Maribeth Price and Jason Tinant
South Dakota School of Mines and Technology
Rapid City, SD 57701
August 14, 2000

Abstract
Canada thistle (Cirsium arvense) is a highly invasive, noxious weed that is widespread throughout the Badlands National Park. This study sought to identify significant correlations between known thistle occurrences and environmental parameters including soils, geology, vegetation communities, slope, aspect, distance to water, distance to roads, and satellite-derived vegetation and moisture indices. Two approaches were tried, a logistic multiple linear regression, and a statistical frequency analysis. Three maps were produced, including a probability map based on the regression, a Z-score map based on the frequency analysis, and a combination map including both approaches. Significant factors correlating with thistle occurrence include soils, geology, vegetation communities, slope, and NDVI. The accuracy of the maps was assessed against known thistle infestations in the park. The maps show areas where thistles are likely to become established and spread, but do not well predict where thistles may be found at any given time.

Introduction
The Badlands National Park (BADL) has contracted with Dr. Maribeth Price and the South Dakota School of Mines and Technology to analyze spatial correlation between Canada thistle and environmental parameters within the Burns Basin area of the National Park (figure 1).

Canada thistle (Cirsium arvense) is a highly invasive, noxious weed that is widespread throughout the Badlands National Park. The potential problems with the widespread occurrence of this pest are the displacement of native plants, potential harboring of predators in black-footed ferret reintroduction sites and causing economic damage to adjacent agricultural lands. The Canada thistle population exceeds the park’s current chemical, mechanical and biological control programs. Thus, an intensive herbicide treatment program has been proposed.

Figure 2. Canada thistle

Tordon, a picloramine compound manufactured by Dow Chemical has been shown to be effective in thistle control. However, the physical properties of Tordon have been a cause of concern for the Badlands National Park. Tordon is a broad-based herbicide, killing native species of plant life as well as Canada thistle. Tordon has a long residence time in soils, leading to potential ground-water contamination. Spatial analysis of the treatment site will better locate areas of infestation, thereby minimizing the amount of pesticide used.

Justification of Research
The rugged nature of the Burns Basin area of the Badlands National Park makes field identification of thistle-infested areas both cost and time prohibitive. A map showing areas where thistles are likely to grow or spread can reduce the time and effort required to search for and locate infestations. In addition, a predictive thistle model will aid in guiding management decisions in the application of Tordon.

Approach
The study sought to identify significant correlations between known thistle occurrence and environmental parameters including soils, geology, vegetation communities, slope, aspect, distance to water, distance to roads, and satellite-derived vegetation and moisture indices. A horseback survey of the Burns Basin (Figure 2) in 1998 provided a map of known thistle locations. The environmental parameters comprised a series of GIS layers obtained from BADL and other sources. Two distinct approaches were applied to develop a GIS model of thistle-infestation probability. Numeric parameters, including the slope, distance, and satellite indices were amenable to analysis by logistic multiple linear regression. The thematic variables, including soil, geology, vegetation community, and aspect, are not suitable for regression analysis, so a statistical approach was applied in assessing the frequency of thistle infestation in particular classes. The final product is a map showing the probability of thistle infestation for the Burns Basin. Three maps are presented, one based on the regression alone, one based on the frequency analysis alone, and one combining the two approaches.

Analysis of thistle locations using multiple linear regression
A logistic multiple linear regression was applied to the following GIS data layers: slope, distance to streams, distance to water bodies, distance to wetlands, distance to roads, Normalized Difference Vegetation Index (NDVI), and Normalized Difference Moisture Index (NDMI). Slope was calculated from the standard USGS 30m Digital Elevation Model (DEM) products obtained from BADL. The distance to roads, streams, water bodies, and wetlands was calculated from the GIS layers of these features obtained from BADL and based on the USGS 1:24,000 Digital Line Graph products. The spring and fall NDVI and NDMI values were derived from a May 03, 1998 and November 17, 1998 Landsat TM image. NDVI is an index of greenness that correlates roughly with biomass and is calculated as NDVI = (B4-B3)/ (B4+B3), where B3 and B4 are Bands 3 and 4 of a Landsat TM image, corresponding to measured red and near-infrared reflectance. NDMI is an analogous index sensitive to soil moisture and is calculated NDMI = (B4-B5)/ (B4+B5).

The logistic regression of the sample data showed fair to poor correlation with the parameters chosen. The strongest predictor of thistles in Badlands National Park was the spring NDVI image with a correlation coefficient of –0.22, followed by the fall NDMI image with a coefficient of 0.19. The other layers had coefficients less than 0.1.

Analysis of discrete variables (geology, soil type, aspect, and vegetation community)
Because logistic regression can only be performed on numeric variables (such as slope), analysis of the discrete variables geology, soil type, aspect, and vegetation types was performed using a probability prediction model. In this model, one assumes that if thistles were randomly located, the number of thistles found in each cover type would be proportional to the area fraction of the cover type in the study unit. One can thus compare the expected number of thistle locations to the observed number to determine cover types for which thistles seem to show an affinity or aversion. A Z-score representing the statistical significance of the apparent affinities or aversions may be calculated.

For each cover type a Z-score was calculated using Z = (N_i – E_i) / [Nq_i(1-q_i)]^0.5 to show the number of standard deviations that the observed value falls from the expected value. A positive Z-score greater than 2 indicates a less than 5% probability that this number of points occurred in that particular cover type by chance. A negative Z-score less than –2 indicates that far fewer thistle points were observed in that unit than would be expected by chance. Thus a negative Z-score less than 2 suggests that thistles show an aversion to the cover type, and positive Z-score greater than 2 suggests that thistles show an affinity for that cover type.

Highly significant positive and negative correlations were found with geology, soil, and vegetation class. Aspect was not found to be a significant indicator of thistle location. Table 2 shows all of the cover types for which a significant Z score (< -2 or > +2) was found.

Maps showing the Z-scores for each cover type group (geology, soils, and vegetation class) were developed and provide a spatial view of the areas of high and low probability of thistle occurrence. Figures 4-6 show the Z-score maps, with the negative Z-scores (thistle aversion) shown in shades of blue, neutral areas shown in white, and positive Z-scores (thistle affinity) shown in shades of orange. More saturated colors indicate a higher affinity or aversion potential of that cover type.

The three individual maps were added together to produce a summed Z-score map, showing the combined Z-scores over the map area (Figure 7). This map serves as a probability map showing the areas of greatest potential thistle affinity and aversion. The maps use the same color scheme as the previous figures.

Combined Z-score and Regression map
We integrated the information in the summed Z-score and regression maps in order to include both types of information in a combined infestation affinity map. To do this, the probability of thistle infestation in the regression map was multiplied by 10 to produce scores between 0 and 10, and the result was added to the summed Z-score map. The number 10 was chosen to equalize the weights applied to each of the four input maps (soil Z-scores, geology Z-scores, vegetation Z-scores, and the regression). The combined map is shown in Figure 8.

Accuracy Assessment
In order to assess the accuracy of the probability map, thistle data was collected along four transects in the park. The transects were chosen to cross a range of Z-scores on the map, cross navigable terrain as much as possible, and start and end near roads (Figure 3 shows the transects best). Approximately every 150 meters along each transect, all the thistles were counted or estimated within a circle 20 m in diameter. The circle was defined using a rope 10 m long, attached to a stake. The person at the center of the circle counted thistles between the center and a knot at 5 meters on the rope, while the other person walked around the circle holding the rope and counted thistles between the end of the rope and the knot. In thick infestations, thistles were estimated by watching the rope crossing the thistles and estimating every time groups of 10 or 20 or 50 thistles were crossed, depending on the thistle density.

In the accuracy assessment, values were determined for the regression probability map, the Z-scores map, and the combined Z-score/regression map for each point in the transects, as well as for each point in the original BADL thistle survey. Each transect point was classified as thistle or no-thistle. All of the BADL survey points were considered thistle points. The distribution of thistle points and non-thistle points falling within three probability ranges were then compared. Because the BADL points were used in the original regression and probability model, those values were tallied separately from the transect values.

Figure 9. Field assistant Marius Vulcan counts thistles from the center of a 10-m radius circle.

The regression map does a poor job of predicting thistle affinity, which is not surprising, given the low correlation coefficients from the regression. However, the combined Z-value/regression map has the highest accuracy of all the maps. Despite the low correlation coefficients, the regression map nevertheless adds some additional information.

Discussion and Conclusions

Maps of thistle affinities were developed for the Burns Basin area of Badlands National Park based on soils, geology, vegetation communities, slope, roads, water sources, and Landsat TM satellite index parameters NDVI and NDMI. The maps show areas where thistles are most likely to become established and spread, but do not predict where thistles will be found at any given time.

During field work in the study area north of the Badlands Loop road , we noted a strong association between water bodies and the presence of thistles, and the failure of this association to show up in the regression model was surprising. Possible reasons for this include: 1) The BADL thistle survey did not extend north of the Loop road; 2) The water bodies shown on the hydrology layer did not well correlate to actual water bodies due to variations in body sizes depending on season or rainfall; or 3) Other factors besides water needed to be present to support thistles. Future work might test z-scores of a buffer zone around the water bodies to see if this association in fact holds in the Park. Another anecdotal association has been noted between prairie dog towns and thistles, which could be tested when the GIS layer for prairie dog towns is complete.

The Z-factor and regression models in this study could be applied to estimate thistle affinities in the entire park based on the correlations discovered in Burns Basin. This map could assist BADL personnel in estimating the total acreage in the park that is susceptible to thistle infestation, and in analyzing the distribution of high-affinity areas within the hydrologic drainage basins to help assess the hazards associated with the spraying of Tordon.

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