Application of Hydrological Balance Approach in the Study of Surface WaterGroundwater Exchange (Case Study: Zayandehrood River)
Sayed Aliasghar Hashemi^{ 1}, Rohollah Fatahi Nafchi^{ 2*}, Hossein Samadi Boroujeni^{ 2}
^{1 }Irrigation and Drainage, Department of Water Engineering, College of Agriculture, Shahrekord University, Shahrekord, Iran.
^{2 }Department of Water Engineering, College of Agriculture, Shahrekord University, Shahrekord, Iran.
A R T I C L E I N F O 

ABSTRACT 
ORIGINAL ARTICLE 

Introduction: Studying the changes in surface water storage and exchanges with groundwater in the hydrological system of rivers is a prerequisite for water resources management in the basin. In this paper, Zayandehrood River has been studied and the historical series of flow has been used in six hydrographic stations located downstream the Zayandehrood Dam.
Materials and Methods: Based on the surface water balance and considering monthly inflows and outflows in each river reach, a general equation for water outflow was extracted for each month, in which the net interaction of surface water with the water in the air and groundwater are in the form of a polynomial of the inflows and a constant.
Results: The obtained equations showed that in two reaches, surface water was increased by groundwater and in the other three reaches, surface water fed the groundwater. The results showed that in normal conditions, 1613 million cubic meters of surface water resources were consumed in the reaches under study. In the event of severe drought, except for the first three reaches (from the sadtanzimi to Lenj), the remaining reaches (downstream Lenj) faced water shortage. The results showed that increasing surface water by groundwater is very important for water supply in drought condition.
Conclusion: Based on the results, the proposed method is an appropriate tool for investigating the exchange of surface water with groundwater. 
Article History:
Received: 22 January 2018
Accepted: 20 April 2018


*Corresponding Author:
Rohollah Fatahi Nafchi
Email:
fatahi2@gmail.com
Tel:
+983832324401


Keywords:
Surface Water,
Groundwater Exchange,
River Flow,
Mass Balance,
River Reach. 
Citation: Hashemi SA, FatahiNafchi R, SamadiBoroujeni H.
Application of Hydrological Balance Approach in the Study of Surface WaterGroundwater Exchange (Case Study: Zayandehrood River). J Environ Health Sustain Dev. 2018; 3(2): 53952.
Introduction
With prevailing methods, surface water and groundwater systems as the main parts of hydrological systems are often studied and managed separately, while these systems are widely interrelated climatically, topographically, and geographically. Accordingly, water can continuously move between surface and groundwater systems, so the method of exploitation and the quality of one resource can affect the other ^{1, 2}. Since these waters are not distinguishable in a hydrological system, understanding their relationship is of great importance to the evaluation of a surface water system, such as Zayandehrood. The evaluation of this relationship is complicate, so researchers have proposed different methods. According to Mencio et al., these methods can be categorized as follows: (a) direct measurement of water flux; (b) thermal tracking techniques; techniques based on Darcy equation; (d) mass balance approaches; and (e) modeling approaches ^{3}. The mass balance approach assumes that any increase or decrease in surface water, or any change in its characteristics, may be related to a particular water source ^{4}, groundwater can be determined in this way. For example, groundwater leakage into the river bed can be calculated from the difference in flow at successive stations along the river. This technique has been used by researchers such as Harvey and Wagner, Farnsworth and Mencio et al., ^{3, 5, 6}. Another method for estimating the contribution of groundwater in the surface flow is the hydrograph separation of stream flow data. In this method, the base flow is assumed to be the discharge of groundwater into the river ^{7}. Among mass balance methods, chemical and environmental tracers have been widely used ^{8, 9}. In this study, a method has been used to investigate water exchange, in which, by consideration a hydrological balance in a river reach, an equation is obtained for outflow that results in the achievement of net exchange between surface water and groundwater. This method is a subcategory of mass balance approaches and a modified version of the method presented by Liu and Sheng. The researchers implemented the method on eight reaches from the Rio Grande River, California, and stated that this method is an appropriate tool for understanding the relationship between surface water and groundwater in dry and semidry regions ^{10}. In the proposed method extractions related to drinking water and industry, return flow and water transfer between river reaches were not considered, and implementation of this method to the complex system of Zayandehrood River will not yield accurate results. Therefore, in this study, there were some corrections in this method and it was used to study the relation between surface water and groundwater in six reaches of downstream Zayandehrood River.
Study site
Zayandehrood River, the most important river in the central region of Iran, originates from ZardkouhBakhtiari heights and after a distance of 350 km to the east it ends up in Gavkhuni swamp. The total reach of Zayandehrood basin is about 26917 km2 in which mainly the downstream dam is influential in providing water flow. Downstream of the dam, which accounts for the largest portion of water consumption in the reach, is a semidry, high tension zone in which chronic water shortages threaten agricultural production and limit economic development ^{11, 12, 13}.In this reach, water distribution is carried out through five new irrigation and drainage networks. More than 60% of irrigation water is supplied through groundwater extraction ^{14}. The reach of the plains downstream the dam is 10698 square kilometers, of which 7350 square kilometers are aquifers and the rest are
hard formations. The average rainfall in the Zayandehrood basin varies from 100 to 1400 mm per year and with decrease in height it decreases from west to the east of the basin. The maximum potential evapotranspiration in the study reach is East of Isfahan and about 2000 mm per year. The longterm average of Zayandehrood annual flow is 1440 million cubic meters per year at Sadtanzimi. During the drought of 19981999, the annual amount of Zayandehrood flow at the aforementioned site decreased to 562 million cubic meters. A schematic of the study reach is presented in Figure 1.
Surface water and groundwater in the Zayandehrood River basin are actively interconnected through various hydrological processes. In this study, a series of historical flow at 6 hydrometric stations (Table 1), is the basis for the study of this relationship. The location of the stations is presented in Figure 1.
Table 1: List and specifications of hydrometric stations located on the Zayandehrood River
Gauge station 
Longitude 
Latitude 
Height (meter) 
Available Data 
Sadtanzimi 
50˚ 47' 
32˚ 43' 
1970 
19682013 
Polzamankhan 
50˚ 53' 
32˚ 29' 
1880 
19482013 
Polkale 
51˚ 13' 
32˚ 32' 
1715 
19482013 
Lenj 
51˚ 33' 
32˚ 23' 
1446 
19802013 
Polchoum 
51˚ 46' 
32˚ 35' 
1551 
19852013 
Varzaneh 
52˚ 39' 
32˚ 25' 
1469 
19482013 
Figure 1: Schematic of the studied stations
Materials and Methods
A common method for investigating the relationship between the river and its bottom aquifer is to measure river flow at specific points. These points divide the river into reaches that by examining the water balance in these reaches, and through the difference in inflows and outflows, the exchange between surface water and groundwater can be obtained. This method depends on accurate measurements of river flow as well as estimation methods of water balance components. ^{15}. In this study, based on the statistics of inflow and outflow flows from a river basin, a net relation between surface and groundwater is obtained. In Zayanehrood, the resources of surface water include runoff caused by rainfall (including surface and underthesurface flow) and water released from dam. Each river reach receives an inflow from its upstream reach and collects rainwater from surrounding and upstream reaches and streams. Then the water in this reach is discharged into the upstream reach or it enters the atmosphere through evaporation from the surface of the river, canals and drains and evaporation from irrigated lands, or by leakage losses from the River, canals and drains and deep penetration of irrigated lands into groundwater. In this study, based on the surface water balance in each reach of the river, an equation is obtained that the sum of the outflows of each reach is obtained as a function of the river inflows in that reach. The parameters of this equation indicate the mode and extent of water exchanges at that reach. In the reach under study, in addition to the river route, water exchange between the reaches through extraction channels and drainage of irrigation networks is also carried out, which should be entered into the equation. For this purpose, in addition to the flow data of the studied stations (Table 1), the historical series of water extraction and transfer data was also used. The source of this data is Isfahan Regional Water Company. The amount of small pumping, extractions fordrinking water and industry and return flow are also the components of the surface water balance in each reach. In this study, the average annual values of these variables reported in previous studies of Salemi et al. were used ^{16}.To test the proposed method, the historical series of data from the water years of 1986 to 2006 were used. In the next section, the application of this data and generation of outflow function reaches presented.
Simulated outflow equation
Groundwater system in this study includes aquifers located on Ben  Saman plains, Lenjanat, Najafabad, BorkharIsfahan and KohpayehSegzi. The aquifers are unconfined and the plains are fed with Zayandehrood river. In this research, the relationship between surface water and groundwater is considered based on the relation between the surface water system of Zayandehrood and groundwater in the floodplains at downstream Zayandehrood. According to Liu and Sheng (2011) and the water balance, the outflow water of each reach can be written as follows ^{10}:
Equation (1) 

In which
is the surface water outflow from each reach to downstream reach,
is the inflow from the upstream reach,
is the change in surface water storage,
is the increase of surface water by the atmosphere (raining and snow melting),
is the losses of surface water through leakage into groundwater,
is surface water increase due to agricultural drainage,
is deep percolation of irrigation water and
is losses due to evapotranspiration from irrigation water. The dimensions of all the variables listed are
. In the above equation, there is no mention of extraction for drinking water and industry from the surface water and their return flow to the river as well as the displacement of water between the reaches water outside the main river route, while in the complex system of Zayandehrood surface water there are numerous and significant cases of such flows. In this study, with the inclusion of extractions for drinking water and industry and transfer between the river reaches, corrections were made in equation (1) and the equation was corrected as in equation (2).
Equation (2) 

In which,
and
are the transferred flow into and out from the reach, respectively,
is extractions for drinking water and industry, and
is the total return flow. By presenting simplifying assumptions of Liu and Sheng, the simulated outflow (Figure 2,
) can be presented as Equation (3). These assumptions include: (1) simulated outflow, is a continuous monthly flow for a certain amount of continuous inflow;(2) changes in surface water depth are overlooked within the month; (3) groundwater level is assumed to be constant. Over the past decade, the Zayandehrood River in several months has dried out. Therefore, the study period in this study (years 1986 to 2006) was chosen so that the assumption of the continuous inflow flow would not be distorted. In Equation 3,
is the simulation of the lefthand side phrase in equation 2 is
^{10}.
Equation (3) 

In the above equation,
,and it shows the relation between surface water and atmospheric water in river reach.
indicates the exchange of surface water with groundwater in that reach. Changes in
,
and
depends on changes in climate and irrigation management within the range of each reach. Also, the inflow into the reach of (
) is necessarily influenced by the climatic conditions and water management in the upstream. So, we can assume that
is a function of
. McLaren extension of this function can be written as follows:
Equation (4) 

In which
represents the constant values. Due to the similarity of the climate in the two reaches, especially in dry and semidry reaches such as the Zayandehrood basin,
equals zero, the value of
is expected to be zero. Now you can use polynomial functions to estimate
. Therefore, a general equation as follow be extracted from equation 3 for simulated outflow.
Equation (5) 

As shown in Figure 2, in this study, a linear form is suitable to express the simulated outflow in a reach. Accordingly, in the linear form of the equation, when
and
equal zero, surface water has no interaction with the groundwater and the atmosphere. If
is larger than zero, the groundwater feeds on surface water, otherwise the surface water system will leak into groundwater.
When
is larger than zero, the surface water system has a net gain from atmospheric water, and whenever it is less than zero, it has net loss to atmosphere.
Figure 2:Simulated monthly outflow of surface water at the studied reaches in two months of Dey, Farvardin.
Change in storage and its ratio in a hydrologic period
In equation 3, it was assumed that the changes in surface water storage equal zero.
Now, from the difference between the actual outflow and the simulated outflow we can obtain changes in the surface water storage by subtractingequation 3 from equation 2 as follows:
Equation (6) 

In which
is the difference in simulated outflow and inflow in the surface water system,
is the change in the groundwater flow, which is related to the net exchange of surface water and groundwater (Note: in equation (1),
, has been equal to
, with the assumption that the static level of
was set to zero.) It should be noted that
in equation 6 indicates the change in storage in groundwater (
). If
is the total change of storage in a reach, the equation 6 can be rewritten as follows:
Equation (7) 

The above equation states that the total change in storage within river reach is a combination of changes in surface water storage and changes in groundwater storage. A positive or negative storage change indicates that a reach stores a larger amount of water or would discharge it to its downstream reach in that month. In a hydrological year, changes in annual storage (i.e.,
is the total positive storage, and
is the total negative storage) can be obtained from changes in monthly storage in that hydrological year by equation 7.
The total annual storage change can be written as
(note that the
value is negative). The remainder of the annual change in storage or the net storage change can also be written as
. Now, the ratio of annual change in storage (R) is defined as follows.
Equation (8) 

According to equation 8, three types of storage changes can be defined
^{10}: (1) balanced, when
15%≤R≤15% (2) positive (increasing), when 15%≤R≤100% (3) negative (decreasing), When
100%≤R≤15%. The normal state means that net change in water in a reach in one year is insignificant
^{10}.
Results
According to the presented method in the previous section, the simulated outflow equations, the storage changes and the relationship between surface water and groundwater in five reaches, were studied and the pattern of relationship between them in normal and drought periods was also evaluated.
Simulated outflow equations
To extract simulated outflow equations downstream the Zayandehrood Dam, river flow data in hydrometric stations of Sadtanzimi, Polzamankhan, Polkale, Lenj, Polchoum and Verzaneh, as well as data related to drinking water and industry and return water were used. The equations were obtained by Excel software using monthly inflows and outflows for five river reaches. A sample of extracted relations for the studied reaches in two months of the year is shown in Figure 2. The values of the simulated equation parameters are also presented in Table 2. In this study, by using inflows and outflows of each reach per month, an equation was extracted. As shown in Figure 2 and Table 2, all reaches have linear simulated outflows.
Table 2: Simulated outflow parameters in the studied reaches.
Reach 
Simulated outflow parameters 
Mhr 
Abn 
Azr 
Dey 
Bah 
Esf 
Far 
Ord 
Khr 
Tir 
Mor 
Shr 
Absolute error 


Sadtanzimi  Polzamankhan 
α_{1} 
0.11 
0.04 
0.04 
0.07 
0.05 
0.05 
0.04 
0.07 
0.05 
0.11 
0.13 
0.11 
0.07 

Cg (MCM/m) 
8.65 
4.47 
3.82 
6.90 
3.64 
1.44 
3.03 
10.51 
4.42 
11.31 
12.32 
8.42 

r^{2} 
0.98 
0.98 
0.97 
0.92 
0.85 
0.94 
0.99 
0.99 
0.97 
0.97 
0.96 
0.96 

Polzamankhan  Polkale 
α_{1} 
0.12 
0.06 
0.02 
0.02 
0.04 
0.02 
0.01 
0.06 
0.07 
0.00 
0.02 
0.12 
0.09 

Cg (MCM/m) 
10.88 
3.04 
6.92 
3.00 
6.55 
3.30 
1.93 
8.34 
14.21 
3.18 
3.01 
17.89 

r^{2} 
0.97 
0.95 
0.95 
0.85 
0.91 
0.97 
0.98 
0.99 
0.96 
0.93 
0.94 
0.98 

Polkale  Lenj 
α_{1} 
0.01 
0.01 
0.00 
0.14 
0.15 
0.03 
0.06 
0.04 
0.05 
0.01 
0.07 
0.10 
0.14 

Cg (MCM/m) 
1.65 
0.47 
7.31 
3.98 
1.23 
1.71 
4.81 
3.03 
0.13 
8.60 
0.18 
9.75 

r^{2} 
0.97 
0.98 
0.97 
0.75 
0.93 
0.98 
0.97 
0.97 
0.93 
0.86 
0.86 
0.90 

Lenj  Polchoum 
α_{1} 
0.31 
0.20 
0.23 
0.24 
0.45 
0.02 
0.14 
0.13 
0.42 
0.34 
0.35 
0.22 
1.98 

Cg (MCM/m) 
24.40 
24.36 
14.18 
4.26 
4.15 
12.99 
28.90 
56.31 
39.02 
72.26 
70.65 
68.73 

r^{2} 
0.73 
0.92 
0.89 
0.49 
0.31 
0.81 
0.86 
0.93 
0.43 
0.51 
0.37 
0.49 

Polchoum  Varzaneh 
α_{1} 
0.66 
0.37 
0.17 
0.03 
0.31 
0.48 
0.42 
0.22 
0.51 
1.00 
0.95 
0.80 
0.41 

Cg (MCM/m) 
64.44 
71.91 
75.65 
61.78 
43.08 
46.58 
85.88 
109.31 
88.16 
65.04 
68.77 
69.92 

r^{2} 
0.17 
0.61 
0.74 
0.71 
0.73 
0.71 
0.56 
0.85 
0.28 
0.00 
0.00 
0.06 

Storage change
As previously mentioned, the annual storage change can be divided into three increasing, decreasing, and balanced modes. In this section, based on equation (7), monthly storage changes in reaches, Polzamankhan to the Varzaneh, were measured, and then the annual storage change ratio index (R) was calculated by Equation (8) and the results were presented in Figure 3, this index shows that in a water year, storage changes in a reach have been rising or falling, or whether or not these changes are insignificant. The average of positive and negative storagechanges in the studied reaches in years when they were increasing, decreasing, and normal conditions are calculated and presented in Table 3. As seen in Figure 3, the reach from the Lenj to the Polchoum is more balanced than the rest of the reaches. In other reaches, a balanced situation has been observed, too. Storage change in the reach between Polzamankhan and Polkale before 1996 has been almost falling, but after that, it has been rising.
Figure 3: The annual ratio of storage change in the studied reaches.
All studied reaches have had positive changes for some years. According to Table 3 and Figure 3, the reach between Polzamankhan and Sadtanzimi had a positive storage change in 9 years with an average of 45 million cubic meters per year. Since 1995, changes in the annual storage in this reach have been positive for most years. Storage changes in the reach leading to the Polkale station has also been rising in 9 years with an average of 76.8 million cubic meters per year. The storage change around the Polkale and the Lenj has been positive for 8 years with an average of 139 million cubic meters per year.
In the reach between Lenj to Polchoum range, positive storage changes over a fiveyear period reached an average of 129 million cubic meters per year. It was observed that changes in the annual storage of this reach were more balanced. Based on the results, the storage changes in the last are have increased over the years. The average annual storage change in this reach was estimated 123 million cubic meters per year.
Based on Figure 3, the first three reaches from the mid1980s to the following decades have encountered increasing storage change and somehow increasing water extraction. As can be seen from Table 3 and Figure 3, all studied reaches also have negative storage changes at some points.
Table 3: Average change of annual storage for the six reaches under study.
Reach 
Storage change (MCM/y) 
Positive (+) 
Negative () 
Residue 
Residue Rate (%) 
Type 
Sadtanzimi  Polzamankhan 
45.4 
22.3 
23.1 
34.1 
Positive 
17.0 
44.7 
27.7 
45.0 
Negative 
26.3 
41.4 
15.1 
22.3 
Balanced 
Polzamankhan  Polkale 
76.9 
10.0 
66.9 
77.0 
Positive 
14.7 
87.9 
73.2 
71.3 
Negative 
50.4 
29.1 
21.3 
26.7 
Balanced 
Polkale  Lenj 
139.4 
24.0 
115.4 
70.6 
Positive 
21.1 
103.5 
82.4 
66.1 
Negative 
34.2 
56.2 
22.0 
24.3 
Balanced 
Lenj  Polchoum 
129.0 
50.3 
78.7 
43.9 
Positive 
41.1 
128.6 
87.5 
51.6 
Negative 
73.0 
48.8 
24.2 
19.9 
Balanced 
Polchoum  Varzaneh 
123.8 
36.2 
87.7 
54.8 
Positive 
34.3 
236.5 
202.3 
74.7 
Negative 
77.9 
76.8 
1.0 
0.7 
Balanced 
Interactions of surface water, groundwater and atmosphere
Interactions in a normal water year
In this study, in order to evaluate the water exchange in a normal water year, the longterm average (19812012) of the Zayandehrood River flow in the Sadtanzimi Station was used. The average flow of the river during this period was 1444 million cubic meters per year.According to the historical series of the river in this place, the amount of flow in the water years of 13741373 is 1446 million cubic meters, the closest number to theaverage. Therefore, by choosing this year as a normal water year, using the outflow equations (Figure 2), the outflow values of the studied reaches are calculated downstream the dam, and the results are presented in Table 4.
Table 4: Interactions calculated in a normal water year, million cubic meters.
Reach Name 
Inflow (Q_{si}) 
Surface water exchange with atmospheric
water 
Surface water exchange with groundwater 
Net surface water exchange

Outflow 
Net surface water
exchange (%) 
Sadtanzimi 




1446^{ a} 
98.3 
Sadtanzimi  Polzamankhan 
1446 
100 
73 
27^{b} 
1431 
1.7 
Polzamankhan  Polkale 
1431 
64 
39 
26^{ a} 
1295 
1.7 
Polkale  Lenj 
1295 
26 
12 
14^{ b} 
702 
0.9 
Lenj  Polchoum 
702 
171 
403 
574^{ b} 
354 
35.6 
Polchoum  Varzaneh 
354 
147 
851 
997^{ b} 
186 
61.8 
Lower Varzaneh 
186 





+ Increased surface water through the atmosphere or groundwater, or both
 Surface water losses to the atmosphere or groundwater, or both
avalues used to calculate total surface water produced downstreamZayandehrood Dam (1471 million cubic meters).
bvalues used to calculate total net consumption of water in the downstream basins of the Zayandehrood Dam (1613 million cubic meters).
As seen from Table 4, almost all surface water released downstream, is from the dam, and only a small amount of 26 million cubic meters (1.7%) in the PolzamankhanPolkale has been added to surface water. In surface water exchange with groundwater and atmosphere, 27 (1/2%), 14 (1/1%), 574 (41.7%) and 997 (56%) cubic meters of surface water respectively have been decreased in the reaches of the SadtanzimiPolzamankhan, Polkale  Lenj, the LenjPolchoum and PolchoumVarzaneh.
According to Table 4, in the normal water year, 186 million cubic meters of surface water and goes out of Varzaneh Station and enters Gavkhoni swamp.
Interactions in a severe drought
According to the hydrograph of Zayandehrood River, annual flow at the set dam station, the most severe drought has occurred at hydrological period 20002001. This hydrological year was selected as a severe drought year and its flow data was used to examine water exchange. The inflows and outflows of each reach are presented in Table 5. The simulated outflow for each reach was calculated using the equations presented in the previous section and the values of the parameters in Table 2 were calculated.The values of flow in a normal water year are also given in Table 5 for comparison with the drought condition. In this section, it is assumed that in the normal water year, surface water of Zayandehrood River downstream the dam can meet all the needs of the studied reaches. Compared to the normal water year, significant changes are observed in surface water exchange with groundwater and the atmosphere under severe drought conditions. During a drought, the inflow water in the set dam can only meet the needs of the first three reaches and, as shown in Table 5, the other two reaches faced water shortage. In the first and third reaches, surface water is fed by groundwater. This increase in surface water is respectively 13% and 4% outflow of these reaches in drought conditions.
Table 5: Water exchange during normal and drought periods, million cubic meters.
Reach 
Observed or calculated Inflow (MCM/y) 
Observed or calculated Outflow (MCM/y) 
Net supply (+) or use ()^{a} (MCM/y) 
Simulated outflow^{b} (MCM/y) 
Storage change (MCM/y) 
Water deficit^{c} (MCM/y) (%^{d}) 
Gain from Groundwater (MCM/y) (%^{e}) 
Sadtanzimi  Polzamankhan 






Normal 
1446 ^{f} 
1431^{ g} 
27 
1431 
0 

73 (5%) 
Drought 
563 ^{f} 
564^{ f} 
34 
609 
44 

73 (13%) 
Difference 
883 
867 
61 
822 
44 

Polzamankhan  Polkale 






Normal 
1431 ^{g} 
1295 ^{g} 
26 
1295 
0 


Drought 
564 ^{f} 
198 ^{f} 
13 
369 
171 
Difference 
867 
1097 
39 
926 
171 
Polkale  Lenj 






Normal 
1295 ^{g} 
702 ^{g} 
14 
702 
0 

12 (2%) 
Drought 
198 ^{f} 
282 ^{f} 
11 
380 
99 
12 (4%) 
Difference 
1097 
420 
25 
321 
99 

Lenj  Polchoum 






Normal 
702 ^{g} 
354 ^{g} 
574 
354 
0 


Drought 
282 ^{f} 
199 ^{f} 
507 
97 
119 
68 
Difference 
420 
298 
68 
257 
119 
(12%) 
Polchoum  Varzaneh 






Normal 
354 ^{g} 
186 ^{g} 
997 
186 
0 


Drought 
199 ^{f} 
1 ^{f} 
864 
35 
356 
133 
Difference 
298 
185 
133 
151 
356 
(13%) 
a Net supply (+) or use () = outflow–inflow.
b Simulated outflow
c Water deficit = Net use () in drought – net use () in normal.
d The percentage is the ratio of water deficit in the absolute value of its net use in normal year.
e The percentage is the ratio of gain from groundwater in outflow.
f Observed.
g Calculated
Discussion
In this study, the simulated outflow equations were extracted for the five reaches downstream Zayandehrood Dam and the results were presented in Table 2 and Figure 2. According to Table 2, the simulation of the outflow flow in the last two reaches has been less accurate. In such a way that the explanation coefficients in the two reaches leading to the Chum bridge and Varzaneh are less than other reaches. The absolute error value also confirms the decrease in the accuracy of the simulation in these two reaches. This low accuracy is due to the complexity of the surface water system and the lack of precise measurements of water extraction and water exchange between the last two reaches. The only surface water inflow to reach 1 (Sadtanzimi  Polzamankhan) is the released water from the Zayandehrood dam. In this reach, there is no water transfer to the outside of the basin, and extraction from the river only includes small pumping and drinking water for local residents. The average annual extraction of water and rainfall in this reach has been reported to be 3 and 1.2 cubic meters per second, respectively ^{15}. Surface water gaining from groundwater in the Sadtanzimi  Polzamankhan can be as a result of hydraulic connections of the Zayandehrood reservoir with groundwater in this reach. Groundwater in this reach is discharged through 80 deep and semideep wells, 278 qanats and 589 springs. It is noted that groundwater extraction is more than springs and qanats, and nearly 85% of it is consumed in the agricultural sector ^{14}. With groundwater modeling, more accurate information can be obtained on the relationship between surface water and groundwater in this reach.
In the reach between Polzamankhan and Polkale in addition to the water outflow from Polkale station, upstream this station, drinking water is transferred to Isfahan and Yazd. Transfer of Isfahan's drinking water began in1988 and its transfer to Yazd began in 1999. The average annual transferred water from Isfahan during the study period (water years of 1986 to was 4.5 cubic meters per second and the transferred water to Yazd was 1.8 cubic meters per second. In Salemi et al. study, extraction of drinking water and pumping in this reach of the river was reported to be 1.7 cubic meters per second ^{16}.
The distance between the Polkale Station and the Lenj station is the start of important water extractions from Zayandehrood. The only inflow to this reach is the main river flow from the Polkale station. Outflows of this reach in addition to the flow of the Zayandehrood River at Lenj station, include transferred water to MahyarJarghouyeh network and water diversion into Nekoabad network. The average annual extraction of industrial water and pumping in this reach were reported to be 2.5 and 6.6 cubic meters per second, respectively ^{17}. According to the reports from the map, the groundwater level in the Zayandehrood Basin, around the PolkaleLenj, the direction of flow is from the groundwater to the river and the outflow of the reach ^{14}. The results of this study also indicate the feeding of surface water by the aquifer in this reach and subsequently confirm the movement of groundwater towards the river. The presence of Shour river basin on the right bank of the river with a drainage surface of 1700 square kilometers, artificial feeding plans in the basin and deep penetration of agricultural lands within this reach can be the reasons for the increasing of net surface water by groundwater in this reach of the river.
In the reach between Lenj and Polchoum, surface water has losses to both atmosphere and groundwater. The existence of agricultural lands of Nekoabad and Borkhar water supply networks and the existence of more than 12,000 deep and semideep wells in this reach testify to the high consumption of water resources. The average annual discharge of 690 million cubic meters of water from the aquifer in this region has led to thedrop in static level and, as a result, the feeding of aquifers by the river ^{14}. It should be noted that Borkhar's water supply network from the Nokabad dam is at the upstream reach and off the main river. Since the Nekoabad irrigation network site is located upstream the Lenj Station, therefore, the historical series of water extractionfrom this network in the reach upstream the Lenj Station as transferred outflow and downstream reach as inflow transferred water entered the equation 2.The drinking and industrial extractions and pumping in this reach of the river were reported to be 1.77 and 4m^{3} per second, respectively ^{17}. The water extraction for waterfall network is also in this reach, where the historical series of this deviation entered equation (2) as outflow.
In the last reach between Polchoum and Varzaneh, on average, approximately 2,225 million cubic meters of surface water have been annually delivered to the two irrigation networks of waterfall and Roudasht. This reach has a surface water loss to the atmosphere. Approximately 700 million cubic meters of aquifers in KouhpayehSegzi reach are often discharged for agricultural use annually ^{14}. Therefore, in this reach of the river, feeds the aquifer, and this confirms the results obtained in Table 2 and Figure 2. Since the water deviation for waterfall network is located upstream Polchom station, the historical series of this extraction was considered as the inflow of the fifth reach.
Based on Figure 3, there were rising and falling storage changes in all reaches. Positive storage change is one of the characteristics of the reaches with water shortages in these years and hydrological periods, and one of the characteristics of reaches with a negative storage change can be the presence of excess water in that reach. Storage changes in PolzamankhanPolkale reach have been increasing since the mid1980s before which
was decreasing . Polkale station is located downstream the Chamaseman dam, the point where Isfahan's drinking water and transferred water to Yazd are extracted. With increasing capacity of Babashikhali's water treatment plant, extraction of Isfahan's drinking water increased since 1993. Also, Yazd water transfer tunnel opened in 1999. So, since the midseventies, less water has been discharged into the downstream reach. Hence, during this decade, the storage condition of this reach has been changed from negative to positive.
Investigating the interaction of surface water and groundwater under normal conditions showed that the studied reaches from Polzamankhan to Varzane received a net amount of about 64 million cubic meters (the sum of the positive values in the third column of Table 4) from the atmosphere every year. And also loses 444 million cubic meters (the sum of the negative values
in the third column of Table 4) per year through evaporation, evapotranspiration. Salemi and Heidari in addition to evaluating the resources and uses of Zayandehrood basin, considered the third phase of water consumption (19862009) concurrent with the opening of Koohrang tunnel in 1365, followed by an increase in water consumption to 1500 million cubic meters in a year and proper flows in the basin outflow (550 million cubic meters per year). The net increase in surface water through the atmosphere has occurred only in the reach leading to Polkale, while net water losses to the atmosphere are distributed among other reaches, in a way that the reaches of set damPolzamankhan, PolkaleLenj, LenjPolchoum, and PolchoumVarzaneh, respectively, account for 23, 6, 38 and 33 percent of the water discharge into the atmosphere (evaporation and evapotranspiration). Zayandehrood River downstream the dam is fed by a net amount of 85 million cubic meters per year (the total of positive valuesin the fourth column of Table 4) through groundwater and 1293 million cubic meters per year (the total of negative valuesin the fourth column of Table 4) is lost through leakage to the groundwater.
Table 5 shows that during the drought, the first three reaches did not suffer from shortage. extractions and water exchange have been such that the observed outflow of these three reaches were reduced to half the inflow. In contrast, the fourth and fifth reaches, respectively, faced shortages of 68 and 133 million cubic meters per year, and these shortages account for 12 and 13 percent of water use in normal conditions, respectively. In the first and third reaches surface water has net gain under drought conditions, while under normal conditions, these reaches extracted water. According to the results of Table 5, the rest of storage changes also showed that in drought conditions, the first three reaches had positive storage changes. This means that the maximum change in the increasing storage was related to the second reach with 171 million cubic meters per year, and the maximum change in decreasing storage in the last reach was 356 million cubic meters per year. The annual storage ratio of the first to fifth reaches in drought was 78, 100, 98, 53 and 84 percent, respectively.
Conclusion
Economic development and population growth over the past decades have overloaded the water resources of the Zayandehrood basin, and it has been difficult to allocate water, especially in water shortage conditions. Interbasin water transfer and the lack of integrated, interconnected management of surface water and groundwater have increased the intensity of this tension. The relationship between surface water and groundwater has a great impact on the quantity and quality of water. One of the management strategies to increase the security and sustainability of water resources is reducing the water share of water carriers in the basin. While the relationship between river systems and groundwater in Zayandehrood basin remains unknown. Therefore, the consequences of reducing allocations in a complex basin, such as Zayandehrood, will be uncertain and controversial.
In this study, a method for assessing the exchange of surface water and groundwater was proposed. This method evaluates the exchange of surface water and groundwater using cumulative flow data at the inflow and outflow of each river reach, and the extraction for drinking water and industry and return water in each reach. Based on this, a general equation for the simulated outflow was obtained. This equation is a polynomial function of the inflow flow. Based on the balance of water in the studied reach, the constant value of the function indicates the relation between surface water and groundwater and the rest of the function statements indicate the relation between surface water and the water in the atmosphere. In this study, all reaches had linear simulated outflows. On the basis of the obtained equations, surface water in the first three reaches in some months of the year and in the last two reaches in all months, hadlosses in the atmosphere. The results showed that surface water in the reaches which end up to the Polzamankhan and Lenj stations, have net gain by groundwater, while in other reaches, surface water losses to groundwater.
The results of this study showed that in the normal state, 1471 million cubic meters of surface water are exchanged annually with groundwater and the atmosphere, almost all of which are supplied from the Zayandehrood dam, and a small amount in the PolzamankhanPolkale is added to it which is from the net exchange of atmospheric and groundwater with surface water. In the net exchange of surface water with groundwater and the atmosphere, in a normal year, 1613 million cubic meters are used in downstream reaches of the dam. The reaches leading to the Polzamankhan, Lenj, Polchoum and Varzaneh use 1.7, 0.9, 35.6 and 61.8% of surface water, respectively. Similarly, the exchange of water in a water year with severe drought was also studied. The results showed that in these conditions, the first three reaches did not suffer from water shortage and supplied their own water, but other reaches faced water shortage. The net increase in surface water by groundwater in the first and third reaches compared to the outflow of these reaches was higher in the drought than in the normal water year, which indicates the importance of groundwater under drought conditions.
Due to the lack of detailed information on extractions and return water to the river, the components of the surface water balance of the reaches in this study entered into the equation in general, and some of the average annual data was used to discuss them. However, the results obtained in this study and their comparison with the data and information from previous studies showed that the proposed method is a suitable tool for assessing the exchange of surface water with groundwater. Therefore, it is suggested that in future studies this method be studied with more accurate data on extraction and return water. Comparing the results of this method in different time dimensions with various management and hydrological scenarios can be the basis of other studies in this regard.
Acknowledgments
This study was funded by Shahrekord University as a doctoral dissertation for a student of Irrigation and Drainage, which is highly appreciated. Meanwhile, I’d like to thank and appreciate Mr. Malek Mohammadi from Isfahan Regional Water Company who cooperated with the required data.
Funding
The thesis did not benefit from any financial support from any organization or private company.
Conflict of interest
There are no conflicts of interest.
This is an Open Access article distributed in accordance with the terms of the Creative Commons Attribution (CC BY 4.0) license, which permits others to distribute, remix, adapt and build upon this work, for commercial use.
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