¹ Assistant Engineer, China Institute of Water Resources and Hydropower Research

² Senior Engineer, China Institute of Water Resources and Hydropower Research

Tel: 86-10-68412173,Fax: 86-10-68412316,E-mail: hanlm@iwhr.com

Abstract: Groundwater in the region of middle and lower reach of Daguhe River Basin is one of the main water supply sources for the Qingdao City. However, due to excessive and non-planned withdrawal of groundwater, serious environmental impacts arise, such as groundwater contamination, land subsidence and seawater intrusion, etc. Therefore, an appropriate groundwater management is imperative in the region and Daguhe Groundwater Reservoir Project is carried out. This paper analyzes the water conditions of the groundwater reservoir and uses the two-dimensional mathematical model to simulate the groundwater flow field. Finite difference method is applied for the solution of the model and parameters are determined by the typical year recorded values. This paper also provides a parameter calculation process, which is to improve the groundwater flow model. Programme of this model is used as a modular of the fundamental model of Qingdao water resources macro-management.

Keywords: daguhe groundwater reservoir, groundwater flow model, parameter calculation

The Qingdao City is one of the major cities with serious water shortage in the north part of China. The mean annual precipitation is 680mm and the averaged annual water supply per person is about 370m3 . As a result of continuous economic growth, rapid increase of population and highly improved living standard, the water demand is continuously increased. And water shortage will seriously restrict the economic development. This requires an effective water resources utilization and water supply management for a sustainable development. Daguhe Groundwater Reservoir is carried out to mitigate the water shortage in Qingdao City. This project consists of two major parts:

• Building underground diaphragm wall to cut off the hydraulic relationship between groundwater and sea water;
• Carrying out artificial recharge projects to replenish groundwater resources.

In addition, the monitoring system, ecological and environmental protection system as well as management system are to be established for the groundwater reservoir.

The Daguhe Groundwater Reservoir is located in the plain region of middle and lower reach of Daguhe River Basin. Its length from north to south is 51km and averaged width from west to east is 5-7km. covering 421.7km² with an alluvial gravel layer of 5.19m for groundwater storage. The total capacity is 384million m³. The control mode of “4-dry-year-1-wet-year” will be adopted for the groundwater exploitation.

This paper analyzes the characteristics of Daguhe Groundwater Reservoir and uses two-dimensional mathematical model to simulate the groundwater flow field. To improve the groundwater flow model, a parameter calculation process is also proposed. The results of this model are verified by a 3 years recorded data and applied in the fundamental model of Qingdao water resources macro-management.

As part of the fundamental model of Qingdao water resources macro-management, groundwater flow model for Daguhe Groundwater Reservoir simulates the groundwater flow field of the reservoir and provides basic data of water information for analysis and assessment of the Daguhe Groundwater Reservoir. The model calculation program are based on the Software of MODFLOW, which is a modularized finite difference solution for groundwater flow model programmed by Michael G Mc. Donald and Arlen W Harbaugh from U.S.G.S.

2.1    Conceptual model of the water storage layer

The water storage layer in this area is a single-layer groundwater system. The groundwater flow can be treated as a two-dimensional non-stabilized underground flow. Due to different structures in different places, the capacity for water storage and water penetration differs in the region. The east and west boundaries are confining boundaries. And the south and north boundaries are open boundaries. The bottom of the water storage layer is the water-tight stratum. The water storage layer is opened to the air. The replenishment of the groundwater is mainly from the precipitation and influent stream feeding. Discharge of the groundwater is mainly by means of exploitation.According to the above analysis, the groundwater flow model for the Daguhe Groundwater Reservoir can be described by the following formula:

where: H—groundwater level

B—bottom level of the groundwater storage layer

m —storage coefficient of the groundwater storage layer

K—percolation coefficient

W— vertical water exchange quantity for the groundwater storage, including Q_rain, Q_stream, Q_evaporation and Q_exploitation

G ₂second type of boundaries

G ₁first type of boundaries

District area available of permeation

2.2    Boundaries and grid division

the boundary conditions are determined by a statistics of the characteristics of the groundwater storage layer. The east and west boundaries are the natural boundaries of the layer and groundwater storage stops at the boundaries. The north boundary is located at the end of the river valley, which is a feeding boundary, and the south boundary is located at the dividing line of the freshwater and seawater. The vertical boundary is the bottom of groundwater storage layer, which is composed of clay rock, shale or malmstone.

There are totally 470 cells in the computation area.(See Fig.1)

Fig.1    Cells division of Daguhe Groundwater Reservoir and parameter distribution

2.3    Parameters of the groundwater storage layer

The whole area is divided by different sectors according to the different layer parameters, which is determined by the characteristics of the soil and the experimental data in a previous survey by water pumping. According to the survey, the parameters of the groundwater is depicted in Fig.1

2.4    Adjustment of parameters according to observed data

To adjust the parameters in the model, the observed data from Dec. 30, 1986 to Dec. 31 1987, which is comparatively more reliable and more complete, are adopted. Series of time interval are 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 days. To verify the parameter values, the observed data from 1988 (low groundwater level) to 1990 (high groundwater level) is used. Series of time interval are 182, 184, 181, 184, 181, 184 days.

The water level of Dec. 30, 1986 is adopted as the initial water level. Data of water level observed by 112 monitoring bores are used to plot the contour lines of groundwater levels. Therefore, groundwater level of each cell can be obtained by interpolition.

The boundary conditions can be determined according to the groundwater level difference between each side of the boundary, thickness of groundwater storage layer, soil characteristics and width of the cross section.

• Precipitation feed for groundwater

The average annual precipitation is 672.6mm, which is concentrated in June to September. Precipitation feed for groundwater can be calculated by the formula Q_rain =a ´ P´ F, where a is the coefficient, P is precipitation and F is area. a can be determined by the observed data.

• Influent stream feed for groundwater storage layer.

Q_stream =C_r´ K´ D H´ L´ B/N, where: C_r is the coefficient; K is percolation coefficient for the soil layer under the riverbed; D H is the difference between stream water level and the groundwater level; L is the stream length across the cell. N is the thickness of the soil layer under the riverbed. Due to different conditions of the soil of riverbed, parameter value differs in different cells. In this model, three types of parameter values are applied to the cells. The parameter values are calculated out with the data of three cross sections of the river. The calculation process is described in the third section of this paper.

• Extracted groundwater quantity

The average water extraction for the whole region, which is obtained from the total water extraction and cell numbers, is used as the calculation groundwater extraction for each cell,

• Groundwater evaporation

Observed data for surface water evaporation in Nancun Station is used as the maximum groundwater evaporation. For each cell, the following formula is used to calculate the groundwater evaporation:

R_etm—the maximum groundwater evaporation

h—groundwater level

h_s—land level

d—the maximum depth for groundwater evaporation

For each cell, h_s can be obtained by the topographical map and d is 3.0m according to the local soil condition.

sections of the river are used for the parameter calculation, which is an improvement to the estimated parameter of Qstream.
As described in the second section of this paper, Influent stream feed for groundwater can be calculated as the following:
Qstream =Cr´K´DH´L´B/N, which can be simplified as: Qstream =Criv´DH,
where Criv= Cr´K ´L´B/N, DH=Hr-Hgw, where Hr is the stream water level and Hgw is the groundwater level.
In case of a too low groundwater level, permeation stops above the groundwater level where Qstream can not be described as Qstream =Criv´DH. In this case the maximum groundwater level is Hbot. Therefore Qstream can be described as the following:
Qstream = Criv ´( Hr - Hgw) when Hgw > Hbot
Criv ´( Hr - Hbot) when Hgw < Hbot
where Criv can be defined as the parameter of stream feed capacity for groundwater.
To calculate the parameter value of Criv, an observed data series of DH and Qstream are provided. The Criv values for the No.5 cross section, No. 7 cross section and No.8 cross section (which are indicated in Fig.1) are worked out by linear regression of DH and Qstream. Fig.2 shows the calculation case of No.7 cross section.
The results of the parameter calculation are showed in part 4 of this paper.

4    RESULTS

Results of parameter calculation: 
Criv5=20575.9m2/d, Criv7=4331.5m2/d, Criv8=16000m2/d.
When applying the values into the whole model of Qingdao water resources macro-management, the result of total stream feed for groundwater is 74.49million the year of 1985, which is in accordance with the observed data of 71million.
By applying the parameter into the groundwater flow model for Daguhe Groundwater Reservoir, groundwater level can be obtained at any given time and can be used for predicting the groundwater level. 

Fig.2    Linear relationship between Q-ΔH for No.7 cross section

5    CONCLUSION

To simulate the groundwater flow in Daguhe Groundwater Reservoir, a two-dimensional model is applied. Finite difference method is applied for the solution of the model and parameters are determined and adjusted according to observed groundwater flow data. To improve the model, parameter of the influent stream feed for groundwater are calculated out. Observed data for three cross sections of the river are used for the parameter calculation, which is an improvement to the estimated parameter value. 
The results of this model are tested by the 3 years observed data and the model are successfully used in the fundamental model of Qingdao water resources macro-management.

References

Michael G Mc. Donald & Arlen W Harbaugh, A modular Three-dimensional Finite-Difference Groundwater Flow Model, U.S.G.S, 1988.
Hui Shibo&Lei Zhidong, Water Resources Utilization and Conservation, Tsinghua University (in Chinese), 1992.8.