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

Stochastic and deterministic components of the soil P content initial
distribution
Among the various P compounds present in the soil, we focused on the plant available P reservoir, on which
most of fertilization recommendations and soil databases rely (Aurousseau, 2001; Schvartz et al., 2005). The
initial soil P content landscape was built using three different scales of spatial variability. Two experimental
variograms were used to stochastically derive short- and long-range variability components, and a
deterministic approach was used to model a medium-range component which accounted for the effect of
field history.
A short-range variogram was derived from a nested survey of a 6 ha cultivated field located in Essonnes
(Central France) and sampled on 70 sites in 1996 (ITCF, unpublished data). We derived from this data set a
short-range spatial structure (0 to 120 m), which accounted for intra-field variability (equation (1)). A long-
range variogram was derived from the French Soil Analysis Database (BDAT) which brought together more
than 147,000 soil analyses over a large part of western France, including the study area (Walter et al., 1997)
(equation (2)). To preserve the anonymity of the farmers, the spatial resolution of the database was
downscaled to the township of the soil analyses. We randomly reallocated the analyses in a radius of 1 km
around their township to derive a regional variogram, thus reliable for a distance between 2000 to 25,000 m.
The spatial structures derived from the soil databases were fitted by least square approximation to the P
experimental semi-variances using Splus (Kaluzny et al., 1998), leading to the following spherical and
exponential variograms:
short range h={01050 3
2 h 1
115 − 2 h
3
115 } , if 0≤h≤115
(1)
1050, if h115
−h
long rangeh=53004200 1−exp 11 500
Geostatistical simulations of P at these scales were conducted over the landscape using equations (1) and (2)
to derive respective random function (RF) models that would be representative of the study area
(Fig. A.I.35.a). The generation of each corresponding short- and long-range spatial component had to be
separated into two stages due to the large number of values to simulate (90,000 pixels) with the available
statistical tools: the rfsim function of SPLUS (Kaluzny et al., 1998) was used to model a gross distribution
(300 by 300 m pixels) with the Cholesky decomposition method (Cressie, 1991), and then the resolution was
increased (50 by 50 m pixels) by sequential Gaussian simulations (Goovaerts, 1997) using KRAIG, a
software designed by the Australian Centre for Precision Agriculture.
Annexes I : Virtual landscapes to assess monitoring strategies – p. 172
(2)