In this paper, we develop, present and evaluate a refined, statistical index of model performance. This ‘new’ measure (d_r) is a reformulation of Willmott's index of agreement, which was developed in the 1980s. It (d_r) 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 d_r. 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 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.

When evaluating the performance of quantitative models, dimensioned errors often are characterized by sums-of-squares measures such as the mean squared error (MSE) or its square root, the root mean squared error (RMSE). In terms of quantifying average error, however, absolute-value-based measures such as the mean absolute error (MAE) are more interpretable than MSE or RMSE. Part of that historical preference for sums-of-squares measures is that they are mathematically amenable to decomposition and one can then form ratios, such as those based on separating MSE into its systematic and unsystematic components. Here, we develop and illustrate a decomposition of MAE into three useful submeasures: (1) bias error, (2) proportionality error, and (3) unsystematic error. This three-part decomposition of MAE is preferable to comparable decompositions of MSE because it provides more straightforward information on the nature of the model-error distribution. We illustrate the properties of our new three-part decomposition using a long-term reconstruction of streamflow for the Upper Colorado River.

Earthquake‐triggered landslides are a significant hazard in seismically active regions, but our ability to assess the hazard they pose in near‐real‐time is limited. In this study, we present a new globally applicable model for seismically induced landslides based on the most comprehensive global data set available; we use 23 landslide inventories that span a range of earthquake magnitudes and climatic and tectonic settings. We use logistic regression to relate the presence and distribution of earthquake‐triggered landslides with spatially distributed estimates of ground shaking, topographic slope, lithology, land cover type, and a topographic index designed to estimate variability in soil wetness to provide an empirical model of landslide distribution. We tested over 100 combinations of independent predictor variables to find the best fitting model, using a diverse set of statistical tests. Blind validation tests show that the model accurately estimates the distribution of available landslide inventories. The results indicate that the model is reliable and stable, with high balanced accuracy (correctly versus incorrectly classified pixels) for the majority of test events. A cross‐validation analysis shows high balanced accuracy for a majority of events as well. By combining near‐real‐time estimates of ground shaking with globally available landslide susceptibility data, this model provides a tool to estimate the distribution of coseismic landslide hazard within minutes of the occurrence of any earthquake worldwide for which a U.S. Geological Survey ShakeMap is available.

Spatially weighted averages of Palmer Drought Severity Index (PDSI) over central and southern California show that the 1 year 2014 drought was not as severe as previously reported, but it still is the most severe in the 1895–2014 instrumental record. Using the typical adjustment procedure that matches the mean and standard deviation of tree ring PDSI values to those of instrumental data shows over 10 droughts from 800 to 2006 that were more severe than the 1 year 2014 drought, with the 2014 drought having a return period of 140–180 years. Quantile mapping allows for a closer correspondence between instrumental and tree ring PDSI probability distributions and produces return periods of 700–900 years for the 1 year 2014 drought. Associated cumulative 3 and 4 year droughts, however, are estimated to be much more severe. The 2012–2014 drought is nearly a 10,000 year event, while the 2012–2015 drought has an almost incalculable return period and is completely without precedent.