Spatial representativeness of a long-term climate network in Canada

Users of climate records frequently require data at geographical locations where no direct measurements of climatological variables are collected. Climatological conditions at the areas or points of interest have to be estimated by interpolating observations from neighbouring stations. An objective of assessing spatial representativeness of a network of observing stations is to outline the areas for which the network is capable of providing sufficiently accurate climatological information, i.e., where interpolation errors do not exceed a value acceptable to the user. Two statistical methods: Gandin's point-to-point optimal interpolation and Kagan's point-to- area interpolation were applied to monthly, seasonal and annual total precipitation records gathered by a long-term, high quality, nationwide network of Canadian climate stations. Due to substantial differences in seasonal climate conditions in the Arctic versus the rest of the country, the national network had to be split into two subsets: north and south of 60 degreesN latitude. Both interpolation techniques use a spatial correlation function to compute interpolation errors. The correlation function of departures or ratios from the first guess field of long-term averages can be considered homogeneous and isotropic over a wide range of distances. Exponential functions are especially suitable to model correlation of precipitation. Alone, they can supply an abundance of information about the nature of precipitation, random observational errors and microclimatic uncertainties. The widely scattered northern stations showed poor spatial correlation and consequently unacceptably large interpolation errors in all cases except summer. The conclusion was that at present the climate network does not provide adequate climatological information north of 60 degrees latitude. The southern stations exhibited fairly good spatial correlation, which allowed computation of the longest acceptable interstation distances that satisfy various interpolation error criteria. The results were tabulated to serve as a reference. In Gandin's case, the areas where the interpolation error does not exceed 65% of a local standard deviation were delineated for all months and seasons using so-called circles of representativeness. This example revealed vast regions without adequate precipitation gauge coverage, especially in summer and winter. Kagan's method, which is concerned with area averages, produced less demanding results. Intuitively, a less dense network is required for area-average estimates than for point value estimates. At the same time though, acceptable areal relative errors should be set at lower values. Assuming an arbitrary 10% relative error in the areal estimate, the southern half of the country is adequately represented by the network except for some relatively small sections around Hudson Bay.