Having endured much frustration trying to use Geographically Weighted Regression to determine relationships between the patch metrics I calculated using FRAGSTATS, I’ve decided to change things up a bit for my final blog post. I’ll continue working with Geographically Weighted Regression, but rather than applying it to FRAGSTATS-derived metrics (shape index, edge:area ratio etc.), I will experiment with a different LandTrendr output: forest biomass.

Dataset:

Explaining more about the dataset here will help me articulate the research question below. So, the biomass layer is a raster calculated using a Tassled Cap Transformation, which is a method of enhancing the spectral information content of Landsat imagery. It is essentially a measure of per-pixel brightness (soil), greenness (vegetation) and wetness (soil and canopy moisture). I will be using yearly time-series biomass layers and “time-stamped” clear-cut disturbance patches.

Research Question:

I’m still not sure how well I can articulate the question, but here goes: Is there a statistically significant relationship between the mean biomass value within a clear-cut patch at the timing of the clear-cut, and the mean biomass within that same patch, before and after the clear-cut?

 

Hypothesis:

Clear-cutting obviously results in a loss of biomass, and I expect that quantities of biomass within a clear-cut patch before, during and after a clear-cut will exhibit a significant relationship.

Approach:

While I had easy access to the biomass data, creating a dataset of disturbance patches with attributes for biomass before, during, and after the timing of each clear cut was a carpal-tunnel inducing task. I ought to have approached it programmatically, and I did try, but my Python skills were lacking. I ended up using a definition query to filter disturbance patches by year, and then ran three Zonal Statistic operations on the biomass layers (one for the year before a given set of clearcuts, one during, and one after). I then joined each biomass calculation back to the clear-cut patches. Below is an attribute table for one set of disturbance patches (note the three mean biomass values) and an example of a disturbance patch overlaid on a “before, during, and after” set of images. I did this for three sets of yearly clear-cuts, and then merged them into one dataset of roughly 700 features.

 

I then ran Geographically Weighted Regression, with “mean biomass after clear-cut” as the dependent variable, and “mean biomass before” and “mean biomass at timing of clear-cut” as explanatory variables.

Results:

I experimented with multiple combinations of the three biomass mean variables, and also tried adjusting the kernel type. The most significant run was that on the left, which had parameters as described above.

         

 

Significance:

While it was satisfying to finally produce some significant statistics, I recognize that the analysis is not groundbreaking. While change in biomass is certainly of interest to forest managers and ecologists, the way in which it was calculated here (as a mean of an annual snapshot within a patch) may not have significant implications.

What I learned:

If this course is nicknamed “Arc-aholics Anonymous” then you could say I had somewhat of a relapse, as most of my analyses throughout the quarter made use of tools I had used in ArcMap before. That said, I gained a much more thorough understanding of their functionality, and feel I have a better command over interpreting their sometimes perplexing results. I now have a much better idea of the types of datasets and variables that lend themselves to certain methods, and the experience of working with a large dataset of Landsat time-series-derived forest disturbance will be invaluable to my research moving forward. I learned a great deal from others in the course and am glad to have made some new contacts (especially you coding gurus). Some of the work produced in this course was truly outstanding and I feel inspired to hone my own skills further, particularly with open-source software.

 

Background

The Willamette Valley of the Terminal Pleistocene (10,000+ years ago) was a wildly different place than the valley we are used to seeing today. There were massive animals roaming the valley floor, which was a lot wetter, with more marshes, bogs, and lakes. Oak savannah and forested swaths of land made their way towards the Willamette River… This wonderful landscape was likely also inhabited by humans, though that is a very difficult question to explore.

In order to find out where in the Pleistocene Willamette Valley people might have lived, we must first understand the sediments that lay under our feet here in the valley, and the best way to do that is by extracting it from the ground and analyzing it.

This project is a part of a bigger picture study that seeks to use sediment cores extracted from a buried peat bog found at Woodburn High School in Woodburn, Oregon and identify the sediments buried within that are of the appropriate age and environment to find both potential Pleistocene aged archaeological sites as well as more evidence of Pleistocene megafauna.

 

Research Question

For the purposes of this project, I am seeking to find a different method for identifying stratigraphic breaks in a sediment profile. The most popular methods for identifying stratigraphy is through visual examination, multivariate statistical analysis, or by texturing the sediment.

Using x-ray fluorescence geochemical data, and Wavelet Analysis, a method typically used for studying time-series data, is it possible to determine the site stratigraphy using one or two different variables?

 

The Data

The dataset consists of XRF data taken at 2mm intervals, from 65 1.5-meter core samples. These cores come from 14 different boreholes covering the majority of the defined study area which is approximately a 200×50-meter area. The cores were extracted using a Geoprobe direct-push coring rig.

 

The Site:

The Geoprobe in action at the site:

The core samples were halved and run through an iTrax core scanning unit. The iTrax scans the cores using an optical camera, a radiograph (similar to medical x-ray), and an x-ray fluorescence scanner, which collects geochemical data consisting of 35 different element counts at 2mm intervals. The data is organized into 14 CSV files containing the XRF results.

 

The iTrax:

Hypothesis

Using wavelet analysis, significant increases and decreases of geochemical properties can indicate where stratigraphic breaks in the sediment occur. This pattern should be repeatable across all of the gathered cores.

 

Approach

The method I chose to analyze my core data and attempt to break apart the stratigraphy was Wavelet Analysis using an R package called “WaveletComp”.

‘WaveletComp” takes any form of continuous data, typically time-series data, spatial data in this case, and uses a small waveform called a wavelet to run variance calculations along the dataset. The resulting output is a power diagram, which shows (in red) the locations along the dataset where there is a great change in variance. A cross-wavelet power diagram can also be generated. This can indicate when two different variables are experiencing rises and/or drops at the same time.

 

Example of a wavelet.

There are two equations used when generating a wavelet power diagram…

The above equation uses the dataset to calculate the appropriate size of the wavelet according to the number of points in the dataset.

The above equation uses the wavelet to run variance calculations across the dataset and output the power diagram.

 

Using the ‘WaveletComp” package in R, I processed 5 different core scans. In order to properly conduct the analysis, elements had to be selected in order to do both univariate and bivariate analysis. There were a variety of ways that I could have selected the data, but ultimately, in the test sample, I chose to look at the elements that had the most obvious changes, aluminum and iron.

The details on how to actually run the “WaveletComp” package can be found in my wavelet analysis tutorial.

 

Results

 

After all of the tests were run, the resulting wavelet power diagrams were placed alongside line graphs of the element that was run, as well as a cross-wavelet power diagram, which indicates when the two selected elements change at the same time.

The wavelet power diagrams show significant changes in the waveform, as indicated by the red (high variance). The blue in the power diagram shows low variance. In the cross-wavelet power diagram (the one on the far right), the arrows indicate if the waveforms of the two elements are in-phase (pointing left) or out of phase (pointing right) with each other.

In order to identify stratigraphic breaks, I looked at the “taller” red plumes in the wavelet power diagrams, which indicated a significant change in the amount of an element present, either a great increase or a great decrease. This result was compared to the graph, as well as the image of the core (for visual identification of changes in color or texture). The spots that have the high plumes, and correspond with a significant color or texture change in the image are presumably the stratigraphic breaks.

Each of the five cores showed promise that we can identify stratigraphy using wavelet analysis. The two most significant cores are discussed below:

The results for the first core segment shows various distinct changes as indicated by the tall red plumes in the power diagrams, but there is one major problem with the results. The graphed data shows areas where there is zero data at points, as indicated by the drops to the very bottom of the graph. These spots also have the most distinct plumes (for the most part), but about 2/3 of the way down there is a distinct plume that, while contains zero values, also is a spot with a distinct texture change in the sediment. At this point the sediment changes texture and feel entirely.

The results of the second core sample were more interesting, as there were no zero values. The Al+Fe cross-wavelet diagram shows significant plumes where almost all of the significant looking color changes in the stratigraphy are in the profile.

The second core was the most interesting of the analysis, due to the lack of zero/null data. With a little bit of data management, the zero data can be reduced by interpolating some of the values and re-running the data with the interpolated data, That should help reduce the effects of the zero data as demonstrated in the above results.

 

Significance

Wavelet analysis is an excellent tool for observing patterns in spatio-temporal data that is sequential. As for the significance of this project…

Once all of the observed kinks are fixed in the data, this could serve as a new method for identifying changes in stratigraphy. This could be a good method to identify stratigraphy in sediment cores that are extremely similar in color or texture.

 

What I learned about the software

R is an excellent tool for conducting many different kinds of spatio-temporal analysis. From running wavelet analysis to regression, and really any other tool that ArcGIS has to offer.

ArcGIS is an excellent tool for data visualization, but it is a very finicky program that has to

 

What I learned about statistics.

Statistical applications in geospatial analysis are very important to understanding even the smallest of changes, such as an increase or decrease in iron in a sediment core.

 

Background

The relationship between microbiome composition and host health has recently generated a great deal of attention and research. The importance of host-associated microbiomes is still poorly understood, although significant relationships between gut micobiome composition and host health have been described. Although the gut microbiome has received the most attention, each body site is home to its own distinct microbial community. The nasal microbiome has received relatively little attention, although a few studies suggest that there is a relationship between nasal microbiome composition and incidence of infections. Using a unique system of closely studied semi-wild African Buffalo, I propose to study the drivers of nasal microbiome composition in a social species.

Data Collection

Our study herd of semi-wild African Buffalo (Syncerus caffer) is kept in a 900 hectare predator-free enclosure located in Kruger National Park, South Africa. Every 2-3 months, all 60-70 individuals are captured, and biological samples are collected for diagnosis as part of a larger study that the Jolles lab is conducting on Foot-and-Mouth Disease. Age, sex, and body condition are recorded, in addition to a number of other physiological parameters. Degree of relatedness is known for each pair of individuals in the herd. Each animal is fitted with a GPS collar that is programmed to record location every 30 minutes, and with a contact collar that records identity and duration of contacts with other buffalo. The GPS data used in this exploratory analysis was collected between October-December 2015.

Overarching Hypotheses

My research is guided by the following two hypotheses:

1. Conspecific contacts drive nasal microbiome similarity and disease transmission.
2. Habitat overlap drives nasal microbiome similarit and disease transmission.

I also propose to examine the relationship between the other parameters (age, sex, body condition, relatedness, etc) on nasal microbiome composition, but for this class I focused on the spatial parameters.

Approaches

The first step toward addressing hypothesis 1 is to quantify conspecific contacts. I tested several approaches during the course of this class. The first approach, presented during my first presentation was to generate buffers in ArcGIS around each animal at a given time point and generate a measure of “crowdedness.” The second method was to generate a contact matrix in R (see figure 1) to show distances between each individual at a given time point. Detailed methods and R code are given in my first blog post.

Figure 1: Sample distance matrix, generated for a subset of 5 animals at a single time point. Distances range between 3-18 meters.

As an intermediate step towards addressing my second hypothesis, it will be necessary to measure the percent habitat overlap between every pair in the herd. I used a suite of tools to carry out a test analysis using GME, ArcMap, and excel. Detailed methods are outlined in my second blog post. In summary, I used GME to generate kernel densities and 95% isopleths for two individuals, then used the identity feature in Arc to calculate area of overlap. Figure 2 shows a sample of the output from the identity tool.

Figure 2: Habitat overlap between two individuals in the study herd. Individuals’ home ranges are colored yellow and purple, respectively. Area of overlap between the two animals is outlined in red. Overlap between the two animals is 80% and 90%, respectively.

Eventually, once I have determined contact network and habitat overlap matrices, I will look at correlation between microbiome similarity and habitat overlap and average distance with conspecifics.

Significance

1. Distance matrix: this analysis showed potential usefulness for researching herd behavior and structure, and I will likely return to it in future analysis. However, since my question of interest relates to microbe transmission, which is likely to be associated only with close contacts, I plan to focus my current efforts on utilizing the contact collars I described in the data section. Although I will lose some spatial information, it will simplify my analysis and increase temporal resolution.
2. Habitat overlap: The method described here for measuring habitat overlap shows great promise for use in my research, especially if the process can be automated. I will explore iteration functions in GME and ArcGIS ModelBuilder to find the best way to expedite this analysis across multiple pairs of individuals at multiple time points.

Potential Issues

A few problems that I will likely need to deal with as my analysis progresses:

1. The possibility of high correlation between conspecific contacts and habitat overlap. I will try to control for this by looking for animals that have high spatial overlap but low contact rate, and vice versa.
2. Non-matching pairwise percent overlap. For example, individual 13 showed 90% overlap with individual 1, whereas 1 showed only 80% overlap with 13. I can deal with this by looking at pairwise averages, unless the percent overlap is too different, in which case I will need to explore other options.

Lessons Learned

Software Packages:

Thanks to help from my classmates, I became much more comfortable and familiar with geospatial functions in R. I also used GME for the first time and discovered that it has great potential usefulness for my future analyses. I became familiar with ModelBuiler in ArcGIS while attempting to iterate the buffering analysis. I still have a lot to learn with all these tools, but I feel much more confident than I did prior to this class.

Statistical methods:

Although I did not utilize any of the statistical methods outlined in the syllabus due to the unique nature of my dataset, I learned a great deal from watching my classmates present. I expect that hotspot analysis, multivariate statistics, and different types of regression models will be part of my future. In particular, I plan to use regression models and PCA to help analyze my data in the future.

 

 

 

 

Mapping Weeds in Dryland Wheat: A spectral trajectory approach

Introductions: Into the weeds

When I started this course, I had a central goal in mind: I wanted to use remotely sensed data to identify weeds. What I didn’t have, was a clue as to how I was going to get there. I had a few data sets to work with, and although I had made some limited progress with them, I had not yet been able to ask the kind of spatial questions I knew were possible with them.I had data that I knew As a part of this course, I formed this central goal into two research questions:

• How does spectral trajectory relate to weed density? Can variation in spectral trajectory be used to distinguish weed species from crop species?

• Can this information be used to distinguish the spatial extent of weeds in dryland cropping systems? How well do different methods of assessing weed density perform?

Originally, I had planned on using some low altitude aerial imagery I had taken in 2015 for addressing this question. After many many late nights trying to get these data into a form that was suitable for analysis, I decided for the sake of brevity and actually getting something done in this class, I would use an alternative data set.

My alternative data set consisted of 3 kinds of reference data with regards to the location and species of weeds in a 17 acre field NE of Pendleton OR, as well as Landsat 8 images taken over the course of summer 2015. The reference data sets I had consisted of transect data where species level density counts were made, spectral measurements of green foreign material made during harvest, and observations made from the front of a combine at the time of harvest. In the landsat data set I used in this class, I only included cloud free images from the duration of the growing season, 2015.

 

Motivations and Relevance:

My goal with the work I had hoped to achieve in this class was to use variation in phenology between weed and crop species to distinguish weed density using time series landsat data. One of the major issues with weeds in cropping systems however, is that they typically represent only a very small fraction of the total cover in a pixel. The revised hypotheses I ended up testing in this class were:

1. Weeds and crop can be distinguished based on their relative rates of change in greenness (NDVI).
2. Visual estimates of weed density will be more accurate at estimating weed density than automated inline assessments.

The main reasons why I find these questions interesting, is the fact that species level discrimination in satellite based remote sensing is still such a challenge. In most remote sensing efforts to identify weeds using satellite data generally perform poorly. A major reason for this, is the typically low signal weeds will have in a cropping system. Advancement in the methodologies for identifying species in satellite imagery would be a significant contribution. As well, there have been few attempts at using a time series approach to distinguishing weed to the species level. Most work has concentrated on increasing the spatial resolution or the spectral resolution of imaging efforts for making species level classifications. As well, the data I was working represented as complete a sampling of the field as is reasonably possible. All plant material from the field had been cut and measured by the spectrophotometer. In this way, the spatial resolution of my reference data was very fine.

Methods:

In this class, I ended up attempting to answer these hypotheses using two general approaches that were made available to us in the class. I used hotspot analysis to identify areas of the field that were statistically significant positive values as “weedy”.  I then used the output of the hotspot analysis as a predictor variable in a geographically weighted regression, with NDVI as the explanatory variable. With previous attempts at classification, I typically ended up with poor results when comparing the spectrally generated data set to my reference data set. Hotspot allowed me to overcome this, in that the classification was not as sensitive to extremely high or low values. The improved performance is likely a result of the fact that hotspot analysis takes into consideration the neighborhood of values a measurement resides in. I then used the output of the hotspot analysis as the predictor variable in a geographically weighted regression. With geographically weighted regression, we remove the assumption of stationarity, and fit regression models based on a local neighborhood rather than to the entire dataset. Finally, I classified the output of the regression analysis based on the coefficients for each of the terms of the local linear models. My goal here was to attempt to get at why the relationships between weed density and NDVI appeared to vary as they do.

Results:

The specific details of each of these analyses are available in their individual posts, but overall the results were very promising. I was able to improve the classification accuracy of a spectrophotometric assessment of weed density from ~50% to 85%, as good as a human observer. This results indicates that the in-situ assessment of weed density may be a real possibility in the near future, which has implications for farmers as well as scientists and land managers. Generation of quality reference data is very difficult to do over broad spatial areas, and any way to improve that process is a good thing.

Regarding the output of the geographically weighted regression, I find I’m still grappling with the results. While I did end up with distinct areas of the field having differing responses of weed density to NDVI, i’m finding difficulty in interpreting the output. I think that if additional explanatory variables for why weeds respond the way they do, and if this is predicted by geographically weighted regression, wouldn’t one simply include those variables into their original model for predicting weed density? So while geographically weighted regression may be suitable for a data exploration exercise, I’m not sufficiently convinced of its utility in predicting weed density. More work is necessary to come to a conclusive answer as to why local relationships between NDVI and weed density appear to vary as they do.

 

Learning:

I learned an incredible amount this quarter, mostly from the incredibly high quality presentations and conversations I had with my colleagues in this class. An incredibly high bar was set by the work done by this cohort. Although I didn’t get as far as I might have liked to with these data, this was my first foray into spatial statistics. I had the advantage of being very comfortable in R, but this class forced me to branch out into ArcMap, and even by the end of the quarter, into Python and Earth Engine. One of the major issues I had, was that the data set I was working with was not as high a resolution as I had originally intended. I wanted to be using methods from machine learning on an a very high resolution multispectral data set i’ve been working on, but it wasn’t ready for analysis by the time I needed to produce results.  I ended up doing a lot of work that never saw the light of day, looking at issues in spatial variance and resolution, that with more time, I would have liked to present on.

 

Research Question:  What is the correlation between the location of leatherback sea turtles, sea surface temperature, and chlorophyll?

Data:

Leatherback sea turtle locations: The leatherback turtle dataset was obtained from http://seamap.env.duke.edu/dataset.  The dataset was in point feature format.  The extent of the dataset is within the Gulf of Mexico. Observations of each sea turtle was collected from January through December 2005.

Figure 1: Sea turtle locations in the Gulf of Mexico, derived from http://seamap.env.duke.edu/

Sea Surface Temperature: The Sea Surface Temperature (SST) dataset was obtained from NOAA.  The dataset was downloaded from the NOAA website in .csv format with latitude and longitude coordinates and temperature data associated with each coordinate.  The extent of the dataset was the Gulf of Mexico.  The SST data was the average daily maximum for January and December 2005.  The data ranged from 2.44 – 26.89 Celsius, the mean was 23.57 Celsius.

Figure 2: Sea Surface Temperature (Celsius) data for January 2005 within the Gulf of Mexico, derived from NOAA.

Chlorophyll-a: The chlorophyll data was obtained from NOAA.  The dataset was downloaded from the NOAA website in .csv format with latitude and longitude coordinates and chlorophyll data associated with each coordinate.  The extent of the dataset was the Gulf of Mexico.  The Chlorophyll data was a 3-day composite in December 2005.  The data ranged from 0 to 1.63 mg/m³, the mean was 0.29 mg/m³.

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

Hypothesis: I expected leatherback sea turtles to be clustered in areas based on high jellyfish concentrations.  Jellyfish tend to be located in areas that have higher chlorophyll-a concentrations and where sea surface temperature is low.  Thus sea turtle locations should correlate well with higher values of chlorophyll-a and lower values of SST.

Analysis Approaches:  To test my hypothesis, I utilized the hotspot analysis, Spatial autocorrelation (Moran’s I), Geographically Weighted Regression, Kernel Density tools in ArcGIS.  In addition, I also utilized R statistical package to create a graph that correlated chlorophyll with SST.

a.  Hotspot Analysis: The spatial distribution of the sea turtle locations appeared to be clustered toward the middle of the Gulf of Mexico.  The hotspot analysis tool helps to identify where statistically significant hotspots or clusters of sea turtles are located within the Gulf of Mexico.

b.  Spatial Autocorrelation (Moran’s I): This tool measures spatial autocorrelation using feature locations and feature values simultaneously. 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. I tested the spatial autocorrelation of chlorophyll 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).

c.  Ordinary Least Squares: This tool performs a global linear regression to “generate predictions or model a dependent variable in terms of its relationships to a set of explanatory variables.  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.”   This model was run three separate times, increasingly adding more explanatory variables each time.  Each OLS run used Chlorophyll as the dependent variable.  The first OLS run, SST as the explanatory variable.  The second run, used SST and depth (m) as the explanatory variables and the third run, used SST, depth, and turtle count as the explanatory variables.

d.  Geographically Weighted Regression: Based on the observations and results found in the OLS analysis (the data being nonstationary).  I decided to conduct a Geographically Weighted Regression analysis.  This tool performs a local form of linear regression used to model spatially varying relationships.  The dependent variable used for this tool was the Chlorophyll and the explanatory variable was SST.

Results:

Hotspot Analysis:  The results of the hotspot analysis (shown below) suggest that the turtle locations are significantly clustered off the coast of Louisiana and Texas between approximately 2000 to 3,000m depth of water.  However, the results of this analysis appear to be quite deceptive.  Upon taking measurements of turtles in the hotspot cluster it appears as though they may be more dispersed.  Further analysis is needed in order to determine further patterns of Sea turtle locations.

Figure 4: Results of the hotspot analysis for leatherback sea turtle locations

Spatial Autocorrelation (Moran’s I) – 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 5: Sea surface temperature results for Moran’s I tool.

Spatial Autocorrelation (Moran’s I) – 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 6:  Results of the spatial autocorrelation Moran’s I for chlorophyll-a at the leatherback sea turtle locations.

Ordinary Least Squares:  This model was run three separate times, increasingly adding more explanatory variables each time.  Each OLS run used Chlorophyll as the dependent variable.  The first OLS run, SST as the explanatory variable.  The second run, used SST and depth (m) as the explanatory variables and the third run, used SST, depth and turtle count as the explanatory variables.

Model 1:

Model Structure:  Chl-a = f(SST)

Model Results:

a) Overall r2: 0.449473

b) Coefficient on SST in model: -0.052654

The results suggest that Chl is negatively related to SST and given the p-value of 0.000, we can deduce that SST is a significant predictor of Chlorophyll-a.

Model 2:

Model Structure:   (Chl =f(SST), (Depth))

Model Structure:

1. a) Overall r2: 0.452436
2. b) Coefficient on SST: -0.051769
3. C) Coefficient on depth: -0.000015

The results suggest that SST and Depth are negatively correlated with Chlorophyll.  Given the p-value of 0.056397 for depth, this is not a statistically significant relationship.  The p-value for SST is 0.0000 suggesting that it is a statistically significant relationship and is a better predictor of chlorophyll-a than depth.

Model 3:

Model Structure:  (Chl =f(SST), (Depth), (Count))

Model Structure:

1. a) Overall r2: 0.460299
2. b) Coefficient on SST: -0.050454
3. c) Coefficient on Depth: -0.000014
4. d) Coefficient on Count: 0.121644

The results suggest that SST and Depth are negatively correlated with Chlorophyll and the count is positively correlated.  Given the p-value of 0.067482 for depth, this is not a statistically significant relationship.  The p-value for Count is 0.001815, suggesting that the relationship is statistically significant.  The p-value for SST is 0.0000 suggesting that it too is a statistically significant relationship.  In this model we see that the number of turtles found at each location and the SST values have statistically significant relationships to Chlorophyll.  SST has the lowest p-value and would suggest that it is the best indicator for chlorophyll, though we should not discount the count variable.

Overall results: Running the model using three explanatory variables provided the best Overall R-Square value of .46.  The model significance proves to have an overall statistical significance due to the Koenker (BP) statistic being statistically significant, therefore I used the Joint Wald Statistic as an assessor of the model significance.  The Joint Wald Statistic was significant as shown below:

Figure 7: OLS model 3 – Joint Wald Statistic

The Koekner statistic is used to assess model stationarity.  This statistic revealed that the model was not stationary in geographic space and/ or data space due to its significance and having a p-value <0.05 as shown below:

Figure 8:  OLS model 3 – Koenker BP Statistic

Since the Koekner statistic was significant it was appropriate to look at the robust probabilities of each variable to assess their effectiveness.  The Robust Probability scores for each of variables reveals that the count and SST are statistically significant (as shown below) thus they are found to be important to the regression model.  However, it also appears as though the model is a good candidate for Geographically Weighted Regression due to it being nonstationary.

Figure 9: OLS model 3 – Variable Statistics

 

Geographically Weighted Regression:

Model Structure:  (Chl =f(SST), (Depth), (Count))

Model Result

a) spatial pattern of r2 values (map)

Figure 10: Geographically Weighted Regression Analysis: Map of the Local R-Squared values

After conducting the GWR analysis using the chlorophyll as the dependent variable and the Sea Surface Temperature as the explanatory variable I mapped the local R-Squared values of each feature location to show where the model predicted well and where it predicted poorly.  The map shows that predicts are made best where turtle locations appear to be in areas where Sea Surface temperature is cooler off the Texas coastline.

b) Spatial pattern of coefficients for SST

Figure 11:   Geographically Weighted Regression Analysis: Map of the coefficients

I mapped the coefficients in order to understand regional variation of the model.  When using GWR to model the Chlorophyll (dependent variable) I was interested in understanding the factors that contribute to the turtle locations (or chlorophyll at each of the turtle locations).  I was also interested in examining the stationarity of the data being that the OLS model revealed that it was not stationary.  In order to do these tasks I mapped the coefficient distribution as a surface to show where and how much variation was present.  As shown below in the map, it appears that Sea surface temperature has a negative relationship with Chlorophyll.  The range of the coefficients is -0.066176 to -0.64989.  There is very little variation in the coefficients.  The results of this test help to inform policies at a regional scale.

Significance: What did you learn from your results?  How are these results important to science? to resource managers?

The results of the tests suggest that chlorophyll-a has a negative relationship to sea surface temperature in the Gulf of Mexico according to leatherback sea turtle locations.  Sea turtles are located in areas where sea surface temperature is low and chlorophyll values are higher.  After mapping the coefficients of the variables we see that there is little variation in the data suggesting that policies regarding the protection of leatherback sea turtles should extend throughout the entirety of the Gulf of Mexico rather than in a few selected areas.

Learning Outcomes:

Programming in R:

With the help of Mark Roberts, I was able to use the R software programming to load and utilize the ggplot2 package to plot the correlation between chlorophyll-a and sea surface temperature. Lots of room for improvement here!  The following is the code used to make the plot as well as the plot outcome:

Figure 12: ggplot code used in R to plot the correlation between chlorophyll-a and sea surface temperature.

 

Figure 13: Correlation between chlorophyll-a and sea surface temperature.

 

What did you learn about spatial statistics:

I think scale is an important factor.  You need to understand your data and be sure to not take the results as they are.  You should investigate everything to make sure that the data and results make sense.  If the results appear incorrect they probably are incorrect.   I also  learned that it is dangerous to conduct spatial statistical analyses on data unless you can interpret what makes sense. The spatial autocorrelation conducted on SST and Chl-a indicated that they were clustered but I was still confused about this outcome.  While conducting research it is important to thing about scale of the data to ensure that all of the data line up.  I encountered an issue with the SST data due to the way it was sampled. I had many sea turtle locations that did not have sea surface data associated with them because of the way the SST data was sampled.   A classmate pointed out that I did not consider the effects of currents on jellyfish.  This could be a significant factor that may lead us to understand why sea turtles are present in Gulf of Mexico since jellyfish are partially distributed by currents.  Another lesson learned is that it is important to remember the basic principles of geographic information systems while conducting these analyses.  For instance it is important to turn on extensions, and be sure that all the data is properly projected prior to conducting any analysis as this can and will through off the results. Overall, it is important to know your data.