1. Introduction
Watershed runoff generation is a dynamic and complex hydrological process that plays an important role in the formation of flood events. Understanding the relationship between rainfall and runoff is a key issue in the management and control of water resources (Balkhair et al. 2018). Runoff is generated by the rainfall that remains after the losses that take place through evaporation, vegetation interception, filling, and infiltration. Generally, the loss of rainfall, including the processes of interception, infiltration, evaporation, and surface depression storage, during the period from the beginning of rainfall to the generation of runoff is termed initial abstraction (Ia). The value of Ia is strongly related to climatic and watershed antecedent wetness conditions. The estimation of Ia is of great significance in determining runoff, which influences flood management and forecast.
At present, based on two runoff generation mechanisms, the infiltration-excess (Horton 1933, 1941) and the saturation-excess mechanisms (Dunne 1978; Loague et al. 2010), many methods have been proposed to calculate watershed runoff generation, such as the Green–Ampt method (Green and Ampt 1911), and the Soil Conservation Service curve number (SCS-CN) method (SCS 1972). Of all the runoff generation methods, the SCS-CN method, proposed by the USDA Soil Conservation Service, is most widely used because of its relatively few input parameters and simple structure. Soil texture, topographic factors, vegetation condition and land use of the watershed are considered, which makes the SCS-CN method suitable for the estimation of runoff for long-term gauged watersheds as well as ungauged watersheds. Many hydrological models, such as CREAMS (Knisel 1980), AGNPS (Young et al. 1989), SWAT (Arnold et al. 1996), and Hydrologic Engineering Center Hydrologic Modeling System (HEC-HMS; USACE 2008), employ the SCS-CN method to determine the runoff.
In the SCS-CN method, Ia is a sensitive parameter that is difficult to acquire from observed data and generally varies from different rainfall–runoff events. However, due to its temporal variation, Ia typically needs to be calibrated for each event in the event-based model, for instance, the HEC-HMS model. Therefore, according to the definition of Ia and the analysis of a large amount of rainfall–runoff event data, the Soil Conservation Service recommends that Ia should be taken as 0.2 times the potential maximum retention S of the watershed, or, in other words, the initial abstraction ratio (λ = Ia/S) is 0.2. Nevertheless, this assumption has recently been challenged (Hawkins et al. 2002; Woodward et al. 2003; Shi et al. 2009; Fu et al. 2011; Noori et al. 2012; Hawkins et al. 2019). The Ia/S value has a significant impact on the accuracy of flood prediction. Hawkins et al. (2002) suggested that Ia/S is not a constant value; rather, it varies between different storms and different basins. Noori et al. (2012) found that Ia/S = 0.05 provides superior results compared to the recommended value of 0.2. Fu et al. (2011) analyzed 757 rainfall–runoff events in Shaanxi and Gansu Provinces to quantify the Ia/S, indicating that the average value of Ia/S is 0.08 and the median value is 0.05 in the Loess Plateau of China.
As is mentioned above, Ia is related to the rainfall loss through all processes, including evaporation, vegetation interception, infiltration and surface depression storage, during the period from the onset of rainfall to the generation of runoff. Many researchers have begun to study the influence of various potential factors upon Ia. Mishra et al. (2006) held that Ia varies inversely with antecedent moisture and proposed an improved Ia–S relation incorporating antecedent moisture. Lin et al. (2013) proposed an empirical power-function relationship between Ia and initial discharge, which makes hydrological models more useful in flood forecasting. In all of these studies, Ia is understood to be closely related to antecedent watershed conditions. Brocca et al. (2009) utilized the observed soil moisture data to estimate wetness conditions of five nested catchments in central Italy; they also employed two antecedent precipitation indices (API) and one baseflow index (BFI) to estimate wetness conditions for the SCS-CN method. However, there is no observed data on soil moisture content for most watersheds.
In general, soil moisture data can be obtained through site measurement, land surface modeling (LSM) and satellite retrieval (Liu et al. 2019). Yet, the instrumental sites are extremely sparse due to the high cost of maintenance. Accordingly, the application of remotely sensing soil moisture data has become a prevalent method in the field of hydrology for solving the problem of ungauged watersheds in recent years (McDonough et al. 2018; Bhuiyan et al. 2017). Among the various LSM and satellite retrieval soil moisture products, the GLDAS-Noah is representative and has a wide range of applications (Wang et al. 2011; Yuan et al. 2015; Wang et al. 2016). Vissa et al. (2019) have predicted the ENSO-induced groundwater changes in India using monthly soil moisture data from GLDAS-Noah datasets. Liu et al. (2019) have utilized soil moisture data from GLDAS-Noah datasets to analyze global drought. In addition to soil moisture data, evaporation data from GLDAS-Noah datasets have also frequently been adopted. Xing et al. (2018), for instance, have applied the evapotranspiration data from GLDAS-Noah datasets to estimate the monthly evapotranspiration across different climatic regions. Given that Ia is related to evaporation and antecedent soil moisture conditions, the soil moisture and evaporation data from GLDAS-Noah datasets have the potential to predict Ia.
To clarify the relationship between Ia and evaporation, soil moisture and other watershed wetness condition factors, the application of data-driven approaches, which have gained popularity in recent years, can be taken into account (Ouyang et al. 2016). Many data-driven methods, such as the Box–Jenkins method (Box and Jenkins 1970), the support vector machines (SVM) method (Vapnik 1995) and machine learning algorithms have been widely employed to forecast hydrologic variables (Kaur and Jothiprakash 2013). Kumar et al. (2019) have applied recurrent neural network (RNN) and long short-term memory (LSTM) methods for forecasting monthly rainfall. Several similar studies (Moustris et al. 2011; Kashid and Maity 2012; Ramana et al. 2013; Mekanik et al. 2013) have shown the applicability of machine learning algorithms in forecasting rainfall. Hu et al. (2018) proposed the artificial neural network (ANN) and LSTM approach for flood forecasting, and the results illustrated that both the two networks are suitable for rainfall–runoff models and better than conceptual and physically based models. ANN is a nonlinear statistical data modeling tool, which is often used to capture the complex relationships between input variables and output variables. It has the unique advantages of distributed parallel processing, nonlinear modeling and adaptive learning ability, which provides an effective means of simulating and evaluating the process of nonlinear complex systems. ANN has been applied in many fields, such as classification, pattern recognition and nonlinear modeling (Tayfur et al. 2008). Therefore, ANN is employed to capture the relationship between Ia and its driving factors in this study.
The objectives of this study are 1) to determine the driving factors of Ia by identifying the relationship between Ia and potential driving factors extracted from measured rainfall–runoff events and GLDAS-Noah datasets; 2) to propose an Ia-estimation method, and specifically construct an ANN model to reveal the complex relationship between Ia and its driving factors; and 3) to assess the proposed Ia-estimation method by simulating flood events in the event-based HEC-HMS model to investigate the superiority of ANN-estimated Ia.
2. Study area and data
a. Study area
The verification was performed in the drainage area of the Zijingguan hydrological station and the Wulongji hydrological station, situated in the northeastern part of China. The Zijingguan hydrological station, which controls a 1760-km2 watershed area, is in the upstream of the Juma River in the Daqing River basin (Fig. 1a). The length of the main stream is 81.5 km with an average slope of 5.5%. The climate in the Zijingguan watershed is typical temperate continental and semiarid, with a mean annual precipitation of 650 mm. Flood events in the Zijingguan watershed are mostly generated by rainstorms in flood season.
Location of the hydrological station and rain gauges for the two study areas (a) Zijingguan watershed and (b) Wulongji watershed.
Citation: Journal of Hydrometeorology 21, 5; 10.1175/JHM-D-19-0202.1
The Wulongji hydrological station is situated in Chengde County, Hebei Province, the middle reaches of Luanhe River. The Wulongji watershed, with the drainage area of 30 100 km2, is located in northeast China, accounting for 67.7% of the Luanhe River basin area (Fig. 1b). Most of the precipitation is concentrated in July and August, accounting for more than 50% of the whole year. The annual precipitation of the Wulongji watershed ranges from 885.8 to 338.7 mm with an average precipitation of 587.8 mm. Location of the hydrological station and rain gauges for the Zijingguan and Wulongji watersheds are shown in Fig. 1.
b. Data collection
1) Rainfall–runoff events selection
Two datasets were collected from the Zijingguan hydrological station and Wulongji hydrological station. For the first set, hourly flood discharge data at the Zijingguan hydrological station and hourly rainfall data from eight gauges in the Zijingguan drainage area were collected from 1956 to 2014, which include 103 rainfall–runoff events in total. Only 64 rainfall–runoff events were selected in this study. The selection criteria are as follows:
A 2-yr return period flood is considered as threshold flow (specifically, 39 m3 s−1 in the Zijingguan watershed and 44 m3 s−1 in the Wulongji watershed). A flood with a 2-yr return period, which is often regarded as natural bankfull discharge, is a good alternative for watersheds without a predefined warning level (Weeink 2010) and can even be set as a global minimum flood protection standard (Scussolini et al. 2016). Consequently, a 2-yr return period flood can be regarded as the criterion for determining that floods have occurred, and it symbolizes the magnitude of flood events that can be used for rainfall–runoff event analysis.
A 6-h interval, a widely adopted length (Loukas and Quick 1996; Rahman et al. 2002; Manfroi et al. 2004; Baltas et al. 2007), was applied as the interval length to separate the rainfall events, as a long interval length of rainfall events potentially increases the complexity of their effects on runoff because of drying during intraevent rainless periods (Dunkerley 2008). In addition, since with single-peak runoff events can better estimate effective rainfall (Gupta et al. 1986) and avoid uncertainty in determining the peak timing for multipeak events (Tang and Carey 2017), runoff events with multiple peaks have been excluded. Single-peak runoff events are often preferred in conducting rainfall–runoff event analysis (Furey and Gupta 2005; Schwab et al. 2017; Tarasova et al. 2018).
Storms satisfying P/S ≤ 0.456 should be excluded and considered as small storms for SCS-CN application (Hawkins et al. 1985). The use of smaller events could bias the results toward a larger CN (Woodward et al. 2003; Hawkins et al. 2009; Noori et al. 2012), yet low rainfall events with a high CN bias can be found in essentially every dataset (Mishra et al. 2007). This criterion, namely, storms satisfying P/S > 0.456 were selected, guarantees that 90% of rainfall events will generate runoff in different watershed antecedent moisture conditions and minimizes the upward bias in the determination of CN (Simanton et al. 1996).
Flood frequency analysis was performed to classify the magnitude of the 64 rainfall–runoff events into four categories (Ministry of Water Resources 2006) according to the return periods T (yr), namely, small floods (T < 5 yr), moderate floods (5 < T < 20 yr), large floods (20 < T < 50 yr) and extraordinary floods (T > 50 yr). Additionally, for small datasets, the ratio for splitting the size of the training and test sets in machine learning is usually determined as 80/20, where 80% of the data are allocated for training and 20% for testing (Shan 2016). Thus, 14 out of the 64 rainfall–runoff events, including all the flood categories, were selected to construct the HEC-HMS model and used as the test datasets for the ANN model. The remaining 50 rainfall–runoff events were employed to determine the statistical Ia and to train the ANN model.
For the Wulongji watershed, hourly flood discharge data and the corresponding rainfall data from 57 rain gauges from 1992 to 2014 were collected, including 67 rainfall–runoff events. According to the selection criteria and flood frequency analysis, 42 rainfall–runoff events were selected in this study, including 10 events for the HEC-HMS model simulation (test datasets of ANN model) and 32 events for Ia statistical analysis (training datasets of ANN model), respectively.
2) GLDAS data collection
The related antecedent watershed conditions data, such as soil moisture content and evaporation, were extracted from GLDAS-Noah datasets (Rodell et al. 2004; Beaudoing et al. 2015). NASA Global Land Data Assimilation System (GLDAS) ingests satellite and ground-based observational data products using advanced land surface modeling and data assimilation techniques. GLDAS-Noah land surface state and flux products are provided by the Hydrology Data and Information Services Center (HDISC), a component of the NASA Goddard Earth Sciences Data and Information Services Center (GES DISC). GLDAS-Noah v2.0 currently covers the period from January 1948 to December 2014 (updated at 27 November 2019) and contains 36 parameters, with a 3-h temporal interval and 0.25° spatial resolutions. Soil moisture and evaporation data from the GLDAS-Noah datasets were used in this paper because they are closely related to Ia. The potential driving factors of Ia adopted in this study are listed in Table 1.
Potential driving factors of Ia.
GLDAS-Noah soil moisture grid data in the watersheds (a) Zijingguan watershed and (b) Wulongji watershed.
Citation: Journal of Hydrometeorology 21, 5; 10.1175/JHM-D-19-0202.1
The soil moisture content data from one time step before rainfall were used to represent antecedent soil moisture conditions, which are available with a 3-h temporal interval. For evaporation data and rainfall characteristics, including antecedent precipitation index (API), maximum rainfall intensity (MRI), and average rainfall intensity (ARI), the data collection time is the period from the beginning of the rainfall to the start of runoff generation. API, MRI, ARI, and initial discharge (ID) were collected by analyzing observed rainfall–runoff events. API represents the summation of daily precipitation amounts over the 5 days before the selected rainfall–runoff events (Sahu et al. 2007; Brocca et al. 2009; Singh et al. 2015).
3) Land use and land cover data
The land use and land cover (LULC) maps for the Wulongji watershed for the years 1992, 1995, and 2014 were obtained from the European Space Agency (ESA) Climate Change Initiative (CCI) (http://maps.elie.ucl.ac.be/CCI/viewer/), which provides the global LULC maps ranging from 1992 to 2014. Yet, the earlier LULC maps for the Zijingguan watershed are needed. Accordingly, the LULC data for the Zijingguan watershed for the years 1980, 1995, and 2015 were collected from the Institute of Geographic Sciences and Resources of the Chinese Academy of Sciences (http://www.resdc.cn/), which provides the LULC maps of China for every 5 years beginning in 1980. Harmonized World Soil Database (HWSD) v1.1 soil data of the year 1995 were utilized to extract the soil groups for the two study areas.
3. Methods
The framework of the proposed Ia-estimation method and the assessment method is shown in Fig. 3.
Framework of the Ia-estimation method and the assessment method adopted in this study.
Citation: Journal of Hydrometeorology 21, 5; 10.1175/JHM-D-19-0202.1
a. Collection of Ia and its driving factors
1) Calculation of Ia/S
The procedures for determining the Ia/S, namely, the λ value, for each rainfall–runoff event are as follows.
Intuitively, S can be acquired using the rainfall (P), the direct runoff (Q), and the initial abstraction (Ia). The first curial step is separating the baseflow to obtain the direct runoff hydrograph. Thus, synchronized hourly rainfall and runoff data were required. The rainfall depth when direct runoff began was taken as Ia. The start time of direct runoff is defined as the time when the gradient of direct runoff hydrograph changes abruptly (Fischer et al. 2016). After that, with the known values of Q, Ia, and P, S can be derived using Eq. (6). Finally, λ for each rainfall–runoff event was obtained by calculating Ia/S.
The filter coefficient β, generally ranging from 0.990 to 0.999, affects the baseflow separation. If a low-filter coefficient was applied, the shape of filtered baseflow more closely followed the hydrograph and became increasingly more muted with increasing β. Figure 4 illustrates the sensitivity of β varied between 0.990 and 0.999 for the Zijingguan watershed during 1958–59. Eventually, a filter coefficient β of 0.995 was selected for both of the two study areas.
Sensitivity of β varied between 0.990 and 0.999 for the Zijingguan watershed.
Citation: Journal of Hydrometeorology 21, 5; 10.1175/JHM-D-19-0202.1
2) Identification of the driving factors affecting Ia
Hence, the MIC method could play a role in judging the dependence relationship between Ia and its driving factors. The range of the MIC is also between 0 and 1. The higher the absolute value of the PCC and the MIC, the greater the correlation between Ia and its driving factors.
The analytical hierarchy process (AHP), one of the most widely used tools for decision-making (Saaty 1977), is employed to arrange the factors based on the value of PCC and MIC. Four main procedures were involved in the AHP process. First, a hierarchy structure is built, namely, PCC and MIC were chosen as criterion layers. Then, according to the value of PCC and MIC, the pairwise comparisons between 14 potential driving factors were carried out to develop the comparison matrices. After that, the local and global weights can be derived by adopting an eigenvector method. The last step is to apply a consistency check.
b. Development of artificial neural network
1) Description of artificial neural network
The ANN model is adopted as an efficient tool to reveal nonlinear relationships between inputs and outputs. The ANN model is commonly composed of an input layer, a hidden layer, and an output layer. Figure 5 displays the structure of the three-layer feed-forward type of ANN used in this study.
Schematic diagram of artificial neural network employed in this study.
Citation: Journal of Hydrometeorology 21, 5; 10.1175/JHM-D-19-0202.1
2) Model development
Flowchart of the ANN model developed in this study.
Citation: Journal of Hydrometeorology 21, 5; 10.1175/JHM-D-19-0202.1
The input data are usually divided into training datasets and validation datasets. However, when the amount of source data is small, the number of validation datasets becomes even smaller, which leads to great differences in the evaluation results on the validation datasets. The evaluation results are thus not reliable. Consequently, the K-fold cross validation method (Ling et al. 2019) was adopted to divide the datasets into training data and validation data. In the process of the training model, K-fold cross validation divides the datasets into K parts. One group of datasets is set as the validation datasets, while the remaining K − 1 parts act as the training datasets. The final evaluation results are the average value of K-fold evaluation scores. In this study, the selected 14 and 10 flood events from four categories in the Zijingguan and Wulongji watersheds, respectively, were utilized as test datasets, which were also applied to build the HEC-HMS model. The corresponding data from the rest rainfall–runoff events were used as training datasets, which were divided into training datasets and validation datasets using the K-fold cross validation method and computed in the ANN model. Note that the selected flood events for building the HEC-HMS model were not used as ANN model training datasets.
The ANN model was implemented using TensorFlow and Keras, from the Python deep learning library (Chollet 2016). A three-layer ANN model was employed, with each layer adopting ReLU as the activation function. To avoid the overfitting problem, the dropout method was utilized in the input and hidden layers. Mean square error and RMSprop were chosen as the loss function and optimizer, respectively. The number of epochs should be set cautiously to prevent overfitting or underfitting. In the training and validation process, the initial value of epochs was set as 100. The number of epochs for the test process is based on the performance of the training and validation evaluation. The different cases, composed of different input factors, were all trained in the ANN model using the same process to explore the most significant factors affecting Ia. After determining the number of driving factors and the well-trained ANN model, the test datasets were utilized to estimate Ia.
3) Performance evaluation metrics
c. HEC-HMS model
The HEC-HMS model, developed by U.S. Army Corps of Engineers, is a physically based and conceptual semidistributed hydrological model. In each subbasin, the parameters should be calibrated according to the land surface conditions and then the rainfall–runoff process could be simulated. The HEC-HMS distributed hydrological model is composed of four main parts: basin model, meteorological model, control specifications and time series model. The rainfall–runoff process could be obtained through four modules: loss, transformation, routing, and baseflow.
1) Model setup
Based on differences in topography and river network shape, the Zijingguan watershed and the Wulongji watershed was divided into 11 subbasins and 29 subbasins adopting HEC-GeoHMS, respectively. The average rainfall of the watershed was estimated using the Thiessen polygon method.
The HEC-HMS model includes 11 loss estimation methods, 7 rainfall–runoff transformation methods, 6 routing methods, and 5 baseflow methods, from which the SCS-CN, SCS unit hydrograph, Muskingum, and recession methods were selected, respectively.
CN is a comprehensive parameter reflecting the characteristics of the watershed before rainfall and is related to the antecedent moisture condition (AMC), slope, vegetation, soil type, land use and land cover of the watershed. Theoretically, the value of CN ranges between 0 and 100. Based on the AMC classes, soil type, and land use and land cover of the study area, we determined the initial value of CN using the National Engineering Handbook (1972).
Lag time is the only parameter to be determined for the SCS unit hydrograph method. Using the average basin slope, the longest flow path and initial CN value, the initial value of lag time can be acquired. The parameters of Muskingum K and X in the routing module and the recession constant in the baseflow module were determined during the calibration process.
As for Ia, three different sets of values estimated by different methods were employed to run the HEC-HMS model in this paper. In scenario one, the fixed median value of Ia/S, determined by analyzing rainfall–runoff events in the study area, is taken as the HEC-HMS model input. The median value of Ia/S is normally adopted as a representative value for the study area in hydrological models (Shi et al. 2009; Fu et al. 2011). Scenario two utilizes the ANN-estimated Ia, which was extracted from the GLDAS datasets and considered the antecedent watershed conditions. For scenario three, HEC-HMS model flood simulations with statistical Ia were carried out. Given that the statistical Ia is obtained from the hydrograph analysis of each flood event, the statistical Ia is considered to be the approximate true value of Ia. Under these circumstances, for parameter Ia, no calibration process is carried out, as Ia is estimated for each flood event based on the hydrograph analysis or the proposed ANN model. Note that other parameters of the HEC-HMS model were calibrated and validated under scenario one to demonstrate the reliability of the model. Specifically, eight events in the Zijingguan watershed were applied for calibration, and six events were employed for validation. In the Wulongji watershed, the number of events for performing calibration and validation was six and four, respectively. After fixing the optimal calibrated parameters of CN, lag time, Muskingum K, X and recession constant in the HEC-HMS model, the value of Ia was adjusted to another corresponding two scenarios to reveal the effects of the variable Ia values on flood simulation. Comparisons between these three scenarios were performed based on the simulation results of flood events.
2) Sensitivity analysis
4. Results
a. Statistical values of Ia and its driving factors
1) Ia/S for rainfall–runoff events
The results illustrated that Ia/S varies from different events and different watersheds. The calculated Ia/S for 50 rainfall–runoff events in the Zijingguan watershed ranges from 0.001 to 0.48, with an average value of 0.12 and a median of 0.046. For the Wulongji watershed, the average value of Ia/S is 0.058, with a median of 0.015. Over 75% of the Ia/S values are less than 0.2. Therefore, the results indicated that the traditional Ia/S value of 0.2 is overestimated in these two study areas. In this study, the median value of Ia/S, namely, 0.046 and 0.015 for the Zijingguan and the Wulongji watershed, respectively, were taken as the representative value, that is, the input value of Ia in the HEC-HMS model under scenario one.
2) Identification of factors affecting Ia
The PCC and MIC values between the Ia and its potential driving factors (listed in Table 1) were calculated for the two study areas, as shown in Fig. 7. The results presented that the degree of correlation between each factor and Ia varies greatly from different methods and watersheds. An absolute value of the PCC below 0.2 is considered to be a weak correlation. The MIC values of all the factors are above 0.2. It is obvious that there is a strong correlation between Ia and some potential factors, such as API, MRI and ARI. To identify the most significant driving factors, AHP was adopted to sort the potential factors to train the optimal ANN model, as shown in Table 2.
PCC and MIC values between Ia and 14 potential driving factors (abbreviations: ZJG, Zijingguan watershed; WLJ, Wulongji watershed).
Citation: Journal of Hydrometeorology 21, 5; 10.1175/JHM-D-19-0202.1
The AHP weights of 14 potential driving factors for the two watersheds.
Based on the order of each factor, different cases were designed, and then the ANN model was computed for different cases with different input factors. Case 1 consists of the first five high correlation factors of Ia, and the new factor was added in turn to the new cases according to the AHP results. Consequently, total 10 cases were designed to train the ANN model. By evaluating the performance, the most significant factors influencing Ia were determined. The evaluations of different cases in ANN model are listed in Table 3.
Evaluation of ANN model under different cases. Abbreviations: TR, training process; VA, validation process. Bold indicates the best results.
Overall, it can be seen that the evaluation of the ANN model training process outperformed that of the validation process in most cases. Intuitively, case 8 in the Zijingguan watershed, which is composed of API, MRI, SM0_10, SM40_100, RZSM, SM10_40, EV, ARI, ID, PET, CWE, and TR (a total of 12 factors), is considered to be the best fitness. For the Wulongji watershed, case 4 including API, EV, TR, SM100_200, MRI, SM0_10, RZSM, and SM10_40 (a total of 8 factors), is the optimal combination.
b. ANN estimation results of Ia
Taking the Zijingguan watershed as an example, Fig. 8a illustrates the performance plots of the ANN model in training and validation process under the best fitness case 8 for four statistical indicators. It is clear that when epochs are equal to 55, four statistical indicators provide the best fitness. Otherwise, an overfitting problem arises, that is, the evaluation results on the validation process become worse. Accordingly, during the test process, we set epochs equal to 55.
ANN estimation of Ia. (a) Performance plots of ANN model in training and validation process under the best fitness case 8 for four statistics indicators in the Zijingguan watershed; (b) correlation plot of the statistical Ia and the ANN-estimated Ia for the two study areas.
Citation: Journal of Hydrometeorology 21, 5; 10.1175/JHM-D-19-0202.1
The correlation plot of the statistical Ia and the ANN-estimated Ia for flood events in the two watersheds (Fig. 8b) demonstrates that scattered points are evenly distributed on both sides of the trend line. The correlation coefficient (CR) between statistical Ia and ANN-estimated Ia is more than 0.7 in the two study areas, and the coefficient of determination (R2) exceeds 0.6, reaching 0.83 in the Zijingguan watershed, which indicates that although ANN model underestimates or overestimates in some cases, ANN model could capture the relationship between statistical Ia and estimated Ia in general.
c. Land use and land cover change analysis
Five categories were made for LULC maps, namely, water, forest, agricultural land, grassland, and urban areas. Change analysis was performed by calculating the areas of different land cover types in 1980 for the Zijingguan watershed (1992 for the Wulongji watershed) and its corresponding areas in 2015 for the Zijingguan watershed (2014 for the Wulongji watershed), as shown in Fig. 9.
LULC change analysis for the two study areas. LULC map for the Zijingguan watershed in (a) 1980 and (b) 2015, and its corresponding LULC classes area percentage pie chart of (c) 1980 and (e) 2015; LULC map for the Wulongji watershed in (f) 1992 and (g) 2014, and its corresponding LULC classes area percentage pie chart of (h) 1992 and (j) 2014; (d) LULC change during 1980–2015 in the Zijingguan watershed; (i) LULC change during 1992–2014 in the Wulongji watershed.
Citation: Journal of Hydrometeorology 21, 5; 10.1175/JHM-D-19-0202.1
For the Zijingguan watershed, there was an increase in forest and urban areas, followed by a decrease in agricultural land and grassland during 1980–2015. However, the water area basically remained unchanged. The largest change in LULC in the Zijingguan watershed was concentrated on the conversion between forest and grassland. Li and Feng (2011) simulated the impact of the change in LULC on floods in the Zijingguan watershed during 1980–2000. The results indicated that the mutual transformation among the three land use types of agricultural land, forest and grassland would not cause dramatic changes in flood peak and flood volume.
In this study, a total of 14 flood events in the Zijingguan watershed were selected to explore the effect of LULC change on discharge. The CN values in the HEC-HMS model for 1980 and 2015 land use conditions were determined according to the LULC and the soil type, and the other parameters remained unchanged. The flood simulation results, as shown in Table 4, indicated that the flood peak and depth decreased slightly, with a reduction percentage of <3%, as forest cover increased from 1980 to 2015. The effects of LULC change were relatively small for large flood events (T > 10 yr), with a percentage of approximately 1%, which is consistent with the results of numerous studies (Bathurst et al. 2011; Birkinshaw et al. 2010; Bathurst et al. 2016).
Comparison of the percentage change in discharge values for the Zijingguan watershed under two different LULC scenarios.
Additionally, the variation in CN values for the whole watershed under two different LULC scenarios was analyzed, and the values fluctuated from 59.3 to 58.4 during the period of 1980–2015. As a result, the flood slightly decreased due to the decrease in CN values. The possible reason lies in that the LULC of the Zijingguan watershed was mainly concentrated in the conversion between forest and grassland according to the LULC analysis. However, the CN values of these two land use types are similar. In the NEH-4 table (SCS 1956), the CN values for forest are slightly lower than those for grassland. Thus, the increase in forest and decrease in grassland led to a decrease in CN values. Although the urban area, regarded as the primary factor leading to the significant change in flood peak and volume (Sanyal et al. 2014; Younis and Ammar 2018; Koneti et al. 2018), expanded, the CN values of the whole watershed still decreased.
In addition to the area of land use change, there are other factors affecting flood generation. Bathurst et al. (2016) illustrated that the extent to which changes in forest cover can alter flood peak discharges depends on the proportion of the catchment affected and on the location of the change in the catchment. Generally, the change in forest cover must apply to 20%–30% of the catchment area to affect the hydrological response. In some cases, the effects of forest cover change would become attenuated on a larger scale due to nonuniform rainfall or a greater heterogeneity of land use (Birkinshaw et al. 2010). Additionally, most of the selected floods in the Zijingguan watershed occurred before 1995, so the effect of LULC on discharge was even less obvious.
For the Wulongji watershed, it can be found that there was a slight increase in grassland, urban areas and water area from 1992 to 2014, while the area of agricultural land and forest decreased. All the change percentages are within 1%. Thus, the LULC change in the Zijingguan and Wulongji watersheds had a small impact on the flood simulation. In this study, the LULC maps and soil maps of 1995 were used to generate CN values as the initial input and then calibrated to obtain the optimal CN in HEC-HMS model.
d. Sensitivity analysis of the HEC-HMS model
Given that the model structure is determined, sensitivity analysis was only performed for two flood events occurring in 1963 and 1975 in the Zijingguan watershed to test the influence of flood magnitude on Ia. The maximum peak discharge in 1963 and 1975 were 4490 and 139 m3 s−1, respectively, which represents floods of different magnitudes. The sensitivity of six parameters for the HEC-HMS model was calculated using the MMS method. The value of the parameters varied from the optimal value to 50% of the optimal value with an increment step of 10%. The impacts of the six parameters on flood peak, flood depth, and flood peak appearance time were studied.
The results illustrated that the sensitivity of parameters differed for different flood characteristics and different flood magnitudes. With respect to the flood peak of the 1963 flood event, CN was the most sensitive parameter, followed by Muskingum K and Ia. For the flood depth of the 1963 flood event, Ia was the second most sensitive parameter, following CN. Ia had no impact on the flood peak appearance time of the 1963 flood event, and the most significant parameter was lag time. With respect to the flood peak and flood depth of the 1975 flood event, Ia ranked second, following CN. In addition, Ia affected the flood peak appearance time of the 1975 flood event. The results indicated that Ia was basically the most sensitive parameter, except for CN, in flood events of different magnitudes. Moreover, Ia had a higher impact on flood events of lesser magnitude.
e. Comparison of the HEC-HMS model under three scenarios
The HEC-HMS model was computed under three scenarios. Scenario one computes the HEC-HMS model with the fixed median value of Ia/S, which is obtained by statistical analysis of rainfall–runoff events. The second scenario takes ANN-estimated Ia as the HEC-HMS model parameters, whereas the third scenario applies statistical Ia as the HEC-HMS model input. The simulations of the HEC-HMS model under these three scenarios are shown in Fig. 10. The performance of the HEC-HMS model under three scenarios are evaluated with NSE and the relative error (RE) of flood peak and flood depth, as listed in Table 5.
Observed and simulated hydrographs for total 24 flood events with ANN-estimated Ia, statistical Ia, and the median Ia/S at calibration, validation stage in the two study areas (a) Zijingguan watershed and (b) Wulongji watershed.
Citation: Journal of Hydrometeorology 21, 5; 10.1175/JHM-D-19-0202.1
HEC-HMS model simulation for NSE and RE of flood peak and flood depth under three scenarios. Abbreviations: ZJG, Zijingguan watershed; WLJ, Wulongji watershed; CA, calibration; VA, validation; Obs., observed value; Sim., simulated value; Sta., statistical; Med., median; RE, relative error; and NSE, Nash–Sutcliffe efficiency coefficient.
From Fig. 10, it can be clearly observed that there is a dramatic deviation between the observed hydrograph and the simulated hydrograph when statistical median Ia/S is adopted for flood events 1, 2, 7, 9, and 14 in the Zijingguan watershed, and flood events 1, 2, 3, 4, 7, and 8 in the Wulongji watershed. The RE of flood peak or flood depth for these flood events exceeds 20%, which fails to meet the accuracy requirement.
In contrast, in more than half of the flood simulation results, employing statistical Ia as the HEC-HMS model input gives satisfactory results. For total 24 flood events in the two study areas, the number of flood events with the smallest RE of flood peak, flood depth and the best NSE accounts for 50% under this scenario. Hence, the simulation under scenario three is proved more reliable in accurate prediction of flood discharge.
Meanwhile, the results indicate that the number of flood events simulation under scenario two with the smaller RE of flood peak, flood depth and better NSE is twice of that of scenario one. Accordingly, the HEC-HMS model built with ANN-estimated Ia outperforms the median Ia/S value. Over 60% of flood events, the RE of flood peak and flood depth simulated by ANN-estimated Ia are smaller than those of the scenario one. Furthermore, NSE and RE of flood peak and flood depth of five flood events in the Zijingguan watershed (events 4, 5, 6, 9, 11) and six flood events in the Wulongji watershed (events 2, 3, 4, 5, 8, 10) under scenario two demonstrates better fitness than scenario one. Additionally, as shown in Table 5, the average RE of flood peak and flood depth for total 24 flood events under three scenarios are 8.9% (statistical Ia), 9.2% (ANN-estimated Ia), 18.0% (median Ia/S), and 12.6%, 14.8%, 20.3%, respectively. In particular, the average RE of flood peak with median Ia/S is almost twice of that of ANN-estimated Ia, and a deviation of approximately 10% can be found for the average RE of flood depth between these two scenarios. In contrast, the difference between statistical Ia and ANN-estimated Ia for the average RE of flood peak and flood depth is all within 2.2%.
Consequently, compared with the median Ia/S as input, the error of flood peak and flood depth between the observed and simulated values can be reduced with ANN-estimated Ia in the HEC-HMS model. Although the ANN model underestimates the statistical Ia of flood event 4 (2 August 1963) in the Zijingguan watershed, the flood event with large magnitude is not sensitive to Ia. Therefore, the accuracy of flood simulation from flood event 4 (2 August 1963) is not affected.
5. Discussion
Ia is a sensitive parameter in hydrological models and is difficult to obtain due to a lack of observed data. Given that the watershed antecedent wetness conditions and rainfall characteristics are diverse for each flood event, Ia varies from different flood events. Consequently, in the event-based hydrological model, Ia must be calibrated for each event. However, for every flood event, the calibration of model parameters to find a set of parameters that make simulated flood events fit the observed flood events well is time consuming. Moreover, the optimal parameters, which are explored during the automatic calibration process, often lose their physical significance.
Several studies have revealed that the adjustment of Ia/S to 0.05 from the traditional value of 0.20 in the SCS-CN method can produce better estimates of runoff (Hawkins et al. 2002; Shi et al. 2009; Fu et al. 2011; Noori et al. 2012; Hawkins et al. 2019). Noori et al. (2012) have also obtained superior results with Ia/S = 0.05 in a study exploring the effect of the variation of Ia/S on simulating urbanization impacts with the HEC-HMS model. Hence, in this paper, taking the temporal variations of Ia into consideration, the factors influencing Ia are extracted from observed rainfall–runoff events and GLDAS datasets to estimate Ia for each flood event. A hydrological model is constructed with varying Ia parameters for each flood event, depending on antecedent wetness conditions and rainfall characteristics. In addition, the calibration of model parameters for Ia can be omitted, which saves time and effort.
In the proposed Ia-estimation method, great significance should be attached to the prediction accuracy of the ANN model. Since the two study areas are in subhumid and semiarid area, there is not enough rainfall in the flood season. Consequently, insufficient rainfall–runoff events data were collected to build the ANN model, which might affect the accuracy of Ia estimation. However, despite that ANN model underestimates or overestimates Ia in some cases, it brings about little influence on the results of flood simulation. The most possible reason lies in that the sensitivity of Ia in the HEC-HMS model varies from different flood events. For instance, the flood event with large magnitude is not sensitive to Ia. In general, the accuracy of hydrological model simulation applying ANN-estimated Ia can meet the requirements.
The dominant driving factors affecting Ia vary from different river basins, while the antecedent precipitation index (API) is the most influential factor on Ia in general. Maximum rainfall intensity (MRI) also greatly affects Ia, both ranking among the top five influencing factors of Ia in these two watersheds. For the Zijingguan watershed, the API, MRI, ARI, and soil moisture ranging from 0 to 100 cm are the most important factors affecting Ia, which proves that rainfall characteristics and surface soil moisture are crucial to Ia for small watersheds. Nevertheless, in the Wulongji watershed, evapotranspiration lists among the top three potential driving factors of Ia.
The possible reason is that the dominant driving factors of Ia in different watersheds may be related to the watershed characteristics as well as rainfall properties. The Zijingguan watershed is located in the mountain area of the Daqing River basin, with an average watershed slope reaching 27.2‰, which is almost 1.5 times that of the Wulongji watershed. In addition, the average MRI value for a total of 64 rainfall–runoff events in the Zijingguan watershed was 9.2 mm h−1, which was more than twice that of the Wulongji watershed. Consequently, the flood in the Zijingguan watershed rises rapidly due to the high rainfall intensity and the high basin slope. As a result, according to the definition of Ia, the duration of the beginning of rainfall to the start of runoff generation, namely, the Ia generation time, is relatively short in the Zijingguan watershed. Through statistical analysis from all selected rainfall–runoff events for the two watersheds, the Ia generation duration was only 10.2 h in the Zijingguan watershed, which was one-fifth of that in the Wulongji watershed. In this paper, evapotranspiration data are extracted only during the Ia generation duration for Ia impact analysis. Therefore, in this short Ia generation duration for the Zijingguan watershed, evapotranspiration may have little effect on Ia, while rainfall intensity is the dominant factor in the smaller-scale watershed. In contrast, for the Wulongji watershed, the effect of evapotranspiration on Ia cannot be neglected in the duration of Ia generation. Accordingly, to predict Ia more accurately, the identification of the potential driving factors affecting Ia is also significant.
The biggest superiority of ANN model is that as long as there is sufficient rainfall–runoff data to train ANN in a given river basin, the predicted Ia can be obtained based on the antecedent watershed conditions of each flood event, so as to provide a more reliable and physically based Ia value for the construction of watershed hydrological model. In future, the spatial characteristics of antecedent wetness conditions in the subbasins should be considered to improve the accuracy of Ia estimation for the hydrological model. Furthermore, the proposed ANN estimation method only applied in two study areas, a small watershed with 1760 km2 and a large watershed with 30 100 km2, more verification should be performed on the basis of sufficient available data in more river basins around world in the near future.
6. Conclusions
This paper investigates the potential of soil moisture and evaporation data from GLDAS-Noah datasets for estimating Ia. The motivation of the study was to propose the new Ia estimation methods for hydrological models and prove its feasibility. The main conclusions of this paper are drawn as follows.
Ia/S varies from different events and different watersheds. For the 50 rainfall–runoff events over the period from 1956 to 2014 in the Zijingguan watershed, Ia/S ranges from 0.001 to 0.48, with an average value of 0.12 and a median of 0.046. For the Wulongij watersheds, the average value of Ia/S is 0.058, with a median of 0.015. Over 75% of the Ia/S values are less than 0.2 in the two study areas.
The driving factors affecting Ia are different in the two watersheds. Noticeably, antecedent precipitation index (API) is the most significant factor of Ia. Rainfall characteristics and surface soil moisture in small watershed are the main factors of Ia, while evaporation in large watershed cannot be ignored.
Among the three scenarios, employing statistical Ia as the HEC-HMS model input demonstrates the best performance, where the simulated flood peak and flood depth fitted the observed well. Although the derivation between simulated hydrograph with ANN-estimated Ia and observed hydrograph can be found in the modeling results, the HEC-HMS model built with ANN-estimated Ia outperforms the tradition methods, namely, the median value of Ia/S. Over 60% of flood events in two study areas, both the RE of flood peak and flood depth simulated by ANN-estimated Ia performed better than those of applying median Ia/S in the HEC-HMS model. The proposed Ia estimation method can meet accuracy requirements and reduce parameter calibration work in hydrological modeling.
Ia for each flood event is derived using the ANN estimation method proposed in this paper and serves as the input parameter in the hydrological model. The temporal variations of soil moisture, evaporation and other antecedent conditions of the watershed are taken into account, which makes the estimation of Ia physically based. Hence, this method saves time and effort in calibrating parameters in the hydrological model.
Acknowledgments
This research is supported by the National Key Research and Development Program of China (2018YFC0407902) and the National Natural Science Foundation of China (51779165). The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. GLDAS-Noah v2.0 datasets are available from https://giovanni.gsfc.nasa.gov/.
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