Spatial Sampling Designs - Sampling Spatial Units for Agricultural Surveys - page 188

Table 7.4 CPU time (in seconds) taken by each algorithm to select one sample, calculated using
the average time needed to select ten replicated samples, for different population sizes N and
sample sizes n

R version C version
SCPS LPM 1 LPM 2 SCPS Nn GRTS CUBE DUST LPM 1 LPM 2

500 10 0.056 0.980 0.031 1.519 3.719 0.867 0.015 0.003 0.002

500 50 0.359 0.975 0.070 1.387 3.522 0.875 0.014 0.003 0.002

500 100 1.058 0.978 0.123 1.364 3.360 0.840 0.014 0.003 0.002

1,000 10 0.069 1.941 0.298 6.091 14.911 3.478 0.062 0.012 0.007

1,000 50 0.478 1.943 0.429 5.466 14.346 3.462 0.062 0.012 0.007

1,000 100 0.886 1.939 0.471 5.405 15.220 3.449 0.062 0.012 0.007

7.8.2 A Case Study: Assessing the Ecological Condition
of Lakes in Northeastern USA

The data used in this design-based simulation come from the Northeast lakes survey
of the US Environmental Protection Agency s Environmental Monitoring and

Assessment Program (EMAP). This was part of the Space Time Aquatic Resources
Modeling and Analysis Program (STARMAP) at Colorado State University (Larsen
et al. 2001 ). Between 1991 and 1995, researchers from the US Environmental
Protection Agency conducted an environmental health study of the lakes in the
Northeastern States of the USA. For this study, a sample of 334 lakes (or more
accurately, lake locations) was selected from a population of 21,026 lakes in these
States, using a random systematic design. The variable of interest was the acid
neutralizing capacity (ANC), an indicator of the acidification risk of water bodies.
ANC is a measure of the ability of a solution to resist changes in pH, and is
measured in meq/L (micro equivalents per liter). A small ANC value for a lake
indicates that it is at risk of acidification. The total number of observed sites was
349 with a total of 551 measurements, because some lakes were visited several
times during the study period and some were measured at more than one site. We
decided to average these multiple measurements of the same lake. In addition to
ANC values, the EMAP data set also contained the geographical coordinates of the
centroid of each lake in the target area (Salvati et al. 2010 ).
To show how the suggested design can be practically used to estimate the ANC,
we treated this sample as a population to plan a second-phase survey for measuring
ANC. Multiple-phase surveys are widely used in agricultural, environmental, and
forestry statistics, because expensive field work experiments may be necessary to
produce accurate measurements. A first-phase, where some covariates are observed
and used to calibrate the final selection, is thus generally considered a practical and
advantageous sampling strategy.
The semivariogram of the ANC (see Fig. 7.9 ) has a curious shape; steep
increases are immediately followed by a fast decrease. This is frequently symp-
tomatic of

'

the presence of cycles in the data or, more reasonably, of