Question Asked

I would like to understand how the spatial variability of forage fish in the California Current Ecosystem is related to the spatial pattern of seascape classes (based on remotely sensed sea-surface variables)? In exercise 1, I will asking “what is the spatial pattern of forage fish in the California Current ecosystem?” In order to address this question, I will be testing the use of different types of interpolation on my point-data.

Approaches Used and Methods

To address these questions, the Kriging Interpolation and Inverse Distance Weighting Interpolation tools were employed in ArcMap. All processes were completed in ESRI ArcMap 10.6.1. Interpolation is described as a method of constructing new data using existing data as references. In spatial and temporal analyses, there are a range of different types of interpolation that can be used.

The original data, which includes a series of about 1300 trawls, the catch per unit effort (CPUE) per species per trawl, the latitude, longitude, and water column depth of each trawl, and the functional group of each species caught, were loaded into ArcMap using the “Display X,Y Point Data” function. The four functional groups used in this analysis are Forage, Young-of-the-Year Rockfish (YOYRock), YOYGround, and crustaceans. In the case of this analysis, all fishes that are part of the YOYRock functional group were included.

Representation of the raw YOYRock Trawl data in ArcMap

After the data were uploaded, they had to be converted to feature classes. For the purposes of this exercise, all trawl data from 2002 to 2015 was included as one feature class, though the way in which the data are organized make it easy to break the trawls down at a finer temporal resolution. The result was a Point Shapefile that was then binned into four abundance groups to make interpretation easier. The IDW and Kriging tools (from the “Spatial Analyst” Toolbox) were then employed. The base equation for both interpolations is virtually the same, and both are commonly used methods for continuous data in point form, but there are some major differences in the calculation of some of the stated variables:

Representation of the equation used to assign values to missing cells using the IDW and Kriging methods. Z(si) = the measured value at the ith location, λi = an unknown weight for the measured value at the ith location, s0 = the prediction location, and N = the number of measured values

Z(si) = the measured value at the ith location, λi = an unknown weight for the measured value at the ith location, s0 = the prediction location, and N = the number of measured values

1) IDW: IDW, or Inverse-distance weighting, is what’s known as a deterministic interpolation method, as it relies on surrounding values to populate the resulting surface. One of the major assumptions with using IDW is that it assumes that the variables being mapped decrease in influence linearly as you move away from a given value. In IDW, the weight given to the “measured value at the ith location” is solely calculated linearly, decreasing as you move farther away from a given value. In this case, the “power” value, which corresponds to the weight, was the default 2.

2) Kriging: Kriging is an interpolation method based on geostatistics including autocorrelation. The equation used to calculate the missing values is the same as for IDW, except that the weight variable is calculated using a mathematical function within a certain specified radius of the missing value. For this reason, one of the main assumptions when using Kriging is that the “distance or direction between sample points reflects a spatial correlation that can be used to explain variation in the surface.” (ESRI, ND).

Results

The resulting interpolations can be found below. I’ve included output that focuses on the significant region of Monterey Bay to provide context regarding the proximity of the trawls to one another and to show detail on the boundaries of the interpolations.

Full Interpolation using IDW

Full Interpolation using Kriging

Detail of IDW in Monterey Bay, CA

Detail of Kriging in Monterey Bay, CA

Critiques of Methods

Any analysis of the results will conclude that the Kriging Tool provided a much more robust interpretation of the same patterns that can be observed in the original data and in the IDW interpolation. Both interpolations displayed significant patterns near Monterey Bay, and the Kriging Interpolation also represented additional areas of higher abundance north of San Francisco. While I do believe that both interpolation methods provide a good place to begin analysis, I believe that several adjustments will have to be made in order to create a useable result.

My first mistake was using the entire time series – since the interpolations are distance-based and extremely sensitive to points within close proximity to one another, the clear clusters of point most likely influenced the interpolations. A next step for me will be breaking the data down to an annual resolution, as I feel that shapefiles with one point at each trawl location will provide better data for interpolation. Additionally, this will provide multiple maps, which will allow for a chance to observe how the modeled patterns of YOYRock abundance have changed over time.

Another next step will be exploring the fine adjustments available within each interpolation method. I now have a greater understanding of the mechanics which drive IDW, so I’m eager o rerun the analyses at different powers to see how each impacts the interpolation. Similarly, the radius used to decide which points are considered while calculating a Kriging Interpolation can be adjusted, so that will be done in the future as an experiment.

Finally, I ran out of time to explore the symbology of the results – I hypothesize that classification by a smaller number of classes would result in more robust interpolation maps, as the visualizations now show a vast majority of the space to fall into the lowest class. The interpolation data is relatively bimodal in nature, so an adjustment in the symbology tab would likely result in a a more accurate and precise representation of abundance.

Overall, I see interpolation as a valuable way to identify spatial patterns from point data. In the case of species abundance data, I believe that Kriging is the superior method, as it does not have the linear influence assumption that’s baked into IDW. Additionally, the geostatical methods used in Kriging generally allow for a more robust and precise interpolation regardless of the type of continuous data being used.

The next steps mentioned above will be taken before the presentation of Tutorial 1.

References

http://desktop.arcgis.com/en/arcmap/10.3/tools/3d-analyst-toolbox/how-idw-works.htm

http://desktop.arcgis.com/en/arcmap/10.3/tools/3d-analyst-toolbox/how-kriging-works.htm

Santora, Jarrod & Hazen, Elliott & Schroeder, Isaac & Bograd, Steven & Sakuma, KM & Field, JC. (2017). Impacts of ocean-climate variability on biodiversity of pelagic forage species in an upwelling ecosystem. Marine Ecology Progress Series. 580. 10.3354/meps12278.