Carbon Balance and Management(7)

MAIi = ωi·C2W (11)

ωi = NPPi·CU (12)

Bi=epci ωi (1 bi) {r 1 [1 (1+r) Ri] Ri (1 θi) (1+r) Ri}

(13)

fracslp = 1 - fracllp (15)epci = pci·leaki (16)

Net present value of agriculture

The net present value of agriculture (Ai) is calculated witha two-factor Cobb-Douglas production function (equa-tion 17). It depends on the agriculture suitability and thepopulation density. A high agriculture suitability and ahigh population density causes high agricultural values.The value ranges between a given minimum and a maxi-mum land price. The parameters ai and γi determine therelative importance of the agriculture suitability and thepopulation density and νi determines the price level forland. The agriculture suitability and the population den-sity are normalized between 1 and 10.

Ai=νi SAgSiαi SPdiγ

i

(17)

SAgSi=

10

AgSi≥0.5 1+9 AgS/0.5AgSi<0.5

(18)γi = αi (20)

Decision of deforestation

The deforestation decision is expressed by equation (21).It compares the agricultural and forestry net present valuescorrected by values for deforestation and carbon seques-tration. For the deforestation decision the amount ofremoved biomass from the forest is an important variable.The agricultural value needed for deforestation increaseswith the amount of timber sales and its concomitant flowto the HWP pool. On the other hand the agriculture valuewill be decreased by the amount of released carbon to theatmosphere. This mechanism is expressed by a deforesta-tion value (DVi, eq. 22). The model also allows for com-

pensation of ancillary benefits from forests. This

additional income is modeled either as a periodicalincome or a one time payment and will increase the for-estry value by (IPdiscounted, which has been done in equation (23).

i). If it is a periodic payment it has to be YesAi+DVi>Fi Hi+IPi

Defor=

∧not Protected A(21)

i+DVi≤Fi Hi+IPi

No∨Protected

handled. Two mechanisms are realized in equation (21).One is to pay the forest owner to avert from the deforest-ation, the other is to introduce a carbon price that the for-est owner gets money by storing carbon and paying forreleasing it. The introduction of a carbon price focuses themoney transfer to the regions where a change in biomasstakes place. Payments to avoid emissions from deforesta-tion can be transfered to cover all of the globe's forests,target to large "deforestation regions" or individual grids.

Deforestation rate

Once the principle deforestation decision has been madefor a particular grid cell (i.e. the indicator variable Defori =1) the actual area to be deforested within the respectivegrid is to be determined. This is done by the auxiliaryequation (24 – 25) computing the decrease in forestshare. We model the deforestation rate within a particulargrid as a function of its share of forest cover, agriculturalsuitability, population density and gross domestic prod-uct. The coefficients c1 to c6 were estimated with a general-ized linear model of the quasibinomial family with a logitlink. Values significant at a level of 5% were taken and areshown in table 1. The parameters of the regression modelwere estimated using R [6]. The value of c0 was determinedupon conjecture and directly influences the maximumpossible deforestation rate. For our scenarios the maxi-mum possible deforestation is set to 5% of the total landarea per year. That means, a 0.5° × 0.5° grid coveredtotally with forests can not be deforested in a shorter timeperiod than 20 years.

0Defor=No

Fdeci=

Fsi

Ftdeci>Fsi∧Defor=Yes(24)

Ftdec

iFtdeci≤Fsi∧Defoor=Yes