Connecting Point-Level and Gridded Moments in the Analysis of Climate Data

The need to draw climate-related inferences from historical data makes understanding the biases and errors in these data critical. While climate data are collected at point-level monitoring sites, they are often postprocessed by averaging sites within a geographic area to align the data to a grid, easing analysis and visualization. Although this aggregation generally provides reasonable estimates of the mean, its use can be problematic for characterizing the full distribution of climate measures. Specifically, the process of averaging point-level data up to grid level can lead to inconsistencies, particularly when the grid box is heterogeneous and extremes are of interest. Point-level data are measured at individual points, while gridded data are the averaged product of many measurements within a larger spatial area. Because of this aggregation, point-level and grid-level distributions differ in many fundamental properties, such as their shape, skew, and tail behavior. This paper highlights these differences and their effects on analyses pertaining to current climatological questions. Mathematical relationships are derived to link the distributions of grid-level climate measures to the distributions of point-level climate measures using the notion of effective sample size. Then, these relationships are leveraged to propose a correction factor to use when modeling higher moments and extreme events.