Stratigraphic Noise in Time Series Derived from Ice Cores

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Abstract
Because of snow drifting, two time series of any variable derived from two adjacent ice cores will differ considerably. The size and statistical nature of this noise element is discussed for two kinds of measured substance. A theory is developed and compared to data from Greenland and Canadian Arctic ice cores. In case 1, the measured substance can diffuse and the seasonal cycle degrade with time and depth, e.g. δ(18O). In case 2, the measured substance cannot diffuse, e.g. microparticles. The case 2 time series contain drift noise proportional to that in the accumulation series. For accumulation series, the spectral power is concentrated at the high frequencies, i.e. is “blue”. Such noise can be easily reduced by taking relatively short time averages. The noise in the case 1 time series, however, starts out “blue” but quickly diffuses to have a “red” character with significant power at longer wavelengths, and many decades of such series must be averaged to reduce the noise level. Because the seasonal amplitude of any given variable is an important input to the drift noise and because the seasonal amplitudes of some variable types are latitude-dependent, some sites have inherently less drift noise than others.