Spatial Autocorrelation (Moran’s I): This tool measures spatial autocorrelation using feature locations and feature values simultaneously.   The spatial autocorrelation tool utilizes a multidimensional and multi-directional factors.  The Moran’s I index will be a value between -1 and 1. Positive spatial autocorrelation will show values that are clustered. Negative autocorrelation is dispersed. Random is close to zero. The tool generates a Z-score and p-value which helps evaluate the significance of the Moran’s index.

Figure 1: Calculations used for the Moran’s I tool. (ESRI image)

The output of the Moran’s I tool can be found in the results section of ArcGIS.  Upon opening the HTML report for the Moran’s I results you will see a graph showing how the tool calculated the data and whether or not the data is dispersed, random, or clustered.  This report will also include the Moran’s Index value, z-score, p-value.  It will also provide a scale for the significance of the p-value and critical value for the z-score.

Figure 2: Sample output for the Moran’s I tool. (ESRI image)

Data and Analysis

Before conducting this test, I sampled the SST and the CHL-a values at each of the feature locations (sea turtle locations) using the Extract Multi Values to Points tool. This tool “Extracts cell values at locations specified in a point feature class from one or more rasters, and records the values to the attribute table of the point feature class.”

Figure 3: Sea turtle locations in the Gulf of Mexico, derived from http://seamap.env.duke.edu/

Figure 4: Chlorophyll-a(mg/m^3) data for January 2005 within the Gulf of Mexico, derived from NOAA.

Figure 5: Sea Surface Temperautre (Celsius) data for January 2005 within the Gulf of Mexico, derived from NOAA.

I tested the spatial autocorrelation of chlorophyll-a and sea surface temperature at each feature location.  The conceptualization of spatial relationships method used was the inverse distance and the Euclidean distance measure was used for the distance method.  I selected a 500km distance (smaller distances were too small for the study site).

Results:

Sea Surface Temperature: The results of the spatial autocorrelation tool suggest that the pattern of sea surface temperature at each feature location is clustered. The Moran’s Index was 0.402514, the z-score was 2.608211, and the p-value was 0.009102.  Since the critical value (z-score) was greater than 2.58 there is less than 1-percent likelihood that the clustered pattern is a result of random chance.

Figure 6: Sea surface temperature results for Moran’s I tool.

Chlorophyll-a :  The results of the spatial Autocorrelation tool suggest that the pattern of chlorophyll at each feature location is clustered.  The Moran’s Index was 0.346961, the z-score was 2.216243, and the p-value was 0.026675.  The critical value (z-score) was less than 2.58 but greater than 1.96 thus suggesting that there is less than 5-percent likelihood that the clustered pattern is a result of random chance.

Figure 7: Results of the spatial autocorrelation Moran’s I for chlorophyll-a at the leatherback sea turtle locations.

What does this mean:

As suggested in the hotspot analysis there is clustering of the data.  The spatial autocorrelation tool indicates that clustering is occurring with regard to the sea surface temperature and chlorophyll values at their respective locations with regard to sea turtles.   Conducting an ordinary least squared analysis may lead to more information about which factors contribute more to the clustered pattern.