Comparison of temporal and unresolved spatial variability in multiyear time-averages of air temperature

When compiling climatological means of air temperature, station data usually are selected on the basis of whether they exist within a fixed base period (e.g. 1961 to 1990). Within such analyses, station records that do not contain sufficient data during the base period or only contain data from other base periods are excluded. If between-station variability is of interest (e.g. a map or gridded field is needed), then removing such stations assumes that spatial interpolation to the location of culled stations is more reliable than using a temporal mean from a shorter or different averaging period-the latter is a process that we call 'temporal substitution.' Data from the United States Historical Climate Network (HCN) are used to examine whether spatial interpolation or temporal substitution is more reliable for multiyear averages of monthly and annual mean air temperature. After exhaustively sampling all possible 5-, 10-, and 30-yr averaging periods from 1921 to 1994, spatially averaged interpolation and substitution errors are estimated for all months and for annual averages. For all months, temporal substitution produces lower overall error than traditional spatial interpolation for both 10- and 30-yr averages. Maps of mean absolute error (for all averaging periods) show that spatial interpolation errors are largest in mountainous regions while temporal substitution errors are largest in the northcentral and eastern USA, especially in winter. A spatial interpolation algorithm (topographically aided interpolation, TAI) that incorporates elevation data reduces interpolation error, but also produces larger errors than temporal substitution for all months when using 30-yr averages and for all months except January, February, and March when using 10-yr averages. For 5-yr averages, however, TAI produces lower errors than temporal substitution, especially in winter. For the USA, therefore, it is suggested that for averaging periods less than 10 yr in length, elevation-aided spatial interpolation is preferable to temporal substitution. Conversely, for averaging periods longer than 10 yr in length, temporal substitution is preferable to spatial interpolation. Analysis of the 1961 to 1990 period using a wide range of network densities demonstrates that temporal substitution generally is more reliable than spatial interpolation of 30-yr averages, regardless of network density.