Introduction

Although water is abundant in some regions of the world, it is generally becoming increasingly scarce, both in terms of quantity and quality (^{Quispe, 2008}); so much so that there are figures showing that about 1.1 billion people in the world do not have access to good quality water sources.

The main source of freshwater is groundwater (^{Neri, 2009}). Since 1940, global water extraction has increased by 2.5% to 3% per year, compared with annual population growth ranging from 1.5% to 2%. This problem has led to the excessive exploitation of many aquifers.

In México, about 60% of the total volume levied for consumptive uses is extracted from aquifers, and 106 are overexploited. Most of the rural population depends significantly on groundwater, and in some arid areas the dependence is total (^{CONAGUA, 2012}). The current state of the water resource in the state of Tlaxcala, México, is critical due to the increase in demand, the reduction of the aquifer and water pollution (^{Magaña, 2006}). The municipality of Calpulalpan depends entirely on groundwater.

Rainwater harvesting is proposed as an alternative to address the problem of water supply and to reduce the exploitation of aquifers. The objective of this research was to design three rainwater harvesting systems, one to allocate water for human consumption in a school of 1,000 users, another for drinking water in a four-member household; and a third system to irrigate a half a hectare greenhouse of Stevia revaudiana. The hypothesis is that the capture of rainwater to be used for human consumption, domestic use and irrigation, is economically viable.

The study region is located in the northwestern part of Tlaxcala state (19° 38’ and 19° 27’ north latitude, and 98° 25’ and 98° 42’ west longitude) (^{INEGI, 2009}), in the town of Calpulalpán. The methodology consisted of an analysis of rainfall data and the systems design. The rainfall data were taken from the registry of the 29035 Calpulalpan weather station, as it is the operating station currently closer to the study site. Missing data were estimated using the US National Weather Service method (^{Aparicio, 2010}).

The recorded rainfall can be adjusted to a distribution function, which allows to know the probability of rainfall. According to ^{Aparicio (2010)}, the most commonly used probability distribution functions in applied hydrology are Normal, Log-Normal, Pearson and Gumbel. The goodness of fit tests are used to choose the distribution that best matches rainfall data. In this paper the Kolmogorov-Smirnov test, defined by ^{Aparicio (2010)} and the Smirnov test, reported by ^{Ortiz (2011)} were used.

For the systems design, net design precipitation was estimated from the mean monthly precipitation with 75% probability and the following expression was applied:

Where: PN_j = j month’s net precipitation (1,2,3,...,12), (mm); P_j ⁷⁵= total precipitation of the j month (1,2,3,...,12) with a probability of 75%, (mm); and Ce= coefficient of flow, (dimensionless).

The runoff coefficient depends on the material of the catchment area and is presented by ^{Anaya (2011)}. The net rainfall of design is the sum of the probable rainfall of each month.

In order to estimate the annual water demand for domestic use and human consumption, considering a requirement of 100 and 1.5 liters daily per person, respectively, the number of beneficiaries is multiplied by the water requirement per day and by the number of days to cover the demand. For the calculation of water demand in the stevia greenhouse, the annual irrigation sheet is multiplied by the surface to be irrigated. In the latter case, drip irrigation with an efficiency of 90% and an effective irrigation area of 362 m² were considered. For the design of the gutters, rectangular PVC and slope of 2% were proposed.

In order to obtain the value of the irrigation sheet, the crop evapotranspiration (Etc) is divided by the irrigation efficiency (Er). The crop evapotranspiration (Etc) is obtained by multiplying the reference evapotranspiration (Eto) by the crop coefficient (Kc), which depends on its phenological stages. To estimate the reference evapotranspiration inside a greenhouse the methodology proposed by ^{Zamarripa et al. (2013)} was used.

From the quotient of the annual water demand and the net design rainfall, the required catchment area was determined. For the design of the conduction system, the gutters are designed first and to know the expense that they must be able to transport, it is enough to multiply the rainfall intensity by the effective area of capture and to equal that expense to the one obtained from the continuity equation, where the flow velocity is obtained using the expression of Manning and the area proposing the sections dimensions. Subsequently, the downstream pipeline is designed from expression 2, presented by ^{Anaya (2011)}.

Where: D= diameter of the downstream pipes in m; Q= gutter flow (m³); v= wáter velocity (m s^-1).

The storage system is the most expensive part of the rainwater collection system, so its dimensioning must be done carefully. In the mass balance method the accumulated differences of the inputs (net rainfall) and outputs (monthly demand) are obtained and the maximum value is taken as the minimum volume required for the storage system. In order to obtain the cost per cubic meter of water, both underground and rainfall, the methodology presented by ^{Cruz (2009)} was used, using expression 3.

Total costs are the sum of fixed costs and variable costs, to calculate the first it was considered that the well that supplies for the region operates 365 days a year 22 hours per day, extracting an annual volume of 520 344 m³. For variable costs, a worker who worked the entire year with a salary of $ 238.63, 10% of the cost of equipment as maintenance expenses, and the cost per annual consumption of electric energy was obtained from the receipts issued to the Comisión de Agua Potable y Alcantarillado (CAPAM) of the municipality.

Results and discussion

With the normal function rainfall was obtained with a 75% occurrence probability, and is shown in Table 1.

Table 1 Average monthly rainfall with 75% occurrence probability in mm. 

From the information in Table 1 and applying Equation 1, a total net precipitation of 324.1 mm was obtained, being 50% of the average precipitation, according to ^{INEGI (2009)}, 650 mm, which implies greater security of obtaining the estimated water. A runoff coefficient of 0.85 corresponding to metal surfaces was considered.

The capacity of the cistern was obtained considering two conditions: to supply water all year round and to supply only during rainy season. Regarding the design of the gutters the result was that its dimensions should be at least 10 x 15 cm. The results of the three designs of rainwater harvesting systems are shown in Table 2.

Table 2 Results of the design of the three rainwater harvesting systems.  

It is shown that the required capacity of the cistern is considerably lower when only rainwater is captured and used in rainy season. Rainwater harvesting only in rainfall season is recommended when the system can not be built due to economic reasons, as indicated by ^{Palacio (2010)}, the initial investment of the systems is very high, which can render it inaccessible.

Table 3 illustrates the calculation of the cistern capacity for water intended for human consumption, considering capturing and using it only during the rainy season.

Table 3 Calculation of the cistern capacity for human consumption.  

In order to obtain the cost per cubic meter of water extracted from the well, the fixed cost was $369 881.6, the variable cost of $1 267 608.19 and the cost per annual consumption of electric energy of $975 848.05. Finally, the extraction cost was $3.15 m^-3 considering all the volume extracted by the well; however, if it was only considered building a well for human consumption, ie extract 300 m³ year^-1 as calculated on the demand, the cost would be $ 2 199.1 m^-3. Of course economically it is not feasible to build and operate a well to extract such a low volume, the comparison is made with the intention of demonstrating that rainwater harvesting is an economically viable option for small volumes.

In the case of extracted water for irrigation, the considered volume of 1 575 m³ year^-1, the total cost was $ 668 882.23, meaning a $ 424.69 per m³. The cost per cubic meter of captured water was obtained using the same economic method and the results are shown in Table 4. The results show that extracting groundwater is economically viable when dealing with large volumes which in turn affects the excessive exploitation of aquifers, while rainwater harvesting is economically more viable for small volumes and as indicated by ^{Palacio (2010)} those are projects that aim at sustainability.

Table 4 Cost of collection systems and water per cubic meter.  

The cost of catchment systems is high due to the initial investment but is offset by the low cost per cubic meter of water.

Conclusions

Capture rainwater is more economical than extracting groundwater when it comes to relatively small volumes, between 146 and 1 575 m³. Besides that the rainfall of the area is enough to supply water all year round in the studied cases. The implementation of rainwater harvesting systems is widely recommended.