Many physically-based hydrological models such as Noah Land Surface Model (Noah LSM), Soil Water Atmosphere Plant (SWAP), and Community Land Model (CLM) have been used widely in estimating soil moisture dynamics. These models incorporated with their own inherent model structures and parameterization approaches influence root zone soil moisture estimates and result in uncertainties under the given model conditions. Without identifying uncertainties due to different model parameterizations and structures, the robustness of model outputs from various hydrological models may be elusive. In this study, we explored a multiple model simulation approach for estimating effective soil moisture dynamics and reducing the uncertainties due to inaccurate model parameters and structural drawbacks. The objectives of this research were to develop a Bayesian model averaging (BMA) based multi-model simulation approach integrated with a genetic algorithm (GA) and evaluate different model parameter and structural uncertainties under various hydro-climate conditions.
2.1 MULTI-MODEL SIMULATION APPROACH
In this study, we developed a multi-model simulation approach adapting three different land surface models based on a Bayesian model averaging (BMA) scheme. The BMA scheme is a statistical scheme that infers a probabilistic prediction for possessing more skill and reliability for different models selected. This approach was integrated with an optimization scheme (genetic algorithm-GA) for searching optimized parameters of each hydrological model [Ines and Mohanty, 2008]. GAs are based on the principle of natural fittest mechanism in searching for optimal solutions in the search space. The multi-model simulation approach adapted the Noah LSM, SWAP, and CLM models for simulating the root zone soil moisture dynamics including their inherent weakness due to different model structures. In turn, this approach aggregated the simulated root zone soil moisture from these three models and estimated the effective (averaged) soil moisture by conditioning the individual output. Then, the uncertainties due to different model parameterizations and structures were evaluated under various hydro-climate conditions.
2.2 MODEL UNCERTAINTY EVALUATION
A large number of model input parameters are required for the model performance. Several major input parameters related to soil moisture dynamics for each model were selected based on the model parameter sensitivity literature. The input parameters for the three hydrological models were derived by the GA. For uncertainty analysis, the GA used the multiple-population with different random seed numbers. The root zone soil moisture dynamics based on the derived parameters were simulated in a forward mode. Then, the uncertainty boundary of root zone soil moisture estimates for each model was assessed. Here, we applied the BMA scheme to the multi-model approach integrated with the GA, because predictive uncertainties due to different model structures can be described based on the BMA scheme. The BMA scheme adapted a differential evolution adaptive metropolis Markov chain monte carlo algorithm that can search a global optimal solution through running the multiple chains simultaneously [Vrugt et al., 2008]. The Noah LSM and CLM models can predict the root zone soil moisture estimates during the rainy period well, while the SWAP model performs better during the relatively dry season. It may be inferred that these uncertainties are due to different model structures. In order to avoid this bias, we categorized root zone soil moisture measurements based on the land surface wetness conditions (e.g. wet and dry conditions) using a K-mean clustering algorithm. Then, our approach assigned different weights to the individual simulated soil moisture data of each model corresponding to the categorized soil moisture conditions and estimated the effective (averaged based on different weights) soil moisture dynamics for reducing uncertainties.
2.3 STUDY AREAS
In this study, the Little Washita (LW13), Oklahoma and Walnut Gulch (WG82), Arizona sites were selected for testing our approach under sub-humid and semi-arid climate conditions, respectively. We validated our methodology with in-situ root zone soil moisture measurements during the Southern Great Plains experiment 1997 (DOY: 170 197) for the LW13 site and Soil Moisture Experiment 2004 (DOY: 216 238) for the WG82 site.
We compared the estimated root zone soil moisture dynamics (derived by the GA only) for each model to the observations for the two sites. The predicted root zone soil moisture estimates matched well with the in-situ measurements (R2 : 0.75 ~ 0.83 and RMSE : 0.045 ~ 0.055 for LW13 site; R2 : 0.81 ~ 0.85 and RMSE : 0.015 ~ 0.016 for WG82 site). However, the soil moisture estimates for each model showed different trends during the simulation period. It was inferred that the difference between the simulation results was caused by different model structures. Figure 1 shows the effective soil moisture dynamics (representing that uncertainties were compensated) derived by the BMA-based multi-model simulation approach. The result indicated that the effective soil moisture estimates identified better with the observations (R2 : 0.873, RMSE : 0.033 for the LW13 site and R2 : 0.861, RMSE : 0.014 for the WG82 site) with reduced uncertainties as compared to the results derived by the GA only.
In this study, a multi-model simulation approach was developed for estimating the effective root zone soil moisture and reducing the model parameter and structural uncertainties under various hydro-climate conditions. The root zone soil moisture dynamics derived by the GA only matched well with the observation, although the simulated results for three hydrological models had slightly different trends. When the soil moisture estimates were conditioned by the BMA-based multi-model simulation approach, the effective soil moisture estimates were more identifiable with the observations. Based on these findings, we demonstrated that our proposed methodology can be useful for improving the predicted root zone soil moisture estimates by accounting for the characteristic weakness in the model structure of various hydrological models.
Ines, A.V.M. and B.P. Mohanty (2008), Near-surface soil moisture assimilation for quantifying effective soil hydraulic properties using genetic algorithm: I. Conceptual modeling. Water Resources Res., 44, W06422, doi:10.1029/2007WR005990.
Vrugt JA, ter Braak CJF, Clark MP, Hyman JM, Robinson BA (2008), Treatment of input uncertainty in hydrologic modeling: doing hydrology backwards with Markov Chain Monte Carlo simulation. Water Resour. Res., doi:10.1029/2007WR006720.