Quantifying the trade-off between cost and precision in estimating area of forest loss and degradation using probability sampling in Guyana

Guyana is a high forest cover, low deforestation country. Since 2011-2014 the Guyana Forestry Commission (GFC) has used visual interpretation of 5 m resolution RapidEye imagery to map forest loss and nearby degradation for the entire country. According to the GFC produced national map, 58% of all forest loss events cover less than 1 ha, so forest loss is very rare and occurs at a scale that can be difficult to detect and monitor. Nearly all (similar to 97%) of the forest loss and nearby degradation is due to small-scale mining and its associated infrastructure. For any country wanting to accurately map and monitor forest loss, sample-based area estimation can be considerably less expensive than wall-to-wall mapping. To quantify the tradeoff between precision and cost, we evaluated the standard errors of area estimators for several sample-based strategies using Guyana as a case study. We partitioned Guyana into 374 blocks, with each block 24 km x 24 km to align with the image tiles provided by RapidEye's 3A product. The area of forest loss and area of degradation for each of the 374 blocks were determined from the GFC map to create the population data used to evaluate the precision of different sample-based strategies. We compared the standard errors of estimators of area of forest loss and area of degradation obtained from simple random, stratified random and systematic sampling as applied to these population data. To construct strata for the stratified design, we evaluated two forest loss maps produced from Landsat data, a 30 m global forest loss product and a 30 m national forest loss map produced specifically for Guyana. For both of these maps, several options for defining stratum boundaries and allocating sample size to strata were evaluated. All stratified design options reduced the standard error of the area estimators relative to simple random sampling. The Dalenius-Hodges and Jenks methods for choosing stratum boundaries yielded greater improvements in precision than the Equal Area method. For this Guyana case study, optimal and equal allocation of sample size to strata led to substantially better precision than proportional allocation. Only small improvements in precision were attained by increasing the number of strata from three to five. For simple random sampling, incorporating the global and national forest loss map information in a regression estimator reduced standard errors of estimated area of forest loss and area of degradation relative to the standard error of the Horvitz-Thompson estimator that does not incorporate the forest loss map information. However, the best performing stratified sampling design options had better precision than the regression estimator. RapidEye data cost 800 USD per '3A' tile so the annual imagery cost for mapping Guyana would be 274,000 USD. For an investment of 75,200 USD (the cost of 94 RapidEye tiles, the largest sample size evaluated), the best performing stratified random sample achieved a relative standard error (100% times the standard error divided by area) of 7% for estimating area of forest loss and 6% for estimating area of degradation. This study demonstrates the utility of Landsat-based forest loss maps to provide effective strata to improve precision of area estimators produced from a sample of RapidEye imagery in a country for which forest loss and degradation are very rare features of the landscape.