3　Construction of Water Resources Supply and Demand Balance Model

3.1　Calculating partitions,compute units,and analysis units

3.1.1　Calculating partitions

According to the main water source for irrigation in Jingnan river network,the study area is divided into four subareas:Three rivers subarea(three rivers in Jingnan is the main water source,hereinafter referred to as〝TRS〞),Yangtze River subarea(Yangtze River is the main water source,hereinafter referred to as〝YRS〞),Lake subarea(lakes are the main water source,hereinafter referred to as〝LS〞)and reservoir subarea(reservoirs are the main water source,hereinafter referred to as〝RS〞).

3.1.2　Calculation units

In the reservoir subarea and lake subarea,every single reservoir and lake is a calculation unit.In the Yangtze River subarea and three rivers subarea,the calculation nodes are corresponding calculation units.In this paper,the computational nodes are divided into 3 types:the water level-flow control point,the water level point and the water flow point.Furthermore,the computational nodes are defined as mentioned below and the generalization of these nodes is shown in Fig.2.

(1)The water level-flow control point is the starting and terminal point of the calculation river reach.The attributes of this point include the every ten days water level,the every ten days flow rate and the rating curve of the section where this point locates.If the node is a branch point or a confluence point,it contains relevant attribute information such as the split ratio and the confluence ratio.

(2)The water level point is the independent sluice or auxiliary water source project for the sluice gate station at the calculation river reach(except the starting and terminal point),and this point attributes include the every ten days water level and the every ten days flow rate.

(3)The flow point is the independent pumping station water source project at the calculation river reach(except the starting point and the terminal point),and the node attributes only include the every ten days flow rate.Irrigation pump stations(separated),waterwork intakes and industrial water intakes are all recorded as flow points.

There are 31 reservoirs and 25 lakes in the study area.Therefore,there are 56 calculation units in the reservoir subarea and the lake subarea in total.According to the definition of calculation node,there are 118 computing nodes in the three rivers subarea,including 18 water flow points,65 water level points and 35 water level-flow control points.And there are 34 calculation nodes in the Yangtze River subarea,including 7 water flow points,16 water level points and 11 water level-flow control points.

3.1.3　analysis units

The agricultural water supply and demand balance is analyzed by irrigated area element,and the irrigation water requirement,water supply and water shortage are collected.Then the calculation and analysis of water deficient ratio and irrigation guarantee rate are carried out.The results of non-agricultural supply and demand are statistically analyzed by water intake element.

3.2　Calculation process and train of thought

3.2.1　Three rivers subarea

(1)Take ten days as a calculate interval,and calculate by every ten days.

(2)Take the calculation node as the calculation unit,and calculate by every river reach and every calculation node.

(3)Distinguish the type of calculation node(water level-flow control point,water flow point,water level point).Read the relationship between water level and discharge,the length of river reach,slope of river reach,split ratio and some other calculation factors.Then figure out the water level and water flow of the calculated node.

(4)While considering the water consumption of industry and living in the three rivers,it is necessary to distinguish the type of water intake,including two categories,namely industry and life intake and irrigation intake.

(5)If the water intake is the industry or life water intake,the available water supply can be determined by comparing the water inflow and the design flow of the water intake.And then the actual water supply can be figured out by comparing the available water supply with the industry and life water demand.Finally,the next calculated node flow can be obtained by subtracting actual water supply from water inflow.

(6)While calculating the water balance of irrigation intakes,the irrigation area and gross irrigation quota and other attributes factors should be read firstly,then the irrigation water requirement(the irrigation water requirement is the irrigation water requirement after deducting the water supply of canal ponds and ditches)can be calculated.Afterwards,distinguish the type of water project of the calculation node,and the project types mainly include water level point(independent sluice gate,gate station matching project)and flow point(independent pump station).Finally,different calculation methods are used to calculate the supply-demand balance according to the node type.More specifically,the discharge capacity of sluice gate is calculated in accordance with the broad crested weir and that of sluice(circular)is calculated in accordance with pressure or non-pressure short hole.When calculate the supply-demand balance of the gate and station supporting project,water supply-demand balance is firstly calculated,and supply water through the pump station when the water demand cannot be satisfied.

(7)Since the deep water troughs have water supply function while watercourse is dry up,they should be treated as special ponds(or reservoirs)strung on river reach,which only have volume and no water level.When using deep water trough to supply water,it should be confirmed that only the pump station can supply water and the sluice gate cannot.

(8)Finally,irrigation(non-agriculture)water demand,available water supply,actual water supply and water shortage of every calculation unit will be obtained and summarized on the analysis unit.

3.2.2　Calculation principle of deep trough

It is assumed that the maximum water storage in deep water trough is Wmax,the storage capacity is W0 at the beginning of the ten day period,and the storage capacity is W1 at the end of the ten day period:

(1)When Win≥Wd,namely the amount of water inflow(Win)is greater than or equal to the water demand(Wd):

if Win-Wd+W0＞Wmax,then W1=Wmax,after deducting the water demand and the storage capacity of the deep water trough,the remaining water quantity is taken as the inflow of next calculation node,and the water amount in deep trough is the maximum water storage in the deep water trough;

if Win-Wd+W0≤Wmax,then W1=Win-Wd+W0,after the water demand is deducted,the remaining water is all stored in the deep water trough,so the inflow of next calculating node is 0.

(2)When Win＜Wd,namely the amount of water inflow is less than water demand:

if Win-Wd+W0＞0,then W1=W0-(Wd-Win),the water inflow is less than the water demand,whereas the sum of the inflow water and the water in the deep water trough meets the requirement of water demand,then the water in the deep water trough reduce,and the inflow of next calculating node is 0.

if Win-Wd+W0≤0,then W1=0,the sum of inflow and water in the deep water trough cannot meet the irrigation demand,then the water in the deep water trough is reduced to 0,and inflow of the next calculating node is 0.

3.2.3　Yangtze River subarea

The calculation process and thought of Yangtze River subarea are similar to that of three rivers subarea.More specifically,they all take ten days as a calculate interval and calculate by every river reach and every calculation node.On the other hand,the inflow of calculation node has nothing to do with the water consumption of upstream node and the available water supply depends on the the water capacity of corresponding water source project,which is because the water supply capacity of Yangtze River is sufficient.

3.2.4　Lake subarea and reservoir subarea

(1)Calculate the water balance of every lake and reservoir by every ten days.

(2)While calculating the available water supply of lakes,the water supply capacity of pump station(intake)requires to be take into account,since the lake supply water for irrigation by pump.

3.3　Main calculation parameters

3.3.1　Calculation and determination of water quota

Use the daily observation data from 1971 to 2000 of 4 meteorological stations(Gongan County,Shishou City,Songzi City and Jingzhou District)as meteorological data,and determine the reference crop requirement by Penman-Montieth method.Based on these,the actual crop requirement can be calculated.Then,the irrigation norm of rice(early season,middle-season,late),vegetables,wheat and cotton is calculated through water balance.

The industrial,construction industrial,the tertiary industrial,domestic and ecological water quota should be determined by comprehensively referring to the〝Jingzhou official report on water resources(2014)〞,tough water management measures,〝Hubei province water quota〞.

3.3.2　Utilization coefficient of irrigation water

The coefficient of status quo year is determined by the situation of current projects in irrigation area,whereas that of the planning year should be determined by according to〝modern development program of irrigation in Hubei province〞,efficiency index in tough water management measures,and〝the design specifications of irrigation and drainage project〞.And since the irrigation areas in Jingnan river network area have multi scattered water sources and more diversion and lifting projects,the utilization coefficient of irrigation water in this area is a bit higher than the other similar irrigation area in Hubei province.After comprehensive consideration,the utilization coefficient of irrigation water of different water sources in status quo year are determined as follows:ponds are 0.75,deep canals are 0.75,lakes are 0.55～0.7,reservoirs are 0.5～0.7,sluice stations are 0.5～0.7;and in the planning year,the corresponding coefficients are determined as follows:ponds are 0.8,deep canals are 0.8,lakes are 0.6～0.75,reservoirs are 0.6～0.75,sluice stations are 0.6～0.75.

3.3.3　Water inflow

The Lake River network 1-D sedimentation mathematical model,which aim to research the river reach from Yichang to Datong of Yangtze River main stream,three outlets along Jingjiang river reach,Dongting Lake and Poyang Lake,was constructed.And this model adopts the three stage solution of river network,and uses measured data of 2003—2009 years to calibration and validate the flow and sediment deposition rate[7].Afterwards,this model was utilized to simulate the everyday water level and flow at the water level-flow control point in status quo year and planning year(2022,2032,2042,2052).

Generally,the lake(reservoir)inflow is calculated according to water balance.However,due to the lack of measured data,the inflow should be calculated through the method of runoff coefficient,and the runoff coefficient can be determined by referring to feasibility study report of continue auxiliary and water-saving improvement projects of the Weishui River irrigation area.

The calculation of water supply of ponds and canals adopts SCS method.The water supply time of the ponds is the wet period(from May to October),and the water supply time of canals is dry season(from November to April in next year).Pond re-storage times is 2 in high flow years,1.5 in normal flow years,1 in low level years,and 0.75 in dry years,whereas canal re-storage times is 0.75 in every year.

3.3.4　Average water level gradient at every river reach in different level years

According to the prediction results of water level at different water level-flow control points in different level year,the average water level gradient at every river reach in different level years is determined.

3.3.5　Rating curve of water level-flow control points

According to the prediction results of water level at different water level-flow control points in different level year,imitative effect of the stage-discharge relation at water level-flow control point is good(typical stage-discharge relation is shown in Fig.3),so it can be used for model calculation.Then,use quartic polynomial to fit the rating cure of water level-flow control points.

3.3.6　Split ratio

Because the split ratio is affected by many factors,the fitting relation between the flow rate of the main stream and the split ratio is not good,and the long series of split ratio is adopted to improve the calculation accuracy.

3.3.7　Water level and flow of every station

Water level and discharge at three outlets are simulated by one-dimensional water sediment model,and the flow of each calculation node is equal to the flow of the last calculation node deduct the actual water supply(if there're sinks in the river reach,the water storage in sinks should also be deducted).Furthermore,the water level at the water level-flow control points can be determined according to the relation between water level and flow,and the water level of calculated nodes between the two water level-flow control points can be calculated in terms of the water level gradient.