Modelling and forecasting reservoir sedimentation of irrigation dams in the Guinea Savannah Ecological Zone of Ghana

Effective management of reservoir sedimentation requires models that can predict sedimentation of the reservoirs. In this study, linear regression, non-linear exponential regression and arti ﬁ cial neural network models have been developed for the forecasting of annual storage capacity loss of reservoirs in the Guinea Savannah Ecological Zone (GSEZ) of Ghana. Annual rainfall, in ﬂ ows, trap ef ﬁ ciency and reservoir age were input parameters for the models whilst the output parameter was the annual sediment volume in the reservoirs. Twenty (20) years of reservoirs data with 70% data used for model training and 30% used for validation. The ANN model, the feed-forward, back-propagation algorithm Multi-Layer Perceptron model structure which best captured the pattern in the annual sediment volumes retained in the reservoirs ranged from 4-6-1 at Karni to 4-12-1 at Tono. The linear and nonlinear exponential regression models revealed that annual sediment volume retention increased with all four (4) input parameters whilst the rate of sedimentation in the reservoirs is a decreasing function of time. All the three (3) models developed were noted to be ef ﬁ cient and suitable for forecasting annual sedimentation of the studied reservoirs with accuracies above 76%. Forecasted sedimentation up to year 2038 (2019 – 2038) using the developed models revealed the total storage capacities of the reservoirs to be lost ranged from 13.83 to 50.07%, with 50% of the small and medium reservoirs ﬁ lled with sediment deposits if no sedimentation control measures are taken to curb the phenomenon.


INTRODUCTION
The development and management of dams have been become a necessity in recent years, due to the seasonality of rainfall and water scarcity in many parts of the world (Yusuf & Yusuf 2012).Dams and their associated reservoirs store water during the rainy season and make it available for humans and animals to use in their immediate environment (Huang et al. 2018;Adongo et al. 2019).The contribution of irrigation dams towards boosting agricultural production is crucial, especially in dryland environments such as arid, semi-arid and other water-scarce areas in the world (Chihombori et al. 2013).As of 2011, the Global Reservoir and Dam estimated about 16.7 million dams with a total storage capacity of about 8,070 km 3 in the world (Lehner et al. 2011).
Despite the numerous importance of dams, one of the critical problems in their operation and management is the continuous deposition of sediments in their reservoirs via inflows (Chihombori et al. 2013).The construction of a dam and its reservoir on rivers and streams automatically cuts off sediment transport to the downstream side of the dam (Salimi et al. 2013), and this development has made the reservoir become a natural means for retention of the transported sediment (Hasan et al. 2011).Sedimentation results in loss of reservoir depth, storage capacity and reduction of designed lifespan of reservoirs (Basson 2010) and blocks irrigation canals, damages This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/).power generating turbines, and degrades reservoir water quality (Halcrow 2001).According to White (2001) and Schleiss et al. (2016), the existing reservoirs worldwide lose between 0.5% and 1.0% of their total storage capacity yearly with Basson (2010) reporting the global average sedimentation rate as between 0.7% and 0.8% per annum with highest occurrence in arid and semi-arid regions.Adongo et al. (2019) reported that reservoirs in northern Ghana are losing their storage capacities to sedimentation at a rate of 0.26 to 0.91% per year.
Modelling and forecasting of reservoir sedimentation has been the subject of several empirical studies since the 1950s (Jothiprakash & Garg 2009).In recent years, the artificial neural network (ANN) technique has shown excellent performance in regression, especially when used for pattern recognition, function estimation, forecasting and modelling (ASCE 2000).Jothiprakash & Garg (2009) noted that ANN is a highly non-linear mathematical model that can capture complex interactions among the input and output variables without any prior knowledge about the nature of these interactions.In the fields of hydrology and water resources engineering, ANNs have been extensively applied because of their ability to model both linear and non-linear systems without the need to make assumptions as are done in most conventional statistical approaches (Nourani 2009).Sarangi & Bhattacharya (2005) compared the performance of ANN models for sediment yield prediction with a linear regression model for the Banha watershed in India.Sarangi et al. (2005) developed ANN and linear regression models using watershed geomorphologic parameters to predict surface runoff and sediment yield of the St. Esprit Watershed, Quebec, Canada.Jothiprakash & Garg (2008) found that linear regression techniques sometimes underestimate or overestimate observed values and need modifications.Jothiprakash & Garg (2009) modelled the annual volume of sediment retained in the Gobindsagar Reservoir in India using the ANN and linear regression models.Salimi et al. (2013) also applied both ANN and linear regression models to model the sedimentation rate of the Karaj Dam Reservoir in Iran.
In this study, an ANN, linear and non-linear exponential regression models were explored and developed for estimation of annual rate of sedimentation of nine (9) reservoirs in the Guinea Savannah Ecological Zone of Ghana.The novelty of this study is that it used input parameters (Figure 2) that have direct influence in the sedimentation process of reservoirs in the Guinea Savannah Ecological Zone of Ghana in developing the ANN models for estimating and forecasting reservoir sedimentation in the study area and other areas with similar characteristics.

Description of study area
The study was carried out in nine (9) reservoirs in the Guinea Savannah Ecological Zone (GSEZ) of northern Ghana, namely Daffiama, Karni and Sankana reservoirs in the Upper West Region; Bontanga, Golinga and Libga reservoirs in the Northern Region; and Gambibgo, Tono and Vea reservoirs in the Upper East Region.Figure 1 is a map showing the study reservoirs whilst the principal characteristics of the reservoirs are presented in Table 1.The study reservoirs represent 3% of the number of reservoirs in the GSEZ of northern Ghana with all the three (3) large-sized reservoirs covered and with six (6) being small-and medium-sized reservoirs.Small, medium and large reservoirs are reservoirs with maximum storage capacities of ,1 Mm 3 , 1 to 3 Mm 3 and .3Mm 3 respectively (Basson 2007;Kolala et al. 2015).

Linear regression and non-linear exponential regression models
Linear regression (LR) and non-linear exponential regression (NER) analyses were performed, relating the output parameter (annual deposited sediment volume) and the input parameters (annual inflow, annual rainfall, annual reservoir trap efficiency and age of reservoir) using Minitab software, version 16.0 and R software, version 3.6.3respectively.
A general mathematical model of the form (Equation ( 1)) which provides a linear relation for SV with constant variance and good fits to the assembled data is given as:  2)) which provides a non-linear exponential relation for SV with constant variance and good fits to the assembled data is given as: (2) where: SV ¼ predicted annual sediment volume retention (m 3 ); AR ¼ annual rainfall (mm); AI ¼ annual water inflow (m 3 ); ATE ¼ annual trap efficiency (%); Ra ¼ age of reservoir (y); u 1 ¼ model scaling coefficient; u 2 to u 5 ¼ scaling exponents of predictors.Values of the parameters u 2 to u 5 were found using multivariate optimization in R software.

Artificial neural network (ANN) model
An artificial neural network (ANN) was used to model the rate of reservoir sedimentation in the irrigation dams.ANN is a black box and programmed computational non-linear modelling tool that has an input layer, a hidden layer and an output layer.Each layer consists of several neurons and the layers are interconnected by sets of correlated weights.The neurons receive inputs from the initial inputs or the interconnections and produce outputs by the transformation, using an adequate non-linear transfer function (Sultana & Naik 2016).Four (4) steps were followed in the design and development of the ANN model as described by Vilas et al. (2011).Using the input parameters; that is, annual inflows, annual rainfall, reservoir trap efficiency and age of the reservoir and the output parameter; that is, annual deposited sediment volume for each reservoir, the trial-and-error procedure of Jothiprakash & Garg (2009) and Salimi et al. (2013) was used to select the appropriate ANN architecture.
The input parameters were chosen on the basis of their influence in the reservoir sedimentation process.Also, the trial-and-error approach was used to determine the number of hidden layers and the number of neurons in each hidden layer.The number of neurons in the hidden layer plays an essential role in the performance of the ANN model.Due to the single output nature of the model, the linear transfer function corresponding to the hidden layer and the sigmoid transfer function corresponding to the single output layer (annual deposited sediment volume) were used to select the best ANN architecture.All the considered data set values were pre-processed and normalized using Equation (3) given by Salimi et al. (2013) to make the entries standardized.The transformation of the observed data was necessary to make them compatible with the attributes of the transfer where: x n ¼ normalized data; x i ¼ real amount of data; x min ¼ minimum entry data and x max ¼ maximum entry data.Min-max normalization preserves the relationships among the normalized and original data values (Vamsidhar et al. 2010).
In order to train and validate the proposed ANN model, the split-sample method was applied, in which 70% of the data was used for training the model and then the remaining 30% was used for validation.This split of dataset (70% training and 30% validation) gave the best accuracies in the training and validation stages.Similarly, Salimi et al. (2013) and Sultana & Naik (2016) recorded the highest accuracies using the 70% training and 30% validation split.The feed-forward back-propagation (FFBP) ANN training algorithm presented in Figure 2 was used to model the data.

Estimation of annual water inflows to the reservoirs
The Natural Resource Conservation Service-Curve Number (NRCS-CN) method developed by the United States Department of Agriculture (USDA-NRCS 1985) was used to estimate the water inflows into the study reservoirs.The method has its major input parameters as landuse/landcover classes, hydrologic soil groups, antecedent soil moisture conditions, rainfall, maximum potential soil retention, curve number and weighted curve number (USDA-NRCS 1985).Equations ( 4)-( 6) as developed by USDA-NRCS (1985) were very useful in the estimation of the water inflows into the reservoirs.

CN wt
where: CN wt ¼ area weighted curve number; CN i ¼ curve number of each LULC class; A i ¼ area of each LULC class (km 2 ) and A ¼ area of the catchment (km 2 ).where: Qd ¼ runoff depth (mm); P ¼ daily rainfall (mm) and S ¼ potential maximum soil moisture retention after runoff begins (mm).

Estimation of trap efficiencies of reservoirs
The trap efficiencies of the large reservoirs; that is, Tono, Vea and Bontanga, were estimated using the empirical model of Gill (1979) for medium-grained sediment given in Equation ( 7): where: TE Gill ¼ Gill's trap efficiency for medium-grained sediments (%); C ¼ designed storage capacity (m 3 ) and I ¼ annual water inflow to the reservoir (m 3 ).
The trap efficiencies of the small and medium reservoirs; that is, Gambibgo, Libga, Karni and Daffiama and Golinga and Sankana, were determined using the empirical model of Ward (1980) given in Equation ( 8): where: TE Ward ¼ ward's trap efficiency (%); C ¼ designed storage capacity of the reservoir (m 3 ) and I ¼ annual water inflow to the reservoir (m 3 ).

Estimation of annual sediment volume retention in the reservoirs
The grab sampling method (Mavima et al. 2011) was used to estimate sediment transported into the reservoirs annually via surface runoff with Equation (9) developed by Strand & Pemberton (1982) used in computation of the annual sediment volume in the reservoirs: where: SV ¼ annual volume of sediment retained in the reservoirs (m 3 /y); TASLtotal annual sediment concentration in water inflows to reservoir (mg/L); AI ¼ annual water inflow (l) and ATE ¼ annual trap efficiency of the reservoir (%).

Modelling input and output parameters of reservoir sedimentation
The four (4) input parameters used to model the rate of sedimentation of the reservoirs were annual rainfall, annual water inflow, annual trap efficiency and age of reservoir, whilst the output parameter was annual volume of sediment deposit (Table 2).These input parameters were selected because of their high influence in the sedimentation process of a reservoir.Salimi et al. (2013) and Sultana & Naik (2016) noted that reservoir sedimentation cannot occur without the influence of rainfall, water inflows, sediment inflows and the sediment trapping efficiency of the reservoir.As presented in Table 2, the annual rainfall in the reservoirs was found to vary between 617.20 mm and 1,382.30mm for the period of 2009-2018.The recorded annual water inflows to the reservoirs ranged from 197,836 m 3 at Daffiama to 55,371,500 m 3 at Tono.This variation of annual water inflows among the various catchments was noted to be influenced by catchment size, vegetation cover, antecedent moisture content, rainfall amount, land uses and soil characteristics.The trap efficiency of the reservoirs was found to range from 45.56 to 99.91%, with the least and highest trap efficiencies being recorded at Gambibgo and Tono reservoirs, respectively.The small and medium reservoirs were noted to have lower trap efficiencies than the large reservoirs and this could be due to their frequent annual spillage, hence higher sediment outflows.
In a similar study by Sultana & Naik (2016), a trap efficiency range of 41.80-99.99% for the Sriramsagar reservoir, a large reservoir in Nizamabad was obtained.The annual volume of sediment retained in the reservoirs was estimated to range from 1,594.42 m 3 at Daffiama reservoir to 355,016.9 m 3 at Tono reservoir.These levels of sediment retention were noted to be influenced by poor land use practices in the catchments and buffer zones of the reservoirs causing high levels of sediment production and inflows into the reservoirs.The reservoirs also lacked the facilities to flush out sediment, hence little sediment outflow from the reservoirs.

Reservoir sedimentation modelling using linear and non-linear exponential regression
Relating the output parameter to the four (4) input parameters in Minitab version 16.0, the overall response of the multi variate linear regression analysis for each of the study reservoirs is presented in Table 3 and the non-linear exponential regression models in Table 4.The linear regression (LR) models recorded an R 2 of 0.763-0.902(Table 3), thus suggesting that the selected input variables accounted for about 76.3 to 90.2% of the volume of sediment retained in the reservoirs, whilst other factors accounted for about 9.8-23.7%.The results also showed that an increase in the annual rainfall by a unit resulted in an increase in the volume of sediment retention in the reservoirs by 6.05-42.02%(Table 3).A unit increase in annual water inflows also resulted in an increase in volume of sediment retention in the reservoirs by 0.49-1.08%.For annual trap efficiency, the   2)-( 10) presented in Table 3 can be used as the models for estimating annual volume of sediment retention in reservoirs with accuracy between 76.3 and 90.2%.Table 4 presents the expression for SV, which indicates that reservoir capacity loss increases with an increase of the independent variables; that is, AR, AI, ATE, and Ra.The exponent of Ra in Equations ( 11)-( 19) is less than one, thus indicating that the rate at which sediment is retained in the reservoirs is a decreasing function of time.This is expected because those areas of the reservoir that are conducive to settlement of fine sediments will fill quickly in the early years and then no longer be available for deposition.Shrinkage of deposited silt also takes place from weathering action and the superimposed loads of additional sediment, thereby reducing the sedimentation rate with time (Froehlich et al. 2017).
The study developed Generalised Linear Regression (GLR) and Non-linear Exponential Regression (NER) models for application on different reservoirs in the Guinea Savannah Ecological Zone (GSEZ) of northern Ghana using the data of the nine (9) study reservoirs.The details of the GLR model are presented in Table 5, whilst the details of the NER model are presented in Table 6.It can be observed that the accuracy of the models increased with increased number of input parameters.The models with the highest R 2 are Equation ( 28) for the GLR model and Equation (37) for the NER model.These models were therefore considered the best models for predicting annual rate of reservoir sedimentation in the GSEZ.The R 2 of 0.913 for the GLR model and 0.941 for the NER model indicate that the input parameters account for about 91.3% and 94.1%, respectively, of the variations in annual reservoir sedimentation in the GSEZ.Both models show that annual Bontanga SV ¼ 0:3011[(AR 0:37 )(AI 0:39 )(ATE 0:82 )(Ra 0:09 )] 0.858 11 Golinga SV ¼ 0:1380[(AR 0:23 )(AI 0:42 )(ATE 0:79 )(Ra 0:07 )] 0.797 12 Libga SV ¼ 0:2131[(AR 0:27 )(AI 0:34 )(ATE 0:74 )(Ra 0:12 )] 0.845 13 Gambibgo SV ¼ 0:4423[(AR 0:21 )(AI 0:31 )(ATE 0:59 )(Ra 0:18 )] 0.872 14 Tono SV ¼ 0:2415[(AR 0:25 )(AI 0:44 )(ATE 0:91 )(Ra 0:09 )] 0.913 15 Vea SV ¼ 0:5102[(AR 0:38 )(AI 0:48 )(ATE 0:77 )(Ra  volume of sediment retention increases as all the independent variables (AR, AI, ATE and Ra) increase.In Equation ( 37), as presented in Table 6, the exponent of Ra is less than one (1) and this indicates that the rate of sedimentation is a decreasing function of time.This is because those areas of the reservoir that are conducive for settlement of fine sediments will fill quickly in the early years and then no longer be available for deposition.Also, shrinkage of deposited silt takes place from weathering action and the superimposed loads of additional sediments thereby reducing the sedimentation rate with time.

Reservoir sedimentation modelling using artificial neural network (ANN)
A Multi-layer Perceptron (MLP) ANN architecture model consisting of three (3) layers was developed for each reservoir using the R tool.Since there was a large variation among the data sets, all the data were normalised between a range of 0 and 1.The model was trained using 70% of the data and the remaining 30% was used for validation.A satisfactory model was selected based on the minimum MSE values and the optimum values of R 2 generated during the training and validation stages.Performance statistics for the ANN model for each reservoir are presented in Table 7.
Based on the minimum MSE values of 0.034-0.143during the training stage and 0.069-0.187during the validation stage (Table 7), it was found that the Feed Forward, Back Propagation (BP ANN) models with structures ranging from 4-6-1 at Karni reservoir to 4-12-1 at Tono reservoir generated the best trend of the observed volume of sediment retained in the reservoirs.The detailed architecture of the proposed models are illustrated in Figure 3.According to Jothiprakash & Garg (2009), the best ANN prediction model is the ANN structure

Comparison of reservoir sedimentation prediction models
The three (3) reservoir sedimentation prediction models were compared based on their accuracies (Table 8).The accuracy of the linear regression (LR) model ranged from 76.3 to 90.2%, non-linear exponential regression model ranged from 79.7 to 91.3% and the ANN model ranged from 83.5 to 94.9%.The results from the ANOVA showed no significant difference among the models, as can be seen in Figure 4. Therefore, all the models were observed to be efficient and suitable for predicting the annual sedimentation of the reservoirs, as they recorded accuracies above 76% (Table 8).

Forecast of annual sediment volume retention in the study reservoirs
The developed linear regression (LR), non-linear exponential regression (NER) and artificial neural network (ANN) models were used to forecast the volume of sediment that would be retained in the reservoirs within the next 20 years; that is, by year 2038 and the results presented in Table 9 and Figure 5.

Figure 1 |
Figure 1 | Map of northern Ghana showing the study reservoirs (Adapted from Adongo et al. 2019).

Figure 2 |
Figure 2 | Detailed artificial neural network architecture of the reservoir sedimentation model.I ¼ input layer (Four input parameters were used), H ¼ hidden layer (dependent on the training algorithm), O ¼ output layer (the annual sediment inflow data were used).

Figure 3 |
Figure 3 | Detailed architecture of artificial neural network (ANN) model for the study reservoirs.

Table 1 |
Description of study reservoirs

Table 2 |
Input and output parameters for modelling of reservoir sedimentation

Table 3 |
Response of linear regression model a unit increase resulted in an increase in volume of sediment retention in the reservoirs by 16.01-87.23%.A unit increase in age of reservoir resulted in a 0.55-6.35%increase in volume of sediment retention in the reservoirs.Equations (

Table 4 |
Response of non-linear exponential regression modelInput parameter(s)NER prediction models for annual reservoir sedimentation of study reservoirs R 2 Eq.

Table 5 |
Linear regression models for estimating annual reservoir sedimentation in the GSEZ LR, linear regression; SV, annual sediment volume (m 3 ); AR, annual rainfall (mm); AI, annual inflow (m 3 ); ATE, annual trap efficiency (%), and Ra, age of reservoir (y); R 2 , coefficient of determination; Eq, equation, * -Developed and proposed model for application on different reservoirs in the Guinea Savannah Ecological Zone of northern Ghana.

Table 6 |
Non-linear exponential regression models for estimating annual reservoir sedimentation in the GSEZ

Table 7 |
Performance statistics of the ANN model for predicting annual reservoir sedimentation that best captured the pattern of the observed data set.Also, the R 2 values of 0.857-0.996and 0.814-0.931during the training and validation stages, respectively, suggest that averagely, about 81.35 to 96.60% of the variables are explained by the output of the models during the training and validation stages.The average accuracy of the