1

Snow depth distribution

Neumann et al. (2006)

2Neumann et al. (2006)

3

Measurement Errors

• The number and quality of data, as well as their statistical nature, impose limitations on the information that can be usually deduced; in fact, all measurements are inaccurate to some degree.

• The observer’s procedures, the instruments and their maintenance, data transmission and transcription, may each contribute individually or collectively to errors in the published values.

4

• Errors may be random, such as mistakes in transcribing numbers, or systematic, such as a bias introduced by an observer or an instrument.

• Random errors tend to cluster around the mean value and are generally both positive and negative so that “normal” or “Gaussian” statistics apply.

• Some “obvious” errors can be easily explained and corrected; others must be rejected if they lack a sound physical explanation, but should not be discarded, since later evidence may provide an explanation.

5

• Errors that fall within reasonable limits of possibility are the most insidious since they are virtually impossible to detect.

• A mean value of several measurements is a better estimate of the true value, provided systematic errors are negligible; similarly, the average of a time series may give a superior measure of it true (normal) value.

6

• Systematic errors may either be constant or proportional to the magnitude of the variable, or appear only under specific environmental conditions, e.g., when snow is wet and adhesive rather than dry and easily transported by the wind.

• Such errors are minor in data for indices, but are serious in data required for quantitative values. Adjustment factors can be determined to compensate for exposure bias but are somewhat subjective and cannot be freely transposed to other seasons or sites.

7

• Most snow courses are established to aid in predicting runoff volumes and peaks.

• Their data measurements are used as indices so that the measured values need not be representative of a large area.

• Preferably they indicate snowcover amounts over areas that contribute substantially to runoff.

8

• A simple comparison with values in the same general area will often indicate the extent to which exposures are comparable.

• Major differences should be explainable in terms of elevation, land form, vegetation, or other climatic of physical features.

• Snowfall and snowcover data are highly amenable to statistical analyses and probabilistic statistical association.

9

• Peculiarities of the data must always be kept in mind (e.g., the data must be examined critically for the occurrence of “zero” values and for the frequency distribution most appropriate for analysis.

• The choice of the most suitable theoretical distribution to be fitted depends on each dataset; for instance the incomplete gamma function is use to represent many snowfall and snowcover variables.

10

• The distribution of a single variable can frequently be expressed in a linear form such that:

• X(F) = X + s k(F)• Where X(F) is the expected value of the variable

whose probability of not being exceeded is F, X is the estimated mean of the population, s is the estimated standard deviation, and k(F) is the frequency factor which is chosen to correspond to a given probability level, F, and whose magnitude depends on the frequency distribution and sample size.