### TSI Analysis - Comparisons to Cruise and Scale

Data presented with the kind permission of Island Timberlands

We conducted an experiment to understand the ability of TSI to predict the volume of blocks, comparing TSI outputs to cruise and scale for 427 blocks. Although both cruise and scale have their own strengths and weaknesses as metrics, understanding the relationship between these two metrics can give context to understanding the comparisons with TSI. We ran multiple regressions with TSI as the dependant variable (Y) and cruise/scale as the independent variable (X).

This, in practice, poses the question:

Given a cruise or scale estimated volume, what is the expected volume prediction by TSI?

Through this we define continuous equations representing the relationship between TSI, cruise,and scale. We can use these to grasp the scale of these differences, providing a starting point for investigating acceptable difference, estimate reliability, and create a standard to measure against.

#### Total Volume Comparison by Block

We regressed total block volume using TSI against total block volume using cruise and scale. Sample size is 427 blocks. These figures show that TSI matches well to both cruise and scale. It is, however, significantly closer to scale, carrying a volume unit ratio of 1 to 1.02 (for every 1 unit increase in scale, TSI is projected to increase by 1.02). The TSI cruise ratio is 1 to 0.86.

From these coefficients we can see that TSI predicts volume slightly lower than cruise and higher than scale, in effect landing between the two estimates. Although the intercepts (CR - 562, scale - 247) appear significant, it is important to understand real weight. These are unweighted block volume differences. Median block volume for cruise is 9,600, scale is 8,634, which give a weighted error of 0.05 and 0.02 respectively.  #### Individual Analysis of Old Growth and Second Growth

In the figure below, Old Growth and Second Growth have been separated. As in the previous comparison between cruise and scale, TSI converges with both metrics in Second Growth and diverges with both metrics in Old Growth.

Second Growth  Old Growth  Because scale and TSI were already so close, the benefit seen in the SG is extremely small, from 1.023 to 1.022. As expected the coeffect in the OG cruise against TSI (bottom left) is very similar to the OG cruise against scale(seen previously), the former being 0.74 the latter 0.77. This follows logically because of the greater uniformity in the Second Growth compared to the Old Growth. Decay waste and breakage take a toll on all estimators, creating larger scale of error.

#### Cruise Bias

If TSI were perfectly matching cruise or scale, the formula of the regression line would be TSI = (1)CR/Scale + 0, which is of course a 1:1 ratio. This is displayed by the 45 degree dashed line in Figure A below.

The difference between the two lines is TSI's "bias" based on the data. We see that the lines diverge as the block sizes grow, this follows logically because these block volumes are not weighted by size; we would expect a larger block to have a larger difference in volume although the weighted difference could be very small.

In Figure B below, we have displayed the individual block differences (y-axis) against the Individual block averages. This gives us a look at the distribution of differences as well as the block size. We can see the mean difference = -1,139.69 which is a different way of representing the coefficient bias being 0.86 in Figure A. They quantify the predictive difference between cruise and TSI. We also added a 95% confidence interval, which displays that 95% of block differences lie between the lower and upper bounds. This makes it easy to find and examine our outliers.  #### Scale Bias

Similar to the cruise bias, we can see the TSI "bias" against the scale data. The bias is represented by the difference between the regression line and the 45 in Figure A and the difference between the mean difference line and 0 in Figure B. These are quantified by the coefficient 1.02 in Figure A and the mean 484.34 in Figure B. These display the nature of TSI's slight positive bias compared to the scale data.  ### Individual Block Analysis

Below you will find an analysis done by TSI on a few of the 427 blocks used in this study.

#### Example 1

The first block is a second growth harvest block with an area of 27.1 ha. The elevation range is from 275m to 354m and TSI segmented 8,433 trees. The LiDAR was flown September of 2011 and the block was harvested in Decemver 2012.  The block is predominately douglas fir, with secondary species of western hemlock, western red cedar, amabilis fir (balsam), and red alder. Of the 8,433 trees segmented by TSI, 1,315 recorded a volume above 2 cubic meters each, and 5,399 had a volume over 1 m3. In this block, TSI found that 82% of the volume was made up of Douglas Fir, and 13% was made up of Western Hemlock. Compared to the Scale percentages of 87% (Fir), 12% (Hemlock), and the Cruise percentages of 79% (Fir) and 19% (Hemlock), this demonstrates TSI's high degree of accuracy.

#### Example 2

This second block is an old growth harvest block with an area of 28.7 ha. The elevation range is from 948m to 1,217m and TSI segmented 10.985 trees. The LiDAR was flown September 2011 and the block was harvested in October 2013.  The block is predominantly western hemlock, with secondary species of amabilis fir (balsam), yellow cedar (cypress), and douglas fir. Of the 10,985 trees found by TSI, 2,456 recorded a volume above 2 cubic meters each, and 6,652 had a volume over 1 m3. With the Cruise finding 51% Hemlock, 35% Cedar, 8% Alder, and 6% Fir and TSI finding 58% Hemlock, 26% Cedar, 9% Alder, and 7% Fir, TSI demonstrates it's ability to cope with complex areas with a large variety of species.

TSI is also able to determine the primary product of each tree. In this example, 1,782 trees yielded saw logs as their primary product. 