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

Virtual landscape evolution
Three interacting processes influenced the evolution of the soil P landscape: annual landuse evolution,
annual fertilization practices and a soil P budget accounting for fertilization out-takes, crop in-takes, and soil
P immobilization.
Stochastic landuse evolution
We used a transition probability matrix to model the landuse evolution year after year as a probabilistic
Markov chain (Cressie, 1991). We therefore assumed that landuse allocation was a random function only
depending on the previous landuse. The probabilities can be represented as follows:
[ p
Pp Pp pPp Tp pPp C p
]
Pp M
pTp Pp pTp Tp pTpC pTp M
pC Pp pC Tp pC C pC M
pM Pp pM Tp pM C pM M
where p i j is the probability of changing from a landuse i to a landuse j between year y and y+1. Pp stands
for permanent pasture, Tp for temporary pasture, C for cereal, and M for maize. The probabilities were
designed to model the global trend of landuse evolution observed in this region between the 1960’s and
today: a diminution of pastures, an augmentation of maize fields and a rather constant number of temporary
pastures and cereal fields (Table A.I.11). This flexible approach allows the design of different landuse
evolution scenarios by solely changing the transition probabilities (Walter et al., 2003).
Annexes I : Virtual landscapes to assess monitoring strategies – p. 175