Jasper A. Vrugt

Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation

[1] There is increasing consensus in the hydrologic literature that an appropriate framework for streamflow forecasting and simulation should include explicit recognition of forcing and parameter and model structural error. This paper presents a novel Markov chain Monte Carlo (MCMC) sampler, entitled differential evolution adaptive Metropolis (DREAM), that is especially designed to efficiently estimate the posterior probability density function of hydrologic model parameters in complex, high-dimensional sampling problems. This MCMC scheme adaptively updates the scale and orientation of the proposal distribution during sampling and maintains detailed balance and ergodicity. It is then demonstrated how DREAM can be used to analyze forcing data error during watershed model calibration using a five-parameter rainfall-runoff model with streamflow data from two different catchments. Explicit treatment of precipitation error during hydrologic model calibration not only results in prediction uncertainty bounds that are more appropriate but also significantly alters the posterior distribution of the watershed model parameters. This has significant implications for regionalization studies. The approach also provides important new ways to estimate areal average watershed precipitation, information that is of utmost importance for testing hydrologic theory, diagnosing structural errors in models, and appropriately benchmarking rainfall measurement devices.

Improved evolutionary optimization from genetically adaptive multimethod search

In the last few decades, evolutionary algorithms have emerged as a revolutionary approach for solving search and optimization problems involving multiple conflicting objectives. Beyond their ability to search intractably large spaces for multiple solutions, these algorithms are able to maintain a diverse population of solutions and exploit similarities of solutions by recombination. However, existing theory and numerical experiments have demonstrated that it is impossible to develop a single algorithm for population evolution that is always efficient for a diverse set of optimization problems. Here we show that significant improvements in the efficiency of evolutionary search can be achieved by running multiple optimization algorithms simultaneously using new concepts of global information sharing and genetically adaptive offspring creation. We call this approach a multialgorithm, genetically adaptive multiobjective, or AMALGAM, method, to evoke the image of a procedure that merges the strengths of different optimization algorithms. Benchmark results using a set of well known multiobjective test problems show that AMALGAM approaches a factor of 10 improvement over current optimization algorithms for the more complex, higher dimensional problems. The AMALGAM method provides new opportunities for solving previously intractable optimization problems.

Present and future global distributions of the marine Cyanobacteria Prochlorococcus and Synechococcus

The Cyanobacteria Prochlorococcus and Synechococcus account for a substantial fraction of marine primary production. Here, we present quantitative niche models for these lineages that assess present and future global abundances and distributions. These niche models are the result of neural network, nonparametric, and parametric analyses, and they rely on >35,000 discrete observations from all major ocean regions. The models assess cell abundance based on temperature and photosynthetically active radiation, but the individual responses to these environmental variables differ for each lineage. The models estimate global biogeographic patterns and seasonal variability of cell abundance, with maxima in the warm oligotrophic gyres of the Indian and the western Pacific Oceans and minima at higher latitudes. The annual mean global abundances of Prochlorococcus and Synechococcus are 2.9 ± 0.1 × 1027 and 7.0 ± 0.3 × 1026 cells, respectively. Using projections of sea surface temperature as a result of increased concentration of greenhouse gases at the end of the 21st century, our niche models projected increases in cell numbers of 29% and 14% for Prochlorococcus and Synechococcus, respectively. The changes are geographically uneven but include an increase in area. Thus, our global niche models suggest that oceanic microbial communities will experience complex changes as a result of projected future climate conditions. Because of the high abundances and contributions to primary production of Prochlorococcus and Synechococcus, these changes may have large impacts on ocean ecosystems and biogeochemical cycles.

Self-Adaptive Multimethod Search for Global Optimization in Real-Parameter Spaces

Many different algorithms have been developed in the last few decades for solving complex real-world search and optimization problems. The main focus in this research has been on the development of a single universal genetic operator for population evolution that is always efficient for a diverse set of optimization problems. In this paper, we argue that significant advances to the field of evolutionary computation can be made if we embrace a concept of self-adaptive multimethod optimization in which multiple different search algorithms are run concurrently, and learn from each other through information exchange using a common population of points. We present an evolutionary algorithm, entitled A Multialgorithm Genetically Adaptive Method for Single Objective Optimization (AMALGAM-SO), that implements this concept of self adaptive multimethod search. This method simultaneously merges the strengths of the covariance matrix adaptation (CMA) evolution strategy, genetic algorithm (GA), and particle swarm optimizer (PSO) for population evolution and implements a self-adaptive learning strategy to automatically tune the number of offspring these three individual algorithms are allowed to contribute during each generation. Benchmark results in 10, 30, and 50 dimensions using synthetic functions from the special session on real-parameter optimization of CEC 2005 show that AMALGAM-SO obtains similar efficiencies as existing algorithms on relatively simple unimodal problems, but is superior for more complex higher dimensional multimodal optimization problems. The new search method scales well with increasing number of dimensions, converges in the close proximity of the global minimum for functions with noise induced multimodality, and is designed to take full advantage of the power of distributed computer networks.

Differential Evolution Markov Chain with snooker updater and fewer chains

Differential Evolution Markov Chain (DE-MC) is an adaptive MCMC algorithm, in which multiple chains are run in parallel. Standard DE-MC requires at least N=2d chains to be run in parallel, where d is the dimensionality of the posterior. This paper extends DE-MC with a snooker updater and shows by simulation and real examples that DE-MC can work for d up to 50–100 with fewer parallel chains (e.g.N=3) by exploiting information from their past by generating jumps from differences of pairs of past states. This approach extends the practical applicability of DE-MC and is shown to be about 5–26 times more efficient than the optimal Normal random walk Metropolis sampler for the 97.5% point of a variable from a 25–50 dimensional Student t3 distribution. In a nonlinear mixed effects model example the approach outperformed a block-updater geared to the specific features of the model.

Improved extraction of hydrologic information from geophysical data through coupled hydrogeophysical inversion

Improved extraction of hydrologic information from geophysical data through coupled hydrogeophysical inversion A.C. Hinnell 1 , T.P.A. Ferre 1 , J.A. Vrugt 2 , J.A. Huisman 3 , S. Moysey 4 , J Rings 3 , and M.B. Kowalsky 5 Hydrology and Water Resources, University of Arizona, Tucson, AZ, 85721-0011 Center for Nonlinear Studies (CNLS), Mail Stop B258, Los Alamos, NM 87545 ICG 4 Agrosphere, Forschungszentrum Julich, 52425 Julich, Germany Environmental Engineering and Earth Sciences, Clemson University, Clemson, S.C. 29634 Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720 Abstract There is increasing interest in the use of multiple measurement types, including indirect (geophysical) methods, to constrain hydrologic interpretations. To date, most examples integrating geophysical measurements in hydrology have followed a three-step, uncoupled inverse approach. This approach begins with independent geophysical inversion to infer the spatial and/or temporal distribution of a geophysical property (e.g. electrical conductivity). The geophysical property is then converted to a hydrologic property (e.g. water content) through a petrophysical relation. The inferred hydrologic property is then used either independently or together with direct hydrologic observations to constrain a hydrologic inversion. We present an alternative approach, coupled inversion, which relies on direct coupling of hydrologic models and geophysical models during inversion. We compare the abilities of coupled and uncoupled

Real-Time Data Assimilation for Operational Ensemble Streamflow Forecasting

Abstract Operational flood forecasting requires that accurate estimates of the uncertainty associated with model-generated streamflow forecasts be provided along with the probable flow levels. This paper demonstrates a stochastic ensemble implementation of the Sacramento model used routinely by the National Weather Service for deterministic streamflow forecasting. The approach, the simultaneous optimization and data assimilation method (SODA), uses an ensemble Kalman filter (EnKF) for recursive state estimation allowing for treatment of streamflow data error, model structural error, and parameter uncertainty, while enabling implementation of the Sacramento model without major modification to its current structural form. Model parameters are estimated in batch using the shuffled complex evolution metropolis stochastic-ensemble optimization approach (SCEM-UA). The SODA approach was implemented using parallel computing to handle the increased computational requirements. Studies using data from the Leaf River...

Obtaining the Spatial Distribution of Water Content along a TDR Probe Using the SCEM-UA Bayesian Inverse Modeling Scheme

Time domain reflectometry (TDR) has become one of the standard methods for the measurement of the temporal and spatial distribution of water saturation in soils. Current waveform analysis methodology gives a measurement of the average water content along the length of the TDR probe. Close inspection of TDR waveforms shows that heterogeneity in water content along the probe can be seen in the TDR waveform. We present a comprehensive approach to TDR waveform analysis that gives a quantitative estimate of the dielectric permittivity profile along the length of the probe and, therefore, the distribution of water content. The approach is based on the combination of a multisection scatter function model for the TDR measurement system with the shuffled complex evolution Metropolis algorithm (SCEM-UA). This combined approach allows for the estimation of the 40 parameters in the transmission line model using a series of simple calibration measurements. The proof of concept is given with measurements in a layered system consisting of air and water. Finally, TDR waveforms from layered soil samples were analyzed to estimate the distribution of the water content along the length of the probe. Results show that the proposed method provides much more reproducible results than obtained with the traditional travel time method. Because the proposed method can be fully automated, it increases the applicability of the TDR method, especially in applications where detailed (real-time) data are required on heterogeneous infiltration.

Application of parallel computing to stochastic parameter estimation in environmental models

Parameter estimation or model calibration is a common problem in many areas of process modeling, both in on-line applications such as real-time flood forecasting, and in off-line applications such as the modeling of reaction kinetics and phase equilibrium. The goal is to determine values of model parameters that provide the best fit to measured data, generally based on some type of least-squares or maximum likelihood criterion. Usually, this requires the solution of a non-linear and frequently non-convex optimization problem. In this paper we describe a user-friendly, computationally efficient parallel implementation of the Shuffled Complex Evolution Metropolis (SCEM-UA) global optimization algorithm for stochastic estimation of parameters in environmental models. Our parallel implementation takes better advantage of the computational power of a distributed computer system. Three case studies of increasing complexity demonstrate that parallel parameter estimation results in a considerable time savings when compared with traditional sequential optimization runs. The proposed method therefore provides an ideal means to solve complex optimization problems.

Toward improved identifiability of soil hydraulic parameters: on the selection of a suitable parametric model

We present a thorough identifiability analysis of the soil hydraulic parameters in the parametric models of Brooks and Corey (BC; Brooks and Corey, 1964), Mualem-van Genuchten (VG; van Genuchten, 1980), and Kosugi (KC; Kosugi, 1996, 1999) using the recently developed Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm (Vrugt et al., 2002b, and unpublished data). Because the SCEM-UA algorithm globally thoroughly exploits the parameter space and therefore explicitly accounts for parameter interdependence and nonlinearity of the employed parametric models, the algorithm is suited to generate a useful description of parameter uncertainty and its antithesis, parameter identifiability. A set of measured water retention characteristics of the UNSODA database (Leij et al., 1996) spanning a wide range of soil textures and three transient laboratory outflow experiments with decreasing flow rates were used to illustrate that a parameter identifiability analysis facilitates the selection of an adequate parametric model structure and provides useful information about the limitations of a model. Moreover, results suggest that one should be especially careful in establishing pedotransfer functions without knowledge of the underlying posterior uncertainty associated with the soil hydraulic parameters using direct estimation methods.