Spherical cap harmonic analysis of geomagnetic secular variation over Canada 1960–1983

Abstract

The new technique of spherical cap harmonic anaylsis has enabled a model of secular variation to be constructed that applies to an area of over 30 million square kilometers and a time interval of over 20 years. This technique is a regional analog of the ordinary method of spherical harmonic analysis and ensures that the curl and divergence of the secular variation vector are zero. By making each harmonic coefficient a polynomial in time, the model provides both spatial and temporal continuity. The secular variation data, from 1960 to 1983, comprise 1227 first central differences of annual mean values from 24 observatories in Canada, United States, Greenland, and Iceland, and 939 first central differences from 138 Canadian and American repeat stations, divided by their respective time intervals. The secular variation model includes terms up to spatial index 4 and temporal degree 2. Although such a model allows for 75 coefficients, only 39 were found to be statistically significant. The temporal behavior of the model at observatories and repeat stations is compared on time plots to that of the secular variation data itself. The scatter about the regression model, or standard error of estimate, was 11.8 nT/yr. The model is required both to update aeromagnetic survey data for producing Canadian geomagnetic main field charts at 1985.0 and to provide annual change information for the extrapolation of those charts up to 1990. The average secular variations derived from the Definitive (DGRF) and Provisional (PGRF) International Geomagnetic Reference Fields agree well with the model, but the average secular variation for 1980–1985 from the predictive International Geomagnetic Reference Field (IGRF) does not.