Scaling Problems in Snow Hydrology
Gnter Blschl 1 and Kelly Elder 2
The concept of scale can be used to quantify three different things, (a) a natural process (such as the
correlation length of the spatial SWE variability); (b) a measurement (such as the size of a snow
density sample or the footprint of the satellite sensor), and (c) a model (such as the DEM grid size).
We denote the different types of scale as process scale, measurement scale, and model scale, respec-
tively. Scaling problems arise because measurements never capture all the detail of the natural varia-
bility and because model scales are generally different from the measurement scales. Hence some
sort of interpolation, extrapolation, aggregation, or disaggregation of the data is needed. We will
discuss three alternative genres of methods for interpolation, extrapolation, aggregation, or disaggre-
gation. In all three genres we view the effects of measurement scales and model scales as a filter
where the ratios of measurement scale on process scale, and model scale on process scale are the
driving parameters. Methods of the first genre are based on the spatial correlation structure of, say
,
SWE or snow cover. Based on the variogram we demonstrate that (i) aggregation always reduces
variance, (ii) large footprints of satellite images will bias the spatial variance, (iii) that these and
other biases introduced by the measurement scale and the model scale can be estimated and correct-
ed by regularization methods. Methods of the second genre consist of running physically based
distributed models. The main advantage over the first method is that here we can represent nonlinear
snow processes, and that we can explicitly account for process controls such as solar radiation and
terrain effects. However, there are a number of fundamental scaling problems with distributed mod-
els, some of which are related to the incompatibility of the process scale and the model scale of the
computational grid. We will discuss grid resolution effects on model performance and whether there
exists an optimum grid size. We will give methods for estimating subgrid variability and point to
potential avenues for parameterising subgrid variability. Methods of the third genre attempt to com-
bine the advantages of the other two. They are sophisticated enough to retain the important processes
controls, but parsimonious enough to avoid some of the scale issue of methods of the second type
and to capitalize on some of the analytical results of methods of the first type.As an example we will
discuss the SWETREE model, which uses binary decision trees (regression trees) to estimate the
spatial distribution of SWE. This models uses physically based independent variables (net solar
radiation, topography, soil and vegetation cover type) and SWE measured at individual points as
inputs. While most of the presentation will focus on physical snow processes, similar conclusions
apply and similar methods are applicable to chemical and biological processes.
1
Institut fr Hydraulik, Gewsserkunde und Wasserwirtschaft, Technische Universitt Wien, Karlsplatz 13/
223, A-1040 Wien, Austria
2 Department of Earth Resources, Colorado State University, Fort Collins, CO 80523, USA
37
Previous Page
