Willmott Index Of Agreement

The purpose of this article is to examine all the above indices and propose a logical, stable, unique and simple index to evaluate the performance of the model. The chord index (d) developed by Willmott (1981) as a standardized measure of the degree of prediction error of the model varies between 0 and 1. A value of 1 indicates a perfect match, and 0 indicates no match (Willmott, 1981). The results are presented on the maps in Fig. 5. All maps show the expected patterns of temporal agreement: areas with a strong dynamic NDVI signal, such as northern cultivation areas, have a higher chord than desert areas where the signal consists mainly of noise. However, there is a big difference where each metric returns negative values: the ? map shows no negative values, Watterson`s M metric map only assumes negative values if the correlation is negative, but Ji & Gallo`s AC index map shows huge ranges of negative values throughout the region. The comparison between ? and r reflects the added value of using the former, which takes into account distortions that are not present in the latter. The size of these biases relative to the total deviations can be spatialized in the map, while the correspondence of the records is displayed on the map independently of these biases. (iii) Legates and McCabe`s index (ELM) (Legates and McCabe 1999) This research shows that the agreement index (d) between variables predicted by a very different model and observed data may approach one (1.0), but may have a lower value for almost similar data sets. The ambiguous and inconsistent behavior of dr is also observed, so it cannot be considered a reliable indicator. Research also shows that efficiency-based indicators such as ENS and ELG are not in agreement with the logical trend (and in some cases show a reverse trend) and also with generally accepted measures based on differences (e.B.

MAE, RMSE). While for simulation year 1, the «odd simulated» values are omitted from the calculation, the statistical indicators based on differences – mean error (MA), mean absolute error (EMA), mean square error (EMS) and relative error (ER) decreased compared to those with «odd simulated values»; which makes sense. Efficiency-based indicators – ENS or ELG, ELM, agreement index and new agreement index dr – decreased; but they should be increased. Similar behaviors are also observed for year 2. Among the statistical indices, some of them quantify the gap between the model results and the observed or experimental measurements, while others focus on the correlation between the predictions and the model measurements. Essentially, Fox (1981) recommended that the following four types of differential measures be calculated and reported: mean error, mean absolute error, variance of difference distribution, and mean square error (or square sound – mean square error). These statistics based on differences quantify the gap between the model results and the measurements. Indicators for specific areas are also proposed….

Sobre el Autor: Luis