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MODELING

An Indicator of Solar Radiation Model Performance based on a Fuzzy Expert System

^a Res. Inst. for Ind. Crops, via di Corticella 133, 40128 Bologna, Italy
^b Dep. of Crop Sci., via Celoria 2, 20133 Milan, Italy

* Corresponding author (g.bellocchi{at}isci.it)

Received for publication October 1, 2001. When evaluating models, various indices or test statistics are computed, quantifying the magnitude of model residuals, the correlation between estimates and measurements, patterns of residuals over external variables, etc. Such indices are variously related to each other, thus making model comparison difficult. Problems of this type emerge when testing solar radiation models. This paper proposes a fuzzy expert system to calculate a modular indicator, I_rad, which reflects an expert perception about the quality of the performance of solar radiation models. Three modules were formulated reflecting the magnitude of residuals (Accuracy), the correlation estimates and measurements (Correlation), and the presence or absence of patterns in the residuals against independent variables (Pattern), respectively. The modules Accuracy and Pattern resulted from the aggregation of three (relative root mean square error, modeling efficiency, and t-Student probability) and two (pattern index vs. day of the year and pattern index vs. minimum air temperature) indices, respectively, while the module Correlation was identified by a single index (Pearson's correlation coefficient). For each index, two functions describing membership to the fuzzy subsets Favorable (F) and Unfavorable (U) have been defined. The expert system calculates the modules according to both the degree of membership of the indices to the subsets F and U and a set of decision rules. Then the modules are aggregated into the indicator I_rad. Sensitivity analysis is presented, along with module and I_rad scores for some application cases.

Abbreviations: BC, Bristow–Campbell (model) • CD, Campbell–Donatelli (model) • DB, Donatelli–Bellocchi (model) • EF, efficiency (index) • F, Favorable (subset) • I_rad, indicator of solar radiation model performance • PI, pattern index • PI_doy, pattern index day of year • PI_Tmin, pattern index daily minimum air temperature • RMSE, root mean square error • RRMSE, relative root mean square error • U, Unfavorable (subset)

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