Wavelet methods in interpolation of high-frequency spatial–temporal pressure

The location-scale and whitening properties of wavelets make them more favorable for interpolating high-frequency monitoring data than Fourier-based methods. In the past, wavelets have been used to simplify the dependence structure in multiple time or spatial series, but little has been done to apply wavelets as a modeling tool in a space–time setting, or, in particular, to take advantage of the localization of wavelets to capture the local dynamic characteristics of high-frequency meteorological data. This paper analyzes minute-by-minute atmospheric pressure data from the Atmospheric Radiation Measurement program using different wavelet coefficient structures at different scales and incorporating spatial structure into the model. This approach of modeling space–time processes using wavelets produces accurate point predictions with low uncertainty estimates, and also enables interpolation of available data from sparse monitoring stations to a high density grid and production of meteorological maps on large spatial and temporal scales.