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United States Department of Agriculture

Agricultural Research Service

Research Project: EMISSION AND DISPERSION OF AIR QUALITY CONSTITUENTS FROM AGRICULTURAL SYSTEMS Title: Concordance correlation for model performance assessment: An example with reference evapotranspiration

Authors
item Meek, David
item Howell, Terry
item Phene, Claude - RETIRED USDA-ARS

Submitted to: Agronomy Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: March 2, 2009
Publication Date: July 7, 2009
Citation: Meek, D.W., Howell, T.A., Phene, C. Concordance correlation for model performance assessment: An example with reference evapotranspiration. Agronomy Journal. 101(4): 1012-1018.

Interpretive Summary: Procedures for assessing model performance in agronomy are often arbitrary and not always helpful. An omnibus analysis statistic, concordance correlation, is widely known and used in many other sciences. An example is presented comparing predictions from two different models with measurements from a published evapotranspiration study. The analysis and related graphs reveal systematic under-estimation of observation location and scale by one of the models. The illustration shows researchers how concordance correlation analysis and related graphs for model performance assessment can provide both a simple and sound probability based omnibus test and add useful analytical insight; thus, it should promote greater use of the method.

Technical Abstract: Procedures for assessing model performance in agronomy are often arbitrary and not always helpful. An omnibus analysis statistic, concordance correlation, is widely known and used in many other sciences. An illustrative example is presented here. The analysis assumes the exact relationship “observations = predictions” is true. An adjusted correlation coefficient (rc) for the exact concordance model is estimated using adjustments on the well-known product-moment correlation coefficient (r) for a scale shift (v) and a location shift (u). Data are for 50 d selected from a published lysimeter - weather station calibration study. Daily totals of measured reference evapotranspiration (ET0) were compared to estimates from two possible weather based models using concordance correlation analysis. Both models use the same weather data inputs and estimate an hourly total. The daily value for Model-1 is the sum of hourly estimates that use a published empirical wind function calibration. The daily value for Model-2 is the sum of hourly estimates that use a published iterative atmospheric-stability-based routine. Using Model-1, r=0.980, rc=0.975, v=1.10, and u=0.025. Using Model-2, r=0.982, rc=0.945, v=1.19, and u=0.215. Hence, although Model-2 predictions have greater precision (less scatter), having a greater r, it is not a better choice because it is not as accurate having both greater u and v values revealing greater systematic under-estimation of observation location (mean bias) and scale (less variance). Researchers should therefore consider concordance correlation analysis and related graphs for model performance assessment because, together, they provide both a simple and sound probability based omnibus test and useful analytical insight. Additional tools of possible interest are also mentioned.

Last Modified: 9/10/2014
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