To solve the problem of estimating and verifying
stream flow without direct observation data, we estimated stream flow in
ungauged zones by coupling a hydrological model with a hydrodynamic model,
using the Poyang Lake basin as a test case. To simulate the stream flow of
the ungauged zone, we built a soil and water assessment tool (SWAT) model for the entire catchment area
covering the upstream gauged area and ungauged zone, and then calibrated the
SWAT model using the data in the gauged area. To verify the results, we
built two hydrodynamic scenarios (the original and adjusted scenarios) for
Poyang Lake using the Delft3D model. In the original scenario, the upstream
boundary condition is the observed stream flow from the upstream gauged area,
while, in the adjusted scenario, it is the sum of the observed stream flow from the gauged area and the
simulated stream flow from the ungauged zone. The experimental results
showed that there is a stronger correlation and lower bias (
In recent years, floods and droughts have occurred frequently (Cai et al., 2015; Tanoue et al., 2016), threatening lives and health, reducing crop yields, and hindering economic development (Lesk et al., 2016; Smith et al., 2014). To reduce the damage to the population, agriculture, and economy, we should attempt to predict floods and droughts precisely. However, in watersheds, ungauged zones lack stream flow observations. The ungauged stream flow is difficult to estimate and is usually neglected in water yield estimations, which can result in flood/drought predictions being not accurate enough.
These ungauged zones are an area of interest in ungauged basins (Sivapalan et al., 2003). Ungauged zones, which stretch from the downstream boundary of a gauged basin to the upper boundary of an adjacent water body, exist in river, lake, and ocean catchments universally. An ungauged zone usually occupies a large proportion of an entire watershed (Dessie et al., 2015; Li et al., 2014); thus, neglecting ungauged zones adds uncertainty in models of estimating the water yield. In addition, the ungauged zone is usually located in flat topography with a dense river network, resulting in turbulent flow without a fixed direction. The dense river network and turbulent flow make it difficult to observe and estimate stream flow in the ungauged zone.
The stream flow simulation in ungauged zones is one area of interest in the Prediction in Ungauged Basins (PUB) research program (Hrachowitz et al., 2013; Sivapalan et al., 2003). In the PUB research program, data acquisition techniques (Hilgersom and Luxemburg, 2012), experimental studies (McMillan et al., 2012; Ali et al., 2012), advanced models and strategies (Harman, 2008), and new hydrological theories (Kleidon et al., 2013) have been developed to improve hydrological prediction results for ungauged zones.
In the PUB research program, methods for stream flow prediction in stream flow ungauged zones focus on simple water balance equations and the transformation of hydrological information (Dessie et al., 2015; Song et al., 2016). For simple water balance equations, there are no parameters to be calibrated. Feng et al. (2013) defined stream flow as the difference between precipitation and evapotranspiration. SMEC (2007) determined the stream flow of the ungauged zone based on a lake water balance equation using measured lake water levels and inflow discharges from the upstream gauged catchment. This method is not suitable for accurate stream flow simulation in the ungauged zone.
Some researchers use regionalization methods to simulate stream flow in ungauged zones. The parameters in the gauged areas are calibrated. Then, the parameters are transformed from gauged to ungauged areas. Wale et al. (2009) constructed a regional model for the relationship between the hydrological model parameters and the catchment characteristics. Based on this regional model, the hydrological parameters in the gauged area were transformed to the ungauged zone. However, verification of the ungauged stream flow is not shown in these studies.
However, other researchers have undertaken verification for the ungauged stream flow simulation. Wang et al. (2007) computed the stream flow in an ungauged zone by classifying the underlying surface. The stream flow of each type of surface was calculated based on the surface characteristics. Wang verified the estimation results by comparing the simulated and observed lake water levels. The verification in Ma and Liu (2011) was based on the water balance of yearly inflow and outflow of the lake. The time resolution is not high enough. Dessie et al. (2015) simulated stream flow in ungauged zones using a rainfall–runoff model and a runoff coefficient. Dessie et al. analyzed the effect of the ungauged zone on the water balance of the lake, which indirectly verified the stream flow simulation result of the ungauged zone. However, the water balance for indirect verification does not represent the water conservation exactly.
Study area and the related data.
An approach coupling hydrology with hydrodynamics could be used to solve the simulation and verification problems. Usually, a water body (a lake, a river, or an ocean) exists downstream of the ungauged zone. The water body is gauged by stream flow gauging stations at the outlet and water level gauging stations on the water surface. The observations can be used to verify the stream flow simulation result by building a hydrodynamic model for the water body. The method coupling hydrology with hydrodynamic models is widely used to represent the catchment water system and the interaction between catchments and water bodies. Inoue et al. (2008) combined hydrology and hydrodynamic models to simulate the hydrological cycle and hydrodynamic characteristics in a coastal wetland of the Mississippi River delta with effective model performance. Dargahi and Setegn (2011) combined a watershed hydrological (soil and water assessment tool, SWAT) model with a 3-D hydrodynamic model (GEMSS) to simulate the Lake Tana basin to address the impact of climate change. Bellos and Tsakiris (2016) combined hydrological and hydrodynamic techniques for flood simulation in the Halandri catchment. However, the method combing a hydrological model and a hydrodynamic model is rarely applied in such ungauged zones. As the ungauged zone is usually located in flat topography with turbulent flow, it is difficult to draw watersheds in the ungauged zone. In addition, allocating the ungauged stream flow to the inflow boundary of a hydrodynamic model is not easy. The methods of drawing watersheds and allocating the stream flow are not mentioned in the previous studies. The details of coupling hydrology and hydrodynamic models in the ungauged are presented in the study.
The Poyang Lake Ungauged Zone (PLUZ) is a typical example of ungauged zones. The PLUZ is adjacent to Poyang Lake. There are stream flow observations at the outlet of the lake. The stream flow from the PLUZ is usually estimated as the difference between the stream flow at the outlet of the lake and the observed stream flow gauging the upstream area. However, the observations at the outlet of the lake cannot respond to the variation of the watershed hydrology quickly and accurately due to water storage and flood regulation of the lake, which makes the stream flow peak clipped and time lagged. The traditional method is too coarse for stream flow simulation in the PLUZ.
More attempts have been made at stream flow simulation in the PLUZ. Huang et al. (2011) developed a runoff flux model especially for the plain area of the PLUZ. The simulation results were verified by comparing observed stream flow at Hukou with the sum of the simulated stream flow in the PLUZ and the gauged stream flow of the gauged upstream at an annual scale. The timescale was coarse. Furthermore, the water storage and flood regulation functions of the lake were not taken into consideration. Guo et al. (2011) simulated the daily runoff of the PLUZ using the variable infiltration capacity (VIC) and multiple-input single-output system (MISO) models. The verification was performed by comparing the simulated results with the estimated results. However, the estimated result was derived from the time lag equation, so it could not replace the observed value exactly for the following two reasons: (1) the time lag equation was a simple hydrodynamic model for the lake, which is not very accurate; (2) in the equation, the stream flow at Hukou was adjusted by a modified coefficient at the annual scale, which is not reasonable to apply at the daily scale. Most recently, Li et al. (2014) combined the hydrological model (WATLAC) and hydrodynamic model (MIKE), where the stream flow in the ungauged area was calculated by the runoff coefficient. However, there was no verification. In summary, there have been few studies that include effective verification for stream flow simulations in the PLUZ. In this study, the method of combining hydrological and hydrodynamic models is introduced to solve the simulation and verification problem in the PLUZ. Our specific objectives are to (1) simulate and the verify the stream flow in the PLUZ, (2) analyze the interannual and intra-annual variations of the ungauged stream flow, and (3) analyze the impact of the ungauged stream flow on the lake water balance.
Poyang Lake is the largest freshwater lake in China and is connected with the Yangtze River in the north of Jiangxi province. The catchment is covered by the five major river sub-catchments and the ungauged zone (Fig. 1a).
As shown in Fig. 1a, the Poyang Lake basin includes three parts: the
gauged area (the five major river catchments), ungauged zone (the PLUZ) and
Poyang Lake. The stream flow of the gauged area was measured by seven
stream flow stations (Qiujin, Wanjiabu, Waizhou, Lijiadu, Meigang, Hushan, and
Dufengkeng). The PLUZ is a plain area and stretches from the seven
stream flow stations to the boundary of Poyang Lake. The PLUZ covers an area
of 19 867 km
The elevation of the lake bed generally decreases from the south to the north,
with differences of approximately 7 m, as shown in Fig. 1b. The discharges
from the gauged area and the ungauged zone flow into the lake at 11 points
(d
We provide data for SWAT and Delft3D models. Data required by the SWAT model
include the forcing elements of daily rainfall, evapotranspiration,
temperature, relative humidity, and wind from 1980 to 2014 collected at 16
national meteorological stations. The stations are distributed uniformly
across the area (Fig. 1a). These data were downloaded from the China
Meteorological Data Sharing Service System (
The procedure for the ungauged stream flow simulation and verification contains three parts (Fig. 2): (1) hydrologic modeling for the Poyang Lake ungauged zone; (2) hydrodynamic modeling for Poyang Lake in two scenarios with or without considering the ungauged stream flow; (3) coupling of hydrological and hydrodynamic models.
Conceptual flow chart for stream flow simulation and verification in ungauged zones by coupling hydrological and hydrodynamic models. The flow chart includes three parts: hydrological modeling, hydrodynamic modeling, and model coupling.
In the first procedure, we built a SWAT model for the entire catchment covering the gauged area and the ungauged zone to simulated stream flow in the PLUZ, and calibrated and validated the SWAT model using the gauged stream flow in the gauged area. In the second procedure, we built the original and adjusted scenarios for the lake hydrodynamic model to further verify the ungauged stream flow. The original scenario did not take the ungauged stream flow into consideration, unlike the adjusted scenario, which accounted for the ungauged zones. In the adjusted scenario, the hydrological and hydrodynamic modes were coupled. In the third procedure, we described the coupling of river hydrological and lake hydrodynamic models in details.
In order to analyze the impact of ungauged stream flow on the lake water balance, we described the water balance equation in Sect. 3.4.
We used a SWAT model (Arnold et al., 1993) to simulate stream flow in the PLUZ. SWAT is a physically based, semi-distributed, and river-basin-scale hydrological model. It has been developed to assess the impact of land management practices on stream flow, sediment and agricultural yields in complex basins with changing soil types, and land use and management over long periods of time. For the purpose of modeling, an entire watershed is divided into sub-watersheds based on rivers and DEM data. Sub-watersheds are portioned into hydrological response units (HRUs), the minimum research units. Water balance is the driving force of hydrological processes. The hydrological cycle includes two divisions: runoff producing on land and flow routing in channels. The surface runoff volume is calculated using the Soil Conservation Service method (USDA Soil Conservation Service, 1972). Flow routed through the channel is calculated by the variable storage coefficient method (Williams, 1969. SWAT has already been widely applied to watersheds around the world for stream flow simulation (Douglas-Mankin et al., 2010; Arnold et al., 2012; Luo et al., 2016).
A SWAT model should be calibrated and validated by the measured data. The
PLUZ is ungauged for stream flow, while there are stream flow gauging stations
(the seven gauging stations) at the upstream boundary of the PLUZ,
controlling the upstream gauged area (Fig. 1a). Thus, we established a
SWAT model for a larger area, more than just the ungauged zone. The modeled
area covers the upstream gauged area and the ungauged zone (the PLUZ),
excluding Poyang Lake (Fig. 1a). We use the long time series of monthly
discharges at six gauging stations (Wanjiabu, Waizhou, Lijiadu, Meigang,
Dufengkeng and Hushan) to perform the calibration from 2000 to 2005 and
validation from 2006 to 2011. The determination coefficient (
To verify the stream flow simulation results in the PLUZ, we built two hydrodynamic scenarios for the lake using the Delft3D model. Delft3D simulates the hydrodynamic pattern via the Delft3D-FLOW (Roelvink and van Banning, 1994) module. Delft3D-FLOW is a multi-dimensional (two- or three-dimension) hydrodynamic and transport simulation program. The program can calculate unsteady flow by building linear or curvilinear grids suitable for the water boundary, which is forced by tidal and meteorological data. Delft3D-FLOW is based on the Reynolds-averaged Navier–Stokes (RANS) equations, which are simplified for an incompressible fluid under shallow water and Boussinesq assumptions. The RANS equations are solved by the alternative direction implicit finite difference method (ADI) on a spherical or orthogonal curvilinear grid. Delft3D has ability to simulate water level variations and flows on surface water bodies in response to forcing elements of inflow discharges and climate factors, which has been proven by applications on many surface water bodies around the world. Delft3D is considered appropriate for the wide and shallow characteristics of Poyang Lake.
In the model, the shoreline of lake was delineated as the maximum area of the lake surface to ensure that the dynamic changes in the lake's surface area did not surpass the inundation area. To better capture the rapid dynamic of inundation area and minimize the computational effort, the size of the model grids ranged from 200 to 300 m. The topographic data were interpolated into each computational node of the model grids. The water level was initialized as the mean of the three hydrological stations in Poyang Lake on 1 January 2001, which are Xingzi, Duchang, and Kangshan. The corresponding velocities were initialized as zero. The upper open boundary was set as the upstream discharges. The lower open boundary was specified as the observed long time series of the daily water level at Hukou station. The model was run from 1 January 2001 to 31 December 2010 and the time step was set as 5 min to meet the Courant–Friedrich–Levy criteria for a stable condition. The long time series of observed data for water levels at Xingzi, Duchang, and Kangshan gauging stations, and outflow discharges at Hukou gauging station, were used for calibration from 2001 to 2005 and validation from 2006 to 2010.
Two scenarios were established, the adjusted scenario and the original scenario. We applied the same hydrodynamic model (Delft3D) in the same study area (Poyang Lake) as the research by Zhang et al. (2015). Therefore, we set the parameters (the Manning roughness coefficient, the eddy viscosity parameter, and the critical water depth for wetting and drying) as the fittest ones calibrated by Zhang et al. (2015) for the Delft3D model. The parameters in the two scenarios are set the same.
The original scenario did not take stream flow in the PLUZ into consideration,
unlike the adjusted scenario, which accounted for the ungauged zones. In the
original scenario, the upper open boundary was the stream flow from the
gauged area, set as the daily discharges from the seven gauging stations;
there are nine inflow points – d1, d2, d3, d4, d5, d6, d7, d8, and
d
The upstream boundary conditions of the Delft3D model in the
original and adjusted scenarios. Od1, Od2, Od3, Od4, Od5, Od6, Od7, Od8, and
Od9 represent the stream flow set at d1, d2, d3, d4, d5, d6, d7, d8, and d9, respectively, in the
original scenario. Ad1, Ad2, Ad3, Ad4, Ad5, Ad6, Ad7, Ad8, Ad9, Ad10, and
Ad11 represent the stream flow set at d1, d2, d3, d4, d5, d6, d7, d8, d9, d10, and d11, respectively, in the
adjusted scenario. b1, b2
As the ungauged zone is usually in low and flat topography with turbulent flow, it is difficult to draw watersheds in the ungauged zone. Additionally, allocating the stream flow in the ungauged zone to inflow boundary of hydrodynamic model is not an easy task.
The upper boundary condition of the hydrodynamic model in the adjusted scenario is the sum of the gauged stream flow from the gauged area and the simulated stream flow from the ungauged zone (the PLUZ). To determine the upper boundary condition in the adjusted scenario, we coupled the hydrological model and hydrodynamic model in space and time.
To make sure the hydrological model and hydrodynamic model were coupled perfectly in space, the delineated sub-basins, rivers, and the outlets of the PLUZ basin should follow the following constraints. (1) River networks in the PLUZ must be delineated to link the five major rivers and the inflow points of the lake. (2) The seven gauging stations must be set as the outlets of the gauged basins and the inlets of the PLUZ basin, and the most downstream boundary of the gauged basins should coincide with the most upstream boundary of the PLUZ basin. (3) The outlets of the PLUZ must completely coincide with the inflow points of the lake in the hydrodynamic model, and the most downstream boundary of the PLUZ basin should coincide with the boundary of the lake. (4) The sub-basins of the PLUZ should cover the whole area of the PLUZ. Following these principles, the catchment hydrological model can be seamlessly coupled with the lake hydrodynamic model in space. We first drew the sub-basins, rivers, and outlets using the SWAT model. Since the delineated results from the SWAT model may not satisfy these constraints, we edited the rivers, the boundary of sub-basins, and the outlets to meet the constraints (Fig. 2).
As shown in Fig. 2, the PLUZ was divided to 14 sub-basins (b1, b2
The calibration and validation of the SWAT model was conducted at a monthly scale. However, hydrodynamic model simulation is at a daily scale. To couple the two models in the same timescale, we use the same parameters of the monthly SWAT model to simulate the ungauged stream flow at the daily scale.
To allocate the ungauged stream flow to different inflow points of the lake,
the sub-basins were sorted into 11 groups (group1, group2,
group3
The abridged general view coupling the catchment and lake models
in space:
Based on the sub-basin groups, we determined the ungauged stream flow
gathering to each inflow point of the lake. The stream flow produced by the
PLUZ gathering to
Over time, water yield can reflect the total amount. So we analyzed
the water yield variable instead of stream flow. Water yield is computed as
the accumulative stream flow in a specific duration. Monthly water yield is
the accumulative stream flow in a specified month. Annual water yield is the
accumulative stream flow in a specified year. In the paper, the units of
stream flow, monthly water yield, and annual water yield are m
The ungauged stream flow allocated to the lake inflow points of the
dynamic model in the adjusted scenario.
In order to analyze the effect of ungauged zone on the lake balance, we
construct water balance equations for the lake based on water conservation
principles that the difference between input and output stream flow equals
storage change of the lake, as follows:
When the ungauged stream flow is taken account (in the adjusted scenario),
To adjust the models to be applied in the Poyang Lake basin, we
undertook calibration and validation for the SWAT model and the Delft3D
model. Table 3 and Fig. 4 show the calibration and validation results for
the SWAT model. The observations and simulations at the six gauging stations
(Wanjiabu, Waizhou, Lijiadu, Meigang, Hushan, and Dufengkeng) come to
satisfactory agreement, with an
Quantitative assessment of calibration and validation for SWAT model.
Comparison of observations and the results simulated from the SWAT
model for calibration (2000–2005) and validation (2006–2011). Panels
Comparison of the observed (red dotted line) and simulated (black
solid line) lake water level at Xingzi, Duchang, and Kangshan stations and
outflow discharges at Hukou by the Delft3D model. The calibration period and
validation period are from 2001 to 2005 and from 2006 to 2010, respectively.
Quantitative assessment of calibration and validation for stream flow simulation for the Delft3D model.
Table 4 and Fig. 5 show the calibration and validation results for the
Delft3D model. The observations and simulations at the four gauging stations
(Xingzi, Duchang, Kangshan, and Hukou) come to satisfactory agreement, with
an
To further verify the stream flow simulation results in the ungauged zone, we compared the two hydrodynamic simulation results from the adjusted scenario and original scenario. The adjusted scenario took the stream flow in the PLUZ into consideration, while the original scenario omitted the stream flow in the PLUZ. The hydrodynamic simulation result in the adjusted scenario is improved compared to the original scenario, shown in Table 4 and Fig. 6.
Comparison of the simulated stream flow results at Hukou, in the adjusted scenario and original scenario. The outlier is the data which may be affected by the dike burst in 2010.
Table 4 shows the results of the two scenarios in two aspects: the lake
water level and outflow. For the lake water level, the absolute PBIAS
decreases from 0.85, 3.18, and 1.56 % in the original scenario to
0.48, 2.67, and 1.21 % in the adjusted scenario while
Figure 6 show the comparison of the stream flow simulated accuracy in the
adjusted scenario and original scenario. The
We do monthly (Fig. 7) and annual (Fig. 8) statistical analysis of the ungauged
stream flow, to study the intra-annual and interannual variations. As shown
in Fig. 7, monthly water yield of the ungauged zone shows clearly
seasonality. In a particular year, the maximum monthly water yield varies
from 1.676 to 7.712 billion m
Interannual variation is also apparent. Both the month and amount of maximum monthly water yield appear different in different years, as well as that of minimum monthly water yield. For 10 years (2001–2010), the maximum monthly water yield occurred in 2010, when 5 of 12 months had high stream flow (Fig. 7a). Indeed, a flooding event happened in June 2010 due to the dike burst, which risked the lives of more than 10 000 people. The minimum monthly water yield reached the minimum in 2007. In fact, in 2007 Jiangxi province experience severe drought (Feng et al., 2011). The severe flood and drought can also be suggested in Fig. 8. As the water yield is affected by the extreme climate, the long time series of water yields can also reflect flood/drought conditions in Poyang Lake area, in reverse.
The variation trend of the annual water yield of the ungauged zone
from 2001 to 2009. It shows declining trend at a rate
Closing errors of lake water balance:
Annual stream flow of the ungauged zone shows a clear declining trend
(
The mean annual water yield in the PLUZ totals 16.4
In order to analyze the impact of the ungauged stream flow on the lake water
balance (seen in Sect. 3.4), we calculate the closing errors based on Eqs. (2) and (3):
However, there are some exceptional dot pairs colored in red (outlier, only
17 %) in Fig. 9. For the exceptional, the absolute
The ungauged stream flow decreases the annual average closing error of water
balance by 13.48 billion m
A method coupling hydrology and hydrodynamics can be used to simulate and verify stream flow in ungauged zones, solving the simulation and verification problems caused by the unavailability of stream flow observations.
The hydrological and hydrodynamic models are coupled seamlessly in both
space and time. The method of coupling the models was presented in detail
for the first time and was applied in the case study successfully. Using
this method, we estimated that the ungauged zone of Poyang Lake produces a
stream flow of approximately 16.4 billion m
The method can be extended to other lake, river, or ocean basins where stream flow observation data are unavailable, producing reasonable stream flow simulation results in ungauged zones. Reliable stream flow simulation results in ungauged zones contribute to more accurate and reliable water yield predictions, which provides a deep understanding of hydrology for hydrological engineers and scientists and helps governments develop better water management plans. Furthermore, this method is an area of interest of the Prediction in Ungauged Basins (PUB) research program and provides stream flow prediction and validation aids in PUB research.
All data can be accessed as described in Sect. 2.2.
The authors declare that they have no conflict of interest.
This article is part of the special issue “Coupled terrestrial-aquatic approaches to watershed-scale water resource sustainability”. It is not associated with a conference.
This work was funded by the National Natural Science Funding of China (NSFC, 41331174), the National Key Research and Development Program (2017YFB0504103), the Open Foundation of Jiangxi Engineering Research Center of Water Engineering Safety and Resources Efficient Utilization (OF201601), and the LIESMARS special research funding. Edited by: Xuesong Zhang Reviewed by: two anonymous referees