Study area

The Sordo River basin is located in the state of Oaxaca, between the parallels 17° 37' 19.93" and 16° 29' 43.11'' north latitude and the meridians 98° 05' 54.34" and 96° 53' 17.86" west longitude. It has an altitude that goes from 274 meters a.s.l. to 3,349 meters above sea level and covers an area of 7,751.42 km², in which several rivers converge. The most important rivers for its longitude are Peñoles, Labor, Cuchara, Zapote, Yolotepec, and Sordo. The Sordo-Yolotepec river discharge into Ixtlayutla (20021) hydrometric station (Figure 1).

Figure 1 Location of the Sordo River basin, Oaxaca, Mexico. 

This basin comprises four cultural regions: Mixteca (54.4 %), Southern Sierra (30.6 %), Central Valleys (11.7 %), and Cost (3.3 %). It is sited on two main aquifers: Nochixtlán (1 321.84 km²) and Jamiltepec (6 269.18 km²). The climates are humid temperate and sub-humid (48.6 %), semi-warm subhumid (34.0 %), warm sub-humid (16.0 %), and warm semiarid (1.4 %). It registers annual average temperatures that fluctuate between 10 °C and 28 °C. In the north, the rainfall goes from 400 mm to 1 600 mm in the south. It presents nine types of soils, cambisol (22.0 %), rendzina (20.3 %), acrisol (15.4 %), vertisol (10.4 %), litosol (7.7 %), fluvisol (7.5 %), luvisol (6.9 %), phaeozem (6.7 %) and regosol (3.1 %). It also has 13 types of land use and vegetation: pine-oak forest (23.1 %), pine forest (20.6 %), grassland (18.5 %), oak forest (15.6 %), rainfed agriculture (10.7 %), deciduous dry forest (6.4 %), chaparral (2.1 %), oak-pine forest (1.3 %), cloud forest (0.7 %), human settlements (0.5 %), juniper forest (0.2 %), water bodies (0.1 %) and irrigated agriculture (0.1 %).

Soil Moisture Method (WEAP)

The Soil Moisture Method was selected from the five methods that WEAP uses for water balance. This method represents the watershed through two soil layers, it characterizes the vegetation cover and the soil type, and through empirical functions, it estimates evapotranspiration, surface runoff, subsurface runoff, and deep percolation (^{Sieber & Purkey, 2015}; ^{Yates, Sieber, Purkey, & Huber-Lee, 2005}).

In WEAP the basin can be divided into sub-basins, which can be subdivided into N areas with different types of vegetation cover j. The water balance in the root zone and deep zone are calculated according to the type of cover with equations (1) and (2), respectively (^{Yates et al., 2005}).

Where Swj: is soil root zone water storage capacity (mm), z1,j: relative water storage capacity in the soils root zone, given as a fraction of the total effective storage (1, 0), Pe(t): effective precipitation over time t (mm), PET(t): Penman-Monteith reference crop potential evapotranspiration (mm time^-1), Kc,j(t): crop coefficient over time t (dimensionless), LAIj: leaf area index (m² m^-2) (runoff decreases as this value increases), fj: quasi-physical adjustment parameter related to soil type, topography, land use and vegetation that directs water horizontally (fj) or vertically (1-fj) (1.0 = 100 % horizontal, 0 = 100 % vertical), and kj: an estimate of root zone storage conductivity (mm time^-1), Dw: deep zone water storage capacity (mm) z2,j: relative water storage capacity in soils deep zone, given as a fraction of the total effective storage (1, 0) (Figure 2).

Figure 2 Scheme of the soil moisture method (^{Angarita et al., 2018}). 

Model input

Figure 3 shows the methodology used to feed WEAP. The data generated in SWAT for the hydrological response units (HRU) of the Sordo River basin was calibrated by ^{Sánchez-Galindo et al. (2017)} . Previously, these data were weighted according to the surfaces and the conversion of units to areas (branches) where WEAP operates.

Figure 3 Methodology used on the Sordo River basin to feed the WEAP model from SWAT data. 

Based on the delimitation used in SWAT, the general scheme of the basin was used to operate WEAP, through 175 sub-basins with their main channels and the 20021 "Ixtayutla" hydrometric station. Subsequently, in Data ( Demand sites and Catchments, 1 729 branches were manually added, which are the hydrological response units created by SWAT, this was done using the table generated in the "FullHRU" vector layer.

After the scheme, Key Assumptions were created for variables like precipitation, mean temperature, latitude, wind speed, relative humidity, crop coefficient, root zone water storage capacity, leaf area index (runoff resistance factor), root zone hydraulic conductivity and preferential water flow direction. The key assumptions are used when working with a large number of sub-basins that require the same information. This tool, in conjunction with the options Export expressions to Excel and Import expressions from Excel, located in the Edit window, facilitated data entry.

The compilation and arrangement of climatic, hydrometric, and vegetation/soil type data are described below.

From the wgn sheet of the Access book, named as the project created in SWAT, the weather stations used in SWAT for the Sordo River basin were identified (Table 1).

Table 1 Climate stations used in the hydrological modeling of the Sordo river basin. 

Key	Name	Latitude N (°)	Longitude O (°)	Altitude (m)
20026	Chalcatongo de Hidalgo	17.03300	-97.58300	2 250
20038	Santiago Ixtayutla	16.56700	-97.66700	510
20044	Jalapa del Valle	17.06700	-96.88300	1 650
20076	Asuncion Nochixtlán (SMN)	17.46667	-97.21667	2 080
20094	Putla de Guerrero (CFE)	17.11667	-97.87305	1 316
20102	San Agustín Tlacotepec	17.20000	-97.51778	2 018
20105	San Esteban Atatlahuaca	17.06500	-97.67917	2 455
20126	Sta. Cruz Zenzotepec	16.53300	-97.48300	970
20130	Sta. María Yucuhiti	17.01667	-97.79972	1 876
20153	Sto. Domingo Teojomulco	16.60000	-97.21700	1 300
20159	Pedro y Pablo Teposcol.	17.50131	-97.48254	2 183
20167	Sta. Ma. Asunción Tlax. (DGE)	17.26700	-97.68300	2 065
20178	Villa Chalcatongo, (CFE)	17.03306	-97.58305	2 428
20186	Santiago Yosondua, Stgo.Y.	16.89972	-97.59972	2 222
20187	Yutacua, Stgo. Ixtayutla	16.60361	-97.62500	437
20259	Zacatepec, Zacatepec	16.75000	-97.78300	900

The daily precipitation and temperature data entered in the SWAT model were converted to monthly values. Specifically for WEAP, between 1979 and 1985, monthly data on wind speed (VV) and relative humidity (RH) were obtained from the Climate Forecast System Reanalysis, a global scale network (The National Centers for Environmental Prediction (^{NCEP, 2019}). The HR and VV data, corresponding to the basin, was interpolated at the monthly level (with the ArcMap Spline extension), and specific data was extracted for the weather stations’ geographical coordinates as shown in Table 1.

The runoff data used in the calibration and validation of SWAT were obtained from the National Surface Water Data (^{Conagua-IMTA, 2019}) for the Ixtayutla station (^{Sánchez-Galindo et al., 2017}). They were entered into WEAP monthly through the route: Supply and Resources ( River ( “Sordo” ( Streamflow Gauges ( “Ixtayutla” ( ReadFromFile Wizard.

The vegetation/soil variables that compose the WEAP model are described below. The crop coefficient (K_c) methodology was used to calculate crop evapotranspiration under standard conditions (ET_c ), see equation (3). Standard conditions are those that occur in extensive fields, under excellent agronomic conditions and without limitations of soil moisture. Crop evapotranspiration (ET_c ) differs from reference evapotranspiration (ET_o ), generally obtained for grass, in which soil cover characteristics, vegetation properties, and aerodynamic resistance are effects incorporated into the crop coefficient K_c (^{Allen, Pereira, Raes, & Smith, 2006}) (Table 2).

ETc=Kc ETo (3)

Table 2 Kc values used in the Sordo River Basin. Source: ^{Hernández-Vargas (2017)}. 

Key	Description	Crop coefficient (Kc)
BENC	Oak forest	0.9
ENPI	Oak-Pine Forest	0.8
FRSD	Deciduous dry forest	1.0
FRSE	Cloud forest	1.1
MATO	Chaparral	0.6
PASI	Grassland	1.0
PIEN	Pine-oak forest	1.0
PINO	Pine forest	1.0
RIEG	Irrigated agriculture	1.1
RNGB	Juniper forest	0.8
TEMP	Rainfed agriculture	0.9
URMD	Medium density residential	1.0
WATR	Water bodies	0.7

As previously mentioned, a distinctive feature of the Soil Moisture Method is that the basin is represented through two layers of soil. Therefore, the first layer depth of each soil type, Equation (4), was obtained by considering the depths of the reference roots of each vegetation cover, contained in Table 3; the values were based on the default SWAT data presented by ^{Sánchez-Galindo et al. (2017)}. The resulting pondering of the root depths by soil type was rounded to multiples of 50 (Table 4). On the other hand, the thickness of the deep zone of each soil type is presented as the difference between the total depth values (data obtained by ^{Sánchez-Galindo et al. (2017)} from the soil profile layers, series II, of INEGI) and the first layer (Table 4):

Prp=∑i=1nAi USViATs (4)

Where Prp weighted root depth (mm), Ai: land use and vegetation area (ha),  USVi: vegetation depth (mm), ATs: total area of the interest soil type (ha).

Table 3 Radical depths for each land use and vegetation in the Sordo River basin. 

Key	Description	Depth (mm)
BENC	Oak forest	600
ENPI	Oak-Pine Forest	600
FRSD	Deciduous dry forest	500
FRSE	Cloud forest	1 000
MATO	Chaparral	400
PASI	Grassland	200
PIEN	Pine-oak forest	600
PINO	Pine forest	800
RIEG	Irrigated agriculture	600
RNGB	Juniper Forest	500
TEMP	Rainfed agriculture	350
URMD	Medium density residential	650
WATR	Water bodies	0

Table 4 Total and first soil layer depth, for the Sordo River basin. 

Key	Soil	Depth of first WEAP layer (mm)	Total depth (mm)
AC	Acrisol	650	1 100
CM	Cambisol	600	1 250
EL	Rendzina	500	650
FL	Fluvisol	500	1 000
Hc	Phaeozem	450	1 000
Is	Litosol	500	650
Lc	Luvisol	550	1 000
Re	Regosol	500	800
Vc	Vertisol	350	1 000

The root zone (Sw) and deep zone (Dw_s) water storage capacity is calculated by the type of soil (Table 5) with the weighted root depth and the deep layer depth, through Equation (5) and Equation (6). The subbasin (Dw_sub ) deep zone storage capacity values were obtained with Equation (7). The values range from 83 to 294 mm:

Sw=∑i=1nSOL_Zi SOL_AWCi (5)

Dws=∑i=1nSOL_Zi SOL_AWCi (6)

Dwsub=∑i=1nAi DwsiATsub (7)

Where Sw: root zone water storage capacity (mm), Dws: deep zone water storage capacity by soil type (mm), Dwsub: sub-basin water storage capacity (mm), SOL_Z: layer depth (mm), SOL_AWCi: layer available water capacity (mm mm^-1), Ai: soil type area (ha), ATsub: sub-basin total area (ha).

Table 5 Root zone Values water storage capacity values (Sw) and deep zone (Dw_s ) by type of soil, in the Sordo River basin. 

Key	Soil	Sw (mm)	Dws (mm)
AC	Acrisol	340	340
CM	Cambisol	274	274
EL	Rendzina	291	291
FL	Fluvisol	199	199
Hc	Phaeozem	205	205
Is	Litosol	222	222
Lc	Luvisol	296	296
Re	Regosol	212	212
Vc	Vertisol	178	178

The leaf area index (LAI) represents the effect of the canopy on surface runoff; in this case, it is in the third term of WEAPEquation (1). This value is retaken from the SWAT calibration, where it is identified as a maximum leaf area index (m² m^-2), BLAI (Table 6).

Table 6 Leaf area index by type of coverage entered into WEAP for the Sordo River basin. 

Key	Description	IAF or RRF (m2 m-2)
BENC	Oak forest	5.7
ENPI	Oak-Pine Forest	5.7
FRSD	Deciduous dry forest	2.1
FRSE	Cloud forest	5.6
MATO	Chaparral	2.1
PASI	Grassland	1.7
PIEN	Pine-oak forest	5.5
PINO	Pine forest	5.5
RIEG	Irrigated agriculture	3.6
RNGB	Juniper Forest	5.6
TEMP	Rainfed agriculture	3.6
URMD	Medium density residential	8
WATR	Water bodies	0.1

The saturated hydraulic conductivity of the root zone (Ks) and deep zone (Kd), is caused when the relative storage of Z1 and Z2 is respectively equal to 1.0 (saturation). The value of Ks is the division of the flows preferential direction in the subsurface and the percolation to the deep layer. Meanwhile, Kd controls the base flow movement which increases as Kd increases. The values by soil type of Ks and Kds (Table 7) were obtained with Equations (8) and (9), respectively. The hydraulic conductivity information comes from a previous run with SWAT (^{Sánchez-Galindo et al., 2017}). However, the deep zone conductivity parameter was entered at the sub-basin level (Kdsub). Therefore, this was calculated with equation (10) with which a range between 10 and 1241 mm month^-1 was obtained.

Ks=∑i=1nSOL_Zi K24iPr1 (8)

Kds=∑i=1nSOL_Zi K24iPr2 (9)

Kdsub=∑i=1nAi KdsiATsub (10)

Where Ks: root zone hydraulic conductivity (mm month^-1), Kd_s : deep zone hydraulic conductivity by soil type (mm month^-1), Kdsub: sub-basin deep zone hydraulic conductivity (mm month^-1), SOL_Zi: layer depth (mm), K24_i : SOL_K layer (SWAT parameter) multiplied by 24, Pr₁ : weighted root depth by soil type (mm), Pr₂ : deep layer depth by type of soil (mm), Ai: soil type area (ha), ATsub: sub-basin total area (ha).

Table 7 Root zone hydraulic conductivity values (Ks) and deep zone (Kds) by soil type, for the Sordo river Basin. 

Key	Soil	Ks (mm month-1)	Kds (mm month -1)
AC	Acrisol	32	28
CM	Cambisol	569	318
EL	Rendzina	796	10
FL	Fluvisol	1064	1331
Hc	Phaeozem	278	94
Is	Litosol	335	10
Lc	Luvisol	483	212
Re	Regosol	540	10
Vc	Vertisol	121	123

At the beginning of the simulation, the root zone (Z1) and deep zone (Z2) humidity is the relative storage of the first and second layer respectively. It is expressed as the percentage of the total effective accumulation, and for both humidities, 30 % was entered.

Evaluation of efficiency

The efficiency of the WEAP model was evaluated simulating annual and monthly runoff for the period 1975 to 1985, with the year 1975 being the baseline.

The models behavior and performance were evaluated by comparing the simulated runoff and the runoff measured at the exit of the catchment area (^{Krause, Boyle, & Bäse, 2005}). The indices included in this work are described below.

Determination coefficient (r²): describes the variation between the observed data and the data simulated by the model. The values of r² range from 0 to 1, a higher value indicates less error of variation, and a value higher than 0.5 is considered acceptable. This statistic is too sensitive to high extreme values and insensitive to additive and proportional differences between model predictions and measured data (^{Moriasi et al., 2007}).

Nash and Sutcliffe efficiency index (NSE): is a normalized statistic that determines the relative residual variance magnitude (noise) compared to the measured data variation (information). It indicates how well the graphs of the observed versus simulated data fit the line 1:1. It takes values between -∞ and 1; If the result is 1, the fit is perfect; if it is 0, the error is of the same order of magnitude as the variance of the observed data. Therefore, the mean of the observed data can have a similar capacity to predict as the model. Values below zero signify that the mean has a higher capacity to predict than the model, this implies that the simulated values are poor (^{Moriasi et al., 2007}).

Percentage bias (PBIAS): calculates the model's tendency to underestimate (positive values) or overestimate (negative values) the variable of interest. Values with low magnitude indicate an accurate simulation of the model, being 0 the optimal number (^{Moriasi et al., 2007}).

Monthly flows

As part of the results for the Sordo river basin, the monthly and annual flows simulated with SWAT (^{Sánchez-Galindo et al., 2017}) and the biophysical parameters, calibrated in SWAT, for WEAP are presented.

Figure 4 shows, for the period 1976 to 1985, the flows monthly measured versus those simulated by SWAT and WEAP and the NSE y PBIAS values. It is noteworthy, that the base flows were well calculated in WEAP. Meanwhile, SWAT effectively replicated the peak flows, but the recession curve when approaching the base flow presented problems.

This WEAP behavior differs from the results obtained by ^{Ingol-Blanco and McKinney (2013)}, who found in the Conchos river basin, that WEAP is better at reproducing peak runoffs than base flows. Furthermore, the NSE value (0.82) in SWAT was higher than in WEAP (0.73). This implies, according to ^{Moriasi et al. (2007)}, that the NSE values are "very good" for SWAT and "good" for WEAP.

The WEAP index NSE = 0.73 is within the range of results that other authors have obtained, such as ^{Varela-Ortega et al. (2016)} in the Guadiana River basin, Spain, with a NSE > 0.7; ^{Olsson et al. (2017)} Chancay-Huaral basin, Peru, with a NSE ≥ 0.8; and ^{Höllermann, Giertz and Diekkrüger (2010)} in the Ouémé-Bonou basin, Benin, with a NSE ≥ 0.78.

On the other hand, the PBIAS values of -16.05 and -15.92 on WEAP, and SWAT, respectively, indicate that both tools overestimate the observed monthly flow.

Figure 5 shows that the r² of the average monthly runoff of SWAT was slightly higher than WEAP (0.85 vs. 0.84), revealing a lower variation error. However, although r² has been widely used for model evaluation, it only quantifies results dispersion. For example, a model that systematically overestimates or underestimates will show values close to 1.0, even if all the predictions are wrong (^{Krause et al., 2005}; ^{Moriasi et al., 2007}). However, when considering the r² value, departing from the intercept, it is observed that WEAP presents a value closer to zero (6.6) than SWAT (34.9). Therefore, in an observed flow rate of zero, the result in WEAP would be 6.6 and 34.9 in SWAT. Likewise, the line slope reflects an over-prediction of 9.55 % for WEAP and an under-prediction of 15.32 % for SWAT.

Figure 5 Relationship between observed and simulated average monthly flows by SWAT and WEAP in the Sordo River basin. 

In 2016, Adgolign et al. assessed in the Didessa sub-basin of Ethiopia the change in water availability. As in the present study, they also used the same SWAT and WEAP tools. SWAT was used to fill the gaps in the measured flow data. Meanwhile, WEAP was used to model the allocation of surface water resources in the basin.

^{Hussen et al. (2018)} calibrated and validated SWAT’s capacity to simulate the runoff of Abaya-Chamo sub-basin, Ethiopia. In the calibration they obtained an r² = 0.77 and a NSE = 0.76, and in the validation an r²= 0.80 and a NSE = 0.78. Subsequently, the WEAP model was implemented to assign sub-basin water resources under climate change scenarios.

The amount of surface water was assessed in the southern Phuthiatsana Basin, Lesotho. This was done by estimating flows in ungauged basins with SWAT and allocating resources in the basin using WEAP. SWAT was calibrated from 1979 to 2001, NSE = 0.59 and r² = 0.59, and it was validated from 2002 to 2013, NSE = 0.52 and r² = 0.66 (^{Maliehe & Mulungu, 2017}).

Average annual flows

The annual average flows simulated in WEAP reached a NSE = 0.3. Compared to the values observed in the hydrometric station, the adjustment result is "unsatisfactory" (^{Moriasi et al., 2007}), due to the effects the years 1977, 1979, and 1980 (Figure 6). On the other hand, SWAT reached a "good" adjustment with a NSE = 0.73 and a PBIAS = -4.6, which only overestimated by 4.6 %. Something comparable happened with the values of r², where WEAP obtained 0.63 meanwhile SWAT achieved 0.76 (Figure 7).

Figure 6 Observed and simulated average annual flows by SWAT and WEAP in the Sordo River basin. 

Figure 7 Relationship between observed and simulated average annual flows by SWAT and WEAP in the Sordo River basin. 

In Table 8, the indices of r², NSE, and PBIAS demonstrate that simulations in SWAT and WEAP of monthly and annual runoff are reliable. This statement was also formulated by ^{Faiz et al. (2018)} who for WEAP, obtained values of NSE between 0.83 and 0.88, and of r² between 0.86 and 0.92; meanwhile, for SWAT, the values of NSE were 0.80 and 0.81 and of r² between 0.81 and 0.82. Likewise, for ^{Sánchez-Galindo et al. (2017)}SWAT successfully simulated the production of biomass and sediments. It is important to highlight, that this work profited from previously collected and used information to feed SWAT. However, it is feasible to feed WEAP without a precedent model in SWAT, and could even be simpler, due to the robust nature of WEAP. Therefore, choosing between a model depends on the available data, the study objectives, the tools the modeler, knows and the outputs of interest for decision-makers.