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 xjt at site j for year t:where αj and βt are parameters depending upon the site and the year respectively, ηjt and η’jt are random errors with a Gaussian distribution and standard errors σ and σ’ respectively. Assuming some known value for σ’2/σ2 = ρ, the parameters αj and βt, 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.
Multivariate Statistical Analysis of Glacier Annual Balances
