Comparison of EOF-based and traditional techniques for filling short-term gaps in temperature data in dense-station datasets

Missing data is often found in temperature time series observations, and applications using these datasets frequently require filling in data during periods when it is missing. This may be required in order to avoid bias in long-term averages or to provide complete forcing time series for modeling applications. Multiple methods are available to fill missing data; they generally rely on spatial interpolation or extrapolation from other observing stations, or temporal interpolation within the time series, or both. These methods include interpolation based on elevation, i.e., lapsing, diurnal cycle interpolation within the single data series, spatio-temporal correlations among multiple stations, and multiple regressions of temperature data to location, elevation, time and other features. In this study, spatio-temporal correlations in the form of empirical orthogonal functions (EOFs) are used to fill in missing temperature data, and the results are compared to filling using other practical methods. Spatio-temporal EOF-based filling is expected to be beneficial when applied to temperature datasets with multiple observing stations that are located closely enough to be well correlated. A dense set of observations from the Hydrometeological Testbed in the American River Basin in California, a northern Sierra Nevada region of complex terrain, is used to test the effectiveness of each method via cross-validation. Additional station-network datasets are also used to test the generality of the comparisons. The results indicate that spatio-temporal correlations using EOFs can be more accurate than lapse rates or temporal interpolation. The smallest errors are observed with this technique provided that multiple stations are available to ensure the accuracy of this method. When the number of observing stations is reduced below a threshold, the error is shown to increase beyond that of other techniques. Nevertheless, EOF-based filling is found to perform better than traditional techniques such as lapse rate filling under most circumstances where a network of at least approximately 10 stations exist.