Introduction
Landslides are a very common and devastating hazard in Oregon. Its estimated that the average annual repair costs for landslides in Oregon exceeds $10 million, and that depending on the severity of annual winter storms that number can exceed $100 million (USGS). Besides that monetary losses caused by landslides they are also a danger for anyone who is in the area during a mass movement event. Thus it’s critical that we gain a better understanding of the spatial distribution of landslides in Oregon in order to help protect people and property from these hazards. Most landslides in Oregon occur during the rainy season in western Oregon where the perfect combination of steep slopes and saturated soil meet (Oregon Geology). Thus the location of landslides are directly related to the steepness of slope and soil type in the area. The goal of this report is to describe the general state of landslides in Oregon, find the average length of landslides and then determine a critical landslide length and its probability. The final steps are to describe the overall spatial distribution of landslides in Oregon and discuss how the parameterization of point pattern analysis influences the statistical output.
Methods
For this report the study site is the entire state of Oregon, which coincides with our goal of describing the statewide spatial distribution of landslides. The data was downloaded from Oregon’s Department of Geological and Mineral Industries (DOGAMI) then refined into a single text file which has the landslide events and their spatial characteristics. The dataset provided by DOGAMI contains records of landslides in Oregon that have occurred from 1995-2010. This dataset has information on the length, width, depth, area, slope and type of each landslide along with its geographic coordinates. The data was then imported into R for the purposes of analysis. A quadrant analysis was preformed using 36 quadrants for the analysis. Then a map showing the state of Oregon with the analysis quadrants and the number of points per quadrant was created in R. Next the variance mean ratio (VMR) was calculated using the Mean and Variance. With the VMR, the next step was to perform a test statistic in order to find the chi-square value. Finally a Nearest Neighbor Analysis was conducted using the spatstat package in R. The nearest neighbor analysis found the nearest neighbor for each landslide, then we calculated the R (Standardized NND) value which indicates if it is clustered, random or dispersed then using the test hypothesis we proved weather the data is clustered, random or dispersed using the test-hypothesis formula.
Results
- What is the general state of landslides in Oregon? The dataset used in the report has the recorded location of 4550 landslides throughout Oregon and their associated attributes. For the purposes of describing the general state of landslides in Oregon I chose to focus on the length value since it gives good information on the size and impact of a landslide. Other variables such as area would be good to use but I noticed that not all of the landslides have an area calculated for them. The mean length in feet for landslides is 296.5116 ft, and the median is 100 ft. As well the standard deviation for landslide length is 525.9313 ft with a coefficient of variation of 1.77. This tells us that majority of landslides are around 296.5116 ft in length however since the standard deviation is high we also know that the full range of values is large. This is further confirmed when we look at the skewness and kurtosis of the length variable. The skewness for landslide length is 4.4138, and the kurtosis is 30.8079. This tells us that the data is positively skewed and that it has a leptokurtotic kurtosis.
- What is the average length of landslides in Oregon with a 95% confidence interval? The mean length of landslides in Oregon is 296.5116 feet, and with a 95% confidence interval it has an interval of +- 15.28 ft. This means that the range of landslide length with a 95% confidence interval is from 281.23 ft. to 311.79 ft.
- What is a critical landslide length? What is the probability that a landslide will reach at least this length? For this report one of our major concerns is the amount of damage each landslide causes. One of the ways we can look at this is by looking at the length of landslides and determining a critical length value at which landslides are causing a lot of damage. I choose to look at landslides over 1000 feet in length because at that point it is a major landslide and will likely cause a lot of damage. Of the 4550 landslides recorded there are 322 landslides that have lengths of 1000 feet or more. This means that the probability of a landslide of this length occurring is 322/4550= 0.0708 or 7.08% probability.
- What is the spatial distribution of landslides in Oregon? In order to figure out the spatial distribution of landslides we conducted a quadrant analysis and a nearest neighbor analysis on the study area. The results from the quadrant analysis using 36 quadrants shows that the mean of cell frequency is 126.3889 and the variance is 3708509. When inputted into the variance-mean ratio (VMR) this gives a result of 29342.05. Since the VMR has such a high value this is tells us that it is likely for the data to be more clustered. We test this by computing the chi-square statistic. This gives us a chi-square value of 1026972 and a p value of 0. This confirms that the data set is highly clustered, which makes sense considering landslides in Oregon occur mostly in the Western portion of the state. Below is a map showing the quadrants used for the analysis and the number of points in each quadrant.
The second analysis we did was the nearest neighbor analysis. This analysis gave us a mean nearest neighbor distance (NND) of 625.3597 ft. In order to test if the data is clustered, random or dispersed we first calculated the mean nearest neighbor distance in a random pattern (NNDr) then used this to compute the standardized nearest neighbor index (R). The random nearest neighbor distance value was 3743.233 which means the R value is 0.1670641. This tells us that the data is highly clustered since the R value is very close to 0. Then the test statistic Zn was computed in order to determine if the observed NND is significantly different from the theoretical NNDr, this test statistic outputted a value of -107.4851 which indicates that the observed NND is indeed significantly different from the NNDr. The negative value indicates that the area is indeed clustered.
5. How does the parameterization of point pattern analysis influence statistical outputs? How you choose to set up the point pattern analysis is very important because depending upon how you decide to set up the analysis the results can change. For quadrant analysis this is most apparent when choosing the number of quadrants. This happens because different quadrant sizes will produce different results since different amounts of points will be present depending on the quadrant size. A parameterization problem that affects both quadrant and nearest neighbor is the delineation of the study site. By changing the boundary of our study site we change the results of the analysis, in our example because our study site is the entire state we have a clustered result. However if we made the study site a very small portion of the Western portion of the state we might likely find the distribution of landslides to be less clustered. These issues tie in with the common geographic issue of the modifiable area unit problem.
Discussion
The overall results from this study indicate that on a statewide level the spatial distribution of landslides is clustered. The results from both the quadrant and nearest neighbor analysis indicate that the data is clustered, and the map produced from the quadrant analysis backs up the results because the visible pattern of landslides occurring in the Western part of Oregon is easily view able. By doing the analysis we gain statistical evidence that proves the hypothesis that landslides are highly clustered in Oregon. The broader implications of this study are that since landslides are highly clustered in Oregon, there are specific areas that are at higher risk of landslides than others. Therefore more precaution and prevention techniques should be utilized in areas with higher amounts of landslides. In order to improve this study in the future I would recommend changing the study area to focus on the western portion of Oregon where the majority of landslides are occurring. By making the study area smaller and more focused we can obtain results that are more accurate for that smaller area. By spatially constraining the study area of the majority of the landslides we can hopefully get results that will better help us understand the spatial distribution of landslides at a more local rather than state wide level.
References
Oregon Geology “Landslide Facts” http://www.oregongeology.org/sub/publications/landslide-factsheet.pdf
United States Geological Survey (USGS) “Introduction to Landslide Activities in Oregon” http://landslides.usgs.gov/research/inventory/oregon/