3.1. Calculation of the Exchange Fluxes in 2016
According to the method described in
Section 2.1., combined with the actual situation of the study reach (recharge of the stream is composed of upstream flow, tributary flow, and the direct and runoff recharges of precipitation, and the discharge is composed of evaporation and downstream flow), the equilibrium equation can be obtained as:
where
refers to the mean daily flow of Xiaolinzi station on the ith day. Similarly,
and
refer to the flow in Liaoyang station and Qianyantai station, respectively. All the flow data were measured by vessel-mounted ADCP.
Precipitation recharge (
, m
3) refers to the amount of water directly supplied by the precipitation on the river surface. As only the daily rainfall data of Xiaolinzi station is collected, and with consideration the reach scale of the study area, the precipitation of Xiaolinzi station can be regarded as the mean precipitation in the study reach (
P, mm). The area of river surface (
Ariver, km
2) is determined using Arcgis platform by supervised classification based on satellite images of the study reach in June 2016, which is 5.09 km
2. The calculation of
is:
Similar to precipitation recharge, river surface evaporation (
, m
3) is also based on the mean daily evaporation of the
Φ20 cm evaporator at Xiaolinzi station. For China, the amount of evaporation observed by the
E601 evaporator is close to that of natural large water bodies [
23,
24]. Therefore, when calculating
, the evaporation of the
Φ20 cm evaporator (
E20, mm) needs to be converted into
E601 type using a conversion coefficient
C.
C (
Table 2) is selected according to the
Water Resources of Liaoning Province [
25], which is based on the data of simultaneous observation of two evaporators at 27 stations for a total of 480 years in plain area of the Liaoning Province. The equation for river surface evaporation (
, m
3) is:
The runoff (
, m
3) refers to the volume of precipitation that appears as runoff within the catchment area (
Acatchment, km
2) and is calculated by the average annual runoff coefficient
α.
Acatchment refers to the difference between catchment area controlled by Xiaolinzi station and Liaoyang and Qianyantai station, which is 1060 km
2. According to the
Water Resources of Liaoning [
25], the runoff coefficient of the study reach from 1956 to 2000 was 0.1–0.2, while 0.15 was selected for the calculation. The calculation equation is:
The upstream and downstream flow, and precipitation of the study reach in 2016 are shown in
Figure 3a. In 2016, the downstream flow was greater than the upstream flow (the sum of the flows from the Liaoyang and Qianyantai stations serve as the upstream flow), and occasionally, the opposite situation occurred (marked by the black circle). Therefore, it is preliminarily determined that the GW-SW interactions were mainly gaining stream. In addition,
Figure 3a shows the apparent hysteresis of the stream from upstream to downstream.
Hysteresis is a non-linear behavior that is common in natural systems, which is also common in the relation between the streamflow of upstream and downstream. Due to the limitation of the flow velocity and river length, when a certain part of fluxes cannot flow from upstream to downstream within a day, resulting in hysteresis. Therefore, when water balance is calculated on a daily scale, error occurs. In the period of low and stable flow, the error caused by fluxes lag will decrease as the water balance calculation results accumulated and can be negligible. However, when the daily flow becomes large and unstable, the error cannot be ignored. Here we provide a solution. The lag time at the typical flow peak points was counted, as shown in
Table 3, with 70% of the flow peak points showing a lag time of one day. Therefore, when calculating the volume of cumulative exchange fluxes, Equation (5) should be corrected to:
The results of cumulative exchange fluxes calculated by Equations (5) and (9) with a lag time of one day and without lag time are shown in
Figure 3b. Most of the time, the results are well fitted, and there are deviations only in May and in the late stages of July. As the stream flow is large during this period, the influence of the hysteresis effect increases, and the exchange fluxes shows different results. Taking the stage of the black rectangle (April 27–June 4) in
Figure 3 as an example, the flows with a lag time of one day and without lag time are shown in
Figure 4a,b, respectively. The comparison results show that a false appearance showing the upstream flow to be greater than the downstream flow will appear without the consideration of the hysteresis effect, which changes the final result. Considering a lag of one day is more representative of the real situation of the flow (
Figure 4b), the hysteresis effect can have a false effect on the results of some periods, but the impact on the results for one hydrologic year is minimal. The exchanged fluxes are 21.68 × 10
7 m
3 and 21.69 × 10
7 m
3, respectively, without hysteresis consideration and with a lag time of one day. The result with a lag time of one day is considered the final result.
3.2. Analysis of the Exchange Fluxes in 2016
The amount of cumulative exchange fluxes showed an overall upward trend in 2016, indicating the occurrence of gaining stream. However, the exchange situation is different at different stages, showing typical stages. The trend of the cumulative curve reveals 7 stages (
Figure 3,
Table 4), of which the changes in stages 1, 6, and 7 are relatively stable, while stages 2–5 change drastically.
Stage 1, from January to April, showed stable gaining stream. During this period, there was less precipitation and no large groundwater exploitation, which caused the groundwater level in irrigation area to decline (
Figure 5). The SWD and FWD in the center of the irrigation area began to rise on April 1, contemporaneous with precipitation; thus, precipitation recharge may have been the cause. However, the XM, near the Taizi River, has always been in a downward trend, which may due to the large exchange intensity between the groundwater and the surface water, such that the recharge of precipitation is insufficient to compensate for the discharge into the stream. The upstream and downstream flow is stable, and the volume of cumulative exchange fluxes changes stably (
Figure 3b). The exchange rate was 3.13 × 10
5 m
3/day in stage 1, which can be regarded as the rate of gaining stream under natural conditions. This stage can be considered as natural-controlled type.
River flow increased sharply at stage 2 on April 29 (
Figure 3a), without any significant precipitation before, indicating that the steep increase in flow was caused by the draining of the Shenwo Reservoir, which caused the river level to rise rapidly (
Figure 5). On the other hand, the Liaoyang Irrigation District began to enter the field soaking period in May, and the Taizi River was drained to irrigate from the Efang canal head. A large amount of stream was recharged into the groundwater, causing the groundwater level to rise rapidly (
Figure 5). The river and the groundwater level changed rapidly at this stage, causing fluctuation in the exchange fluxes (
Figure 3b) and stream recharge into the groundwater. However, stage 2 still exhibited the gaining stream scenario as a hole, with a very low exchange rate of 0.36 × 10
5 m
3/day. This stage can be considered as a reservoir- and irrigation-controlled type.
In stage 3, the interstitial release of water from the reservoir, with the decrease in the discharge flow, caused the river level to fluctuate and decrease significantly compared with stage 2. The rice was in the tillering stage, with a decrease in the irrigation intensity (irrigation interval is 8 d with duration of 8 d), causing the groundwater level to fluctuate and slightly increase (
Figure 5). Therefore, compared with stage 2, the difference between the groundwater and stream level increased, and the exchange rate rapidly increased to 11.24 × 10
5 m
3/day. This stage can be considered as irrigation-controlled type.
In stage 4, due to the increase in water discharge from the reservoir, the stream level increased rapidly again, which weakened the recharge intensity gaining stream caused by irrigation, and the exchange rate decreased to 2.69 × 105 m3/day. This stage is similar to stage 2, which was controlled by reservoir and irrigation together. However, the reservoir discharge duration is not long; thus, this stage lasted for a short time.
Stage 5 is an irrigation-controlled type stage, similar to Stage 3. The groundwater level reached its peak at this stage, and the water-level difference increased (
Figure 5), which caused the exchange rate to reach its peak at 17.32 × 10
5 m
3/day.
In stage 6, the Shenwo reservoir no longer performed large-scale water release, as the irrigation of the paddy fields had ceased. The river and groundwater level were both in a downward trend. The rate of groundwater recharge into the river water was 6.48 × 105 m3/day, indicating that although the irrigation was stopped, the influence of previous irrigation still existed, and the groundwater level was still higher than the natural state. Therefore, the exchange rate was still greater than that in the natural state, and this stage can be considered as irrigation-hysteresis type.
The flow in stage 7 gradually recovered to that in stage 1, as the impact of irrigation basically disappeared. The exchange rate was 3.76 × 105 m3/day, which was close to that in stage 1. Therefore, this state could be considered as natural-controlled type.
In summary, the GW-SW interactions in the study reach were mainly gaining stream, and the recharge rate in the natural state was approximately 3.45 × 105 m3/day (average of stages 1 and 7). The draining of the reservoir can weaken the recharge capacity of gaining stream and even make the stream discharge into the groundwater. Irrigation enhances the recharge of groundwater into the stream; thus, the increased amount should be attributed to the Taizi River water coming through the Efang channel head. Some of these waters are lost to the atmosphere, some are absorbed by the crops, and the rest are returned to the Taizi River in the form of seepage. The additional exchange fluxes caused by irrigation can reach 7.8–13.87 × 105 m3/day, which is 2.26–4.02 times that of natural recharge. After the irrigation was stopped, its influence still existed, which slightly enhanced the seepage with a duration of approximately 48 d and an increased recharge rate of approximately 3.03 × 105 m3/day.
3.3. Verification of Method’s Accuracy
To verify the correctness of the method, taking the XLZ monitoring section as an example, the changes in the GW-SW level of seven stages are shown in
Figure 6. According to the duration of each stage, six levels are uniformly taken to represent the water level change process of the seven stages, simultaneously.
It can be seen from
Figure 6 that the changes in the GW-SW level in stages 1 and 7 are slight, reflecting the relatively stable process of gaining stream, which is consistent with the steady increase in cumulative exchange fluxes. The flow in stages 2 and 4 increases instantaneously, and the water level increases greatly, as well (
Figure 6), which changes the relationship of the GW-SW interactions from simply gaining stream to alternating gaining and losing stream. In stage 2, the interaction was mainly losing stream, while after the flow was reduced, the interaction was changed back to gaining stream, which is consistent with the results. The water level changes in stages 3, 5, and 6 are relatively small compared to those of stages 2 and 4 (
Figure 6). The groundwater level is generally higher than the river level, reflecting the gaining stream, which is consistent with the results in
Figure 3.
Therefore, the GW-SW interactions reflected by the section is consistent with the result calculated by the cumulative exchange fluxes method. However, in terms of exchange rate, the rate of the section cannot represent the entire reach because of the influence of the topography and the anisotropy of hydrogeological conditions.
3.4. Error Analysis of Exchange Fluxes Calculation
According to Equation (9), the factors affecting the result mainly include lag time, measurement error of hydrometeorological data, and runoff coefficient. The effect of lag on the result increases with increasing flow fluctuations, and the lag time is related to the topography of the basin and the length of the study reach, which can be determined according to the typical flow peak point. Hysteresis has little effect on the result of the exchange fluxes in a hydrological year. There exist system errors in the measurements of hydrometeorological data that the error of flow measurement is ±3%, with precipitation of ±0.05 mm and evaporation of ±0.1 mm. As the mass balance is a simple summation, the error of hydrometeorological data measurement (
) is a linear error propagation and can be obtained as:
The is 0.51 × 107 m3 and the relative errors is ±2.35% compared with the result of 21.69 × 107 m3, which is relatively small.
The runoff coefficient reflects the ratio of precipitation to runoff. This method considers runoff as an equilibrium term, as Equation (9) shows. The average annual runoff coefficient of the study reaching from 1956 to 2000 was between 0.1 and 0.2 [
25]. The effect of different values of runoff coefficient on the result is shown in
Figure 7. It can be seen that the runoff coefficient mainly changes the amount of exchange fluxes when the precipitation is large. When the precipitation is small, the runoff is primarily not generated, and the impact is basically negligible, such as from January to March and from October to December. In the hydrological year of 2016, when the runoff coefficient was 0.1 and 0.2, the amount of exchange fluxes was 26.31 × 10
7 m
3 and 17.07 × 10
7 m
3, respectively. Compared with 0.15, the relative errors are 21.32% and −21.31%, respectively. It is important to reduce the errors caused by runoff coefficient, especially in non-humid regions. A solution is proposed here. Considering that the runoff coefficient changes greatly during a year, using the monthly-varying runoff coefficients will reduce the error. The variation of the runoff coefficient of the study reach and the corresponding results are shown in
Figure 7. It can be seen that the result using monthly-varying runoff coefficients from January to July are basically consistent with result when runoff coefficient is 0.15. The increase in runoff coefficient and precipitation in August made the curve begin to deviate. Compared with 0.15, the relative error is 3.67%. Since the monthly-varying runoff coefficients are closer to the real situation, it is recommended to reduce the error. Although difference exists, the GW-SW interactions reflected by two curves at different stages is consistent. In the absence of monthly-varying runoff coefficient data, the constant runoff coefficient can still be considered.
3.5. The Applicability of Cumulative Exchange Fluxes Method
This method is based on the principle of surface water balance, so it is applicable to the reach with downstream and upstream flow monitoring data. In addition, the dates of precipitation and evaporation and other equilibrium items that change the stream flow are required. The method is applicable to the study of watershed scale and can also be used to analyze the impact of reservoir regulation and paddy irrigation on GW-SW interactions. For streams with multiple flow monitoring stations, the GW-SW interactions can be studied in a different reach.
As with other methods, this method has certain limitations. First, the study reach cannot be an arbitrary reach; it must be a reach between two flow monitoring points. In addition, the results are mostly affected by the runoff coefficient, which means that for areas with large changes in runoff coefficients, the error increases without sufficient accuracy in the runoff coefficient, e.g., mountains with large changes in topography and areas with large land use changes [
26]. However, it is pretty suitable for plains, which have a smaller runoff coefficient. For a reach with a long length, the hysteresis effect of the flow should be considered and can be corrected by the comparison of the typical flow peak points. The calculation results represent the GW-SW interactions of the entire river section, but it is not possible to accurately determine the exchange fluxes of any particular location in the stream, which is also a disadvantage of other methods.