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New Indices to Quantify Patterns of Residuals Produced by Model Estimates

^a Research Institute for Industrial Crops, Via di Corticella, 133, 40128 Bologna, Italy
^b DiProVe, Università di Milano, Via Celoria 2, 20133 Milano, Italy

View larger version (15K): [in a new window]   Fig. 1. Example of three macropatterns in model residuals (solid line: average value; dotted lines: upper and lower bounds).

View larger version (33K): [in a new window]   Fig. 2. Results of power evaluation for range- and F-based pattern indices compared against runs test, under conditions of normal distribution and unit variance. PI, range-based fixed pattern index; PI-F, F-based fixed pattern index; PI, range-based variable pattern index; PI–F, F-based variable pattern index.

View larger version (34K): [in a new window]   Fig. 3. Results of power evaluation for range- and F-based pattern indices compared against runs test, under conditions of heterogeneous variances. PI, range-based fixed pattern index; PI-F, F-based fixed pattern index; PI, range-based variable pattern index; PI–F, F-based variable pattern index.

View larger version (35K): [in a new window]   Fig. 4. Results of power evaluation for range- and F-based pattern indices compared against runs test, under conditions of uniform distribution. PI, range-based fixed pattern index; PI, range-based variable pattern index; PI–F, F-based variable pattern index.

View larger version (42K): [in a new window]   Fig. 5. Daily radiation estimates performed with the models BC and DB at Tel Hadya (Syria) in 1988: residuals vs. day of year (doy) and vs. minimum air temperature (Tmin).

View larger version (17K): [in a new window]   Fig. 6. Daily radiation estimates at Tel Hadya (Syria) in 1988: pattern indices vs. day of year (doy) computed with BC and DB. PI, range-based fixed pattern index; PI, range-based variable pattern index; PI–F, F-based variable pattern index.

View larger version (19K): [in a new window]   Fig. 7. Daily radiation estimates at Tel Hadya (Syria) in 1988: pattern indices vs. minimum air temperature (Tmin) computed with BC and DB. PI, range-based fixed pattern index; PI, range-based variable pattern index; PI–F, F-based variable pattern index.

View larger version (36K): [in a new window]   Fig. 8. Relation of z-scored range-based fixed pattern index (PI) and range-based variable pattern index (PI) (min. 20%) with three and four groups to root mean square error (RMSE), as computed from 48 simulations of soil water content (m3 m–3) performed with the model MACRO. The exponential curve interpolates across dominant solutions. Critical values of the pattern indices are reported for p = 0.05 (solid line) and p = 0.01 (dotted line).