Discussion of Results
Examining the summary of the results from the spatial analyses for each of the areas in the proglacial zone of Bridge Glacier (Table 8) it is possible to see that the distribution of variables is very complex. It would be possible to go through each of the areas of the proglacial zone and discuss the findings from each of the types of analyses, however, as will be discussed below, the results that are present for a given area may not actually be applicable to the whole area.
Why the Findings of this Study Refute the Presence of Patterns Within Specific Areas:
When examining the results from each of the defined areas as displayed in Table 8, it becomes clear that there are no distinct patterns within any of them that can be applied to the area as a whole. There are three main lines of evidence that lead to this conclusion:
These three points focus on the fact that many of the analyses in this study highlight specific polygons, however there are a few analyses used that are more representative of general trends, namely, trend surface analysis and spatial autocorrelation analysis (in conjunction with distribution maps). This is because, unlike the other analyses which may indicate isolated polygons with distinctive results, they take into account the values of a larger area. Although hot spot analysis does this to a certain extent, in this study, it still isolated specific polygons as opposed to groups of polygons in given areas.
Why the Findings of this Study Refute the Presence of Patterns Within Specific Areas:
When examining the results from each of the defined areas as displayed in Table 8, it becomes clear that there are no distinct patterns within any of them that can be applied to the area as a whole. There are three main lines of evidence that lead to this conclusion:
- Across all of the areas there tends to be a pattern that notable values are constrained to the same polygon (eg. polygon 14 in the main valley glacial outwash deposits, polygon 19B in the main valley spillway outwash deposits, etc). Conversely, the areas in this study are composed of several polygons, often many of which, are not even mentioned in the results. To extrapolate the interesting findings of one polygon to another, even if it is in close proximity, is not justifiable due to the fact that it is clearly visible from the distribution maps that values of variables may be completely different in two adjacent polygons. Because of this, results from analyses that correspond to specific polygons do not necessarily correspond to the area as a whole and must therefore be disregarded.
- Within one area there are often instances where both high and low values of a given variable are found (eg. high and low RA index value in South Creek tributary valley). Because there are both high and low values can be found a given variable within the same defined area, this indicates that there is no distinct pattern can be assigned to the deposits within that area.
- Different analyses do not necessarily agree for a given variable within the different areas. This is illustrated by the fact that although some spatial analyses may find areas of high or low values for a variable, other analyses may not find anything notable (eg. C40 index hot spot in main valley spillway outwash is not backed up by the other analyses).
These three points focus on the fact that many of the analyses in this study highlight specific polygons, however there are a few analyses used that are more representative of general trends, namely, trend surface analysis and spatial autocorrelation analysis (in conjunction with distribution maps). This is because, unlike the other analyses which may indicate isolated polygons with distinctive results, they take into account the values of a larger area. Although hot spot analysis does this to a certain extent, in this study, it still isolated specific polygons as opposed to groups of polygons in given areas.
Analysis of Error
Within the Methods
Due to the fact that scale is not uniform across an air photo, slight error and distortion was introduced to the georeferenced air photos, especially near the edges. The error associated with the georeferenced air photos was somewhat mediated during the sediment polygon allocation by using up to three air photos to create a single polygon map. This type of error is not of great importance in this study as it only leads to slight error within the shape and size of the polygons, or relative positional error. Another type of error that can occur when working directly off of an aerial photograph is relief displacement, however, the area that was being examined for this project is relatively flat, therefore there is likely no significant error introduced due to relief displacement.
Data collection in the field is difficult for many reasons, especially for studies like these where a site must be chosen to represent a large area that may not be uniform. Despite best efforts, there will always be bias associated with sample site selection as this type of selection is quite subjective, different people will choose different criteria upon which to choose a site. Despite the fact that polygons were delineated with the intention to only contain deposits with similar characteristics, there is always small scale variations across the area, for example, vegetation density is usually always higher in low-lying, less well drained areas. In addition to the bias associated with site selection, there is also error that is introduced during measurement. This error can originate from inaccurate measurement instruments, misreading of the instruments, as well as improper data recording.
Within the Analysis
One major assumption that this study makes by using polygons to represent the proglacial areas is that the areas represented by the polygons are uniform and that the edges of the polygons are distinct and abrupt. While field observations of the different deposits due tend to verify that one type of deposit is quite distinct from another (ie. there is a visible difference between two polygons), there are most certainly areas where the border between two polygons is much less distinct. It would be interesting to conduct another study using fuzzy membership as a way to eliminate the error associated with the distinct edges of polygons.
Spatial Distribution
The error associated with the spatial distribution analysis originates primarily from the error that is associated data collection (measurement error) and the use of samples collected from a single area to represent the whole area. If there is error in the values that have been entered in to represent a given area, this will change the value that is displayed on the map.
Trend Analysis
The trend surface analysis was not necessarily the best type of analysis to do given the distribution of points within the proglacial area as trend analyses are good for areas where there is an even distribution of points. This is especially true for the area in the proglacial zone that is covered by the lake, despite the fact that there are no values for the variables examined in the lake, the trend surface analysis still takes that area into account. In addition to there being a lack of points, because the area that the trend surface is being created for is so small and the trend surface analyses are highly susceptible to outliers (extremely high and low values), especially at the edges, one high or low value near the edge of the map may play a large role in how the trend surface is calculated. Even though, as mentioned before, the trend surface is one of the best indicators of large scale patterns, there is so much error associated with this type analysis in this study, it is difficult to draw any firm conclusions from its results.
Hotspot Analysis
Due to the lack of data for all of the polygons in the proglacial area, especially for variables such as vegetation density, there was not much data for the hot spot (HS) analysis to be conducted on. This means that there were very few hot spots found during the analyses and the polygons that were found to be hot spots were completely isolated, making it hard to conclude that the area was actually a hot spot for the given variable. In addition, the hot spots that were found were only based on a few surrounding polygons as for most cases, there were only two or three polygons that actually surrounded the hot spot areas.
Ordinary Least Squares Analysis
Ordinary least squares analyses are based on the principle that the values of one of the variables predicts the values of another variable. For this study, the dependent and response variables were somewhat random chosen, meaning that there was not prior evidence that one predicted the other, consequently, even though a regression line may statistically significantly predict one variable based on another, it is difficult to say for sure which one is in fact the dependent variable. This can be seen when comparing the two analyses of the C40 index and the RA index, where an analysis is done with each of them as the dependent. As both of them are statistically significant, it is difficult to determine which one is actually predicting the other, or if they are simply correlated. Alternatively, instead of the relationship of two variables being linear, as is what an OLS analysis presumes, their relationship may be much more complex (ie. non linear). Further examinations of the scatterplots of two variables may help to decide if a polynomial regression analysis should be done instead.
Spatial Autocorrelation
As with the other types of analyses, the error associated with spatial autocorrelation is linked to the lack of data for many of the variables. Like in the hot spot analysis, spatial autocorrelation uses the values of proximal polygons to determine if there is a pattern present in the overall area. When there are very few polygons (or values) in a given area, the likelihood that a pattern exists there must be based off of a limited set of data.
Due to the fact that scale is not uniform across an air photo, slight error and distortion was introduced to the georeferenced air photos, especially near the edges. The error associated with the georeferenced air photos was somewhat mediated during the sediment polygon allocation by using up to three air photos to create a single polygon map. This type of error is not of great importance in this study as it only leads to slight error within the shape and size of the polygons, or relative positional error. Another type of error that can occur when working directly off of an aerial photograph is relief displacement, however, the area that was being examined for this project is relatively flat, therefore there is likely no significant error introduced due to relief displacement.
Data collection in the field is difficult for many reasons, especially for studies like these where a site must be chosen to represent a large area that may not be uniform. Despite best efforts, there will always be bias associated with sample site selection as this type of selection is quite subjective, different people will choose different criteria upon which to choose a site. Despite the fact that polygons were delineated with the intention to only contain deposits with similar characteristics, there is always small scale variations across the area, for example, vegetation density is usually always higher in low-lying, less well drained areas. In addition to the bias associated with site selection, there is also error that is introduced during measurement. This error can originate from inaccurate measurement instruments, misreading of the instruments, as well as improper data recording.
Within the Analysis
One major assumption that this study makes by using polygons to represent the proglacial areas is that the areas represented by the polygons are uniform and that the edges of the polygons are distinct and abrupt. While field observations of the different deposits due tend to verify that one type of deposit is quite distinct from another (ie. there is a visible difference between two polygons), there are most certainly areas where the border between two polygons is much less distinct. It would be interesting to conduct another study using fuzzy membership as a way to eliminate the error associated with the distinct edges of polygons.
Spatial Distribution
The error associated with the spatial distribution analysis originates primarily from the error that is associated data collection (measurement error) and the use of samples collected from a single area to represent the whole area. If there is error in the values that have been entered in to represent a given area, this will change the value that is displayed on the map.
Trend Analysis
The trend surface analysis was not necessarily the best type of analysis to do given the distribution of points within the proglacial area as trend analyses are good for areas where there is an even distribution of points. This is especially true for the area in the proglacial zone that is covered by the lake, despite the fact that there are no values for the variables examined in the lake, the trend surface analysis still takes that area into account. In addition to there being a lack of points, because the area that the trend surface is being created for is so small and the trend surface analyses are highly susceptible to outliers (extremely high and low values), especially at the edges, one high or low value near the edge of the map may play a large role in how the trend surface is calculated. Even though, as mentioned before, the trend surface is one of the best indicators of large scale patterns, there is so much error associated with this type analysis in this study, it is difficult to draw any firm conclusions from its results.
Hotspot Analysis
Due to the lack of data for all of the polygons in the proglacial area, especially for variables such as vegetation density, there was not much data for the hot spot (HS) analysis to be conducted on. This means that there were very few hot spots found during the analyses and the polygons that were found to be hot spots were completely isolated, making it hard to conclude that the area was actually a hot spot for the given variable. In addition, the hot spots that were found were only based on a few surrounding polygons as for most cases, there were only two or three polygons that actually surrounded the hot spot areas.
Ordinary Least Squares Analysis
Ordinary least squares analyses are based on the principle that the values of one of the variables predicts the values of another variable. For this study, the dependent and response variables were somewhat random chosen, meaning that there was not prior evidence that one predicted the other, consequently, even though a regression line may statistically significantly predict one variable based on another, it is difficult to say for sure which one is in fact the dependent variable. This can be seen when comparing the two analyses of the C40 index and the RA index, where an analysis is done with each of them as the dependent. As both of them are statistically significant, it is difficult to determine which one is actually predicting the other, or if they are simply correlated. Alternatively, instead of the relationship of two variables being linear, as is what an OLS analysis presumes, their relationship may be much more complex (ie. non linear). Further examinations of the scatterplots of two variables may help to decide if a polynomial regression analysis should be done instead.
Spatial Autocorrelation
As with the other types of analyses, the error associated with spatial autocorrelation is linked to the lack of data for many of the variables. Like in the hot spot analysis, spatial autocorrelation uses the values of proximal polygons to determine if there is a pattern present in the overall area. When there are very few polygons (or values) in a given area, the likelihood that a pattern exists there must be based off of a limited set of data.
Further Studies
While this study has found that there were no discernable large-scale patterns between areas of the proglacial zone, this does not mean that patterns do not exist. For example, if, instead of looking at the distribution of a whole series of variables, only one variable or a couple variables that correlate (eg. the C40 index and RA index) was examined, there may be detectable and significant patterns across the proglacial zone using several types of spatial analyses. This is backed up by the fact that, although different spatial analyses often contradict each other, sometimes they show similar findings (eg. high vegetation density values from the trend surface analysis and hot spot analysis in South Creek tributary valley).
The next step in this study will be to use the results from the spatial analyses and instead of trying to find patterns within distinct areas of the outwash plain, instead try to find patterns within specific types of deposits (glacial, fluvial, etc). As there is likely more similarities between deposits of the same origin, there is likely to be more obvious patterns that emerge. Another type of study that could be done using the spatial analysis data collected in this study would be to look distinctly at the specific polygons that one or more of the spatial analyses found to have significant values.
The next step in this study will be to use the results from the spatial analyses and instead of trying to find patterns within distinct areas of the outwash plain, instead try to find patterns within specific types of deposits (glacial, fluvial, etc). As there is likely more similarities between deposits of the same origin, there is likely to be more obvious patterns that emerge. Another type of study that could be done using the spatial analysis data collected in this study would be to look distinctly at the specific polygons that one or more of the spatial analyses found to have significant values.