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Davis, Stanley N. (4)Duckstein, Lucien (4)Woolhiser, David A. (4)Evans, Daniel D. (3)Neuman, Shlomo P. (3)Shuttleworth, James (3)Simpson, Eugene S. (3)Bales, Roger C. (2)Davis, Donald R. (2)View MoreTypes
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Parameter estimation for hydrometeorological models using multi-criteria methods

Bastidas, Luis Alberto, 1950- (The University of Arizona., 1998)

There are three components of error in the ability of land-atmosphere models (e.g., BATS, SiB, etc.) to simulate/predict observed land-surface state variables and output fluxes (e.g. lambdaE, H, Tg, Q, etc.). The first is caused by model structural error associated with simplifications and/or inadequacies in the functional representations of underlying physical processes. The second component is measurement error associated with the input and output data. The third is caused by error in specification of the values of the model parameters. Automatic parameter tuning (model calibration) methods allow minimizing of the parameter error, thereby obtaining an estimate of the remaining error components. This work describes an automatic multi-criteria approach and its use to tune all 27 parameters of the BATS model using data measured in the field. The parameters were adjusted to simultaneously optimize the ability of the model to reproduce observed values of several output fluxes and/or state variables (e.g., latent heat flux, sensible heat flux, ground temperature, etc.). The results indicate that not only does the procedure result in conceptually reasonable and consistent parameter estimates, but the calibrated model is able to provide significant improvement in performance (33% or more reduction in error) over the "un-calibrated" model (i.e., using the BATS default parameter values for the associated region). Substantial improvements of this kind can have important implications for studies that seek to evaluate alternative model structures or to regionalize parameters. To reduce the dimensionality of the optimization problem a multi-criteria extension of the Regionalized Sensitivity Analysis (RSA) has been developed.

Calibration of the soil moisture accounting model using the adaptive random search algorithm

Weinig, Walter Theodore,1960- (The University of Arizona., 1991)

Random search techniques are being applied to a variety of non-linear parameter estimation problems. Random search for global optimization has the potential to overcome many of the problems associated with direct or pattern search techniques. In this research, an adaptive random search algorithm was applied to a conceptual rainfall-runoff model to study the efficiency of the algorithm in locating an optimum set of model parameters. The goal of the study was to determine how changes in internal algorithm control variables and objective functions affected the efficiency of the algorithm. Results indicated that the value of internal control variables did not have a strong influence on algorithm efficiency. Neither objective function gave demonstrably better results in calibration runs. Variability in results due to the random number seed was observed. Recommendations for further research are presented.

Analysis of the National Weather Service soil moisture accounting models for flood prediction in the northeast floods of January 1996

Hogue, Terri Sue (The University of Arizona., 1998)

Extensive flooding occurred throughout the northeastern United States during January of 1996. The flood event cost the lives of 33 people and over a billion dollars in flood damage. Following the "Blizzard of '96", a warm front moved into the Mid Atlantic region bringing extensive rainfall and causing significant melting and flooding to occur. Flood forecasting is a vital part of the National Weather Service (NWS) hydrologic responsibilities. Currently, the NWS River Forecast Centers use either the Antecedent Precipitation Index (API) or the Sacramento Soil-Moisture Accounting Model (SAC-SMA). This study evaluates the API and SAC-SMA models for their effectiveness in flood forecasting during this rain-on-snow event. The SAC-SMA, in conjunction with the SNOW-17 model, is calibrated for five basins in the Mid-Atlantic region using the Shuffled Complex Evolution (SCE-UA) automatic algorithm developed at the University of Arizona. Nash-Sutcliffe forecasting efficiencies (Er) for the calibration period range from 0. 79 to 0.87, with verification values from 0.42 to 0.95. Flood simulations were performed on the five basins using the API and calibrated SAC SMA model. The SAC-SMA model does a better job of estimating observed flood discharge on three of the five study basins, while two of the basins experience flood simulation problems with both models. Study results indicate the SAC-SMA has the potential for better flood forecasting during complex rain-on-snow events such as during the January 1996 floods in the Northeast.

A physically-based snow model coupled to a general circulation model for hydro-climatological studies

Jin, Jiming (The University of Arizona., 2002)

A Snow-Atmosphere-Soil Transfer (SAST) model has been developed to extend the point snowmelt model to vegetated areas using the parameterization concepts of the Biosphere-Atmosphere Transfer Scheme (Dickinson et al. 1993). The model applications for short-grass and forest fields show that the simulated surface temperature, albedo, and snow depth have close agreement with observations. In addition, because of biases in simulated runoff in the high-latitudes, a Shuffled Complex Evolution (Sorooshian et al. 1993) scheme for automatic calibration has been connected with the SAST model to determine the realistic distribution of runoff components from different soil layers and search the optimized parameter set. The calibrated runoff closely matches observations. Because the Community Climate Model version 3 (CCM3) coupled with the SAST model overestimates snow depth and precipitation and underestimates surface temperature over the Rocky Mountains, remotely sensed snow depth data have been assimilated in the model to alleviate model discrepancies based on energy and mass balances. The improved surface temperature simulations result from the decreased snowmelt and albedo in winter and spring and from the weakened evaporation in summer due to drier soil. Meanwhile, modeled summer precipitation over the Rocky Mountains has a minor improvement. The relationship between the variations of tropical Pacific SST and snowpack anomalies in the western United States (U.S.) has been studied by comparing observations and CCM3 output. The results indicate that in the northwestern U.S., the warm tropical Pacific phase of the El Nino-Southern Oscillation (ENSO) is associated with diminished snowpack while its cool phase is related to enhanced snowpack. This relationship is largely determined by winter precipitation variability for the observations; however, it relies heavily on the variations of temperature due to the biases in atmospheric patterns for the model output. In the southwestern U.S., positive snowpack anomalies for both observations and simulations result from the strong warm phase of the ENSO and negative ones are connected with exaggerated local precipitation in fall.

The use of well response to natural forces in the estimation of hydraulic parameters

Ritzi, Robert William. (The University of Arizona., 1989)

The water level in an open well tapping a confined formation is influenced by natural forces including the solid Earth tide (SET) and atmospheric pressure variation (APV). The spectral method is used to derive an analytical solution for well response to both the random and the periodic components of the combined SET and APV (CSA) forcings. Previously posed models for the individual SET and APV forcings are subsets of this more general model. An inverse theory and an algorithm are developed in order to provide improved results when using such models to estimate the hydraulic parameters associated with a given formation. A complex vector estimation criterion is used in developing a nonlinear, Gauss-Marquardt estimation algorithm. When compared to previous methods of fitting modulus and phase, the complex vector estimation methodology has less bias and variance, and is more robust. An examination of the response surface of the estimation criterion reveals that storativity (S) is relatively non-unique, and thus is not considered in the context of the parameter estimation problem. However, since there is little correlation between transmissivity (T) and S estimators, a good estimate for T is still possible independent of having knowledge of S. An estimate of T is possible only if the data contain sufficient information so that the analysis occurs within an identifiability window, which is defined with respect to the dimensionless transmissivity of the system. The CSA estimation methodology is compared to individual SET and APV schemes. The CSA scheme gives the greatest probability that sufficient information is contained in a data record so that T is identifiable. The results of applications to synthetic data indicate that the OEA scheme gives a T estimate with the most precision, and also that it requires collecting fewer observations.

Groundwater flow simulations and management under imprecise parameters

Shafike, Nabil Girgis. (The University of Arizona., 1994)

This dissertation considers modeling groundwater flow under imprecisely known parameters and managing a plume of contaminant. A new approach has been developed to study the effects of parameters uncertainty on the dependent variable, here the head. The proposed approach is developed based on fuzzy set theory combined with interval analysis. The kind of uncertainty modeled here is the imprecision associated with model parameters as a result of machine or human imprecision or lack of information. In this technique each parameter is described by a membership function. The fuzzy inputs into the model are in the form of intervals so are the outputs. The resulting head interval represents the change in the output due to interval inputs of model parameters. The proposed technique is illustrated using a two dimensional flow problem solved with a finite element technique. Three different cases are studied: homogeneous, mildly heterogeneous and highly heterogeneous transmissivity field. The groundwater flow problem analysis requires interval input values for the parameters, the output may be presented in terms of mean value, upper and lower bounds of the hydraulic head. The width of the resulting head interval can be used as a measure of uncertainty due to imprecise inputs. The degree of uncertainty associated with the predicted hydraulic head is found to increase as the width of the input parameters interval increases. Compared to Monte Carlo simulation approach, the proposed technique requires less computer storage and CPU time, however at this stage autocorrelation and crosscorolation are not configured in the presented formulation. In the plume containment problem two formulations are presented using the hydraulic gradient technique to control the movement of the contaminants. The first one is based on multiobjective analysis and the second, on fuzzy set theory. Multiobjective analysis yields a set of alternative strategies each of which satisfies the multiple objectives to a certain degree. Three different techniques have been used to choose a compromise strategy. Although they follow different principles, the same preferred strategies are selected. It is also noticed that rapid restoration results in a large pumping volumes and high costs. Using a fuzzy formulation for plume containment yields the optimum pumping rates and locations in addition to the membership function at each pumping location. The resulting membership functions at these pumping locations can be used to study the sensitivity of each location to a change in objective function and constraints bounds. Overall, both the fuzzy and multiobjective methodologies, presented in this dissertation, provide new and encouraging approaches to groundwater quality management.

Atmospheric and aqueous flux of sulfur in snow

Stanley, Deena Allison,1956- (The University of Arizona., 1987)

Density, morphology, air permeability and liquid water content of snow were characterized and compared with measured deposition velocities to determine the relative importance of physical characteristics on the uptake of SO2 by snow. Highest deposition velocities (0.10 cm/sec) were associated with melting snow. Deposition velocities were higher for new snow (0.055 cm/sec) than for well metamorphosed snow (0.04 cm/sec). Fumigated snow was also used in melt experiments to evaluate the effects of solute distribution on the concentration of meltwater. Meltwater fractions were collected and analyzed for bisulfite, sulfate and nitrate. Both the melt rate and the distribution of the solute within the snowpack and within the snow grain influenced the elution pattern. Highest concentration effects were observed for bisulfite under conditions of slow melt. Concentrations of the initial meltwater were 2 to 4 times that of the bulk snow for sulfate and 2 to 9 times for bisulfite.

Calibration of the soil moisture accounting model using a gradient-type algorithm and analytic derivatives

Hendrickson, Jene Diane,1960- (The University of Arizona., 1987)

In the pest, derivative-based optimization algorithms have not frequently been used to calibrate conceptual rainfall-runoff (CRR) models, partially due to difficulties associated with obtaining the required derivatives. This research applies a recently-developed technique of analytically computing derivatives of a CRR model to a complex, widely-used CRR model. The resulting least squares response surface was found to contain numerous discontinuities in the surface and derivatives. However, the surface and its derivatives were found to be everywhere finite, permitting the use of derivative-based optimization algorithms. Finite difference numeric derivatives were computed and found to be virtually identical to analytic derivatives. A comparison was made between gradient (Newton-Raphson) and direct (pattern search) optimization algorithms. The pattern search algorithm was found to be more robust. The lower robustness of the Newton-Raphson algorithm was thought to be due to discontinuities and a rough texture of the response surface.

Sensitivity of runoff to small scale spatial variability of observed rainfall in a distributed model

Faurés, Jean-Marc,1961- (The University of Arizona., 1990)

The spatial variability of rainfall is known to play an important role in the process of surface runoff generation. Yet, the typical assumption of uniform rainfall is still applied in modeling the hydrological behavior of small watersheds. To investigate the validity of this assumption, an experiment was conducted in a small catchment (4.4 ha) in a semi-arid environment. The distributed model KINEROS was used to assess the sensitivity of predicted runoff to rainfall variability. Uncertainties in estimating rainfall input were shown to have three major components: measurement errors, spatial variability of the rainfall field, and wind. Their relative importance is a function of the catchment scale, topography and physical properties of the storms. Computation of runoff based on the data from a unique raingage entails a high degree of uncertainty. Even at small scales, the number and location of raingages directly control the accuracy of runoff simulation.

Improving efficiency and effectiveness of Bayesian recursive parameter estimation for hydrologic models

Misirli Baysal, Feyzan (The University of Arizona., 2003)

There are several sources of uncertainties in hydrologic modeling studies. Conventional deterministic modeling techniques typically ignore most of these uncertainties. However, there has been a growing need for better quantification of the accuracy and precision of hydrologic model predictions. Bayesian Recursive Estimation (BaRE) is an algorithm being developed towards considering these uncertainties for parameter estimation and prediction within an operational setting. This dissertation work evaluated and improved the current version of the algorithm. The methodology was improved using a progressive re-sampling of the Highest Probability Density (HPD) region of the parameter space, which concentrated the samples in the current HPD region while terminating computations in the nonproductive portions of the parameter space, rather than evaluating feasible parameter space based on the initial set of samples. The covariance structure of the well behaving parameter sets is used to generate new parameter sets, resulting in significant improvements compared to the original BaRE. Further, to reduce the "model/data overconfidence" problem, an entropy term and a data lack-of-confidence factor were introduced into the probability-updating rule. Comparison to batch calibration using the popular Shuffled Complex Evolution (SCE-UA) optimization method indicated that the improved recursive calibration technique is a powerful tool, especially useful where basins are recently gauged and hydrologic data are not well accumulated. The final method is also effective in tracing the temporal variations of parameters as a response to natural or human induced changes in the hydrologic system.

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