A new approach for suspended sediment load calculation based on generated flow discharge considering climate change

Use of general circulation models (GCMs) is common for forecasting of hydrometric and meteorological parameters, but the uncertainty of these models is high. This study developed a new approach for calculation of suspended sediment load (SSL) using historical flow discharge data and SSL data of the Idanak hydrometric station on the Marun River (in the southwest of Iran) from 1968 to 2014. This approach derived sediment rating relation by observed data and determined trend of flow discharge time series data by Mann-Kendall nonparametric trend (MK) test and Theil-Sen approach (TSA). Then, the SSL was calculated for a future period based on forecasted flow discharge data by TSA. Also, one hundred annual and monthly flow discharge time series data (for the duration of 40 years) were generated by the Markov chain and the Monte Carlo (MC) methods and it calculated 90% of total prediction uncertainty bounds for flow discharge time series data by Latin Hypercube Sampling (LHS) on Monte Carlo (MC). It is observed that flow discharge and SSL will increase in summer and will reduce in spring. Also, the annual amount of SSL will reduce from 2,811.15 ton/day to 1,341.25 and 962.05 ton/day in the near and far future, respectively.


INTRODUCTION
The control of erosion, sediment transport, sedimentation and water quality are considered important issues in watershed management, river engineering and design of hydraulic structures. In recent decades, climatic changes, global warming, increasing population growth and human activities have ruined forests, pastures, wetlands and other natural resources. Humans have developed cities and industrial regions; this matter has reduced permeability of watersheds and has increased flow discharge of floods and erosion of watersheds. By increasing sediment yield, water quality will be reduced and the life of aquatic vegetables, animals and fish will be endangered.
Due to a shortage of sediment data and their low quality, generating synthetic data using methods such as the Markov chain and Monte Carlo methods is necessary. These methods are stochastic approaches used for data generation.
This study deals effectively with different methods for generation of flow discharge and SSL time series and evaluation of the ability of these methods to generate the time series for the future.
The performed researches have paid attention to only one aspect of application of these methods; these studies are classified to the categories below.  These methods use observed data, while the global circulation models (GCMs) and downscaling models utilize various scenarios and their uncertainty is more than those of the applied procedure in this study.

The Marun Watershed
The Marun Watershed is located in the southern part of the

The Markov chain method
The Markov chain method memorizes stochastic characteristics historical data such as mean, variance, skewness coefficient, governing stochastic distribution and so on. In this research, the monthly Markov chain method is applied for generation of synthetic data. The equation used is: in which: i is index of year and j is index of month, Y i,jþ1 is generated data for the ith year and month ( j þ 1)th, Y i,j is generated data for the ith year and jth month, r j is the regression coefficient between observed data of the jth and ( j þ 1)th months, S y is the standard deviation of observed monthly data, Y is the mean of observed monthly data, t iþ1 is a random value that is regarding to the governing probability distribution on data (for normal probability distribution, t iþ1 is equal to the frequency factor (k) of normal probability distribution).

The Monte Carlo (MC) method
This research utilized the Monte Carlo (MC) method to generate data. This method generated 4000 monthly flow discharge time series data. For each month and each time series, the number of generated data is 40.
The MC method is a mathematical method that generates random data considering probability distribution governing the main time series data. This method calculates quantiles and values of different confidence levels (for example 90% (it ranges from 5% to 95%)) of the whole predicted uncertainty bounds. The predicted uncertainty bounds are determined by probability distribution governing the generated time series data.

Methodology
The procedure of this study includes the following steps: 1. Collection of daily flow discharge and suspended sedi-

The performance criteria
In order to evaluate the performance of the models, the following criteria are applied.
Root mean square error (m 3 /s): where: Q pre is the predicted flow discharge and Q obs is the observed flow discharge.
The Nash-Sutcliffe model efficiency coefficient is defined as follows: For an ideal model, the RMSE should be close to zero and E NS should be close to one.

Flow discharge data
Daily flow discharge and suspended sediment load (SSL) time series data during 1968-2014 were derived from data sets collected from the Khuzestan Water and Power Authority (KWPA). These time series have no missing data.
Then, the daily flow discharges and SSLs were converted to monthly flow discharges and SSLs by averaging daily data for each month. Annual data were also calculated in the same way.
The homogeneity of the monthly and annual flow discharge time series data was illustrated by the run test. The run test showed that the p-value of these annual and monthly (from January to December) time series was less than 0.05 and jZjof the normal probability distribution was more than 1.96. Thus, these time series were found to be homogeneous at a significance level of 5%.
The Augmented Dickey-Fuller test (ADF) and the Kwiatkowski-Phillips-Schmidt-Shin test (KPSS) showed the stationary of flow discharge time series data at a significance   Figure 3).
Based on the calculated slope of trend lines by the TSA estimator for different months, the predicted mean values of monthly and annual flow discharges were predicted and illustrated in Figure 4 for the next 40 years and 80 years.

Suspended sediment load (SSL) data
In order to establish a regression relation between input (flow discharges) versus (SSL), the following exponential relation, called the sediment rating relation, is presented.
in which SSL (ton/day) and flow discharge (m 3 /s) are denoted by Q S and Q W , respectively. Since scattering of data is very high, the value of R is relatively low for the sediment rating relation.
The SSL related to the average of 100 generated flow discharge time series data, the driest and the wettest flow

DISCUSSION
According to the applied tests, Pettitt's test, run test, ADF and KPSS, the results illustrated homogeneity and stationarity of monthly and annual flow discharge time series data and proved that these time series data have no change point. Therefore, the trend of these time series data can be determined by the MK trend test.
The MK test showed a significant trend, especially in spring and summer. While, the TSA estimator showed a decreasing trend in winter and spring and an increasing trend in summer and autumn and the annual flow discharge  Comparison between predicted flow discharges in the near and far future, by the TSA estimator method, and 90% of total prediction uncertainty bounds, however, revealed a different truth. In the near future, it was observed that the mean of monthly flow discharges are more than uncertainty bound 95% in August and September while in the far future, the mean of monthly flow discharges are more than uncertainty bound 95% in July, August, September and October and are less than uncertainty bound 5% in April and May. In summer, flow discharge will be significantly increased while in spring, it will be considerably decreased.
In other words, the LHS on MC method can not consider uncertainty developed by climatic change because this method only utilizes observed data to generate data.
Observed flow discharges and SSLs data were used to derive sediment rating relation. Due to the high scatter of SSL data, the correlation coefficient of the obtained Table 1 | The best method and generated In the future, the value of SSL will be reduced in winter and spring (due to reduction of flow discharge) and will be increased in summer and autumn (due to increase in flow discharge). Since most SSL transportation occurs in winter and spring, the annual value of SSL will be decreased in the future (especially in the far future).
The SSL related to the flow discharge time series data generated by the MC method had more compliance with monthly, seasonal and annual predicted SSL data in the near and far future. The Markov chain method stores main characteristics of observed time series data, therefore it can not state a good fitness with predicted time series data in the future.
With respect to reduction of monthly flow discharge from December to June in future, SSL related to the driest generated flow discharge time series data had more compliance with monthly predicted SSL data in the near and far future. Due to increasing monthly flow discharge from July to October in future, SSL related to the wettest generated flow discharge time series data had more compliance with monthly predicted SSL data in the near and far future. In November, the variation of monthly flow discharge in future was relatively low, therefore SSL related to the average of 100 generated flow discharge time series data had more compliance with monthly predicted SSL data in the near and far future. Since the Markov chain method stores characteristics of observed flow discharge time series data, it is considered the superior method in this month.
Considering reduction of annual and seasonal flow discharge in spring and winter in future, SSL related to the driest generated flow discharge time series data had more compliance with annual and seasonal predicted SSL data in the near and far future. Due to increasing seasonal flow discharge in summer in future, SSL related to the wettest generated flow discharge time series data had more compliance with seasonal predicted SSL data in the near and far future. In autumn, the variation of seasonal flow discharge in future was less than the other seasons; therefore, the Markov chain method, which stores characteristics of observed flow discharge time series data, was considered a robust method in this season. On the other hand, due to decreasing precipitation and flow discharge in December, SSL related to the driest generated flow discharge time series data had more compliance with seasonal predicted SSL data in the near and far future in autumn.

CONCLUSIONS
Sediment yield in rivers can cause several problems for hydraulic structures such as pumps, sluices and so on. The climatic change and global warming will change hydrological and meteorological parameters such as precipitation, temperature and flow discharge in future. These changes  This study proved that the MC method is a superior method to generate flow discharge data in most months. The data generated by this method have more compliance with predicted SSL in the near and far future. The wettest generated time series in months must be considered when flow discharge will increase and the driest generated time series in months when flow discharge will decrease to predict SSL in future.
The annual value of SSL will reduce from 2,811.15 ton/day to 1,341.25 and 962.05 ton/day in the near and far future, respectively. The greatest reduction and increase in monthly value of SSL will occur in December and July, respectively.
Adib & Mahmoodi () illustrated that the amount of SSL will increase in the future for flood conditions at the Idanak Station. This fact shows that climatic change can increase the probability of occurrence of extreme conditions such as severe floods and droughts in the future.

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