### Results Master Thesis

#### by ustroetz

Three things result from this research:

- From the Statistical Analysis a better understanding of the influence of the input variables on
*Harvest Cost*and the spatially explicit cost equation - The specific
*Harvest**Costs*for the Colorado State Forest - The
*Cost Surface*based on the spatially explicit regression for the Colorado State Forest

**1. Statistical Results**

Overall the four variables explain 98.28% of the *Harvest Cost* using the given model. All of them have an importance in predicting *Cost*. The *Trees per Acre* variable, with 3.2% explanatory value, has the least importance, followed by *Slope* with 9.5%. *Skidding Distance* is the most important spatial variable with 29.9% explanatory value. And *Volume per Tree* is the most important variable out of the four, with 55.7% explanatory value. The two spatial variables taken together explain 39.4% of the *Cost*.

Relative importance metrics:

lmg I(VPT^(-0.72)) 0.55669591 TPA 0.03239262 S 0.09457912 SD 0.29918160

The big thing that results form the statistical analysis is the spatially explicit regression. It was validated in the statistics section and has a R-squared of 0.4212. The degree to which it is useful is discussed later.

C = 22.83 + 0.3306 x S + 0.007526 x SD +ε_{i}

**2. Harvest Costs Colorado State Forest**

For the 74 timber sale stands of the CSF the *Harvest Cost* based on the full model, on the regression model with all predictors, and on the spatially explicit regression model was calculate. The mean *Harvest Cost* of all stands is 36.38 $/ton from the full model, 35.62 $/ton from the full equation, and 39.3 $/ton from the spatially explicit equation. The full model and the full equation have roughly the same standard deviations, while the spatially explicit equation’s standard deviation is significantly lower.

The graph below gives an exemplary overview of the *Harvest Cost* of 10 stands. The graphs compare the different models:

**3. Cost Surface**

The last things, and most important thing, that results from this paper, is the *Cost Surface*. Check out the Application Example at www.wald.io to see the full Cost Surface. In the Cost Surface you can really see the heavy influence of the *Skidding Distanc*e on the *Cost*. Everything close to a road is green (less expensive). The further away you get the more expensive it gets (red). I created the *Cost Surface* with numpy arrays which made the process quite fast. But since I only have a old MacBook the process for the southern part of the Forest still took five days. Once I have a more powerful machine again, I will calculate the *Cost Surface* for the entire forest. Below in image of the *Cost Surface* and the roads covering the State Forest.