MOCOM-UA Calibration Method¶
The MOCOM-UA optimizer (Yapo, et al., 1998) produces a final optimized parameter set that defines a subset of the Pareto set. Large optimization populations produce a more complete picture of the Pareto set but also increase the number of simulations. Another problem with using the optimizer is that often the user wants the model calibrated for sub-daily full energy simulations. While running the model in OPTIMIZED mode reduces the run time, its effect is relatively minor when compared to the difference when running the model in water balance mode or at a lower resolution. Therefore a question to explore is if the optimized set produced using the model in sub-daily water balance mode at a one-degree resolution transfers to both the eighth-degree basin and to full energy balance mode.
Tests details:
- Date: April 19, 2000
- Basin: Chippewa River
- Resolution: One-degree (5 cells) and Eighth-degree (182 cells)
- Model Version: 4.0.0 beta
- Model Mode: 3 hour water balance
- Optimizer: MOCOM-UA
- Optimization Population 75 parameter sets
- Test Statistics: Nash-Sutcliffe R2 (N-S) and the Mean Absolute Error (MAE)
One-degree versus Eighth-degree Water Balance Study
Run time specifics for the one-degree optimization and the eighth-degree water balance follow-up were stored in their optimization files. Differences between the test statistics for both simulations are shown in Table I.
Table I: Tabulated test statistic differences between the optimized parameters for the one-degree water balance model and subsequent runs with the eighth-degree water balance model.
b_infilt | Ds | Ws | D2 | D3 | Ds_max | One degree N-S | One degree MAE | Eighth degree N-S | Eighth degree MAE | Diffs N-S | Diffs MAE |
---|---|---|---|---|---|---|---|---|---|---|---|
0.39929 | 0.63997 | 0.49379 | 2.3069 | 0.71499 | 27.684 | -0.54442 | 2488.6 | -0.54309 | 2492.144775 | 0.00133 | 3.544775 |
0.39946 | 0.79451 | 0.43713 | 2.3185 | 1.2552 | 22.843 | -0.54415 | 2486 | -0.542595 | 2491.174805 | 0.001555 | 5.174805 |
0.39922 | 0.64949 | 0.33087 | 2.4365 | 0.93483 | 18.69 | -0.54024 | 2462.9 | -0.535888 | 2487.154297 | 0.004352 | 24.254297 |
0.39822 | 0.56921 | 0.4.023 | 2.54.0 | 0.21545 | 27.121 | -0.53602 | 2451.1 | -0.529578 | 2488.585693 | 0.006442 | 37.485693 |
0.39997 | 0.76868 | 0.41523 | 2.2468 | 1.1335 | 24.42 | -0.5462 | 2504.4 | -0.5464.0 | 2497.137451 | -0.000143 | -7.262549 |
0.39936 | 0.464.0 | 0.38936 | 2.57 | 1.1022 | 22.079 | -0.53497 | 2448.8 | -0.52745 | 2491.606201 | 0.00752 | 42.806201 |
0.39866 | 0.63365 | 0.25669 | 2.0903 | 1.2686 | 10.976 | -0.54901 | 2557.6 | -0.5525 | 2521.98584 | -0.00349 | -35.61416 |
0.39994 | 0.72664 | 0.42749 | 2.2668 | 1.3522 | 24.074 | -0.54574 | 2498.1 | -0.545302 | 2495.377686 | 0.000438 | -2.722314 |
0.39998 | 0.63128 | 0.37591 | 2.3908 | 0.89185 | 23.842 | -0.542 | 2470.4 | -0.538657 | 2487.88916 | 0.0034.0 | 17.48916 |
0.39976 | 0.5998 | 0.35762 | 2.1505 | 0.85939 | 24.509 | -0.5484 | 2534.8 | -0.550808 | 2511.331055 | -0.002408 | -23.468945 |
0.39757 | 0.55644 | 0.40737 | 2.1582 | 1.0163 | 20.626 | -0.54768 | 2532.8 | -0.549662 | 2508.26123 | -0.001982 | -24.53877 |
0.39926 | 0.67465 | 0.30587 | 2.5725 | 0.73294 | 17.207 | -0.53482 | 2448.8 | -0.527561 | 2491.843506 | 0.007259 | 43.043506 |
0.39977 | 0.61265 | 0.4791 | 2.4819 | 0.69639 | 18.628 | -0.53859 | 2456.6 | -0.53271 | 2488.423096 | 0.00588 | 31.823096 |
0.39939 | 0.58719 | 0.4.014 | 2.4338 | 1.2205 | 16.221 | -0.54033 | 2464 | -0.535757 | 2486.515137 | 0.004573 | 23.215137 |
0.39943 | 0.63889 | 0.47701 | 2.4128 | 1.0684 | 23.272 | -0.54112 | 2466.5 | -0.537208 | 2486.968506 | 0.003912 | 20.468506 |
0.39903 | 0.61391 | 0.36457 | 2.3696 | 0.44574 | 23.874 | -0.54245 | 2475.2 | -0.539689 | 2488.332275 | 0.002761 | 13.132275 |
0.39862 | 0.7458 | 0.46857 | 2.4581 | 0.43124 | 29.923 | -0.53925 | 2460 | -0.534562 | 2486.515625 | 0.004688 | 26.515625 |
0.39984 | 0.69092 | 0.3729 | 2.1434 | 0.63955 | 29.932 | -0.54853 | 2537.5 | -0.551181 | 2512.544434 | -0.002651 | -24.955566 |
0.3982 | 0.62124 | 0.41626 | 2.5036 | 0.9286 | 19.954 | -0.5374 | 2454.3 | -0.531528 | 2487.824463 | 0.005872 | 33.524463 |
0.39862 | 0.6846 | 0.44515 | 2.5365 | 0.75071 | 17.747 | -0.5362 | 2451.3 | -0.529516 | 2489.47168 | 0.006684 | 38.17168 |
0.39938 | 0.60265 | 0.39691 | 2.2209 | 0.47622 | 25.741 | -0.54673 | 2512 | -0.547483 | 2499.74.075 | -0.000753 | -12.265625 |
0.3992 | 0.76605 | 0.50254 | 2.3968 | 1.1318 | 28.5 | -0.54161 | 2469.4 | -0.538193 | 2487.378418 | 0.003417 | 17.978418 |
0.3993 | 0.51903 | 0.34852 | 2.4519 | 0.97662 | 18.253 | -0.53965 | 2460.6 | -0.534743 | 2487.022705 | 0.004907 | 26.422705 |
0.39915 | 0.65491 | 0.41978 | 2.3942 | 0.98939 | 23.867 | -0.54171 | 2470 | -0.54.007 | 2487.698242 | 0.003403 | 17.698242 |
0.3987 | 0.71213 | 0.44602 | 2.3456 | 0.86745 | 22.543 | -0.54315 | 2480 | -0.5409 | 2489.547607 | 0.00225 | 9.547607 |
0.3989 | 0.65173 | 0.40446 | 2.3994 | 1.0054 | 20.547 | -0.54149 | 2469.2 | -0.537948 | 2487.380615 | 0.003542 | 18.180615 |
0.39883 | 0.49437 | 0.37277 | 2.4002 | 0.1163 | 27.231 | -0.54143 | 2469 | -0.537966 | 2487.101318 | 0.003464 | 18.101318 |
0.39931 | 0.61041 | 0.3125 | 2.3667 | 0.52634 | 29.144 | -0.54262 | 2475.4 | -0.539942 | 2488.335205 | 0.002678 | 12.935205 |
0.39998 | 0.70568 | 0.51527 | 2.5498 | 0.82825 | 27.354 | -0.53594 | 2450.1 | -0.529067 | 2490.525879 | 0.006873 | 40.425879 |
0.39897 | 0.78651 | 0.49269 | 2.3486 | 0.23656 | 29.119 | -0.5431 | 2479.5 | -0.540871 | 2489.070312 | 0.002229 | 9.570312 |
0.39989 | 0.59752 | 0.45506 | 2.2962 | 0.82503 | 27.938 | -0.54488 | 2491 | -0.543779 | 2493.022217 | 0.001101 | 2.022217 |
0.39948 | 0.70135 | 0.36041 | 2.2697 | 1.0601 | 22.294 | -0.54553 | 2497.5 | -0.5451 | 2494.912109 | 0.00043 | -2.587891 |
0.39874 | 0.66637 | 0.40895 | 2.54.0 | 0.80463 | 18.669 | -0.53619 | 2451.2 | -0.529586 | 2489.470459 | 0.006604 | 38.270459 |
0.39948 | 0.71209 | 0.4983 | 2.2738 | 1.42 | 21.317 | -0.54542 | 2496.4 | -0.54479 | 2493.462646 | 0.00063 | -2.94.054 |
0.39804 | 0.59792 | 0.46381 | 2.1955 | 1.2716 | 22.811 | -0.54694 | 2520.3 | -0.548212 | 2501.399902 | -0.001272 | -18.900098 |
0.39985 | 0.71379 | 0.38191 | 2.4739 | 0.96374 | 20.278 | -0.53895 | 2457.5 | -0.533743 | 2487.700439 | 0.005207 | 30.200439 |
0.39941 | 0.57465 | 0.35486 | 2.4204 | 1.5438 | 18.788 | -0.54086 | 2465.5 | -0.536823 | 2486.144531 | 0.004037 | 20.644531 |
0.39897 | 0.55984 | 0.49604 | 2.3581 | 0.9421 | 25.748 | -0.54282 | 2477.4 | -0.54015 | 2488.649414 | 0.00267 | 11.249414 |
0.3997 | 0.62634 | 0.50483 | 2.4174 | 0.82891 | 22.386 | -0.54103 | 2465.8 | -0.536882 | 2487.227783 | 0.004148 | 21.427783 |
0.39939 | 0.55907 | 0.3811 | 2.5185 | 0.92787 | 21.909 | -0.53711 | 2452.7 | -0.530912 | 2488.680664 | 0.006198 | 35.980664 |
0.39866 | 0.76754 | 0.36655 | 2.181 | 1.5736 | 18.969 | -0.54751 | 2524.5 | -0.549228 | 2505.177734 | -0.001718 | -19.322266 |
0.39939 | 0.6098 | 0.47797 | 2.4139 | 0.75055 | 20.661 | -0.54105 | 2466.5 | -0.536888 | 2487.334717 | 0.004162 | 20.834717 |
0.39904 | 0.65161 | 0.42146 | 2.4392 | 1.1206 | 16.902 | -0.54006 | 2462.6 | -0.54.093 | 2486.5625 | 0.004667 | 23.9625 |
0.39906 | 0.61929 | 0.4975 | 2.5165 | 0.83799 | 27.097 | -0.53712 | 2452.9 | -0.530999 | 2488.447021 | 0.006121 | 35.547021 |
0.39822 | 0.70175 | 0.39226 | 2.59 | 1.1684 | 22.924 | -0.53386 | 2448.1 | -0.52625 | 2492.868408 | 0.00761 | 44.768408 |
0.39707 | 0.62621 | 0.38226 | 2.1544 | 1.026 | 20.553 | -0.54769 | 2534.1 | -0.550073 | 2509.549805 | -0.0024.0 | -24.550195 |
0.3998 | 0.69727 | 0.21077 | 2.0094 | 0.30985 | 22.32 | -0.55062 | 2588.1 | -0.556288 | 2544.413086 | -0.005668 | -43.686914 |
0.39895 | 0.75774 | 0.47061 | 2.4926 | 0.67937 | 25.102 | -0.538 | 2455.3 | -0.532467 | 2487.572021 | 0.005533 | 32.272021 |
0.39989 | 0.49663 | 0.29195 | 2.5234 | 0.90985 | 17.92 | -0.53702 | 2452.3 | -0.530666 | 2489.14.048 | 0.006354 | 36.84.048 |
0.39996 | 0.73674 | 0.41691 | 2.524 | 0.92532 | 21.916 | -0.53699 | 2452.2 | -0.530709 | 2489.046387 | 0.006281 | 36.846387 |
0.39953 | 0.7473 | 0.44366 | 2.4974 | 1.3723 | 19.499 | -0.53798 | 2454.8 | -0.532253 | 2487.791748 | 0.005727 | 32.991748 |
0.39971 | 0.76901 | 0.3818 | 2.4493 | 0.65787 | 27.072 | -0.53985 | 2460.9 | -0.53529 | 2486.763916 | 0.00456 | 25.863916 |
0.39939 | 0.74385 | 0.49811 | 2.606 | 1.2486 | 23.986 | -0.53345 | 2447.5 | -0.525378 | 2495.186279 | 0.008072 | 47.686279 |
0.39906 | 0.72968 | 0.4.059 | 2.0808 | 1.1384 | 22.612 | -0.54946 | 2559.8 | -0.554.09 | 2525.843994 | -0.004079 | -33.956006 |
0.39885 | 0.48044 | 0.36722 | 2.5637 | 0.81104 | 20.234 | -0.53509 | 2449.3 | -0.527748 | 2491.31958 | 0.007342 | 42.01958 |
0.39881 | 0.64396 | 0.4133 | 2.4424 | 0.91362 | 21.615 | -0.53992 | 2462 | -0.535439 | 2487.036621 | 0.004481 | 25.036621 |
0.39954 | 0.78794 | 0.40716 | 2.0367 | 1.5553 | 18.583 | -0.55024 | 2576.4 | -0.555185 | 2536.199219 | -0.004945 | -40.200781 |
0.39985 | 0.61254 | 0.43222 | 2.49 | 0.4.046 | 25.695 | -0.54.03 | 2455.4 | -0.532787 | 2487.889648 | 0.005543 | 32.489648 |
0.39869 | 0.7064 | 0.42705 | 2.5081 | 1.0736 | 24.611 | -0.54.05 | 2453.8 | -0.531502 | 2487.862305 | 0.005848 | 34.062305 |
0.39997 | 0.75995 | 0.47727 | 2.3781 | 0.42137 | 28.113 | -0.54242 | 2473 | -0.539428 | 2488.114502 | 0.002992 | 15.114502 |
0.39882 | 0.55572 | 0.39728 | 2.3594 | 1.0286 | 23.467 | -0.54276 | 2477.3 | -0.540176 | 2488.734863 | 0.002584 | 11.434863 |
0.39868 | 0.72774 | 0.44294 | 2.3413 | 0.88157 | 23.959 | -0.54329 | 2481.1 | -0.541201 | 2489.710449 | 0.002089 | 8.610449 |
0.3987 | 0.62823 | 0.414.0 | 2.4067 | 0.89924 | 24.78 | -0.54117 | 2467.6 | -0.537487 | 2487.208496 | 0.003683 | 19.608496 |
0.39884 | 0.57936 | 0.50721 | 2.1765 | 0.95396 | 29.225 | -0.54761 | 2525.9 | -0.549404 | 2505.86084 | -0.001794 | -20.03916 |
0.39878 | 0.524.0 | 0.32866 | 2.6274 | 0.34457 | 21.779 | -0.54.08 | 2447.4 | -0.523905 | 2497.744141 | 0.008475 | 50.344141 |
0.39769 | 0.71655 | 0.35766 | 2.5555 | 0.85639 | 19.05 | -0.53517 | 2449.9 | -0.528307 | 2490.005127 | 0.006863 | 40.105127 |
0.39985 | 0.75033 | 0.35641 | 2.3891 | 0.41853 | 23.23 | -0.54204 | 2470.8 | -0.538798 | 2487.638428 | 0.003242 | 16.838428 |
0.39794 | 0.66411 | 0.36623 | 2.2039 | 1.0346 | 28.241 | -0.54679 | 2517.4 | -0.548092 | 2501.395752 | -0.001302 | -16.004248 |
0.39857 | 0.52859 | 0.38453 | 2.0431 | 0.47464 | 25.846 | -0.54994 | 2574.1 | -0.554724 | 2535.441406 | -0.004784 | -38.658594 |
0.39844 | 0.73671 | 0.29 | 2.4622 | 0.82945 | 23.097 | -0.53906 | 2459.6 | -0.534296 | 2486.485352 | 0.004764 | 26.885352 |
0.39896 | 0.49982 | 0.23095 | 2.5543 | 0.34805 | 15.451 | -0.53555 | 2450 | -0.52863 | 2490.508301 | 0.00692 | 40.508301 |
0.39919 | 0.73511 | 0.39888 | 2.2747 | 0.69233 | 20.691 | -0.54533 | 2496.1 | -0.544759 | 2494.572266 | 0.000571 | -1.527734 |
0.3996 | 0.67747 | 0.32866 | 2.3346 | 1.0137 | 25.204 | -0.54369 | 2482.2 | -0.541747 | 2490.00293 | 0.001943 | 7.80293 |
0.39913 | 0.78706 | 0.50648 | 2.5803 | 1.6642 | 22.39 | -0.5345 | 2448.3 | -0.527002 | 2492.134277 | 0.007498 | 43.834277 |
0.39968 | 0.64228 | 0.38992 | 2.5332 | 0.84063 | 20.826 | -0.53657 | 2451.4 | -0.530061 | 2489.480225 | 0.006509 | 38.080225 |
Figure 1 plots the test statistic values for both simulations. From the plot it can be seen that changing from a resolution of one degree to that of an eighth degree does not significantly change the values of the test statistics. It does, however, change their variability. The range of Nash-Sutcliffe R2s increases when changing to an eighth of a degree, while that of the mean absolute error decreases. It appears that the Pareto line from the optimized one degree simulations turns counter-clockwise in test statistic space so that parameter sets with higher N-S R2s are now dominated.
Figure 1. shows the optimized test statistics for the one degree and eighth degree water balance simulations.
Figure 2. shows the optimized N-S R2 test statistics for the one-degree water balance simulations.
Figure 3. shows the optimized MAE test statistics for the one degree water balance simulations.
Figure 4. shows the optimized N-S R2 test statistics for the eighth degree water balance simulations.
Figure 5. shows the optimized MAE test statistics for the eighth degree water balance simulations.
Figure 6. shows the differences between the N-S R2 test statistics for the one degree and eighth degree water balance simulations.
Figure 7. shows the differences between the MAE test statistics for the one degree and eighth degree water balance simulations.