Ž .
Ž .
Fig. 10. General distance relations. Difference Dif, y-axis vs. distance x-axis between on-site and off-site correction factors in case of snow fraction sampled off-site. Temperaures T -y28C are considered.
between. A possible sign of anisotropy, which is confirmed in Fig. 8, is broken down into twelve sub-graphs, each having a fixed on-site station. The 25–75 percentile varies
greatly across the distance groups. If, however, analysis is further restricted to temperatures t - y18C and t - y28C, a
more consistent distance relation will emerge. In fact, Fig. 9 and Fig. 10 display attempts at extrapolating off-site snow fraction information under these conditions. For
Ž .
distances above 100 km the numerical analyses non-parametric Wilcoxon tests demon- strate D-groups systematically biased away from zero, although 25–75 percentiles of the
Box Plots generally are within 0.02 levels, i.e., less than 2. A possible conclusion would consequently be that information concerning snow can
safely be extrapolated from off-site measurements situated less than 100 km away if the temperature is t - y18C.
4. Discussion
In this study, the defined on-site off-site D-differences were created to reflect spatial Ž
. variability of the four controlling variables V s wind speed
during precipitation , Ž
. Ž
. I s rain intensity
liquid precipitation , T s temperature during precipitation , and
Ž . a s snow fraction through the correction factors K , and K
from Eq. 1 . Other
1 2
Ž .
authors have contributed by analyses e.g., Mortensen et al., 1999 of variability of either one or more of these variables in a standard frame of analysis, where, e.g., wind
measurements at a number of stations constitute the data. While such analyses create stochastic models to study temporal and spatial variability based solely on wind
measurements, it has been an important practical aspect of the present analyses to conduct and define analyses of differences in terms of observed consequences for the
calculations of the correction factors. cf. the aim of analyses stated earlier: how far away from a gauge can values of the controlling variables be sampled with only minor
Ž . consequences for the level of correction factors calculated through the model 1 ? It is
assumed that the on-site measurements of precipitation and controlling variables are collected under conditions specified for a standard synoptic weather station.
The analysis strategy can be viewed as a simple transformation of the four-dimen- Ž
.
2
sional independent variable a , V, T, I utilizing knowledge of residual errors s and
s
s
2
from the original fitting of the model.
r
During the analyses, which aimed at revealing relations dependent on distance only, the data were sub-grouped according to two important background factors: time and year
Ž .
Ž .
month and region WestrEast . The structure revealed in Figs. 4–10 should be, ideally, invariant towards such subdivisions of data.
The effect of regionalization vanished. However, in the general residual errors when test statistics were calculated across the 8-year study period 1989–1996, and only in
combination with a further restricting of the observations to the winter months, this regionalization becomes weakly visible.
The effect of subdividing data according to month of year can be visualized in Fig. 11 and Fig. 12. These figures display a subdivision of Fig. 4, in which all four variables
a , V, T, I are extrapolated from off-site into two seasons: summer and winter. It is
Ž .
Ž .
Fig. 11. General distance relations. Difference Dif, y-axis vs. distance x-axis between on-site and off-site correction factors in case of all four independent variables sampled off-site. Winter season.
Ž .
Ž .
Fig. 12. General distance relations. Difference Dif, y-axis vs. distance x-axis between on-site and off-site correction factors in case of all four independent variables sampled off-site. Summer season.
characteristic for these subdivisions that the distance related structure remains the same, Ž
. but ‘‘summer’’ shows less variability shorter Box Plots compared to ‘‘winter’’.
5. Conclusions
