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         Advanced spatial statistics and GIScience

May 4, 2017

Tutorial 1: Using a Geographically Weighted Regression to assess the spatial relationship between blue whales and chlorophyll-a

Filed under: 2017,Tutorial 1 2017 @ 4:41 pm

Research Question

The goal of my spatial problem is to assess the relationship between blue whales in the South Taranaki Bight region of New Zealand and the environmental factors which define their habitat and influence their spatial distribution. Chlorophyll-a (chl-a) concentration is an indicator of productivity in the marine environment. Chl-a can be remotely-sensed, and the concentration reflects the abundance of phytoplankton, the tiny photosynthesizing organisms which form the base of the marine food web. Blue whales do not directly feed on phytoplankton. However, krill, which feed on aggregations of phytoplankton, are the main prey type for blue whales. Remotely-sensed chl-a can therefore be used as a proxy for the location of productive waters where I might expect to find blue whales. For this exercise, I asked the following question:

“What is the spatial relationship between blue whale group size and chlorophyll-a concentration during the 2017 survey?”


I downloaded a chl-a concentration raster layer and used the “extract values to points” tool in Arc in order to obtain a chl-a value for each blue whale group size value. I then used the geographically weighted regression (GWR) tool from Arc’s spatial statistics toolbox in order to investigate the spatial relationship between the whales and the concentration of chl-a.


The chl-a concentration layer was downloaded from the NASA Moderate Resolution Imaging Spetrometer (MODIS aqua) website. MODIS data can be accessed here, and available layers include numerous sources of remotely-sensed data besides chl-a concentration (Figure 1). Chl-a concentration values are averaged over a 4 km2 spatial area and a one-month time period. I downloaded the raster for February 2017, as our survey lasted for three weeks during the month of February.

Figure 1. NASA Moderate Resolution Imaging Spectrometer (MODIS) data sources, including chlorophyll-a concentration which is used in this tutorial.

I then used the extract values to points tool, which is located in the extraction toolset within Arc’s spatial analyst toolbox, to extract values from the chl-a concentration raster for each of the blue whale sighting data points. This resulted in a layer for blue whale sightings which contained the location of each sighting, the number of whales sighted at each location (group size), and the chl-a concentration for each location (Figure 2).

Figure 2. Blue whale sighting locations and group sizes overlaid with chlorophyll-a concentration.

The geographically weighted regression tool is found within the spatial statistics toolbox in Arc. The dependent variable I used in my analysis was blue whale group size, and the explanatory variable was chl-a concentration. I used a fixed kernel, and a bandwidth parameter of 20 km (Figure 3). Functionally, what this means is that the regression looks at point values that are within 20 km of one another, and then fits a linear relationship across the entire study area.

Figure 3. The geographically weighted regression tool in Arc’s spatial statistics toolbox.


The results of the GWR are shown graphically in the figure 4. The GWR fits a linear equation to the data, and the values which are plotted spatially on the map are coded according to their deviation from their predicted values. Many of the points are > 0.5 standard deviations from their predicted values. One point, which appears in red in figure 4, is > 2.5 standard deviations above its predicted value, meaning that blue whale group size at that location was much higher than expected given the chl-a concentration at that same location.

Figure 4. Result of the geographically weighted regression (GWR). Color codes represent the deviation from the expected values for blue whale group size according to the chl-a concentration value at that location.

The attribute table from the GWR output layer shows all of the components of the equation fitted by the GWR, as well as the predicted values for the dependent variable according to the fitted linear equation (Figure 5). It appears that there are several points which are far from their predicted values according to the GWR, such as the row highlighted in figure 5.

Figure 5. The attribute table associated with the geographically weighted regression (GWR) output layer. The highlighted row is an example of where the observed value was dramatically different from the predicted value.

The local R2 values are < 0.04 for all values, demonstrating that the data do not fit the relationship fitted by the GWR very well at all. My interpretation of this result is that, across the spatial scale of my study area, the relationship between blue whale group size and chl-a concentration is not linear. This is apparent from looking at the raw data as presented in figure 2, as it appears that there are several whales in an area of high chl-a concentration and some large groups of whales that are in an area of low chl-a concentration.

Critique of the Method

Although the results showed that there was no linear relationship between blue whale group size and chl-a concentration across the spatial extent of my study area, this is a very useful result. The ecological relationship between blue whales and chl-a concentration is not direct—remotely-sensed chl-a concentration indicates locations of productivity, where phytoplankton are present in high abundance. These areas of high phytoplankton are presumed to drive the location of dense aggregations of krill, the prey source for blue whales. However, there is likely both spatial and temporal lag between the phytoplankton and the blue whales. The fact that the ecological relationship of the two variables investigated here is an intricate one is reflected by the fact that a simple linear relationship does not capture how the variables are related to one another in space. I look forward to exploring this relationship further, perhaps incorporating other environmental factors that contribute to the location of krill patches such as sea surface temperature.

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