The transition matrix concept gives support to the LUC module in the model. These matrices, elaborated by state and biome, make use of information obtained through satellite imagery for land use changes (LUC) observed between 2002 and 2010 (MCT, 2015). This information was processed to distinguish three major types of land use, Crops (CROP), Pastures (PASTURE) and Forestry (planted forests, FORESTRY), and a residual type identified in the model as UNUSED, which refers to native forests. These transition matrices are detailed by state and, within each state, by six distinct biomes: Amazon, Cerrado, Caatinga, Atlantic Forest, Pampa and Pantanal. An example can be seen in Table 1 , which displays the observed original transitions for the Mato Grosso state.

_Table 1. Transition matrix for the state of Mato Grosso, Cerrado biome. Millions of hectares._

||1 Crop|2 Pasture|3 PlantForest|4 Unused|Total 2002|
|---|---|---|---|---|---|
|1 Crop|8.32|0.82|0.02|0.05|9.20|
|2 Pasture|2.23|37.57|0.06|0.53|40.38|
|3 PlantForest|0.00|0.00|0.02|0.00|0.03|
|4 Unused|0.47|0.98|0.00|13.16|14.61|
|Total 2010|11.01|39.37|0.10|13.73|64.22|

Source: model database.

The transition matrix in Table 1 shows, for example, that 0.53 million hectares (Mha) of physical units of land of the Cerrado biome in the state of Mato Grosso, which was natural vegetation in 2002, became Pasture in 2010, while 13.16 Mha remained as natural vegetation. In the same state and period, 0.82 Mha of Pasture was transformed into Crops. The model has, therefore, for each biome in every state, a complete transition matrix. The data observed in the period mentioned above was processed to show the Markov probability that each hectare under given use in a certain year will be in another use the following year.

These transitions are also price influenced. Transition from pastures or forests to crops, for example, accelerates with the growth of the relative prices of agricultural products. Moreover, the model is flexible enough to allow exogenous projections of the level of deforestation according to desired patterns. In this case, the Transition Matrix ensures information consistency, that is, the increase of pasture, crop and forestry area in a given year must respect the increase in the available area given by deforestation in the previous year.

The transition matrices, then, determine the total land available for each broad land use group (Crops, Pasture, Forestry and Natural Forests or Unused). Once the amount of each aggregate category is determined, the model will allocate land among the activities within each category. Crop area, for example, will be allocated among the eleven agricultural activities of the model, through a CES (Constant Substitution Elasticity) function, based on the relative prices of the products of these activities.

An emissions matrix in LUC is associated to the transition matrices described above. This matrix accounts for emissions in LUC, and has the same dimensionality. The GHG emissions matrix associated to the LUC module (MCT, 2015), then, shows observed emissions on LUC transitions, by state and biome. This allows a detailed accounting of emissions on land use transitions, and the computation of sinks on forest restoration.

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