Determination of the sub-catchments physiographic characteristics

The Amacuzac river, also known as Texcaltitlán river, is a tributary of the Balsas River and has its origin at the foot of the Nevado de Toluca volcano, inside the locality of San Martín Tequesquipan, State of Mexico, which has an approximate altitude of 2 600 meters above sea level. The Amacuzac River has a total length of approximately 253 km, down to the confluence with the Balsas River (^{IMTA, 2012}). The study area is located in the Alto Amacuzac river basin, which has a surface of 2 611.98 km². The main rivers in the watershed are the Texcaltitlán, the Chontalcuatlán and the San Jerónimo (^{INEGI, 2017}).

The following criteria were used to define the suitable construction sites for small hydropower plants in this watershed: 1) The slope in the river segment should be of at least 0.03 (3%) due to the digital terrain model resolution and 2) A minimum reach drop height of three meters, because the commercial turbines work with heads of more than two meters (^{Ortiz, 2011}). After this, the sub-catchments were delimited and their main characteristics such as area, length of the mainstream, mean slope of the mainstream, and time of concentration were obtained. These characteristics are necessary for the SMA model.

Longitudinal profiles determination

To determine the vertical drop and the horizontal distance of the stream, and to afterward calculate a mean slope, the longitudinal profiles of the tributary streams that coincided with the perennial streams of the sub-catchments were drawn (^{INEGI, 2017}). Figure 2 shows a typical profile obtained with the 3D-Analyst tool. The routine ArcToolbox - 3D Analyst Tools - Functional Surface - Interpole Shape is used to convert the 2D profiles into 3D ones.

Figure 2 Longitudinal profile of the Amacuzac river mainstream. 

Vegetation and soil type identification

To define the initial parameters depending on the basins geomorphologic characteristics, the type of vegetation and soil types in the study area were determined. This was done using as a base those reported in other works. Figure 3 shows the characteristic vegetation and land use for the Alto Amacuzac basin. The dominant soil type, according to Natural Resource Conservation Service of the United States, formerly the Soil Conservation Service (SCS) classification (^{Aparicio, 2010}) was obtained from the pedology digital information with texture classes 1, 2 and 3 (^{INEGI, 2004}). Figure 4 shows the main types of soil and their location in the Alto Amacuzac basin. The NA class corresponds to the urban areas.

Figure 3 Vegetation type and land use (Source: elaborated by the authors using INEGI data). 

Figure 4 Type of soil and urban area (Source: elaborated by the authors using INEGI data). 

Location of elements of exclusion

The surfaces where the water cannot be used for hydropower generation are considered as areas of exclusion. For example, protected areas, existing construction projects, low precipitation zones, and those where land use does not allow it, such as urban or agricultural areas. Figure 5 shows urban areas, existing infrastructure and the protected natural areas that belong to the Nevado de Toluca and Desierto del Carmen National Parks, as well as the Santuario Del Agua Temascaltepec. All of these sites are located in the Alto Amacuzac basin.

Figure 5 Location of the protected natural areas and urban area (Source: elaborated by the authors using INEGI data). 

Climatologic information review

To obtain a fixed influence area of each climatological station, the Thiessen polygons (^{Aparicio, 2010}) were drawn using the ArcMap software. These influence areas are necessary to assign a spatial weight to the precipitation that is registered in the meteorological model of the HEC-HMS software. The Thiessen polygons help to determine the climatological stations influence area for many basins at the same time. To this end, 23 climatological stations were used, five of which are located in the state of Morelos, 14 in the State of Mexico, and 4 in Guerrero. The daily precipitation data was reviewed and the missing data deduced to complete the historical data series according to ^{Aparicio (2010)}. Four out of the nine climatological stations for the Chontalcuatlán basin presented considerable porosity. For example, for the case of Meyuca Station, 12 months of daily information were missing; 20 months were missing for San Fco. Oxtotilpan; 33 months for Coatepec Harinas; and nine months for Nevado de Toluca. There was more missing data for this particular subbasin than any of the others analyzed. For the Troja Vieja station, two months of missing data were estimated. For the case of Coatepequito and Dos Bocas, two months of daily precipitation were filled, and one more month for El Mirador. In most of the cases, estimated missing data corresponded to the less rainy months, and in all of them, there was a logical correlation in the monthly precipitation data.

Mean daily streamflow analysis

Five hydrometric stations were employed to perform this analysis. These stations are located in the Amacuzac, San Jerónimo, Chontalcuatlán and Texcaltitlán rivers basins. There are no established rules to select the calibration and validation periods. However, some authors (e.g.^{Bottcher, Whiteley, James, & Hiscock, 2012}) recommend that the validation period should be of at least two times the calibration one. For the cases of the Texcaltitlán and Chontalcuatlán basins, four years of daily streamflow historic data was used, and 8 and 16 years respectively, for the validation. The Coatepequito parameters were calibrated using five years, and their validation was performed using 20 years. For the Dos Bocas and Amacuzac basins the parameters were calibrated using six years of registered data and the validation was done with 16 years of daily data. In ^{Ortiz (2011)}, it is mentioned that the flow and frequency duration curves should be obtained using existing historic information, preferably of more than 10 years for the case of SHP plants. The mentioned procedure was carried out to perform simulations in the sub-watersheds, employing the precipitation data used in the validation period.

Figure 6 shows the location of the climatological and the hydrometric stations used for the analysis, as well as the Thiessen polygons that were drawn. The name of each watershed was assigned according to the name of the corresponding hydrometric station.

Figure 6 Location of the climatological and hydrometric stations (Source: elaborated by the authors using INEGI data). 

Sensibility analysis

To perform a sensibility analysis, the proposal for the parameter values was made based on those reported in the works of ^{Bennett (1998)} and the ^{Grupo de Emisarios Submarinos e Hidráulica Ambiental de la Universidad de Cantabria (2004)}. The corresponding simulation was performed in the Texcaltitlán watershed. Afterwards, it was decided to multiply parameter values that are necessary for the SMA model, by factors of 10 and 0.2, changing one at a time. This was done for all the parameters except five of them, which represent the canopy, surface, soil and subsoil storage at the beginning of the simulation. These parameters were spared because they do not affect the results obtained when performing the continuous simulation for several years (^{Bennett, 1998}).

Model Calibration

The parameters were optimized using the objective functions “sum of absolute errors”, “sum of squared residuals”, “percent error in peak”, “peak-weighted root mean square error” and “percent error in volume”, to perform the calibration (^{USACE, 2017}). An error of less than 10% between the simulated and the observed volumes was established as the acceptance criterion. This is because in this case, the interest is centered in the knowledge of the daily streamflow in the sub-basins.

Model validation

The Nash-Sutcliffe efficiency coefficient (^{Nash & Sutcliffe, 1970}) is used to determine the goodness of the hydrologic model adjustment. The acceptable values for these coefficients are between 0 and 1, being one the optimal one. A value of less than zero indicates that the mean of the observed values is a better predictor than the model.

Run-of-river SHP plants feasibility

It is necessary to decide which should be the design flow rate for small hydropower plants when performing the feasibility study. For this reason, the flow duration curve is used to determine the viability of the project, according to each one of the stream flows present in the stream during the year. Site 351, code 7 749 located on the Chontalcuatlán basin will be used as example. The design power is the same as the one obtained with netload, i.e., the gross or available load, minus the losses in the pipe. The minimum power is that at which the turbine works acceptably, and it is obtained with the 16% of the design flow rate, according to the performance curve, which is almost horizontal for values between 16% and 100% of the maximum design discharge (^{Osserberg, 2017}).

To determine hydraulic losses in the pipe, it is proposed to consider a stainless steel one, with a Manning roughness coefficient of n=0.014 . This pipe was chosen seeking that less than 10% of the available load, given by the topographic fall, is lost. The internal return rate (IRR) and the net present value (NPV) were used as criteria to determine the profitability of the project. The first refers to the effective annual rate at which the present net value of the costs is equal to the present net value of the benefits (^{Fernández, 2007}). The civil works and the forced pipe can have a life of approximately 50 years, but the turbine life is around 35 years, and that of the generator is between 14 and 25 years, depending on the capacity. For this reason a useful life of 25 years is considered for each project. If the small central were to be used for up to 50 years, the project would require an extra investment in replacing the generator or the turbine.

Sensitivity analysis

From the sensitivity analysis, it was defined that the Soil Capacity, the Tension Zone Capacity, the Groundwater 1 Storage Coefficient, the Groundwater 2 Storage Coefficient, the Groundwater 2 Percolation Rate and the Groundwater 1 Storage Coefficient and Groundwater 2 Storage Coefficient are the parameters that most influence the discharge variation obtained in the simulation. Therefore, special attention must be paid in proposing initial values for these parameters.

Model Calibration

When simulations were run using the different objective functions, the most similarity between the measured and the simulated hydrographs was observed with the “percent error in volume” function. Also, it was observed that the model has a tendency to reach stability after the first rainfall event, and that it can model continuous data for periods as short as a year, with acceptable precision. This leads to the conclusion that the usage of a shorter data period for the calibration and validation makes no big difference. The optimized parameters, obtained through the calibration process, are shown in table 1.

Model validation

Very good results were obtained when determining the model's efficiency to simulate accumulated volume under the hydrograph. The Nash-Sutcliffe coefficient was 0.9 or higher for all the watersheds, as can be observed in Table 2. Besides, for the simulated peak flow, the model is not that efficient. The simulated peak flow represents less than 50% of the observed one. Nevertheless, the model efficiently represents the daily mean streamflow for the 8-year simulation for the Texcaltitlán watershed. This is also the case for the 20-year simulation for Coatepequito, and the 16-year simulation for the Chontalcuatlán, Dos Bocas y Amacuzac watersheds. This was confirmed by the observation of values between “satisfactory” and “adequate” (^{Moriasi et al., 2007}).

It is more important for the objectives of this work to adequately represent runoff volumes and the daily mean streamflow rather than peak flows. Figure 8 shows the parameters validation results for the Amacuzac basin.

Figure 8 Obtained hydrograph for the Amacuzac basin, validation period. 

Run-of-river SHP plants feasibility

It was obtained, as a result of the feasibility analysis, that the most convenient design is the one that uses Q90W hich, according to the IRR, yields the greater benefit from the investment. At the same time, the net present value indicates that the project that would bring the most revenue is the one built with a design discharge equivalent to Q30 as the one shown in Figure 11. Nevertheless, Q90 is considered appropriate for the design of run-of-river plants, because it is desired that the plant work as much time as possible.

Figure 11 Profitability of the project on the site 351, code 7 749, Chontalcuatlán Basin.