The transformation mechanism of multiscale decisionmaking
A broad array of data sources are used to represent key dynamics in the land use decisionmaking. These data sources include economic/price, land use, and agricultural census information. Crop price, melon and fruit price, and vegetable price are considered exogenous and uniform for all households. Crop price for corn is an average derived from Mizhi county Agricultural Census data sources. Our land use data does not allow us to discriminate with a sufficient level of accuracy what melon and fruit are being grown and what vegetable species being grown in agricultural areas. Thus, we simplify the model to a crop class, a single melon and fruit class, and a single vegetable class in our model runs.
Land ownership boundaries were derived from the parcel maps provided by the Mizhi County Land Resource office for 2000. These parcel boundaries provide the essential information. Therefore, agents are assigned to the landscape over time. In order to reveal the land use change, the household interview was conducted in 2007 and 2008.
The rule of the multiscale transformation is the key to realize the transformation from the individual household to the whole household. In this paper, the NSC is used for the scale transformation. Benenson and Torrens use NSC to research the urban residential choice, their scale transformation methods provide a useful reference [17]. The transformation mechanism is shown in Figure 1.

(1)
The decisionmaking of the whole households is affected by the household groups. The effect weight coefficient W_{
ikt
} of each group is described as:
{\displaystyle \sum _{i=1}^{n}}{W}_{ikt}=1
Where i is household group i; k is the land use type k ;

(2)
The decisionmaking of the household groups is affected by the households. The effect weight coefficient w_{
ikt
} of each group is described as:
{\displaystyle \sum _{j=1}^{n}}{w}_{ijkt}=1
Where j is household j ;
Model description
The whole household decisionmaking model
The whole household decisionmaking is related to the household groups' decisionmaking and their weight. The whole household decisionmaking formula is:
wholehousehol{d}_{kt+1}={\displaystyle \sum _{i=1}^{3}}{W}_{ikt}householdtyp{e}_{ikt}
(1)
Where wholehousehold_{kt+1}is the decisionmaking of the k land use type of the whole household at time t+1; W_{
ikt
} is the influence coefficient of the k land use type of the household group i at time t; householdtype_{
ikt
} is the decisionmaking of the k land use type of the household group i(i = 1, 2, ..., n) at time t.
The influence coefficient formula is described as following:
{W}_{ikt}=\frac{{\displaystyle \sum _{j=1}^{n}}Incom{e}_{ijkt}\phantom{\rule{0.3em}{0ex}}*\phantom{\rule{0.3em}{0ex}}Are{a}_{ijkt}}{{\displaystyle \sum _{i=1}^{3}}{\displaystyle \sum _{j=1}^{n}}Incom{e}_{ijkt}*Are{a}_{ijkt}}
(2)
Where Area_{
ijkt
} is the land area of the k land use type of the individual household j in the household group i at time t; Income_{
ijkt
} is the earnings of the k land use type of the individual household j in the household type i at time t.
The household groups' decisionmaking model
The household groups' decisionmaking is related to the individual household decisionmaking and their weight. The formula of the household groups' decisionmaking is:
householdtyp{e}_{ikt+1}={\displaystyle \sum _{j=1}^{n}}{w}_{ijkt}househol{d}_{ijkt+1}
(3)
Where w_{
ijkt
} is the influence coefficient of the k land use type of the individual household j in household group i at time t; household_{ijkt+1}is the decisionmaking of the k land use type of the individual household j in the household group i at time t+1.
The formula of the influence coefficient w_{
ijkt
} is described as following:
{w}_{ijkt}=\frac{Incom{e}_{ijkt}*Area}{{\displaystyle \sum _{j=1}^{n}}Incom{e}_{ijkt}*Are{a}_{ijkt}}
(4)
The individual household decisionmaking model
Combined with the actual situation in the household investigation, household land use intention model comes with a number of assumptions:

■ The shortterm land use decisionmaking is considered.

■ There is little difference in planting technique among households.

■ The natural conditions of the valley land are similar.

■ During the study, planting technology does not change.
Under the framework of the rational decisionmaking, this paper attempt to construct the individual household decisionmaking, it is the function of the factor of the institute, market, households themselves and the interaction between households. The individual household decisionmaking formula is described as following:
\begin{array}{c}househol{d}_{ijkt+1}=f\left(institutio{n}_{ijkt},marke{t}_{ijkt},{h}_{ijkt},actio{n}_{ijkt}\right)\\ ={h}_{ijkt}+\lambda \times institutio{n}_{ijkt}+\alpha \times \phantom{\rule{0.3em}{0ex}}marke{t}_{ijkt}+\beta \times actio{n}_{ijkt}\end{array}
Where househol{d}_{ijkt+1} is the decisionmaking of the k land use type of the individual household j at time t+1; institutio{n}_{ijkt} is the influence of the policy to the k land use type of the individual household j in the household group i at time t. In this paper, the policy influence is mainly referred to the turning of cultivated land into forests or grasslands policy and the enactment of rent; marke{t}_{ijkt} is the effect to the k land use type of the individual household j in the household type i at time t; actio{n}_{ijkt} is the interaction among the individual household j which has the k land use type in the household group i at time t; \lambda ,\alpha ,\beta is the influence coefficient of the policy, the market and the interaction among households respectively, and \lambda +\alpha +\beta =1.
The turning of cultivated land into forests or grasslands policy began in 1999. According to the approved area, the government appropriate food subsidies, planting seeds and cash benefit to the household. In study area, this policy is aimed at the hilly area land and sloping land. This paper concerns about the valley land, therefore, its land use pattern has less affected by this policy. Because quite a number of the valley is dominated by the grassroots level government, the rent is relative stable.
The institutional factors provide the macro background. Because of the stable rent and the effect range of the policy, the effect of the institutional factors to the household decisionmaking is equal to zero.
The factor of the household themselves mainly includes rotate, risk averse and the crop importance. The formula of decisionmaking of the individual household is described as following:
{h}_{jkt}=f\left(rotate,\phantom{\rule{0.3em}{0ex}}rluderisk,\phantom{\rule{0.3em}{0ex}}cropimportance\right)
Where rotate is the rotate factor, this paper mainly refers to the watermelon rotation to corn or vegetable; rluderisk is the factor of risk averse; cropimportance is the factor of crop importance;
■ The rotate factor.
In this paper, the household plants three major crops: corn, vegetables and watermelon. Because of consuming larger soil fertility, the watermelon can not be planted in the same filed for two consecutive years. In the study area, the household has the habit of planting watermelon. Therefore, the planting period of the field of corn or vegetable is beyond 2 years, the field is rotated to watermelon. Above can be expressed as following:
If "the planting crop is watermelon" then
watermelon → corn
Or watermelon → vegetable
If "the planting crop is corn or vegetable" then
If the planting period ≥ 2
corn or vegetable → watermelon
If the planting period < 2
corn or vegetable → corn or vegetable
■ The factor of the risk averse
Because of the unknown of the future climate, the water source and market, although seeking to maximize benefit, the households make their cultivation as far diversification as possible in order to reduce the planting risk. Therefore, this paper comes with a number of assumptions; which can be described as the following:
If "the count of the household field" ≤ 2 then
"the land use can not change"
If "the count of the household field" > 2 then
"cultivation as far diversification as possible"
■ The Cropimportance factor
In this paper, the cropimportance factor is referred to the importance contrast between corn and vegetable. The contrast includes the cattle, the household planting habit, the crop benefit and the land use area. Under satisfied the factor of the rotate and the risk averse, the household will planting corn as possible if having cattle, or contrasts the importance between corn and vegetable. The crop importance judgment is described as following:
If "satisfied the factor of the rotate and the risk averse" then
If "the household has cattle" then
If the household planting crop and vegetable simultaneously then
(corn or vegetable) → corn
Or
If "the household only plants watermelon and corn,
or watermelon and vegetable" then
cropimpor\mathsf{\text{tan}}c{e}_{jkt}=marke{t}_{jkt}
End if
cropimpor\mathsf{\text{tan}}c{e}_{jkt}
Where cropimpor\mathsf{\text{tan}}c{e}_{ijkt} is the importance of the k land use type of the individual household j in the household type i at time t. its formula is described as following:
cropimpor\mathsf{\text{tan}}c{e}_{jkt}=\frac{Are{a}_{kjt}\times Incom{e}_{kjt}}{{\displaystyle \sum _{k=1}^{n}}\left(Are{a}_{kjt}\times Incom{e}_{kjt}\right)}
(5)
The formula interaction among households is described as following:
actio{n}_{ijkt}={\phi}_{jkt}\times {h}_{jkt}
(6)
where:
{\phi}_{jkt} is the influence coefficient among households.
Its formula is:
{\varphi}_{jkt}=\frac{\left(\mathsf{\text{max}}\left\{{h}_{jkt},j=1,2,\dots n;k\ge 2\right\}{h}_{jkt}\right)}{\mathsf{\text{max}}\left\{{h}_{jkt},j=1,2,\dots n;k\ge 2\right\}}
(7)
The decisionmaking of each household is affected by the market. In order to find out a quantitative expression of the influence of the market to the decision making of household, 2 assumptions are made as follows:
The pattern of the valley land reflects the current market information;
The household masters the earning information of all kinds of the land use types.
There is a difference influence of the market for each household type. Through analyzing the LUCC pattern of each household type and their earning from the land, we can obtain the whole effect to each land use type by the market. The formula is:
{M}_{jkt}=\frac{{\displaystyle \sum _{j=1}^{n}}Area{k}_{jkt}*Income{k}_{jkt}}{{\displaystyle \sum _{j=1}^{n}}{\displaystyle \sum _{k=1}^{m}}\left(Area{k}_{jkt}*Income{k}_{jkt}\right)}
(8)
We can use formula (1) to obtain the current land use type importance of the planted household; and combining the formula (6), the market effect to each type land use is calculated. The formula is described as follows:
{market}_{jkt}=\left\{\begin{array}{l}{M}_{jkt}{h}_{jkt}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{If}}\phantom{\rule{0.3em}{0ex}}{M}_{jkt}=\mathsf{\text{max}}{M}_{jkt},\phantom{\rule{0.3em}{0ex}}\mathsf{\text{and}}\phantom{\rule{0.3em}{0ex}}{h}_{jkt}<marke{t}_{jkt}\hfill \\ 0,\phantom{\rule{0.3em}{0ex}}\mathsf{\text{If}}\phantom{\rule{0.3em}{0ex}}marke{t}_{jkt}=\mathsf{\text{max}}marke{t}_{jkt},\phantom{\rule{0.3em}{0ex}}\mathsf{\text{and}}\phantom{\rule{0.3em}{0ex}}{h}_{jkt}\ge marke{t}_{jkt};\hfill \\ {M}_{jkt}{h}_{jkt},\phantom{\rule{0.3em}{0ex}}\mathsf{\text{If,}}\phantom{\rule{0.3em}{0ex}}{M}_{jkt}\ne \mathsf{\text{max}}{M}_{jkt}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{and}}\hfill \\ {h}_{jkt}>marke{t}_{jkt};\hfill \\ 0,\phantom{\rule{0.3em}{0ex}}\mathsf{\text{If}}\phantom{\rule{0.3em}{0ex}}{M}_{jkt}\ne \mathsf{\text{max}}{M}_{jkt}\phantom{\rule{0.3em}{0ex}}\mathsf{\text{and}}\hfill \\ {h}_{jkt}\le marke{t}_{jkt}\hfill \end{array}\right.
(9)
Therefore, the formula of the finial decisionmaking of the individual household is described as:
\begin{array}{c}househol{d}_{jkt+1}\\ \phantom{\rule{0.3em}{0ex}}\phantom{\rule{0.3em}{0ex}}={h}_{jkt}+\alpha \times actio{n}_{jkt}+\beta \times marke{t}_{jkt}\end{array}
(10)
Where \beta can use the economic crop land change within two years to express market effect. Namely,
\beta =\frac{Area{k}_{t}Area{k}_{t+1}}{Area{k}_{t}}
(11)