Nonlinear Parameter Estimation (Yonathan Bard)

SIAM Review ◽  
1975 ◽  
Vol 17 (4) ◽  
pp. 703-704 ◽  
Author(s):  
H. E. Reinhardt
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Parameter ◽  
Nonlinear Parameter Estimation

scholarly journals Inverse distributed hydrological modelling of Alpine catchments

2006 ◽  
Vol 10 (3) ◽  
pp. 395-412 ◽  
Author(s):  
H. Kunstmann ◽  
J. Krause ◽  
S. Mayr
Keyword(s):  
Parameter Estimation ◽  
Hydrological Model ◽  
Model Performance ◽  
Horizontal Resolution ◽  
Nonlinear Parameter ◽  
Model Complexity ◽  
Distributed Hydrological Model ◽  
Nonlinear Parameter Estimation ◽  
Estimated Parameters ◽  
Physically Based

Abstract. Even in physically based distributed hydrological models, various remaining parameters must be estimated for each sub-catchment. This can involve tremendous effort, especially when the number of sub-catchments is large and the applied hydrological model is computationally expensive. Automatic parameter estimation tools can significantly facilitate the calibration process. Hence, we combined the nonlinear parameter estimation tool PEST with the distributed hydrological model WaSiM. PEST is based on the Gauss-Marquardt-Levenberg method, a gradient-based nonlinear parameter estimation algorithm. WaSiM is a fully distributed hydrological model using physically based algorithms for most of the process descriptions. WaSiM was applied to the alpine/prealpine Ammer River catchment (southern Germany, 710 km2 in a 100×100 m2 horizontal resolution. The catchment is heterogeneous in terms of geology, pedology and land use and shows a complex orography (the difference of elevation is around 1600 m). Using the developed PEST-WaSiM interface, the hydrological model was calibrated by comparing simulated and observed runoff at eight gauges for the hydrologic year 1997 and validated for the hydrologic year 1993. For each sub-catchment four parameters had to be calibrated: the recession constants of direct runoff and interflow, the drainage density, and the hydraulic conductivity of the uppermost aquifer. Additionally, five snowmelt specific parameters were adjusted for the entire catchment. Altogether, 37 parameters had to be calibrated. Additional a priori information (e.g. from flood hydrograph analysis) narrowed the parameter space of the solutions and improved the non-uniqueness of the fitted values. A reasonable quality of fit was achieved. Discrepancies between modelled and observed runoff were also due to the small number of meteorological stations and corresponding interpolation artefacts in the orographically complex terrain. Application of a 2-dimensional numerical groundwater model partly yielded a slight decrease of overall model performance when compared to a simple conceptual groundwater approach. Increased model complexity therefore did not yield in general increased model performance. A detailed covariance analysis was performed allowing to derive confidence bounds for all estimated parameters. The correlation between the estimated parameters was in most cases negligible, showing that parameters were estimated independently from each other.

Analysis of Fisher Information and the Cramér–Rao Bound for Nonlinear Parameter Estimation After Random Compression

2015 ◽  
Vol 63 (23) ◽  
pp. 6423-6428 ◽  
Author(s):  
Pooria Pakrooh ◽  
Ali Pezeshki ◽  
Louis L. Scharf ◽  
Douglas Cochran ◽  
Stephen D. Howard
Keyword(s):  
Parameter Estimation ◽  
Fisher Information ◽  
Nonlinear Parameter ◽  
Nonlinear Parameter Estimation ◽  
Cramer Rao Bound
Sign in / Sign up

Export Citation Format

Share Document