First Aid for Cruises (Part II)
This is the second part of an article that discusses some typical problems that occur after a cruise has been completed. In Part I we discussed some things that can and can't be done when areas are added or dropped from a completed cruise. In Part II we will discuss some options for updating older cruises.
Problem: "I cruised this sale a couple years ago, then it was taken off the sale list. Now it's back on the list, but it has been growing. Do I have to recruise it to get the current volume?"
Given that the sale area has not changed, the basic problem is one of estimating the growth and mortality that has occurred since the stand was first cruised. Whether one is concerned about growth will depend on how fast the stand is growing. In older timber the growth rates can be slow and a year or two probably will not make a big difference. Younger stands on good sites can grow rapidly. Again the question is, "How much of a difference really matters?" Given that growth is a concern, there are a couple ways to handle this.
Growth and yield models are designed for the purpose of estimating how stands will change. Models differ in the data required to run them, and in the resolution of the information that they provide. For simplicity, we will broadly classify models as those that project entire stands (stand models) and those that project trees (tree models).
Stand models are generally the simplest and usually require only basic stand level information like site productivity, age, and density to project the stand. The information provided for a projected stand is also generally limited to stand variables like future volume per acre. Stand type models are generally not well suited for projecting mixed species stands.
Tree models project a list of trees that are then aggregated to provide information about a stand. A tree list is required that includes the species, diameter, height, and possibly crown ratio. It will also require knowing the trees per acre that each tree (or diameter class) represents. This is sometimes called an "expansion factor" by modelers. Many tree models will compute estimates for heights and crown ratios that are not measured, but these estimates are based on regional averages. Relying totally on regional averages can greatly reduce the accuracy of the model for a given stand, so these variables should at least be sampled.
One should select a model that is appropriate for the location and timber type of interest to protect against biased projections. For more information on models see "Cruising and Growth Models", Issue no. 13).
One type of simple growth model that may have application for this problem is the "stand table projection." This method takes a stand table constructed from the cruise, then applies growth estimates to each DBH class to create a future stand table. Volumes in each case are computed using local volume equations (DBH only) or using estimated heights from a Height/DBH curve.
Diameter class change must consider the diameter growth, the loss due to mortality, and any addition of new trees growing into the smallest diameter class (ingrowth). Estimates of periodic diameter growth can be obtained from increment cores or remeasurements (adjusting for bark thickness) from the stand of interest. Change in the diameter will estimate how many trees stay in a class and how many move up into the next class.
Ingrowth of small trees can be considerable in young fast-growing stands, but the biggest challenge in applying stand table projections is accounting for mortality. Also, over long periods, the Height/DBH relationships will change. This method is best used for short projections in stands with little mortality or ingrowth of small trees.
When using models it should be remembered that they normally project stand development with only mortality due to normal competition, and do not necessarily account for mortality due to insect outbreaks, diseases, or storms. While volumes may be computed to specified merchantability standards (especially with tree models that use taper equations) they do not consider defects (e.g. rot, sweep, broken tops) or grades (e.g. surface characteristics). For short projections it may be reasonable to project a total volume (or total volume by species), then adjust this for grade and defect based on the proportions in the original cruise.
Another possible problem with using models occurs when the original cruise used a relatively large minimum diameter limit and ignored smaller trees. This will have the effect of providing biased density measures (such as lower basal area per acre) to the model. Depending upon the model, this may bias the growth estimates (lower densities normally mean higher percentage growth rates).
It is reasonable to think that the sampling error after the projection will be worse than the original sampled volume, because the model projections have an additional variation (errors) associated with them. These would normally have to be added together to get the SE for the updated volume. However, models do not generally provide variance estimates with their projections, making it very difficult to make a confidence statement about the updated volume estimate.
Projecting the Change in a Plot Cruise
Another way to update a plot cruise is by using double (or "2-phase" sampling) with a ratio estimator. This is done by relocating and remeasuring a random or systematic sample of the original plots (not just the ones along the road; we recommend a systematic sample) and creating a ratio of the remeasured plot volume to the original plot volume. The new volume and statistics are estimated by:
New Volume = Original Volume * Ratio
SE%new2 = (SE%original2 + SE%ratio2)
The correction ratio is [total remeasured volume ¸ total original volume] for the resampled plots. This method has the advantage of not having to recruise all the plots, takes care of growth and mortality, and provides an estimate of the sampling error - but you will have to go into the field to relocate and measure a few plots. The statistics for the ratio are calculated for what is called a "ratio of means" estimator.
Projecting the Change in a 3P cruise.
This procedure will provide updated volumes, grades and statistics. This assumes that the sum of the KPIs changes in the same ratio as the sample trees. If mortality is small this will probably not be a big deal. Any growth and mortality will be reflected in the ratios which "correct" the sum of the estimates.
3P cruises do not necessarily collect data to run models. We must always collect information on the sum of the KPIs, but might not keep KPIs for all individual trees. Also, KPIs are selected because they are related to volume, and may not relate directly to a density measure required by a model.
If you estimate and keep the diameter of each tree (in the process of making the KPI estimate) then at the end of the cruise you will have a stand table for the entire stand. These diameters can be used to estimate density for a stand model, and the sample trees will provide heights and crown ratios for a tree list (see "Why Use the DBH in 3P Sampling?", Issue No. 29).
Remember that data is normally reported for a 3P cruise as a total for the area cruised, and you must estimate the volume per acre by dividing that total into the area of the stand.
How much insurance do you want to buy?
Here are a few things to think about:
Originally published January 2001
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