Concordance correlation for model performance assessment: An example with reference evapotranspiration observations
The assessment procedures for agronomic model performance are often arbitrary and unhelpful. An omnibus analysis, the concordance correlation coefficient (rc), is widely used in many other sciences. This work illustrates model assessment with two rc measures accompanied with a mean-difference (MD) plot and a distribution comparison. Each rc is an adjusted value of the usual Pearson correlation coefficient, r, assuming the exact relationship observations = predictions. The adjustments use a scale shift, u, and a location shift, v. Both of these measures also can indicate the similarity of the two variables' distributions; however, a formal test, the Kolmorgov-Smirnov D statistic, is used to statistically compare the distributions. Daily evapotranspiration data (ET0) from a published study are compared with estimates from two possible weather observation based models. Although the first model has slightly lower r than the second (0.980 vs. 0.982), its predictions reasonably agree with observations by having comparatively small location and scale shifts [(u = 0.025, v = 1.10, D = 0.12 (p ≤ 0.86)] and, consequently, a higher rc (0.975 vs. 0.946). Results for the second model are comparatively unacceptable having larger scale and location shifts (u = 0.215, v = 1.19, D = 0.28 [p ≤ 0.04]) with the bias != 0 (p ≤ 0.05) as clearly shown in the associated MD plot. Researchers should consider using rc with an MD plot and distribution comparison in their model assessment toolkit because, together, they can provide a simple and sound probability based omnibus test as well as add useful insight.