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As described previously, there exists a very weak trend between the precipitation data and the elevation. The project was suddenly halted until a good relationship could be found because no actual model could be confidently constructed without some sort of relationship between the two datasets. A variety of transformations was been performed on the precipitation data in the hopes of seeing a better relationship with elevation. This difficulty was alleviated by a study done by Daly et al. in 1994 that appeared in the Journal of Applied Meteorology. Daly et al. proposed a simple but intuitive way of modeling precipitation enhancement attributed to the topography. The following discussion describes the modeling methods proposed.
Daly et al. (1994) suggested an objective precipitation distribution model that describes precipitation over complex terrain called PRISM (Precipitation-elevation Regression on dependent Slopes Model). The model framework incorporated three main concepts: (1) the effect of elevation on precipitation, (2) the spatial scale at which orographic effects are observed, and (3) the spatial patterns of an orographic regime over complex terrain. They suggested that a relatively coarse resolution DEM could be used to model orographic precipitation more effectively. This is due to the fact that enhancement processes work in a certain spatial scale depending on the terrain itself. This idea agrees with Barry’s (1981) description of the effect of orographic scale dependence. The operating scale of orographic effect may in fact be much larger than the resolution and scale of a geostatistics based modeling method. This makes sense in the context of the current project because it is uncommon to see orographic enhancement operating at a 20 m or even 25 m scale. In order to capture the orographic effect, the DEM layer was aggregated and smoothed at various scales. The smoothed out DEM layer became what Daly et al. termed as “orographic elevation”. This value does not represent the absolute elevation value. Rather, it incorporates the surrounding topography to produce a mean value. This in turn accounts for the effect of surrounding topography on the precipitation at a certain point in space. Table 4 shows the result of various aggregating and smoothing schemes and the correlation value with orographic elevation. The table clearly shows that high correlation values exist between the current precipitation data set and the orographic elevation. Figures 11 and 12 show the original DEM with the weather stations and the smoothed out DEM layer at 10 km respectively. It was decided that a resolution of 500 m smoothed out at a 10 km scale would be used for modeling. This decision was made based on the trade-off between oversimplification and high correlation. Figure 8 shows a levelling trend of correlation values after the 10 km smoothing. The smoothing operation, in this context, essentially describes how topography from 10 km away would affect the precipitation regime at a certain point in space. A good example of this process can be seen at the North Vancouver Wharves.
The mean annual precipitation value for the North Vancouver Wharves station is approximately 1,700 mm while its elevation is only 6 m. This is due to the enhancement of precipitation caused by the mountains to the north. This process was effectively captured with a smoothing operation of 10 km that accounted for the topography of the surrounding the site. This modeling method was further validated by the fact that summer periods post relatively poor correlation values. This can be attributed to the dominance of convective precipitation process in the summer months, where there is very little expectation of an orographic uplifting effect. The modeling method is also supported by an appearance of an outlier in the plot between orographic elevation (10 km smoothing) and precipitation. Lions Bay station shows an exceptionally high orographic elevation but has a relatively low precipitation value. The intuitive explanation for this result is the location of this particular site. Lions Bay is located on the leeward side of the Northshore Mountains, nestled between the sea and the steep, high ridges. The smoothing operation incorporates this greatly varied topography. However, the modeling method has not considered the slope aspect of such a site and its implication on the precipitation values. Lions Bay station appears to have a high orographic elevation and it is therefore reasonable to predict precipitation. In truth it has relatively low precipitation due to this factor. Figure 13 shows the outlier along with the plot of all the other stations.
Daly et al. (1994) also consider aspect, slope, wind direction, moisture content and their potential effect on the precipitation distribution. Due to a lack of expertise in programming statistical software packages for customized analyses, a simple linear regression analysis on orographic elevation is used to construct the model. There are a number of assumptions that have to be satisfied for a valid linear regression analysis to take place. Kleinbaum et al. (1998) provide a good overview on these assumptions. Among them, the assumptions of linearity, existence, homoscedasticity, and normal distribution appear to be satisfied. However, the assumption of independence between each of the samples (mean monthly precipitation of each station) appears to be weak (Personal communication: Dr. Carl J. Schwarz; Department of Statistics, Simon Fraser University). The implication of this will be discussed later in the report.
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