# Design-based sampling methods for environmental monitoring

Zhao, Xin;## Abstract

Efficient strategies for environmental monitoring are proposed with an emphasis on the importance of using available information. In environmental monitoring, it is common to use area frames covering the assumed spread of the population of inter-est. By using such a frame, a sample unit is usually not a unit in the population, rather a point on a surface. The population unit of environmental surveys exits in a spatial context where nearby units often have similar values to each other. When this is the case, we can estimate the unknown population parameters more efficiently if the sample is well spread over the population. Spatially balanced sampling is sam-pling designs that employ available auxiliary variables to select well-spread sam-ples. When applying such a design with equal inclusion probabilities, we match the sample distribution to the population distribution of the auxiliary variables, which can improve the estimation of the state of the population. Paper I presents a new sampling strategy for the Swedish national forest inventory using spatially balanced sampling designs for an area frame. When estimating change, we wish to update the sample at the following occasions using the most recently available information. When updating the sample, we also want to have a certain degree of overlap between the successive samples. By doing so, we can get more precise estimates for states and the change between two states simultaneously. Therefore, there is a demand for selecting well-spread and partially overlapping samples over time. In Papers II and III, the focus is on such samples, and more specifically, on positively coordinated and spatially balanced samples. In Paper II, a sampling strategy of selecting positively coordinated and spatially balanced samples is proposed for monitoring the change of environmental variables, while the objective of Paper III is to estimate the variance of an estimator of change using such samples. When a single survey does not provide sufficient quality of estimates for some domain, we can plan for a complementary survey or combine existing surveys to improve the quality. When multiple surveys are combined, there is a risk of introducing bias to the estimators. Combining several surveys to use all available information when estimating the population parameters thus becomes a challenge. In Paper IV, we investigate the possibility of producing less biased or unbiased estimators when combining several independent surveys of a finite population.

## Keywords

auxiliary variables; sampling strategy; area frame sampling; inclusion probabilities; spatially balanced sampling designs; the local pivotal method; spatially correlated Poisson sampling; sample coordination; combining samples

## Published in

Acta Universitatis Agriculturae Sueciae 2021, number: 2021:51

ISBN: 978-91-7760-780-9, eISBN: 978-91-7760-781-6

Publisher: Department of Forest Resource Management, Swedish University of Agricultural Sciences

## Authors' information

## UKÄ Subject classification

Environmental Sciences related to Agriculture and Land-use

Forest Science

## URI (permanent link to this page)

https://res.slu.se/id/publ/112985