Current issue: 53(2)

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Silva Fennica 1926-1997
Acta Forestalia Fennica

Articles containing the keyword 'stratified sampling'.

Category: Research article

article id 943, category Research article
Terje Gobakken, Lauri Korhonen, Erik Næsset. (2013). Laser-assisted selection of field plots for an area-based forest inventory. Silva Fennica vol. 47 no. 5 article id 943.
Highlights: Using laser data as auxiliary information in the selection of field plot locations helps to decrease costs in forest inventories based on airborne laser scanning; Two independent, differently selected sets of field plots were used for model fitting, and third for validation; Using partial instead of ordinary least squares had no major influence on the results; Forty well placed plots produced fairly reliable volume estimates.
Field measurements conducted on sample plots are a major cost component in airborne laser scanning (ALS) based forest inventories, as field data is needed to obtain reference variables for the statistical models. The ALS data also provides an excellent source of prior information that may be used in the design phase of the field survey to reduce the size of the field data set. In the current study, we acquired two independent modeling data sets: one with ALS-assisted and another with random plot selection. A third data set was used for validation. One canopy height and one canopy density variable were used as a basis for the ALS-assisted selection. Ordinary and partial least squares regressions for stem volume were fitted for four different strata using the two data sets separately. The results show that the ALS-assisted plot selection helped to decrease the root mean square error (RMSE) of the predicted volume. Although the differences in RMSE were relatively small, models based on random plot selection showed larger mean differences from the reference in the independent validation data. Furthermore, a sub-sampling experiment showed that 40 well placed plots should be enough for fairly reliable predictions.
  • Gobakken, Norwegian University of Life Sciences, Department of Ecology and Natural Resource Management, Ås, Norway ORCID ID:E-mail:
  • Korhonen, University of Eastern Finland, School of Forest Sciences, P.O. Box 111, FI-80101 Joensuu, Finland ORCID ID:E-mail: (email)
  • Næsset, Norwegian University of Life Sciences, Department of Ecology and Natural Resource Management, Ås, Norway ORCID ID:E-mail:

Category: Article

article id 7169, category Article
Aarne Nyyssönen, Pekka Kilkki, Erkki Mikkola. (1967). Eräiden metsänarvioimismenetelmien tarkkuudesta. Acta Forestalia Fennica vol. 81 no. 4 article id 7169.
English title: On the precision of some methods of forest inventory.

This paper reports on tests made for the study of alternative methods in forest survey. Data were acquired by measurements in five areas in Finland and in Mexico, varying in size from 20 to 900 ha. The principal characteristics used in the analysis was the entire volume. By the combination of neighbouring plots, the variation could be studied for different plot sizes and survey strips. Variable (relascope) plots could be compared.

A starting point for the comparison of different sampling methods, calculations were made of the coefficients of variation for each plot type; total and within the strata. The amount of decrease of variation with an increasing plot size could be established. Comparisons have been made of the following sampling methods: simple random, stratified random, simple systematic, and stratified systematic sampling.

On comparisons of the standard error of sample mean it was found that in both stratified sampling and different types of systematic sampling there is, with increasing size and diminishing interval of sample plots, an increase in the relative improvement of the result against simple random sampling. Only in exceptional cases did systematic surveys give results which were less precise than those derived by other methods.

In discussion of some methods for determination of the precision of systematic sampling, possibilities of theoretical determination of the degree of precision was considered. An empirical study was made of the behaviour of some equations based on the sample itself. The larger the plot size and the shorter the plot interval, the more the equations overestimated in general the variance of sample mean.

As none of the equations studied gave reliable results, regression equations were calculated for the relative standard error on the basis of the data measured. The independent variables were plot size, plot or strip interval, area of survey unit and mean volume. The results arrived at are based mainly on the complete measurement of one area only. To enable extension of the scope of application, more material is needed with a complete enumeration of trees.

The PDF includes a summary in Finnish.

  • Nyyssönen, ORCID ID:E-mail:
  • Kilkki, ORCID ID:E-mail:
  • Mikkola, ORCID ID:E-mail:
article id 7168, category Article
Aarne Nyyssönen, Pekka Kilkki. (1966). Estimation of strata areas in forest survey. Acta Forestalia Fennica vol. 81 no. 3 article id 7168.

Highest degree of precision in determining the areas of different strata in forest survey is achieved when the areas are measured from a map. However, in practice the stratum-areas usually need to be determined on the basis of samples taken in the field or from aerial photographs. The goal of the present investigation was to determine the precision in stratum-area estimation on the application of different sampling methods.

Three sampling methods were used: 1. sampling with random plots, 2. uniform systematic plot sampling, and 3. sampling with equidistant lines.

The dependence of the standard error of stratum-areas in systematic line and plot sampling was examined by regression analysis. The models for regression equations were derived from random sampling formulae. It appears that the characteristics of these formulae were applicable as variables in the regression equations for systematic samples. Also, some characteristics of the distribution of the stratum was found, which seem to influence the error in sampling with equidistant lines.

The results as regards uniform systematic plot sampling indicate that the use of random sampling formulae leads to considerable over-estimation of the standard error. Nonetheless, unless relatively short intervals between sample plots are used in the forest survey made on the ground, it is of advantage to study the division of the area into strata by measuring the distribution of the survey lines in these strata.

The results can be used in two ways: for estimation of the precision in a survey already made, or to predetermine the sample size in a survey to be made. The results may be applicable to areas ranging from 100 to 1,000 ha in size, as well as to larger areas.

  • Nyyssönen, ORCID ID:E-mail:
  • Kilkki, ORCID ID:E-mail:

Category: Special section

article id 287, category Special section
Mikko Peltoniemi, Juha Heikkinen, Raisa Mäkipää. (2007). Stratification of regional sampling by model-predicted changes of carbon stocks in forested mineral soils. Silva Fennica vol. 41 no. 3 article id 287.
Monitoring changes in soil C has recently received interest due to reporting under the Kyoto Protocol. Model-based approaches to estimate changes in soil C stocks exist, but they cannot fully replace repeated measurements. Measuring changes in soil C is laborious due to small expected changes and large spatial variation. Stratification of soil sampling allows the reduction of sample size without reducing precision. If there are no previous measurements, the stratification can be made with model-predictions of target variable. Our aim was to present a simulation-based stratification method, and to estimate how much stratification of inventory plots could improve the efficiency of the sampling. The effect of large uncertainties related to soil C change measurements and simulated predictions was targeted since they may considerably decrease the efficiency of stratification. According to our simulations, stratification can be useful with a feasible soil sample number if other uncertainties (simulated predictions and forecasted forest management) can be controlled. For example, the optimal (Neyman) allocation of plots to 4 strata with 10 soil samples from each plot (unpaired repeated sampling) reduced the standard error (SE) of the stratified mean by 9–34% from that of simple random sampling, depending on the assumptions of uncertainties. When the uncertainties of measurements and simulations were not accounted for in the division to strata, the decreases of SEs were 2–9 units less. Stratified sampling scheme that accounts for the uncertainties in measured material and in the correlates (simulated predictions) is recommended for the sampling design of soil C stock changes.
  • Peltoniemi, Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, FI-01301 Vantaa, Finland ORCID ID:E-mail: (email)
  • Heikkinen, Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, FI-01301 Vantaa, Finland ORCID ID:E-mail:
  • Mäkipää, Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, FI-01301 Vantaa, Finland ORCID ID:E-mail:

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