Water balance assessment of an ungauged area in Poyang Lake watershed using a spatially distributed runoff coef fi cient model

The Poyang Lake ungauged area (PLUA) is an essential hydrology buffer surrounding Poyang Lake. For such a data-scarce area, a novel spatially distributed runoff coefficient model (SDRCM) was developed based on the underlying surface properties using remotely sensed precipitation and reanalysis data after their validation. The runoff simulated by the SDRCM based on both sets of gridded precipitation data were validated in a subbasin where R and ENS are larger than 0.87. In addition, a hydrodynamic model was applied to validate the proposed model further by considering the estimated water yield for PLUA that involves boundary inputs, in which the result more closely aligns to the monthly observed discharge. On an annual basis, the PLUA water flow accounted for 12%–19% of the total annual water flow within the watershed, which was approximately equal to the proportion of the area of PLUA in relation to the entire watershed. Finally, the water balance between inflow and outflow of Poyang Lake was investigated, with relative errors observed at the Hukou gauging station all being less than 10% from 1998 to 2009. The proposed model will be helpful in understanding the significance of water yields of such ungauged plain area when evaluating the water balance. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). doi: 10.2166/hydro.2018.017 s://iwaponline.com/jh/article-pdf/20/5/1009/486079/jh0201009.pdf Jianzhong Lu Xiaoling Chen (corresponding author) Ling Zhang State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, Wuhan 430079, China E-mail: xiaoling_chen@whu.edu.cn Xiaoling Chen Key Laboratory of Poyang Lake Wetland and Watershed Research, Ministry of Education, Jiangxi Normal University, Nanchang 310022, China Sabine Sauvage José-Miguel Sánchez-Pérez ECOLAB, Université de Toulouse, CNRS, INPT, UPS, 31400 Toulouse, France


INTRODUCTION
It is likely that runoff estimation for ungauged basins is one of the most challenging tasks for hydrologists. This longstanding issue has received increased attention recently due to the PUB (Prediction in Ungauged Basins) initiative launched in 2003 (Hrachowitz et al. ). Because the water cycle on the Earth's surface is influenced by ongoing human activities and climate change, more research is warranted to understand, simulate and predict the hydrological regimes of the system (Wagener et al. ). The Poyang Lake plain, at the heart of the Yangtze River watershed, is an indicator of climate change and is connected to the Yangtze River through the Hukou waterway (Zhang et al. a). It suffers a high likelihood of an increase in frequency and severity of flooding and droughts. Ungauged area, an area of interest in ungauged basins (Sivapalan et al. ), which stretches from the downstream boundary of a gauged basin to the upper boundary of an adjacent water body, universally exists in river, lake, and ocean catchments (Zhang et al. ). The Poyang Lake ungauged area (PLUA), located in the Poyang Lake plain, has not been gauged to develop stream flow records, which prevents hydrological engineers and scientists from accurately predicting the volume of water resources and analyzing water balances. Due to the complexity of drainage networks and lakes in a flat area, such as the PLUA, it is difficult to develop a distributed hydrological model for water flow prediction. In addition, little observation data are available to calibrate and validate a sophisticated hydrological model. Therefore, it is necessary to develop a new method to assess the water balance in this ungauged area.
Hydrological prediction is limited by absent hydrological observations and insufficient data quality and reliability, which is especially true for developing countries where watersheds are often ungauged (Piman & Babel ).
Because traditional data gathering is usually constrained by During the PUB decade, hydrological scientists made significant efforts to better understand spatiotemporal heterogeneity and hydrological processes (Hrachowitz et al.  () reported surface runoff estimation for lake plain area using a coarsely constant runoff coefficient of 0.6 for the whole area; the estimated result was implicitly given but not yet validated for the lake plain area in this study. Zhang et al. () set up a subbasin validated Soil and Water Assessment Tool (SWAT) model and transferred it to simulate the streamflow in the ungauged area. However, in such a flat plain with complex river networks, it is difficult to calibrate parameters for a processes-based hydrological model due to the scarcity of data in this ungauged area.
There is also not adequate observed data to validate and evaluate the modeling results. In order to solve these issues, we developed a spatially distributed runoff coefficient method (SDRCM) after investigating the slope and land use to predict the water flow in the data-scarce area of PLUA. This process was based on remote sensing precipitation products and weather data from CFSR. A lake hydrodynamic model was also applied to validate runoff in the PLUA estimated by the SDRCM. Combined with observation data from the upstream hydrological gauging station for the entire Poyang Lake watershed, the water balance is investigated by comparing these results to observations made at the Hukou gauging station.

Study area
The Poyang Lake watershed drains an area of 16 × 10 4 km 2 and five main tributaries including the Xuishui River, Ganjiang River, Fuhe River, Xinjiang River, and Raohe River, with seven inlets discharging into the lake ( Figure 1). Water storage contributions to the lake are mainly derived from catchment discharges and the interaction with the Yangtze River at the northern end of the lake. There is abundant rainfall in the Poyang Lake region with an annual mean of approximately 1,500-2,000 mm and an annual mean temperature of 17 C-19 C. The PLUA, an important hydrology buffer surrounding the lake, is separated by seven upstream hydrological gauging stations (Qiujin, Wanjiabu, Waizhou, Lijiadu, Meigang, Hushan, and Dufengkeng at seven inlets) for the five main tributaries that discharge into Poyang Lake. The PLUA is located downstream of hydrological gauging stations to the river outlet which is not gauged by any hydrological station. With an area of approximately 2.9 × 10 4 km 2 , it is larger than the Xiushui River, Fuhe River, Xinjiang River, and Raohe River basins and slightly smaller than the Ganjiang River basin. Further, it is a major component of the total water resources in the watershed. In this study, we attempted to estimate water yields of the PLUA based on reanalysis and remote sensing data.

Hydro-meteorological data
In order to sufficiently estimate the water flow in the PLUA, three types of meteorological data were used to compare estimated results in this study, including the TRMM, CFSR precipitation and Ground-based Meteorological Station (GMS) weather data. TRMM is a joint mission between the United States National Aeronautics and Space Administration and the Japan Aerospace Exploration Agency designed to determine rainfall in tropical and subtropical regions of the Earth for weather and climate research. The TRMM satellite, with a design lifetime of three years, was launched in November 1997 to produce valuable scientific data. Among the five instruments carried on the TRMM satellite, the instrument PR (precipitation radar) was the first space-borne instrument designed to provide three-dimensional maps of storm structure and rain information including the rain intensity and distribution, rain type, storm depth, and height at which the snow melts into rain.  Xingzi, Duchang, and Tangyin stations in Poyang Lake, which is used to validate the lake hydrodynamic model.
Daily water discharge and daily water level records were collected at Hukou gauging station, which is located at the junction of Poyang Lake and the Yangtze River ( Figure 1).
The water discharges at Hukou station were used to investigate the differences between inflow and outflow of Poyang Lake in magnitude and in time synchrony, while the water levels at Hukou station were applied as open boundary condition of Poyang Lake hydrodynamic model.

Water balance equation for Poyang Lake
For a certain period of time, water balance for the PLUA can be described by the following equation: where Q in is the water volume discharging into Poyang Lake from the tributaries around the lake; Q out is the water volume flowing out of Poyang Lake and ΔV represents water volume changes, including ground water exchange, precipitation, and evaporation in the lake, which affect water storage in the lake.
The water volume out of Poyang Lake can be expressed by the observed discharge at Hukou gauging station outlet, while the water volume discharging into Poyang Lake can be described by the total water flow discharging from all five main tributaries (seven gauging stations) and the water yields in the PLUA ungauged area and can be represented as: where Q Hukou is observed water discharge out of Poyang Lake at the Hukou gauging station; Q Qiujin , Q Wanjiabu , Q Waizhou , Q Lijiadu , Q Meigang , Q Hushan , and Q Dufengkeng are the observed water discharged into the PLUA at Qiujin, Wanjiabu, Waizhou, Lijiadu, Meigang, Hushan, and Dufengkeng gauging stations, respectively, and Q PLUA is the water flow calculated for the PLUA, which is unknown and had to be calculated for this study.

Distributed runoff coefficient model setup
Due to difficulties with delineating river network and subbasins in a plain flooding area, and modeling spatial variability of water production and convergence, as well as groundwater exchange, infiltration, and evapotranspiration, the empirical approaches using runoff coefficient have been often applied in estimating hydrology. The rational method is usually the method most often applied by hydraulic and drainage engineers to estimate discharges for small watersheds. Thus, the rational method (Kuichling ) computes the water discharge using the following equation: where Q is water discharge (m 3 /s); P is rainfall intensity (mm/h); C is the runoff coefficient (dimensionless) to reflect the ratio of rainfall to surface runoff; A is the drainage area (km 2 ) and m is the dimensional correction factor for unit conversion (m ¼ 3.6).
In the equation, the runoff coefficient is the most important factor to estimate water production and convergence for a basin. It is also essential for flood control and the deli-  Table 1, refers to these properties of runoff convergence under different land uses and slope ratio impacts. The larger values correspond to higher runoff and lower infiltration.
To predict the water flow in the PLUA, we developed a SDRCM based on the slope ratio and land use classifications to compute the water convergence in the area using CFSR and TRMM precipitation data. By overlaying the land use and slope ratio, and setting runoff coefficient values for each pixel, a spatially distributed runoff coefficient map was generated (Figure 3) according to the values listed in Table 1. The runoff coefficients were defined as the ratio

Hydrodynamic model setup
In this study, the Delft3D-FLOW numerical modeling system, which has been widely applied in hydrodynamic simulations of lakes, is used to set up the two-dimensional hydrodynamic model of Poyang Lake. This system has been developed for the modeling of unsteady water flow, temperature, salinity, and cohesive/non-cohesive sediment transport in shallows seas, estuarine and coastal areas, In order to evaluate the model performance, the following three indices, the root mean square error (RMSE), the correlation coefficient (R 2 ) and Nash-Sutcliffe efficiency coefficient NSE (E NS ), were applied in this study. The RMSE, E NS and R 2 are defined by following equation: where Q i and S i is observed and simulated data, respect-

CFSR and TRMM precipitation validation by data from ground meteorological stations
In order to understand the performance of CFSR and TRMM monthly rainfall, we must assess the accuracy of the CFSR and TRMM precipitation data before applying the model. The CFSR and TRMM rainfall were first   Figure 6 shows the comparison between monthly streamflow simulated with CFSR and TRMM precipitation data and the observed monthly streamflow during 2007 for the SJZ subbasin.
According to the comparison between monthly simulated water yields based on CFSR and TRMM rainfall data and observed streamflow in the SJZ subbasin, both the simulated water yields agreed with the observed data,     TRMM rainfall data, respectively. The total water flow simulated with TRMM rainfall data was slightly more accurate than that of the CFSR data. When comparing the evaluation indexes R 2 and E NS between Figure 9 and Figure 10, it shows that the accuracy of the estimated monthly water flow provided in Figure 10 was much lower than that of the hydrodynamic model simulation. This may be due to a water flow time-lag effect from the upstream river to the lake. Indeed, from the gauging station to the lake inlet, a time delay was observed for water flowing into the PLUA, which is a flat plain where water flows slowly. In this case, it is likely that the outlet discharge simulated by the hydrodynamic model was more precise than the monthly total water flow that was simply added together for the five tributaries and the PLUA.
In order to assess the difference between the observed annual net outflow of the lake at Hukou gauging station and the simulated annual water flow into the lake, an experiment was conducted. According to Equation (1), ΔV, the water volume difference between discharging into and flowing out of the lake, represents water volume changes, including ground water exchange, precipitation, and evaporation in the lake, which affect water storage in the lake.
Therefore, we investigated whether the observed outflow at Hukou gauging station was equal to the total water flow from the PLUA and all subbasins including the Xiushui River basin, Ganjiang River basin, Fuhe River basin, and Raohe River basin, so as to assess the annual change of water storage (the ΔV in Equation (1)) for the Poyang Lake. The purpose of the experiment was to discern whether there was a balance between the simulated discharge observed at Hukou gauging station and the simulated water flow according to the proposed model and water balance equation over the period of a year.  The runoff hydrograph at the Hukou outlet is not measured precisely by the Hukou gauging station. Specifically, areas located near the Hukou gauging station are often inundated with water during floods. During these events, water flows along other paths instead of through the gauging sections, resulting in a large amount of water that is not measured (Guo et al. ). What is more, at times, water will flow in reverse to Poyang Lake at its outlet to the Yangtze River.
Therefore, the hydrological records at Hukou gauging station might only be a general representation of the real hydrological regime that exists between Poyang Lake and the Yangtze River. Consequently, hydrologists will only be able to discern a regular pattern for the hydrology regime between Poyang Lake and Yangtze River if the differences in the net water flows out of the watershed were evaluated according to both the model estimation and direct observation at Hukou gauging station.

CONCLUSIONS
While Poyang Lake is an essential regulator of hydrology and climate for the Yangtze River watershed, little has been determined previously regarding the hydrological regime of the ungauged area around the lake. Using the PLUA as a representation, a spatially distributed runoff coefficient model (SDRCM) was developed based on the land use and slope ratio in this area. The results, derived from both sets of gridded precipitation data during 1998 to 2013, showed the proposed model had rather high efficiency and accuracy to predict runoff in ungauged areas. This study presented an established hydrodynamic model for river outlets water Poyang Lake that was applied by using the simulated water yields and observed discharges at gauging stations as boundary conditions, so as to validate the simulated results from the proposed SDRCM in the PLUA.
This method, integrating a hydrodynamic model of river outlet water to validate hydrologic results can be widely used for the ungauged area that is located downstream of gauging stations to the river outlets. The water flow in the PLUA based on both gridded CFSR and TRMM precipitation data, accounted for 12%-19% of the total annual water flow However, although inconsistencies were found between the simulated and observed water flow, the results were considered reasonable for studying the hydrology of the ungauged area. As reasons for these anomalies, the impoundment of the Poyang Lake leads to a time lag for the water retention in the lake and that unique characteristics of the Hukou gauging station also play an important role, which make it necessary to develop a hydrodynamic method for validation of hydrological prediction in this little-understood area. Therefore, with the aid of reanalysis and remotely sensed gridded data, the proposed SDRCM in this study is able to quickly predict and simulate hydrology to a reasonable extent for this data-scarce area. It is a robust tool for studying water balance of inflow and outflow of the lake as it relates to flooding in the Poyang Lake watershed.