Event-based hydrological models are extensively adopted for the estimation of design floods and in operational flood forecasting frameworks. However, an accurate estimation of the initial hydrologic condition (IHC) is essential in enhancing the predictive capability of an event-based hydrological model. Hence, in this study, IHCs of an event-based conceptual model are estimated using two different methods: (1) assimilation of observed variables such as streamflow and soil moisture using an ensemble Kalman filter and (2) states obtained from the continuous model calibrated using four different calibration metrics. The observed flood events at the Jagdalpur catchment are simulated using a conceptual hydrologic model setup at two spatial resolutions (lumped and semi-distributed). The results of the study demonstrate that IHCs estimated by the continuous models perform better than those obtained through data assimilation. The performance of semi-distributed event-based models was found to be outperforming their lumped counterparts demonstrating the advantage of increased model resolution. The states obtained from the continuous models calibrated using Nash–Sutcliffe Efficiency (NSE) are performing well in initialising the event-based models. The median efficiency of the semi-distributed event-based model (based on states from the NSE calibrated continuous model) is 0.91 and 0.77 during calibration and validation periods, respectively.

  • Methods to estimate the initial hydrologic condition (IHC) to initialise event-based models were evaluated.

  • Streamflow assimilation in both lumped and semi-distributed models led to improved simulations.

  • Soil moisture assimilation yielded slightly better predictions in the semi-distributed model.

  • Semi-distributed event-based model, initialised by IHCs extracted from the corresponding continuous model, is outperforming other models.

Flood is one of the most destructive natural disasters around the world that can cause catastrophic impacts on day-to-day operations (Alfieri et al. 2017; Manohar Reddy & Ray 2023). Real-time flood forecasting systems with sufficient lead time are considered as the most efficient and effective way to mitigate flood risk (Yatheendradas et al. 2008). Flood forecasting based on the integration of meteorological and hydrological models has shown markedly better improvement in recent times due to the advancements in computational power, remote-sensing based observations, and improved understanding of hydrological processes (Das et al. 2022). In the context of a flood modelling framework, event-based models are often considered as sound alternatives to continuous models as they are easier to calibrate and require only data at the event scale (Tramblay et al. 2012). However, the efficiency of both continuous and event-based hydrologic predictions, irrespective of the model structure, is highly influenced by the optimal simulation of model states/initial hydrological conditions (IHCs) (often considered as soil moisture) within the modelled watershed (Crow & Ryu 2009; Loizu et al. 2018). Consequently, multitudes of modelling efforts were reported so far on the accurate estimation of the magnitude of floods, particularly on minimising the uncertainties associated with the estimation of IHCs (Brocca et al. 2008, 2009, 2010; Berthet et al. 2009; Tramblay et al. 2010; Alvarez-Garreton et al. 2014, 2015).

In general, a separate method is needed to estimate the initial states of the event-based models that are separately estimated by establishing relationships between IHC and external predictors. For instance, Antecedent Precipitation Index (API), computed by cumulating rainfall values of preceding days, is often used as a predictor in models based on the Soil Conservation Service Curve Number method (SCS-CN). Various predictors were reported so far in literature to accurately estimate the IHC for event-based models, such as piezometric levels (Coustau et al. 2012), baseflow (Franchini et al. 1996; Longobardi & Villani 2003), Antecedent Discharge Index (Tramblay et al. 2012), outputs from continuous models (Huang et al. 2016; Yao et al. 2019; Hegdahl et al. 2020), and in situ or remote-sensing based observables (Meng et al. 2017; Bahramian et al. 2021). Real-time measurements or climatology-based values can be directly used for updating if the simulated model states reliably represent the observable model states (Berthet et al. 2009). Moreover, it is also worth noting that the relationship between the model states and the external predictors is determined by the model structure and uncertainty in the input data.

Data assimilation (DA) techniques are widely employed to reduce the uncertainties associated with inputs, model states, and output variables (McLaughlin 2002). DA updates the model states by optimally combining the information from observations and model simulations, leading to improved estimates of the initial states of a hydrological model (Sun et al. 2016). Observed datasets used to update the states of a hydrological model include streamflow (Seo et al. 2003), soil moisture (Brocca et al. 2010), snow-covered area, snow water equivalent (Andreadis & Lettenmaier 2006; Clark et al. 2006), and satellite observations of soil moisture and discharge (Andreadis et al. 2007). Discharge data is the most frequently assimilated variable since it contains the collective information of all other hydrological states (Clark et al. 2008). However, due to the difficulty in obtaining observations in real-time, many studies have used satellite-based soil moisture for DA (Alvarez-Garreton et al. 2015; Baguis & Roulin 2017; Abbaszadeh et al. 2020). In the majority of DA studies, soil moisture observations are rescaled into the model space prior to assimilation, which influences the assimilation efficiency (Crow & Van Loon 2006; Crow & Reichle 2008). For instance, a poor rescaling method coupled with incorrect assumptions of the observational and model structural errors deteriorates the performance of DA (Tugrul Yilmaz & Crow 2013).

A recent study by Nayak et al. (2021) showed that the efficiency of DA in reliable simulation of streamflow depends on the model structure. Various model structures are available based on runoff generation mechanisms such as physics-based, conceptual, and data-driven, and based on the spatial resolution of the model such as lumped, semi-distributed, and distributed. However, in real-time operational applications, a trade-off between input data, model structural complexities, and computation costs is necessary to issue reliable and timely flood warnings (Butts et al. 2004). Although physics-based, fully distributed models account for the spatial heterogeneity of meteorological forcing and physical features within the basin leading to better simulations, they are data intensive and demand more computational resources (Young 2002). On the contrary, the utilisation of conceptual hydrologic models (CHMs) in operational streamflow forecasting has been amplified over the past few years because their computational efficiency and simplicity proved their effectiveness in streamflow forecasting (Hapuarachchi et al. 2011). Many of the DA studies were reported on the lumped versions of conceptual hydrological models and only a few were reported on semi-distributed continuous models (Berthet et al. 2009; Pathiraja et al. 2012; Alvarez-Garreton et al. 2014, 2015; Loizu et al. 2018). Previous studies reported that accounting for spatial variability in CHMs enhances model simulations (Das et al. 2008; De Lavenne et al. 2016). Hence, it is essential to understand the relevance of DA-estimated initial states in improving the performance of an event-based conceptual hydrological model.

In scenarios where the initial states for event-based models are estimated through their continuous counterparts, the choice of calibration metrics plays a key role. This is due to the fact that the commonly used calibration objective functions have the tendency to emphasise on particular flow segments of a hydrograph and this bias gets translated into the model states simulated by the continuous models (Mizukami et al. 2019). Hence, this study is intended to assess the performance of a lumped and a semi-distributed event-based conceptual model with initial conditions estimated using DA and their continuous counterparts corresponding continuous models calibrated using different calibration objective functions.

Study area

The Jagdalpur catchment, a sub-basin of the Godavari River Basin in India, is chosen as the study watershed in this study. The catchment of Jagdalpur was delineated from the flood forecasting stations at Jagdalpur, resulting in a catchment area of 7,382 km2. Figure 1 illustrates the location map of the study watershed, including its elevation and the stream network.
Figure 1

Location map of Jagdalpur watershed with detailing of stream network and elevation.

Figure 1

Location map of Jagdalpur watershed with detailing of stream network and elevation.

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Hydrometeorological data

The daily streamflow data at Jagdalpur, from 1965 to 2018, is available at the India-WRIS portal. The observed flood events are separated from the streamflow data using the warning level obtained from the Central Water Commission appraisal report on Flood Forecasting and Warning Network Performance (CWC 2018). In this study, the daily gridded meteorological forcing datasets are obtained from India Meteorological Department (IMD) at a spatial resolution of 0.25° × 0.25° (precipitation) and 1° × 1° (minimum and maximum temperature) (Srivastava et al. 2009; Pai et al. 2014). For assimilation of soil moisture, root zone soil moisture is obtained from the Global Land Data Assimilation System (GLDAS), Catchment Land Surface Model, V2.0, where the data are available from 1948 to 2014.

Hydrological model

In this study, two versions (lumped and semi-distributed) of modèle du Génie Rural à 4 paramètres Journalier (GR4J) were used to simulate the flood events at Jagdalpur (Table 1). GR4J, originally developed by Perrin et al. (2003), is a soil moisture accounting based daily lumped conceptual rainfall-runoff model with four parameters to be calibrated. The semi-distributed version of GR4J utilises the lumped model to simulate streamflow at each sub-basin, using mean areal precipitation, evapotranspiration, and temperature. The Muskingum routing method is then used to route the simulated streamflow from each sub-basin outlet to the catchment outlet. This requires two parameters, and x, where K is determined by the reach length () and wave celerity (), and x is a dimensionless weighting factor. The wave celerity is considered constant across all sub-basins to reduce parameter dimensionality. The study area is divided into four sub-basins, and a total of 21 parameters (four parameters for each sub-basin and one constant for wave celerity) need to be optimised. Figure 2 provides a schematic representation of both the lumped and semi-distributed versions of the GR4J model.
Table 1

Description and ranges of parameters to be calibrated in the lumped and semi-distributed versions of the GR4J model

ParameterDescriptionRange
Semi-distributed GR4J GR4J XProduction reservoir capacity (mm) 1 to 1,500 
XInter-catchment exchange coefficient (mm/day) −10 to 5 
XRouting store capacity (mm) 1 to 500 
XUnit hydrograph time constant (days) 0.5 to 4 
Muskingum routing  Average wave celerity in the stream network in m/s 0 to 5 
 Dimensionless weighting factor 0 to 0.5 
ParameterDescriptionRange
Semi-distributed GR4J GR4J XProduction reservoir capacity (mm) 1 to 1,500 
XInter-catchment exchange coefficient (mm/day) −10 to 5 
XRouting store capacity (mm) 1 to 500 
XUnit hydrograph time constant (days) 0.5 to 4 
Muskingum routing  Average wave celerity in the stream network in m/s 0 to 5 
 Dimensionless weighting factor 0 to 0.5 
Figure 2

Schematic representation of lumped GR4J model structure (left) along with the semi-distributed version of GR4J (right), state variables, and parameters of the model.

Figure 2

Schematic representation of lumped GR4J model structure (left) along with the semi-distributed version of GR4J (right), state variables, and parameters of the model.

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Implementation of DA

Ensemble Kalman filter (EnKF)

A background matrix () of dimensions is defined in Equation (1), in which represents the number of state variables of the hydrological model and denotes the number of ensemble members.
(1)
where represents the model state vectors for each individual ensemble member in prior to updating the states. The ensemble mean is given by Equation (2):
(2)
The anomaly for the ith ensemble member is computed as , and the ensemble of anomalies () is computed as given in Equation (3):
(3)
The ensemble anomalies are used to estimate the model error covariance using Equation (4):
(4)
The equation to update the model states using the model error covariance is given in Equation (5):
(5)
where

In Equation (4), represents the analysis of model states posterior to the update, is an operator to covert model states to the observational space with dimensions , represents the vector of observations with dimensions ( denotes the number of observations), K represents the Kalman gain, and R is the observation error covariance matrix with dimensions . It should be noted that each ensemble member is updated individually using Equation (5). In general, in the implementation of EnKF, each of the ensemble member is updated using vectors of observations. The values of for each ensemble member are used to generate vectors of observations by sampling from a distribution with observations as mean and R as variance.

Bias correction of the GLDAS root zone soil moisture data

Model simulated soil moisture is commonly utilised to correct the bias in GLDAS root zone soil moisture prior to assimilation, given that both datasets do not accurately represent the true conditions. To address this, a straightforward mean-variance approach is employed, which demonstrates comparable performance to more intricate techniques. The simulated soil moisture is used to correct the raw values of GLDAS root zone soil moisture using Equation (6):
(6)
where denotes bias-corrected root zone soil moisture, and represents the average value of simulated soil moisture and GLDAS root zone soil moisture, respectively, and and are their respective standard deviations.

Forecast error

To address input uncertainty, meteorological datasets such as precipitation and evapotranspiration are stochastically perturbed. To achieve this, Clark et al. (2008) recommend perturbing daily meteorological observations using multiplicative stochastic noise at each time step. A first-order autoregressive model is employed to ensure the temporal correlation of time-variant forcings and physical consistency. To generate 100 ensemble meteorological forcing datasets, a temporal decorrelation length of 1 day and 2 days were used for rainfall and evapotranspiration, respectively, with a fractional error parameter set to 0.65. For a more detailed explanation of the perturbation method, refer to Clark et al. (2008).

Observation error

In addition to ensuring an optimal ensemble spread to represent the model uncertainties, it is also important to estimate the observation error for enhanced assimilation. In this study, a normally distributed random noise with zero mean and a variance of is used as observation error. The random noise is formulated as a function of observations as given in Equation (7):
(7)

Following the study by Piazzi et al. (2021), the error parameter was set to 0.1. To prevent the underestimation of error variances at lower values of observations, the minimum threshold for defining the error variance was assumed to be the 10th percentile value of observations . Following Thirel et al. (2010), the variance is evaluated proportionally to for observed values below .

Model calibration and validation

In this study, the lumped and semi-distributed GR4J models are calibrated during the period 1970–1980 and validated during the period 1981–1993, with a warmup period from 1967 to 1969. The IHC/initial model states to initiate the event-based GR4J models are obtained from their corresponding calibrated continuous models. To calibrate the continuous models, four calibration objective functions were used, namely, Nash–Sutcliffe Efficiency (NSE) (Nash & Sutcliffe 1970), NSE of logarithmic transformed flows (logNSE) (Oudin et al. 2006), Kling–Gupta Efficiency (KGE) (Gupta et al. 2009), and Fourth root Mean Quadruple Error (R4MS4E) (Baratti et al. 2003). The equations for the chosen calibration objective functions are given in Equations (8)–(11):
(8)
(9)
(10)
(11)
where and denote simulated and observed discharge values at time t, respectively, and T denotes the total number of values, , , and represent the standard deviations of simulated and observed values, respectively, and and represent the mean value of simulated and observed streamflow.
A total of 20 flood events were identified using the flood warning level, with 10 events used for calibration and the other 10 events for validation. The parameters of the event-based models are automatically calibrated using genetic algorithm with NSE as an objective function. For both continuous and event-based models, the population size is set as 100 for a maximum of 2,000 generations, i.e., 200,000 simulations were performed in the calibration of models. A detailed flowchart demonstrating the methodology adopted in this study is given in Figure 3.
Figure 3

Flowchart demonstrating the detailed methodology adopted to evaluate the performance of event-based models under different schemes of estimation of initial hydrologic conditions.

Figure 3

Flowchart demonstrating the detailed methodology adopted to evaluate the performance of event-based models under different schemes of estimation of initial hydrologic conditions.

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Performance evaluation

A set of hydrologically relevant performance evaluation metrics are employed in lieu of single traditional lumped measures to assess the accuracy of simulated hydrographs at all flow segments of the observed hydrograph (Yilmaz et al. 2008; Manikanta & Vema 2022). Four evaluation metrics, namely Fourth Root Mean Quadruple Error (R4MS4E), NSE of logarithmic transformed flows (logNSE), Percentage Bias (PBIAS), and Skill Score (SS), were employed to assess the agreement between observed and simulated hydrographs in terms of peak flow, low flow, water balance, and flow frequencies, respectively. The equations to compute the values of PBIAS and SS are given in Equations (12) and (13):
(12)
(13)
where and are the frequency values of simulated and observed discharge values at ith bin, respectively, and represents the total number of bins. In this study, a bin size of 5 m3/s was used to compare the frequency distributions of observed and simulated streamflow.
The performance of the event-based models in simulating the observed flood hydrographs is evaluated using four metrics namely, Percentage Error in Peak Flow (PEPF), Percentage Error in Timing to Peak (PETP), PBIAS, and NSE given from Equations (14) and (15). In addition, the indicative performance ratings of the chosen metrics are given in Table 2 (Katwal et al. 2021):
(14)
(15)
where denote simulated and observed flood peaks and denote the time taken by simulated and observed flood peaks.
Table 2

Indicative performance ratings of the statistics employed for the evaluation of the event-based model

Performance evaluation measureRangePerformance rating
NSE 0.75–1.00 Very good 
0.65–0.75 Good 
0.50–0.65 Satisfactory 
PBIAS <± 10% Very good 
±10% to ±15% Good 
±15% to ±25% Satisfactory 
PEPF <± 15% Very good 
±15% to ±30% Good 
±30% to ±40% Satisfactory 
PETP <± 10% Very good 
±10% to ±15% Good 
±15% to ±30% Satisfactory 
Performance evaluation measureRangePerformance rating
NSE 0.75–1.00 Very good 
0.65–0.75 Good 
0.50–0.65 Satisfactory 
PBIAS <± 10% Very good 
±10% to ±15% Good 
±15% to ±25% Satisfactory 
PEPF <± 15% Very good 
±15% to ±30% Good 
±30% to ±40% Satisfactory 
PETP <± 10% Very good 
±10% to ±15% Good 
±15% to ±30% Satisfactory 

Performance evaluation of continuous streamflow simulation

The accuracy of the streamflow simulated by the continuous lumped and semi-distributed GR4J models is evaluated using a set of metrics as described in Section 3.4. The performance evaluation metrics for the calibration and validation periods are tabulated in Tables 3 and 4, respectively. From Table 3, it can be noticed that the performance of the R4MS4E calibrated lumped GR4J model is good at simulating the peak flow values. Higher values of logNSE and Skill Score of the lumped GR4J model with streamflow assimilation indicate its better performance in terms of matching the observed flow frequencies and also in terms of simulating the low flows. The PBIAS of the KGE calibrated lumped model is found to be low attributable to the bias factor () in the formulation of KGE. Furthermore, the PBIAS values of the R4MS4E calibrated model show its overestimation bias, whereas the other models slightly underestimate the flows (< −10%). In the case of semi-distributed GR4J, a significant improvement is observed in both open-loop (without assimilation) and assimilated models in terms of all chosen evaluation criteria. The R4MS4E values in semi-distributed GR4J models were reduced by an average of 18.9% in all models, when compared to their lumper counterparts. The PBIAS values of streamflow and soil moisture assimilated models along with NSE and KGE calibrated open-loop models were found to be less than ±5%, whereas logNSE and R4MS4E calibrated models were found to be underestimating and overestimating the flows, respectively. It can also be noticed that the performance of KGE calibrated models in terms of logNSE and Skill Score is low (–0.07 and 0.45) showing its inability to capture low flows. In summary, the performance of the semi-distributed GR4J model with soil moisture assimilation is poor in continuous simulation of streamflow. The semi-distributed GR4J model, with streamflow assimilation and model calibrated with NSE, logNSE, and KGE, comparatively performs well in terms of chosen evaluation criteria in the calibration period. Similar performance can be observed in the validation period for both lumped and semi-distributed GR4J models (Table 4). This indicates better transferability of the calibrated parameters and better assimilation efficiency in the validation period.

Table 3

Performance evaluation metrics computed for observed streamflow and ensemble mean of streamflow simulated using lumped and semi-distributed GR4J model setups with and without data assimilation during the calibration period

R4MS4ElogNSESkill scorePBIAS
Lumped GR4J 
 Soil moisture assimilation 543.47 −0.75 0.65 −12.12 
 Streamflow assimilation 407.5 0.9 0.89 10.61 
 NSE calibrated 345.23 0.74 0.67 −3.08 
 KGE calibrated 360.22 0.66 0.63 0.7 
 logNSE calibrated 402.33 0.87 0.79 −11.79 
 R4MS4E calibrated 312.36 0.7 0.78 40.22 
Semi-distributed GR4J 
 Soil moisture assimilation 426.07 0.06 0.64 5.15 
 Streamflow assimilation 340.38 0.92 0.85 4.55 
 NSE calibrated 238.59 0.87 0.66 −1.41 
 KGE calibrated 291.23 −0.07 0.45 0.73 
 logNSE calibrated 380.12 0.91 0.86 22.58 
 R4MS4E calibrated 251.94 0.73 0.66 29.05 
R4MS4ElogNSESkill scorePBIAS
Lumped GR4J 
 Soil moisture assimilation 543.47 −0.75 0.65 −12.12 
 Streamflow assimilation 407.5 0.9 0.89 10.61 
 NSE calibrated 345.23 0.74 0.67 −3.08 
 KGE calibrated 360.22 0.66 0.63 0.7 
 logNSE calibrated 402.33 0.87 0.79 −11.79 
 R4MS4E calibrated 312.36 0.7 0.78 40.22 
Semi-distributed GR4J 
 Soil moisture assimilation 426.07 0.06 0.64 5.15 
 Streamflow assimilation 340.38 0.92 0.85 4.55 
 NSE calibrated 238.59 0.87 0.66 −1.41 
 KGE calibrated 291.23 −0.07 0.45 0.73 
 logNSE calibrated 380.12 0.91 0.86 22.58 
 R4MS4E calibrated 251.94 0.73 0.66 29.05 

Ideal values for different model settings are bolded.

Table 4

Performance evaluation metrics computed for observed streamflow and ensemble mean of streamflow simulated using lumped and semi-distributed GR4J model setups with and without data assimilation during the validation period

R4MS4ElogNSESkill ScorePBIAS
Lumped GR4J 
 Soil moisture assimilation 438.33 −0.86 0.69 −14.73 
 Streamflow assimilation 337.84 0.9 0.91 10.7 
 NSE calibrated 280 0.83 0.77 −3.34 
 KGE calibrated 325.5 0.78 0.73 0.94 
 logNSE calibrated 363.18 0.85 0.86 −10.24 
 R4MS4E calibrated 256.75 0.6 0.66 45.7 
Semi-distributed GR4J 
 Soil moisture assimilation 341.77 0.36 0.69 17.03 
 Streamflow assimilation 286.17 0.92 0.87 4.75 
 NSE calibrated 224.92 0.89 0.84 4.44 
 KGE calibrated 316.53 0.36 0.53 2.67 
 logNSE calibrated 368.96 0.89 0.75 22.05 
 R4MS4E calibrated 253.09 0.59 0.53 35.62 
R4MS4ElogNSESkill ScorePBIAS
Lumped GR4J 
 Soil moisture assimilation 438.33 −0.86 0.69 −14.73 
 Streamflow assimilation 337.84 0.9 0.91 10.7 
 NSE calibrated 280 0.83 0.77 −3.34 
 KGE calibrated 325.5 0.78 0.73 0.94 
 logNSE calibrated 363.18 0.85 0.86 −10.24 
 R4MS4E calibrated 256.75 0.6 0.66 45.7 
Semi-distributed GR4J 
 Soil moisture assimilation 341.77 0.36 0.69 17.03 
 Streamflow assimilation 286.17 0.92 0.87 4.75 
 NSE calibrated 224.92 0.89 0.84 4.44 
 KGE calibrated 316.53 0.36 0.53 2.67 
 logNSE calibrated 368.96 0.89 0.75 22.05 
 R4MS4E calibrated 253.09 0.59 0.53 35.62 

Ideal values for different model settings are bolded.

Performance evaluation of event-based models

In this study, the performance of the lumped and semi-distributed GR4J models in simulating the historical flood events using the IHC estimated from different methods (through data assimilation and continuous models) has been tested. Berthet et al. (2009) suggested that, for evaluating the predictive performance of event-based models, careful selection of evaluation criteria is essential which emphasises the match between magnitude, volume, and timing observed, as well as the simulated flood hydrographs. In addition to quantitative measures, a visual inspection of the match between observed and simulated flood hydrographs is necessary. Accordingly, four quantitative performance assessment metrics were selected namely, NSE (objective function), Percentage Error in Peak Flow (PEPF), PBIAS, and Percentage Error in Timing to Peak (PETP), to evaluate the simulated flood response.

Performance of event-based models using IHC obtained through DA

The aforementioned statistics are computed for both lumped and semi-distributed event-based models with IHC estimated by assimilating soil moisture and streamflow (Table 5). In Table 5, the statistics are computed for each flood event using the observed flow and ensemble mean of simulations. The median value of the statistics computed for the events used for the calibration and validation periods separately are given in Table 5. The median NSE value of the event-based lumped model based on soil moisture-based data assimilation (SM-DA) and streamflow-based data assimilation (Q-DA) is higher than 0.5 in the calibration period, indicating satisfactory performance. However, the performance of continuous simulations from the lumped model based on SM-DA and Q-DA in simulating the flood hydrographs during the calibration period is found to be low (median NSE < 0.4). In the validation period, the performance of all lumped models based on DA is not satisfactory in terms of the median NSE value (<0.5). Additionally, the median NSE values in the validation period suggest that the temporal transferability of the calibrated parameters is poor, leading to poor simulations.

Table 5

Median values of performance evaluation metrics computed for the flood events simulated using lumped and semi-distributed event-based GR4J model setups with data assimilation at Jagdalpur during calibration and validation periods

Assimilation variableNSEPEPFPBIASPETPNSEPEPFPBIASPETP
Lumped Calibration
 
Validation
 
 SM-EVT 0.56 −29.37 −12.5 −19.46 0.28 −48.58 −34.94 
 Q-EVT 0.6 − 22.64 6.25 16 0.39 − 37.91 0 − 29.96 
 SM-CONT −0.04 −59.45 −16.67 −46.8 0.95 −77.94 −15.48 −67.82 
 Q-CONT 0.39 −47.16 0 18.13 0.46 44.63 14.93 
Discretized 
 SM-EVT 0.82 − 4.45 0 − 6.25 0.44 −39.93 −23.54 
 Q-EVT 0.64 14.7 −14.13 0.57 26.33 0 27.16 
 SM-CONT 0.41 −46.92 −19.54 0.3 −50.83 −25.56 
 Q-CONT 0.42 −14.3 14.29 12.04 0.38 16.66 15.48 9.47 
Assimilation variableNSEPEPFPBIASPETPNSEPEPFPBIASPETP
Lumped Calibration
 
Validation
 
 SM-EVT 0.56 −29.37 −12.5 −19.46 0.28 −48.58 −34.94 
 Q-EVT 0.6 − 22.64 6.25 16 0.39 − 37.91 0 − 29.96 
 SM-CONT −0.04 −59.45 −16.67 −46.8 0.95 −77.94 −15.48 −67.82 
 Q-CONT 0.39 −47.16 0 18.13 0.46 44.63 14.93 
Discretized 
 SM-EVT 0.82 − 4.45 0 − 6.25 0.44 −39.93 −23.54 
 Q-EVT 0.64 14.7 −14.13 0.57 26.33 0 27.16 
 SM-CONT 0.41 −46.92 −19.54 0.3 −50.83 −25.56 
 Q-CONT 0.42 −14.3 14.29 12.04 0.38 16.66 15.48 9.47 

Note that SM represents soil moisture assimilation and Q represents streamflow assimilation. EVT represents simulations from the event-based model, whereas CONT represents simulations from continuous models.Ideal values for different model settings are bolded.

In summary, the performance of both continuous and event-based lumped models based on Q-DA is found to be satisfactory with lower values of PEPF, PBIAS, and PETP, indicating satisfactory performance when compared to other models. The simulated flood hydrographs obtained from the event-based and continuous lumped models with SM-DA and Q-DA during the calibration period are plotted for calibration and validation periods in Figure 4 and Supplementary Figure S1, respectively, along with the observed values. The figure shows that the ensemble spread of simulations from continuous models is higher than that of their event-based counterparts. This indicates that updating the model states continuously by assimilation preserves the spread induced through perturbation. In contrast, despite the ensemble of IHCs used in event-based models, the spread in event-based simulations is lower than that of their continuous counterparts. Furthermore, the ensemble spread of SM-DA-based simulations is higher than that of Q-DA-based simulations.
Figure 4

Simulated flood hydrographs by the continuous and event-based lumped model based on soil moisture (SM) and streamflow data assimilation. Observed flood hydrographs are also plotted for the selected flood events at Jagdalpur during the calibration period. The coloured envelope used for each hydrograph represents the 0.01 and 0.9 interquartile values. The interquartile values are calculated using 100 streamflow ensemble members. The dotted line represents the ensemble median.

Figure 4

Simulated flood hydrographs by the continuous and event-based lumped model based on soil moisture (SM) and streamflow data assimilation. Observed flood hydrographs are also plotted for the selected flood events at Jagdalpur during the calibration period. The coloured envelope used for each hydrograph represents the 0.01 and 0.9 interquartile values. The interquartile values are calculated using 100 streamflow ensemble members. The dotted line represents the ensemble median.

Close modal
A significant improvement has been observed in the predictive ability of both continuous and event-based semi-distributed based GR4J, based on SM-DA and Q-DA, than their lumped counterparts in terms of NSE, PEPF, PETP, and PBIAS. During the calibration period, the event-based semi-distributed model with SM-DA showed the highest performance, with a median NSE value of 0.82. This highlights the advantage of incorporating spatial variability in the model. However, similar to lumped models, the temporal transferability of the semi-distributed models in the validation period was poor. Nevertheless, the event-based semi-distributed model with Q-DA demonstrated satisfactory performance with median NSE values of 0.64 and 0.57 in calibration and validation periods, respectively. Compared to lumped models, semi-distributed models exhibited better PETP values, indicating a more accurate capture of the timing to peak. Additionally, the PEPF and PBIAS values of the semi-distributed models were relatively lower than those of the lumped models. The flood hydrographs generated from semi-distributed models during the calibration and validation periods are presented in Figure 5 and Supplementary Figure S2, respectively. The ensemble spread of semi-distributed model simulations was lower than that of the lumped models, plausibly due to accounting for spatial heterogeneity. The calibration process may have also compensated for biases in soil moisture, leading to improved performance of SM-DA in the semi-distributed models.
Figure 5

Simulated flood hydrographs by the continuous and event-based semi-distributed model based on soil moisture (SM) and streamflow data assimilation. Observed flood hydrographs were also plotted for the selected flood events at Jagdalpur during the validation period. The coloured envelope used for each hydrograph represents the 0.01 and 0.9 interquartile values. The interquartile values are calculated using 100 streamflow ensemble members. The dotted line represents the ensemble median.

Figure 5

Simulated flood hydrographs by the continuous and event-based semi-distributed model based on soil moisture (SM) and streamflow data assimilation. Observed flood hydrographs were also plotted for the selected flood events at Jagdalpur during the validation period. The coloured envelope used for each hydrograph represents the 0.01 and 0.9 interquartile values. The interquartile values are calculated using 100 streamflow ensemble members. The dotted line represents the ensemble median.

Close modal

Performance of event-based models using IHC obtained through continuous models calibrated with different objective functions

The continuous lumped and semi-distributed models were calibrated using NSE, logNSE, KGE, and R4MS4E. The resulting model states were utilised as IHCs for their respective event-based models. The performance assessment statistics of these event-based models are provided in Table 6. The median NSE values of the event-based lumped models calibrated using NSE, KGE, and R4MS4E in the calibration period were good (>0.65), except for the logNSE calibrated model. The PEPF (<30%) and PETP values indicate that the performance of all lumped models in capturing the magnitude and timing of flood peaks was satisfactory during the calibration period. The KGE-calibrated lumped event-based model was found to perform the best in capturing the flood peak in both calibration and validation periods. However, a decline in the performance of all models, in terms of the chosen evaluation statistics, was observed during the validation period. Nevertheless, the performance of all models during the validation period, in terms of NSE values, was found to be satisfactory (>0.5). The flood hydrographs observed and simulated during the calibration period and validation period are presented in Figure 6 and Supplementary Figure S3, respectively. The figures show that all the simulated flood hydrographs are approximately parallel, and their disposition highly depends on the IHC. This similarity in the performance of all event-based lumped models coupled with continuous models calibrated using different metrics is due to their reliance on the same IHC.
Table 6

Median values of performance evaluation metrics computed for the flood events simulated using lumped and semi-distributed event-based GR4J model setups calibrated using multiple objective functions at Jagdalpur during calibration and validation periods

Calibration objective functionNSEPEPFPBIASPETPNSEPEPFPBIASPETP
Lumped Calibration
 
Validation
 
 KGE 0.69 25.65 0 9.34 0.55 24.72 0 5.33 
 R4MS4E 0.67 25.96 2.61 0.55 25.58 − 0.35 
 logNSE 0.49 −30.63 −12.57 0.51 −30.1 −14.15 
 NSE 0.7 26.57 5.58 0.57 26.43 2.86 
Discretized 
 KGE 0.85 2.99 4.23 0.65 12.88 0 − 2.27 
 R4MS4E 0.79 13.67 3.86 0.68 23.32 10.03 
 logNSE 0.77 −11.36 2.57 0.56 −24.83 −8.42 
 NSE 0.91 − 3.25 0 0.44 0.77 13.21 −8.73 
Calibration objective functionNSEPEPFPBIASPETPNSEPEPFPBIASPETP
Lumped Calibration
 
Validation
 
 KGE 0.69 25.65 0 9.34 0.55 24.72 0 5.33 
 R4MS4E 0.67 25.96 2.61 0.55 25.58 − 0.35 
 logNSE 0.49 −30.63 −12.57 0.51 −30.1 −14.15 
 NSE 0.7 26.57 5.58 0.57 26.43 2.86 
Discretized 
 KGE 0.85 2.99 4.23 0.65 12.88 0 − 2.27 
 R4MS4E 0.79 13.67 3.86 0.68 23.32 10.03 
 logNSE 0.77 −11.36 2.57 0.56 −24.83 −8.42 
 NSE 0.91 − 3.25 0 0.44 0.77 13.21 −8.73 

Ideal values for different model settings are bolded.

Figure 6

Observed and simulated flood hydrographs from the event-based lumped model at Jagdalpur for selected flood events during the validation period. The event-based model is initialised using the model states obtained from the corresponding continuous model calibrated using different metrics (NSE, logNSE, KGE, and R4MS4E).

Figure 6

Observed and simulated flood hydrographs from the event-based lumped model at Jagdalpur for selected flood events during the validation period. The event-based model is initialised using the model states obtained from the corresponding continuous model calibrated using different metrics (NSE, logNSE, KGE, and R4MS4E).

Close modal
In the case of semi-distributed models, the simulated flood hydrographs accurately represent the observed flood hydrographs. During the calibration period, the median NSE value of all semi-distributed models exceeds 0.77, indicating good performance. Moreover, the semi-distributed model based on KGE, R4MS4E, and NSE-calibrated continuous models demonstrate good performance in the validation period (NSE > 0.65). The PEPF values are below 30% in both calibration and validation periods, indicating that the models can capture the observed flood magnitudes effectively. The observed and simulated hydrographs for the semi-distributed event-based model coupled with multiple calibrated continuous models are shown for both calibration and validation periods in Figure 7 and Supplementary Figure S4, respectively. Unlike lumped models, the simulated hydrographs for semi-distributed models are not parallel because of the unique parametrisation of each sub-basin and channel routing. Moreover, the simulated hydrographs are capable of capturing the observed peaks during most of the events in the calibration period. However, in the validation period, a slight underestimation bias is present in all semi-distributed models.
Figure 7

Observed and simulated flood hydrographs from the event-based semi-distributed model at Jagdalpur for selected flood events during the validation period. The event-based model is initialised using the model states obtained from the corresponding continuous model calibrated using different metrics (NSE, logNSE, KGE, and R4MS4E).

Figure 7

Observed and simulated flood hydrographs from the event-based semi-distributed model at Jagdalpur for selected flood events during the validation period. The event-based model is initialised using the model states obtained from the corresponding continuous model calibrated using different metrics (NSE, logNSE, KGE, and R4MS4E).

Close modal

This study evaluates the performance of event-based models based on the IHC/model states using different methods. The current study on event-based models led to the following insights:

  • (i)

    Streamflow assimilation (Q-DA) in both lumped and semi-distributed models led to improved simulations at the catchment outlet during both calibration and validation periods. In contrast, assimilating soil moisture (SM-DA) did not enhance continuous streamflow simulations in the lumped model, but showed a slight improvement in the semi-distributed model.

  • (ii)

    Semi-distributed models resulted in enhanced streamflow simulation in both SM-DA and Q-DA, when compared to their lumped counterparts. This result is in line with the findings of Alvarez-Garreton et al. (2015).

  • (iii)

    Compared to simulations produced by continuous models with DA, the ensemble spread of simulations generated from the event-based model using IHCs obtained through DA is lower. However, simulations based on SM-DA have a higher ensemble spread than those based on Q-DA.

  • (iv)

    In event-based models with initial conditions generated through assimilation, SM-DA-based semi-distributed models performed exceptionally well in the calibration period exploiting the advantage of model spatial resolution.

  • (v)

    The event-based semi-distributed GR4J initialised by IHCs extracted from the corresponding NSE calibrated continuous model is found to be outperforming other models in terms of capturing the magnitude, timing, and volume of the observed flood events.

In conclusion, the findings suggest the potential benefits of assimilating streamflow and employing a semi-distributed model structure. However, limitations such as overfitting of parameters and uncertainties in channel characteristics may affect model performance (Khakbaz et al. 2012; Jehn et al. 2019). Future research can explore the integration of rainfall spatial variability in a lumped model to exploit its computational advantage (Zhou et al. 2021). Additionally, further investigation is needed to evaluate the efficiency of the combined assimilation of soil moisture in IHC estimation and to assess the suitability of EnKF for assimilation in various hydrological models. Overall, this study provides valuable insights for practical applications and calls for large sample investigations using multiple model structures (Gupta et al. 2014).

This work has been funded by the Indian Institute of Tropical Meteorology under Monsoon Mission Phase-II (Project no IITM/MM-II/NIT/2018/IND-6/).

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.

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