Efficient Accommodation of Local Minima in Watershed Model Calibration

The Gauss-Marquardt-Levenberg (GML) method of computer-based parameter estimation, in common with other gradient-based approaches, suffers from the drawback that it may become trapped in local objective function minima, and thus report optimized parameter values that are not optimized at all. This c...

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Bibliographic Details
Main Authors: Skahill, Brian E, Doherty, John
Format: Report
Language:English
Subjects:
ALGORITHM PERFORMANCE
ALGORITHMS
AUGMENTATION
CALIBRATION
Computer Programming and Software
COMPUTERIZED SIMULATION
CORRELATION
COVARIANCE
EFFICIENCY
ESTIMATES
GAUSS-MARQUARDT-LEVENBERG METHOD
HSPF PARAMETERS
Hydrology, Limnology and Potamology
INVERSE PROBLEMS
LEVEL(QUANTITY)
LOCAL MINIMA
MODEL CALIBRATION
NUMERICAL ANALYSIS
Numerical Mathematics
OBJECTIVE FUNCTION MINIMA
OPTIMIZATION
PARAMETER ESTIMATION
PARAMETERS
PARAMETRIC INSTABILITY
PD MS1 ALGORITHM
PD MS2 ALGORITHM
PEST PARAMETER ESTIMATION PACKAGE
REPRINTS
SENSITIVITY
TEMPORARY PARAMETER IMMOBILIZATION
TRAJECTORY REPULSION SCHEMES
WATER QUALITY
WATERSHED MODELING
WATERSHEDS
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Summary:The Gauss-Marquardt-Levenberg (GML) method of computer-based parameter estimation, in common with other gradient-based approaches, suffers from the drawback that it may become trapped in local objective function minima, and thus report optimized parameter values that are not optimized at all. This can seriously degrade its utility in the calibration of watershed models where local optima abound. Nevertheless, the method also has advantages, chief among these being its model-run efficiency, and its ability to report useful information on parameter sensitivities and covariances as a by-product of its use. It also is easily adapted to maintain this efficiency in the face of potential numerical problems caused by parameter insensitivity and/or parameter correlation. The present paper presents two algorithmic enhancements to the GML method that retain its strengths, but which overcome its weaknesses in the face of local optima. Using the first of these methods, an intelligent search for better parameter sets is conducted in parameter subspaces of decreasing dimensionality when progress of the parameter estimation process is slowed either by numerical instability incurred through problem ill-posedness, or when a local objective function minimum is encountered. The second methodology minimizes the chance of successive GML parameter estimation runs, finding the same objective function minimum by starting successive runs at points that are maximally removed from previous parameter trajectories. As well as enhancing the ability of a GML-based method to find the global objective function minimum, the latter technique also can be used to find the locations of many non-global optima (should they exist) in parameter space. This can provide a useful means of inquiring into the well-posedness of a parameter estimation problem, and for detecting the presence of bimodal parameter and predictive probability distributions. To be published in the Journal of Hydrology, 2006. Prepared in cooperation with the Department of Civil Engineering, University of Queensland, St. Lucia, Australia, and Watermark Numerical Computing, Brisbane, Australia. The original document contains color images.