Improving the precision of sample-based forest damage inventories through two-phase sampling and post-stratification using remotely sensed auxiliary information

Abstract

Many countries have a national forest inventory (NFI) designed to produce statistically sound estimates of forest parameters. However, this type of inventory may not provide reliable results for forest damage which usually affects only small parts of the forest in a country. For this reason, specially designed forest damage inventories are performed in many countries, sometimes in coordination with the NFIs. In this study, we evaluated a new approach for damage inventory where existing NFI data form the basis for two-phase sampling for stratification and remotely sensed auxiliary data are applied for further improvement of precision through post-stratification. We applied Monte Carlo sampling simulation to evaluate different sampling strategies linked to different damage scenarios. The use of existing NFI data in a two-phase sampling for stratification design resulted in a relative efficiency of 50 % or lower, i.e., the variance was at least halved compared to a simple random sample of the same size. With post-stratification based on simulated remotely sensed auxiliary data, there was additional improvement, which depended on the accuracy of the auxiliary data and the properties of the forest damage. In many cases, the relative efficiency was further reduced by as much as one-half. In conclusion, the results show that substantial gains in precision can be obtained by utilizing auxiliary information in forest damage surveys, through two-phase sampling, through post-stratification, and through the combination of these two approaches, i.e., post-stratified two-phase sampling for stratification.

Appendix

For simulation of GRELOC damage population, we let the frequency of damage-affected grid cells decrease away from the epicenter using the following functions:

$$ f\left(x,y\right)=g(x)\cdot g(y) $$

(19)

where

$$ g(x)={\left[1-{\left(\frac{\left|x-wx\right|}{xm}\right)}^{pov}\right]}^{1/pov} $$

(20)

where wx = 1,600,000, xm = ym = 1.5, pov = pns = 0.99, and

$$ g(y)={\left[1-{\left(\frac{\left|y-wy\right|}{ym}\right)}^{pns}\right]}^{1/pns} $$

(21)

where wy = 7,070,000.

Equation 13 returns values from 0 to 1, and we multiplied it by the pine volume share in areas with 0.6 or more pine volume. x and y are independent. α = −10 and β = 20 in Eq. 6 (F(x)). We drew a random number r ∈ U(0, 1) for each grid cell, and if F(f(x, y) * ptall) − r > 0, the grid cell was considered affected by the damage.

Table 4 Estimated coefficients of variance ($\hat{\mathrm{CV}}$) called CV below, number of repetitions where damage area was estimated to zero (# 0), and the relative efficiency (RE) as compared to SRSwoR sample of same size, for each estimator of damaged area in the county

Table 5 Estimated coefficients of variance ($\hat{\mathrm{CV}}$) called CV below, number of repetitions where damage was estimated to zero (# 0), and the relative efficiency (RE), for each estimator of number of damaged trees in the county compared to SRSwoR-estimator

Table 6 Description of errors in simulated auxiliary data (precision, specificity, sensitivity, and overall accuracy)

Table 7 Relative bias of estimates of total affected area and numbers of damaged trees for all sample sizes, auxiliary data qualities, and for all damage scenarios

Table 8 “Cover” indicates the empirical coverage rates (%) from estimates of total damage−affected area, while “above” shows the rate of CI that fail from above (real value higher than maximum value of CI), and “below” the rate of CI that fail from below (real value below minimum of CI)

Table 9 “Cover” indicates the empirical coverage rates (%) from estimates of total number of damaged trees, while “above” shows the rate of CI that fail from above (real value higher than maximum value of CI), and “below” the rate of CI that fail from below (real value below minimum of CI)