The bigcone spruce (Pseudotsuga macrocarpa) occupies high elevations from the Santa Barbara region south to San Diego County.

The most complete description of its habitat was this: "Commonly localized in stands on steep north and west facing slopes in the mountains, especially at the heads of canyons in the interior." (Smith, 1976).

The study region is the Madulce Peak 7.5' quadrangle, in the northeastern portion of Santa Barbara county, for the model. Terrain is extremely rugged, varying from 800-2000 feet.

I developed a simple map algebra-based model using only terrain derivatives that could be calculated from a digital elevation model:

BIGSPRUCE = (ASPECT == NORTH OR WEST) AND (SLOPE > 33) AND (ELEV > 1500)

Here is a representation of the terrain by the 30 meter USGS DEM "Madulce Peak", here considered to be ground truth for the sake of demonstrating the modeling concept.

Here is elevation data for the quadrangle from the USGS 1 degree series, at about 85 meter resolution:

Running the habitat model on the 30m data results in the following habitat distribution:

Running the habitat model on the 85m data results in a much different distribution:

Suppose that the 30m data represents the (unavailable) ground truth. Instead we have only the 85m data and a collection of 250 randomly sampled GPS points, as shown in the following map:

How can these data be used to characterize bigcone spruce habitat most appropriately?

One approach is to use the GPS points to develop an error surface for the entire region, and then subtract this error surface from the 85m data to produce a more correct DEM. This DEM can then be used as input to the habitat model. Here ordinary kriging is used to develop the error surface. Variogram analysis resulted in a spherical model with 0 nugget, range of 900 meters and a sill of 1400, which was used to assign weights for interpolation. The kriged error surface and resulting improved DEM are presented below:

A drawback to kriging is that, like any interpolation procedure, the resulting surface is overly smooth. The impact on the habitat model is that slopes and aspect are poorly represented. The habitat model is similar to the one calculated for the 85m data alone:

An alternative is to employ conditional simulation. The same variogram model is used, but the approach results in a set of error realizations that reproduce the texture of the error surface. One of these error realizations is shown below, along with the resulting DEM:

Here is the habitat model resulting from using this DEM:

The habitat model can then be run on a whole series of DEM realizations and the results summarized in a probability map. Below is an image generated by calculating the number of times (out of 50) that each cell was considered suitable for spruce habitat by the model, compared with the habitat suitability map derived from the 30m "truth" data:

This map reproduces much of the areas designated as habitat in the 30m "ground truth" data set, though it used just 250 (out of a possible 22,000) points!