2　Analysis of Runoff Yield Model in Basins Influenced by a Group of Reservoirs

For a basin with a large number of hydraulic projects，the amount of runoff due to a specific rainfall depends on two factors：(a)basin physical elements，such as topography，forest cover，soil，etc.；and(b)hydraulic project elements，i.e.their kind，size，amount，operating rules，etc.The mechanisms that produce runoff are quite different.It is necessary to adopt a variable method to suit variable conditions.According to the above analysis，the runoff yield model influenced by a group of reservoirs may be established.First，the entire basin is divided into three categories：large-to-middle-size reservoirs.small reservoirs，and residual area.Next，net rainfalls for each category are computed as follows：(a)for the residual area，conditions are natural.The usual runoff yield model may be applied directly to calculate net surface rainfall(i.e.excess rainfall)and net subsurface rainfall；(b)for large-to-middle-size reservoir areas，the net surface and subsurface rainfall into the reservoirs may be computed according to the specific runoff yield model in the natural condition.After regulation，the abandoned water over spillways and the water released for special generation go directly to streams and become the net surface rainfall hydrograph for the reservoir.The net subsurface rainfall in the natural condition combines with the irrigation return water supplied by the reservoir to form the whole net subsurface rainfall hydrograph after building the reservoir；(c)for a great deal of scattered small reservoirs，the inflows are calculated by a runoff yield model in the natural condition.After regulation，this should be separated into irrigation water.power release and abandoned water.The same procedure as above is adopted in order to derive the surface and subsurface rainfall for the group of small reservoirs.Finally，items(a)，(b)and(c)are summed up to obtain net surface and subsurface rainfall for the entire basin.Routing this to the outlet of the basin，a simulated flood hydrograph is obtained.The above calculations of the model are explained in detail below.

2.1　Basin Runoff Yield Model in the Natural Condition

In China，basin runoff yield models are generally divided into two categories.runoff yield from excess infiltration and runoff yield from excess storage(Zhao，1977).The choice is dependent on local physical conditions.In the Fengshuba basin，the excess storage model was selected.

2.2　Computation of Irrigation Water Requirement

Water that is artificially supplied to crops in a given period of time for their normal growth is known as the irrigation water requirement，and is denoted by .In the southern part of China， equals the sum of crop water requirements in fields irrigated for rice growing(denoted by )and conveyance loss for canal systems(denoted by ).For thetth interval，the equation for may be written as：

(a)Crop water requirement in field The equivalent equation on thetth day in a crop field is：

where D(t-1)，D(t) are depths of water in field at the beginning and end of thetth day，respectively，in mm；

P(t)　istth day’s rainfall，in mm；

EE(t)　istth day’s evapotranspiration，in mm；

F(t)　istth day’s field infiltration，in mm；

，Dp(t)are depths of water for irrigation and draining on thetth day，respectively，in mm；

Dl(t)，Du(t)are the lowest and highest allowable water depths in the field for the corresponding growth period，in mm；and

Dm(t)　is the most suitable depth for the corresponding growth period，in mm.

When P(t)，EE(t)andF(t)are known，the daily may be derived from equation(2)，adoptingDl(t)，Du(t)andDm(t)as controlling conditions.DefineD′(t)as：

When D′(t)＞Du(t)then ，Dp(t)=D′(t)-Du(t)andD(t)=Du(t)；When Dl(t)≤D′(t)≤Du(t)，then and D(t)=D′(t)；and When D′(t)＜Dl(t)，irrigation is needed and has to reach a suitable depth；so and D(t)=Dm(t).In this way，values of daily and D(t)are obtained.D(t)of today will be D(t-1)of the next day：thus for each day can be evaluated.The crop water requirement in the field，，for each day is calculated by multiplying by the irrigation areaAgi.e.

For the above formulae，P(t)can be obtained from theHy drologicɑl Yeɑrbook；Du(t)，Dl(t)，Dm(t)andAgare obtained from on-the-spot investigations.Values ofEE(t)are determined by using the following formula：

whereE(t)is the value observed from the water surface evaporator(mm)，andαtis a coefficient responding toE(t)，determined by the experimental data of water surface evaporation and irrigation.As for daily infiltrationF(t).it is deduced from irrigation norms in practice.Applying this procedure for the Fengshuba basin，F(t)calculated for various periods are：F(t)=8mm day-1 for 21 March-9 April(soaking field period of early rice)；F(t)=3.7mm day-1 for 10 April-30 June(growth period of early rice)；F(t)=3.8mm day-1 for 10-19 July(soaking field period of late rice)；F(t)=3.7mm day-1 for 20 July-19 October(growth period of late rice).Except for the soaking field period of eafly rice，F(t)values in other periods are rather steady.There is fair agreement with the mechanism of infiltration.These values are within the limits of published data.

(b)The conveyance loss in canal systems is directly proportional to the irrigation water requirement .The following expression may be used：

whereβis the coefficient of conveyance loss，which may be estimated through experiments and on-the-spot investigation.In the Fengshuba basin.βis approximately 0.3.

2.3　Determination of Regulated Special Generation Water

from Groups of Small Reservoirs

For convenience.the term“a group of small reservoirs”is denoted by GSR below.Special generation water denotes that part of the water released from GSR is used for the generation of electricity，without the combination of irrigation.After this part of the water is regulated，it becomes regulated special generation discharge .The discharge of a small reservoir with generation work may be determined by the analysis of some generation records observed in advance.For example.the following equation is used for theith reservoir in Fengshuba basin：

where： is the regulated special generation discharge for theith reservoir in thetth interval，inm3 s-1；wet season and dry season are considered as the periods of April-September and October-March respectively；

Qw，i，Qd，i　are average irrigation discharge in wet season and dry season，respectively，inm3 s-1；

Ni　is the installation capacity for theith reservoir，in kW；

tn，i　is the installation time utilized in h；

B　is the power coefficient(here6.5isadopted)；

Hi　is the average head，in m；

r　is the ratio of generated energy in the wet season to that over the whole year；and 4380 is the duration of wet or dry season.in h.

Ni，tn，i，Hi may be obtained by on-the-spot investigation；ris estimated by the operation recorder of a small reservoir with irrigation and electricity generation(0.689 in Fengshuba).In a unit basin， is calculated for individual small reservoirs.These are then summed up and multiplied by the seconds in an interval，thus yielding .

2.4　Computation of Regulation for a Large-to-middle-sized Reservoir

Most of the large-to-middle-sized reservoirs are multipurpose.built for flood control，irrigation，generation of electricity，etc.Each of them has fixed operating rules.Hence，regulation computations may be successively carried out，interval by interval.as the usual calculation method of regulated reservoirs.based on the computed inflow.The computations result in hydrographs of abandoned water，irrigation，power release，etc.

2.5　Computaion of Regulation for GSR

GSR are large in number，widely scattered，linked in parallel with each other and basically similar in operational rules.Therefore，one can generalize the storage characters and regulation procedures of GSR.The details are as follows：

(a)Curve of storage capacity of GSR A great number of small reservoirs in the basin have different storage capacities and drainage areas.In Fig.1 the ordinate represents storage capacity of theith reservoir，Ri，equal to the reservoir's effective storage divided by its drainage areaAi.Riis arranged in magnitude from small to large，with its correspondingAiindicated as abscissa∑Ai.In order to facilitate computations，Fig.1 may be converted to aV′S′ɑ，curve(GSR storage capacity curve)as shown in Fig.2.The procedure for producing this is as follows：for eachRi，the runoff volumeVi(=Ri∑Ai)and storage capacitySɑ，i(from the hatched part in Fig.1)are derived；for the series ofRi，a series ofViandSe，iare obtained.The curve may then be drawn.

(b)Basic operating rules of small reservoirs Based on numerous investigations，the basic operating rules of small reservoirs may be summarized as follows：(i)For irrigation，the reservoirs release water as crops demand until they are empty，they store water when there is runoff until they are full；they abandon water after they are over-full.(ii)For generation，under guarantee of irrigation water，if there is more surplus water，it is used for special generation by ；if there is no more surplus water，there is no special generation.

(c)Regulation calculation of GSR If the runoff volumeV(t)，irrigation water requirement and special generation water volume for thetth interval have been computed by the above methods，Vg(t)，Vd(t)，Sɑ(t)，Vq(t)andS(t)for each time interval can be calculated step-by-step by the following methods：

（i）Storage volume in thetth intervalSɑ（t）：For the first interval at the beginning of a year，if the base waterS（t-1）is distributed in each reservoir in an area ratio of its basin，an invented runoff volumeV′（t-1）into reservoirs can be determined by an inverse trans formation fromS（t-1）in Fig.3（a）.This invented runoff is added to the teal runoff volumeV（t）to give a total runoff volume[V′t一1）+V（t）]in this interval，under the condition of empty reservoirs.The invented total storage corresponding to[V′（t-1）+V（t）]is obtained from Fig.3（a）.The real storageSɑ（t）can be determined as follows：

For subsequent intervals，base waterS(t-1)at the beginning of intervaltmay yield the result that all the reservoirs have released water[Vg(t-1)+Vd(t-1)]for irrigation and generation.The runoff volumeV(t)should first restore this part of the reservoir volume，following which the rest of the runoff will only storeΔU(t)(Fig.3(b)).Then，forV(t)≤Vg(t-1)+Vd(t-1)：

and for

whereΔU(t)is the storage volume when the base water is[S(t-1)+Vg(t-1)]and the runoff is[V(t)-Vg(t-1)-Vd(t-1)].The method for its calculation is shown in Fig.3(b).

(ii)Irrigation water volumeVg(t)and regulated special generation water volumeVd(t)：When ，for irrigation：

Luo Wensheng etɑl.for generation：

if

if

for

for

whereα1，α2，α3are the ratios of the drainage area of generation reservoirs to the total drainage area of GSR，the ratio of effective storage of generation reservoirs to the total effective storage of GSR，and the ratio of the irrigation area of the generation reservoirs to the total irrigation area of GSR，respectively.

When ，for irrigation：

for generation：

(iii)Abandoned waterVq(t)：forS(t-1)+V(t)-Vg(t)-Vd(t)-Sɑ(t)＞0

for

(iv)Storage volume at the end of thetth intervalS(t)

TheS(t)of any interval will be theS(t-1)of the subsequent interval.

Vg(t)，Vd(t)，Vq(t)andS(t)are calculated successively，interval by interval.

2.6　Calculation of Irrigation Return WaterVh(t)

The irrigation return water would be the sum of irrigation seepage loss in fields and canals.The former equalsF(t)Agwhen there is no rainfall，and it is approximately[Dg(t)/{Dg(t)+P(t)P}]F(t)Agwhen there is rainfall.The latter is approximatelyβVg(t).The irrigation return water，then，is

whereDg(t)is the irrigation water depth in thetth interval，which can be determingd asVg(t)in the above section(c)：Regulation calculation of GSR.