Multivariate Statistical Analysis of Glacier Annual Balances

A statistical analysis has been made of the annual balances collected during 16 consecutive years at 32 sites on the ablation area of the Glacier de Saint-Sorlin (French Alps). Only 38% of the 32 × 16 balances are known; moreover in 8 cases only the total balance for 2 consecutive years is known, and in one case the balance for 4 consecutive years. A comprehensive study of the errors leads us to assume the following linear model for the annual balance x jt at site j for year t: where α j and β t are parameters depending upon the site and the year respectively, η jt and η’ jt are random errors with a Gaussian distribution and standard errors σ and σ’ respectively. Assuming some known value for σ’ 2 / σ 2 = ρ , the parameters α j and β t , their variance–covariance matrix, and the variance covariance matrix of the residuals are estimated in the most general case. The estimators being stable against variations in ρ, the value ρ = o may be assumed; this value docs not conflict with the behaviour of the estimates of the residuals. A test of the linear model derived from Tukey’s non-additivity test is positive. Although a much more general, non-linear model gives a better representation of 13 × 6 balances forming a complete table of data, the linear model with σ ≈ 0.20 m is good enough to be used in theoretical studies or in routine work.