Journal of Applied Mathematics

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Modeling of Water Quality, Quantity, and Sustainability

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Volume 2014 |Article ID 673485 | https://doi.org/10.1155/2014/673485

T. L. Qin, D. H. Yan, G. Wang, J. Yin, "Water Demand Forecast in the Baiyangdian Basin with the Extensive and Low-Carbon Economic Modes", Journal of Applied Mathematics, vol. 2014, Article ID 673485, 10 pages, 2014. https://doi.org/10.1155/2014/673485

Water Demand Forecast in the Baiyangdian Basin with the Extensive and Low-Carbon Economic Modes

Academic Editor: Yuefei Huang
Received13 Dec 2013
Revised28 Apr 2014
Accepted05 May 2014
Published05 Jun 2014

Abstract

The extensive and low-carbon economic modes were constructed on the basis of population, urbanization level, economic growth rate, industrial structure, industrial scale, and ecoenvironmental water requirement. The objective of this paper is to quantitatively analyze effects of these two economic modes on regional water demand. Productive and domestic water demands were both derived by their scale and quota. Ecological water calculation involves the water within stream, wetland, and cities and towns. Total water demand of the research region was obtained based on the above three aspects. The research method was applied in the Baiyangdian basin. Results showed that total water demand with the extensive economic mode would increase by 1.27 billion m3, 1.53 billion m3, and 2.16 billion m3 in 2015, 2020, and 2030, respectively, compared with that with low-carbon mode.

1. Introduction

Affected by climate change and economic-social development, water resource problems such as excess water, water shortage in quantity and quality, aggravation of hydroecological and hydroenvironmental system, disorder of hydrosedimentary system, low water efficiency, and unsustainable water resource management which has been discussed by Wang [1] have become more diverse and serious. These problems have led to water resource crisis and intensified the relationship between water supply and water demand.

Water demand forecast has gained more attention in water-deficient areas due to the increasing water requirement of rapid economic development. It is not only the basis of national economic and social development plans, water resource plans, and operation plans of hydraulic projects and water management, but also the equilibrium point between social-economic system and ecoenvironmental system, as discussed elsewhere [2, 3]. Different economic development modes should be taken into consideration of the water demand forecast of different level years in the future for targets of economic and social development, energy conservation and pollution reduction, and water resources protection. It becomes a key technique for rational allocation of water resources towards the low-carbon development mode, rational deployment of water resources based on macroeconomic structure, and ecology-oriented reasonable deployment of water resources, as discussed elsewhere [47].

Research of water demand abroad began at the 1st evaluation of national water resources in USA in 1968. Water use structure in most developed countries such as EU and US has changed into sustainable mode steadily. Forecast method of water demand is becoming mature. Gistau et al. established pattern recognition model to forecast short-term domestic and industrial water demand [8, 9]. Zhou et al. applied time series method in the city of Melbourne to forecast daily urban water demand [10]. Mays established logarithmic and semilogarithmic regression model relating water demand and relative factors for the media-long term and applied it to Texas of USA [11]. Adamowski established peak daily water demand forecast modeling using artificial neural networks [12]. Yasar et al. forecast water demand of Adana city of Turkey using stepwise multiple nonlinear regression analysis model [13].

In China, water demand forecast began when the 1st evaluation of national water resources started in 1980. Zhong et al. constructed comprehensive prediction method based on the general formula, integrating advantages of some common methods [14]. Zhang et al. forecast domestic water demand of Beijing with multiple-linear regression model [15]. Lv et al. established practical dynamic model of urban water consumption [16]. Zhang et al. established projection pursuit model of water demand prediction based on IEA which solved high dimension, nonlinear, nonnormal problems, and so forth [17].

Research advances above show that the developments of mathematical methods and computer simulation technique promote water demand forecast methods. There are three types of forecast methods, including trend analysis, time series, and numerical simulation. Some methods are in common use at present, such as pattern recognition model, regression model, comprehensive prediction method based on the general formula, practical dynamic model to predict water consumption, grey system method, projection pursuit means, and artificial neural networks [1824].

These above means are produced and applied to water demand forecast in different basins. However, they lack effect analysis of low-carbon economic development mode on water consumption and comparison of water demand forecast between varied economic modes. Economic development mode of China is being changed into green, low-carbon, and sustainable mode so that water demand forecast has to consider its effect on regions and different water users.

The purpose of this paper is to analyze effect of extensive and low-carbon economic development mode on total regional water demand and different water users. In the former mode, many kinds of resources are consumed to keep rapid economic growth but there exists unreasonable structure of industries and water use, resulting in the occupancy of ecological water demand, excessive water consumption by economic-social system, large energy consumption, and carbon emission. The content of carbon dioxide in the atmosphere could increase, which could intensify regional climate change. In the latter mode, total water consumption, energy consumption, and carbon emissions are all reduced by decreasing quota of water use and optimizing the structure of industries, water use, and energy consumption and considering reasonable water demand of ecosystems. This mode can promote the construction of low-carbon society and mitigate climate change. Key factors of the two modes are detailed in Table 1.


ItemExtensive economic modeLow-carbon economic mode

Economic growth rateRate of 2010Optimal economic growth rate
Industrial structureStructure of 2010Optimal structure
Water use quotaQuota of 2010Decreasing water quota in accordance with Twelfth Five-Year Plan of Water Conservancy
Water use structureStatus of 2010Adjusting the structure of water use in accordance with the optimal industrial one
Natural ecological water demandNo considerationConsidering reasonable ecological flow requirement within the stream and wetland ecological water demand

2. Materials and Methods

2.1. Study Area

The Baiyangdian basin is located in the middle of the North China Plain and Haihe River basin. Its geographic coordinates are roughly E113°40′~E116°48′ and N38°10′~N40°03′. The basin covers an area of about 34878.25 km2.

Rivers stretch through Shanxi province, Hebei province, and Beijing municipality. The inflow is mainly from upstream rivers including Juma River, Zhong-yishui River, Baigou River, Puhe River, Caohe River, Qingshui River, Tanghe River, Zhulong River, and Cihe River. Through Zaolinzhuang conjunction, these rivers flow into Zhaowang New Channel and then converge into Dongdian of Baiyangdian wetland. After that they flow into Xiaobai River in the lower reach and then flows into Haihe River through Duliujian River, as discussed by Bai and Ning [25], shown in Figure 1.

Annual average precipitation volume of the basin is 1.902 billion m3, 70%–80% of which falls in the flood season from June to September, as discussed by Wang and Xu [27].

Total amount of water consumption was about 4.65 billion m3 in 2010, of which productive, domestic, and ecoenvironmental water consumption were, respectively, 4.05 billion m3, 0.47 billion m3, and 0.13 billion m3. Gross domestic product (GDP) was about 460.26 billion RMB in the same year, of which the growth rate was greater than 10%. Economic development and population growth brought about high water consumption. There are series of ecoenvironmental problems in the basin, including water resource shortage, groundwater overexploitation, ecological water being taken possession, occupied ecological land, and deteriorated water quality.

2.2. Basic Data

Water demand forecast involves six types of data, consisting of socioeconomic development, water resource, scale and quota of water consumption, water use indexes, and hydrological observation data. Details and sources are listed in Table 2.


Data typeDetailsMajor source

Socioeconomic developmentPopulation, urbanization level, GDP, industrial structure, and investment in fixed assetsStatistical yearbook of Beijing municipality, Hebei province, and Shanxi province during 2005–2010
Water resource amountWater consumptionWater resources bulletin and attached list during 2001–2010
Water-consumption scaleIrrigation area, forestland area, fish pond area, the number of livestock and poultry, and green land area of citiesStatistical yearbook of Beijing municipality, Hebei province, and Shanxi province during 2005–2010
Water-consumption quotaIrrigation quota, water-consumption quota of animal husbandry and fishery, and water-consumption quota of secondary and tertiary industryWater conservancy yearbook during 2005–2010 and Twelfth Five-Year Plan of Beijing municipality, Hebei province, and Shanxi province
Water-consumption indexWater efficiency of irrigation and cannelsWater conservancy yearbook of Beijing municipality, Hebei province, and Shanxi province during 2005–2010
Hydrological dataDaily flow dischargeHydrological yearbook during 1956–2000

2.3. Forest Method

Water demand forecast of research region includes productive, domestic, and ecological part. Details are listed in Table 3. The two former parts and ecological demand for cities and towns were derived by multiplying scale by quota. The technical framework of this paper is detailed in Figure 2.


Water usersMajor divisions

Productive users
 Primary industryAgriculture, forestry, animal husbandry, and fishery
 Secondary industryGeneral industry and construction
 Tertiary industryOther industries except for the primary and secondary industry, including service, banking, insurance, transportation, medical treatment, and education
Domestic usersResidents of cities and villages
Ecological usersNatural and artificial ecosystem

In respect of production water demand, based on the historical data of GDP, optimal economic growth rate and GDP were obtained with Cobb-Douglas production function which had the lowest total energy consumption. Optimal industrial structure and water use one were derived with Markov chain. The product of primary industry, secondary industry, and tertiary industry is, respectively, obtained based on forecasted results of optimal GDP and industrial structure. Then, the water demand scale of secondary industry and tertiary industry can be derived. Energy intensity was forecast with linear trend extrapolation method. Total energy consumption and carbon emissions were both derived based on these factors. Relationship of the above forecast methods is shown in Figure 3.

In respect of domestic water demand, population was forecast with the rate of natural population increase and urbanization level with linear trend extrapolation method.

In respect of water demand of natural ecosystem, ecological flow demand within stream was forecast based on the monthly runoff of major hydrostation and ecological water demand of wetland was forecast based on the monthly water level for different guaranties.

2.4. Forecast of Population and Urbanization
2.4.1. Population

The rate of natural population increase was considered in population forecast, while mechanical growth rate was not considered in this paper because of its uncertainty. Regional population was forecasted with the following formula: where and are the total population of planning level year and status year, respectively, is the number of planning level years, and is the natural increase rate during planning years.

2.4.2. Urbanization Level

Urbanization level is an important index weighing regional economic development. Trend extrapolation method was adopted to forecast it based on urbanization evolution during 2000–2010. Forecast methods of the two above factors are suitable for both extensive and low-carbon economic modes.

2.5. Economic Index
2.5.1. Economic Growth Rate

Economic growth rate of extensive economic mode was the same as that of 2010. In low-carbon economic mode, Cobb-Douglas productive function model was adopted to forecast and optimize economic growth rate. Then, GDP was obtained.

This model relates optimal economic growth rate with low energy consumption, meeting the target of low-carbon mode. Moon and Sonn established Cobb-Douglas productive function model to research the relationship between economic growth and energy consumption [28]. It is as follows:

Zhu et al. integrated employment rate and scientific technology factor into this function to improve it [29]. Then, improved optimal steady economic growth rate is as follows: where is energy intensity of the year , which is ton of standard coal equivalent per 10 thousand RMB of GDP; is the labor population of the year ; is the total population of the initial year; is the labor force participation rate, the same as employment rate; is the annual average rate of population growth; is the capital output elastic coefficient; is the labor output elastic coefficient; is the growth rate of total factor productivity; is the risk aversion coefficient; is the rate of time preference; is error term; .

2.5.2. Industrial Structure

The ratio of the primary, secondary, and tertiary industry was forecast with Markov chain. Its result was used in low-carbon mode, while structure of 2010 was used in extensive mode.

2.6. The Forecast of Production Water Demand
2.6.1. The Primary Industry

Irrigation water demand is affected by precipitation, cultivated land, crop structure, irrigation area, and efficiency. In this paper, the point is economic development and agricultural planting so precipitation forecast is not considered temporally.

In the low-carbon economic mode, gross irrigation water requirement of the 2015 level year was forecast based on cultivated land area, crop structure, irrigation quotas of different crops, and water use efficiency of irrigation requested by Twelfth Five-Year Plan. The above factors related to irrigation were the same as those of 2010 except for cultivated land area with the extensive economic mode. However, in the low-carbon mode, they were forecast with methods as follows.

Change rates of cultivated land area in 2015, 2020, and 2030 were forecast with trend extrapolation method on the basis of the status land area and the request of Twelfth Five-Year Plan. The results showed that change rates of Beijing municipality, Hebei province, and Shanxi province were −4.8%, +1.4%, and +1.48%, respectively.

Net irrigation quotas of different crops were referred to those set in Technique routine of high efficient water use of Hebei province and Local standard of water use of Hebei province (DB13), shown in Table 4. Irrigation quotas of Beijing Municipality and Shanxi province were similar as those of Hebei province because data collection was too difficult.


RegionWheatSummer cornSpring cornCottonFruitVegetableMiscellaneous cereals

Mountainous region218 56 99 225 306 28
Hilly region218 113 98 225 303
Plain region191 112 117 225 261

Water efficiency of irrigation of Beijing municipality is required to reach up 53% and of Hebei province 74% in 2015. There is no request for Shanxi province.

Water requirement of livestock was forecast based on livestock number and water consumption norm. In low-carbon economic mode, daily water requirements of large livestock, small livestock, and poultry were 0.1 m3, 0.025 m3, and 0.001 m3, respectively, according to local standard of water use of Hebei province (DB13). In extensive economic mode, this quota was the same as that of 2010. Amount of livestock was forecast with trend extrapolation method using historical data during 2000–2010, shown in Table 5. It is improved according to the requirements in the Twelfth Five-Year Plan. The result was used in two economic modes.


YearLarge livestockSmall livestockPoultry

2015765915964
2020635574369
2030775996180

The result showed that the amount of livestock would be controlled in 2015 but would increase in 2030 due to scientific cultivation technology and people’s diet. Forestry water demand was forecast based on the area and water use amount per area. Gross demand of forestry was derived with efficiency of water supply system. Growth rate of forestry area of Beijing municipality, Hebei province, and Shanxi province would be 8%, 1%, and 0.5%, respectively, according to the demand of the Twelfth Five-Year Plan. As a result, the area of Baiyangdian basin would be 55457 ha, 58177 ha, and 68427 ha in 2015, 2020, and 2030. The data is for both extensive and low-carbon economic modes.

Fishery demand was forecasted based on the area of fishing ground and water requirement per hectare. Because of the shortage of historical data of water use amount per fishing-ground area in Beijing municipality and Shanxi province, their quotas were forecasted with trend extrapolation method on the basis of historical sequence in Hebei province during 2000–2010. Gross quota of the whole basin would be 10.7 thousand m3, 11.4 thousand m3, and 9.2 thousand m3 per hectare in 2015, 2020, and 2030, respectively. With trend extrapolation method based on historical sequence during 2000–2010, the area of fishing ground would be 5115.6 ha, 5112.6 ha, and 5106.7 ha in 2015, 2020, and 2030, respectively.

In view of the two parameters mentioned above and efficiency of water supply system, gross water demand of fishery was obtained. In the extensive mode, efficiency of water supply system was the same as that of 2010; in the low-carbon mode, it was set according to the request of Twelfth Five-Year Plan.

2.6.2. The Secondary and Tertiary Industry

Water demand of the secondary and tertiary industry was forecasted based on GDP, status and planning industry quota, efficiency of water supply system, and utilization ratio of recycled water.

GDP of the secondary and tertiary industry was forecasted based on industrial structure and optimal economic growth rate, which is shown in Table 6.


Type201520202030

The secondary industry301.87428.54751.89
The tertiary industry230.09335.95612.97

Water consumption of the whole basin was 22.8 m3 per 10 thousand GDP in 2010, which was adopted in the extensive mode. According to Twelfth Five-Year Plan, this index of Beijing municipality and Shanxi province would decrease by 15%, 30%, and 16.3%, respectively, so that the whole basin would decrease by 25%. It was adopted in the low-carbon mode.

The rate of treated sewage and reclaimed wastewater would increase to 85% and 15% according to Twelfth Five-Year Plan of National Municipal Wastewater Treatment and Reclaimed Wastewater Facility Construction.

2.7. Domestic Water Demand

Domestic water demand was forecasted through multiplying population by water quota per person based on population, urbanization level, the quota of domestic water use, and efficiency of water supply system. The last parameter was the same as that from Twelfth Five-Year Plan for the low-carbon mode, while it was the same as status data of 2010 in the extensive mode.

Natural population growth rates of Beijing municipality, Hebei province, and Shanxi province should not be bigger than , , and , which were specified by Twelfth Five-Year Plan. According to forecast result of natural growth rate, population of the whole basin would be 14.79 million, 14.91 million, and 15.01 million in 2015, 2020, and 2030.

Results showed that urbanization level would rise up to 55.13%, 59.72%, and 63.59% in 2015, 2020, and 2030. Net quota of domestic water use for each people was forecast with trend extrapolation method on the basis of historical sequence of domestic water use and population during 2001–2010. Net quota of cities would be 54.4 L/d, 49.2 L/d, and 46.8 L/d, while net rural quota would be 56.6 L/d, 57.5 L/d, and 57.9 L/d.

2.8. Ecological Water Demand

Ecological water users include natural system and artificial system. The former one involves ecological flow requirement within the stream and wetland ecological water demand and the latter one involves water demand in green land of cities and towns. This part was also considered in the low-carbon mode.

2.8.1. Ecological Flow Demand within Stream

Considering both calculation requirement and present data, ecological flow demand within stream equaled the maximum value between 90% of flow frequency and average runoff of the driest period. Ecological flow demand within stream of lack-data watershed was converted with area compared to the one having data. That was because hydrological stations with observation data were all in the upstream and there was no main stream in Baiyangdian basin.

2.8.2. Ecological Water Demand for Wetland

Ecological water demand for Baiyangdian wetland was forecasted to protect the wetland and brought into full play its ecoenvironmental and social-economic effect. Considering factors such as protection targets, protection scale, constituents of ecosystem, and trophic structure of Baiyangdian wetland, ecological water demand for wetland was assessed under different schemes.

2.8.3. Ecological Demand for Cities and Towns

This part involves grassland and sanitation. Relevant quota was set according to Twelfth Five-Year Plan of Water Resource. Based on status water use of Haihe River basin and Integrated Plan of Water Resource in Hebei, quotas of grassland and sanitation are 3000 m3 and 900 m3 per hectare. The ratio of green land in Beijing municipality, Hebei province, and Shanxi province is requested to be 57%, 35%, and 36% in 2015, respectively.

3. Results and Discussion

3.1. Population and Urbanization Level

Results showed that the population of Baiyangdian basin would be 14.79, 14.91, and 1.51 million persons and urbanization level would be 55.1%, 59.7%, and 63.6% in 2015, 2020, and 2030.

3.2. Economic Growth and Energy Consumption

Linear regression analysis was used to derive key parameters of Cobb-Douglas productive function model of Baiyangdian basin with SPSS, shown in Table 7.


ParameterValue -test valueSignificance level

1.6664.4950.002
0.0092.5820.033
0.4876.0150.000
0.0990.5710.586

Results demonstrated that equation fitting rate was equal to 0.995 and significance levels of , , and were under that of 5% except which was not significantly related to economic growth rate. As a result, the labor force participation rate was not involved in this model and the function is changed as follows:

That may be caused by short sequence of historical data. Penetration rate of carbon emission reduction and energy saving technology can be integrated into the model if possible in the future.

Optimized economic growth rate simulated from the function model should conform to the actual growth rate so this could be a constraint condition for the regulation of and . Thus we got and .

Based on the estimation of the above parameters, optimal economic growth rate and energy consumption were derived for the low-carbon economic mode, shown in Table 8.


YearExtensive modeLow-carbon mode
Energy consumption (Mtce)Economic growth rate (%)Energy consumption (Mtce)Optimal economic growth rate (%)

201599.112.374.68.2
2020176.9912.391.66.9
2030564.5812.3119.95.2

3.3. Water Demand of Production

Water demand of the primary industry accounts for more than 60% of the total demand of production. However, rapid development of the secondary and tertiary industry leads to the low weight of the primary industry. Results showed that no matter whether the water use was maintained in the current situation or according to the Twelfth Five-Year Plan, gross water demand of the primary industry would decrease, while the secondary and tertiary industry would increase, which is shown in Table 9.


TypeStatus levelPlanning level
201520202030201520202030

Agriculture32.1232.7233.0519.8120.120.39
Forestry2.042.523.851.772.183.33
Livestock1.621.41.650.90.780.91
Fishery0.550.580.470.470.510.41
Primary industry 36.32 37.22 39.03 22.95 23.56 25.05
Secondary industry6.89 9.78 17.20 2.98 4.23 7.42
Tertiary industry2.45 3.58 6.54 1.06 1.55 2.82

3.4. Domestic Water Demand

According to the result, with the increase of urbanization, water demand of cities would have an increasing trend and that of villages would have a decreasing trend, which is shown in Table 10. Due to the increasing water efficiency of cities and decreasing quota of each person, the increase rate of domestic water demand would slow down in the future.


StatusPlan

201520202030201520202030
CityVillageCityVillageCityVillageCityVillageCityVillageCityVillage
2.272.372.402.162.541.801.972.052.081.872.201.56

3.5. Ecological Water Demand
3.5.1. Ecological Water Demand within Stream

Monthly water demand within stream was derived with the principle of no river blanking based on natural monthly data of Wang Kuai, Xidayang, Zijinguan, Angezhuang, Zhang Fang, and Hengshanling hydrological station. Results are shown in Table 11.


Hydrological stationWang KuaiXidayangZijinguanAngezhuangZhang FangHengshanling

River nameZhulong RiverCi RiverJuma RiverZhongyishui RiverJuma RiverCi River
Monthly runoff of 90% frequency0419 589 0718 0.00
Average annual value530 101993520 154447
Monthly water demand5304195892071847

Both Zi-jinguan and Zhang-fang hydrological station are in the Jvma river. As a result, their maximum was chosen as the monthly water demand of the river. There is a lack of observation data of Pu River, Cao River, and Qingshui River. Their annual water demand was converted through comparing area of them to that of Zhong-yishui river. Annual ecological water demand of main rivers in the upstream was derived and that of the whole basin was 0.214 billion m3, shown in Table 12. It would be 0.136 billion m3 only if the monthly runoff of 90% frequency was considered.


RiverJuma RiverZhongyishui RiverPu River, Cao River, and Qingshui RiverTang RiverSha RiverCi RiverWhole basin

Amount of ecological water demand within stream0.860.020.060.500.640.062.14

Monthly forecast of ecological water demand within stream was not completed because of incomplete data of precipitation, runoff and evaporation, and no match on spatial and temporal scale. If enough regional data is got, dynamic analysis will be done.

3.5.2. Ecological Water Demand of Baiyangdian Wetland

65% and 75% guaranties of the monthly water level are suitable for bulrush production, fishery production, diversion and storage of floods, and keeping the habit of target species, the great reed warbler, as discussed by Zhao [30]. Corresponding annual water demand of wetland is 0.472 and 0.389 billion m3. The latter was more suitable for this paper considering the cost of water supply.

3.5.3. Ecological Demand for Cities and Towns

Forecast results of ecological demand for cities and towns are shown in Table 13.


StatusPlan

201520202030201520202030
15040.7717883.1625885.2512533.9814902.6321571.04

3.6. Total Water Demand

Total water demand was derived based on the above results and it was demonstrated that it would increase by 1.269, 1.529, and 2.163 billion m3 in 2015, 2020, and 2030 with the extensive economic mode compared to that of low-carbon mode, shown in Table 14.


YearProductive water demandDomestic water demandEcological water demandTotal water demand
ExtensiveLow-carbonExtensiveLow-carbonExtensiveLow-carbonExtensiveLow-carbon

201545.6626.984.644.021.508.1151.8039.11
202050.5829.344.563.951.798.3556.9341.64
203062.7735.294.343.762.599.0269.7048.07

4. Conclusions

Taking Baiyangdian basin as the example, this paper constructed the extensive and low-carbon economic mode and quantitatively analyzed their effects on regional water demand. Results showed that total water demand with the extensive mode would increase by 1.27 billion m3, 1.53 billion m3, and 2.16 billion m3 in 2015, 2020, and 2030, respectively, compared with that of low-carbon economic mode.

Low-carbon economic mode has optimal economic growth rate. It can not only be in accordance with the target of carbon emission reduction, but also control productive and domestic water demand and meet the requirement of ecological system. Results of Baiyangdian basin can provide data for water resource plan, target of ecoenvironmental conservancy plan, and water resource allocation of intake area of south-to-north project.

Some aspects of this research have to be improved, including forecast of economic growth rate, irrigation, and ecological water demand within stream if enough data is collected.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

The paper was supported by the Project of Influence Mechanism of Climate Change on Water Cycle in Huang-Huai-Hai River Area and Water Resources Security Evaluation (2010CB951102) of the National Program on Key Basic Research Project (973 Program) and the General Program of the National Natural Science Foundation of China (Grant no. 51279207).

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Copyright © 2014 T. L. Qin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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