Modeling and predicting suspended sediment load under climate change conditions: a new hybridization strategy

In the present study, for the first time, a new strategy based on a combination of the hybrid leastsquares support-vector machine (LS-SVM) and flower pollination algorithm (FPA), average 24 general circulation model (GCM) output, and delta change factor method has been developed to achieve the impacts of climate change on runoff and suspended sediment load (SSL) in the Lighvan Basin in the period (2020–2099). Also, the results of modeling were compared to those of LS-SVM and adaptive neuro-fuzzy inference system (ANFIS) methods. The comparison of runoff and SSL modeling results showed that the LS-SVM-FPA algorithm had the best results and the ANFIS algorithm had the worst results. After the acceptable performance of the LS-SVM-FPA algorithm was proved, the algorithm was used to predict runoff and SSL under climate change conditions based on ensemble GCM outputs for periods (2020–2034, 2035–2049, 2070–2084, and 2085–2099) under three scenarios of RCP2.6, RCP4.5, and RCP8.5. The results showed a decrease in the runoff in all periods and scenarios, except for the two near periods under the RCP2.6 scenario for runoff. The predicted runoff and SSL time series also showed that the SSL values were lower than the average observation period, except for 2036–2039 (up to an 8% increase in 2038).


INTRODUCTION
The suspended sediment movements are important in different fields, such as water resource management, water structure designs, and river and dam engineering. Modeling the amount of suspended sediment in the river is an essential issue to design water storage and flow control facilities, such as dams and canals. Also, the suspended sediments affect the quality of drinking water requirements of residential areas and the quality of water requirements of agriculture and industry. On the other hand, the suspended sediments are the result of complex and nonlinear flow processes in the river (Nourani et al. ). Therefore, modeling the nonlinear relationship between suspended sediments and river flow using different nonlinear methods has become one of the important challenges for different scientific societies, such as engineering and water resources management.
Meanwhile, machine learning algorithms are more popular than physical and mathematical methods, due to their high accuracy, lower cost, and few number parameters. In  (Yang ) was also effective in increasing the accuracy of machine learning methods, such as ANN (Wang et al. ) and ANFIS (Farrokhi et al. ). Also, in the study conducted by Wu et al. (), the Extreme Learning Machine (ELM) optimized by the FPA was used to estimate the reference evapotranspiration. In this study, the hybrid ELM and flower pollination had more accuracy than the hybrid of ELM with genetic and ant algorithms. Also, mentioned methods had successful applications in other fields such as the optimal operation of the reservoir (Ehteram et al. a; Mohammadi et al. ) and the optimal design of the open channel (Farzin & Valikhan Anaraki ).
Naturally, there is a specified pattern in sediment transportation and flow in the river. However, the phenomenon of climate change has increased the speed of the hydrological cycle and changed the magnitude and temporal pattern of runoff with the increasing temperature and changing precipitation patterns. This can increase the concentration of sediments in the rivers and, consequently, the riverbed instability, and it can damage the structures around the river, as well as causing problems for living organisms.
Therefore, the effect of climate change is necessary to study on the suspended sediment load (SSL).
The effect of climate change on the amount of SSL has been investigated by Azari et al. ()  To the best of our knowledge, there are few studies for modeling runoff and SSL. Added to this, some of these studies considered climate change in predicting runoff and SSL. Hence, in the present study, for the first time, a new hybridization strategy has been developed for modeling and predicting runoff and SSL under climate change conditions. For this purpose, the hybrid of LS-SVM and FPA (LS-SVM-FPA) is employed for modeling and predicting runoff and SSL under climate change conditions. In this regard, the average of 24 GCM outputs, namely Ensemble GCM, is used for considering climate change conditions. Moreover, the delta change factor method is used for downscaling outputs of ensemble GCM. Thus, it is worth mentioning that after modeling, the results are compared with standalone LS-SVM and ANFIS to demonstrate the ability of LS-SVM-FPA in modeling runoff and SSL.

MATERIALS AND METHODS
Case study and the used data Lighvanghai Basin is located in the northwest of Iran and the southern city of Tabriz, and on the northern slopes of Sahand Mountain. This basin is the sub-basin of the Urmia Lake, and it is extended from eastern lengths of 46 -20 0 -30″-46 -27'-30″ to the north latitude of 37 -42 0 -55″-37 -49 0 -30″. The basin drains an area of 76 km 2 , with an average discharge of 24.6 MCM. The basin has a rainy and humid climate. The maximum amount of runoff in the Lighvan Basin is related to spring. The average slope of the Lighvan Basin is 11%, and therefore, the soil of this basin is under severe erosion. In the present study, the Lighvan Basin is investigated because the Lighvan River is one of the largest subdivisions of the Lighvan Chai River, which discharges to Urmia Lake. Figure 1 illustrates the Lighvan basin location in the Urmia Lake Basin and in Iran.
In the present study, the runoff and SSL are modeled using meteorological data of the Lighvan Tabriz and Sahand synoptic stations and runoff and SSL data of the Lighvan hydrometric station. The statistical properties of the survey data are shown in Table 1. Also, to investigate the effect of climate change on runoff and SSL, the largescale precipitation and temperature data of ensemble GCMs from the fifth report under three scenarios, including RCP2.6, RCP4.5, and RCP8.5, are used, downloaded from supported and distributed data in Canadian climate change scenarios network (http://climate-scenarios.canada. ca/?page=gridded-data). The ensemble model is obtained by averaging from 24 GCMs from the fifth report, considering equal weight (equal to 1) for each GCM. The names of these 24 GCMs and their weights for contracting the ensemble GCM are found in http://www.cccsn.ec.gc.ca. Table 2 indicates the characteristics of the three considered scenarios. Based on this table, RCP8.5 is the worst scenario. In the present study, based on the available statistical data, In the present study, a new strategy has been developed for modeling and predicting SSL under climate change   RCP2.6 Before 2100, the maximum radiation will be 3 W·m À2 , which will reach 2.6 W·m À2 by 2100. The annual temperature rises to 1.5 C.
RCP4.5 It has more stability with less oscillations. The amount of radiation in 2100 will be 4.5 W·m À2 . The annual temperature rises to 2.4 C.
RCP8.5 In 2100, radiation is about 8.5 W·m À2 . Also, the annual temperature will rise by 4.9 C.
conditions. In the proposed strategy, the hybrid of LS-SVM and FPA, LS-SVM, and ANFIS is used for modeling and predicting runoff and SSL, and the delta change factor method is used for the downscaling large-scale precipitation and temperature of the ensemble GCM. In this strategy, there are two sections, including modeling and predicting (Figure 2(a)). In the modeling section, the observed precipitation, temperature, runoff, and SSL data are standardized, lagged with different lagging times, and divided into training and testing periods. The standardized relation is as follows: where X new is standardized data, X is original data, X mean is the mean of data in the training period, and std(X) is the standard deviation of data in the training period.
Afterward, observed precipitation and observed temperature data in different stations are used as input data, and observed runoff data are used as target data for rain- Afterward, the predicted runoff data are used as inputs of the best runoff-SSL model, and SSL data are predicted for future periods. The scheme of the proposed method for predicting SSL is shown in Figure 2 where e t is the error parameter, and C is the penalty coefficient. This objective function can be solved by the optimization algorithms. To handle constraints in a defined objective function, the Lagrangian method is used. By using the Lagrangian method, the final objective function is given as follows: where α is known as Lagrangian coefficients, and O t is the observation output. By taking partial derivation from relation (4) to W, b, e, and α (Deo et al. ): In SVM, to solve such objective functions, the quadric optimization method is used. However, unlike the SVM method, LS-SVM uses the least-square optimization method for solving this objective function. It is worth mentioning that the least-square optimization method has lower computational cost and more efficiency than the quadric optimization method. To solve relations (4) and (5) by the least-square optimization method, these relations must be rewritten as follows: Thus, Kernel is known as the kernel function. After solving relation (6), the final relation between inputs and outputs is rewritten as follows (Farzin et al. ): The kernel function is a nonlinear function with different types, including linear, polynomial, and radial base kernel functions. According to the study conducted by Ghosh (), the radial kernel function is more accurate than other mentioned kernel functions. Therefore, the radial base kernel function is used as follows: Here, σ represents the width of the kernel function. In the LS-SVM algorithm, a model can be developed only by determining two parameters of C and σ. These two parameters have a significant impact on the final results of LS-SVM. However, there is no specific method for determining these parameters. Figure 3 shows the schematic of LS-SVM.

Flower pollination algorithm
The FPA is proposed by Yang ( to simulate this motion. Global search on FPA algorithm is performed by the following relation: where X tþ1 i , X t i , X Ã , and L represent the new position, the current position, the best position, and the parameter corresponding to Levy flight, respectively.
Self-pollination in the FPA algorithm is also considered as a local search. The following relation is used to accomplish this action: where ε is a random number with a uniform distribution between 0 and 1. Therefore, relation (6) leads to smaller motions, and it is considered as a local search. There is also a specific probability of p to down one of each global or local search. Hence, the positions of search agents in FPA are updated as follows: where p is the probability of change (between global and local search). Figure 4 demonstrates the pseudo code of FPA. In the present study, the parameters of the maximum number of iterations, population size, and the probability of change were considered equal to 500, 20, and 0.8 by trial and error, respectively. See Yang () for more information.
The hybrid of LS-SVM and FPA As mentioned, the LS-SVM has two parameters of C and σ, while there is no specific method for determining these parameters. These two parameters have a high impact on the final accuracy of LS-SVM. Therefore, in the present study, FPA has been used to optimally determine these parameters.
(1) For this purpose, first, the parameters of C and σ are randomly assigned to each of the FPA search agents.
(3) Afterward, the fitness function (R 2 ) is calculated for each search agent, and the best position or search agent is determined with the more fitness function. The fitness function is calculated as follows: The position of the search agents will evolve based on relationships (10) and (11), and steps 2 to 4 will be repeated until the termination condition is reached. Finally, the optimal solution problem (C, σ) is returned. Figure 5 demonstrates the schematic of the LS-SVM and FPA hybrids.
Adaptive neuro-fuzzy inference system The ANFIS algorithm was first developed (

Downscaling of precipitation and temperature
One of the most common, but simple methods to downscale the outputs of GCMs, is the delta change factor method, which has been used in many studies such as Ehteram et al. (b). In this method, the monthly average data are used instead of using direct outputs of GCMs. Also, the changes in temperature and precipitation under climate change are calculated in this method as follows: In which, T t is the future temperature, P t is the future precipitation, T obs,t is the observed temperature, P obs,t is the

Evaluation criteria
In the present study, the accuracy of the runoff and SSL modeling results are evaluated using evaluation criteria, including determination coefficient (R 2 ), relative rootmean-square error (RRMSE), and Nash-Sutcliffe efficiency (NSE) coefficient, which are presented as follows:   and R values are also obtained from the following relations:

Runoff and SSL modeling
In this study, the runoff is modeled using the data of precipitation and mean temperature at the Lighvan station, precipitation, mean temperature, minimum temperature, maximum temperature, and solar radiation at Tabriz stations, as well as the mean temperature, minimum temperature, and maximum temperature at the Sahand station.
Since each combination of inputs can have a different effect on the accuracy of the results, 11 combinations with 0-10-month period lag time are defined for the inputs of the investigated algorithms. Table 3   LS-SVM and ANFIS algorithms. Also, it is indicated that the LS-SVM algorithm is more accurate than the ANFIS.
The    Therefore, SSL data from the previous months have not been used as the inputs for SSL modeling. Also, the dispersion parameters of SSL data, such as standard deviation and range are significantly more than runoff data. These issues lead to less accuracy of SSL modeling than runoff modeling in Figures 7 and 8.

Downscaling precipitation and temperature
Precipitation and temperature are the most important components in the hydrology cycle. The changes in these components are the most important factors in river regime changes and, consequently, sediment production changes in the basin. Precipitation and temperature are predicted by large-scale GCMs. Therefore, in the present study, the downscaling of precipitation and temperature has been investigated using the delta change factor method to investigate the effect of climate change on river SSL more precisely. The delta change factor method converts largescale precipitation and temperature into local-scale precipitation and temperature. In Table 5, effect of climate change on precipitation and mean, maximum, and minimum temperature at three stations of Lighvan, Tabriz, and Sahand is investigated, using the comparison of values predicted in four future periods (which include 2020-2034, 2035-2049, 2070-2084, and 2085-2099) with those in the observation period (1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004). The bold values in Table 5   This pattern is also seen in the scenarios of RCP2.6, RCP4.5, and RCP8.5. However, the predicted monthly average runoff in the spring for all three scenarios in the four investigated periods is lower than or close to the similar values in the observation period. Also, the magnitude of this runoff reduction for all three scenarios in the two periods of 2020-2034 and 2035-2049 is less than in the other two periods (Figure 9).  12.10 11.6 11.6 11.6 11.6 11.6 11.6 11.6 11.6 11.61 11.6 11.6 11.6 Change (%) 0 Therefore, it can be concluded that the runoff has a decreasing trend. It is also observed that the amount of runoff decreased by the increases in precipitation, which can be due to the increase in mean, minimum, and maximum temperature and, accordingly, evaporation.
Also, in the winter and autumn seasons, when the temperature is low as a result of evaporation, the increase in precipitation has increased the predicted runoff for the two near future periods compared to the observation period. In the next two periods, the runoff in the two seasons of winter and autumn is less than the observed runoff ( Figure 8). scenario has the greater slope (À0.0046). Also, the amount  of predicted runoff in the 2070-2099 period is less than the runoff in the observation period. As mentioned before, this descending trend in runoff is due to the increase in predicted temperature. Also, by more attention to Figure 9, it can be seen that the moving average of annual runoff oscillates.
This oscillation may be for the decrease in precipitation in all three scenarios. Thus, increasing temperature parameters, such as minimum, mean, and maximum temperature, can lead to more snowmelt, change in the pattern of precipitation from snow to rain, and increase in extreme events such as heavy precipitation. Figure 11 shows the monthly mean SSL in the observation and future periods. According to this figure, the predicted SSL is less than the SSL observed in all months of the year, except for May, June, and July. This is in full accordance with Figure 9 because, in this figure, the amount of future runoff is lower than the forecasted runoff.
However, the amount of SSL in May, Jun, and July is increased since the SSL is modeled based on the runoff with 0-and 1-month time delays, and the SSL in the mentioned months has been increased by the increase of runoff in the previous months, and more runoff leads to the more production of SSL. As can also be seen in Figure 11, SSL is highly sensitive to runoff changes, such that the SSL is sig- results could be due to the close results of downscaled temperature parameters in Table 6. (0.94 m 3 ·s À1 and 14.5 ton·day À1 for runoff and SSL, respectively). Accordingly, in all three scenarios, the SSL in the years 2036-2039 is more than the observed SSL, which could cause damage to the hydraulic structures. Thus, the slope change of SSL is more than runoff in all scenarios and periods, which is due to more sensitivity of SSL to changes of runoff.

CONCLUSION
In the present study, the hybrid of LS-SVM algorithm and FPA (LS-SVM-FPA) were used to model and predict the runoff and SSL. The results were also compared using LS- Also, in SSL modeling, the values of R 2 , RRMSE, and NSE criteria were equal to 0.85, 0.58, and 0.65, respectively.