Knowledge reference for national forest assessments - modeling for estimation and monitoring
8. Monitoring over timeMonitoring over time allows estimation of change and trends in forest attributes. The changes and trends can be estimated from a collection of permanent sample plots -see section 8.1- temporary plots -see section 8.2- or a combination of both. Temporary plots are well suited for obtaining estimates of the current state of the forest, while permanent plots are better suited for obtaining estimates of change over time. Using a mixture of permanent and temporary plots is akin to sampling with partial replacement. This is an efficient design, but requires complex equations to insure proper analysis of the data. It can be very difficult to obtain a true estimate of change or its variance. Change estimates are frequently evaluated against some expectations or a set of targets, and estimates of the precision of the change estimate are important in this situation. Predictions of future values can be made from observed trends if one is willing to believe that past trends will apply equally, or after some type of calibration, to the future.
The simplest change equation for a trait Y measured at time t and then again at some future time t + Δt is:
Where Yt is the initial measurement at time t, Yt + Δt is the future measurement at time t + Δt, and ΔYΔt is the change in Y from time t to time t + Δt.
The variance of an estimated change, or the variance in ΔYΔt, depends on the type of plots (or mixture of plots) used for the data collection. Any correlation between measurements at two points in time must be accounted for in estimation of the variance of a change.
From the above equation describing change, an estimate of change can be obtained algebraically:
where all terms are as defined above. In the simplest case, the variance of the change estimate is equal to the following:
where Var denotes the variance, Cov is the covariance, and ρ is the correlation between the original and future measurements. A strong positive correlation will help reduce the variance of a change measurement.
8.1 Estimating Change Using Remeasured Permanent Plots
Permanent plots refer to forest sampling locations that are monumented or otherwise uniquely identified and remeasured at different points in time. For overstory measurements, this usually means that a plot center (for circular plots) or plot corners (for rectangular plots or transects) are permanently marked with a stake or by some other method. Individual trees within the sample plot are usually marked, and care is taken to measure variables on individual trees and at the plot level as precisely as possible using the available measurement instruments.
There are at least two advantages to permanent plots:
- Relatively few plots are established, and each variable is measured very precisely each time a measurement is taken. It is usually possible to further reduce errors by comparing present measurements with past measurements as a means of error checking both sets of data.
- The correlation between subsequent measurements tends to be both positive and relatively high, meaning that precision of the estimates of change can often be improved. The correlations between successive measurements can deteriorate quickly with the length of the measurement interval.
- It can be difficult to locate permanent plots at subsequent measurement times. Even with GPS equipment, it can sometimes be difficult to identify the exact plot center or to locate marked trees if there is an interval of several years between measurements.
- Permanent plots are often assumed to be treated the same as the surrounding similar areas, unless contrasting treatments are part of the investigation objective. Identical treatment may be difficult if the plot is marked conspicuously. Harvesting crews or even livestock and wildlife may treat areas differently if trees are painted or if the unavoidable disturbance associated with plot establishment and measurement is obvious. Tree markings can also attract attention and in the worst case can lead to vandalism or other interference.
8.2 Estimating Change Using Temporary Plots
Independent surveys can be established at different times, with plots only measured at one time.
There are at least two advantages to using temporary plots:
- Temporary plots do not have to be monumented or relocated, making it possible to use more temporary plots than permanent plots in most situations and making field work faster.
- Record keeping is often easier because the information required to relocate permanent plots is not needed and individual trees do not have to be matched at each measurement.
- Since the surveys at different times are taken on different plots, the correlation between succeeding estimates tends to be low and may be assumed to be zero in some cases. There are situations though, where the correlation can be positive and relatively high. Areas dominated by young rapidly growing plantations provide but one example. It is even possible, for short measurement intervals, to have a negative correlation between pairs of estimates. A negative correlation implies that the variance of the change estimates will be inflated over that obtained from permanent plots, even though more temporary plots may be established at each measurement time, resulting in less precise estimates of change.
- Individual trees on temporary plots are usually measured more quickly and with less precision than those on permanent plots, reducing the precision in the estimates and the resulting estimate of change. This can be offset by the use of a greater number of temporary plots. It is not possible to use combinations of measurements for error checking purposes though, like it is on permanent plots.