Final Project, 36-402

December 19, 1997

Due no later than: Thursday, May 2, 1996, 9am Late projects will NOT be accepted.

This is your final project. Please present your own work and do not discuss the problem with anyone other than Mike Meyer. You should prepare a preliminary analysis by April 18, 1996. The preliminary report should show your initial explorations and give some indication of how you intend to complete the analysis. It should be no more than 2 pages long. If you fail to submit a preliminary report you will not be directly penalized, but you will be indirectly penalize because you will not get feedback on your work.

The final report must contain an executive summary (something that a non-technical person like you boss can understand) together with a technical summary. All tables and detailed output should be place in an appendix.

Effects of Skidders on Two Types of Forest Soils

Description

Modern forestry requires considerable specialized equipment. First, a feller cuts trees and lays them down on the ground. Then, a skidder pulls those trees to bring them to the road where the branches will be removed by a delimber. The skidders ride on trails where they must make many round trips. These trails are not made of asphalt or gravel, but rather of soil. The intensive use of these trails leads to the formation of ruts and soil compaction on the surface which can be damaging. In this study, FERIC (Forest Engineering Research Institute of Canada/Institut canadien de recherches en génie forestier) with Université du Québec in Abitibi-Témiscamingue, has studied the modifications to two types of soil caused by the traffic of skidders on skid trails.

The experimental design is as follows. Two types of soil were studied: clay and sand. For each type of soil, three trails which had never been used were set up where a mechanical cut with regeneration protection was performed a few weeks earlier. Each trail was 30 m long and 4.5 m wide. On each trail a skidder made 15 round trips; going into the forest, the skidder was empty, outbound the skidder was full. Some physical characteristics of the trail were measured before the first round trip as well as after trips one, three, five, seven, eleven, and fifteen.

The different measurements taken after each trip previously mentioned are the following. The first is the slippage of the wheels of the skidder, defined as the mean slippage of the four wheels. The slippage of each wheel is a function of the total number of spins and the speed of the skidder. These quantities are determined from the recordings of two video cameras on each side of the trail. Under the weight of the load, the skidder modifies the ground by forming rims and ruts. The rut depth as well as the surface of displaced materials have been computed by taking the average of these measures for three different transversal profiles as follows. For each profile of the width, the height of the ground (with respect to the level before the first trip of the skidder) has been measured at 20 points after the return of the skidder. For a rut, the height is negative whereas it is positive for a rim. The depth of the ruts of a profile is defined as the absolute value of the smallest height among the 20 measured points. The surface of displaced materials for a profile is defined as a function of the absolute value of these 20 heights. Three other characteristics of soil have been measured for each of the trips previously mentioned. The anhydrous density of the soil is considered as an indicator of soil compaction. Measured with a device at depths of 10, 20, and 30 cm under the ruts, only the measurements at 10 cm will be used. Moreover, resistance to penetration (i.e., the strength that must be used to stick a needle in the soil) and the limit of shear resistance (the maximal strength that must be used to provoke a free movement of the soil) are two other parameters measured in prediction models of the effect of traffic on soil. The resistance to penetration is computed by taking means of pressures at depths 5, 10, 15, 20, 25, and 30 cm in mineral soil, but only the measurements at 5 cm will be used. Limit of shear resistance in the ruts is the mean of 10 readings of a shear measurement device sunk in about 10 cm of mineral soil.

The objective of this study is to construct prediction models for the variables describing modifications to the soil in terms of the other variables. We want to explain the depth of ruts, the surface of displaced materials, and the density, all measured after the trip, in terms of the density of the soil before the trip, the resistance to penetration before the trip, the slippage, the number of trips of the skidder, and the limit of shear resistance before the trip. Note that the measurements being taken after the trips, the measurements before the trip (density, resistance to penetration and resistance to cutting) are obtained by interpolation with respect to the previous trips (except for the first trip for which we also have the measurements before the trip). Two different skidders were used for the sand trails and the clay trails.

The data set as we received it contains 36 cases with 13 variables, that is six trips (1, 3, 5, 7, 11, and 15) for each of the three trails and two types of soil. Each case corresponds to the measurements (or interpolations) obtained before or after a trip of the skidder on a trail.

The variables are:

1. trail: number of the trail;

2. soil: 1 for sand and 2 for clay;

3. trip: cumulative number of trips on the trail (including this one);

4. mean.slip: mean slippage during the trip;

5. shearadj: resistance to cutting before the trip (estimated by interpolation);

6. pen5adj: resistance to penetration at 5 cm before the trip (estimated by interpolation);

7. rut: maximal depth of ruts after the trip;

8. totsur: surface of displaced materials after the trip;

9. density: density measured after the trip;

10. denadj: density before the trip (estimated by interpolation);

11. diffden: difference between the densities after the trips adjusted by the number of trips;

12. diffdepth: difference between the depths of ruts adjusted by the number of trips;

13. difftotsur: difference between the surfaces of displaced materials adjusted by the number of trips.

Note that the three variables measuring a difference are adjusted by the number of trips between the two measurements. For instance, the difference after the third trip is the measurement after the third trip minus that after the first, all divided by two, whereas the difference after the eleventh trip is the measurement after the eleventh trip minus that of the seventh divided by four. The same kind of adjustments are used for interpolation.

Your task

Your task is to do a preliminary analyses of these data. You might consider many pictures, linear regression analyses for each individual dependent variable (depth of ruts, surface of displaced materials, and density of the soil after the trip) with model selection techniques, and/or separate analyses for the sand and clay trails. Transformations of variables might be considered. In particular, in the case of sand trails, the difference in rut depths might be used instead of the depth itself. Are there appropriate ANOVA models for these data? Are there discrete data components to the problem? Can you use survival methods?

The data

The data are available in /afs/andrew/stat/data/402/ferice.dat This problem statement is

in /afs/andrew/stat/data/402/final.tex