H14A-01
Time Varying Parameterization of Hydrological Models
Hydrological models are frequently used for forecasting, water management or design to provide information for decision making. Due to the simplification of the complex natural processes and the limited availability of observations the parameters of these models cannot be identified perfectly. Usually the parameters of the models are assumed to be time independent. However some properties of the catchments might change in from one event to another in an unpredictable manner. The purpose of this paper is to develop a methodology to estimate selected model parameters as random variables changing in time. The distribution of the model parameter is assessed in calibration phase using different assumptions. During the application of the model these distributions are used to estimate the expected hydrological behavior and the uncertainty too. The methodology will be demonstrated on mezo-scale catchments in the Neckar basin in South-West Germany. The systematic differences between model behavior and observations are demonstrated using a set of selected events. Calibration and uncertainty estimation are demonstrated by an example application to a distributed HBV model. The model residual distributions are presented and compared to a standard calibration method. Further, it is shown that the new methodology leads to more realistic confidence intervals for model simulations.
H14A-02
Incorporating Search History into the Dynamically Dimensioned Search (DDS) Optimization Algorithm
The Dynamically Dimensioned Search (DDS) algorithm (Tolson and Shoemaker, 2007) was recently introduced as a parsimonious, efficient and robust optimization algorithm for automatic calibration of environmental models. DDS was designed to find practical or high quality solutions to a model calibration problem within a reasonable computational timeframe rather than the globally optimal solution. The simple structure of the original DDS algorithm only stores and utilizes the best current solution to guide the search. Population-based global optimization algorithms maintain a population of typically good quality solutions to influence the search. In this research, we examine how to utilize the search history of DDS to improve algorithm performance while maintaining the parsimonious and algorithmically simple nature of the original DDS algorithm. The modification to the original DDS algorithm involves storing a subset of relatively high quality solutions previously identified in the search and selecting one solution from which to make the next perturbation in order to sample a new candidate solution. Both the function value and their proximity to one another in multi-dimensional parameter space influences the likelihood of selecting a particular solution to perturb. This approach is motivated by initial results showing that for the same total computational budget, DDS with multiple restarts can sometimes be more effective than one longer DDS optimization trial. The history-based revisions discussed above allow the algorithm to search more of the parameter subspace, thus exploiting the strength of the less- refined restart approach, but with a higher likelihood of success. Results will be presented for a relatively simple problem as well as a more complex, high-dimensional automatic calibration problem. Results will also be assessed for various computational budgets.
H14A-03
Global Optimization With a Limited Budget of Function Evaluations
Selection of a computationally efficient and robust optimization algorithm has always been a key consideration for calibration of watershed simulation models. This goal was the primary reason for the development of the Shuffled Complex Evolution (SCE-UA) algorithm by Duan et al. in the early 1990s. The widely used SCE-UA algorithm was developed with the aim of finding global optimal solutions within the feasible parameter domain. Recently, Tolson and Shoemaker introduced a stochastic neighborhood search algorithm, entitled Dynamically Dimensioned Search (DDS) capable of finding good parameter combinations fast. In their work, it was determined that DDS is a more computationally efficient and robust optimization algorithm than SCE-UA in the context of distributed watershed model automatic calibration. In this talk, we will demonstrate that it is possible to significantly increase the convergence rate of SCE-UA by simple modification of the values of the algorithmic parameters. It is shown that a much faster initial decay of the objective function can be achieved when the reflection and contraction step lengths in the Simplex method are changed from their default values. Our studies clearly show that the modified SCE-UA is the preferred method of choice to find high quality parameter solutions with a limited budget of function evaluations.
H14A-04
Estimation of Land Surface Water and Energy Balance Closure Relation Using Conditional Sampling
Numerical models of heat and moisture diffusion in the soil-vegetation- atmosphere continuum are linked through a closure relationship that characterizes soil moisture limits on moisture flow (e.g., root-extraction limitations, relative evaporation efficiency or beta functions, soil relative humidity or alpha functions, etc.). The performance of various models of water and energy is highly dependent on the nature of these closure relationships, but as important as they are, they remain largely invalidated especially across diverse soil and vegetation conditions. In this presentation a new approach for estimating the functional form for the water and energy closure relationship is proposed. The approach is scalable to diverse climates and land surface conditions using remotely sensed measurements. Parameters of the system (water balance and Energy balance) are estimated by developing objective functions that link atmospheric forcing, surface state and unknown parameters. This approach is based on conditional averaging of heat and moisture balance equations. Conditioning states are land surface temperature and moisture states which will ultimately be obtained from global remote sensing measurements. Based on conditional averaging, a single objective function is expressed that measures the moisture and temperature dependent errors solely in terms of observed forcings (e.g. precipitation, radiation) and surface states (moisture and temperature). This objective function can be minimized with respect to parameters to identify evaporation and drainage models and estimate water and energy balance.
H14A-05
Speed-up of Markov Chain Monte Carlo Simulation Using Self-Adaptive Different Evolution with Subspace Sampling
Markov chain Monte Carlo (MCMC) methods are widely used in fields ranging from physics and chemistry, to finance, economics and statistical inference for estimating the average properties of complex systems. The convergence rate of MCMC schemes is often observed, however to be disturbingly low, limiting its practical use in many applications. This is frequently caused by an inappropriate selection of the proposal distribution used to generate trial moves. Here we show that significant improvements to the efficiency of MCMC algorithms can be made by using a self-adaptive Differential Evolution search strategy within a population-based evolutionary framework. This scheme differs fundamentally from existing MCMC algorithms, in that trial jumps are simply a fixed multiple of the difference of randomly chosen members of the population using various genetic operators that are adaptively updated during the search. In addition, the algorithm includes randomized subspace sampling to further improve convergence and acceptance rate. Detailed balance and ergodicity of the algorithm are proved, and hydrologic examples show that the proposed method significantly enhances the efficiency and applicability of MCMC simulations to complex, multi-modal search problems.
H14A-06
Parameter Estimation for a Physically-Based Model Using Multi-Objective Approach Constrained With Additional Internal States
Parameter estimation (i.e. model calibration) is a critical procedure for not only determining a successful model application, but also assessing model uncertainties, thus helping improve model development. Physically-based distributed hydrological models are increasingly used as required in water management because of the complexity of the processes to be represented. Given the fact that the distributed catchment characteristics, represented by parameters, could not be directly measured in most cases, model calibration is therefore inevitable. Calibration and uncertainty assessment for such complex models are more challenging than for those simpler ones due to the large number of parameters associated with integrated multiple processes description and large computing resources demands. There is ample literature on the approaches to model parameter estimation and applications of such approaches. Multi-objective Pareto-optimality approaches, such as MOSCEM-UA, are amongst the state-the-art approaches in modeling practices. The multi-objective optimization approaches, however, have not yet widely applied to physically-based distributed models, due to the aforementioned challenging issues. This work presents an application of MOSCEM-UA algorithm to a newly developed physically-based model REWASH. REWASH is a model based on the Representative Elementary Watershed (REW) concept that describes hydrological processes at the watershed scale, using the basic physical conservation laws. The elementary watersheds, i.e. the sub-watersheds are the hydrological response units of a catchment when using REWASH model. In this study, REWASH model was applied to simulate rainfall-runoff relation for the Hesperange catchment in Luxembourg. Due to its physically-based and semi-distributed nature, the applied hydrological model reproduces not only stream flows at the catchment outlet and the sub-watersheds' outlets, but subsurface flows and groundwater table variations as well. Therefore, in addition to the use of stream flow measurements for model calibration and uncertainty analysis, groundwater table gauging data were also used to help constrain parameter space. In model parameter identification, objective functions in favor of both high flows and low flows were employed to optimize the model performance. Results of this study show that parameters for subsurface processes are better identifiable than those for surface processes. This work also demonstrates that MOSCEM-UA is an efficient tool in parameter identification giving more insight to the structural behavior of the model.
H14A-07
Use of KNN technique to improve the efficiency of SCE-UA optimisation method applied to the calibration of HBV Rainfall-Runoff model
The Calibration of Rainfall-Runoff models can be viewed as an optimisation problem involving an objective function that measures the model performance expressed as a distance between observed and calculated discharges. Effectiveness (ability to find the optimum) and efficiency (cost expressed in number of objective function evaluations to reach the optimum) are the main criteria of choose of the optimisation method. SCE-UA is known as one of the most effective and efficient optimisation method. In this work we tried to improve the SCE-UA efficiency, in the case of the calibration of HBV model by using KNN technique to estimate the objective function. In fact after a number of iterations by SCE-UA, when objective function is evaluated by model simulation, a data base of parameter explored and respective objective function values is constituted. Within this data base it is proposed to estimate the objective function in further iterations, by an interpolation using nearest neighbours in a normalised parameter space with weighted Euclidean distance. Weights are chosen proportional to the sensitivity of parameter to objective function that gives more importance to sensitive parameter. Evaluation of model output is done through the objective function RV=R2- w |RD| where R2 is Nash Sutcliffe coefficient related to discharges, w : a weight and RD the relative bias. Applied to theoretical and practical cases in several catchments under different climatic conditions : Rottweil (Germany) and Tessa, Barbra, and Sejnane (Tunisia), the hybrid SCE-UA presents efficiency better then that of initial SCE-UA by about 20 to 30 %. By using other techniques as parameter space transformation and SCE-UA modification (2), we may obtain an algorithm two to three times faster. (1) Avi Ostfeld, Shani Salomons, "A hybrid genetic-instance learning algorithm for CE*QAL-W2 calibration", Journal of Hydrology 310 (2005) 122-125 (2) Nitin Mutil and Shie-Yui Liong, "Improved robustness and Efficiency of the SCE-UA model calibrating algorithm"
H14A-08
Hierarchical Data Assimilation for Multiple Source Uncertainty Estimation
Even the most intensive of today data-acquisition platforms cannot provide sufficient access to the spatial heterogeneity of geophysical system or the biological states of the environment and often are a source of conflicting information. Hydrologic models are laden, therefore, with a profusion of unobserved state variables. Reconciling model with observed behavior (inverse modeling) in order to improve understanding is quintessentially an issue of demonstrating, beyond reasonable doubt, that matching of the two approximations of the truth has not been achieved at the expense of imposing absurd values to the model parameters. We use a hierarchical data assimilation approach to provide a convenient mechanism for explicitly accounting for uncertainty by specifying manageable joint distributions that can be formulated by three separate components: Data Model, Process Model, and Parameter Model. In this way a quite complex joint statistical model can be specified in terms of a sequence of conditional models. For example, distinctly different data models can be specified so that they are conditioned on the same underlying process, and this underlying process can then be, in turn, specified so that it is conditioned on a set of model parameters. The hierarchical models also have the ability for explicit accounting of uncertainty in multiple components of the model. The specification of mechanistic models in the process component of a hierarchical framework explicitly assumes the model is wrong, but can account for this source of uncertainty by allowing for a quantifiable process model error term; at the same time, the framework allows the parameters pertaining to the distributional forms of the data models and process models to be random and directly accounts for their inherent uncertainty. The framework also allows for the incorporation of multiple data types within the same model (useful for simultaneous use of observations of natural processes in several distinct ways simultaneously). In the present work we present an application of this hierarchical framework to the SAC-SMA model as a step towards application in distributed modeling. Some of the significant computational challenges involved are also discussed.