Results & Discussion

1) Ecosystem Classifications (western North America)

2) Ecosystem Classifications (southwestern USA)

3) Probability & Confidence Maps

The discriminant analysis (DISCRIM) procedure discussed in 'Statistical Analysis' was used to generate ecosystem classifications for the the entire western North America study area for both the present climate data and for two periods of paleoclimate data: 6,000 and 21,000 YP.

To compare these classifications to the climate data of the time, you may view the compared mean annual temperature (MAT) and mean annual precipitation (MAP) of the three time periods here:

In both the above images, the colour legend has been kept consistent between time periods to allow for easy comparison of the climate changes. In the 21,000 YBP MAT image, there is no data shown for the northeastern portion of the study area. The temperature data for this area doesn't appear as it is beyond (negatively) the range of present-day temperature upon which the legend was applied. For a complete look at the 21,000 YBP temperature data, click here.

1) Ecosystem Classifications (Top)


(Click for larger image)

Present Day: Western North America ecosystem classifications produced through the DISCRIM procedure.


(Click for larger image)

6,000 YBP: Western North America ecosystem classifications produced through the DISCRIM procedure.

While the climatic conditions at this time were not exceptionally different to the present conditions, there are very interesting climatic differences that have certainly influenced how the ecosystems throughout the study area are classified. Especially fascinating in this image is the fluctuation of the transition zones between ecozones. The changes are subtle, but indicative of the climatic variables that differentiate the different ecosystem classes.

  • North America ice sheet coverage at 6,000 YBP (click here - ice shown in blue)
  • Comparison of ecosystem classifications between 6,000 YBP and the present day (click here)


(Click for larger image)

21,000 YBP: Western North America ecosystem classifications produced through the DISCRIM procedure.

It should be noted that a substantial portion of northern North America was covered by continental ice sheets at this time. Having said that, any classifications made in the ice-covered areas of the study area are meaningless from an ecosystem perspective--though highly important from a modelling and variable refinement perspective. See the discussion below for more on this phenomenon.

  • North America ice sheet coverage at 21,000 YBP (click here - ice shown in blue)
  • Ice sheet coverage at 21,000 YBP overlayed on DISCRIM ecosystem classifications (click here)
  • Comparison of ecosystem classifications between 21,000 YBP and the present day (click here)

A closer look at the southern extent of the study area shows minimal difference between the present-day and 6,000 YBP data, but a dramatic change in the 21,000 YBP period.


(Click for larger image)

Present Day:

In the present day climate data, the ecosystem classifications in the more southerly areas of North America may not be particularly meaningful. The ecosystem classes are based on Alberta and British Columbia classification systems. There exist ecozones outside these provinces that do not have a reasonable equivalent zone in Alberta and BC. While there are similar ecozones, the present day climatic conditions differ greatly. For this reason, the Alberta and B.C. ecosystem classes as applied to areas well outside this geographic and climatic range.

(Click for larger image)

6,000 YBP:

Because of the similarity of climatic conditions in this time period to those of the present day, the ecosystem classifications in this southern area at this time may not be meaningful in their own right. However, examining the differences between this time period and the present day, given the minimal climatic changes could lend insight into how the ecosystem distributions in the model respond to even small climate fluctuations.


(Click for larger image)

21,000 YBP:

In the southern regions of this time period, the ecosystem classes that are somewhat meaningless in the present and 6,000 YBP maps become of prime interest. In this time period, as the climatic conditions of southern USA resemble those of present-day western Canada, the ecosystem classes developed for the Alberta and B.C. region have more applicability.

It is important to remember that the classification of paleo-ecosystems assumes an instantaneous migration by plants and trees and does not consider variations in succession order or post-ice migration rates. However, the large timescale of the data may negate any ‘migration latency effects’ that would affect ecosystem classification, especially given the rapid response of plants to climate changes that has been shown in past research (Williams et al. 2002). If there is an area of concern, I would assume that ecosystem classifications made at the periphery of continental ice sheets , where soils, etc. may not be fully developed, would be most affected by this phenomenon.

 

2) Probability and Confidence Maps (Top)

In addition to producing the new ecosystem classifications, the DISCRIM procedure also produces a classification 'probability' as part of the data output. This probability is essentially a classification confidence. It corresponds to the Mahalanobis distance from the assigned class and whether there are other classes in the same ranges that could potentially be correct. As with any probability, the higher the value, the more likely that the classification is appropriate. Because these probabilities are attached to spatial data, they can be mapped just like any other data variable. What is produced is a map of the study area showing the confidence levels that the DISCRIM procedure has applied to each data point. In the following images, the probability is mapped from red to yellow (red being highest probability/confidence and yellow being the lowest). For a single image comparison of all time periods, click here. In all images, the values range from zero (yellow) to 1 (red).


(Click for larger image)

Present Day:

The majority of classification uncertainty appears in the Canadian region while the highest confidence is seen in the lower latitudes of the United States, particularly along the coastline. The areas from which the calibration (baseline) data was generated seem to show some of the lowest probabilities.

(Click for larger image)

6,000 YBP:

While similar to the present-day confidence map, there is a trend towards higher confidence throughout the United States and into the Canadian prairies. Also, while the Canadian Rockies appear to show a higher classification probability, the north and interior regions of B.C. remain largely unchanged.


(Click for larger image)

21,000 YBP:

A dramatic change in the confidence in the northern regions is seen stretching from the coast to the prairies. Interestingly, the confidence in the southern United States appears to be decreasing as climate conditions similar to the baseline data shift southwards.

When first viewed, I found these probabilities to be quite counterintuitive--almost the exact opposite of what I expected to see. I anticipated a high level of confidence in the baseline areas of Alberta and British Columbia, as these are the locations upon which the classification system was calibrated. I also expected to see very low probabilities in the far outlier locations (southern USA in the present-day and 6,000 YBP maps and the northern locations in the 21,000 YBP image). Instead, the probabilities are exactly the opposite. The DISCRIM procedure assigns the highest probabilities to the areas in which I would expect the data to be well outside of the baseline calibration data. While this seems paradoxical, an understanding of the DISCRIM procedure explains the phenomenon.

The discriminant analysis procedure assigns classes based on a new data point's distance from the centre-point of the nearest class from the calibration data (the baseline data). Hence, a new data point that falls well within the cluster of calibration points is bound to be reasonable close to a multitude of baseline classification centre-points--leaving a higher potential for a misclassification. Conversely, any outlier data, such as the far north points of the 21,000 YBP data set are outside the mass of baseline data, leaving them close to only whichever classification centre-point is at the edge of the baseline data (see figure on left for an illustration of this).

While the classification probability values produce a powerful visual image of the classification confidence, these figures can also be misleading. Remember, this is not a confidence in the actual ecosystem characteristics (plant communities, etc.). It is merely a probability that the DISCRIM procedure has placed a novel data point into the most appropriate class available to it. Because the analysis is constrained to the classifications provided in the calibration data (the baseline data in this case), it merely places novel data points into the best category available, regardless of how closely the new data matches the calibration data in that particular class. This is more easily explained in the following examples:


(Click for larger image)

Example 1: The potential classification of a new data point with extremely cold temperature values.

In the 21,000 YBP climate data, nearly half the data points (mostly in the north) have be assigned to the alpine sub-zone. This classification is likely based on the extremely low temperature values in this area during this time period. The only reasonable classification from the calibration data that resembles this temperature is found in the alpine areas. In fact, the 21,000 YBP northern data is so cold that it would be "off the charts" of the baseline data, or outlier temperature data. Due to this large temperature difference, the DISCRIM procedure has assigned it to the nearest ecosystem class (the Mahalanobis distance is shortest to the alpine class of the calibration group, even though the distance itself may be relatively large).


(Click for larger image)

Example 2: The potential classification of a new data point with extremely cold temperature values AND extremely wet moisture values.

A potential fix for this issue could be to re-assess the variable inputs for the discriminant analysis, placing more emphasis on variables reflecting continentality. Alternatively, using variables . Because all the climate variables were used in this analysis, placing more emphasis on certain variables would involve removing other redundant variables (such as pure temperature or precipitation variables) that, by their presence in the analysis, reduce the importance of other more critical variables. Again, revisiting the principal component analysis would help isolate these redundancies. I have discussed the potentially overlooked importance of other principal components that I did not consider in this first analysis (see 'Statistical Analysis').

The issue with this explanation is that northern Canada in the 21,000 YBP period exhibits much drier conditions that the present day. Therefore, the idea of the CWH classifications being due to high moisture values doesn't hold water, so to speak. Evidently, further analysis and contemplation is necessary to solve this puzzle.

The assignment of ecosystem classifications to the extreme outlier climatic conditions (as is seen in the northern areas of the 21,000 YBP classification) with a very high probability represents a different but related problem to the classification probabilities. As discussed previously, because this range of climatic data (primarily extremely low temperatures) has no appropriate EQUAL among the modern baseline classifications, the discriminant analysis forces the areas into the closest available category—and does so with a very high level of confidence. This makes sense after looking at the principal component plots (see 'Statistical Analysis'). If a new climatic condition were to fall a great distance away from the plot, it could not be reasonably classified with the baseline ecosystem classifications that are available. However, this would not prevent the DISCRIM procedure from assigning it to an ecosystem class.

The mapped probability values become even more interesting when they are compared to the ecosystem classification maps to which they correspond:


(Click for larger image)

From this comparison image, it is evident that the highest probabilities are assigned to ecosystem classifications which are potentially well outside the range of the baseline calibration data set. Furthermore, it shows that there are clearly areas of lower probability around the boundaries (or ecotones) between different zones. This fits with the explanation above, as these would be data points for which there would be more than one class centre-point within a similar distance.

The next step in the classification procedure would be to establish some threshold values for classification distances, potentially linked to the probability. This is discussed further in 'Future Directions'.

<<<< Back to Statistical Analysis | Top of this page | Continue on to Future Directions >>>>

References:

Manly, B. F. J. (2005). Multivariate Statistical Methods: A Primer. 3rd Ed. Chapman & Hall / CRC Press, Boca Raton.

Williams, J. W., D. M. Post, et al. (2002). "Rapid and widespread vegetation responses to past climate change in the North Atlantic region." Geology 30(11): 971-974.

© 2007 - David Roberts, University of Alberta