling longwave flux at TOA assuming clear sky LWTUPCLRCLN W m–2 BTU ft–2 h–1 and no aerosol SWGDN Surface incoming shortwave flux W m–2 BTU ft–2 h–1 SWGDNCLR Surface incoming shortwave flux assuming clear sky W m–2 BTU ft–2 h–1 SWGNT Surface net downward shortwave flux W m–2 BTU ft–2 h–1 Surface net downward shortwave flux assuming no W m–2 SWGNTCLN BTU ft–2 h–1 aerosol Surface net downward shortwave flux assuming W m–2 SWGNTCLR BTU ft–2 h–1 clear sky Surface net downward shortwave flux assuming SWGNTCLRCLN W m–2 BTU ft–2 h–1 clear sky and no aerosol SWTDN TOA incoming shortwave flux W m–2 BTU ft–2 h–1 SWTNT TOA net downward shortwave flux W m–2 BTU ft–2 h–1 TOA net downward shortwave flux assuming no SWTNTCLN W m–2 BTU ft–2 h–1 aerosol TOA net downward shortwave flux assuming clear SWTNTCLR W m–2 BTU ft–2 h–1 sky TOA net downward shortwave flux assuming clear SWTNTCLRCLN W m–2 BTU ft–2 h–1 sky and no aerosol TS Surface skin temperature K K 3.1.1.1 Summary of Unit Conversions The MERRA-2 assimilated data are distributed in SI units, which may or may not require additional conversions to match those required by the EICM. Table 7 summarizes the unit conversions for the most common variables.
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From page 11... ...
3.1.2.2 Data Evaluation Many of the datasets or data tables include similarly named variables. For example, net longwave and shortwave radiation data are included in the Flux, Radiation, and Land datasets, which may or may not be equivalent.
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From page 12... ...
Figure 1. Locations selected for MERRA-2 data extraction.
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From page 13... ...
• tavg1_2d_rad_Nx becomes RAD – Represents assimilated radiative forcing climate variables over land and water. Longwave Radiation The net downward longwave radiation variables at the Earth's surface for the different dataset collections are listed here and illustrated in Figure 2: • LWLAND-LAND – Net longwave radiation over land area only within nodal area.
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From page 14... ...
Shortwave Radiation The net incoming shortwave radiation at the Earth's surface for the three different MERRA-2 data tables are listed and defined here: • SWLAND-LAND – Net shortwave radiation over land area only within total nodal area. • SWNETSRF-INT – Surface net downward shortwave flux over land and water within nodal area.
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From page 15... ...
Interpretations and Applications 15 Figure 4. Incoming, outgoing, and net longwave radiation at the Earth's surface from the RAD MERRA-2 table. Total Net Radiation The total net radiation, which was calculated using the net shortwave and net longwave data presented previously, at the Earth's surface for the three different MERRA-2 data tables is listed and defined here: • TOTALNET-LAND = SWLAND-LAND + LWLAND-LAND • TOTALNET-INT = SWNETSRF-INT + LWGNET-INT • TOTALNET-RAD = SWGNT-RAD + LWGNT-RAD Figure 5. Net shortwave radiation versus time for different MERRA-2 data tables over a 7-day period in July 2014.
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From page 16... ...
. Overall, the total net radiation (i.e., shortwave and longwave)
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From page 17... ...
MERRA-2 Table Name MERRA-2 Variables MERRA-2 Variable Description LWLAND Net longwave over land only SWLAND Net shortwave over land only Land surface diagnostics LHLAND Latent heat flux land (tavg1_2d_lnd_Nx) SHLAND Sensible heat flux land PRECTOTLAND Total precipitation land; bias corrected LWGNET Surface net downward longwave flux Vertically integrated diagnostics SWNETSRF Surface net downward shortwave flux (tavg1_2d_int_Nx)
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From page 18... ...
For each of the locations shown in Figure 1, the following steps were performed to analyze and compare the energy balance variables using different MERRA-2 tables and the empirically calculated longwave, shortwave, and total net radiation at the ground surface: 1. Calculate the net longwave, shortwave, and total radiation using the empirical formulas currently implemented in the EICM.
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From page 19... ...
The analysis results are presented and discussed for each climate variable in the following sections: • Net Longwave Radiation Analysis Results • Net Shortwave Radiation Analysis Results • Net Total Radiation Analysis and Results Net Longwave Radiation Analysis Results Results and Discussion. The boxplot distributions of average annual net longwave radiation were generated to compare the range of values included for each climate dataset, as shown in Figure 8. The same data are then separated by each climate region, as shown in Figure 9.
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From page 20... ...
and interactive effects were significantly different than the null hypothesis and conclude that one or Climate Dataset EICM LAND INT RAD Wet freeze Wet non-freeze Net Longwave Radiation (BTU/h-ft2) Dry freeze Dry non-freeze EICM LAND INT RAD EICM LAND INT RAD Figure 9. Mean annual net longwave radiation for each climatic zone and climate dataset.
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From page 21... ...
The complete analysis compares all combinations between the climate dataset levels and climate zone levels. Some of these combinations are not necessarily relevant to the overall conclusions and were excluded from Table 10.
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From page 22... ...
* Wet freeze Dry freeze –5.587 –6.760 –4.413 0.000 *
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From page 23... ...
Dry freeze Dry non-freeze EICM LAND INT RAD EICM LAND INT RAD Figure 11. Mean annual net shortwave radiation for each climatic zone and climate dataset.
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From page 24... ...
The ANOVA statistical analysis results for net shortwave radiation are summarized in Table 11. The results show that only the main effects (i.e., climate dataset and climate zone)
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From page 25... ...
Net Total Radiation Analysis Results Results and Discussion. The total net radiation is calculated by summing the net shortwave and net longwave radiation. The boxplot summary for total net radiation for each climate dataset is shown in Figure 12, while the same data separated by climate zone are shown in Figure 13.
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From page 26... ...
The results from the ANOVA for net total radiation are summarized in Table 13. The results show that both the main effects (i.e., climate dataset and climate zone)
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From page 27... ...
* Wet freeze Dry freeze –1.675 – 3.181 –0.168 0.023 *
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From page 28... ...
3. Many of the differences between the EICM-calculated net longwave and shortwave radiation are due to the models and regression constants being developed using data from a specific region, which is not representative of other climatic zones or locations.
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From page 29... ...
Figure 16 illustrates the differences between the two geographical locations for the virtual climate station and the single station. The results show that the monthly average temperatures for the virtual station are almost identical to the single station data for the flat region.
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From page 30... ...
Single station NOTE: In Figure 15b, the white flag and the green single station point location underneath it possess the same meaning. Figure 15. MERRA-2 grid point locations selected to compare a virtual station to an individual MERRA-2 grid point for a highly variable elevation area.
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From page 31... ...
The inverse distance weighted interpolation method may not be appropriate for all geographical locations. Other more sophisticated spatial interpolation methods have been developed that may provide a better estimate for locations between MERRA-2 grid points.
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From page 32... ...
Evaluation of Geographical Distinctions As discussed earlier, two distinct geographical regions were selected for spatial interpolation: an area with relatively constant elevations (i.e., a flat region) and an area with highly variable elevations changes (i.e., a mountainous region)
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From page 33... ...
Similar to the mountainous region, MERRA-2 ID-144148 (Location 5 in Figure 18) , along with the eight surrounding MERRA-2 grid points, was selected to represent the locations with minimal elevation differences for spatial interpolation.
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From page 34... ...
IDs 1, 2, 3, and 4 in Table 16 were grouped to represent the low elevation group, while IDs 6, 7, 8, and 9 represent the high elevation group. Spatial Interpolation Results. The data period of each grid point is from 1985 to 2021 and collected temperature, wind speed, percent sunshine, precipitation, and relative humidity for every hour.
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From page 35... ...
The spatial interpolation results using 2D kriging for a mountainous region are summarized in Table 17. Based on the analysis results, similar RMSE values were exhibited across variogram models within each category.
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From page 36... ...
Conversely, in the flat region, those two interpolation results showed similar performances; however, 3D interpolation exhibited better performance in Group 1, providing lower RMSE values compared to 2D interpolation for most variables. The results presented between 2D and 3D kriging were surprising because the initial assump tion was that 3D kriging would result in lower RMSE values compared to the 2D analysis since it directly accounts for altitude when calculating the distance between the target location and the other grid points in the analysis.
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From page 37... ...
• Additional Use Cases – One benefit of the spatiotemporal interpolation methods is that they can interpolate values at multiple points. For example, if multiple coordinates along a roadway are specified, point value estimates can be determined for each point to represent "roadway specific" climate data.
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From page 38... ...
3.2.2.3 Investigate Methods to Improve Pavement Temperature Predictions During Precipitation Events The EICM does not currently directly account for the change in pavement temperature with respect to precipitation. The pavement temperature is expected to closely reflect the air tempera ture during precipitation events, as the amount of rain or snow will either cool or warm the Table 20. Spatial interpolation RMSE results using 2D kriging for a mountainous region using nine MERRA-2 grid point locations.
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From page 39... ...
The following variables were calculated: • NetRad: Total net radiation equal to the sum of net shortwave and longwave radiation. These represent the radiative forcing variables.
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From page 40... ...
• Based on these results, the sum of longwave and shortwave radiation is approximately equal to the sum of latent heat flux, sensible heat flux, and ground heat flux. Compare Different Energy Balance Variables to Precipitation and Identify Whether Any Significant Correlations Exist The hourly data for an entire year (2013)
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From page 41... ...
Results and Discussions The instantaneous effect of precipitation on the pavement temperature is not really shown in the data. One potential reason for this observation is that the impact of precipitation on the surface or skin temperature is accounted for in the latent heat flux variable due to the evaporation and transpiration processes.
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From page 42... ...
3.3.2.1 Arizona SMP Flexible One-to-One Comparison The MERRA-2 shortwave and longwave radiation data were used to calculate the total net radiation, which is used to predict pavement temperature in the EICM. Figures 21 and 22 show the one-to-one comparison between the predicted pavement temperature (y-axis)
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From page 43... ...
Interpretations and Applications 43 Figure 21. Predicted pavement temperature versus measured pavement temperature using MERRA-2 shortwave and longwave radiation data. Figure 22. Predicted pavement temperature versus measured pavement temperature using the PMED empirical shortwave and longwave radiation equations.
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From page 44... ...
Residual Error Histogram The residual error between the measured pavement temperature and MERRA-2- and EICM predicted pavement temperatures were compared to identify which method was best. The residual error was calculated for each hour the measured data were available.
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From page 45... ...
The pavement temperatures predicted using the MERRA-2 shortwave and longwave radiation data resulted in a slightly better prediction overall for the Arizona SMP location. Table 21. MERRA-2 versus measured pavement temperature hypothesis test results for the Arizona SMP site.
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From page 46... ...
The average pairwise difference between the MERRA-2- and PMED-predicted pavement temperatures was less than 1 °F, which is practically insignificant even though the null hypothesis was rejected. The slope and intercept hypothesis tests were also significantly different statistically, while the value esti mates were practically the same as the null hypothesis.
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From page 47... ...
The MRE provides additional information regarding the over- or under-prediction of the pavement temperature compared to the measured values. The MRE is calculated by averaging the difference between the predicted pavement temperature and the measured pavement temperature.
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From page 48... ...
Residual Error Histogram The residual error between the measured pavement temperature and the MERRA-2- and EICM-predicted pavement temperatures was compared to identify whether one method is better than the other. The number of observations within each residual error group was counted and summarized using a histogram, as shown in Figure 28.
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From page 49... ...
Interpretations and Applications 49 Figure 26. Manitoba -- predicted pavement temperature versus measured pavement temperature using the PMED empirical shortwave and longwave radiation equations. Figure 27. Manitoba -- MERRA-2-predicted pavement temperature versus PMED-predicted pavement temperature.
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From page 50... ...
Similar to the Arizona SMP site discussed previously, the results are not practically different from one another. For the Manitoba SMP site, the pavement temperatures predicted using the current EICM/PMED empirical method resulted in a slightly better prediction overall.
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From page 51... ...
The MRE provides additional information regarding the over or underprediction of pavement temperature compared to the measured values. The results show that the MERRA-2 showed consistent overpredictions of the measured pavement temperature in the summer months compared to the PMED-predicted pavement temperatures.
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From page 52... ...
Measured PMED vs. Measured Jan 5.6671 5.8833 Feb 5.1477 5.2050 Mar 5.9336 4.8380 Apr 7.1151 7.4873 May 10.0232 8.0472 Jun 11.4496 8.8364 Jul 13.6512 10.6845 Aug 10.7856 9.6286 Sep 8.1492 8.8387 Oct 5.9329 6.1718 Nov 3.7311 4.4478 Dec 3.5202 3.8112 Table 31. Monthly R2 for the Manitoba SMP site.
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From page 53... ...
Measured PMED vs. Measured Jan –1.61980 –3.23759 Feb 1.68547 –2.15505 Mar –0.93808 –0.78334 Apr –4.05513 –2.91052 May –6.48289 –4.79631 Jun –9.04629 –5.02854 Jul –10.94665 –7.31495 Aug –8.42947 –5.82500 Sep –6.73355 –6.99886 Oct –4.53724 –4.75415 Nov –1.08053 –2.49417 Dec 1.09107 –0.50313 Figure 29. Georgia -- predicted pavement temperature versus measured pavement temperature using MERRA-2 shortwave and longwave radiation data.
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From page 54... ...
The EICM- and PMED predicted pavement temperatures resulted in a better overall prediction of the measured pavement temperatures. Linear Regression and Hypothesis Tests The pairwise comparison, intercept, and slope hypothesis test results for the MERRA-2 and EICM/PMED comparisons with the measured pavement temperature data are summarized in Tables 33 and 34, respectively.
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From page 55... ...
Interpretations and Applications 55 Figure 31. Georgia -- MERRA-2-predicted pavement temperature versus PMED-predicted pavement temperature. Figure 32. Georgia -- count of residual error data points that fall within each temperature bin category for MERRA-2and PMED-predicted pavement temperatures.
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From page 56... ...
–5.2215 0.0000 Intercept = 0 5.5025 0.0000 Slope = 1 0.9954 0.4882 Table 34. PMED-predicted pavement temperature versus measured pavement temperature hypothesis test results for the Georgia SMP site. Hypothesis Test Value Estimate P-Value Paired t-test (mean difference)
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From page 57... ...
• The scatter around the line of equality is less at lower pavement temperatures compared to the scatter at higher pavement temperatures. • Overall, both cases compare fairly well against the measured pavement temperature values.
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From page 58... ...
58 Mechanistic–Empirical Pavement Design Model: Enhancements of Climatic Inputs Figure 33. New Jersey -- predicted pavement temperature versus measured pavement temperature using MERRA-2 shortwave and longwave radiation data. Figure 34. New Jersey -- predicted pavement temperature versus measured pavement temperature using the PMED empirical shortwave and longwave radiation equations.
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From page 59... ...
Overall, the predicted pavement temperatures compare well with one another. Residual Error Histogram The residual error between the measured pavement temperature and MERRA-2- and EICMpredicted pavement temperatures was compared to help determine whether one method was better than the other.
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From page 60... ...
Hypothesis Test Value Estimate P-Value Paired t-test (mean difference) 0.5450 0.0000 Intercept = 0 –4.8158 0.0000 Slope = 1 1.0683 0.0000 Table 40. PMED-predicted pavement temperature versus measured pavement temperature hypothesis test results for the New Jersey SMP site.
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From page 61... ...
The slope and intercept hypothesis tests were also statistically significantly different, while the value estimates were practically the same as the null hypothesis. Overall, the MERRA-2- and PMED-predicted pavement temperatures are in good agreement.
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From page 62... ...
Measured PMED vs. Measured Jan 0.78041 0.85902 Feb 0.62763 0.73319 Mar 0.76379 0.84519 Apr 0.69023 0.89584 May 0.44842 0.55755 Jun 0.66984 0.71744 Jul 0.63106 0.68083 Aug 0.59732 0.61735 Sep 0.57300 0.75560 Oct 0.73847 0.72264 Nov 0.75760 0.81876 Dec 0.75236 0.80613 3.3.3 Summary In summary, the validation results using a subset of LTPP SMP sites showed generally good agreement between the measured and predicted pavement temperature regardless of which method was used.
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From page 63... ...
– Sensible heat, latent heat, and ground heat effects were not included in the overall energy balance calculations and could have a significant effect. The amount of sensible heat, latent heat, and ground heat is dependent on the location.
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From page 64... ...
Assumed or Default Input Variable Units Values Total depth 360 in Assumed as the Initial nodal temperature ºF or ºC MAAT Constant temperature of last layer Set as the MAAT ºF or ºC Upper temperature limit of freezing range in which water is 32 ºF partially frozen and unfrozen Lower temperature limit of freezing range 30.2 ºF BTU / h Maximum allowable convection coefficient Hard coded to 3 – ft2 –ºF Analysis time step 0.1 h Time step for analysis outputs 1 h Emissivity factor 0.93 Longwave back radiation factor 0.77 Geiger longwave radiation factor 0.28 Rho factor 0.074 Vapor pressure of atmosphere near surface Hard coded to 5 mmHg Time of day when minimum temperature occurs 4.0 (4 am) Time of day when maximum temperature occurs 15.0 (3 pm)
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From page 65... ...
Common Inputs for All Analysis Types The hourly climate inputs required by the EICM are summarized in Table 46. Additional variables calculated from the hourly input data include daily, monthly, and yearly averages; wet days; freezing index; and freeze-thaw cycles.
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From page 66... ...
– Saturated permeability or hydraulic conductivity: Direct input or calculated (ft/h or m/h) – Initial volumetric water content: Calculated (%)
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From page 67... ...
If the layer is compacted, the following equation is used to determine the maximum dry density: c d - max = 142.115 - 1.959 # wopt If the material is not compacted, the following equation is used: c d - max = 1.0156 # `142.115 - 1.959 # wopt j - 2.464 Specific Gravity of Solids, Gs. The specific gravity of solids uses a value of 2.7 by default and can also be specified directly by the user. D60. The grain size diameter corresponding to 60% passing is calculated based on the percent passing of individual sieve sizes.
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From page 68... ...
Based on the known quantities at the time of the analysis, the porosity is calculated using the following equation: cd n = 1 G s # cw Saturated Hydraulic Conductivity, ksat. For non-plastic granular materials and when wPI = 0, the following equation is used to estimate the saturated hydraulic conductivity: k sat = 10 -6 # 10 5.3#D a D 60 D 10 k - 0.1#P 200+ 1.5 10 +0.049#D 10 +0.0092# Additionally, if ksat > 10, then it is set to a value of 10. For plastic soils, the following equation is used to estimate the saturated hydraulic conductivity with units of cm/s: k sat = 10 7.014- 0.0376#LL - 0.361#c - 7.932#Log` PI j+ 0.249#c #PI 0.105 d d The saturated hydraulic conductivity undergoes a unit conversion internally from cm/s to ft/h, 1 cm/s = 118.11023 ft/h.
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From page 69... ...
Factor h rf = 500 wPI = P200 # PI For non-plastic soils, the following equations are used to determine the Fredlund and Xing factors: Fredlund (a) Factor a f = -2.79 - 14.1 # Log `D 20 j - 1.9 # 10 -6 # P 200 4.34 + 7 # Log `D 30 j + 0.055 # D 100 R V S 40 + log` D 60 jW W SSm 1 W D 100 = 10 T X 30 m1 = R V Slog `D 90 j - log `D 60 jW T X • If af < 1, then af = 2.25 × P 0.5 200 + 5 • NCHRP Project 09-23 reports an additional calculation not present in the EICM source code (10)
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From page 70... ...
Factor h rf = 100 Saturated Permeability or Hydraulic Conductivity • Direct input or calculated value in ft/h or m/h 3.4.1.2 EICM Climate Models Energy Balance Near the Ground Surface The following energy balance equations are used to calculate the climatic and radiation data for each time increment for the given day and hour. The subroutine within the EICM calcu lates the net shortwave radiation, net longwave radiation, net total radiation, and convection coefficient.
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From page 71... ...
Pavement Temperature The pavement temperature is adjusted for each node throughout the pavement structure, starting from the pavement surface. The calculations are performed for the different node types (i.e., surface, interface, and interior)
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From page 72... ...
The calculations are applied at the pavement surface location, interior nodal locations where the material properties are the same, and at interface locations where different layer types are accounted for. At the Pavement Surface. The finite difference equation for nodal locations at the pavement surface is shown here: k ccDX `T2 - T1 j + H `Tair - T1 j + Q rad = `Tl1 - T1 j DX 2Di where k represents the hydraulic conductivity, T1 and T2 are the temperature of node 1 and node 2, Tair is the air temperature, Qrad is the total net radiation (shortwave and longwave)
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From page 73... ...
The stability checks are presented here: Surface Node ccDX Di < 2 aH + k DX k Interior Node ccDX 2 Di # 2k Interface Node c ` n j c ` n j DX `2n j + c ` n+1 j c ` n+1 j DX `2n+1 j Di # 2 ak ` n j + k ` n+1 j k Moisture and Temperature Models The moisture model adjusts the unbound base and natural subgrade material moisture conditions on an hourly basis. The calculations are presented in the following section.
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From page 74... ...
• Nodal depths are converted from in to cm. Hourly Calculation Step 2 – Convert Units for Density, Nodal Elements, Saturated Hydraulic Conductivity, and Thermal Conductivity • Density is converted from lb/ft3 to g/cm3.
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From page 75... ...
– If the node is above the water table, then adjust the saturated hydraulic conductivity to an unsaturated hydraulic conductivity value. • Average temperature between node "n" and node "n+1" – If the soil is in a freezing condition, but not yet frozen, then the freezing pore pressure is calculated using the following equation: - `1.1389 # t e + 2445.5646 j J N K O + 8.2312 `273.1 + t e j K O K O K O K O HL = 10841.441 # `273.1 + t e j # KK # Log10 `273.1 + t e j - 11.098907 - 0.010188 # t e OO K O K O K - 0.12486 # 10 -5 # t 2e + 9.084 # 10 -8 # t 3e O L P • Saturated hydraulic conductivity is multiplied by a permeability reduction factor.
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From page 76... ...
. Hourly Calculation Step 9 – Calculate the Apparent Heat Capacity for Current Conditions. The heat capacity changes as a function of water content, quantity of ice, density, and heat capacity of water and soils.
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From page 77... ...
• cs = cal/g − °C is the heat capacity of the soil. Hourly Calculation Step 10 – Calculate the Convective Heat Flux. This step calculates the convective heat flux for the hourly nodal domain boundary per CRREL frost model.
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From page 78... ...
• Parameter fine-grained materials (P200 less than 50) – a = −0.3123 – b = 0.3 – km = 6.8157 • Coarse-grained materials – a = −0.5934 – b = 0.4 – km = 6.1324 Resilient Modulus of Unbound Layers for Recovering Conditions. For unbound materials under thawing (or recovering)
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From page 79... ...
In other words, the resilient modulus of the fully thawed material is equal to the modulus of unfrozen material. 3.4.2 Other Improvements 3.4.2.1 Input File and Run-Time Improvements The EICM input text file (input.tmp)
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From page 80... ...
The following inputs and hard-coded values will be deprecated: – Longwave and shortwave radiation empirical methods, – Calculations for sunrise and sunset, and – Extraterrestrial solar radiation based on location and solar declination angle. • Adjust the values that set the constant deep ground temperature lower boundary condition to accommodate areas where the MAAT is less than 32 °F/0 °C.
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From page 81... ...
One major benefit of refactoring is that the source code can be modularized so that each method is easily identified, modified, or replaced. Some other potential benefits of refactoring the EICM include the following: • Upgrades the EICM source code to modern software standard procedures for applications and code bases; • Includes all documentation, algorithms, data requirements, and data structure definitions as a part of the source code repository; • Is essential for maintaining long-term code and implementing future enhancements and standardized automated testing; • Has the potential for improved analysis run-time; • Improves customization options for selecting which intermediate outputs to generate; • Can become a standalone tool for researchers to build and test new models; and • Integrates the EICM into new or existing applications.
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