Predictions in Ungauged Basins using Distributed Hydrologic Models: Regionalization of Parameters and Quantification of Predictive Uncertainty
The major focus of studies pertaining to Predictions in Ungauged Basins is to develop appropriate tools for generating hydrologic response of the basin in the absence of hydrologic data. Even though physics based distributed hydrologic models are considered to be best suited for the ungauged basins, they are quite data intensive. Hence, uncertainty in model simulations may be very high in the absence of accurate parameter estimations. A successful application of these models in making hydrologic response in ungauged basins requires accurate estimation of parameters to minimize output uncertainty. Regionalization of model parameters by developing appropriate functional relationship between the parameters and basin characteristics is one of the potential approaches to employ watershed simulation models in ungauged basins. However, there are lots of concerns in applying regionalization methods. Many of the current model structures are incapable of simulating the behavior of a basin with a single parameter set simultaneously in all ranges of flow. The current study proposes a method to derive probability distribution of sensitive parameters of the model and to generate an ensemble of predictions with minimum uncertainty in prediction in all ranges of flow. The methodology employs Monte Carlo simulation of the hydrologic model using samples of parameter sets generated by 'Latin Hypercube Sampling'. Subsequently, the sensitivity of the model parameters is computed using a global sensitivity analysis technique, which helps in pruning the parameters to be considered in further analysis. The posterior probability distributions (PDF) of the sensitive parameters are computed using Bayesian approach using a multi criteria likelihood index. Within the Monte Carlo simulations, those parameter sets which produced reasonably good predictions in all ranges of flow are identified, and a combined likelihood is estimated. This combined likelihood values of simulations are employed for sizing the parameter range to help reduce the predictive uncertainty and for deriving the posterior PDF of the parameters. The updating of the PDF is continued till both the distributions (prior and posterior) converge in successive cycles of simulations. The characteristics of the derived PDF of the sensitive model parameters and the basin characteristics are then regressed using neural network technique to develop functional relationship between them, which can be employed for generating a regionalized PDF of the parameters. The proposed methodology is illustrated through a case study of 8 hydrologically different watersheds in USA. While all the basins were gauged, in the current analysis one of them is assumed to be un-gauged (pseudo- un-gauged). The Soil and Water Assessment Tool (SWAT) model was considered for the application. Sobol sensitivity analysis was performed for 15 model parameters that influence the stream flow simulation in SWAT model and the PDF of sensitive parameters were obtained. The regression equations were developed between the PDF of parameters and 7 physiographic catchment characteristics and 3 climatic characteristics. Using the regionalized PDF of parameters and their corresponding range, ensemble simulation of the pseudo- un-gauged watershed was performed. The results of the study were encouraging and can be employed as a viable approach for building confidence in the application of distributed watershed models in un-gauged basins.
Genetic Algorithm Based Framework for Automation of Stochastic Modeling of Multi-Season Streamflows
Synthetic streamflow data generation involves the synthesis of likely streamflow patterns that are statistically indistinguishable from the observed streamflow data. The various kinds of stochastic models adopted for multi-season streamflow generation in hydrology are: i) parametric models which hypothesize the form of the periodic dependence structure and the distributional form a priori (examples are PAR, PARMA); disaggregation models that aim to preserve the correlation structure at the periodic level and the aggregated annual level; ii) Nonparametric models (examples are bootstrap/kernel based methods), which characterize the laws of chance, describing the stream flow process, without recourse to prior assumptions as to the form or structure of these laws; (k-nearest neighbor (k-NN), matched block bootstrap (MABB)); non-parametric disaggregation model. iii) Hybrid models which blend both parametric and non-parametric models advantageously to model the streamflows effectively. Despite many of these developments that have taken place in the field of stochastic modeling of streamflows over the last four decades, accurate prediction of the storage and the critical drought characteristics has been posing a persistent challenge to the stochastic modeler. This is partly because, usually, the stochastic streamflow model parameters are estimated by minimizing a statistically based objective function (such as maximum likelihood (MLE) or least squares (LS) estimation) and subsequently the efficacy of the models is being validated based on the accuracy of prediction of the estimates of the water-use characteristics, which requires large number of trial simulations and inspection of many plots and tables. Still accurate prediction of the storage and the critical drought characteristics may not be ensured. In this study a multi-objective optimization framework is proposed to find the optimal hybrid model (blend of a simple parametric model, PAR(1) model and matched block bootstrap (MABB) ) based on the explicit objective functions of minimizing the relative bias and relative root mean square error in estimating the storage capacity of the reservoir. The optimal parameter set of the hybrid model is obtained based on the search over a multi- dimensional parameter space (involving simultaneous exploration of the parametric (PAR(1)) as well as the non-parametric (MABB) components). This is achieved using the efficient evolutionary search based optimization tool namely, non-dominated sorting genetic algorithm - II (NSGA-II). This approach helps in reducing the drudgery involved in the process of manual selection of the hybrid model, in addition to predicting the basic summary statistics dependence structure, marginal distribution and water-use characteristics accurately. The proposed optimization framework is used to model the multi-season streamflows of River Beaver and River Weber of USA. In case of both the rivers, the proposed GA-based hybrid model yields a much better prediction of the storage capacity (where simultaneous exploration of both parametric and non-parametric components is done) when compared with the MLE-based hybrid models (where the hybrid model selection is done in two stages, thus probably resulting in a sub-optimal model). This framework can be further extended to include different linear/non-linear hybrid stochastic models at other temporal and spatial scales as well.
Nonparametric Streamflow Disaggregation Model
Stochastic streamflow generation is generally utilized for planning and management of water resources systems. For this purpose a number of parametric and nonparametric modeling alternatives have been suggested in literature. Among them temporal and spatial disaggregation approaches play an important role particularly to make sure that historical variance-covariance properties are preserved at various temporal and spatial scales. In this paper, we review the underlying features of nonparametric disaggregation, identify some of their pros and cons, and propose a disaggregation algorithm that is capable of surmounting some of the shortcoming of the current models. The proposed models hinge on k-nearest neighbor resampling, the accurate adjusting procedure, and a genetic algorithm. The model has been tested and compared to an existing nonparametric disaggregation approach using data of the Colorado River system. It has been shown that the model is capable of (i) reproducing the season-to-season correlations including the correlation between the last season of the previous year and the first season of the current year, (ii) minimizing or avoiding the generation of flow patterns across the year that are literally the same as those of the historical records, and (iii) minimizing or avoiding the generation of negative flows. In addition, it is applicable to intermittent river regimes. Suggestions for further improving the model are discussed.
A desktop GIS approach to topographic mapping of surface saturation
Agricultural watersheds are generally highly modified environments. Accurately modelling topographic features in these environments can be difficult due to surface modifications inherent to agricultural practice, this was addressed by collecting high resolution topographic data. Airborne Laser Scanning (ALS) is a remote sensing technique whereby high resolution and high accuracy elevation data is collected throughout a landscape. In March of 2006 an ALS dataset was collected in the Thomas Brook Watershed located in Annapolis Valley, Nova Scotia. This data was collected over the watershed for high resolution modelling. Multiple topographic indices including topographic position index, topographic wetness index, slope gradient, curvature, and catchment area were modelled using 1m, 5m, and 10m DEM resolutions. The models were then compared to ground sampled soil surface moisture data that were collected during the 2006 and 2007 field seasons. A Student's T- test revealed that the topographic models agreed with the theories of surface wetness prediction, although the direct correlation between the models and the ground data was weak. A landform classification algorithm was augmented to incorporate the topographic models based on the theories of surface wetness prediction and a surface saturation map was generated. Tests revealed that the 5m DEM resolution yielded the most accurate results when compared directly to the surficial sampled surface moisture data. It was shown that the Surface Saturation Landform Classification algorithm can be used to predict zones of surface moisture throughout an agricultural watershed.
Assessing the use of Singular Value Decomposition for Model and Data Intercomparison of Hydrological Process Controls.
Global climate is closely coupled to the processes of the hydrologic cycle. An integral component of the hydrologic cycle, soil water content, strongly influences climate at local, regional and global scales through interactions with the land-surface and atmosphere. Atmospheric processes, surface hydrology and biogeochemical cycles are moderated and controlled by soil moisture interactions. For accurate parameterization of these processes in land-surface schemes, such as the Canadian Land Surface Scheme (CLASS), an understanding of soil water content and its variability is crucial. Previous land surface scheme comparisons, such as PILPS (the Intercomparison of Land-surface Parameterization Schemes), have revealed divergence among models in the capturing of soil moisture variability; therefore, the identification of techniques to evaluate process controls in land surface schemes is necessary. The aim of this research is to evaluate the processes controlling soil moisture variability within the Canadian Land Surface Scheme using singular value decomposition (SVD). The processes controlling soil moisture variability were derived from a principal component analysis (PCA) of a regional scale soil water content network over Alberta, Canada. An identical PCA analysis was computed for CLASS to determine the process controls of soil moisture variability within the model. Following this, SVD was used to analysis the cross-covariance between the data and model. The results of the SVD were used to confirm linkages between the PCs of the observed and modelled data.
Deriving Global Drainage Networks From SRTM Elevation Data
SRTM elevation data are widely used to produce hydrographic derivatives such as river networks and watershed delineations. Its seamless, near-global coverage makes the data particularly interesting for large scale applications, but standard GIS software is typically ill prepared for dealing with the large data quantities when processing SRTM data at a global scale. After developing various customized GIS tools, a new hydrographic database has been created, termed HydroSHEDS, which is derived from SRTM elevation data at 3 arc-second (90 m) resolution at global extent. The original SRTM data have been hydrologically conditioned using a sequence of automated procedures and supported by various ancillary data sources. Several of the processing steps used in the development of HydroSHEDS represent standard GIS techniques for hydrographic applications, such as sink detection and filling, stream burning, and deriving flow directions. However, because of the unique characteristics of SRTM data and the large-scale aspect of the applied procedures, some new techniques and algorithms were developed, including customized methods of data filtering, valley carving, and iterative processing. Extensive manual corrections were made where necessary. Finally, an algorithm was developed to upscale HydroSHEDS data to coarser resolutions which are better suited for global applications. Quality assessments indicate that the accuracy of HydroSHEDS significantly exceeds that of existing global watershed and river maps. In future steps, HydroSHEDS will be coupled with global runoff models to derive high-resolution discharge estimates, and with global lake and reservoir databases. HydroSHEDS data is offered by USGS free of charge for non-commercial applications at http://hydrosheds.cr.usgs.gov/
Incomparability and the search for robustness through the evaluation of the distribution of solutions in objective space and parameter space
There is an increasing trend in the use of multi-objective optimization methods for estimating parameter sets in the calibration of hydrological models. Typically, the outcome is a set of several parameter sets usually referred to as Pareto set (or Pareto frontier) which forms a trade-off between the objective functions. The Pareto set is a set of incomparable parameter sets as each solution has unique parameter values in parameter space with competing accuracy in the objective function space. As would be required for decision making purposes a single parameter set is usually chosen to represent the model calibration procedure. In this presentation we will illustrate the evaluation of a Pareto set that was generated using the Non- dominated Sorting Genetic Algorithm II (NSGA-II) to calibrate the Soil and Water Assessment Tool (SWAT) for streamflow simulation based on model bias and root mean square error. The Pareto set evaluation uses a model characterization framework to search for robust, sensitive and equifinal solutions by evaluating the linkages between the distribution of solutions in objective space and patterns observed in parameter space. Our presentation will demonstrate the use of cluster analysis to evaluate the distribution of solutions, and a conditional probability to combine the patterns observed in both objective space and parameter space. A key finding in the combined analysis of the distribution of solutions in both parameter space and objective is that we are able to identify and separate robust solutions from sensitive and non-local equifinal solutions. Key words: calibration, multi-objective optimization, incomparability, robustness.
Assessing and Reducing Hydrogeologic Model Uncertainty
NRC is sponsoring research that couples model abstraction techniques with model uncertainty assessment
methods. Insights and information from this program will be useful in decision making by NRC staff,
licensees and stakeholders in their assessment of ground-water flow and subsurface radionuclide transport.
All analytical methods that quantify ground-water flow and radionuclide transport in the environment implicitly
involve different levels of model abstraction. Our formalized model abstraction process provides a systematic
approach for understanding the adequacy of model simplification and facilitating communication and
transparency of the model to regulators, stakeholders and the general public. The objectives of model
abstraction are: to improve the reliability and reduce uncertainty of simulations; to make the modeling results
more explicable and transparent; and to enable more efficient use of available resources in data collection and
computation. The coupling of model abstraction to uncertainty assessments uses a streamlined methodology
that focuses on conceptual, parameter and scenario uncertainties within a model abstraction framework. Both
the model abstraction process and the streamlined methodology are demonstrated using a simple field study
analysis involving ground-water flow.