A Method for Quantifying Uncertainty in Spatially Interpolated Meteorological Data with Application to Daily Maximum Air Temperature

Abstract. Conventional point estimate error statistics are not well-suited to describing spatial and temporal variation in the accuracy of spatially interpolated meteorological variables. This paper describes, applies, and evaluates a method for quantifying prediction uncertainty in spatially interpolated estimates of meteorological variables. The approach presented here, which we will refer to as DNK for “detrend, normal score, krige,” uses established methods from geostatistics and we apply them to interpolate data from ground-based weather stations. The method is validated using daily maximum near-surface air temperature (Tmax). Uncertainty is inherent in gridded meteorological data, but this fact is often overlooked when data products provide single-value point estimates without a quantitative description of prediction uncertainty. Uncertainty varies as a function of spatial factors, like distance to the nearest measurement location, and temporal factors, like seasonality in sample heterogeneity. DNK produces not only point estimates but predictive distributions for each location. Predictive distributions quantitatively describe uncertainty suitably for propagation into physical models that take meteorological variables as inputs. We validate the uncertainty quantification by comparing theoretical versus actual coverage of prediction intervals computed at locations where measurement data were held out from the estimation procedure. We find that, for most days, the predictive distributions accurately quantify uncertainty and that theoretical versus actual coverage levels of prediction intervals closely match one another. Even for days with the worst agreement, the predictive distributions meaningfully convey the relative certainty of predictions for different locations in space. After validating the methodology, we demonstrate how the magnitude of prediction uncertainty varies significantly in both space and time. Finally, we examine spatial correlation in predictive distributions by using conditional Gaussian simulation in place of kriging. We conclude that spatial correlation in Tmax errors is relatively small, and that less computationally expensive kriging-based methods will suffice for many applications.