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

- farm-types have specific spatial structures: does the crop AWDs computed for a given farm-type
significantly differ from the crop AWDs computed over the whole catchment?
- within a farm-type, crops have specific spatial structure: does the farm-type crop AWDs
significantly differs from the global farm-type AWD?
Preferential allocation of crops with soil waterlogging
13% of the total agricultural area is located on waterlogged soil. For each crop, this value was compared with
the series of annual crop proportions located on this class (expressed as a percentage of the total crop area).
Structure of the crop transition models
For comparison purposes, we implemented two stochastic models whose purpose was to simulate the
summer crop transition at the field level. Rotomatrix is an implementation of a temporal first order-Markov
chain and will serve as a reference model for comparison with Stochastree, which is based on stochastic
decision trees. Both model types were implemented either with consideration for farm-types (hereafter called
specific models) or without (hereafter called generic models).
Rotomatrix, a temporal first order Markov chain
Markov chains have been extensively used both in landuse/landcover change and crop transition modeling,
therefore Rotomatrix description is only succinctly described here. More details concerning Markov chain
formalism in the landcover change context can be found in Anderson an Goodman (1957), Usher (1992),
Logofet and Lesnaya (2000), Coppedge et al. (2007), and Castellazzi et al. (2007b). Our approach of crop
transition modeling followed a discrete description of time (annual summer crop transition) and a finite
number of crop classes (the 10 crop classes observed in Naizin during 1993-2002). It is therefore possible to
represent mathematically all the possible crop transitions as a temporal first order Markov chain with a
square matrix P of dimension m (where m is the number of crop classes) in which each Pij represents the
probability for a crop j to succeed after the previously grown crop i. The P matrix can be built
experimentally from a dataset by (i) counting all the observed annual transitions from a crop i to a crop j, (ii)
converting these frequencies of transition into probabilities as follows:
P ij = n ij
m
∑ j=1
n ij
where nij is the number of transitions from crop i to crop j and m is the number of crop classes.
A temporal first order Markov chain model particularly assumes the following properties:
- the transition probabilities to the succeeding crop j are not statistically independent of the possible
previous crop i so that they could possibly form a first order Markov chain. The statistical
independence of the probability matrix P is tested by the following statistic:
III. Stochastree, un modèle de successions de cultures basé sur des arbres de décision stochastique – p. 78
(2)