1
Modeling Domestic Food Flow in China due to Food Stocks
and Economic Gradient
Toshiaki ICHINOSE* , Qinxue WANG* and Kuninori OTSUBO *
*
National Institute for Environmental Studies, 16-2 Onogawa, Tsukuba, Ibaraki 305-8506, Japan
Abstract: We developed two numerical models (a non-market type and a market type) to evaluate the
vulnerability of the food supply in China as estimated from current land use and supply-and-demand of food. In
the northeastern plain and the middle-downstream reaches of the Yangzi River, food production is greater than
food demand. In big cities such as Beijing, Shanghai, and Tianjin, the coastal zone along the Pacific Ocean, the
Yun-Gui Plateau, and most western China, food demand is greater than food production. In the eastern part, large
plains and better climatic conditions bring about high productivity; and increasing investment in agriculture has
also contributed to the high productivity there . We performed numerical simulations of food stocks on a model
island and in middle-south China. The results showed that there is some risk of decreasing food stocks in the
hinterlands of the productive regions and in urban regions far from the productive regions, especially in the
coastal zone of southern China. Input data (population density, GDP density, food demand, food supply) was
based on 20-km grid data for 1995 (Otsubo, 1999). In the simulation where there was no food transportation,
severe food shortages appeared in urban regions. In the non-market-type model, food was transported from grid
cells with positive food stocks to grid cells with negative food stocks. In this model, food shortages gradually
disappeared as the coefficient of transportation intensity increased. Thus, food excess in productive regions also
decreased, and regional imbalances of food stocks almost disappeared. In the market-type model, each grid cell
absorbed food from surrounding cells in proportion to its GDP (economic potential). As the coefficient of food
absorption was increased, some coastal urban regions showed a quick accumulation of food stocks; at the highest
coefficient of food absorption a wide-scale food crisis appeared in inland regions.
Keywords: food balance, food transportation, numerical model, market system, economic potential
1. Introduction
In this research, we aimed to evaluate the vulnerability of foods stocks and the flow of food in China as estimated
from the current land use and supply -and-demand o f food (crops). We also aimed to determine the pressure of
land use change on food stocks . We regarded food transportation as reflecting not only supply-and-demand but
also the economic gradient, i.e., the energy and cost of transportation. The major factor influencing the energy
and cost of transportation is distance. We expect that patterns of food transportation introduced by our numerical
models referring to current supply-and-demand of food and the economic gradient will contribute to
comparisons with observed patterns and to discussions on the sustainability of supply-and-demand.
To estimate food stocks in middle-south China, we developed two types of model. A 20-km-grid dataset
created by OTSUBO et. al.1) was used as the input data, and the numerical simulations were initialized with data
from 1995. Parameterization of the models was performed considering the stability of computing: all input data
were scaled from 0 to 9 (no dimension, Table 1); both food production and food consumption shared the same
scaling; and 20-km distances were scaled to 1 (no dimension).
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Table 1
Scaling of supply-and-demand of food per grid cell
Grade (—)
0
1
2
3
4
5
6
7
8
9
Range
0
40 000
80 000
120 000
160 000
200 000
240 000
280 000
320 000
360 000
(kg/year)
– 40 000
– 80 000
– 120 000
– 160 000
– 200 000
– 240 000
– 280 000
– 320 000
– 360 000
–
2. Structures of the Models
2.1 Non-market-type model
In this model (depicted schematically in Figure 1), food is transported proportionally to the ratio of GDP (shown
in eq. 4) from grid cells with excess food to grid cells with a shortage of food. The basic equations of the model
are:
dS a = (Pa – Ca + Ia – Oa ) dt
(1)
Ia =Σb Oba
(2)
Oa =Σb Oab
(3)
Oab = k(Gb /Ga )(S a – S b )/Rab
(4)
where
S a is food stock in grid cell a
S b is food stock in grid cell b
Pa is annual food production in grid cell a
Ca is annual food consumption in grid cell a
Ia is annual food inflow to grid cell a
Oa is annual food outflow from grid cell a
Ga is GDP in grid cell a (GDP density)
Gb is GDP in grid cell b (GDP density)
Rab is distance between grid cell a and grid cell b
Oab is food outflow from grid cell a to grid cell b
t is time and dt is set to 0.1 in our simulation
k is a constant with a dimension of velocity (food transportation intensity coefficient [TIC]: food
transportation per unit time)
Figure 1 Structure of non-market-type model
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In the case where (S a – S b ) < 0, Oab is assumed to be 0. In other words, food is not transported from grid cell a to
grid cell b .
2.2 Market-type model
In this model, the potential absorption of food into a grid cell is defined in proportion tothe GDP in that grid cell.
When the pattern of food transportation is decided in this way, according to market theory, it is possible for food
to be transported from a region of food shortage to a region of food excess. To resolve such imbalances,
adjustments must be made in food production and food consumption (including emigration of people from that
grid cell); therefore, we consider that this model better expresses the actual situation in China. The basic
equations of this model are generally the same as those of the non-market-type model, but the definitions of Ia
and Oa are different.
When the potential inflow of food to grid cell a (Ia ) is defined as equation 5 using population (Na ) and GDP
(Ga ) in grid cell a, the inflow of food from grid cell b to a (Iab ) is described as equation 6 with density function,
f. The potential to collect food in a grid cell is therefore regarded as proportional to the population and the GDP.
Ia = pNa Ga / G0
(5)
Iab = Ia f(Rab )/∫b f(Rab )dRab
(6)
p is the potential absorption of food per unit time per capita (food absorption coefficient [FAC], i.e., food
demand per unit time per capita).
G0 is the spatial mean of GDP.
Rab is the distance between grid cell a and grid cell b.
Ga / G0 is regarded as relative economic potential.
Equation 6 is introduced because one of the concepts of this model is that a grid cell with large GDP collects food
widely and thinly, while a grid cell with small GDP collects only from nearby grid cells. The food budget per unit
time per grid cell is the same as the non-market-type model. Variability per unit time is adjustable by p.
No inflow is assumed to occur to grid cell a if the food stock of grid cell b is not positive (eq. 7). On the
other hand, the outflow from grid cell a, Oa , is defined as the sum of inflow from grid cell a to all other grid cells
and is expressed as equation 8.
Iab = 0 in the case of S b ≦ 0
(7)
Oa =Σb Iba
(8)
The density function f has the characteristics shown in equation 9, where R is the distance from grid cell a.
f(R) = 1/ Ga exp(–R / Ga )
(9)
3. Results and Discussion
3.1 Behavior of the models for a model island
To evaluate the basic functions of the models before applying them to China, we applied the two models to a
pseudo island (a model island) with a size of around 360 km × 360 km. Land use (Figure 2), population density,
GDP density, and food consumption and production (Figure 3) are arbitrarily assumed for this island. This island
is a perfect closed system, and there is no export or import of food. Population and GDP are assumed to be in
proportion to food consumption. The initial value of food stocks was fixed to 10 in all grid cells on the island.
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Figure 2 Land use in a model island
Figure 3 Food consumption and food production on a model island (10 grades)
Figure 4 Food stocks in a model island (non-market-type model: at time -step 20)
One line of margin was excluded.
No transportation (upper left), Transportation Intensity Coefficient: 0.003 (upper
right), Transportation Intensity Coefficient: 0.01 (lower left), Transportation
Intensity Coefficient: 0.03 (lower right)
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In the non-market-type model, the computed result at time -step 20 for different TICs is shown in Figure 4.
In the case where there was no food transportation, severe food shortages occurred in urban areas. As the TIC
increased, the food shortages disappeared followed by decreasing food stocks in productive areas. In the case of
a TIC of 0.03, food concentrated rapidly into urban areas and food stocks became stable at around 10 in the
margins of productive areas and around 15 in their centers.
The density function f in the market-type model expresses the decreasing food absorption potential as the
distance from grid cell a increases. Values relative to 1.0, the absorption potential for a self-referential grid cell,
are shown in Table 2. A grid cell with a GDP density of 1.0 collects food from grid cells located up to 2 grid cells
away, while a grid cell with a GDP density of 9.0 collects food from up to 9 grid cells away.
Figure 5 shows the distribution of the sum of the density function f (calculated between all grid cells) in the
model island.
When the FAC was 0.003, urban areas could not accumulate food and food shortages did not disappear.
When the FAC was 0.03, food shortages in urban areas disappeared. This behavior was the same as that found in
the non-market-type model. When the FAC was 0.1, some cities started to collect a lot of food and food stocks in
productive areas became stable at around 10 to 20. When the FAC was 0.3, all urban areas established huge food
stocks. On both sides of the mountains, where both GDP and food production were low, food stocks almost
completely disappeared (Figure 6).
Table 2 The influence of the economic potential at absorbing grid cell a ( Ga ) to decrease the ratio
of food absorption potential as distance between grid cells (R) increases
Ga
1
2
4
9
R
0
1.0
1.0
1.0
1.0
1
0.4
0.6
0.8
0.9
2
0.1
0.4
0.6
0.8
3
0.0
0.2
0.5
0.7
4
0.0
0.1
0.4
0.6
5
0.0
0.1
0.3
0.6
6
0.0
0.0
0.2
0.5
7
0.0
0.0
0.2
0.5
8
0.0
0.0
0.1
0.4
9
0.0
0.0
0.1
0.4
(Values relative to 1.0, the absorption potential for a
self-referential grid cell)
Figure 5 Distribution of the sum of the density function f in a model island
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Figure 6 Food stocks on a model island (market-type model: at time -step 20)
Food absorption coefficient: 0.003 (upper left), Food absorption coefficient: 0.03
(upper right), Food absorption coefficient: 0.1 (lower left), Food absorption
coefficient: 0.3 (lower right)
3.2 Case study in middle-south China
The two models were applied to a region 2220 km × 2220 km, covering the area from Shanghai to Kunming and
Lanzhou (east–west), and from Guangzhou to Beijing (south–north). We compared the results at time-step 25.
Although the marginal zone of the computed domain has some interaction with outside regions, it cannot be
described here. Thus, our discussion on the results had to exclude the marginal zone of the inland side (Figure 7).
Negative values were shown for the ocean and regions outside of China (including Chinese Taipei). Food
consumption was assumed to be in proportion to the population (400 kg per year per capita). Population was
concentrated in the coastal cities, the Sichuan basin, the Huabei Plain, and around Wuhan and Xi’an. Food was
produced mainly around large cities (especially in the eastern region), the Huabei Plain, the Sichuan basin,
Wuhan, Changsha, Nanchang, and Xi’an. In further computing, the initial value of food stock was set to 0.
In the non-market-type model where there was no food transportation, Wuhan, Changsha, the Sizhuan basin,
Nanchang, eastern China, the Shandong peninsula, and the Huabei Plain accumulated food stocks, while food
shortages occurred in the coastal cities, Chongqing, and the Yun-Gui Plateau. As the TIC increased, this
imbalance disappeared, and at 0.005 no local imbalance could be observed. At a TIC of more than around 0.04,
the spatial distribution of food stocks and the ultimate concentration of food in the regions at high risk of food
shortages reversed (Figure 8).
In the market-type model, sensitivity of food absorption to distance between grid cells was set to a thirdthat
of the model island due to the extent of the domain. As FAC increased, some coastal cities rapidly accumulated
food stocks and an extended food crisis occurred in the inland regions caused by decreasing food stocks in
productive regions (Figure 9).
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Figure 7 Population density (upper left), GDP density (upper right), food consumption (lower left),
and food production (lower right) in middle-south China, 10 grades
Figure 8 Food stocks in middle -south China at time -step 25 (non-market-type model)
White areas indicate a value of > 5; black areas indicate a value of < – 5. One line of
the margin was excluded.
No transportation (upper left), TIC: 0.0005 (upper right), TIC: 0.001 (middle left)
TIC: 0.005 (middle right), TIC: 0.04 (lower left)
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Figure 9
Food stocks in middle-south China at time -step 25 (market-type model)
White areas indicate a value of > 5; black areas indicate a value of < –5. One line of
the margin was excluded.
FAC: 0.01 (upper left), FAC: 0.05 (upper right), FAC: 0.1 (middle left)
FAC: 0.5 (middle right), FAC: 1.0 (lower left)
4. Conclusions
We established two food transportation models, a non-market type and a market type, and performed numerical
simulations on the temporal and spatial variability of food stocks on a pseudo island and in middle -south China.
In the case of no food transportation, severe food shortages occurred in urban regions. In the non-market-type
model, food shortages gradually disappeared in urban regions as TIC increased, and food stocks in productive
regions also decreased. Therefore, the local imbalances disappeared. In the market-type model on the other hand,
food stocks accumulated rapidly in coastal urban regions as the FAC increased. The food stocks in productive
regions were delay to decrease in a little , and a spatial imbalance due to food shortages in the inland regions
appeared. The disappearance of the imbalance over time as was shown in the non-market model did not appear.
Reference
1) Otsubo, K., Wang, Q., Nakaya, T., Shimizu, Y., Bito, A., Ichinose, T. and Kondo, A. (2002): 20-km Grid
Analysis on Current and Future Situations of Food Balance in Mainland China, LU/GEC Project Report IIX,
CGER-I053-2002 (ISSN 1341-4356), pp.17-33.