The methodology based upon the SWAT (Soil and Water Assessment Tool) model was structured into two main stages: flow calibration and nutrient estimation.
2.2.1. Flow calibration
Model and software description SWAT Model description
SWAT is a semi-distributed agro-hydrological model [
17] with a daily time step. SWAT is used for evaluating water quality and quantity, agricultural practices management, surface and subsurface water management and sediment, nutrient and pesticide transfer. SWAT is used worldwide by a large scientists community.
This model is based on the water balance equation which is as follows [
18]:
SWt = SWo + Σ (Rday +IRR– Qsurf – Ea – Wseep), (Eq.1)
where SWt is the final soil water content (mm) of the day, SWo is the in soil initial water content (mm), Rday is the daily rainfall (mm), IRR is irrigation volume added to the soil (mm), Qsurf is the surface runoff volume (mm), Ea is the actual evapotranspiration (mm), and Wseep is percolation loss from the soil profile into the shallow aquifer (mm).
SWAT-CUP and SUFI-2 algorithm
Uncertainties may occur while setting up and running the model. Uncertainties come either from measurement errors or from the model itself [
19,
20,
21]. To be used efficiently, the model’s performance must be tested. This study tested the correlation between observed data and simulated outputs statistically and graphically. Thus, Swat-cup (SWAT Calibration Uncertainty Program) was used to optimize the flow model. The program is the most widely used tool by the SWAT community. SWAT-CUP allows to perform calibration, uncertainty and global sensitivity analysis automatically (
Table 1). Several methods are integrated into the SWAT-CUP program. We have Sequential Uncertainty Fitting version 2 (SUFI-2) [
22,
23], Generalized Likelihood Uncertainty Estimation (GLUE) [
24], Particle Swarm Optimization (PSO) [
25], Parameter Solution (PARASOL) [
26] and Markov Chain Monte Carlo (MCMC) [
27].
Because of its simplicity in its use, the SUFI 2 method has permitted to perform global parameter sensitivity analysis, uncertainty analysis and calibration [
28].
Global sensitivity analysis
The analysis of global sensitivity begins with the definition of the objective function. Objcetive functions wthin SUFI2 include R
2, Chi2, NS, and R
2 multiplied by the line regression coefficient b, bR
2, and SSQR (sum of squared errors) coefficients. But for this study, NS and R
2 coefficients were the objective functions used. NS is used to analyse the strength of the model predictions and while R
2 coefficient is related to the correlation between simulations and observed values. Then, the values of the parameters to be optimized, are chosen based on Equation 2 [
29]:
bj,abs _min ≤ bj ≤ bj,abs_max , j=1…m (Eq.2),
where bj is the jth parameter and m is the number of parameters to be estimated.
The parameter global sensitivity in each simulation is accounted by the sensitivity matrix J, of g (bj) [
29] :
Jij = ∆gi/∆bj i=1…C2n (Eq.3),
where bj is the parameter, g is global sensitivity and i is all possible combinations of two simulations and j is the number of columns (number of parameters).
Latin Hypercube sampling is the sampling method used in this study. It makes it possible to calculate the global sensitivity by calculating a multiple regression system of the parameters considered [
29]:
(Eq.4),
where , . and are considered to be the respective standard deviations of the simulated and observed data; and are the averages of the simulated and observed data.
The relative impact of each parameter on the flow is identified from a statistical test. This impact is noted bi. The global sensitivity is related to the variation of the objective function which depends on the observed variation of the parameter considered when all parameters change.
Uncertainty analysis
P-factor and R-factor are used to calculate the uncertainties at 2.5% (Xl) and 97.5% (Xu) percentiles of the cumulative distribution at each point. P-factor indicates the percentage of observed data bracketed by 95PPU. R-factor is the average thickness of the 95PPU band obtained from the standard deviation of the observed data [
20].
Calibration analysis
We chose NSE, R
2 and PBIAS as objective functions to analyze the performance and accuracy of the simulations. The PBIAS measures the percentage of bias. When PBIAS is 0, the simulation is said to be accurate. A positive PBIAS shows an underestimation of the model, while negative values indicate an overestimation of the model bias [
30]. Its use makes it possible to refine and make more precise the predictions of the model [
31] in [
32,
33,
34,
35,
36,
37,
38,
39,
40,
41,
42,
43]. NSE (equation 5) varies from -∞ to 1 (for a strong link between observed and simulated values). Equation (6) is used to calculate PBIAS. Moriasi et al. [
35] made the classification of model performance:
PBIAS <± 10: very good performance model;
±10<PBIAS<±15: good performance model;
± 15 <PBIAS < ± 25: satisfactory performance;
PBIAS > ± 25: unsatisfactory performance.
R
2 is calculated according to equation (7); it varies from 0 to 1, 1 representing a perfect simulation [
44]. A value greater than 0.5 is often accepted because it expresses a good restitution of the observed data [
32].
(Eq. 5)
(Eq. 6)
(Eq. 7)
with Qiobs observed flow, Qisim simulated flow, Qmean average observed flow, average observed flow and average simulated flow.
Model setup
The model implemented follows the methodology adopted by Koua et al (2019) [
45]. The Lobo watershed in Nibéhibé covers an area of 6,442.66 km
2. The delimitation of the watershed and the extraction of the hydrographic network was possible thanks to the processing of the DEM under QSWAT. The D8 algorithm [
46] integrated in QGIS makes it easy to extract watershed boundaries and river network using QSWAT. This step is followed by the integration of meteorological data, land use, pedology and their physico-chemical properties. Then, the hydrological response units (HRU) combining land use type, soil type and slope in a sub-basin were calculated. HRUs are the basis for calculating for the SWAT model. They highlight the differences in evapotranspiration and other hydrological conditions between different types of land cover. the multiple HRU method of the SWAT model made it possible to constitute 163 HRUs. After that, QSWAT established the various input data tables. This made it possible to integrate information relating to the watershed, pedology, hydrometeorology, the HRUs themselves, water resources and their use, watershed management, wetlands, septic tanks, different reservoirs on the watershed, and the watershed master file. At this stage, the hydrological simulation of the Lobo watershed can be done.
Streamflow calibration process
The flow calibration at a monthly time step was possible by using observed data at the Nibéhibé hydrometric station using the SUFI-2 method [
22,
23] in the SWAT-CUP program [
47]. For this study, ten (10) flow parameters have been used. These parameters were the CN2 expressing the humidity conditions II, the quantity of water available in the soil SOL_AWC, the ESCO factor which translates the compensation coefficient of the soil evaporation, RCHRG_DP which is the fraction of percolation water from the deep aquifer, the re-evaporation coefficient of groundwater GW_REVAP, ALPHA_BF (Baseflow alpha factor), the water depth threshold in the shallow aquifer depth GWQMN required for return flow to occur, the water depth threshold in the shallow aquifer REVAPMN for revaporation to occur, the groundwater delay time GW_DELAY, the CANMX (Maximum storage of canopy). Flow calibration was performed over the period 1981 to 1994. A total of 500 iterations were performed during the monthly water flow simulation process. Then, the Nash–Sutcliffe coefficient (NSE), the percentage of bias (PBIAS) and the R
2 determination coefficient were calculated in order to judge the robustness of the SWAT model on this watershed.
2.2.2. Nutrient loads estimation
While reservoir eutrophication processes are significantly influenced by nutrient contents in the water, there exists little information upon the reservoir water quality. Because of the lack of observation data on nitrogen and phosphorus, the estimation of nutrient inputs to the reservoir was made on the basis of the quantity of NPK fertilizers applied to crops in the watershed because these nutrients come from NPK chemical fertilizers [
3,
4]. Data relating to fertilizers, such as the amount, duration, and frequency of application, were integrated into SWAT according to crops by sub-basin and HRU. The mineral fertilizers are of the xN-yP-zK formula, x, y and z representing respectively the proportions in percentage (%) of N, P and K (Potassium) in 1 kg of fertilizer used. If the fertilizer formula is known, the quantities of N, P and K are determined (Eq. 8 & 9) [
48]:
(Eq. 8)
(Eq. 9)
For this study, only N and P quantities were estimated.
From the soil, the crops take Nitrogen in the form of nitrates [
48]. Nitrate transportation within the watershed is done via surface runoff, lateral flow, or percolation. The amount of nitrate contained in runoff is assessed from the nitrate concentration in moving water. This concentration is a proportion of the nitrate mass in the runoff volume [
48]. It is calculated according to Eq. 10:
(Eq. 10),
where is the concentration of nitrate in mobile water for a given soil layer (Kg N/mm H2O), expresses the quantity of nitrate (Kg N/ha), is the amount of mobile water in the layer (mm H2O), is the porosity fraction on which the anion exclusion depends, is the water content when the soil layer is saturated (mm H20).
The amount of mobile water in the soil layer is assumed equal to that lost by runoff, lateral flow or percolation and can be estimated by equations 11 and 12.
for top 10 mm (Eq. 11)
for lower soil layers, (Eq. 12)
is the depth of surface water runoff on the given day (mm H2O), is the height of water escaping from the layer laterally (mm H2O), is the amount of percolation water in the underlying soil layer on the given day (mm H2O).
Surface runoff transports nutrients to the top 10 mm above the soil. Equation 13 was used to calculate the amount of nitrate in runoff.
(Eq. 13)
is the quantity of nitrate retained during surface runoff (Kg N/ha), represents the nitrate percolation coefficient, expresses the concentration of nitrate in the runoff water for the top 10 mm of soil (Kg N/mm H2O), is the runoff height of the given day (mm H2O).
Surface runoff allows organic nitrogen mostly attached to sediments transfer to the main channel in the watershed. The amount of organic nitrogen transported with thesediments to the watercourse is calculated using Equation 14 [
49,
50]:
(Eq. 14),
where is the amount of organic nitrogen contained in surface runoff transported in Kg N/ha, is the concentration in g N/tonne of soil organic nitrogen in the first 10 mm above soil (g N/metric ton soil), sed is the amount of sediment produced on the given day (metric tons), area is the HRU area (ha), and is the nitrogen enrichment rate.
The nitrogen enrichment rate is estimated according to Menzel [
51]. Thus, the equation 15 was used to calculate the nitrogen enrichment rate:
(Eq. 15),
where is the in runoff sediment concentration (Mg sed/m3 H2O).
The concentration of sediment in surface runoff is calculated according to equation 16 :
(Eq. 16),
where sed where sed is the amount of sediment on a given day (metric tons), is the HRU area (ha), and is the amount of runoff on a given day (mm H2O).
The movement of soluble phosphorus in the soil is by diffusion. Due to its low mobility, transfer by surface runoff only concerns soluble phosphorus stored in the top 10 millimeters of soil [
50]. The amount of soluble P transferred is calculated from Equation 17:
(Eq. 17),
where is the quantity of soluble phosphorus retained during runoff, expressed in Kg P/ha, is the quantity of soluble phosphorus in solution in the first 10 mm (Kg P/ha), is the quantity of surface water runoff on the day in question (mm H20), is the soil density over the first 10 mm expressed in Mg/m3, is the depth of the surface layer (10 mm), and is the partition coefficient of phosphorus in the soil (m3/Mg).
Surface runoff to the main channel allows the organic and mineral phosphorus attached to soil particles transfer. All the nutrients parameters were integrated in SWAT model and nutrients flows were simulated running one time only the model with stream flow calibrated parameters.