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?(t)?x?(k)??x?(0)(i) x(1)(1)i?1t?1?(1)(t?1)?x?(1)(t?1)?x?(1)(t),(t?0,1,2,...). ?(t?1)??x?(0)(i), we getxSincex(1)i?1t?15.2.2 Principle of Gray Metabolism Model GM (1, 1)[2]
After making a gray prediction and getting the latest information，it adds this
information into the original data series and wipes off the oldest information at the same time.Then, using the new one as original series, it repeats the above step 1.1 to set up GM（1,1） Model，so on and so forth, until the fulfillment of all the prediction objectives, and that is the Gray Metabolism Model we wanted。
5.2.3 Accuracy testing
Relative error and posterior difference ratio C are two most commonly used way to test the model, and its basic process is following:
?(0) is the series simulated by GM Model and?is residual x(0) is original series，x?(0)(t), the relative error sequence isp?1??, sequence。Within it is ?(t)?x(0)(t)?xand thus the total water resource amount in t?1 year??(?1,?2,...,?n) could be obtained. Hereinto we have?t?|?(t)x0(k)|, and ?t is the simulated relative error of the
1npoint, and????kis the average relative error.p?1??is defined as the
nt?1prediction accuracy, which is displayed in percentage.
S1??(?i??)2n?1(0),????i n(0)?(x(0)(t)?x)2?x(0)(k)S2?，x?
n?1nC?S1 S2Where S1is the mean variance of residual；S2 is the mean variance of original series;Cis the posterior difference ratio.
Here is a reference table attached that illustrates the model accuracy
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classification in details:
Table 2: The accuracy of the model
Accuracyof model Relative error/% Averagerelative accuracy (p, %) First class Second class Third class 1 5 10 Value of C ?95 80?p?95 70?p?80 ?0.35 0.35?C?0.5 0.5?C?0.65 ?70 ?0.65 disqualification 20 Thus, the method of predicting water resource amount in one place and checking the accuracy could be gained.
5.3Model of water supply capacity of a region
We define water scarcity F(t) as:
2?????at0at2?F?t??Y?t??W?N0?exp???bt0????exp?bt???B?t??C?t??D?t?22??????
In order to estimate the situation of the region[3], we lead in variable water lacking rate u:
u?F(t)*100%E(t)
For measuring the degree of water lacking in this region, we set 4th level
evaluation on the basis of water shortage rateuthe standard see table 3:
Table 3: The classificatory standard
Scarce situation Sufficient Light Middle Heavy shortage rate <5 5~10 10~20 >20 Main problems Achieves the balance between supply and demand of water resources Normal years in balance, but in the average year, the water supply may occur. Not only in design level year of water shortage occurs, also in normal times Water supply gap is extremely serious. Wading activities are severely restricted
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5.4 Strengths & Weakness
Strengths
☆It overcomes the traditional method on the forecasting water supply, facing the problems of the shortage of samples, difficult implementation and high requirement.
☆In the prediction process, we can weed out the old data and add new data constantly, maintaining the higher prediction precision.
☆It makes up the situation of Logistic population grows negatively. ☆The model is fit for many areas.
☆the models of industry, agriculture, ecological water consumption are concluded from the change rules, are sufficient in scientific nature.
Weakness
☆Without considering the uncertainty of social development, the model not always reflects the future water resources condition.
☆The model can only be used over a period of time for prediction. It is limited for extreme conditions.
☆ the models of the subsystem may not form a linear relationship in various countries, unless the situation is close to China.
6Choose a regionto analyze
In addition to the model, we also choose the region of North China to analyze.
6.1 Brief introduction
The North China is an important part of the Great Plains in the east of China，which located at north latitude 32°～40°and in the east longitude 114°～121°. North China's border is very large.The border of north is the south of Yan Mountains. The southern border is on the north side of the Dabie Mountains .The western boundary in Taihang to the Funiu Mountain Adjacent to the East is the Bohai Sea and the Yellow Sea, also with a total area of 300 thousand square kilometers. Plain has too much advantage such as flat terrain, many rivers, convenient transportation and advanced economy. From ancient times to the present, North China is the center of China in the economy, politics and culture area. And also, Beijing, the capital of China, is in its northern part.（see Figure 2）
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Figure 2: the region in red curve is the chosen area.
North China is one of the most water-lacking area of the nation, with only 6% gross、11% per capita of theaverage level. Why it is scarce in water, and how? We conclude the reasons from the physical and economic aspects, including social and environmental objects.
6.2 Physical scarcity:
The amounts of the water resources is poor. The region is alluvial plain, and lacked of rivers and lakes. What’s more, the vegetation coverage is not enough, the rain fall flows away with the solid. Thus the water conservation is poor. For many years, Water resources per capita average volume is 335 cubic meters, reaches nearly 15% of the national per capita.
Water resources are uneven distributed of time and space. Annually, it mainly performs in the event of a wet year and dry year phenomenon; within one year, mainly in summer and autumn, the precipitation and water resources quantity is more, while less rainfall in winter and spring. The uneven distribution of water resources in space mainly reflect that the water resources quantity change with zonal and surface evaporation is uneven distribution.
This region belongs to monsoon climate of medium latitudes, the rainfall is comparatively scarce.
These above are environmental causes.
The huge population and giant consumptions. The plain population accounts for about 20% of the total population, with only 6% gross、15% per capita of theaverage level.
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The urbanization and developing economics increase the demand of water in unit area. And this obviously stress the water supplying.
These above are social causes.
6.3Economical scarcity:
Serious pollution and waste, wastewater treatment rate is low. Industrial development and popularization of various kinds of agricultural chemicals leads to serious pollution. Set an example Deterioration of water quality is an important fact of water shortage in north China. Such as the Yong ding River upstream of the Guan Ting reservoir in Beijing, because of the serious pollution of water upstream reservoir has lost the function of water supply, adding to the water shortage situation in Beijing. What’s more, sewage treatment capacity in the region is not different, Beijing and Tianjin municipal wastewater treatment rate is higher, while other urban wastewater treatment rate is low.
Human activities. On the one hand, the development and utilization of water resources, and on the other hand, is characterized by the influence of land use. Due to the shortage of water resources and they have to excessive exploitation of groundwater. The region exploit 54.78% of the amount of the groundwater in China. Urbanization caused rainfall infiltration to groundwater recharge, and expanding agricultural irrigation area, increase the water evaporation consumption. The quantity of surface water and groundwater in the natural system greatly reduced—this forms a vicious circle in obtaining water.
7 Prediction model for the North China
According to the model of task 1 and the data statistics, which used to express water supply in North China, in task 2. Respectively. The model of water consumption and water supply were calculated.
7.1Model of water consumption in North China.
Table 4:the total population from 2008 to 2014 in the North
China[4](unit：thousand)
Sequence 1 2 3 4 5 6
Year 2008 2009 2010 2011 2012 2013 Population 133470 135490 140290 142080 143810 145500 Increase 2020 4800 1790 1730 1690 Growth rate per annum 0.015134487 0.035426969 0.012759284 0.012176239 0.011751617