By Russ Frith University of Alaska at Anchorage Civil Engineering Department Estimating Alaska Snow Loads

Abstract

Problem Statement Snow loads are an important aspect of structural design in cold climates. In some areas, the weight of accumulated snow on a structure represents the most significant load that the structure will endure in its lifetime. In Alaska, snow load data are calculated from snow water equivalent (SWE) measurements at weather/climate stations. There are relatively few climate stations in Alaska that reliably report SWE measurements. As a result, SWE measurements or estimates are unknown for most of the land area in Alaska. The presentation presents a method for reliably estimating SWE at ad-hoc locations in Alaska. The estimation technique uses ArcMap’s Geostatistical Analyst extension.

Front Matter : Model A SWE estimation model was selected. Snow depth was estimated using the Helsinki University of Technology snow emission model-based iterative inversion algorithm. Pullianen, J.T., Grandell, J. & Hallikainen, M. (1999). HUT snow emission model and its applicability to snow water equivalent retrieval. IEEE Transactions on Geoscience and Remote Sensing 37(3), Results of this model are readily available in NETCDF files from the National Snow and Ice Data Center. This model was applied to 30 years of European Space Agency satellite observations covering Alaska. The data produced from this model have rigorous quality control checks. This is one of the few models applied to physical observations from a long period of record and which outputs are publicly available. Other comparable models exist but many of these models’ outputs are not publicly available or are not processed for such a lengthy period of record.

Front Matter : Data 1.Global Snow Monitoring Network makes daily satellite observations. The observational data is fed into the SWE model which then estimates SWE for given latitude and longitude on a given grid that covers Alaska’s land area. 2.SWE estimates from the model are bundled into NETCDF. 3.The NETCDF files are held by the National Snow and Ice Data Center, 4.The NETCDF locations are converted into ArcInfo shape point shape files. 5.NETCDF (Network Common Data Form) is a product of Unidata Corporation is a set of software libraries and self-describing, machine-independent data formats that support creation, access, and sharing of array-oriented scientific data.

Front Matter : Data 1.Each green dot represents a satellite location for a modeled SWE estimate for a 25 km grid cell starting around Each blue dot represent a Global Historical Climate Network SWE monitoring site. 3.At each location, a 50 year mean recurrence interval (MRI) value of SWE was calculated. 4.The values were stored in a geodatabase.

SWE Point Estimates

SWE Estimation Methodology

Predicting SWE at Satellite Sample Points Use Kriging to Estimate 50 Year-MRI 1. Kriging Fits function to a)Specified number of points, b)All points within specified radius. 2. Kriging is based on the idea that one can make inferences regarding a random function Z(x), given data points Z(x 1 ), Z(x 2 ), …, Z(x n ). 3. The basis of this technique is the rate at which the variance between points changes over space. 4. The variance is expressed in a semivariogram which shows how the average difference between values at points changes with distance between points. 5. Z(x) = m(x) + g(h) + e a)m(x) is the constant mean b)g(h) is a random spatially correlated component c)e is the residual error

Variogram The amount and form of spatial autocorrelation can be described by a semivariogram that shows how differences in values increase with geographical separation. Semi-Variogram A semi-variogram is a function that relates semi-variance (or dissimilarity) of data points to the distance that separates them.

Calculating the Semi-Variogram 1.To compute a variogram, need to determine how variance increases with distance. 2.Begin be dividing the range of distance into a set of discrete intervals. 3.For every pair of points, compute distance and the squared difference in z values. 4.Assign each pair to one of the distance ranges, and accumulate the total variance in each range. 5.After every pair has been used (or a sample of pairs in a large dataset) compute the average variance in each distance range. 6.Plot this value at the midpoint distance of each range.

Example

Scatter Plots For each h-scatterplot, a value γ is calculated. These values are used to fit a variogram model.

Kriging Example Estimate a value for point 0 (65E, 137N), based on the seven surrounding sample points. The table indicates the (x,y) coordinates of the seven sample points, their corresponding values of V, the variable of interest and their distances from point 0.

Spatial Continuity Parameters

Kriging Matrices

First, find the distance matrix Covariances are calculated based on the distance between points using the model:

Kriging Matrices

Results

ArcGIS & Kriging Using the Statistical Analyst Extension

Recall that the only places where SWE (i.e. snow load) are measured directly are at GHCN stations. GHCN SWE Monitoring Site The green dots are locations where SWE is estimated by the model. How good are these estimates? Using Kriging, predict the GHCN measurements from the model estimates.

Predicting Measured Values from Modeled Calculations – Results!

The Process –Decision Making Using GIS