A method for quantifying uncertainty in spatially interpolated meteorological data with application to daily maximum air temperature

Abstract. Uncertainty is inherent in gridded meteorological data, but this fact is often overlooked when data products do not provide a quantitative description of prediction uncertainty. 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 to produce not only point estimates (i.e., a single number) but also predictive distributions for each location. Predictive distributions quantitatively describe uncertainty in a manner suitable for propagation into physical models that take meteorological variables as inputs. We apply the method to interpolate daily maximum near-surface air temperature (Tmax) and then 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 predictions and errors using conditional Gaussian simulation to sample from the joint spatial predictive distribution. In summary, this work demonstrates the efficacy and value of describing uncertainty in gridded meteorological data products using predictive distributions.