B RIVER xGW
3. RESULTS AND ANALYSIS 1 Calibration and Model Parameterization
3.2 Model Validations
The three-layer VIC model simulations for the water and the energy balance were carried out over a period of 50 years (1950 to 1999) using daily forcing — precipitation, maximum temperature, minimum temperature, and wind speed — at daily timestep. The water balance simulations were performed at daily time step at 1/8° spatial resolution and the simulations for the energy budget were carried out at an hourly time step and 1° spatial resolution. Disaggregation of precipitation is carried out using the procedure in Maureret al. (2002). The VIC-3L results were analyzed for the Upper Mississippi river basin over a period of 50 years (1950 to 1999) as well as separately for the range of drought year 1988 (and adjacent years 1987 and 1989) and the flood year 1993 (and adjacent years of 1992 and 1994).
3.2.1 Streamflow Comparison over a Period of 50 Years (1950 to 1999)
The streamflows were compared for the basin outlet of the Mississippi River at Grafton, IL and the Illinois River at Valley City, IL. The Valley City station is located on the stretch of the Illinois River just before its confluence
Simulation of Water and Energy Budgets 105
with the Mississippi River. The locations of these two stations are shown in Figure 5.1b.
The daily streamflow scatter-plot for the Mississippi River at Grafton, IL (Figure 5.2a) between USGS measured discharge and model-simulated streamflow for the period 1950 to 1999 shows a reasonable R2 value of 0.74 and a bias of 32,438 cfs. The value of bias gives an indication of systematic departures whereas the R2 values give us an estimate of the linear correlation between two quantities. The percentage difference of the mean flow for the bias (bias/mean flow) translates to around 15%. Figure 5.2b shows a reasonably good monthly streamflow comparison between the measured and simulated streamflow. The model simulation of the peaks and also the overall performance over a period of 50 years is presented in Table 5.1. Similarly, Figure 5.3a depicts the daily scatter-plot between the model-simulated streamflow and the USGS measured discharge for the period 1950 to 1999 at the Illinois River at Valley City, IL. The comparison gave a lower (compared to the basin outlet) R2 value of 0.61 and a bias of 2719 cfs. The monthly discharge comparison over the 50-year period for Valley City, IL shows overestimation by the model. The streamflow comparisons for the Mississippi River at Grafton, IL with the USGS measured stream discharges are more consistent than those for the Illinois River at Valley City, IL. There could be a possible effect of aggregation at the outlet.
In addition, the Illinois River basin has watershed regulations that would affect the streamflow at the outlet. Also, routing models have limitations and the input data may have sources of error, specifically when we interpolate the rainfall input for the various 15-km × 15-km grid cells. Errors due to gridding the model could have contributed to the streamflow errors.
Table 5.1 tabulates the percentage differences in monthly streamflow comparisons over a period of 50 years at the Mississippi River at Grafton, IL. In general the months of late winter and spring have the maximum percentage errors and also the largest absolute differences, and the summer and early fall months have the least difference, similar to the results of the study by Maurer et al. (2002). The overall difference in the modeling over a period of 50 years (1950 to 1999) is about 13%.
3.2.2 Comparison with Illinois Soil Moisture Observations
Figures 5.4a-d depict the individual monthly average soil moisture comparisons for the different soil layers with the Illinois State Water Survey Board measurements for a period of 19 years (1981 to 1999). The top two soil moisture layers (0-10 cm, 10-40 cm) show greater variation in the observed data compared to the model simulations, whereas an inverse (greater variation in model than observed data) is seen in the case of layer 3 (40-140 cm). The aggregated soil moisture for the 140-cm layer simulations (0-140 cm) is depicted in Figure 5.4d. The differences can be attributed to the fact that the model-simulated soil moistures are average over a cell of approximately 15 km
× 15 km area whereas those from the Illinois Water Survey data are point measurements. The scatter plots for the different layer comparisons are shown in
106 Watershed Models
Figures 5.5a-d. The values of R2 improved with the depth of the layers from about 0.3 for layer 1 (0-10 cm) to 0.6 for the aggregated layer (0-140 cm). The comparisons from the integrated soil water for the simulated 0 to 140-cm layer (Figure 5.4d) exhibit the same seasonal pattern as the observations. This highlights our ability to model water movement and conserve moisture.
Figure 5.2 (a) Scatterplot of daily streamflow at the Mississippi River at Grafton, IL, 1950–1999. (b) Monthly mean streamflow at the Mississippi River at Grafton, IL, 1950–
1999.
y = 0.87x + 25676 R2 = 0.74 Bias=32580 cfs RMSD=43946 cfs
0.00E+00 2.00E+05 4.00E+05 6.00E+05 8.00E+05
0.00E+00 2.00E+05 4.00E+05 6.00E+05 8.00E+05 Simulated Discharge in cfs
Measured Discharge in cfs
(a)
0.00E+00 1.00E+05 2.00E+05 3.00E+05 4.00E+05 5.00E+05 6.00E+05
Oct-54 Mar-60 Sep-65 Mar-71 Aug-76 Feb-82 Aug-87 Jan-93 Jul-98 Jan-04 Year
Discharge in cfs
Simulated Measured
(b)
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Table 5.1 50-year monthly average streamflow distribution table for the Upper Mississippi River at Grafton, IL
Measured The standard deviation of the Illinois measurements for layer 1 (0-10 cm) is 5.46 mm in comparison to 1.93 mm of the model-simulated soil moisture for the layer. The coefficient of variation (standard deviation / mean) of the Illinois observations is 0.19 and those for the model simulations are 0.08. In the case of layer 2, the variation is much higher for layer 2 (10-40 cm) for the Illinois measurements (coefficient of variation = 0.14, standard deviation = 13.7 mm) than those of the model simulations (coefficient of variation = 0.08, standard deviation = 5.7 mm). Conversely, the third layer (40-140 cm) displays lower variation in soil moisture for the observations as compared to the model (coefficient of variation for simulated soil moisture = 0.16 and for observations
= 0.06). For the aggregated layer (Figure 5.4d), the coefficient of variation for the Illinois observation (about 0.14) is in the range of the model simulations (about 0.10). However, it is true that one explanation would not suffice for the two, i.e., both have over- and undervariability. Our only explanation would be that in some way the model physics for the deeper layer (layer 3, 40-140 cm) are much more active than they should be. However, it should be noted that the three-layer aggregate, i.e., 0-140 cm, soil moisture coefficients of variation are reasonably close for observations (0.14) and model simulations (0.10).
The overprediction of streamflow (Figure 5.3) is probably the cause for the underprediction of soil moisture (Figure 5.4). We acknowledge that the present scheme of calibration of the streamflow parameters is not comprehensive, yet, for our purpose of studying the changes in the soil moisture (specifically the
108 Watershed Models
third layer, 40-140 cm) in the spectrum of floods and droughts, it is adequate as demonstrated by the comparisons with the Illinois soil moisture data.
Figure 5.3 (a) Scatterplot of daily streamflow of the Illinois River at Valley City, IL, 1950–1999. (b) Monthly mean streamflow of the Illinois River at Valley City, IL, 1950–
1999.
3.2.3 Surface Temperature Comparisons with TOVS
The model-simulated surface temperatures were compared with TOVS surface temperature data for the basin for a period of 20 years (1980 to 1999) for both the morning and afternoon overpasses of the satellite. The time of observation for each pixel is different depending on the latitude and distance from nadir. The exact time of each observation is included in the data. The
VIC-y = 0.73x + 8383 R2 = 0.62 Bias=2719 cfs RMSD=12941 cfs
0.00E+00 5.00E+04 1.00E+05 1.50E+05 2.00E+05 2.50E+05
0.00E+00 5.00E+04 1.00E+05 1.50E+05 2.00E+05 2.50E+05 Simulated Discharge in cfs
Measured Discharge in cfs
(a)
0.00E+00 1.00E+04 2.00E+04 3.00E+04 4.00E+04 5.00E+04 6.00E+04 7.00E+04 8.00E+04 9.00E+04 1.00E+05
Oct-54 Mar-60 Sep-65 Mar-71 Aug-76 Feb-82 Aug-87 Jan-93 Jul-98 Jan-04 Year
Discharge in cfs
Simulated
Measured (b)
Simulation of Water and Energy Budgets 109
3L model-simulated surface temperatures, for the individual pixels were matched with the exact time of TOVS observations. If the TOVS data were not available, no comparisons were made for that particular record or pixel. Daily surface temperature comparison between the TOVS and VIC-3L simulated results for all the years from 1980-1999 for both morning and afternoon overpasses are given in Table 5.2. The R2 values range from about 0.72 to 0.89 and the average bias is around 1.3 K. The root mean squared difference (RMSD) of about 6.77 K was obtained from the study. The statistics for the 20-year comparison (shown in Table 5.2) indicate a consistent model performance in simulation of land surface temperature. The spatially averaged surface temperatures for the basin are shown in Figure 5.6 a, b for a period of 20 years for the morning (R2 value of 0.87 and a bias of 0.64 K) and the afternoon overpasses (R2 value of 0.86 and a bias of 2.53 K), respectively. The surface temperature patterns averaged over space are more agreeable with the average TOVS observations over the region. The comparison of modeled and observed land surface temperatures for 4 days, March 21, 1999; July 22, 1999; September, 22, 1999; and December 22, 1999 (chosen on/around the spring, summer, autumn, and winter solstices) are shown in Figure 5.7 for a particular 1° pixel (42.5N latitude, 93.5W longitude). The satellite overpass for the particular pixel occurred around 10 am and 10 pm. On an hourly time step, the TOVS surface temperature differs from the model simulations (as seen in Figure 5.7), but on a monthly scale the simulations are closer in value to the observations.
The comparison of TOVS vs. VIC-3L monthly mean surface temperatures shows good spatial agreement for the summer months of the years 1988 and 1993 afternoon overpasses (Figures 5.8 and 5.9 respectively). The north to south temperature gradients, as well as the seasonal warming-cooling cycles, are well displayed for both the years. The months of May and August for the year 1988 afternoon satellite overpass show comparable spatial variations in surface temperature with those of model simulation (Figure 5.8). The range of variation of surface temperature in the TOVS data is higher in a few pixels. This could be a result of inadequate representation of vegetation classes for the particular year, as a static or nonvarying monthly average Leaf Area Index and vegetation cover have been assumed in the VIC-3L model simulation. The months of July and August 1993 (afternoon satellite overpass) show a lower temperature than the corresponding months in 1988, which could be attributed to the higher amount of soil moistures during the midwestern floods (Figure 5.8). Figure 5.8 and 5.9 also depict the difference between the VIC-3L and TOVS surface temperature for the two years 1988 and 1993. The VIC-3L simulated surface temperatures were higher than TOVS observations by around 3-5 K during the flood period of summer 1993. During the droughts of summer 1988 the TOVS surface temperatures are slightly higher than VIC-3L simulations.
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Figure 5.4 Illinois State averaged monthly soil moisture comparison, 1981–1999.
(a)
(b)
(c)
(d)
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Figure 5.5 Scatterplot of Illinois State averaged monthly soil moisture comparison, 1981–
1999.
At individual pixels and at a daily time scale, there are large variations of surface temperatures. They could be attributed to the errors in TOVS surface temperature retrievals and also due to the fact that TOVS retrievals were performed at even 20% cloud free conditions. The TOVS data are not error free and have a low (0-1 K) bias and 4-5 K standard deviation when compared to field observations of surface temperatures collected in field experiments (FIFE, HAPEX, BOREAS) (Lakshmi and Susskind, 2001a). Therefore TOVS provides good datasets to compare spatial averages over grid cells (which is what a model simulates) compared to point observations. In a philosophical discussion of actual comparisons of satellite data with point observations, Lakshmi and Susskind (2001a) have found that there is an almost constant difference in the root mean square sense of 5 K and a zero bias that is independent of the region of study. Therefore, in that light, the results obtained in this study are consistent with those (Lakshmi and Susskind, 2001a) findings.
(a) (b)
Best Fit Line y = 0.21x + 17.50 R2 = 0.35
Bias = 5 mm RMSE=7 mm
Best Fit Line y = 1.68x - 28.10 R2 = 0.49
Bias = 21 mm RMSE=24 mm
(c) (d)
Best Fit Line y = 0.35x + 245.90 R2 = 0.54
Bias = 27 mm RMSE= 47 mm
Best Fit Line y = 0.6259x + 205.74 R2 = 0.62
Bias = 46 mm RMSE= 60 mm
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Figure 5.6 Upper Mississippi River basin averaged surface temperature (a) morning
overpass and (b) afternoon overpass.
y = 0.90x + 27.80 R2 = 0.87 Bias=0.64 K RMSD=4.14 K
220 240 260 280 300 320 340
220 240 260 280 300 320 340
TOVS Surface Temperature (K)
VIC Surface Temperature (K)
(a)
y = 0.95x + 17.28 R2 = 0.86 Bias=2.53 K RMSD=5.6 K
220 240 260 280 300 320 340
220 240 260 280 300 320 340
TOVS Surface Temperature (K)
VIC Surface Temperature (K)
(b)
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Figure 5.7 Hourly surface temperature comparison between VIC and TOVS for 4 days in the year 1999 for a 1° pixel (42.5N latitude, 93.5W longitude).
114 Watershed Models
Figure 5.8 Surface temperature comparison – TOVS vs. VIC Year 1988, afternoon overpass column (a) is TOVS, column (b) is VIC, and column (c) is the difference
between VIC and TOVS.
(a) TOVS (b) VIC (c) Difference January
February
March
April
May
June
July
August
September
October
November
December
Surface Temperature (K)
Surface Temperature Difference VIC – TOVS (K)
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Figure 5.9 Surface temperature comparison – TOVS vs. VIC Year 1993, afternoon overpass column (a) is TOVS, column (b) is VIC, and column (c) is the difference
between VIC and TOVS.
(a) TOVS (b) VIC (c) Difference January
February
March
April
May
June
July
August
September
October
November
December
Surface Temperature (K)
Surface Temperature Difference VIC – TOVS (K)
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Table 5.2 VIC vs. TOVS surface temperature comparison 1981–1999 Year Approximate
Overpass Time am/pm
Best Fit Line R2 Bias (K) Root Mean squared Difference
1981 8 am y = 0.82x + 51.61 0.72 1.01 6.85
1981 8 pm y = 0.90x + 31.39 0.85 4.38 6.45
1982 8 am y = 0.75x + 72.48 0.73 2.29 7.57
1982 8 pm y = 0.86x + 43.89 0.83 4.17 6.91
1983 3 am y = 0.73x + 76.45 0.82 2.12 5.60
1983 3 pm y = 0.84x + 48.56 0.82 4.07 8.14
1984 3 am y = 0.73x + 75.56 0.79 1.22 5.47
1984 3 pm y = 0.87x + 38.65 0.78 2.98 7.69
1985 8 am y = 0.75x + 71.79 0.83 1.86 5.54
1985 8 pm y = 0.84x + 50.77 0.78 4.62 8.92
1986 3 am y = 0.79x + 59.67 0.81 0.54 4.94
1986 3 pm y = 0.86x + 44.04 0.74 4.39 8.96
1987 8 am y = 0.85x + 42.00 0.77 0.08 6.04
1987 8 pm y = 0.92x + 27.28 0.87 3.83 5.92
1988 8 am y = 0.79x + 59.85 0.82 0.14 6.46
1988 8 pm y = 0.89x + 31.81 0.88 3.45 6.11
1989 8 am y = 0.83x + 48.66 0.78 0.29 6.56
1989 8 pm y = 0.92x + 24.29 0.86 3.21 6.14
1990 8 am y = 0.85x + 41.68 0.75 0.09 6.22
1990 7 pm y = 0.89x + 35.76 0.81 3.33 6.12
1991 3 am y = 0.79x + 60.06 0.82 1.45 5.05
1991 3 pm y = 0.83x + 53.02 0.74 3.36 8.86
1992 3 am y = 0.74x + 73.52 0.77 1.85 5.12
1992 2 pm y = 0.75x + 73.29 0.68 2.93 8.76
1993 3 am y = 0.76x + 67.97 0.80 1.83 5.40
1993 2 pm y = 0.84x + 47.57 0.69 2.42 8.30
1994 8 am y = 0.74x + 72.54 0.75 1.16 6.96
1994 8 pm y = 0.88x + 37.09 0.83 3.13 6.26
1995 8 am y = 0.84x + 46.75 0.78 1.00 6.29
1995 8 pm y = 0.89x + 34.44 0.84 2.62 6.09
1996 8 am y = 0.72x + 78.46 0.75 1.33 7.17
1996 8 pm y = 0.80x + 59.50 0.80 2.42 6.92
1997 8 am y = 0.73x + 75.54 0.76 0.83 6.28
1997 8 pm y = 0.83x + 50.58 0.80 2.11 6.55
1998 8 am y = 0.81x + 58.24 0.82 0.79 5.69
1998 8 pm y = 0.83x + 60.23 0.79 3.16 7.89
1999 3 am y = 0.81x + 53.82 0.82 0.49 4.40
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4. MODEL CHARACTERIZATION OF EXTREME EVENTS –