https://orcid.org/0000-0001-8728-2642
ABSTRACT
The modeling of the rainfall–runoff (RR) process is a key component for water resources projects, planning, and management for which conceptual and data-driven modeling techniques are utilized. However, these techniques in the modeling of the RR process have their own benefits, and their performance need to be explored in real basins. In this paper, five conceptual models (namely, AWBM, Sacramento, SimHyd, SMAR, and TANK) and an artificial neural network (ANN) model have been developed and their performances have been assessed using the rainfall, runoff, and other climatic data derived from the Bird Creek Basin, USA. The results obtained from the study suggest that the SimHyd performed the best among all the conceptual models during testing. The ANN model performance in simulating the RR process was found to be the best among all the models developed in this study during testing with the highest values of R = 0.941, E = 0.994 and all threshold statistics and least values of AARE = 38.9 and NRMSE = 0.031. Overall, it can be concluded that although the conceptual models are highly comprehensible, the ANN models are able to simulate the flow more accurately than any of the conceptual models developed in this study.
HIGHLIGHTS
Five conceptual models with a varied number of parameters are developed for rainfall–runoff (RR) process in a basin.
Artificial neural network (ANN) model is developed for the same data set.
Using standard statistical measures, the performances have been evaluated.
It was found that the ANN RR model outperformed all the conceptual RR models, but is less comprehensible as compared to their conceptual counterparts.
INTRODUCTION
The rainfall–runoff (RR) process plays a crucial role in the majority of water resource management activities. For modeling the RR process, mainly two approaches are used: conceptual models and data-driven models. The conceptual models involve simple mathematical equations of water movement based on mass and energy conservation principles which were first introduced by Mulvany in 1850. Later many researchers came up with various conceptual RR models that varied in their complexity: Soil Moisture and Accounting Model (SMAR) (O'Connell et al. 1970), SACRAMENTO (Buchtele 1993), SimHyd (Chiew & McMahon 1994), AWBM (Boughton 1996), PREVIS (Birikundavyi et al. 2002). The application of conceptual RR modeling is a prevalent method for simulating hydrological phenomena within catchment areas and apart from these models, the HEC-HMS and SWAT models have been explored by many researchers (Pandey et al. 2017). Recent studies have also shown new models being developed to better represent the hydrological processes in heterogeneous catchments (Soni et al. 2022; Vidyarthi & Jain 2023a, b). One such model is the Variable Contributing Area (D-VCA) model proposed by Zeng & Chu (2021), which considers the spatial variations of soil characteristics and land use to simulate the variability of runoff generation across a catchment. Although the conceptual models are comprehensive, the requirement of large information of basin in terms of data and their performance limits their applicability during operational use. Moreover, the choice of the modeling technique for a specific catchment depends upon the data availability, their simple calibration procedure, and their performance in modeling the RR process. Due to these reasons, data-driven techniques came into existence which provide higher accuracy and less data requirement in their model development. Statistical, stochastic and machine learning methods come under data-driven technique. Mohammadi et al. (2019) used cross-wavelet–linear programming-Kalman filter and GIUH methods in RR modeling. Ghorbani et al. (2010) investigated the application of catastrophe theory to examine its suitability to identify possible discontinuities in the RR process. Artificial neural network (ANN), which is one of the data-driven techniques, gained popularity within the field of hydrology and water resources engineering including open channel hydraulics (Ayaz et al. 2023; Shekhar et al. 2023; Baranwal & Das 2024), RR process, groundwater (GW) modeling and drought forecasting (Azmathullah et al. 2005; See et al. 2009; Kashani et al. 2016; Vidyarthi & Jain 2020; Rahimzad et al. 2021; Vidyarthi & Jain 2023a; b); and few researchers reported the superiority of ANNs over conceptual techniques in modeling the RR process (Demirel et al. 2009). Nevertheless, despite the superior accuracy of ANNs in comparison to conceptual models, the opaque nature of ANN creates skepticism among field operators and policymakers, limiting its adoption in water resource projects, planning, and management (Vidyarthi & Jain 2023a; b). Thus, it is essential to develop models for simulating the RR process in a basin using both conceptual and ANN techniques and evaluate their performance and comprehensibility to establish their efficacy in operational use. A study on the comparison of conceptual models with the ANN model is few and far and only a few conceptual models have been compared with the ANN model. Therefore, it is interesting to compare the popular and established conceptual models with the ANN technique.
This study aims to compare the performance of five popular conceptual models with the performance of the ANN model in simulating the RR process. The specific objectives of the study are to (1) develop conceptual AWBM, Sacramento, SimHyd, SMAR, and TANK models for RR process simulation; (2) develop an ANN model for RR process simulation; (3) compare the performance of conceptual models; (4) compare the best conceptual model with the ANN model in simulating RR process. The average rainfall and stream flow data on a daily timescale derived from the Bird Creek River basin have been employed to develop all the models in this study.
Several standard statistical performance metrics have been employed to validate all the developed models. The paper commences with a concise overview of both the conceptual models and ANN, followed by a comprehensive explanation of the methodology utilized in model development. Subsequently, the results and discussion section are presented. The paper ends with the concluding remarks at the last.
TOOLS AND TECHNIQUES
In this study, five different conceptual models with varied number of parameters and the calibration process are developed for simulating the RR process. The models are compared on the basis of their performance in capturing the low, medium and high runoff (peak discharge). For the same basin, the ANN model is also developed and their performance is also compared with the developed conceptual models in this study. The methods and approaches utilized in this study are discussed briefly in the subsequent sections.
Conceptual modeling technique
A conceptual rainfall–runoff (CRR) model employs a distinct approach where the movement of water is not described by the mass, energy, and momentum equations, rather a simplified conceptual representation of physics involved in the process is adopted. This depiction often comprises interconnected storage units and streamlined budgeting techniques, which always ensure a comprehensive mass balance encompassing all inflows, outflows, and changes in storage. In this study, five CRR models are developed, namely, AWBM, Sacramento, SimHyd, SMAR, and TANK models. A brief discussion is given in the following subsections.
Australian water balance model
Schematic diagram of the AWBM model.
The AWBM model consists of three surface storage elements for simulating partial runoff areas and their water balance (WB) is calculated for each three of them separately. The AWBM model works on eight parameters: A1, A2, and A3 representing the corresponding areas of the catchments; C1, C2, and C3 are surface storage capacities of the corresponding three surface storages; surface flow recession (KS) and base flow recession (KB) constant. The overall outlet runoff is thus a combination of baseflow and the routed surface runoff.
Sacramento model
Structure of the Sacramento model.
The size and saturation of these storage compartments dictate how much rain is absorbed, the actual ET, and the lateral/vertical water movement from the storage. Excess rainfall beyond absorption becomes runoff, passing through an empirical unit hydrograph or similar mechanism. Additionally, the model incorporates water movements laterally from soil moisture stores, influencing resulting stream flow. The Sacramento Model consists of five distinct storage components: upper zone tension water (UZTW), upper zone free water (UZFW), lower zone tension water (LZTW), lower zone primary free water (LSFWP), and lower zone supplementary free water (LZFWS). The model incorporates 16 parameters in total. Among these, five parameters define the dimensions of soil moisture reservoirs, three parameters each are responsible for computing lateral outflow rates, percolation from upper to lower soil moisture reservoirs, and overall system losses, while an additional two parameters handle the calculation of direct runoff.
SimHyd model
Structure of the SimHyd model.
Soil Moisture and Accounting Model
Structure of the SMAR model.
The model offers daily assessments of various hydrological components for the entire catchment, including surface runoff, GW discharge, ET, and soil profile leakage. The surface runoff encompasses different forms such as overland flow, saturation excess runoff, and saturated through-flow from perched GW areas, characterized by rapid response times. The SMAR model is comprised of two consecutive components: a WB component and a routing component. It relies on time series data of rainfall and E to simulate the catchment outlet discharge (Tan & O'Connor 1996).
TANK model
Structure of the Tank model.
In this method, precipitation is added to the top tank, and E is gradually deducted as we progress downward through the tanks. As each tank is depleted, any E deficit is drawn from the subsequent tank in sequence until all the tanks are emptied, and the lateral outlets generate the calculated runoff values. The result from the uppermost tank indicates surface runoff, the second tank's output signifies intermediate runoff, the third tank's output represents sub-base runoff, and the fourth tank's output indicates base flow. This tank-oriented model is employed to assess daily discharge by integrating daily precipitation and E inputs.
All the conceptual models have been developed using the Rainfall–Runoff Library (RRL) in this study. The RRL is a library created by the Cooperative Research Centre for Catchment Hydrology (CRC), Australia in 2004. Its design aims to replicate catchment runoff through the utilization of daily precipitation, runoff, and ET/PET data, making it suitable for catchments with areas ranging from 10 to 10,000 km². This library currently contains five RR models as explained above, eight optimizers for the calibration of parameters, and a choice of ten objective functions. A detailed description of all these models is available on the RRL website and its user manual, http://www.toolkit.net.au/Tools/RRL/documentation. The sum of square error (SSE) and Genetic Algorithm (GA) are utilized as the objective function and as an optimizer, respectively, in developing all conceptual models in this study. A detailed description of the GA optimization technique can be found in Deb (1999).
Artificial neural network
Three-layered ANN structure.
The main objective of supervised training involves reducing the output layer error by finding connection strengths that make the ANN outputs match or come closer to the desired targets. A widely used approach for supervised training is the back-propagation training algorithm, which is commonly employed in various engineering applications (Zurada 1994).
The effectiveness of the models created in this study is assessed using four established statistical measures, namely, average absolute relative error (AARE), normalized root mean square error (NRMSE), Pearson correlation coefficient (R), and threshold statistics (TS). These error metrics have been commonly utilized in the assessment of hydrological models, and their comprehensive explanation can be found in Vidyarthi et al. (2020).
MODEL DEVELOPMENT
This section provides a comprehensive discussion of the study area, data, and the procedural approach taken in developing both the conceptual and ANN models for the modeling of the RR process.
Study area and data
Map of the Bird Creek Basin.
The training (or calibration) set covers the period 01 March 1995 to 25 May 2003 and the testing (or validation) set covers the period 26 May 2003 to 31 November 2008. The basic statistics of the data are outlined in Table 1. The maximum runoff is found to be 24.11 mm/day with an average value of 0.75 mm/day with right-skewed and high peaked runoff data.
Basic statistics of the data
| Statistics | Rainfall (mm/day) | Runoff (mm/day) | PET (mm/day) |
|---|---|---|---|
| Maximum | 135.4 | 24.11 | 9.15 |
| Minimum | 0 | 0.024 | 0.12 |
| Average | 2.8 | 0.75 | 3.62 |
| Std. dev. | 9.16 | 1.71 | 1.99 |
| Skewness | 5.43 | 5.24 | 0.15 |
| Kurtosis | 39.83 | 37.99 | −0.97 |
| Statistics | Rainfall (mm/day) | Runoff (mm/day) | PET (mm/day) |
|---|---|---|---|
| Maximum | 135.4 | 24.11 | 9.15 |
| Minimum | 0 | 0.024 | 0.12 |
| Average | 2.8 | 0.75 | 3.62 |
| Std. dev. | 9.16 | 1.71 | 1.99 |
| Skewness | 5.43 | 5.24 | 0.15 |
| Kurtosis | 39.83 | 37.99 | −0.97 |
Conceptual model development
All the conceptual models (AWBM, Sacramento, SimHyd, SMAR, and TANK) are developed by using the RRL toolkit employing the rainfall, runoff, and PET/ET data for the above-specified period. The RRL toolkit has eight built-in optimizer techniques. In the present study, a GA optimizer has been adopted. The different combinations of mutation probability and population size and the number of iterations were taken in many trials. From the trial-and-error procedure, the best set of optimized GA parameters is given in Table 2.
Best GA parameters for different models
| Model | GA optimizer parameters | |||
|---|---|---|---|---|
| Iterations | Prob. mutation | Nb. points (Population) | Trapez. PDF | |
| AWBM | 500 | 0.01 | 72 | 1.5 |
| Sacramento | 300 | 0.01 | 144 | 1.5 |
| SimHyd | 300 | 0.01 | 63 | 1.5 |
| SMAR | 300 | 0.01 | 81 | 1.5 |
| TANK | 300 | 0.01 | 162 | 1.5 |
| Model | GA optimizer parameters | |||
|---|---|---|---|---|
| Iterations | Prob. mutation | Nb. points (Population) | Trapez. PDF | |
| AWBM | 500 | 0.01 | 72 | 1.5 |
| Sacramento | 300 | 0.01 | 144 | 1.5 |
| SimHyd | 300 | 0.01 | 63 | 1.5 |
| SMAR | 300 | 0.01 | 81 | 1.5 |
| TANK | 300 | 0.01 | 162 | 1.5 |
The calibrated values of all the parameters of these five conceptual models were obtained and presented in Table 3.
Calibrated parameter values of various conceptual models
| Model | No. of parameter | Parameter values |
|---|---|---|
| AWBM | 8 | A1 = 0.134, A2 = 0.433, BFI = 0.3686, C1 = 49.4, C3 = 141.96, C3 = 178.43, KB = 0.898, KS = 0.9843 |
| Sacramento | 16 | Adimp = 0, Lzfpm = 22.549, Lzfsm = 36.078, Lzpk = 0.0196, Lzsk = 0.239, Lztwm = 200.78, Pctim = 0, Pfree = 0.847, Rexp = 1.2, Rserv = 0.3, Sarva = 0.0099, Side = 0, Ssout = 0.001, Uzfwm = 66.51, Uzk = 0.086, Uztwm = 43.137, Zperc = 51.45 |
| SimHyd | 7 | Baseflow Coeff = 0.1176, Impervious Threshold = 1.882, Infiltr Coeff = 398.43, Infilt Shape = 0.392, Interflow Coeff = 0.0117, Pervious Fraction = 0.984, Rainfall Interception Store Capacity = 0.725, Recharge Coeff = 0.50, Soil Moisture Store Capacity = 253.43, |
| SMAR | 9 | C= 0.494, G = 0.827, H = 0.149, Kg = 0.207, N = 1.35, NK = 0.8369, T= 0.9176, Y= 3,941.176, Z = 921.5686 |
| TANK | 18 | H11 = 278.43, a11 = 0.74, a12 = 0.05, a21 = 0.20, a31 = 0.19, a41 = 0.48, alpha = 0.039, b1 = 0.0196, b2 = 1, b3 = 0.854, C1 = 85.098, C2 = 90.98, C3 = 37.64, C4 = 87.84, H12 = 54.59, H21 = 92.55, H31 = 0, H41 = 18.03 |
| Model | No. of parameter | Parameter values |
|---|---|---|
| AWBM | 8 | A1 = 0.134, A2 = 0.433, BFI = 0.3686, C1 = 49.4, C3 = 141.96, C3 = 178.43, KB = 0.898, KS = 0.9843 |
| Sacramento | 16 | Adimp = 0, Lzfpm = 22.549, Lzfsm = 36.078, Lzpk = 0.0196, Lzsk = 0.239, Lztwm = 200.78, Pctim = 0, Pfree = 0.847, Rexp = 1.2, Rserv = 0.3, Sarva = 0.0099, Side = 0, Ssout = 0.001, Uzfwm = 66.51, Uzk = 0.086, Uztwm = 43.137, Zperc = 51.45 |
| SimHyd | 7 | Baseflow Coeff = 0.1176, Impervious Threshold = 1.882, Infiltr Coeff = 398.43, Infilt Shape = 0.392, Interflow Coeff = 0.0117, Pervious Fraction = 0.984, Rainfall Interception Store Capacity = 0.725, Recharge Coeff = 0.50, Soil Moisture Store Capacity = 253.43, |
| SMAR | 9 | C= 0.494, G = 0.827, H = 0.149, Kg = 0.207, N = 1.35, NK = 0.8369, T= 0.9176, Y= 3,941.176, Z = 921.5686 |
| TANK | 18 | H11 = 278.43, a11 = 0.74, a12 = 0.05, a21 = 0.20, a31 = 0.19, a41 = 0.48, alpha = 0.039, b1 = 0.0196, b2 = 1, b3 = 0.854, C1 = 85.098, C2 = 90.98, C3 = 37.64, C4 = 87.84, H12 = 54.59, H21 = 92.55, H31 = 0, H41 = 18.03 |
After the calibration procedure, the simulated runoff obtained from developed models is compared with the observed runoff by comparing the statistical measures during both training and testing periods for all the models developed in this study.
ANN model development
Correlation coefficients of Q(t)
| ACF | CCF | PACF | |||
|---|---|---|---|---|---|
| Flow | Value | Rainfall | Value | Flow | Value |
| Q (t–1) | 0.76 | P (t–1) | 0.49 | Q (t–1) | 0.76 |
| Q (t–2) | 0.53 | P (t–2) | 0.34 | Q (t–2) | −0.13 |
| Q (t–3) | 0.46 | P (t–3) | 0.18 | Q (t–3) | 0.25 |
| Q (t–4) | 0.43 | P (t–4) | 0.14 | Q (t–4) | 0.01 |
| Q (t–5) | 0.40 | P (t–5) | 0.13 | Q (t–5) | 0.12 |
| Q (t–6) | 0.40 | P (t–6) | 0.13 | Q (t–6) | 0.07 |
| Q (t–7) | 0.39 | P (t–7) | 0.12 | Q (t–7) | 0.07 |
| Q (t–8) | 0.38 | P (t–8) | 0.12 | Q (t–8) | 0.05 |
| Q (t–9) | 0.37 | P (t–9) | 0.12 | Q (t–9) | 0.04 |
| Q (t–10) | 0.34 | P (t–10) | 0.12 | Q (t–10) | −0.02 |
| ACF | CCF | PACF | |||
|---|---|---|---|---|---|
| Flow | Value | Rainfall | Value | Flow | Value |
| Q (t–1) | 0.76 | P (t–1) | 0.49 | Q (t–1) | 0.76 |
| Q (t–2) | 0.53 | P (t–2) | 0.34 | Q (t–2) | −0.13 |
| Q (t–3) | 0.46 | P (t–3) | 0.18 | Q (t–3) | 0.25 |
| Q (t–4) | 0.43 | P (t–4) | 0.14 | Q (t–4) | 0.01 |
| Q (t–5) | 0.40 | P (t–5) | 0.13 | Q (t–5) | 0.12 |
| Q (t–6) | 0.40 | P (t–6) | 0.13 | Q (t–6) | 0.07 |
| Q (t–7) | 0.39 | P (t–7) | 0.12 | Q (t–7) | 0.07 |
| Q (t–8) | 0.38 | P (t–8) | 0.12 | Q (t–8) | 0.05 |
| Q (t–9) | 0.37 | P (t–9) | 0.12 | Q (t–9) | 0.04 |
| Q (t–10) | 0.34 | P (t–10) | 0.12 | Q (t–10) | −0.02 |
Plot of ACF, CCF, and PACF.
) at the output neuron. After selecting input and output variables, in the next step, the ANN architecture with a configuration of five input nodes, a variable number of hidden nodes denoted as ‘N,’ and one output node is selected where the optimal value of N is determined using an iterative trial-and-error approach. The logistic sigmoid activation function is utilized as the transfer function for both the hidden and output layers. The training of the ANN architectures utilized the well-known Feed-Forward Back-Propagation (FFBP) algorithm, employing batch learning with the incorporation of a momentum factor during the training process. A number of trial values of learning and momentum constant are taken. The learning rate and momentum constant values of 0.005 and 0.075, respectively, are obtained as the best, respectively, and these values are consistently applied during the training of all the architectures. The best value of N is obtained by varying N from 1 to 20. The Levenberg–Marquardt (LM) algorithm was employed to minimize the MSE at the output layer. The training of the ANN model concluded either when the MSE reached 0.0001 or after 50,000 iterations. The optimal ANN architecture is chosen based on error statistics, as illustrated in Figure 9. 
Plot of error statistics vs. hidden neurons during training.
The optimum number of hidden neurons on the basis of all error statistics shown in Figure 9 is determined to be 14, therefore, 5–14–1 is found to be the best architecture to simulate the RR process in the study area.
RESULTS AND DISCUSSIONS
First, the results obtained from the conceptual models are discussed and the best conceptual models so obtained are then compared with the ANN model in the simulation of the RR process.
Results from conceptual models
Performance statistics of different conceptual models
| Model | E | R | NRMSE | MSE | AARE | TS10 | TS50 | TS75 | TS100 |
|---|---|---|---|---|---|---|---|---|---|
| During Training/Calibration | |||||||||
| AWBM | 0.524 | 0.711 | 0.061 | 1.539 | 126.1 | 6.2 | 32.5 | 57.4 | 75.3 |
| Sacramento | 0.511 | 0.731 | 0.059 | 1.432 | 161.7 | 5.7 | 32.0 | 48.4 | 62.4 |
| SimHyd | 0.776 | 0.750 | 0.057 | 1.344 | 114.9 | 6.2 | 32.1 | 54.2 | 79.1 |
| SMAR | 0.641 | 0.626 | 0.073 | 2.181 | 116.5 | 1.0 | 4.4 | 7.8 | 22.2 |
| TANK | 0.774 | 0.578 | 0.075 | 2.333 | 299.4 | 5.2 | 27.9 | 42.7 | 56.1 |
| During Testing/Validation | |||||||||
| AWBM | 0.216 | 0.626 | 0.061 | 2.164 | 112.1 | 6.4 | 37.4 | 60.4 | 74.5 |
| Sacramento | 0.463 | 0.621 | 0.049 | 1.416 | 156.4 | 5.9 | 31.3 | 47.5 | 61.1 |
| SimHyd | 0.464 | 0.703 | 0.049 | 1.402 | 130.6 | 6.0 | 32.4 | 51.1 | 75.1 |
| SMAR | 0.148 | 0.653 | 0.061 | 2.182 | 100.1 | 0.8 | 4.1 | 8.2 | 12.8 |
| TANK | 0.311 | 0.548 | 0.058 | 1.932 | 216.3 | 5.8 | 32.0 | 44.0 | 52.2 |
| Model | E | R | NRMSE | MSE | AARE | TS10 | TS50 | TS75 | TS100 |
|---|---|---|---|---|---|---|---|---|---|
| During Training/Calibration | |||||||||
| AWBM | 0.524 | 0.711 | 0.061 | 1.539 | 126.1 | 6.2 | 32.5 | 57.4 | 75.3 |
| Sacramento | 0.511 | 0.731 | 0.059 | 1.432 | 161.7 | 5.7 | 32.0 | 48.4 | 62.4 |
| SimHyd | 0.776 | 0.750 | 0.057 | 1.344 | 114.9 | 6.2 | 32.1 | 54.2 | 79.1 |
| SMAR | 0.641 | 0.626 | 0.073 | 2.181 | 116.5 | 1.0 | 4.4 | 7.8 | 22.2 |
| TANK | 0.774 | 0.578 | 0.075 | 2.333 | 299.4 | 5.2 | 27.9 | 42.7 | 56.1 |
| During Testing/Validation | |||||||||
| AWBM | 0.216 | 0.626 | 0.061 | 2.164 | 112.1 | 6.4 | 37.4 | 60.4 | 74.5 |
| Sacramento | 0.463 | 0.621 | 0.049 | 1.416 | 156.4 | 5.9 | 31.3 | 47.5 | 61.1 |
| SimHyd | 0.464 | 0.703 | 0.049 | 1.402 | 130.6 | 6.0 | 32.4 | 51.1 | 75.1 |
| SMAR | 0.148 | 0.653 | 0.061 | 2.182 | 100.1 | 0.8 | 4.1 | 8.2 | 12.8 |
| TANK | 0.311 | 0.548 | 0.058 | 1.932 | 216.3 | 5.8 | 32.0 | 44.0 | 52.2 |
Scatter plots between observed and calculated flows during calibration of conceptual models: (a) AWBM, (b) Sacramento, (c) SimHyd, (d) SMAR, and (e) TANK.
Scatter plots between observed and calculated flows during calibration of conceptual models: (a) AWBM, (b) Sacramento, (c) SimHyd, (d) SMAR, and (e) TANK.
Scatter plots between observed and calculated flows during validation of conceptual models: (a) AWBM, (b) Sacramento, (c) SimHyd, (d) SMAR, and (e) TANK.
Scatter plots between observed and calculated flows during validation of conceptual models: (a) AWBM, (b) Sacramento, (c) SimHyd, (d) SMAR, and (e) TANK.
Time series plots between observed and calculated flow during validation of conceptual models: (a) AWBM, (b) Sacramento, (c) SimHyd, (d) SMAR, and (e) TANK.
Time series plots between observed and calculated flow during validation of conceptual models: (a) AWBM, (b) Sacramento, (c) SimHyd, (d) SMAR, and (e) TANK.
Time series plot of observed and calculated flow model for (a) low, (b) medium and (c) high flows during testing: (i) AWBM, (ii) Sacramento, (iii) SimHyd, (iv) SMAR, and (v) TANK.
Time series plot of observed and calculated flow model for (a) low, (b) medium and (c) high flows during testing: (i) AWBM, (ii) Sacramento, (iii) SimHyd, (iv) SMAR, and (v) TANK.
Comparison results from best conceptual model and ANN model
Performance statistics of simHyd and ANN models
| Model | E | R | NRMSE | MSE | AARE | TS10 | TS50 | TS75 | TS100 |
|---|---|---|---|---|---|---|---|---|---|
| During training/calibration | |||||||||
| SimHyd | 0.776 | 0.750 | 0.057 | 1.344 | 114.9 | 6.2 | 32.1 | 54.2 | 79.1 |
| ANN (5-14-1) | 0.960 | 0.885 | 0.074 | 0.450 | 34.9 | 38.0 | 83.2 | 90.1 | 93.7 |
| During testing/validation | |||||||||
| SimHyd | 0.464 | 0.703 | 0.049 | 1.402 | 130.6 | 6.0 | 32.4 | 51.1 | 75.1 |
| ANN (5-14-1) | 0.994 | 0.941 | 0.031 | 0.079 | 38.9 | 11.7 | 80.4 | 90.4 | 91.7 |
| Model | E | R | NRMSE | MSE | AARE | TS10 | TS50 | TS75 | TS100 |
|---|---|---|---|---|---|---|---|---|---|
| During training/calibration | |||||||||
| SimHyd | 0.776 | 0.750 | 0.057 | 1.344 | 114.9 | 6.2 | 32.1 | 54.2 | 79.1 |
| ANN (5-14-1) | 0.960 | 0.885 | 0.074 | 0.450 | 34.9 | 38.0 | 83.2 | 90.1 | 93.7 |
| During testing/validation | |||||||||
| SimHyd | 0.464 | 0.703 | 0.049 | 1.402 | 130.6 | 6.0 | 32.4 | 51.1 | 75.1 |
| ANN (5-14-1) | 0.994 | 0.941 | 0.031 | 0.079 | 38.9 | 11.7 | 80.4 | 90.4 | 91.7 |
Scatter plots between observed and calculated flows (a) during calibration/training and (b) during validation/testing.
Scatter plots between observed and calculated flows (a) during calibration/training and (b) during validation/testing.
Time series plots between observed and calculated flow during validation/testing: (a) SimHyd and (b) ANN.
Time series plots between observed and calculated flow during validation/testing: (a) SimHyd and (b) ANN.
Time series plot of observed and calculated flow from the best models from each category for (a) low, (b) medium, and (c) high flows during testing.
Time series plot of observed and calculated flow from the best models from each category for (a) low, (b) medium, and (c) high flows during testing.
CONCLUSIONS
Modeling the RR process holds significant importance in water resources project management. The runoff is estimated using various methods and broadly divided into two categories, conceptual techniques or data-driven techniques. However, each method has its own limitations and accuracies in runoff estimation. Their comparison must be assessed before utilizing them in operational uses. Few studies on comparison of a few conceptual models and data-driven techniques are available, the comparison of many conceptual models with ANN is still missing and needs to be assessed. This study was initiated with the aim of the development of five conceptual models, namely AWBM, Sacramento, SimHyd, SMAR, and TANK, along with a distinct ANN model, tailored specifically for the Bird Creek basin in Oklahoma, USA and comparing their performances in runoff estimation. For the conceptual model development, the RRL toolkit is used, while the ANN model is developed using a feed-forward neural network with one hidden layer, and one each of the input and output layers trained using the LM algorithm in the back-propagation step. The inputs are selected on the basis of cross-correlation, auto-correlation, and partial auto-correlation functions. Model performance evaluation was carried out using five different standard statistical performance evaluation statistics, namely AARE, R, E, NRMSE, and TS. The MSE is used as the objective function. The following conclusions are made based on this study:
Conceptual models perform reasonably in simulating the RR process.
Out of all the conceptual models, namely, AWBM, Sacramento, SimHyd, SMAR, and TANK models developed in this study, the SimHyd performed the best. The SMAR and TANK models are not able to simulate the runoff of the basin.
The SimHyd and ANN models both demonstrate the capability to accurately capture low, medium, and high flows. However, the ANN model outperformed all the conceptual models including SimHyd model in simulating the RR process.
The conclusions drawn from this study are based on the models developed using data from a single basin. These findings could be prominently concluded by initiating analogous research on diverse catchments with varying hydro-climatic conditions. In this study, the performance of five conceptual models with a data-driven technique, i.e., ANN is compared, while several conceptual models and data-driven models are in existence and their performances may be assessed which can be instrumental in improving the planning, design, operation, and management of various water resource activities.
ACKNOWLEDGEMENTS
The data used in this study have been obtained freely from USGS (https://waterdata.usgs.gov/nwis) and is duly acknowledged.
FUNDING
There was no funding received to carry out this research.
DATA AVAILABILITY STATEMENT
All relevant data are available from an online repository at https://waterdata.usgs.gov/nwis.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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