New Indices to Quantify Patterns of Residuals Produced by Model Estimates (original) (raw)

Also, effective application of models suffers from the lack of knowledge of model parameters and their uncer-The evaluation of patterns in the residuals of model estimates vs. tainty. For both process-based and statistically based other variables can be useful in both model evaluation and parameter models, proper simulation techniques require the use calibration. New indices that allow quantifying such patterns (pattern indices) are presented. Groups of residuals are created by dividing of parameter values that, in the former case, properly the range of the variable under evaluation into two, three, four, or represent the system under evaluation and, in the latter five subranges. Two types of indices are proposed. The first type case, minimize the difference between estimates and (PI-type) is based on the absolute value of the maximum difference measured values. The process of adjusting parameter between pairwise comparisons among average residuals of each group values is known as calibration (Beck, 1986; Klepper and of residuals. A variant of this index is computed by using variance Rouse, 1991; Klepper et al., 1991), and it is based on ratios (PI-F type). The subranges of the variable that determines the different procedures. In general, the goal of calibration grouping of residuals may be of equal length (PI) or variable length is to minimize the difference between measured and (PI ). In the second case, they are generated by an algorithm that estimated values. The mathematical representation of optimizes subranges to maximize patterns. The power of the diverse pattern indices at identifying patterns was investigated, and their effec-this goal is called the cost (or loss, or objective) function tiveness was compared against the runs test. Critical values for pattern or assessment criterion. Defining an appropriate cost indices were generated by Monte Carlo simulations. Monte Carlo function can be difficult as it may require considerations probability tables, the results of power analysis, and the results of of different type such as the relative dominance of one or using pattern indices at two case studies (i.e., daily radiation and more parameters, the autocorrelation among different soil water content estimates) were presented. The analysis based on parameters, and the drift in time series (Janssen and pattern indices provided insight in model structure and parameter .