A conceptual model simulating the hydrological processes on a drainage basin in a plain area

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1 New Directions for Surface Water ModelingCPvoceedines of the Baltimore Symposium, May 1989) IAHS Publ. no. 181,1989. A conceptual model simulating the hydrological processes on a drainage basin in a plain area Xin Ren Liu Department of Hydrology, Hohai University, Nanjing, China Jing Quan Wang Nanjing Research Institute of Hydrology and Water Resources, Nanjing, China ABSTRACT A conceptual model is proposed to simulate the hydrological processes on drainage basin in plain area where the vertical fluxes predominate and where the groundwater table is very close to the surface and, therefore, the interaction between surface water and groundwater should be taken into account. The hydrological components of the system are described in the model by means of four storages and their governing rules which are drawn from experiences as well as theoratical knowledge. The model predicts the discharge at the outlet of the basin based on the input data of rainfall and pan evaporation. Additionally, it is capable of predicting groundwater table depth at each rainfall station. INTRODUCTION In plain area the flat landform, the braided river network and the shallow groundwater make the hydrology there unique which is considered as a particular subject of hydrology and has already been listed in the IHP-III as project 4.7. Under these topographic conditions, the importance of the horizontal transport in the hydrological cycle is becoming less significant and the vertical one predominates gradually with the slope decreasing. Therefore, many hydrological models developed for steeper catchments are less useful and not sufficient in plain area since they are calibrated totally relying on the data of runoff and predict only the discharge. A new type of model which is able to handle the vertical transport of water and predict groundwater table as well as runoff is required for solving various kinds of problems dealing with water in these areas. The vertical water transport and the interaction between rivers and aquifers involve saturated and unsaturated flow system which is a hot point in hydrology in recent years. A great deal of effort has been devoted to this field and, as a result, uncountable papers have been published on either experimental or theoratical research. Models totally based on the saturated and unsaturated flow theory were proposed by a number of authors, in which Freeze's model is one example (Freeze, 1978). These models have given an insight into what happens under the surface and a clue to the solution of the problem. However, the strictly physically-based model is usually not practical although it is precise in describing the process. Thus 195

2 Xin Ren Liu & Jing Quart Wang 196 approaches of all kinds towards simplification are suggested, such as replacing the unsteady state by the steady state (De Laat, 1976), simplifying the dynamic wave of infiltration as kinematic wave (Smith, 1983), and making a saturated approximation to the unsaturated reality, etc. Besides, the system approach is also made use of to solve the groundwater response to the meteorological conditions on the surface or to the state of rivers (Kontur, 1982; Illangasekare and Morelseytoux, 1982). But, unfortunately, few models found in literature simulate both surface water and ground water for a real catchment or an area with a size of, say, a few thousand square kilometers, using data commonly available. While it is this type of model that needs to be created to meet the requirement in practice. And, therefore, it is taken as the aim of the present study. In the study, a conceptual type of model is preferred since this type of model is more flexible and still remains room for theoratical simulation of any individual components, if necessary and possible. Another consideration in the study is that the data of groundwater level readily available in plain area would provide precious information and therefore, should be introduced into the model being studied. It is believed that the more information is used, the more reliable the results are. As it has been shown that the use of pan evaporation data improves the rainfall runoff model to a great extent, utilizing groundwater level data may also be expected to benefit the modelling of plain hydrology. Under these considerations, a model essentially of a water balance and routing type was designed to predict outflow from a drainage basin and water table at each rainfall station within the basin. An application to a real catchment in a plain area is primarily successful. MODEL STRUCTURE The general structure of the model proposed is illustrated in Fig. 1. It consists of three storages representing respectively (a) soil moisture mainly in the root zone as unsaturated water below field moisture, (b) surface and immediate subsurface saturated water, and (c) groundwater in aquifer. Actually there is one more storage in the model describing channel network which did not appear in Fig. 1, as it is not an important point in the model. «w t i t I' Y r If H s i il "9 Fig. 1 Schematic drawing of the general model structure.

3 197 Conceptual model for hydrological processes in a plain area The model receives rainfall (p) as an input and produces discharge (Qs and Qg) and evaporation (E) as outputs. There are three fluxes (R, f, Eg) linking the three storages and three variables (W, S, H) indicating their states. The soil moisture storage receives rainwater up to its capacity (Wm), any surplus (R) being fed into the surface-subsurface storgae from which water drains (Qs), as from a non-linear or a linear reservoir, to the channel storage (quick response). Percolation (f) also occurs from the surface-subsurface storage, as from a linear reservoir, to the groundwater storage. The groundwater storage drains (Qg), also as a nonlinear reservoir, to the channel storage. The relationship is the subject of a particular development in this paper. The channel storage is represented by one or more linear reservoirs in cascade. Evaporation (évapotranspiration) dra>/s first on the surfacesubsurface storage, and only if this is eliminated, on the soil moisture storage. When there is a certain upward net gradient of potential, an upward flux (Eg), using a simple steady state unsaturated flow equation, from the groundwater storage m3y replenish the depleted soil moisture storage and contribute to the continuation of evaporation. All the three storages operate independently at each rainfall station, thus permitting consideration of the areal variation of rainfall and soil properties. The time interval used in the model is one day, thus the model may be termed as Daily Plain Hydrological Model (DPHM). The advantage of a daily model is that it can make full use of the readily available data of rainfall and is easy to handle in a computer for continuously modelling over a long period. Fortunately, very often in plain area, due to its slow response, the daily averaged peak flow is well coincident with the corresponding instantaneous one. Therefore, in many cases, the hydrograph generated by a daily model is detailed enough in practice. FUNCTIONS AND PARAMETERS Soil Moisture Storage The soil moisture storage is further divided into two parts, ie. upper part and lower part. Rainfall first replenishes the upper part up to its capacity (UM), then the lower part, also up to the capacity of the lower one (LM). While UM + LM = WM And after that, the surplus is fed into the surface-subsurface storage as mentioned before. Soil moisture storage vanishes only through evaporation. After the saturated surface-subsurface storage water depleted, water in the upper part evaporates first at a rate (E) equal to a potential value Em,Em = K.Ep, where Ep is a recorded daily pan evaporation, and K is a coefficient being calibrated mainly based on the catchment water balance over a long period, and it may vary with season, if necessary, reflecting the influence of crops. When the upper part is emptied out, water in lower part evaporates

4 Xin Ren Liu & Jing Quan Wang 198 at a rate (E) proportional both to the potential rate (Em) and to its owi current storage (WL), expressed as follows E = Em. WL / LM In the meantime, an upward flux from the groundwater storage occurs to replenish the soil moisture from below. Saturated Surface-Subsurface storage This storage receives the surplus water from the previous storage and depletes through three ways: (a) evaporation being equal to Em, (b) surface-subsurface runoff (Qs), according to a non-linear relation Qs = S / k1 where K1 is a function of the current storage S, i.e. K1 = f(s) or simply according to a linear relation in which K1 is a constant reflecting the average lag time of the surface-subsurface response, (c) percolation down to the groundwater which is determined by a linear relation, i.e. f = S/K2 where K2 is a constant reflecting the average travel time from the root zone to the groundwater table. Groundwater Storage Groundwater storage is supplied by the percolation from above and depletes through horizontal drainage into the channel storage and upward flux, as groundwater evaporation, into the soil moisture storage. (a) The groundwater drains into rivers intercepted and provides the baseflow of the river. Conventionally, the relationship between baseflow (Qg) and groundwater storage (Sg) is considered as a linear reservoir type, ie. Sg = Kg. Qg where Kg is a constant. This relationship leads to an exponential recession curve of the hydrograph expressed as Qt = QO exp (-Kg.t) where QO is the initial value on the recession curve and Qt is the value at time t. The nonlinearity found in most recession curves is generally interpreted as a result of the fact that the hydrograph is actually a combination of different sources of runoff with different response time. However, in plain area where groundwater is very close to the surface (say, not more than 2-3 meters deep), it is preferred to consider that the nonlinearity of a recession curve results from the fact that groundwater intercepts river network nonuniformly, rather than the combination of different sources of runoff. As shown in Fig.2, when groundwater table rises close to the surface, it intercepts more channels and therefore the travel time under the surface becomes shorter. If the discharge from the groundwater is still expressed as

5 199 Conceptual model for hydrological processes in a plain area sur-pac L, h ~L 2 -j- L water tablex. Fig.2 Schemetical drawing of a vertical profile of a plain area. Qg = Sg / Kg then Kg, also reflecting the travel time, should decrease as water table rises or groundwater storage increases, as shown in Fig.3. Thus a nonlinear type of relationship is suggested to model the groundwater drainage. The Kg-Sg relationship is relatively easy to obtain by using observed hydrograph in rainless period (Liu, 1987). Logically, this relationship should reflect the geometric property of the channel network and the hydraulic property of the soil. Therefore, it may be a useful tool in the drainage design for plain area. (b) Groundwater evaporation is an upward flus governed by the saturatedunsaturated flow equation. It has been shown that during the evaporation period, a simple steady state may be a good approximation to the unsteady state. In the case, only the Darcy-equation is needed: V = - K 3f/a z where V is the vertical flux. In the present study, K is the hydraulic conductivity, and is the potential of soil water = <p + 1 where 0 is the matric potential of soil water, and Z is the gravitational head and is also the vertical space coordinate with its origin set on water table. Integrating this equation upward from the water table where <P =0; Z=0: z Z =J dz = -j û<p /(1+v/k) Fig.3 Hypothetical relationship between groundwater storage and its response time.

6 Xin Ren Liu & Jing Quan Wang 200 This gives a relation of Z-^-v. Given the 0 on surface, V relates to Z. In the present model, the upward flux from groundwater is specified to occur only when the upper part of the soil moisture is empty, which is corresponding to a very small matric potential approximately equal to the wilting point. Thus, given the characteristic curve of the soil, i.e. <M 9 ) and k( e ) where e is the volumetric soil moisture content, the relationship of Z-V may be worked out beforehand. (c) In practice, the groundwater storage (in water depth) should be transformed into water table level by using a coefficient M p = Sg/(H - HO) where HO is the elevation of an artificial datum where the storage of Sg set to be zero, and H is the elevation of the water table corresponding to Sg. In summary, the parameters and relations above mentioned may be broken down roughly into three groups. The first one contains those involved in the determination of runoff volume or the actual évapotranspiration, as viewed from the losses. The second group deals with the routing behaviour of the system including surface, subsurface and groundwater runoff routing and travel time of the vertical transport recharge to the groundwater. The third group refers to the hydraulic properties of soil. The first group is mainly calibrated in terms of the overall accuracy of the predicted mean annual runoff. The second one is basically adjusted by the best fitting of the hydrograph of riverflow at the outlet. And the third one may be determined according to the goodness of the prediction of water table fluctuation and also by the reference of the information available about the soil properties. APPLICATION The model described above has been applied to a real catchment in a plain area. The selected catchment is located in the plain north of River Huai where there is a low and gentle terrain mostly less than 50 m above sea level. The catchment covers an area of 3094 km 2 on River Fenquan, a tributary of River Shaying, controlled by a hydrological station at Shenqiu, Henan Province. The annual precipitation is about 830 mm, and the annual runoff 190 mm. The average depth of the water table is 2.5 m approximately below surface, and it often reaches ground surface during heavy rain seasons and causes flood or waterlogging. Shenqiu station has collected hydrological and meteorological data of more than 35 years since Besides, there are more than eight raingages with data series of at least 25 years being published. Among them three stations observe groundwater table as well. These data and some others have been utilized for the research. A period of 4 yearsfrom 1964 to 1967 is used for the model calibration and another 4 yearsfrom 1968 to 1971 for the verification. Considering the influence of vegetation, the parameter K takes different values separately for the growing season and other periods. The parameters of soil properties are estimated also in the light of other research carried out on an experimental station nearby. A computer program has been worked out and performed on a microcomputer using BASIC. Input data are daily rainfall observed at

7 201 Conceptual model for hydrological processes in a plain area eight stations and daily evaporation observed at Shenqiu with a pan of E 601 type. The program runs for each rain station separately and gives the outputs of water table level at that station and discharge that contributes to the main channel. The predicted water table of each station may be compared with the observed one if available. The discharge then route through a simple routing model to the outlet of the catchment, Shenqiu station, and compared with the observed one. To save space, the resultsof the application are briefly demonstrated by a comparison between the calculated and observed annual runoff listed in Table 1 and hydrographs of one year as an example in Fig.4. Table 1 Comparison of annual runoff (unit: mm) year ~ î~ W7~\ observed predicted CONCLUSION The model proposed is a compromise between the excessively physical and the excessively empirical. Its advantages are: (a) It uses common hydrological and meteorological data. (b) It can be applied to different sizes of drainage basins. (c) It produces groundwater table fluctuations as well as discharge hydrographs. (d) Consideration of the fluctuation of the groundwater table forces Simulated observed water table " water table i 'i «in ii» ii i n M i ill 1 iiiini I 11 i i 1 i' i r Fig. 4 The hydrographs of Shenqiu and water table at Shenqiu(a), Jiangqiao(b) and Wangyemiao(c), 1964.

8 Xin Ren Liu & Jing Quan Wang 202 the simulation of infiltration, evaporation and groundwater flow to be more explicit, and places a constraint on the model structure, which makes it more reliable. The model is only a newly developed one with some unavoidable imperfections. However, it is encouraged by the application and a further improvement is being made. This study is a part of another more comprehensive research project carried on in cooperation with the Institute of Huaihe Valley Planning and Design. An Acknowledgement is gratefully made for their cordination. REFERENCES De Laat, P.J.M. (1976) A pseudo steady-state solution of water movement in the unsaturated zone of the soil. J. hydrol., Vol.30, Freeze, R.A. (1978) Mathematical Models of Hi 1Islope Hydrology, sec. 6 in M.J.Kirkby (éd.): Hillslope Hydrology. Wiley, New York, Illangasekare, T. and H.J. Morel-seytoux (1982) Stream-aquifer Influence coefficients as tools for simulation and management. Wat.Resour. Res., Vol. 18, no. 1, Kontur, I.F. (1982) Stochastic groundwater-precipitation-evaporation models. Session 1, International conference on Modern approaches to groundwater resources. Capri, Italy. Oct Liu, X.R. et al. (1987) A study on the hydrological model of Fenquan river basin in north Huaihe plain. Tech. Rep. (1987) (in Chinese). Smith, R.E. (1983) Approximate soil water movement by kinematic characteristics. Soil Sci. Soc. Am. J., Vol Zhao, R.J. (1984) Hydrological modelling of river basin--xinanjiang model and Shanbei model, Water Resources and Electric Power Press, 1984 (in Chinese).