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.