https://orcid.org/0000-0002-9890-212X
Abstract
Prediction of rainfall and runoff is one of the most important issues in managing catchment water resources and sustainable use of water resources. In this study, the accuracy and efficiency of the Gene Expression Programming (GEP) model and the Regional Climate Model (RegCM) to predict runoff values from monthly precipitation were investigated. For this purpose, monthly precipitation data of 48 synoptic stations, monthly temperature data of 21 synoptic stations, and also monthly runoff data of 40 hydrometric stations located in the Karkheh basin during 45 years (1972–2017) were used. Out of this statistical period, 40 years was used for calibration, and five years (1995–1999) for the validation of the model results. The results showed that the GEP model with an average R2 value of 0.948, average RMSE value of 19.4 m3/s, average NSE value of 0.91, and average SE value of 0.3, had a much more accurate performance than the RegCM model, which had an average R2 value of 0.04, average RMSE value of 298.2 m3/s, average NSE value of −0.64, and average SE value of 4.6 in predicting monthly runoff.
HIGHLIGHTS
The accuracy and efficiency of GEP and RegCM models were investigated in simulating rainfall-runoff processes.
The RegCM4.7 was coupled with the Community Land Model, CLM version 4.5 as a land surface scheme.
The bias correction method was used in this model to improve the accuracy of RegCM results, and the results demonstrate the positive effects of bias correction.
INTRODUCTION
Rainfall and runoff prediction can provide helpful information for planning and managing water resources. Rainfall is one of the main parameters that affect the runoff. Therefore, determining the exact amount of precipitation in a watershed can help improve the accuracy and reliability of runoff prediction. The accurate prediction of rainfall and runoff is a significant criterion for managing water resources. Due to uncertainty and natural nonlinear behaviors of precipitation, there should be a proper understanding of the catchment and its components, to perform the rainfall process to runoff conversion properly (Saha et al. 2014).
There is a great deal of complexity in the conversion of rainfall to runoff in a watershed as a complex and dynamic system (Abushandi & Merkel 2013). As a result, forecasting rainfall and runoff has become one of the most challenging issues in water resources management in recent years; consequently, researchers have presented and used different computer models in different studies; these models are typically classified as experimental, conceptual, and physical models (Sitterson et al. 2018). Empirical models, which do not consider hydrological characteristics, only consider nonlinear statistical relationships between inputs and outputs and hence are called black boxes (Devia et al. 2015). These models offer simple implementation, few parameters to input, and high speed. These models also have the advantages of simplicity of implementation, fewer parameters for input, and high speed; their downside, on the other hand, is that they fail to take into account the relationships between the features of the basin, which is considered a noticeable drawback. Artificial neural network (ANN), SVM, and GEP models are examples of these models. A conceptual hydrologic model, sometimes called a gray box model, describes all facets of precipitation-runoff processes. Models like these are based on empirically observed or hypothesized relationships between various hydrological variables. In contrast, black-box models only consider rainfall–runoff relationships statistically. Among their advantages are their simple structure and easy calibration. A number of conceptual models are also available, including HSPF, HBV, and TOPMODEL (Devia et al. 2015). Physical models represent real phenomena mathematically based on their understanding of the physics of hydrological processes (Vaze et al. 2011). They are based on measurable variables with time and space-dependent characteristics, and their governing equations are derived from the real hydrological response of the basin (Vaze et al. 2011; Devia et al. 2015). They are characterized by their spatial and temporal diversity, as well as their relationship between model parameters and basin physical characteristics, which make them realistic. Mike-SHE, PRMS, and VIC are examples of such physical models.
In addition, a variety of artificial intelligence models have been used to predict rainfall–runoff in recent years. In this regard, Savic et al. (1999) used genetic programming to model rainfall–runoff and observed favorable results. Aytek et al. (2008) studied the effectiveness of ANN and GEP models in modeling the rainfall–runoff process. The results showed the good ability of GEP in rainfall–runoff modeling and showed that GEP can be called as an alternative to ANN models. Shiri et al. (2012) conducted a study to investigate the effectiveness of ANN, ANFIS, and GEP models in modeling the rainfall–runoff process. The study compared the results of these models with the MLR model. The findings indicated that GEP demonstrated good accuracy and can serve as a viable alternative to other artificial intelligence and MLR models. Kashani et al. (2016) have presented a Volterra model integrated with artificial neural networks (IVANN) to simulate the rainfall–runoff process in the forest basin of northern Iran. The results showed the IVANN model has a good performance compared to other semi-distributed and mass models for simulating the rainfall-runoff process. Nourani (2017) developed an emotional artificial neural network (EANN) model for rainfall-runoff modeling. The results showed EANN was superior to ANN. Additionally, the EANN model can accurately estimate peak values of the runoff time series. Danandeh Mehr & Nourani (2018) used a hybrid model, which integrated seasonal algorithm (SA) and multigene genetic programming (MGGP) to model the rainfall-runoff process. The model improved peak flow accuracy and reduced timing error. Ahmadi et al. (2019) applied SWAT, IHACRES, and ANN models to model the rainfall-runoff process in Tehran's western Kan basin. The results showed the ANN model outperformed the other two for daily, monthly, and annual flow simulation. Ghaderpour et al. (2021) conducted a study on the gradual and seasonal changes in streamflow over time at eight major hydrometric stations along the Athabasca River. They utilized the least squares wavelet software (LSWAVE) to analyze climate and hydrological time series. The study highlighted the potential of LSWAVE in analyzing such data as it does not require preprocessing, including interpolation, gap-filling, or de-spiking.
The gene expression programming model, which is a branch of evolutionary algorithms and an advanced form of genetic programming, has the advantage of high convergence speed of calculations, and precise simulation, and it can also be used in modeling most natural phenomena (Roshangar et al. 2015). A further benefit of this algorithm is that it can automatically select the input variables that have the greatest influence on the model (Solgi et al. 2017).
Alternatively, regional climate models (RCMs) have the potential to downscale global climate model (GCM) outputs to reproduce high spatial resolution climate features for assessing regional climate change (Sangelantoni et al. 2021). RegCM is one of the first downscaling dynamic climate models that has been widely used worldwide to simulate precipitation as one of the components of the hydrological cycle (KhayatianYazdi et al. 2021; Komkoua Mbienda et al. 2021). For example, Lu et al. (2021) evaluated the performance of the RegCM model driven by two datasets, including ERA-Interim and the Geophysical Fluid Dynamics Laboratory (GFDL), in simulating dominant water cycle variables (e.g., evapotranspiration, runoff, and precipitation) over China between 1986 and 2005. Results showed that the model was reasonably able to detect seasonal and spatial variations of the water cycle components, albeit runoff is more biased than other outputs. The outputs of the RegCM model, driven by the Hadley Center Global Environment Model version 2 (HadGEM2), were evaluated over the Toyserkan basin located in the west of Iran from 1999 to 2005 (Taheri Tizro et al. 2019). According to the results, the model performs better at simulating daily rainfall, while being able to reasonably capture runoff and temperature cycles on a monthly basis. Based on bias-corrected RegCM outputs, Hassan et al. (2019) simulated future runoff under RCP4.5 and RCP8.5 scenarios for a watershed in Pakistan. It was determined that runoff will continue to increase until the end of the 21st century.
Anwar et al. (2019) compared two runoff parameterization methods in RegCM4.6 (simplified TOPMODEL and VIC) to simulate water and energy cycles in tropical Africa from 1995 to 2010. According to the results, the correct simulation of runoff can lead to the accurate simulation of the hydrological cycle and therefore an accurate energy balance. Moreover, VIC is superior to the simplified TOPMODEL in simulating the hydrological cycle, including surface soil water, infiltration rate, and evapotranspiration rate, so it can be used to improve energy balance simulations in Africa.
Currently, systematic reviews of studies demonstrate the importance of accurately forecasting hydrological parameters, such as rainfall and runoff, for flood control. Several devastating floods have hit Iran in the last two decades, making it one of the most vulnerable countries to climate change. According to the previous research conducted, GEP was found to be a suitable method for modeling nonlinear, complex, and dynamic processes such as runoff among the models mentioned. Additionally, it is worth noting that previous research has demonstrated the forecasting capabilities of the RegCM model in terms of rainfall accuracy. This model has proven to be effective in capturing the spatial and seasonal variations of key water cycle variables, including precipitation, evapotranspiration, and runoff. Thus, this study aims to evaluate and compare the accuracy of both GEP and RegCM models by simulating runoff. However, it is important to consider the potential for floods in the Karkheh basin due to various natural factors such as heavy rainfall, melting snow, topography, and low water absorption capacity of the soil. Furthermore, human factors such as deforestation, land use change, and construction of dams and reservoirs have also contributed to the occurrence of floods in the basin. As a result, the Karkheh basin has a high flood potential and has experienced significant floods. Given that floods have caused extensive damage to residential areas, communication roads, agricultural lands, and gardens in this area in recent years, it was selected as a case study.
MATERIALS AND METHODS
Study region
The geographical location of Karkheh basin and selected hydrometric stations.
Datasets and preprocessing
Characteristics of selected hydrometric stations in the Karkhe basin
| Row | Station name | River name | Latitude | Longitude | Height |
|---|---|---|---|---|---|
| 1 | Polchehr | Gamasiab | 34.33 | 47.43 | 1,280 |
| 2 | Afrineh | Kashkan | 33.32 | 47.89 | 820 |
| 3 | Nazarabad | Simareh | 33.18 | 47.43 | 40 |
| 4 | Abdolkhan | Karkheh | 31.83 | 48.38 | 530 |
| Row | Station name | River name | Latitude | Longitude | Height |
|---|---|---|---|---|---|
| 1 | Polchehr | Gamasiab | 34.33 | 47.43 | 1,280 |
| 2 | Afrineh | Kashkan | 33.32 | 47.89 | 820 |
| 3 | Nazarabad | Simareh | 33.18 | 47.43 | 40 |
| 4 | Abdolkhan | Karkheh | 31.83 | 48.38 | 530 |
The geographical location of hydrometric (a) and synoptic (b) stations in the Karkheh basin.
The geographical location of hydrometric (a) and synoptic (b) stations in the Karkheh basin.
The GEP model
Ferreira introduced the GEP approach as a novel variation of the GP approach to minimize its contradictions. A combination of GP and rudimentary fixed-length linear chromosomes (GA) is used. GEP only transfers the genome to the next generation, so repeating the entire structure is unnecessary. Changes occur in a linear manner. A model with one chromosome was created, containing genes categorized as tail and head. The GEP model consists of genes that are represented by a fixed parametric length, an ending function, and mathematical operators. Additionally, there is a stable connection between the terminals and the chromosome in the genetic code operator.
The unique and multigenic nature of the GEP model is its strength, which allows the evolution of more complex programs composed of several subprograms (Ferreira 2001a; Shiri et al. 2012).
The RegCM model
The latest version of RegCM4 (RegCM4.7) was used in this study with a hydrostatic dynamic core because the model shows enhanced performance compared to the previous version over four different regions, including Europe, East Asia, Africa, and South America (Giorgi et al. 2012). RegCM requires certain preprocessing steps before it can be used for climate simulations. These steps typically involve preparing the input data, setting up the domain and grid, and configuring the model parameters. The input data for RegCM usually include global climate models (GCMs) output data, which needs to be bias-corrected and downscaled to the regional scale. The data may also need to be regarded to match the target domain and resolution. The domain and grid setup involves defining the geographic extent of the study area, such as the boundaries of a country or a region, and specifying the spatial resolution of the model grid. The resolution of the model grid depends on the study objectives and the available computational resources. Finally, the model parameters need to be configured based on the specific research question and the characteristics of the study area. These parameters include atmospheric physics, land surface processes, and other model settings that affect the simulation results. Overall, RegCM preprocessing involves several critical steps that require careful consideration and expertise to ensure accurate and reliable climate simulations.
This paper used 6-hourly fields from the CSIRO-MK3.6 at 1.9° horizontal resolution to provide the lateral and initial boundary conditions for RegCM4.7 simulations. The simulations have been carried out through a one-way procedure in two steps starting from 1 January 1993 to 1 January 2000, considering the first two years of simulations as spin-up runs. In this study, RegCM4.7 was coupled with Community Land Model, CLM version 4.5 as a land surface scheme (Oleson et al. 2013), Modified Holstag as a planetary boundary layer scheme (Holtslag et al. 1990), RRTM as a radiative transfer scheme (Mlawer et al. 1997), and one-dimensional lake model (Hostetler et al. 1993). The CLM4.5 uses a set of parameters, coupling biogeophysical, biogeochemical, and biogeographic processes to describe the exchange of energy, momentum, water, and carbon between the surface and the atmosphere. The grid cells are divided into a first subgrid hierarchy composed of multiple land units (wetlands, vegetation, lakes, and urban) and second and third subgrid hierarchies for vegetated land units, including different snow/soil columns and plant functional types. Biogeophysical processes are calculated for each land unit, column, and then averaged before returning to the atmospheric model. Soil temperature and water content are calculated with a multiple-layer model. CLM4.5 was updated by integrating Moderate Resolution Imaging Spectroradiometer (MODIS) products improving the canopy integration and interception schemes.
) at the grid cell surface as the sum of liquid precipitation reaching groundwater and melting snow. Moisture flux is then divided among surface runoff, surface water storage, and infiltration into the soil. In CLM4.5, the default hydrology scheme is the TOPMODEL (Beven & Kirkby 1979), which uses the Simple TOPMODEL (SIMTOP) described by Niu et al. (2005) for runoff parameterization. The fractional saturated areas (fsat) is a function of soil moisture condition and topographic characteristics, which is computed as:
are the maximum values of 
and decay factor (m−1), respectively, and Δz is the water table depth (m). For each grid cell, 
is the proportion of pixels with topographic indexes (the ratio of the upstream area over a grid cell to its local slope) greater than or equal to the mean. According to sensitivity analysis and comparison with observed runoff, global simulations indicate a decay factor of 0.5 m−1. Surface runoff can then be calculated using 
and 
production. According to Niu et al. (2005), this parameterization improved surface runoff simulation, especially in mountainous areas.Moreover, RegCM4.7 was conducted with four available cumulus convection schemes (Simplified Kuo, MIT-Emanuel, Kain-Fritsch, Tiedtke, and Grell) to find their impacts on the runoff simulations (Giorgi et al. 2012). In the Grell scheme, deep convection is parameterized by the updraft and downdraft circulations in clouds mixed and diluted with their environment only at the base and top of the cloud (Grell 1993). Furthermore, this scheme is triggered once a lifted parcel attains the moist convection level. The Emanuel scheme is based on the highly inhomogeneous and episodic mixing in clouds and convection triggers when the cloud-based level is less than the neutral buoyancy level (Emanuel 1991; Emanuel & Živković-Rothman 1999). Precipitation is formed from parts of the condensed moisture, while the rest forms clouds that mix with their environment. The mixing detrainment and entrainment rates in these clouds are related to their vertical gradients of buoyancy. Also, the Emanuel scheme includes the auto conversion formula of cloud water into precipitation in cumulus clouds and forming ice. The algorithm of the simplified Kuo scheme is based on large-scale moisture convergence (Anthes 1977). Convection activates whenever deep instability and large-scale moisture and heat convergences exist in the lower layer. The Tiedtke scheme, as a mass flux scheme, considers three types of convection: shallow, mid-level, and deep convections. The evaporation from the surface is the main source of shallow convection, whereas large-scale moisture convergence is responsible for the others. The Kain–Fritsch convection scheme incorporates the impact of the entrainment, updraft detrainment, and two-way vertical mass exchange between clouds and their environment (Kain & Fritsch 1993). Since both updraft vertical mass flux and moisture detrainment are functions of the cloud-scale environment, environmental conditions are much more responsible for vertical convective heating and drying than the one-dimensional simple plume model. Also, convection activates when the environmental LCL temperature is much lower than the lifting condensation level temperature of the air parcel.
The outer and inner domains with topography (m) were used in the RegCM simulations.
The outer and inner domains with topography (m) were used in the RegCM simulations.
Evaluation of model performance
In these expressions, n represents the number of months of the study period, 
is the measured value for month i, 
is the predicted value by model for month i, 
is the average of measured data, and 
is the average of the predicted data. The best fit between the predicted value and the observed value is achieved when the values of RMSE and SE approach 0, and the value of R2 approaches 1. NSE ranges from −infinity to 1, with values closer to 1 indicating better model performance.
The framework of study identification and selection process.
RESULT
Predicting by the GEP model
In order to predict the monthly runoff in Polechehr, Nazarabad, Afrineh, and Abdolkhan hydrometric stations, the monthly time series of rainfall, temperature, and runoff data from all the stations in this basin were used for the period 1972–2017. In the following, the performance of the GEP model in predicting the monthly runoff of these stations is evaluated.
GEP model preparation
GeneXproTools 5.0 software was used to run the GEP model. The following steps were performed to develop the model:
- 1.
The RMSE fit function was used to select the fit function.
- 2.
To produce each gene from the chromosome, a set of inputs and functions must be selected.
- 3.
The chromosomal architecture (head length, number of genes, and number of chromosomes) was selected. In this study, head length, number of genes, and number of chromosomes were selected according to the researches, 8, 3, and 30, respectively (Ferreira 2001a, 2001b; Shiri et al. 2012).
- 4.
The linking function was selected; this can be used for different types of functions such as +, −, ×, and /. This study selected the addition function (+) for gene transplantation (Shiri et al. 2012).
- 5.
The last step involves the selection of genetic operators and their amount.
Table 2 summarizes the values of the parameters used in each run.
Genetic operators employed in the GEP models
| Number of chromosomes | 30 | One-point recombination rate | 0.3 |
| Head size | 8 | Two-point recombination rate | 0.3 |
| Number of genes | 3 | Gene recombination rate | 0.1 |
| Linking function | Addition | Gene transposition rate | 0.1 |
| Fitness function error type | RMSE | Insertion sequence transposition rate | 0.1 |
| Mutation rate | 0.044 | Root insertion sequence transposition | 0.1 |
| Inversion rate | 0.1 |
| Number of chromosomes | 30 | One-point recombination rate | 0.3 |
| Head size | 8 | Two-point recombination rate | 0.3 |
| Number of genes | 3 | Gene recombination rate | 0.1 |
| Linking function | Addition | Gene transposition rate | 0.1 |
| Fitness function error type | RMSE | Insertion sequence transposition rate | 0.1 |
| Mutation rate | 0.044 | Root insertion sequence transposition | 0.1 |
| Inversion rate | 0.1 |
The best input pattern
It is essential to select the proper input pattern for the model to achieve a high level of forecasting accuracy. Input parameters and used GEP parameters are listed in Table 3, where the 
, 
, and 
represent the monthly precipitation, monthly temperature, and monthly runoff of the upper reaches or the aggregate runoff from upstream tributaries, respectively. Runoff was normalized in two ways: observed runoff (
) and detrended runoff (
). It should be noted that in order to remove the trend from the monthly runoff data, the double-mass method was used. The steps used in this study to normalized monthly data using the double-mass method are:
- 1.
The cumulative sum of the data and the time index (in months) were calculated separately.
- 2.
The cumulative sum of the data was plotted against the cumulative sum of the time index.
- 3.
The breakpoint was determined (the breakpoint indicates a change in hydrologic conditions at the station).
- 4.
The observed data before the breakpoint were adjusted to the data after the breakpoint using Equation (6).
- 5.
The data obtained from step 4 were plotted cumulatively, and linear regression lines were fitted to them for comparison.
Input patterns to the GEP model to predict monthly runoff
| Input pattern number | The model input pattern on the monthly scale |
|---|---|
| 1 |  |
| 2 |  |
| 3 |  |
| 4 |  |
| 5 |  |
| 6 |  |
| Input pattern number | The model input pattern on the monthly scale |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
Double-mass curves of annual runoff for selected hydrometric stations.
In these expressions, Pa is the adjusted time series, Po is the observed time series, 
is the slope of the graph to which records are adjusted, and 
is the slope of the graph at time 
was observed.
Results of the monthly runoff prediction by the GEP model in the calibration stage
| Station | Pattern number | R2 | RMSE (m3/s) | SE | NSE |
|---|---|---|---|---|---|
| Polchehr | 1 | 0.39 | 29.98 | 1.14 | 0.35 |
| 2 | 0.91 | 11.16 | 0.42 | 0.91 | |
| 3 | 0.92 | 10.96 | 0.42 | 0.91 | |
| 4 | 0.36 | 19.50 | 1.13 | 0.36 | |
| 5 | 0.88 | 8.63 | 0.50 | 0.87 | |
| 6 | 0.85 | 9.59 | 0.56 | 0.85 | |
| Nazarabad | 1 | 0.39 | 65.61 | 0.80 | 0.38 |
| 2 | 0.90 | 26.90 | 0.33 | 0.90 | |
| 3 | 0.90 | 27.07 | 0.33 | 0.90 | |
| 4 | 0.42 | 45.09 | 0.75 | 0.42 | |
| 5 | 0.85 | 23.21 | 0.39 | 0.84 | |
| 6 | 0.85 | 22.93 | 0.38 | 0.85 | |
| Afrineh | 1 | 0.42 | 32.45 | 0.84 | 0.37 |
| 2 | 0.97 | 7.44 | 0.19 | 0.97 | |
| 3 | 0.97 | 7.00 | 0.18 | 0.97 | |
| 4 | 0.44 | 22.71 | 0.78 | 0.44 | |
| 5 | 0.93 | 7.97 | 0.27 | 0.9 | |
| 6 | 0.94 | 7.64 | 0.26 | 0.9 | |
| Abdolkhan | 1 | 0.35 | 124.18 | 0.85 | 0.11 |
| 2 | 0.85 | 59.60 | 0.41 | 0.69 | |
| 3 | 0.82 | 65.59 | 0.45 | 0.63 | |
| 4 | 0.20 | 56.57 | 0.70 | 0.20 | |
| 5 | 0.77 | 30.76 | 0.38 | 0.76 | |
| 6 | 0.69 | 35.32 | 0.43 | 0.69 |
| Station | Pattern number | R2 | RMSE (m3/s) | SE | NSE |
|---|---|---|---|---|---|
| Polchehr | 1 | 0.39 | 29.98 | 1.14 | 0.35 |
| 2 | 0.91 | 11.16 | 0.42 | 0.91 | |
| 3 | 0.92 | 10.96 | 0.42 | 0.91 | |
| 4 | 0.36 | 19.50 | 1.13 | 0.36 | |
| 5 | 0.88 | 8.63 | 0.50 | 0.87 | |
| 6 | 0.85 | 9.59 | 0.56 | 0.85 | |
| Nazarabad | 1 | 0.39 | 65.61 | 0.80 | 0.38 |
| 2 | 0.90 | 26.90 | 0.33 | 0.90 | |
| 3 | 0.90 | 27.07 | 0.33 | 0.90 | |
| 4 | 0.42 | 45.09 | 0.75 | 0.42 | |
| 5 | 0.85 | 23.21 | 0.39 | 0.84 | |
| 6 | 0.85 | 22.93 | 0.38 | 0.85 | |
| Afrineh | 1 | 0.42 | 32.45 | 0.84 | 0.37 |
| 2 | 0.97 | 7.44 | 0.19 | 0.97 | |
| 3 | 0.97 | 7.00 | 0.18 | 0.97 | |
| 4 | 0.44 | 22.71 | 0.78 | 0.44 | |
| 5 | 0.93 | 7.97 | 0.27 | 0.9 | |
| 6 | 0.94 | 7.64 | 0.26 | 0.9 | |
| Abdolkhan | 1 | 0.35 | 124.18 | 0.85 | 0.11 |
| 2 | 0.85 | 59.60 | 0.41 | 0.69 | |
| 3 | 0.82 | 65.59 | 0.45 | 0.63 | |
| 4 | 0.20 | 56.57 | 0.70 | 0.20 | |
| 5 | 0.77 | 30.76 | 0.38 | 0.76 | |
| 6 | 0.69 | 35.32 | 0.43 | 0.69 |
Comparison of observed and predicted runoff by GEP model for calibration stage at the studied stations.
Comparison of observed and predicted runoff by GEP model for calibration stage at the studied stations.
Validation of results stage
The R2, RMSE, and SE of the GEP model for runoff prediction in the validation stage
| Station | R2 | RMSE (m3/s) | SE | NSE |
|---|---|---|---|---|
| Polchehr | 0.96 | 10.99 | 0.37 | 0.92 |
| Nazarabad | 0.93 | 30.63 | 0.29 | 0.91 |
| Afrineh | 0.99 | 3.70 | 0.08 | 0.99 |
| Abdolkhan | 0.91 | 32.34 | 0.37 | 0.80 |
| Station | R2 | RMSE (m3/s) | SE | NSE |
|---|---|---|---|---|
| Polchehr | 0.96 | 10.99 | 0.37 | 0.92 |
| Nazarabad | 0.93 | 30.63 | 0.29 | 0.91 |
| Afrineh | 0.99 | 3.70 | 0.08 | 0.99 |
| Abdolkhan | 0.91 | 32.34 | 0.37 | 0.80 |
Comparison of observed and predicted runoff by the GEP model for the validation stage at the studied stations.
Comparison of observed and predicted runoff by the GEP model for the validation stage at the studied stations.
Runoff simulation with RegCM model
Runoff simulations by the RegCM model coupled with convection schemes including Emanuel, Grell, Kain, Kue, and Tiedtke were conducted in the Karkeh watershed from 1993 to 1999 so that 1993 and 1994 were to spin up and 1999–1995 were considered to evaluate the outputs of the model. Then, the runoff outputs of the model at Polchehr, Nazarabad, Afarina, and Abdul Khan hydrometric stations were compared with the observational data, and the most suitable scheme was selected. Furthermore, the ensemble average of all convection schemes (Ensemble) was also taken into account.
Table 6 shows the performance of the RegCM model in estimating monthly runoff under different convection schemes. According to the results, the Kain scheme outperformed other schemes, owing mainly to the lowest average model errors (RMSE = 298.2 and SE = 4.6), followed by the Grell schemes (RMSE = 366.6 and SE = 5.6), Ensemble (RMSE = 396.7 and SE = 6), Kuo scheme (RMSE = 397.4 and SE = 5.9), Emanuel scheme (RMSE = 442.1 and SE = 6.7), and Tiedtke scheme (RMSE = 543.1 and SE = 6.5) are ranked second to sixth, respectively. Moreover, the very small values of the average coefficient of determination (ranging from 0.048 to 0.13) indicate that there is no linear relationship between model outputs and observations. Also, comparing the results of all the stations shows the Kain scheme to have the lowest model error, with the RMSE ranging from 127.7 (Afrinah station) to 534.4 (Abdol Khan station) and SE ranging from 2.9 (Afrine station) to 6.2 (Abdol Khan station).
Results of the evaluation of the RegCM model coupled with different convection schemes to simulate the monthly runoff of the studied hydrometric stations
| Station | Schemas | R2 | RMSE (m3/s) | SE | NSE |
|---|---|---|---|---|---|
| Polchehr | Emanuel | 0.097 | 235.461 | 7.944 | −35.57 |
| Ensemble | 0.067 | 209.414 | 7.065 | −27.93 | |
| Grill | 0.040 | 200.147 | 6.753 | −25.42 | |
| Kain | 0.037 | 169.900 | 5.732 | −18.04 | |
| Kuo | 0.035 | 199.287 | 6.724 | −25.20 | |
| Tiedtk | 0.099 | 283.546 | 9.566 | −52.03 | |
| Nazarabad | Emanuel | 0.061 | 538.614 | 5.174 | −27.96 |
| Ensemble | 0.047 | 486.047 | 4.669 | −22.59 | |
| Grill | 0.028 | 448.801 | 4.311 | −19.11 | |
| Kain | 0.027 | 360.740 | 3.465 | −11.99 | |
| Kuo | 0.022 | 508.175 | 4.881 | −24.78 | |
| Tiedtk | 0.084 | 656.576 | 6.307 | −42.04 | |
| Afrineh | Emanuel | 0.057 | 180.507 | 4.124 | −14.70 |
| Ensemble | 0.048 | 164.991 | 3.770 | −12.12 | |
| Grill | 0.034 | 160.233 | 3.661 | −11.37 | |
| Kain | 0.026 | 127.691 | 2.918 | −6.86 | |
| Kuo | 0.015 | 162.983 | 3.724 | −11.8 | |
| Tiedtk | 0.097 | 220.762 | 5.044 | −22.49 | |
| Abdolkhan | Emanuel | 0.138 | 813.782 | 9.411 | −124.52 |
| Ensemble | 0.146 | 726.503 | 8.402 | −99.04 | |
| Grill | 0.098 | 657.023 | 7.598 | −80.82 | |
| Kain | 0.071 | 534.416 | 6.180 | −53.13 | |
| Kuo | 0.120 | 718.996 | 8.315 | −96.99 | |
| Tiedtk | 0.240 | 1,011.499 | 11.698 | −192.93 |
| Station | Schemas | R2 | RMSE (m3/s) | SE | NSE |
|---|---|---|---|---|---|
| Polchehr | Emanuel | 0.097 | 235.461 | 7.944 | −35.57 |
| Ensemble | 0.067 | 209.414 | 7.065 | −27.93 | |
| Grill | 0.040 | 200.147 | 6.753 | −25.42 | |
| Kain | 0.037 | 169.900 | 5.732 | −18.04 | |
| Kuo | 0.035 | 199.287 | 6.724 | −25.20 | |
| Tiedtk | 0.099 | 283.546 | 9.566 | −52.03 | |
| Nazarabad | Emanuel | 0.061 | 538.614 | 5.174 | −27.96 |
| Ensemble | 0.047 | 486.047 | 4.669 | −22.59 | |
| Grill | 0.028 | 448.801 | 4.311 | −19.11 | |
| Kain | 0.027 | 360.740 | 3.465 | −11.99 | |
| Kuo | 0.022 | 508.175 | 4.881 | −24.78 | |
| Tiedtk | 0.084 | 656.576 | 6.307 | −42.04 | |
| Afrineh | Emanuel | 0.057 | 180.507 | 4.124 | −14.70 |
| Ensemble | 0.048 | 164.991 | 3.770 | −12.12 | |
| Grill | 0.034 | 160.233 | 3.661 | −11.37 | |
| Kain | 0.026 | 127.691 | 2.918 | −6.86 | |
| Kuo | 0.015 | 162.983 | 3.724 | −11.8 | |
| Tiedtk | 0.097 | 220.762 | 5.044 | −22.49 | |
| Abdolkhan | Emanuel | 0.138 | 813.782 | 9.411 | −124.52 |
| Ensemble | 0.146 | 726.503 | 8.402 | −99.04 | |
| Grill | 0.098 | 657.023 | 7.598 | −80.82 | |
| Kain | 0.071 | 534.416 | 6.180 | −53.13 | |
| Kuo | 0.120 | 718.996 | 8.315 | −96.99 | |
| Tiedtk | 0.240 | 1,011.499 | 11.698 | −192.93 |
Comparison of observed and predicted runoff by Kain scheme from RegCM model in studied hydrometric stations.
Comparison of observed and predicted runoff by Kain scheme from RegCM model in studied hydrometric stations.
Enhancing the RegCM model's accuracy
The evaluation of the monthly bias-corrected runoff the simulated by the RegCM model coupled with different convection schemes in the studied hydrometric stations
| Station | Schemas | R2 | RMSE (m3/s) | SE | NSE |
|---|---|---|---|---|---|
| Polchehr | Emanuel | 0.089 | 49.963 | 1.686 | −0.65 |
| Ensemble | 0.071 | 53.232 | 1.796 | −0.87 | |
| Grill | 0.047 | 51.973 | 1.753 | −0.78 | |
| Kain | 0.049 | 53.660 | 1.810 | −0.9 | |
| Kuo | 0.053 | 54.205 | 1.829 | −0.94 | |
| Tiedtk | 0.055 | 53.300 | 1.798 | −0.87 | |
| Nazarabad | Emanuel | 0.066 | 141.941 | 1.363 | −1.01 |
| Ensemble | 0.053 | 147.796 | 1.420 | −1.18 | |
| Grill | 0.032 | 147.574 | 1.417 | −1.17 | |
| Kain | 0.064 | 142.131 | 1.365 | −1.02 | |
| Kuo | 0.041 | 147.450 | 1.416 | −1.17 | |
| Tiedtk | 0.078 | 139.951 | 1.344 | −0.96 | |
| Afrineh | Emanuel | 0.058 | 62.715 | 1.433 | −0.90 |
| Ensemble | 0.051 | 60.670 | 1.386 | −0.77 | |
| Grill | 0.045 | 59.623 | 1.362 | −0.71 | |
| Kain | 0.014 | 61.406 | 1.403 | −0.82 | |
| Kuo | 0.008 | 68.887 | 1.574 | −1.29 | |
| Tiedtk | 0.081 | 58.522 | 1.337 | −0.65 | |
| Abdolkhan | Emanuel | 0.140 | 92.186 | 1.066 | −0.61 |
| Ensemble | 0.143 | 93.635 | 1.083 | −0.66 | |
| Grill | 0.105 | 98.005 | 1.133 | −0.82 | |
| Kain | 0.096 | 96.500 | 1.116 | −0.77 | |
| Kuo | 0.127 | 94.490 | 1.093 | −0.69 | |
| Tiedtk | 0.232 | 82.893 | 0.959 | −0.30 |
| Station | Schemas | R2 | RMSE (m3/s) | SE | NSE |
|---|---|---|---|---|---|
| Polchehr | Emanuel | 0.089 | 49.963 | 1.686 | −0.65 |
| Ensemble | 0.071 | 53.232 | 1.796 | −0.87 | |
| Grill | 0.047 | 51.973 | 1.753 | −0.78 | |
| Kain | 0.049 | 53.660 | 1.810 | −0.9 | |
| Kuo | 0.053 | 54.205 | 1.829 | −0.94 | |
| Tiedtk | 0.055 | 53.300 | 1.798 | −0.87 | |
| Nazarabad | Emanuel | 0.066 | 141.941 | 1.363 | −1.01 |
| Ensemble | 0.053 | 147.796 | 1.420 | −1.18 | |
| Grill | 0.032 | 147.574 | 1.417 | −1.17 | |
| Kain | 0.064 | 142.131 | 1.365 | −1.02 | |
| Kuo | 0.041 | 147.450 | 1.416 | −1.17 | |
| Tiedtk | 0.078 | 139.951 | 1.344 | −0.96 | |
| Afrineh | Emanuel | 0.058 | 62.715 | 1.433 | −0.90 |
| Ensemble | 0.051 | 60.670 | 1.386 | −0.77 | |
| Grill | 0.045 | 59.623 | 1.362 | −0.71 | |
| Kain | 0.014 | 61.406 | 1.403 | −0.82 | |
| Kuo | 0.008 | 68.887 | 1.574 | −1.29 | |
| Tiedtk | 0.081 | 58.522 | 1.337 | −0.65 | |
| Abdolkhan | Emanuel | 0.140 | 92.186 | 1.066 | −0.61 |
| Ensemble | 0.143 | 93.635 | 1.083 | −0.66 | |
| Grill | 0.105 | 98.005 | 1.133 | −0.82 | |
| Kain | 0.096 | 96.500 | 1.116 | −0.77 | |
| Kuo | 0.127 | 94.490 | 1.093 | −0.69 | |
| Tiedtk | 0.232 | 82.893 | 0.959 | −0.30 |
Comparison of observed and predicted runoff by bias-corrected RegCM output coupled with Tiedtke and Emanuel schemes in the studied hydrometric stations.
Comparison of observed and predicted runoff by bias-corrected RegCM output coupled with Tiedtke and Emanuel schemes in the studied hydrometric stations.
To determine the best model to simulate monthly runoff, Table 8 summarizes the results of bias-correlated RegCM outputs at each station. As shown in Table 8, the average coefficient of determination between simulated and observed values in the GEP model is 0.94, SE is 0.28, and RMSE is 19.4 m3/s. Moreover, the average coefficient of determination between the observed and simulated values in the RegCM model is 0.12, the average SE is 1.33, and the average RMSE is 82.8 m3/s. The RegCM's hydrology model is highly sensitive to uncertainties in precipitation estimates that lead to soil moisture uncertainties and consequent moisture fluxes, which in turn affect runoff simulations. Due to the accumulation of these uncertainties, the RegCM will produce greater runoff simulation errors than a GEP model. It is important to note that several uncertainties can affect runoff simulations, including boundary and initial conditions, dynamic cores, physics schemes, cumulus convection, and radiation schemes. This study, however, concentrated on one of these uncertainties (cumulus convection schemes) that affect runoff simulations. In addition, the overestimation can be attributed to the RegCM climate model's failure to consider local features, such as built dams, that prevent high-intensity runoff. Compared to the RegCM model, the GEP model performed better; therefore, using this model is recommended to simulate monthly runoff.
Summary results of monthly runoff prediction at studied hydrometric stations
| GEP | RegCM | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Station | R2 | RMSE (m3/s) | SE | NSE | Station | R2 | RMSE (m3/s) | SE | NSE |
| Polchehr | 0.96 | 10.99 | 0.37 | 0.92 | Polchehr | 0.09 | 49.96 | 1.69 | −0.65 |
| Nazarabad | 0.93 | 30.63 | 0.29 | 0.91 | Nazarabad | 0.08 | 139.95 | 1.34 | −0.96 |
| Afrineh | 0.99 | 3.70 | 0.08 | 0.99 | Afrineh | 0.08 | 58.52 | 1.34 | −0.65 |
| Abdolkhan | 0.91 | 32.34 | 0.37 | 0.80 | Abdolkhan | 0.23 | 82.89 | 0.96 | −0.30 |
| GEP | RegCM | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Station | R2 | RMSE (m3/s) | SE | NSE | Station | R2 | RMSE (m3/s) | SE | NSE |
| Polchehr | 0.96 | 10.99 | 0.37 | 0.92 | Polchehr | 0.09 | 49.96 | 1.69 | −0.65 |
| Nazarabad | 0.93 | 30.63 | 0.29 | 0.91 | Nazarabad | 0.08 | 139.95 | 1.34 | −0.96 |
| Afrineh | 0.99 | 3.70 | 0.08 | 0.99 | Afrineh | 0.08 | 58.52 | 1.34 | −0.65 |
| Abdolkhan | 0.91 | 32.34 | 0.37 | 0.80 | Abdolkhan | 0.23 | 82.89 | 0.96 | −0.30 |
CONCLUSION
In this study, the accuracy and efficiency of GEP and RegCM models were investigated in simulating rainfall-runoff processes, and the following results were obtained:
A combination of rainfall, runoff, and temperature time series was used as input patterns in the GEP model to simulate the monthly runoff of the main branches, and finally, the input pattern of rainfall and runoff of the main branches had the best performance. A few points should be noted, namely that in upstream Karkheh dam stations, the runoff was simulated without changing the trend, but in downstream stations, the trend was removed before running the simulation.
Using the RegCM model, runoff simulation was carried out with a variety of convection schemes. The results indicate that the Kain scheme has the best runoff simulation performance out of all other schemes, followed by Grell, Ensemble, Kuo, Emanuel, and Tiedtke.
The bias correction method was used in this model to improve the accuracy of RegCM results, and the results demonstrate the positive effects of bias correction. Results showed that the Tiedtke scheme in runoff simulation performed best compared to other schemes, while Emanuel, Kain, Ensemble, Grell, and Kuo schemes were ranked second through sixth.
Due to the use of rainfall and discharge statistics, the GEP model is found to be more accurate than the RegCM model in simulating monthly runoff.
This study has some limitations. Firstly, it only applied the GEP model to discharge and climate data, without taking into account other factors like soil profile, topology, and vegetation. Secondly, the analysis of runoff was limited to only four hydrometric stations in the Karkheh basin, which had relatively long historical data.
ACKNOWLEDGEMENTS
The authors express their gratitude to Bu-Ali University for providing the necessary facilities to conduct the research.
DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.
CONFLICT OF INTEREST
The authors declare there is no conflict.
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