GEOG 566

         Advanced spatial statistics and GIScience

May 24, 2017

Tutorial 2:

Filed under: 2017,Tutorial 2 2017 @ 11:59 am

Research Question

Building upon my question from exercise 2, my research question for exercise 3 seeks to answer how the covariance between SCF and EVI within a wildfire perimeter change over time following the wildfire.

Approach/tools used

For this exercise, I utilized a variety of software programs. While the overall goal of variogram creation required using R, ArcMap and Excel were used significantly in order to process the data into a usable format. As a result, much hopping between programs was required, which was undoubtedly quite tedious/frustrating at times but ultimately proved to be a useful learning experience.

Analysis procedure

To create a cross variogram in R using the gstat package, the process is much smoother using data in table format. As a result, one of the main challenges of creating a cross-variogram was converting my raster data into usable tabular data. To accomplish this, I first converted the SCF and EVI rasters into point shapefiles, then used the “Add XY Coordinates” tool in ArcMap to add two fields to the point shapefiles containing the X- and Y-coordinate information. Next, the attribute table from each point, shapefile was converted to a CSV table. The final step before stepping back into R was to combine all EVI and SCF data for each year into a single CSV table to ease the script writing in R.

After creating the combined EVI-SCF table, I noticed that a few of the columns had different numbers of records. It turns out that I used a slightly different extraction method for a few SCF layers – a product of conducting this analysis across multiple days and not taking diligent notes on the layers used. After correcting this issue, I read the cleaned table into R and created cross-variograms using the code snippet shown below.


My hypothesis for the years following the wildfire was to see the strongest covariance in the first year, then decreasing overall covariance in each year afterwards. However, the plots below tell a different story. There are a lot of things going on in the time-series of cross-variograms, but a couple of evident trends stick out to me. First, although each year shows two clear bumps in the cross-variogram, the lag distance of those bumps shift significantly from year to year. My guess would be that the initial shift from pre-fire to the first year post-fire was primarily due to the variation in burn severity across the landscape. The shifts in ensuing years may be due to varying rates of vegetation recovery or perhaps due to changes in snowpack distribution caused by the wildfire.

Another fascinating pattern is the change in sign of the covariance. Before the wildfire, the covariance is mostly negative except for a few thousand meters of lag distances. This suggests that between most pixels within the burn area, SCF and EVI vary negatively – if snowpack increases between two points, vegetation generally decreases between those two points. Following the wildfire, however, the covariance becomes more and more positive overall. By year 3 following the wildfire, at all distances the covariances are positive, but still showing a similar bumpiness as in the pre-burn cross-variogram. This outcome was a bit baffling, as I would expect the relationship to be strongest (most positive) in the first year post-fire, with a gradual retreat to the pre-fire state.

Another pattern of significance is the consistent cross-variogram valley that occurs at about 5000 meters in each year, even though the peaks on either side shift from year to year. This can be interpreted as the between-patch distance, and is perhaps the more important result of this method – that from year to year, even before the wildfire, the landscape shows similar distances between patches.

Figure 1: Pre-fire (2005) cross variogram between SCF and EVI

                     Figure 2: First year post-fire (2007) cross variogram between SCF and EVI

Figure 3: Second year post-fire (2008) cross variogram between SCF and EVI

Figure 4: Third year post-fire (2009) cross variogram between SCF and EVI

Method critique

By creating cross-variograms for each year following a wildfire and the pre-fire year, I was able to discern the patchiness of the EVI and SCF data as well as the shifts in the snowpack-vegetation relationship. The persistence of the bumpiness across years strengthens the evidence of two patch sizes, but the shift in bump locations results in a cloudier picture of exact patch size.

One disadvantage to this approach was the inability to determine the strength of the SCF-EVI relationship within a given year’s cross-variogram. After researching the interpretation of covariance, it became clear that covariance values can only tell you the sign of a relationship, but cannot lend any insight into the magnitude of the relationship because the data is not standardized. However, because I generated covariograms across multiple years, I was able to glean information regarding the relative shifts in covariance, which is ultimately the type of information I’m most interested in producing.

For the final project, I plan on generating additional covariogram for the next couple of year in order to observe how the covariance continues to change. I’m interested to see at what point the covariance plot starts to look like the pre-fire condition.

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