Construction of the water balance model for the Bontanga irrigation dam in Northern Ghana

Water is essential for all living things, so it must be made available in sufficient amounts and quality to meet both the present and future demand driven by the growing population and agricultural land expansion (Kidane & Andarge 2022). Despite the globally increasing freshwater demand, adequate water resource planning and management and its economic use must be given greater attention for the sustainability of water resources. Analysis of the water balance in the river or in the reservoir is important for water resource monitoring, evaluation, and management, mainly in data-scarce watersheds, when assessing the impact of land use and cover change on the storage capacity of the dam. When surface water flow (stream or surface runoff) is captured by constructing an impounding reservoir, there will always be water losses through evaporation, deep percolation, and seepage (FAO 2006). According to Kidane & Andarge (2022), during the estimation of the water balance, rainfall, evapotranspiration, surface runoff, groundwater table, and soil water content are important parameters of the water balance. Water balance represents the balance between inflow water (surface runoff and rainfall) and outflow water (evapotranspiration, underground seepage, and irrigation water demand) (Roy & Ophori 2012). Normally, water balance is used to evaluate the amount of rainfall that becomes stream flow, surface runoff, or groundwater (Hasenmueller & Criss 2013). In semi-arid regions, water resource availability for domestic, industrial, and irrigation purposes is diminishing day by day due to climate change and increased socio-economic activities as a result of population growth. Agricultural land expansion, deforestation of natural forests, and increased urbanization in the watershed have significantly impacted surface runoff, underground water recharge, and sediment load transportation (Domfeh et al. 2015). For a well-managed water resource system, the inflow volume of water in the river or reservoir should have the same outflow volume of water; however, due to human activities in the watershed, climate change, and poor land conservation management, the volume of water in rivers and reservoirs has decreased for many decades, leading to a reduction of outflow volume of water in comparison to the inflow volume (Juma et al. 2022). Currently, the Bontanga irrigation dam has the capacity to harvest and store 19,553,212.52 m³ of water, enough to irrigate 556.04 ha of paddy. Agricultural activities near the river banks, forest and bush fire, overgrazing, and poor agricultural practices are contributing factors leading to watershed degradation (Tesfahunegn et al. 2021). Studies conducted by Adongo et al. (2020) on the Bontanga watershed regarding sedimentation of irrigation dams reported that the storage capacity of the dam has decreased by 10.80% due to sedimentation as a result of human activities. The researcher primarily concentrated on understanding the implications of soil loss on sediment accumulation within the reservoir. These studies have significantly contributed to the understanding of sediment-related challenges, a crucial aspect that impacts water availability in the Bontanga irrigation dam during the dry season. The researcher has laid down a foundation by emphasizing the importance of managing sedimentation for reservoir sustainability. The present research aims to investigate the details of how reservoir sedimentation impacts water retention in the reservoir. The Bontanga irrigation dam stands as the only large irrigation facility in Kumbungu District, Tamale. This dam plays a pivotal role as the primary water source for essential activities such as drinking and fishing, and serves as a crucial economic resource for small-scale farmers engaged in the cultivation of rice and vegetables. Despite the socio-economic importance of the dam in the community, assessment of the water balance in the reservoir to assist in monitoring, evaluation, and management of water resources for various socio-economic developments has not been examined in this reservoir. According to Adie et al.(2012), water balance analysis is a useful tool that can be used to correlate relationships between climate data, land use and cover change, groundwater flow, surface runoff, and soil characteristics. Due to limited hydrological data from the watershed and within the reservoir itself, model parameters were estimated for the duration of 32 years starting from 1990 to 2022 by evaluating different input model parameters such as surface runoff from the watershed, evaporation on the surface of the reservoir, irrigation water requirements, and rainfall volume on the surface of the reservoir. These input parameters were used to estimate the available water (AV) in the reservoir based on the reservoir water balance models. However, no previous investigations have specifically addressed the Bontanga irrigation dam to comprehend the volume of water retained within the reservoir during the dry season, accounting for the effects of evaporation and irrigation water supply. Hence, the present study aims to develop a predictive model capable of estimating the available volume of water in the reservoir, considering the dynamics of evaporation and irrigation water supply. The novelty of this study lies in the ability to construct a model capable of predicting the available volume of water in the reservoir by incorporating and analyzing multiple explanatory variables simultaneously.

• (1) Meteorological data such as rainfall (P), minimum temperature (T_min), maximum temperature (T_max), wind speed, relative humidity, and sunshine hours for the duration of 32 years from 1990 to 2022 were provided by Savanna Agricultural Research Institute (SARI) Meteorological Station. The collected data were used to compute six sets of crop water requirements, evaporation, and surface runoff corresponding to years 1990, 1994, 1997, 2002, 2013, and 2022.

• (2) Remote sensing Landsat 5 (TM), Landsat 7 (ETM+), Landsat 8 (OLI), and Landsat 9 (OLI-2) remote sensing satellite images of 1997, 2002, 2013 and 2022 and a digital elevation model (DEM) with 30 m spatial resolution were acquired from (https://earthexplorer.usgs.gov/).

• (3) Soil data were collected from the Ghana Irrigation Development Authority (GIDA) in Tamale.

• (4) Due to the limited resolution of Landsat images from the USGS website in 1990 and 1994, no land use and land cover (LULC) change analysis was conducted for those years. Instead, LULC change data from Landsat imagery in 1997 was utilized to estimate surface runoff and soil loss for that specific year.

Soil type, weather conditions, and the size of the irrigable area are critical factors in determining the optimal irrigation method to be employed for crop cultivation. To assess the impact of soil type on irrigation water requirements, 18 disturbed soil samples were randomly collected from the paddy field, ranging from depths of 300 to 600 mm. In the laboratory, soil moisture content at field capacity (FC) and at the permanent wilting point (PWP) was determined using a pressure plate apparatus, while soil texture was analyzed via the hydrometer method and interpreted using a triangular soil classification chart. Utilizing a 10 m spatial resolution Sentinel-2 satellite image obtained from (https://scihub.copernicus.eu/), the net irrigable area for the year 2022 was estimated. After generating a composite band from four Sentinel-2 bands, the image was classified using the supervised maximum likelihood classification method in ArcGIS 10.0. Three distinct land uses were identified: farm ponds, uncultivated land, and cultivated land. The area covered by each identified land use within the scheme was calculated by multiplying the number of correctly classified pixels by the size of one pixel in the ArcGIS 10.0 attribute table.

The Landsat images from 1997, 2002, 2013 and 2022 (Table 1) were classified using the supervised maximum likelihood classification method in ArcGIS 10.0. Various bands were combined to generate a composite band for generating training samples, which in turn, were utilized for land use classification. The accuracy of each Landsat image was assessed based on Overall accuracy, and the Kappa coefficient (K) as suggested by Mewded et al. (2021).

Ra: Monthly rainfall data (mm); R: Annual rainfall data (mm); a: Number of months; Ke: Soil erodibility factor (t·ha·MJ⁻¹ · mm⁻¹); P: Percentage of particles (% of very fine sand + % of silt) * (100 – % clay content); OMC: Organic matter content (% organic carbon * 1.724); x: code of soil structure; y: code of soil permeability; FlowAccum: Flow accumulation; Cellsize: the grid cell size; Ɵ: slope of the land in degrees; Z: Constant dependent on the land slope gradient: taken as 0.50 if the slope angle is greater than 5%, 0.4 on slopes of 3–5%, 0.3 on slopes of 1–3%, and 0.20 on the land slopes less than 1%; NIR: Surface spectral reflectance in the near-infrared band; RED: Surface spectral reflectance in the red band; NDV: Normalized Difference Vegetation Index.

Four key assumptions of a multiple linear regression model were used to assess the reliability and accuracy of the constructed model (John 2015); (a) we assumed a linear relationship between the independent and dependent variables, (b) we assume observations are independent to each other, (c) we assumed that the differences between the observed and predicted values are normally distributed, and (d) the variance of the residuals is constant across all levels of the independent variables. To avoid overfitting the data in the model, the independent variables (x_i) with stronger linear correlation to the dependent variable (y_i) were selected (Montesinos López et al. 2022) using the forward selection method in GenStat software. However, the multiple regression model's effectiveness is limited in capturing non-linear relationships between independent and dependent variables. The following steps were followed to select potential independent variables to be included in the model.

• (1) The first independent variable (x) to enter into the model was derived by regressing the dependent variable (y) against each individual independent variable (x), such as y on x₁, y on x₂, etc. The variable exhibiting the highest adjusted R² and (t_probability) < α = 0.05 was chosen as a potential candidate for inclusion in the model. Once incorporated, this value becomes a permanent fixture within the model, remaining unchanged throughout subsequent analyses.

• (2) The determination of the second independent variable for inclusion in the model involved regressing the dependent variable (y) on the selected independent variable (x) and each of the remaining independent variables individually, such as y on x₁, x₂, y on x₁, x₃, y on x₁, x₄, and so forth. The combination of variables meeting the model selection criteria is characterized by the highest adjusted R² and F_cal > F.dist, was chosen as the potential candidate to be incorporated into the model. The calculation of F_cal was conducted using the following formula.

  

  (26)

  where = sum of squares of the residual with fewer independent variables in the model, = sum of squares of the residual with more independent variables, = residual degree of freedom of model with fewer explanatory variables, and = residual degree of freedom of model with more explanatory variables. Whereas F.dist is reference distribution F (α = 0.05, 1, ⁠).

• (3) The determination of the third independent variable to be incorporated into the model involved regressing the dependent variable (y) on a pair of chosen independent variables (x) and each of the remaining independent variables individually, such as y on x₁, x₂, x₃, y on x₁, x₂, x₄, and so forth. If none of these combinations yields any statistical significance, the analysis is stopped.

An echo sounder and a high-precision GPS were used to measure the depth of water and the geographical position (coordinates) of each collected data point in the reservoir. The actual reservoir bed level of each measurement point was estimated by deducting the echo sounder's recorded depth from the known reservoir water surface level, established with automatic leveling. A topographical map with a 0.60 m intermediate contour and a 1.20 m index contour was generated using Civil 3D AutoCAD software as shown in Figure 1 of Appendix 1, Supplementary material. The results revealed that the current available volume of water in the reservoir (AV) m³ estimated using the Prismoidal formula was found to be 19,553.212.52 m³, as shown in Table 1 of Appendix 1, Supplementary material.

Crop evapotranspiration ET_c (mm/day) was estimated using CROPWAT software version 8.0, developed by FAO, as shown in Equation (2). The results revealed that in 2022, ET_c was 7.050 mm/day, in 2013 it was 7.974 mm/day, in 2002 it was 8.240 mm/day, in 1997 it was 7.621 mm/day, in 1994 it was 6.97 mm/day, and in 1990 it was 7.270 mm/day, as shown in Table 1 of Appendix 2, Supplementary material.

The net depth of water available in the soil for plants to grow was estimated using Equation (3), the plant root zone depth for rice crops was taken as 600 mm, and the permissible depletion factor as 1. Results of the analysis show that the net irrigation depth (d_net) for the Bontanga Irrigation Scheme was found to be 48.00 mm, as shown in Table 1 of Appendix 3, Supplementary material.

The number of consecutive days needed to complete one irrigation cycle was estimated using Equation (4). It was observed that in the year 2022, a span of 7 days was required to accomplish one irrigation cycle, while for the years 2013, 2002, 1997, and 1994, the duration narrowed to 6 days each; similarly, the year 1990 also demanded 7 days to complete one irrigation cycle, as depicted in Table 1 of Appendix 3, Supplementary material.

Water is essential for plants to grow. Equation (5) was used to estimate the amount of irrigation water that the irrigation reservoir should provide to meet the net irrigation crop water requirements (dnet) in the rice field. In this study, the irrigation application efficiency (Ea) was taken as 70%. Results revealed that 68.57 mm of water must be supplied to the irrigation scheme from the reservoir for the crop to grow.

The volume of water required per cropping calendar to bring soil moisture to the field capacity was estimated using Equations (6) and (7). The analysis reveals a direct correlation between the increasing population and the expansion of agricultural land, synchronized with the intensifying demands for irrigation water. Findings revealed that, in 1990, a total net area of 448.50 ha was designated for irrigation, necessitating 6,099,395.29 m³ of water. In subsequent years, this trend persisted: in 1994, the irrigable area covered 454.07 ha, with a water demand of 6,175,111.40 m³; by 1997, the irrigable area had expanded to 461.10 ha, entailing a water requirement of 6,270,827.36 m³. The trend continued with an irrigable area of 472.83 ha in 2002, necessitating 6,430,354.03 m³ of water; in 2013, the irrigable area stretched to 495.00 ha, with a water demand of 6,731,859.75 m³. Similarly, in 2022, an irrigable area of 556.04 ha demanded 6,481,702.68 m³ of water, as shown in Table 1 of Appendix 3, Supplementary material.

The estimation of excess water necessary to bring the soluble salt content beneath the rice crop's root zone in the rice field was estimated using the methodologies outlined in Equations (8) and (9). The findings showed the leaching water requirements for various years: 64,391.145 m³ in 1990, 58,584.321 m³ in 1994, 59,481.900 m³ in 1997, 65,931.415 m³ in 2002, 66,795.300 m³ in 2013, and 77,400.768 m³ in 2022, all of which are presented in Table 2 of Appendix 3, Supplementary material.

The rice crop requires more water to grow than any other crop variety. In lowland irrigation, farmers prefer flood irrigation, maintaining standing water throughout the rice growing period to ensure a sufficient water supply and effective control of weeds and pests. Equation (10) was used to estimate the volume of standing irrigation water in the scheme. Results revealed that the volume of lowland standing irrigation water corresponding to various years was 672,750 m³ in 1990, 681,105 m³ in 1994, 691,650 m³ in 1997, 709,245 m³ in 2002, 742,500 m³ in 2013, and 834,060 m³ in 2022, as presented in Table 3 of Appendix 3, Supplementary material.

The total volume of water that must be released from the reservoir to account for rice crop production, leaching requirements, and the 15 cm of lowland standing water was estimated using Equation (11). The analysis revealed an upward trend in water withdrawal from the reservoir spanning the years 1990–2022. The total volume of water allocated for irrigation purposes exhibited an increase over this period: the total volume of water withdrawal from the reservoir was 6,836,536.44 m³ in 1990, 6,914,800.72 m³ in 1994, further to 7,021,959.26 m³ in 1997, reaching 7,205,530.45 m³ in 2002, peaking at 7,541,155.05 m³ in 2013, and stabilizing at 7,393,163.45 m³ in 2022, as broadly illustrated in Table 4 of Appendix 3, Supplementary material.

Rainfall inflow volume on the surface of the reservoir was estimated by multiplying the average total rainfall by the reservoir surface area. The reservoir surface area was derived from the stage storage capacity of the reservoir, estimated using the Prismoidal formula. Equation (23) was used to estimate rainfall inflow on the surface of the reservoir. The results of the analysis revealed distinct variations in the rainfall inflow volume on the reservoir's surface area across different years. Specifically, the figures were as follows: 2.09 × 10⁶ m³ in 1990, 1.90 × 106 m³ in 1994, 1.88 × 10⁶ m³ in 1997, 1.86 × 10⁶ m³ in 2002, 2.46 × 10⁶ m³ in 2013, and 2.49 × 10⁶ m³ in 2022, all precisely outlined in Table 5 of Appendix 3, Supplementary material.

The reservoir evaporation volume was estimated by multiplying the surface area of the reservoir by the evaporation rate as shown in Equation (24). The reservoir surface area was estimated using the Prismoidal formula, while the evaporation rate was estimated using CROPWAT version 8.0 software. The results of the comprehensive analysis depicted a distinct pattern of volume of evaporation: an evaporation rate of 2.90 × 10⁶ m³ was observed in 1990, slightly reduced to 2.86 × 10⁶ m³ in 1994, followed by a decrease to 2.83 × 10⁶ m³ in 1997, 2.76 × 10⁶ m³ in 2002, 2.73 × 10⁶ m³ in 2013, and ultimately 2.52 × 10⁶ m³ in 2022, as shown in Table 6 of Appendix 3, Supplementary material.

In the study area, seven (7) LULC change classes were identified, namely, grassland, water bodies, mixed shrub and grassland, dense forest, agricultural land, mixed forest and shrub, and built-up area. The results of the analysis revealed that the overall accuracy of classified images corresponding to the years 1997, 2002, 2013, and 2022 was 92, 91.89, 95.27, and 83.64%, respectively. Likewise, the respective Kappa coefficient was 90, 90, 94, and 82%, respectively. Kappa coefficient greater than 81% indicates an almost perfect classification of images (Mfwango et al. 2022).

The SCS-CN model was used to estimate direct surface runoff generated from the watershed corresponding to different land use and land cover (LULC) changes in 1997, 2002, 2013, and 2022, as shown in Figures 1–4 and Table 1 of Appendix 3, Supplementary material. Statistical results revealed that, on average, agricultural land dominates the Bontanga watershed area by 34.93%, followed by mixed shrub and grassland at 21.89%, dense forest at 19.86%, grassland at 10.82%, and finally, mixed forest and shrub land at 8.89%. The alteration in LULC change caused an obvious increase in the surface runoff trend from 1990 to 2022. The progression of surface runoff volumes over the years is as follows: 9.08 × 10⁶ m³ in 1990, 9.09 × 10⁶ m³ in 1994, 9.23 × 10⁶ m³ in 1997, further increased to 12.66 × 10⁶ m³ in 2002, continued increase to 12.71 × 10⁶ m³ in 2013, and finally ended at a peak of 25.05 × 10⁶ m³ in 2022, as highlighted in Table 2 of Appendix 4, Supplementary material.

The InVEST-SDR model integrates RUSLE parameters to compute the amount of sediment load exported downstream of the watershed. The results of the RUSLE parameters are presented in Figures 1–6 and Table 1 of Appendix 4, Supplementary material. Based on the analysis, crop management factor (C) in the watershed ranged from 0.0293 to 0.075, Rainfall erosivity factor (R) from 1,156.50 to 3,466.08, Soil erodibility factor (K) from 0.0474 to 0.0487, and slope length and steepness factor (LS) from 0.00 to 50.858. In this study, the conservation support practice factor (P) was taken as 1. The outputs of the InVEST-SDR model are presented in Figures 1–6 of Appendix 6, Supplementary material. The analysis produced convincing results that highlighted a deep understanding of the impact of land use and land cover (LULC) changes on downstream sediment export from the watershed. Over the course of the years from 1990 to 2022, the sediment load transported downstream exhibited a range between 2,898.38 tons per year and 5,245.92 tons per year. This dynamic progression is vividly highlighted in the figures for each year as follows: a sediment load of 3,752.60 tons per year was observed in 1990, followed by 3,713.09 tons per year in 1994, then increased to 4,453.79 tons per year in 1997, a subsequent decrease to 3,942.78 tons per year in 2002, and 2,898.38 tons per year in 2013, and finally ended at a peak of 5,245.92 tons per year in 2022. These findings are broadly depicted in Table 2 of Appendix 5, Supplementary material.

Sedimentation, filtration, and weighing methods were used to estimate the average wet density of the sediment concentration exported downstream of the Bontanga watershed. The InVEST-SDR model was used to compute the amount of sediment transported to the reservoir. During analysis, the available volume of water in the reservoir was estimated using Equation (22). Through the utilization of sedimentation, filtration, and precision weighing techniques, the average wet density of the sediments was derived by dividing the sediment mass collected at the throwback of the reservoir by the volume of a water–sediment mixture (500 mL), yielding the wet density of the sediments from the watershed of 26.80 grams per cubic centimeter. The results of the analysis revealed a consistent trend in the accumulation of sediment within the reservoir, concurrent with a reduction in the reservoir's water holding capacity from 1990 to 2022. In 1990, the sediment load within the reservoir was at 700,111.94 m³, while the dam's storage capacity at full supply level was recorded as 24,299,888.06 m³. By 1994, the sediment volume had increased to 1,254,304.48 m³, causing a corresponding reduction in the reservoir's water level to 23,745,695.52 m³. Further progression was observed in 1997, with the sediment volume intensifying to 1,752,863.06 m³, leading to a decrease in the reservoir's water capacity to 23,247,136.94 m³. The upward trajectory continued in 2002, as sediment volume reached 2,488,456.34 m³, causing a reduction in the reservoir's water capacity to 22,511,543.66 m³. By 2013, sediment volume had grown to 3,678,089.93 m³, resulting in a water capacity decrease to 21,321,910.07 m³. The trend ended in 2022, with a sediment volume of 5,439,779.48 m³ and a corresponding water capacity in the reservoir decline to 19,560,220.52 m³. These significant results are presented in detail in Table 3 of Appendix 5, Supplementary material.

In the study area, two different cropping seasons, namely, the wet and dry seasons, are observed. Therefore, this model is specifically designed for predicting water balance in the reservoir during the dry season. The rationale behind this limitation lies in the absence of inflow into the reservoir during this period. As a result, considering the quality and accuracy of data used for the construction of the model, its applicability is limited to the Bontanga dam.

The water balance model was constructed using a multiple linear regression model. The interpretation of the results assumes a linear relationship between the explanatory and response variables. The model was tested at level of significance α = 0.05, and coefficient of determination (R²) was found to be 0.7433. This signifies that about 74.33% of dependent variables were well explained by independent variables. Moriasi et al. (2007) and Mbungu (2016) suggested that a model is considered satisfactory when the Residuals Standard Deviation Ratio (RSR) is lower than 0.70. The results of the coefficients of the explanatory variables in the constructed water balance model shown in Equation (29) reveal that every one-unit increase in the evaporation volume of water from the surface of the reservoir (EV) will result in an increase in the available volume of water in the reservoir (AV) by 9.693 units. This suggests that as evaporation from the surface of the reservoir increases, more water is being added to the reservoir. This could be because when the land surface is heated by solar radiation, surface water evaporates, condenses into clouds, and falls as rainfall, contributing to surface runoff, river streams, and replenishing reservoirs, lakes, and oceans (Li 2023). Likewise, model results show that a unit increase in irrigation water requirements (TIWR) will cause a decrease in the available volume of water in the reservoir (AV) by 1.831 units. In practical terms, this indicates that as the demand for irrigation water increases, the available volume of water in the reservoir is projected to decrease. This reduction could occur because water is being withdrawn from the reservoir for irrigation purposes, leading to a decline in the overall volume of water stored (Sampaio et al. 2020). Based on these results, the constructed model will help the water resource manager to examine the coefficients of the explanatory variables to identify which factors have the most significant impact on available water in the reservoir. This information helps to prioritize interventions and allocate resources effectively. Considering estimated R² and RSR, the model can be used as a valuable tool for water resource management predicting the available volume of water in the reservoir during the dry season.

A water balance model for the Bontanga irrigation dam was developed using a multiple linear regression model. During model development, the available volume of water in the reservoir (AV) was considered as a dependent variable, while the irrigation water requirement (TIWR) and evaporation volume from the surface of the reservoir (EV) were considered as an independent variable. The linear relationship between independent variables and dependent variables was measured using R². During analysis, R² was found to be 0.7433. This signifies that about 74.33% of dependent variables were well explained by independent variables. Furthermore, the accuracy of predicted data was compared with the observed data using the ratio of the root mean square error to the standard deviation of measured data (RSR). The estimated RSR was found to be 0.67, which is lower than 0.70. This finding suggests model simulation performance is satisfactory. Therefore, the constructed reservoir water balance model will offer valuable insights to dam managers in several key areas: (1) quantifying the current quantity of water in the reservoir by considering outflows and evaporation, (2) forecasting the future conditions of the reservoir's water through the utilization of historical data, (3) assisting dam managers in identifying critical periods of water scarcity within the reservoir, and (4) optimizing reservoir operations by determining the timing of water releases, allocation strategies, and storage decisions. Additionally, the constructed model provides essential information to stakeholders and policymakers regarding the impact of drought conditions on reservoir water levels. This knowledge enables them to formulate proactive strategies for drought preparedness and mitigation, including the implementation of water conservation measures and the management of water releases during critical periods. The results reveal that the constructed model will perform well; however, the limited availability of accurate observed surface runoff and sediment exported downstream of the watershed was a primary constraint during model construction. Therefore, this study recommends the installation of a gauging station downstream of the watershed to enhance hydro-meteorological data collection.

For optimal water resource management, further studies should be conducted throughout each cropping season to systematically assess the magnitude and dynamics of each explanatory variable, and to identify their respective contributions to water reduction in the reservoir. Additionally, the study encourages further development of the constructed water balance model into a predictive, enhancing comprehension of climate change dynamics and their consequences on water resources.

Many thanks to Savanna Agricultural Research Institute (SARI) for providing valuable updated meteorological data for this study, the University for Development Studies – Nyankpala Campus, and the West Africa Center for Water, Irrigation and Sustainable Agriculture.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.