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SSCI 583: Spatial Analysis and Modeling

PROJECT 5 – INTERPOLATION AND ANALYSIS OF SURFACES

Workflow Due: April 23 th , 11:59pm PT

Report Due: May 2nd (the last day of the semester) 11:59pm PT

ASSIGNMENT DESCRIPTION

For Project 5, you will explore the world of spatial interpolation, specifically with respect to bathymetric data in the Gulf of Mexico. The techniques you will learn are not specific to the Gulf of Mexico. You will learn about various interpolation methods, when they are appropriate, how to compare them, and their levels of accuracy when compared to continuous bathymetric data.

In a perfect world (for analysis), we would have spatial data covering every phenomenon, at every scale, and we could represent and operationalize it. In the real world, we have data collection points that are geographically dispersed, sometimes systematically, and sometimes based on a combination of factors including natural barriers, cost, and convenience.

Interpolation is the process of estimating what is happening between data collection points by analyzing the location and attributes of those known points to fill in the unknowns. This involves taking a series of points and making a surface. Because this is spatial data, the concept is guided by Tobler’s First Law of Geography: points that are closer together will generally share more similarities than points further apart. While intuitive, the concept raises many questions. What criteria constitute similarity? What spatial factors interrupt it? What are the consequences of aggregating characteristics across space? As with most spatial analysis techniques, interpolation ends up being intuitive in theory but more complex in practice.

Interpolation can be used to understand any spatially continuous phenomenon, such as elevation, precipitation, or concentrations of pollutants in the air. This project employs point bathymetry data – the depth under water of sea/lake floor – to interpolate a bathymetric surface. It is also possible to estimate bathymetry values using remotely sensed imagery. These methods are not mutually exclusive; some of the readings associated with this assignment will show the way in which these methodologies can complement each other.

There are a variety of interpolation techniques, and the decision of which one to use will have an effect on your conclusions. These techniques include inverse distance weighting, kriging, nearest (natural) neighbor, thin-plate spline, and trend analysis. Part of this exercise will include learning how these different techniques differ from one another.

Your required tasks are:

● Use kriging, as well as one additional interpolation technique of your choice, to create at least two bathymetric surfaces

● Use the raster calculator to assess the difference between your created surfaces

● Compare the results of your chosen interpolation methods with remotely sensed bathymetric data

Assigned readings and web courses are chosen to help you understand and implement appropriate workflows. Data layers for the required analyses are available to you on the SSI server (see below).

You will work with a partner for this assignment (unless you prefer to work on your own). Each partner must complete approximately half the technical work and half the written product. It is not acceptable to have one partner do all the technical work and the other partner do all the writing. Your final report will contain a summary of your individual contributions to the overall project.

LEARNING OBJECTIVES

● Choose and execute interpolation methods to assess ocean bathymetry using point data and analyze the results

● Compare the accuracy of different interpolation methods with one another, as well as with a continuous bathymetric survey

● Create maps which clearly identify the results of interpolation analyses

● Write a succinct description of analyses and results

INSTRUCTIONS

1. Read/watch the following. These readings are recommended sources for background information of the theory and implementation of spatial interpolation. URLs are provided in Sources and Resources, below.

● Amante, C.J. and Eakins, B.W. 2016. Accuracy of interpolated bathymetry in digital elevation models. Journal of Coastal Research, 76(1), pp. 123-133.

This paper is a good, accessible example of the sort of project you are doing on a smaller scale. The researchers used three different common interpolation techniques and assessed their relative accuracy.

● Kanno, A., Koibuchi, Y. and Isobe, M. 2010. Statistical combination of spatial interpolation and multispectral remote sensing for shallow water bathymetry. IEEE Geoscience and Remote Sensing Letters, 8(1), pp. 64-67.

This article looks at the intersection of interpolation and remote sensing in ocean bathymetry, and proposes novel approaches to the integration of the two. This is not something you will actually conduct in this project, but definitely worth thinking about.

● Esri help pages:

o Raster Interpolation toolset

o Understanding Interpolation Analysis

o Get started with Geostatistical Analyst in ArcGIS Pro

o Comparing Interpolation Methods: How Kriging Works

o Make a chart

o Box-Cox, arcsine, and log transformations

2. Complete the following short Esri web course

● Performing Spatial Interpolation using ArcGIS

3. Inspect your data. Data is available on the H drive at 583/Oil_and_Natural_Gas_Platforms.gdb

● Point data of oil and natural gas drilling platforms of the coast of the US (Homeland Infrastructure Foundation-Level Data, US Department of Homeland Security)

The data layer has an attribute for water depth. You can learn more about the data at: https://hifld-geoplatform.opendata.arcgis.com/datasets/oil-and-natural-gas-platforms The data is projected into WGS 1984 Web Mercator.

4. Plan the required analyses. You should take the following steps and make the following decisions along the way:

● Project your data into a projection more suitable for spatial analysis. Web Mercator is fine for visualization but not appropriate for spatial analysis. Read the Esri blog post “Measuring distances and areas when your map uses the Mercator projection” (URL in Sources and Resources, below) and recall the project in 581 in which you compared distances and areas in data projected in UTM and Web Mercator.

● Create a new layer using only the points located in the Gulf of Mexico.

● Assess your data for kriging.

o Is there a global trend? You can assess this with the Trend tool in ArcGIS. When you run the Geostatistical Wizard you can then use the knowledge gleaned to note whether there is a trend or not.

o Is the data normally distributed? You can assess this by creating charts, such as a histogram and QQ-plot in ArcGIS Pro. Transform your data if necessary.

o Is the data stationary? You could assess stationarity across the region by assessing the variance or standard deviation of sub-regions of the data, and seeing if they are similar. If stationarity is a problem, you could, for instance, run kriging on sub-regions of the data, and later combine the results into one surface.

o You may not be able to achieve perfectly normally-distributed and stationary data groups, but you should be aware of the issues and address them if you can.

● Choose one kriging method. After doing analysis using the default parameters in the Geostatistical Wizard, experiment. As you experiment, note how your choices affect the outcome of the kriging.

● Choose and run a second interpolation method based on your understanding of the data and methods as gleaned from readings listed above.

● Use the raster calculator to assess the difference in estimated values across the study region using your final results. How do the two rasters, based on the two different interpolation approaches, compare to each other? Which one provided a greater estimate in what areas? You can use the ID of the individual platforms as geographic reference points.

● Compare the results to an existing bathymetry data set. If you search online (try keywords such as: Gulf of Mexico bathymetry GIS data) there are multiple data sets available including NOAA’s acoustic bathymetry data (see URL below). How was your chosen data set created? What do you find when you compare your interpolation results with this continuous surface?

There is not one right way to complete the required tasks. Thus, your goal is not to find the one right answer for each task. Your goal, instead, is to complete the tasks in one of a countless number of productive ways.

5. Write up and share your proposed workflows and initial results. Create a short summary of your workflow and work completed to date and post to the appropriate discussion forum (one per partnership) (1.5 pts.)

a. (If neither partner can attend the synchronous session) Put “NON-SYNCHRONOUS” in the subject line of the post.

b. Explain the steps you’ll take to achieve the intended results. You can supplement this with workflow diagrams. Be as specific as possible.

6. Workshop your workflows/initial results with your classmates. Each partner must EITHER attend the synchronous class session to collaborate with classmates to improve each other’s work; OR review the workflows submitted by other students who cannot attend the synchronous session and offer feedback in the Discussion Forum to at least three teams. (1.5 pts.)

7. Revise your proposed workflows as necessary and continue with your work to complete the project.

8. Create basic maps of your study area and maps of your key results. These should include both interpolation methods, as well as a comparison with existing bathymetric data. These should be finished maps, not screenshots of your ArcGIS window, including a comprehensible legend, north arrow, and scale bar.

9. Write up your results in a short report. This should be a finished report, using your own (no quotations), high-quality language, free of spelling and grammatical errors, citing to sources as necessary. You should write out prose in complete sentences for each section, not just use bullet points. The report need only be long enough to clearly respond to the listed topics for each of the following sections:

a. Introduction, including Study Area. State the goal of your project with a quick overview of the topic, methods, and study area with a basic, finished map. (1 pt.)

b. Data and Data Processing. Include a description of the data, including its original projection, and a statement and explanation of the projection you used. (0.5 pt.)

c. Methods. Description of steps for each workflow. Your written description should explain and justify ALL your choices – why did you select the interpolation techniques that you did (not just your second technique, but your choice of kriging method)? What were the model and parameter choices you made, and why did you make them? How did you compare your results with each other? (4 pts.)

d. Results. Description of the results of each analysis, including finished maps. Clearly identify the results of each analysis, including kriging and your technique of choice. Discuss how the two techniques compare with one other and with the existing data set. Describe the existing data set, including how it was created. Maps are not sufficient; you must describe the results of each analysis in your text and describe what your maps show. (3 pts.)

e. Discussion. Critical assessment of your results. Identify any limitations in your results, such as data issues. You can also be creative in how you assess your results. You could circle back to the related literature (from discussion assignments or your own research) and compare your results with those obtained in case studies you reviewed. (1 pt.)

f. Reference list. Offer a list of full academic citations to the sources you cited throughout your document. Citations should be provided for all additional research, web courses, and data sources that you examine and reference in the written report. (0.5 pt.)

g. Appendix. Each partner must itemize their contribution to the overall effort, with each aiming for 50% technical and 50% written contribution. (No points for this, but points may be deducted if the work is not split in this type of way.)