Transcript Snow survey and measurement errors

Snow depth
distribution
Neumann et al. (2006)
1
Neumann et al. (2006)
2
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.
3
• 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.
4
• 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.
5
• 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.
6
• 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.
7
• 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.
8
• 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.
9
• 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.
10
Sources of sampling errors
• Riming of meteorological instruments
• Loss of power
• Incorrect wiring or programming of the
instrument
• Malfunctioning or deteriorating instrument
• Tampering or involuntary displacement
• Others??
11
Examples of mechanical failures
12