Question

How is the occurrence of landslides in western Oregon related to the rate and timing of rainfall? The Northwest River Forecast Center (NWRFC) archives 6-hour rainfall accumulation from more than 2000 recording stations throughout the Pacific Northwest (Figure 1). The challenge is that landslides do not tend to occur in the immediate proximity of these stations, and spatial interpolation must be performed to estimate rainfall amounts at landslide locations.

Figure 1: Location of rainfall recording stations provided by the NWRFC.

The Tool and its Implementation

Kriging was selected over inverse distance weighting to better account for variations in rainfall from east to west. Performance of kriging occurred in Matlab to allow for a better selection of inputs, and to simplify the task, which involved kriging every 6-hour measurement for December (124 times).

Kriging works by weighting measured values using a semivariogram model. Several semivariograms were examined to better identify which model would best fit the dataset (Figure 2).

Figure 2: Examples of semivariogram fits to NWRFC rainfall data.

Based on Figure 2, the exponential semivariogram appeared to be the best choice. Another option is the search radius (i.e. how far the model looks for data points). This value was also varied to illustrate the notion of a poor semivariogram fit (Figure 3).

Figure 3: Examples of varying the search radius (lag distance). Search radii from left to right: 1 degree, 5 degrees, 0.2 degrees.

Once each of the 124 surfaces were produced, values were extracted to the locations of major landslides from this past winter. The extracted values were later used to produce rainfall versus time plots, which are described in the next section.

Results

To simplify results for this project, only one landslide is shown. The Highway 42 landslide occurred on December 23, 2015, closing the highway for nearly one month and costing the Oregon Department of Transportation an estimated $5 million to repair. Rainfall versus time profiles were produced for three popular semivariograms (spherical, exponential, and Gaussian) to gauge the influence of choosing one method over another (Figure 4).

Figure 4: Comparison of results obtained from the different semivariograms and PRISM.

Figure 4 shows little effect due to changing the semivariogram model, which is likely a result of having limited variability in rainfall measurements and the distribution of recording stations near the location of the Highway 42 landslide.

To verify the results of this exercise, PRISM daily rainfall estimates were downloaded for the corresponding time period, and compared (Figure 4). This comparison shows that, while the PRISM data does not capture spikes in rainfall amount, the overall accumulation of rainfall appears to be similar, implying that kriging was effective for this application.