Double Sampling and Sub Sampling are two methods of making a timber cruising effort more efficient while keeping the same or better accuracy. Unfortunately, the terminology of the methods can get confusing. Assisi Forest however must implement them in the correct way and so I thought I'd start a discussion on what they are and how they are processed within Assisi Forest. As always, this is meant to be an open discussion, so pipe in with corrections or comments if you want!

First some definitions...

**Double Sampling**

A "double sample" is used to describe when the same population is sampled twice. The term "double" refers to sampling the same population two times. The design of the two samples are not the same however. They are not simply "resamples" of a stand. The two are designed so that one can be used to improve the results from the other.

In the case of timber cruising, this made possible my relying on the fact that the relationship between BA and volume varies less than BA itself varies within a stand. Since measuring trees for volume takes more effort than measuring stands for BA, one sample is done with the goal of an accurate volume to BA ratio and the other with a goal of accurate stand BA. A simple multiplication of the two then results in the volume for the stand. If both samples have good confidence intervals, the resulting volume will also have good confidence intervals.

The advantage of double sampling is that because volume to BA does not vary as much as BA, one can measure fewer trees for volume then measure many more for BA. BA can be a simple tree count when using a BAF or DBH only when using count plots. The number of tree to measure for volume can often be much much less. Thus the effort to get the same confidence of a volume estimate is much lower.

This is called "Double Sampling" in statistics. In the timber cruise context, the same stand (population) is sampled twice (double) and the two samples combined during compilation.

**Sub Sampling**

A "Sub Sample" refers to a single sample where not all items have been measured for the same traits, ie. additional traits have been measured on a "Sub" set of the same sample. The additional traits are then used to estimate the same traits on the items where they have not been measured.

In timber cruising, a typical example is sub sampling for total height. Here, every tree is measured for species, DBH and more, but only a sub set is measured for total height. The reasoning being that total height is known to have a good relationship to species and DBH. Establish the DBH to total height relationship then apply that to the trees that were not measured for total height.

Sound familiar? Double sampling and sub sampling both rely on not measuring every trait on every item in every plot, yes. But a key difference is double sampling combines two independent samples of the same population, hence the term "double". Sub sampling uses a sub set of the same samples of a population, hence the term "Sub". The two are different. They can be combined, but the math and statistics are different for each.

**Count Plots and Big BAF are Examples of Double Sampling**

The terms "Count Plots" and "Big BAF" are used to describe two methods of carrying out a double sample.

With "Count Plots", the two samples are two sets of plots where in one set all trees are measured for species, DBH and height. These are typically called "measure plots" and are used to calculate the volume to BA ratio. In the other, only species and DBH are measured so that BA can be determined. These are typically called "count plots". Thus the term "Count Plots" is used to describe this method of double sampling. Because different plots are used for measuring than for counting, the measure plots are statistically independent of the count plots and a Count Plot survey is an example of Double Sampling.

In a "Big BAF" double sample, the two samples are done using two different BAFs. At each plot, the larger BAF selects trees to record species, DBH and height so that volume can be calculated. The smaller BAF is then used to record species and tree count which are used to calculate BA. Although both BAFs are used at the same plot locations, because they select different trees, the two BAFs create two statistically independent samples of the same population and a Big BAF survey is an example of Double Sampling.

**Estimating or Regressing Missing Heights are Examples of Sub Sampling**

Estimating or regressing heights that were not measured on all trees in the same sample are examples of sub sampling.

If heights were not measured on all trees, ie. they were measured on a sub sample of trees, that sub sample can be used to estimate the heights on threes that were not measured. This is typically done either by regressing heights against DBH on the measured trees or calibrating an existing height equation using the measured heights. Either way, because a sub set of the same sample is used to estimate traits on other members of the same sample, this is an example of Sub Sampling.

Note that because we are not mathematically combining unmeasured height trees to measured height trees the statistical independence of the trees measured for height and the trees not measured for height is not necessary. In other words, we don't multiply unmeasured by measured, we create an equation from the measured and used that to fill in the unmeasured. What is necessary is the trees measured for height should be an unbiased list of trees that cover the important range of species and DBH, not that they be statistically independent from the unmeasured trees.

**So How Does Assisi Do This?**

Coming Up :)

Great post, Rich! As one of my forestry mensurationist professors used to say, "It's all about the ratios!" The volume:BA ratio makes double sampling very appealing in forest inventories.