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In this paper, we develop, present and evaluate a refined, statistical index of model performance. This ‘new’ measure (dr) is a reformulation of Willmott's index of agreement, which was developed in the 1980s. It (dr) is dimensionless, bounded by − 1.0 and 1.0 and, in general, more rationally related to model accuracy than are other existing indices. It also is quite flexible, making it applicable to a wide range of model-performance problems. The two main published versions of Willmott's index as well as four other comparable dimensionless indices—proposed by Nash and Sutcliffe in 1970, Watterson in 1996, Legates and McCabe in 1999 and Mielke and Berry in 2001—are compared with the new index. Of the six, Legates and McCabe's measure is most similar to dr. Repeated calculations of all six indices, from intensive random resamplings of predicted and observed spaces, are used to show the covariation and differences between the various indices, as well as their relative efficacies. Copyright © 2011 Royal Meteorological Society

A new hybrid empirical downscaling technique is presented and applied to assess 21st century projections of maximum and minimum daily surface air temperatures (Tmax, Tmin) over the Midwestern USA. Our approach uses multiple linear regression to downscale the seasonal variations of the mean and standard deviation of daily Tmax and Tmin and the lag-0 and lag-1 correlations between daily Tmax and Tmin based on GCM simulation of the large-scale climate. These downscaled parameters are then used as inputs to a stochastic weather generator to produce time series of the daily Tmax and Tmin at 26 surface stations, in three time periods (1990–2001, 2020–2029, and 2050–2059) based on output from two coupled GCMs (HadCM3 and CGCM2). The new technique is demonstrated to exhibit better agreement with surface observations than a transfer-function approach, particularly with respect to temperature variability. Relative to 1990–2001 values, downscaled temperature projections for 2020–2029 indicate increases that range (across stations) from 0.0 K to 1.7 K (Tmax) and 0.0 K to 1.5 K (Tmin), while increases for 2050–2059 relative to 1990–2001 range from 1.4 K to 2.4 K (Tmax) and 0.8 to 2.2K (Tmin). Although the differences between GCMs demonstrate the continuing uncertainty of GCM-based regional climate downscaling, the inclusion of weather-generator parameters represents an advancement in downscaling methodology. Copyright © 2006 Royal Meteorological Society

Spatial and temporal sampling errors inherent in large-scale, weather-station (raingauge) climatologies of precipitation are evaluated. A primary goal is to assess whether more representative large-scale precipitation climatologies emerge when (i) more station means are included, even when they are based on unequal periods of record, or (ii) fewer station means are included but all are derived from the same period of record. Observations drawn from the Historical Climatology Network (HCN) are used to estimate temporally averaged precipitation over lo-, 20-, and 30-year intervals at 457 stations within the USA. Two strategies for estimating these ‘observed’ means are examined, one based on temporal ‘substitution’ within each station record, and the other based on spatial interpolation from surrounding stations. Temporally estimated m-year means were obtained by substituting other m-year means, from within the same station record, for each ‘observed’ m-year mean, where m is the length of the averaging period of interest. Spatially interpolated m-year means were estimated from m-year means associated with nearby stations. Climatologies containing a greater number of station averages, even if they are computed over unequal averaging periods, appear to better represent the space-time variability in mean precipitation than climatologies containing fewer, but tem orall indicate that the within-station-record substitution of means is about 1.3 to 2.5 times more accurate than is interpolation from surrounding station means. Within-station substitution errors-associated with estimating any 10-year mean precipitation from any other 10-year mean-for example, were about 8 per cent of the long-term spatial precipitation mean for the USA, or 67.6 mm. Spatially interpolated 10-year means, from nearby stations, were in error by more than 10 per cent, or 88.8 mm on average. Much of the space-time variability in mean precipitation was not resolved adequately by the 457 HCN stations, especially high-frequency spatial variability caused by orographic and convective mechanisms. For many regions of the world, temporally homogeneous precipitation station networks are considerably more sparse than in the USA, further degrading the reliability of interpolated and spatially integrated mean precipitation fields derived solely from those networks.

A new and relatively straightforward approach to interpolating and spatially averaging air temperature from weather-station observations is introduced and evaluated using yearly station averages taken from the Jones et al. archive. All available terrestrial station records over the period from 1881 through to 1988 are examined. Called climatologically aided interpolation, or CAI, our procedure makes combined use of (i) a spatially high-resolution air-temperature climatology recently compiled by Legates and Willmott, as well as (ii) spatially interpolated yearly temperature deviations (evaluated at the stations) from the climatology. Spherically based inverse-distance-weighting and triangular-decomposition interpolation algorithms are used to interpolate yearly station temperatures and temperature deviations to the nodes of a regular, spherical lattice. Interpolation errors are estimated using a cross-validation methodology. Interpolation errors associated with CAI estimates of annual-average air temperatures over the terrestrial surface are quite low. On average, CAI errors are of the order of 0.8°C, whereas interpolations made directly (and only) from the yearly station temperatures exhibit average errors between 1.3°C and 1.9°C. Although both the high-resolution climatology and the interpolated temperature-deviation fields explain non-trivial portions of the space-time variability in terrestrial air temperature, most of CAI's accuracy can be attributed to the spatial variability captured by the high-resolution (Legates and Willmott's) climatology. Our results suggest that raw air-temperature fields as well as temperature anomaly fields can be interpolated reliably.

© 1994 by the Royal Meteorological Society. Available from the publisher's website at http://dx.doi.org/10.1002/joc.3370140405