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# Math and Science Solutions for Businesses/Forest Inventory (species and wood volume)

Question
Hello Randy

On a forest parcel I want to randomly add a number of points which will be center points of sample plots, for the purpose of estimating counts of tree species and wood volume for the entire parcel.  To accomplish this a grid will be placed over an aerial photo, numbers assigned to the grid cells, and cells will be selected by a random number generator.

However I am told that plots determined randomly have a tendency to cluster; this would skew the estimation of the entire parcel.  Every segment of the forest should have an equal chance to be sampled.

I would like to know if there is a method to prevent this clustering, rather than arbitrarily reassigning the points by hand according to what looks right visually. Is there a mathematical method or available software to determine whether there is clustering and to prevent it before the fact, or for correcting it afterwards?

Any help or guidance will be appreciated.

Thanks.

Pete

I looked into this a little bit and didn't find any mention of a tendency to cluster in the "stratified level" sampling method you plan to use.

The basic goal in the sampling is to pick the plots large enough so that the mean of the variables you're measuring (species, wood volume) is reasonably homogeneous, which is to say that the means calculated within the different plots are reasonably close to each other and to the overall mean of the forest tract. This plot size would be tricky to obtain a priori since you need to specify the plot sizes before making any measurements, other than just an overall visual impression from remote sensing.

I don't see how, after chopping up the forest tract into these large-enough plots, you would run into trouble if you just randomly chose a subset of these plots, within which to make your detailed measurements.

Let me know if you have a particular reference regarding the clustering bias problem and I will try to help you interpret it and find a solution.

Math and Science Solutions for Businesses

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#### Randy Patton

##### Expertise

Questions regarding application of mathematical techniques and knowledge of physics and engineering principles to product and services design, optimization, prediction, feasibility and implementation. Examples include sales and product performance projections based on math/physics models in addition to standard regression; practical and cost effective sensor design and component configuration; optimal resource allocation using common tools (eg., MS Office); advanced data analysis techniques and implementation; simulation and "what if" analysis; and innovative applications of remote sensing.

##### Experience

26 years as professional physical scientist and project manager for elite research company providing academic quality basic and applied research for government and defense industry clients (currently retired). Projects I have been involved in include: - Notional sensor performance predictions for detecting underwater phenomena - Designing and testing guidance algorithms for multi-component system - Statistical analysis of ship tracking data and development of anomaly detector - Deployed vibration sensors in Arctic ice floes; analysis of data - Developed and tested ocean optical instrument to measure particles - Field testing of protoype sonar system - Analysis of synthetic aperture radar system data for ocean surface measurements - Redesigned dust shelters for greeters at Burning Man Festival Project management with responsibility for allocation and monitoriing of staff and equipment resources.

Publications
“A Numerical Model for Low-Frequency Equatorial Dynamics” (with Mark A. Cane), J. of Phys. Oceanogr., 14, No. 12, pp. 18531863, December 1984.

Education/Credentials
MIT, MS Physical Oceanography, 1981 UC Berkeley, BS Applied Math, 1976

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Am also an Expert in Advanced Math and Oceanography