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- Author or Editor: Cort J. Willmott x
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Quantitative approaches to the evaluation of model performance were recently examined by Fox (1981). His recommendations are briefly reviewed and a revised set of performance statistics is proposed. It is suggested that the correlation between model-predicted and observed data, commonly described by Pearson's product-moment correlation coefficient, is an insufficient and often misleading measure of accuracy. A complement of difference and summary univariate indices is presented as the nucleus of a more informative, albeit fundamentally descriptive, approach to model evaluation. Two models that estimate monthly evapotranspiration are comparatively evaluated in order to illustrate how the recommended method(s) can be applied.
Quantitative approaches to the evaluation of model performance were recently examined by Fox (1981). His recommendations are briefly reviewed and a revised set of performance statistics is proposed. It is suggested that the correlation between model-predicted and observed data, commonly described by Pearson's product-moment correlation coefficient, is an insufficient and often misleading measure of accuracy. A complement of difference and summary univariate indices is presented as the nucleus of a more informative, albeit fundamentally descriptive, approach to model evaluation. Two models that estimate monthly evapotranspiration are comparatively evaluated in order to illustrate how the recommended method(s) can be applied.
Abstract
Two “smart” interpolation procedures are presented and assessed with respect to their ability to estimate annual-average air temperatures at unsampled points in space from available station averages. Smart approaches examined here improve upon commonly used procedures in that they incorporate spatially high-resolution digital elevation information, an average environmental lapse rate, and/or another higher-resolution longer-term average temperature field. Two other straightforward or commonly used interpolation methods also are presented and evaluated as benchmarks to which the smart interpolators can be compared. Interpolation from a spatially high-resolution, long-term-average air temperature climatology serves as a first approximation, while “traditional” interpolation (from a single realization of annual average air temperature on a single station network) is the other benchmark. Traditional interpolation continues to be the most commonly used interpolation approach within many of the atmospheric and environmental sciences.
Smart approaches are significantly more accurate than either traditional methods or estimates spatially interpolated from a high-resolution climatology alone. A smart interpolation method that makes combined use of a digital elevation model (DEM) and traditional interpolation was nearly 24% more accurate than traditional interpolation by itself. Average error associated with this DEM-assisted interpolation algorithm, for interpolating yearly average air temperatures in the United States, was 0.44°C. The other smart method that was evaluated combines DEM information with a high-resolution average air temperature field. It was even more accurate, as expressed in an overall average interpolation error of only 0.38°C per year, which makes it some 34% more accurate than traditional interpolation. It is likely that the performance of smart interpolation, relative to traditional interpolation, will be even better when used with relatively sparse station networks.
Abstract
Two “smart” interpolation procedures are presented and assessed with respect to their ability to estimate annual-average air temperatures at unsampled points in space from available station averages. Smart approaches examined here improve upon commonly used procedures in that they incorporate spatially high-resolution digital elevation information, an average environmental lapse rate, and/or another higher-resolution longer-term average temperature field. Two other straightforward or commonly used interpolation methods also are presented and evaluated as benchmarks to which the smart interpolators can be compared. Interpolation from a spatially high-resolution, long-term-average air temperature climatology serves as a first approximation, while “traditional” interpolation (from a single realization of annual average air temperature on a single station network) is the other benchmark. Traditional interpolation continues to be the most commonly used interpolation approach within many of the atmospheric and environmental sciences.
Smart approaches are significantly more accurate than either traditional methods or estimates spatially interpolated from a high-resolution climatology alone. A smart interpolation method that makes combined use of a digital elevation model (DEM) and traditional interpolation was nearly 24% more accurate than traditional interpolation by itself. Average error associated with this DEM-assisted interpolation algorithm, for interpolating yearly average air temperatures in the United States, was 0.44°C. The other smart method that was evaluated combines DEM information with a high-resolution average air temperature field. It was even more accurate, as expressed in an overall average interpolation error of only 0.38°C per year, which makes it some 34% more accurate than traditional interpolation. It is likely that the performance of smart interpolation, relative to traditional interpolation, will be even better when used with relatively sparse station networks.
Abstract
January and July surface air temperature fields simulated by the GFDI, OSU, GISS, and UKMO general circulation models (GCMS) are compared to the global surface air temperature climatology compiled by Legates and Willmott. Legates and Willmott's climatology was selected as the verification standard because it provides better spatial and temporal coverage than its predecessors, such as the frequently employed RAND climatology compiled in the early 1970s. Difference maps between each GCM-simulated field and the Legates and Willmott climatology are presented and evaluated. Zonal averages by 10° latitudinal bands for each GCM as well as for the Legates and Willmott and RAND climatologies also are examined.
Results indicate that surface air temperature simulations are greatly influenced by model representations of topography, sea level pressure, and precipitation. Inclusion of the diurnal cycle and the type of ocean model used also impact simulated surface air temperatures. Mean January and July surface air temperatures are well simulated by the GISS and UKMO models, whereas temperatures are overestimated by the OSU GCM and underestimated by the GFDL GCM. GISS and UKMO simulations seem even more accurate, on the average, than the data contained in the RAND observation-based climatology. Simulated equatorial air temperatures are slightly higher than observed, particularly in the Southern Hemisphere. Model simulated air temperatures between 30°S and 60°S are usually lower than observed, while air temperatures poleward of 60°S are overestimated. Northern Hemisphere temperatures are generally better simulated than their Southern Hemisphere counterparts.
Abstract
January and July surface air temperature fields simulated by the GFDI, OSU, GISS, and UKMO general circulation models (GCMS) are compared to the global surface air temperature climatology compiled by Legates and Willmott. Legates and Willmott's climatology was selected as the verification standard because it provides better spatial and temporal coverage than its predecessors, such as the frequently employed RAND climatology compiled in the early 1970s. Difference maps between each GCM-simulated field and the Legates and Willmott climatology are presented and evaluated. Zonal averages by 10° latitudinal bands for each GCM as well as for the Legates and Willmott and RAND climatologies also are examined.
Results indicate that surface air temperature simulations are greatly influenced by model representations of topography, sea level pressure, and precipitation. Inclusion of the diurnal cycle and the type of ocean model used also impact simulated surface air temperatures. Mean January and July surface air temperatures are well simulated by the GISS and UKMO models, whereas temperatures are overestimated by the OSU GCM and underestimated by the GFDL GCM. GISS and UKMO simulations seem even more accurate, on the average, than the data contained in the RAND observation-based climatology. Simulated equatorial air temperatures are slightly higher than observed, particularly in the Southern Hemisphere. Model simulated air temperatures between 30°S and 60°S are usually lower than observed, while air temperatures poleward of 60°S are overestimated. Northern Hemisphere temperatures are generally better simulated than their Southern Hemisphere counterparts.
Abstract
Water balance calculations are becoming increasingly important for earth-system studies. Precipitation is one of the most critical input variables for such calculations because it is the immediate source of water for the land surface hydrological budget. Numerous precipitation datasets have been developed in the last two decades, but these datasets often show marked differences in their spatial and temporal distribution of this key hydrological variable. This paper compares six monthly precipitation datasets—Climate Research Unit of University of East Anglia (CRU), Willmott–Matsuura (WM), Global Precipitation Climate Center (GPCC), Global Precipitation Climatology Project (GPCP), Tropical Rainfall Measuring Mission (TRMM), and NCEP–Department of Energy (DOE) Atmospheric Model Intercomparison Project (AMIP-II) Reanalysis (NCEP-2)—to assess the uncertainties in these datasets and their impact on the terrestrial water balance. The six datasets tested in the present paper were climatologically averaged and compared by calculating various statistics of the differences. The climatologically averaged monthly precipitation estimates were applied as inputs to a water balance model to estimate runoff and the uncertainties in runoff arising directly from the precipitation estimates. The results of this study highlight the need for accurate precipitation inputs for water balance calculations. These results also demonstrate the need to improve precipitation estimates in arid and semiarid regions, where slight changes in precipitation can result in dramatic changes in the runoff response due to the nonlinearity of the runoff-generation processes.
Abstract
Water balance calculations are becoming increasingly important for earth-system studies. Precipitation is one of the most critical input variables for such calculations because it is the immediate source of water for the land surface hydrological budget. Numerous precipitation datasets have been developed in the last two decades, but these datasets often show marked differences in their spatial and temporal distribution of this key hydrological variable. This paper compares six monthly precipitation datasets—Climate Research Unit of University of East Anglia (CRU), Willmott–Matsuura (WM), Global Precipitation Climate Center (GPCC), Global Precipitation Climatology Project (GPCP), Tropical Rainfall Measuring Mission (TRMM), and NCEP–Department of Energy (DOE) Atmospheric Model Intercomparison Project (AMIP-II) Reanalysis (NCEP-2)—to assess the uncertainties in these datasets and their impact on the terrestrial water balance. The six datasets tested in the present paper were climatologically averaged and compared by calculating various statistics of the differences. The climatologically averaged monthly precipitation estimates were applied as inputs to a water balance model to estimate runoff and the uncertainties in runoff arising directly from the precipitation estimates. The results of this study highlight the need for accurate precipitation inputs for water balance calculations. These results also demonstrate the need to improve precipitation estimates in arid and semiarid regions, where slight changes in precipitation can result in dramatic changes in the runoff response due to the nonlinearity of the runoff-generation processes.
