Paysages virtuels et analyse de scénarios pour évaluer les impacts ...

PEi,y= PexportYcrop = PexportN(meanYieldcrop,stdYieldcrop) (9)
where Pexport is the crop P ratio, and Ycrop is the crop yield (Schvartz et al., 2005) derived from a normal
distribution characterized by a mean yield value and a yield standard deviation set to 10% of the mean
(Table A.I.12.b).
Sampling strategies
We kept one realization of the soil P spatio-temporal model to implement different sampling strategies,
which combined four sampling designs, five sample sizes, and two time intervals. We used the sample
median to estimate the landscape median (the median value derived from the whole landscape), a robust
estimator in situation where the distribution of the surveyed variables may be unknown. Each sampling
strategy was repeated 100 times for statistical purposes.
Sampling designs
We tested the following sampling designs:
− regular grid (RG) is an aligned systematic sampling in two dimensions (Cochran, 1977). For a square
grid of n points by side, the sidelength of the landscape was divided in n segments and the starting
site of the grid was randomly allocated within the square defined by the first longitudinal and
latitudinal segments. The other sites were allocated by translating the location of the first site with
the sidelength mentioned above (see mesh sizes on Table A.I.13). Allocated the first year, sample
sites stayed stationary during the remaining 50 years;
− stratified by initial landuse (IL): the landscape area can be divided into four strata based on the four
different landuses considered here. At the first year, a simple random sampling without replacement
was performed on each landuse stratum, each stratum being given the same number of sampling
sites. Allocated the first year, sample sites stayed stationary during the remaining 50 years;
− stratified by current landuse (CL): same process as above, but all the sites were reallocated at each
timestep based on the landuse of the year of interest;
− transects (Tr): a transect is a line of sampling sites separated by a short distance. In this design, each
transect was a line of eight consecutive pixels. Starting points of transects were randomly allocated
and then, the direction of each transect was randomly set among the four possibilities: East-West,
North-South, North East-South West, and North West-South East. The distance between the
consecutive sites of a transect was, in our study, the distance between consecutive pixels: 50 m for
EW and NS directions, 71 m for NE-SW and NW-SE directions. Allocated the first year, sample sites
stayed stationary during the remaining 50 years.
RG and Tr are self-weighting designs, therefore the sample median is an unbiased estimator of the landscape
median (for an even sample size, the sample median was the mean of the lower and upper medians). For IL
and CL designs, we used the median unbiased estimator for stratified samplings suggested by Lohr (1999).
Annexes I : Virtual landscapes to assess monitoring strategies – p. 179