Qingyun Duan

Effective and efficient global optimization for conceptual rainfall-runoff models

The successful application of a conceptual rainfall-runoff (CRR) model depends on how well it is calibrated. Despite the popularity of CRR models, reports in the literature indicate that it is typically difficult, if not impossible, to obtain unique optimal values for their parameters using automatic calibration methods. Unless the best set of parameters associated with a given calibration data set can be found, it is difficult to determine how sensitive the parameter estimates (and hence the model forecasts) are to factors such as input and output data error, model error, quantity and quality of data, objective function used, and so on. Results are presented that establish clearly the nature of the multiple optima problem for the research CRR model SIXPAR. These results suggest that the CRR model optimization problem is more difficult than had been previously thought and that currently used local search procedures have a very low probability of successfully finding the optimal parameter sets. Next, the performance of three existing global search procedures are evaluated on the model SIXPAR. Finally, a powerful new global optimization procedure is presented, entitled the shuffled complex evolution (SCE-UA) method, which was able to consistently locate the global optimum of the SIXPAR model, and appears to be capable of efficiently and effectively solving the CRR model optimization problem.

Shuffled complex evolution approach for effective and efficient global minimization

The degree of difficulty in solving a global optimization problem is in general dependent on the dimensionality of the problem and certain characteristics of the objective function. This paper discusses five of these characteristics and presents a strategy for function optimization called the shuffled complex evolution (SCE) method, which promises to be robust, effective, and efficient for a broad class of problems. The SCE method is based on a synthesis of four concepts that have proved successful for global optimization: (a) combination of probabilistic and deterministic approaches; (b) clustering; (c) systematic evolution of a complex of points spanning the space, in the direction of global improvement; and (d) competitive evolution. Two algorithms based on the SCE method are presented. These algorithms are tested by running 100 randomly initiated trials on eight test problems of differing difficulty. The performance of the two algorithms is compared to that of the controlled random search CRS2 method presented by Price (1983, 1987) and to a multistart algorithm based on the simplex method presented by Nelder and Mead (1965).

Optimal use of the SCE-UA global optimization method for calibrating watershed models

Abstract The difficulties involved in calibrating conceptual watershed models have, in the past, been partly attributable to the lack of robust optimization tools. Recently, a global optimization method known as the SCE-UA (shuffled complex evolution method developed at The University of Arizona) has shown promise as an effective and efficient optimization technique for calibrating watershed models. Experience with the method has indicated that the effectiveness and efficiency of the algorithm are influenced by the choice of the algorithmic parameters. This paper first reviews the essential concepts of the SCE-UA method and then presents the results of several experimental studies in which the National Weather Service river forecast system-soil moisture accounting (NWSRFS-SMA) model, used by the National Weather Service for river and flood forecasting, was calibrated using different algorithmic parameter setups. On the basis of these results, the recommended values for the algorithmic parameters are given. These values should also help to provide guidelines for other users of the SCE-UA method.

A parameterization of snowpack and frozen ground intended for NCEP weather and climate models

Extensions to the land surface scheme (LSS) in the National Centers for Environmental Prediction, regional, coupled, land-atmosphere weather prediction model, known as the mesoscale Eta model, are proposed and tested off-line in uncoupled mode to account for seasonal freezing and thawing of soils and snow-accumulation-ablation processes. An original model assumption that there is no significant heat transfer during redistribution of liquid water was relaxed by including a source/sink term in the heat transfer equation to account for latent heat during phase transitions of soil moisture. The parameterization uses the layer-integrated form of heat and water diffusion equations adopted by the original Eta-LSS. Therefore it simulates the total ice content of each selected soil layer. Infiltration reduction under frozen ground conditions was estimated by probabilistic averaging of spatially variable ice content of the soil profile. Off-line uncoupled tests of the new and original Eta-LSS were performed using experimental data from Rosemount, Minnesota. Simulated soil temperature and unfrozen water content matched observed data reasonably well. Neglecting frozen ground processes leads to significant underestimation/overestimation of soil temperature during soil freezing/thawing periods and underestimates total soil moisture content after extensive periods of soil freezing.

Calibration of rainfall‐runoff models: Application of global optimization to the Sacramento Soil Moisture Accounting Model

Conceptual rainfall-runoff models are difficult to calibrate by means of automatic methods; one major reason for this is the inability of conventional procedures to locate the globally optimal set of parameters. This paper investigates the consistency with which two global optimization methods, the shuffled complex evolution (SCE-UA) method (developed by the authors) and the multistart simplex (MSX) method, are able to find the optimal parameter set during calibration of the Sacramento soil moisture accounting model (SAC-SMA) of the National Weather Service River Forecast System (NWSRFS). In the first phase of this study, error-free synthetic data are used to conduct a comparative evaluation of the algorithms under “ideal” conditions. In 10 independent trials of each algorithm in which 13 parameters of the SAC-SMA model were optimized simultaneously, the SCE-UA method achieved a 100% success rate in locating the precise global optimum (i.e., the “true” parameter values) while the MSX method failed in all trials even with more than twice the number of function evaluations. In the second phase, historical data from the Leaf River watershed are used to conduct a comparative evaluation of the algorithms under “real” conditions, using two different estimation criteria, DRMS and HMLE; the SCE-UA algorithm obtained consistently lower function values and more closely grouped parameter estimates, while using one-third fewer function evaluations than the MSX algorithm.

Simple water balance model for estimating runoff at different spatial and temporal scales

A parametric water balance model was developed based on statistical averaging of the main hydrological processes. The model has a two-layer structure with both a physical and statistical basis for the model parameters. It was developed to fill a need for models with a small number of parameters and of intermediate complexity between a one-parameter simple bucket and more complex hydrologically oriented models with many parameters such as the Sacramento model. The focus was to improve the representation of runoff relative to the simple bucket without introducing the full complexity of the Sacramento model. The model was designed to operate over a range of time steps to facilitate coupling to an atmospheric model. The model can be used for catchment scale simulations in hydrological applications and for simple representation of runoff in coupled atmospheric/hydrological models. An important role for the simple water balance (SWB) model is to assist in understanding how much complexity in representing land surface processes is needed and can be supported with available data to estimate model parameters. The model is tested using rainfall, runoff, and surface meteorological data for three catchments from different climate regimes. Model performance is compared to performance of a simple bucket model, the Sacramento model, and the Oregon State University land surface model. Finally, a series of tests were conducted to evaluate the sensitivity of SWB performance when it is operated at time steps different from the time step for which it was calibrated.

The Representation of Snow in Land Surface Schemes: Results from PILPS 2(d)

Twenty-one land surface schemes (LSSs) performed simulations forced by 18 yr of observed meteorological data from a grassland catchment at Valdai, Russia, as part of the Project for the Intercomparison of Land-Surface Parameterization Schemes (PILPS) Phase 2(d). In this paper the authors examine the simulation of snow. In comparison with observations, the models are able to capture the broad features of the snow regime on both an intra- and interannual basis. However, weaknesses in the simulations exist, and early season ablation events are a significant source of model scatter. Over the 18-yr simulation, systematic differences between the models’ snow simulations are evident and reveal specific aspects of snow model parameterization and design as being responsible. Vapor exchange at the snow surface varies widely among the models, ranging from a large net loss to a small net source for the snow season. Snow albedo, fractional snow cover, and their interplay have a large effect on energy available for ablation, with differences among models most evident at low snow depths. The incorporation of the snowpack within an LSS structure affects the method by which snow accesses, as well as utilizes, available energy for ablation. The sensitivity of some models to longwave radiation, the dominant winter radiative flux, is partly due to a stability-induced feedback and the differing abilities of models to exchange turbulent energy with the atmosphere. Results presented in this paper suggest where weaknesses in macroscale snow modeling lie and where both theoretical and observational work should be focused to address these weaknesses.

The Project for Intercomparison of Land-surface Parameterization / / Schemes PILPS Phase 2 c Red-Arkansas River basin experiment: 1. Experiment description and summary intercomparisons

Abstract Sixteen land-surface schemes participating in the Project for the Intercomparison of Land-surface Schemes (PILPS) Phase 2(c) were run using 10 years (1979–1988) of forcing data for the Red–Arkansas River basins in the Southern Great Plains region of the United States. Forcing data (precipitation, incoming radiation and surface meteorology) and land-surface characteristics (soil and vegetation parameters) were provided to each of the participating schemes. Two groups of runs are presented. (1) Calibration–validation runs, using data from six small catchments distributed across the modeling domain. These runs were designed to test the ability of the schemes to transfer information about model parameters to other catchments and to the computational grid boxes. (2) Base-runs, using data for 1979–1988, designed to evaluate the ability of the schemes to reproduce measured energy and water fluxes over multiple seasonal cycles across a climatically diverse, continental-scale basin. All schemes completed the base-runs but five schemes chose not to calibrate. Observational data (from 1980–1986) including daily river flows and monthly basin total evaporation estimated through an atmospheric budget analysis, were used to evaluate model performance. In general, the results are consistent with earlier PILPS experiments in terms of differences among models in predicted water and energy fluxes. The mean annual net radiation varied between 80 and 105 W m −2 (excluding one model). The mean annual Bowen ratio varied from 0.52 to 1.73 (also excluding one model) as compared to the data-estimated value of 0.92. The run-off ratios varied from a low of 0.02 to a high of 0.41, as compared to an observed value of 0.15. In general, those schemes that did not calibrate performed worse, not only on the validation catchments, but also at the scale of the entire modeling domain. This suggests that further PILPS experiments on the value of calibration need to be carried out.

The project for intercomparison of land-surface parameterization schemes (PILPS) phase 2(c) Red-Arkansas River basin experiment: 3. Spatial and temporal analysis of water fluxes

The energy components of sixteen Soil-Vegetation Atmospheric Transfer (SVAT) schemes were analyzed and intercompared using 10 years of surface meteorological and radiative forcing data from the Red-Arkansas River basin in the Southern Great Plains of the United States. Comparisons of simulated surface energy fluxes among models showed that the net radiation and surface temperature generally had the best agreement among the schemes. On an average (annual and monthly) basis, the estimated latent heat fluxes agreed (to within approximate estimation errors) with the latent heat fluxes derived from a radiosonde-based atmospheric budget method for slightly more than half of the schemes. The sensible heat fluxes had larger differences among the schemes than did the latent heat fluxes, and the model-simulated ground heat fluxes had large variations among the schemes. The spatial patterns of the model-computed net radiation and surface temperature were generally similar among the schemes, and appear reasonable and consistent with observations of related variables, such as surface air temperature. The spatial mean patterns of latent and sensible heat fluxes were less similar than for net radiation, and the spatial patterns of the ground heat flux vary greatly among the 16 schemes. Generally, there is less similarity among the models in the temporal (interannual) variability of surface fluxes and temperature than there is in the mean fields, even for schemes with similar mean fields.

Calibration of watershed models.

Published by the American Geophysical Union as part of the Water Science and Application Series, Volume 6. During the past four decades, computer-based mathematical models of watershed hydrology have been widely used for a variety of applications including hydrologic forecasting, hydrologic design, and water resources management. These models are based on general mathematical descriptions of the watershed processes that transform natural forcing (e.g., rainfall over the landscape) into response (e.g., runoff in the rivers). The user of a watershed hydrology model must specify the model parameters before the model is able to properly simulate the watershed behavior.