Sir,

In a recent paper Reference Grosval’d and KotlyakovGrosval’d and Kotlyakov (1969) review various Soviet glaciological projects. In particular, they discuss mass balance figures for Lednik IGAN, in the Polar Urals, computed for the period since 1818 using meteorological data recorded at the weather station at Syktyvkar. They place stress on the fact that there appears to exist a 22-year periodicity in the plot of the 10-year running mean of net mass balance and they speculate on the relationship this bears to the 22-year fluctuations in solar activity. In view of the interest of the current IHD in the glacier-climate problem these results of Grosval’d and Kotlyakov merit some discussion.

First, the relationship used (maximum snow accumulation versus sum of the average monthly temperature and the total ablation versus the sum of mean monthly temperatures for the summer) seem rather too simple a priori to give a good “explanation” of the data observed over only 11 years of actual field work. The authors claim that the correlation is “satisfactory” but do not mention the form of relationship (regression equation) or discuss the “goodness” of fit of the data to the predictive equations. It is not stated whether the computed correlation coefficients were reduced to take account of the probability of an observed higher correlation arising randomly from a universe with a lower true correlation. With a sample size of 10 an observed correlation of 0.90, for example, must be reduced to 0.72 (which would “explain” just less than half of the observed data) for significance at the 5% level (Reference Ezekiel and FoxEzekiel and Fox, 1967, p. 294).

Secondly, it is not clear whether the meteorological data, used in establishing the relationships mentioned and valid for 11 years, were collected over or near the glacier or at Syktyvkar, but in the former case there would be need for a relationship between meteorological parameters at the glacier and at Syktyvkar. In this connection it might be mentioned that Syktyvkar is apparently located about 900 km away from Lednik IGAN and on the opposite side of the Ural Mountains (the authors do not say where Syktyvkar is).

Further, by plotting the extrapolated mass-balance data in 10-year running mean form, the authors encounter difficulties due to the Slutzky effect (Reference SlutzkySlutzky, 1937; Reference MitchellMitchell and others, 1966) whereby a running mean acts as a mathematical filter. In general, a time series will consist of a sum of Fourier components (a purely random series will have a white spectrum) and the filter will selectively amplify or damp constituent components according to frequency to give rise to a new filtered or distorted time series. The authors’ graph of the 10-year running mean net budget represents a filtered time series and the prominance of the 22-year cycle is probably due to this filtering effect, likewise the phase difference between the 10-year mean for Lednik IGAN and the 5-year mean for the Grosser Aletschgletscher. Reference MitchellMitchell and others (1966) and Reference LliboutryLliboutry (1964–65, Tom. 2, p. 829–32) outline procedures by which the unfiltered time series could be analysed for periodicity and trend if this were felt desirable in the light of the objections previously raised.

With regard to the question of a relationship between solar activity and variations in glacier net balance it should be axiomatic that, if a relationship does exist, it is by way of the atmospheric circulation. However, the problem lies in relating variations in radiation from the sun in the ultra-violet region of the spectrum (absorbed chiefly by ozone and oxygen in the stratosphere and thermosphere respectively) and variations in corpuscular radiation (interacting with the magnetic field of the earth) with gross circulation changes in the troposphere.

14 November 1970