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A distributed parameter approach for evaluating the accuracy of groundwater model predictions: 1. Theory
Author(s) -
McLaughlin Dennis,
Wood Eric F.
Publication year - 1988
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr024i007p01037
Subject(s) - discretization , computer science , process (computing) , sampling (signal processing) , set (abstract data type) , estimation theory , mathematical optimization , errors in variables models , mathematics , stochastic modelling , data mining , algorithm , statistics , machine learning , mathematical analysis , filter (signal processing) , computer vision , programming language , operating system
A systematic stochastic analysis suggests that groundwater model accuracy depends on natural heterogeneity, data availability, model approximations, and method used to estimate model inputs. Distributed parameter estimation theory is used to develop a description of the modeling process which includes all of these factors. This description is based on a set of hybrid state equations which clearly distinguish between the heterogeneous distributed variables of the natural (reference) system and the aggregated variables of the discretized model. Approximate expressions for the first and second moments of the model's prediction error are derived directly from the state equations. The derived moments provide a convenient way to examine a number of questions related to sampling design, robust input estimation, and model performance. They also may be used to design modeling studies before extensive resources are committed to data collection and model development.