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Revista bio ciencias

versión On-line ISSN 2007-3380

Revista bio ciencias vol.9  Tepic  2022  Epub 12-Abr-2024

https://doi.org/10.15741/revbio.09.e1246 

Original articles

Soil urbanization in watersheds in the metropolis of Guadalajara, Mexico: entropy by surface runoff.

Urbanización del suelo en cuencas hidrográficas de la metrópoli de Guadalajara, México: entropía por escurrimientos superficiales

1Adscripción: Maestría en Hidraúlica. Universidad Autónoma de Guadalajara. Av. Patria, 1201, Lomas del Valle. C.P 45129, Zapopan, Jalisco, México.

2Adscripción: Dpto de Estudios del Agua y la Energía. Universidad de Guadalajara. Av. Nuevo Periférico 555, Ejido San José Tateposco. C.P 45425, Tonalá, Jalisco, México.

3Adscripción: Universidad Autónoma de Nayarit. Ciudad de la Cultura, S/N. C.P 63000 , Tepic, Nayarit, México.

4Adscripción: Universidad Autónoma de Sinaloa. Av. De las Américas, S/N. C.P 80040, Culiacán, Sinaloa, Méxic.


ABSTRACT

To consider the current scenarios in terms of urbanization, sectorial decision-making, and implementation of urban-territorial intervention plans and programs, the edaphological and hydrological conditions of the Colomos-Atemajac sub-basin in the metropolis of Guadalajara, Mexico were contrasted for the periods of 2008 and 2022, to determine the variation of the volume of water flow and its relationship with the urbanization process and the increase of impermeable areas. Data obtained in situ were processed in the Qgis geographic information system; in addition, standardized equations and methods in hydrology were used to calculate all parameters for the elaboration of precipitation hydrographs. It was found that in 2008 there were 8.44 km2 of a low-density residential area, and by 2022, said value decreased to 5.56 km2; giving transition to a higher residential density, with an increase of 2.89 km2. The information obtained was conceptualized from the Entropy-Homeostasis-Negentropy systemic model; an extended derivation of the Pressure-State-Response model of the Organization for Economic Cooperation and Development. In conclusion, the current hydraulic infrastructure does not satisfy the stream flow regimes and surface runoff exceeds the retention and transport capacity; as a result, floods annually affect not only the same urban areas but also new areas that have replaced their soil cover.

KEY WORDS: Land Cover; Entropy; Surface Runoff; Urbanization

RESUMEN

A efecto de considerar los escenarios actuales en materia de urbanización, toma de decisiones sectoriales e implementación de planes y programas de intervención urbano-territorial, se contrastaron las condiciones edafológicas e hidrológicas de la sub-cuenca Colomos-Atemajac en la metrópoli de Guadalajara, México en los periodos de 2008 y 2022, con el objetivo de determinar la variación del caudal y su relación con el proceso de urbanización y aumento de áreas impermeables. Para ello, se procesaron datos obtenidos in situ en el sistema de información geográfica Qgis; además, se utilizaron ecuaciones y métodos estandarizados en hidrología para el cálculo de los parámetros necesarios en la elaboración de hidrogramas de precipitación. Se encontró, que en 2008 se tenían 8.44 km2 de área residencial de baja densidad, y para 2022, disminuyó a 5.56 km2; dando a su paso a una mayor densidad residencial, con un aumento del orden de 2.89 km2. La información obtenida fue conceptualizada desde el modelo sistémico Entropía-Homeostasis-Negentropía; una derivación ampliada del modelo Presión-Estado-Respuesta de la Organización para la Cooperación y Desarrollo Económico. El ejercicio concluye, que la actual infraestructura hidráulica no satisface los regímenes de caudales y los escurrimientos superficiales superan la capacidad de retención y transporte; por tanto, anualmente terminan inundándose no sólo las mismas zonas urbanas, sino nuevas zonas que han sustituido su cobertura de suelo.

PALABRAS CLAVE: Coberturas de suelo; Entropía; Escurrimientos Superficiales; Urbanización

INTRODUCTION

Viewed from a systematic perspective, the urban (Thermo) dynamics related to the artificialization of land cover have as a common denominator disorderly, ways of urbanization. This systemic disorder can be analyzed, from the classical concept of entropy. Similarly, it can also be conceptualized from the basis of statistical thermodynamics, which considers entropy (S= K log W) as the "logarithm of the number of micro-states corresponding to a macrostate" (Varadhan, 2015). This logarithmic basis was explained by Ludwig Boltzmann more than a century ago. Indeed, the concept of entropy has transcended physics, chemistry, and biology to be used in social sciences and specifically in studies of urban housing and/or population growth, sustainability, economics, segregation, inequality, etc. (Piñuel-Raigada, 2014; Miguel-Velasco et al., 2008; González-Pérez, 2018; Pacheco-Hernández et al., 2021). The formation of large urban centers has created enormous environmental stresses, both due to land transformation and disorder, as well as to the demand for services in the city system; therefore, an increase in the entropy of a system automatically increases intrinsic disorder (Bascuñán-Walker et al., 2011).

Currently, urban systems have accelerated land consumption for housing purposes, often irreversibly transforming land cover and the systemic functioning of the territory, compromising the sustainability of the natural resources of the watershed. Indeed, "the services provided by the watershed are usually ignored by the societies that inhabit it (...). In many cases, the importance of the ecosystem services provided by the watershed is only noticed when such services are in serious danger of becoming exhausted or have already disappeared" (Aguirre-Nuñez, 2011).

According to the second law of thermodynamics, every system increases its entropy as a function of time. However, living systems need to feed on negative entropy (negentropy) to reduce entropy levels (Schrödinger, 1944). The implementation of this type of negentropic action indefinite phase, i.e. with long-term effects, can reverse a phased increase of entropy. In this case, we question the upper limit in terms of artificialization of land cover and the scope of the implementation of infrastructure to minimize the entropy originated by the substitution of natural covers.

In this context, generally qualitative methodological tools have been developed in the social sciences to assess the physical impact of the intervention. Thus, from the logic of the Entropy-Homeostasis-Negentropy (EHN) model, it is possible to qualify scenarios and their corresponding affectation degree. This abstraction sub-classifies in three phases: the causal forces of entropy or systemic disorder, the homeostasis or state of the system, and the negentropy or implemented responses. Its background uses the premises of the Pressure-State-Response (PSR) model of the OECD (2003) and systemic thermodynamics (Figure 1). The difference between PSR and other derivations such as the Driving force, Pressure, State, Impact, Response (DPSIR) framework, Driving Force-State-Response (DSR) framework, Quality Flow Model (QFM); Pressure-State-Impact-Effect-Response (PEI/ER) and the Pressure-State-Impact-Effect-Response-Management (PEI/ERG) method (Polanco, 2006; Vázquez & Almada, 2018), for the EHN model, lies in the variation of phases that the latter presents, and makes it more specific for the identification of the implemented response phase (interventions) and their corresponding effects (González-Pérez, 2018).

Source: own elaboration based on González-Pérez (2018)

Figure 1 The phases and structure of the EHN model are derived from the PER model. 

Certainly, in urban-housing matters, the implementation of public policies has suffered from sustainability in land cover changes. For example, non-urban-urban (rural-urban) and urban-peri-urban (city-urban periphery) migration have concentrated economic, educational, and service activities (Gordillo & Castillo, 2017) and have caused destabilization by altering natural infiltration-runoff processes and consequently flooding. The negentropy implemented has been limited to interventions with short-term effects. Therefore, people no longer have "(...) the awareness of what happens to the rainfall volumes during precipitation, and this hinders public engagement in prevention programs (Arreguín-Cortés et al., 2016). Likewise, Bascuñán-Walker et al. (2011), argue that in developing countries urbanization implies growth, both physical and in terms of population.

In this regard, soil analysis becomes complex due to the irreversible transformations and modifications of its initial characteristics and functions, deforesting and urbanizing the original surface cover. This pressure (entropy) on the systems (basins) has caused problems for water runoff, not only due to the increasing number of tributaries or the re-direction of runoff but also due to the increase in volume and speed of runoff, the decrease in infiltration and concentration times, erosion and sediment dragging, etc. (Mattos-Gutiérrez et al., 2012; Zapperi, 2014). From the 1980s to 2019, about 18,169 relevant natural disasters have been recorded globally, of which 7,355 were hydrological (40.48%). These, in turn, had overall losses of 4,798 trillion US dollars; of which, 1,046 trillion correspond to hydrological events (21.80%) (MUNICH RE, 2019).

Particularly in Mexico, only in 2016, 13,793 million pesos in damages and losses caused by natural and anthropic disasters were estimated; of these, about 87% were linked to hydrometeorological phenomena; of which, just over 70% corresponded to heavy rains, 25% to tropical cyclones and the remaining 5% to phenomena such as snowfall, frost, strong winds and severe storms (Sistema Nacional de Proteccion Civil, 2016). In this sense, this study aimed to contrast the edaphological conditions of the Colomos-Atemajac sub-system in the metropolis of Guadalajara, Mexico in two periods, to determine the variation of the flow and its relationship with the process of urbanization and the decrease of forest and prairie areas.

In this work, the city is understood as a thermodynamic system that consumes and expels matter and energy; in addition, it is proposed that there is an interaction of anthropic forces capable of reversibly, quasi-reversibly, or irreversibly transforming the original soil conditions, its intra-systemic structure and the characteristics of the diverse subsystems in the environment of interest. Hence, the assumption revolves around a series of causal relationships between non-systemic urban-territorial planning and increases in entropy. The research is geographically circumscribed in one of the most important metropolises in terms of population size. Here, the so-called "Los Colomos zone" was causally chosen; the name is due to the forest adjacent to the area of analysis, which in recent years has undergone a series of land-use changes to favor vertical real estate growth, without considering the areas sensitive to flooding. According to the National Institute of Statistics, Geography, and Informatics this sub-basin had a total population of 215,495 inhabitants in 2010, with just over 44% living in human settlements and 17% in the oak forest; its area is currently just over 81 km2. For this reason, the use of geographic information systems is of utmost importance, since they provide data for decision-making in terms of risk and threats.

Materials and Methods

From Instituto Nacional de Estadistica, Geografia e Informatica (2016), data we proceeded to download the digital elevation model corresponding to the topographic charts shown in Table 1. Likewise, the KML file and the location of the pluviometric stations were obtained from the Servicio Metereologico Nacional (2022). Subsequently, the stations in operation closest to the area under study were taken and analyzed to obtain the quantity and quality of data.

Table 1 Continental relief charts were used. 

Code Title
F13D65B1 Digital elevation terrain model with 5m resolution.
F13D65B2 Digital elevation terrain model with 5m resolution.
F13D65B3 Digital elevation terrain model with 5m resolution.
F13D65B4 Digital elevation terrain model with 5m resolution.
F13D65C1 Digital elevation terrain model with 5m resolution.

Source: Instituto Nacional de Estadistica, Geografia e Informatica (2016)

Once the most appropriate station was chosen, its maximum annual precipitation heights were obtained and the record was adjusted to different probability and statistical distributions, to achieve the best adjustment. With this data, and through isohyet maps of the Secretaria de Comunicacionss de Transportes (2021), rainfall intensities were extracted for one hour, and return periods (Tr) of 10, 25, and 50 years. In this sense, the Intensity-Duration-Frequency (I-D-F) curves were elaborated using the methodology of Campos-Aranda (2008). Similarly, the length and slope of the main basin stream were obtained, necessary to obtain the time of concentration, which was obtained by the Kirpich equation for a return time of 10 years.

Then, the relevant storm intensity was chosen, and using the methodology of Chow-Ven (1994) and information from the Soil Conservation Service (1957) and the United States Department of Agriculture (1986) the peak streamflow was obtained for the current conditions of the basin before the real estate boom. Subsequently, synthetic hydrographs were constructed using the methodology described by Aldama-Rodríguez & Ramírez-Orozco (1998) for both watershed conditions, resulting in increases in direct runoff volumes. In addition, a visit was made to the area under study (in situ) to determine the discharge capacity of the point, as well as to obtain information on the actual field conditions. This information was used to feed the EHN conceptual model and to qualitatively evaluate the degree of impact in the area.

The process to use the available pluviometric information in the form of maximum annual daily precipitation, to convert the values into 24-hour precipitation heights ( P24Tr ), required multiplication by 1.13. "The U.S. Weather Bureau uses the empirical factor 1.13, to convert daily precipitation data into maximum precipitation in 24 h" (Ayuso et al., 2010). In this sense, the coefficients R and F necessary to apply Chen's formula were obtained (Eq. 1 and Eq. 2)

R=P1TrP24TrEq.  1

F=P24100P2410Eq.  2

With the average value of the R ratios that can be evaluated for the return periods of 10, 25, and 50 years, parameters a, b, and c were obtained for 0.10 ≤ R ≤ 0.60 (Eq. 3, Eq. 4, and Eq. 5).

a=-2.297536+100.0389R-432.5438R2+1256.228R3-1028.902R4Eq. 3

b=-9.845761+96.94864R-341.4349R2+757.9172R3-598.7461R4Eq. 4

c=-0.06498345+5.069294R-16.08111R2+29.09596R3-20.06288R4..Eq. 5

If 0.20 ≤ R ≤ 0.70 the parameters a, b, and c can be obtained through equations 6, 7, and 8:

a=21.03453-186.4683R+825.4915R2-1084.846R3+524.06R4.Eq.  6

b=3.487775-68.13976R+389.4625R2-612.4041R3+315.8721R4..Eq.  7

c=0.2677553+0.9481759R+2.109415R2-4.827012R3+2.459584R4..Eq.  8

Subsequently, these parameters are used in Equation 9, where PtTr and P110 are in millimeters; t in minutes for 5 ≤ t ≤ 144 and Tr in years for 5 ≤ Tr ≤ 100.

 PtTr=aP110log102-FTrF-1t60t+bc..Eq.  9

The time of concentration (tcs) was obtained with equation 10.

tcs=0,0003245ltSlc0.77..Eq. 10

where:

tcs

= Time of concentration (h)

lt

= Length of main channel (m)

Slc

= Mean channel slope (m/m).

To obtain the excess rainfall and stream peak flow, the method proposed by the Soil Conservation Service (1957) was used, considering Eq. 11 and Eq.12.

Pe=P-Ia2(P-Ia)+S.Eq.  11

where:

Pe = Precipitation excess in inches.

P = Precipitation height in inches.

S = Maximum potential soil retention after initiation of precipitation event in inches.

I a = Initial abstraction in inches.

Ia=S..Eq.  12

The symbol Ø represents the retention factor and is equal to 0.2, according to the Soil Conservation Service (1957). From this, equation 13 is obtained. However, it should be mentioned that retention factor calibration studies should be performed.

Pe=P-0.2S2P+0.8S..Eq.13

The maximum potential soil retention after the onset of the precipitation event uses equation 14:

S=1000CN-10..Eq.  14

The flow rate or peak flow is obtained through equation 15 and its different parameters through equations 16 to 20:

Qm=2.78A×Z×PedEq.15

X=PedEq.16

tp=0.00505LS0.64Eq.17

For d/tp between 0.05 y 0.4

Z=0.73dtp0.97. Eq. 18

For 0.4 ≤ d/tp ≤ 2

Z=1.89dtp0.23-1.Eq. 19

For d/tp >2

Z=1Eq. 20

where:

tp = Time delay.

d = Duration of the selected storm.

Qm = Amount spent for the established storm and Tr duration.

In the synthetic hydrograph, we chose to construct a fifth-order synthetic hydrograph, which was obtained through Equations 21, 22, and 23:

Q5t;Qp,tp,tb=Qp10ttp3-15ttp4+6ttp5;t0,tpQp1-10t-tptb-tp3+15t-tptb-tp4-6t-tptb-tp5;ttp,tb0;t-,0tb,Eq. 21

Where:

Qp= Expenditure peak.

tp= Time peak.

tb= Timebase.

tr= Delay time.

tp=de2+trEq. 22

Where:

tp= Peak time.

de= Duration in excess.

tr= Delay time.

tb=3tpEq. 23

Where:

tb=Tiempo base

line time

Results and discussion

For the delimitation of the watershed, a Qgis model was fed with Digital Elevation Models with a pixel scale of 5 meters, which were extracted from the Instituto Nacional de Estadistica, Geografia e Informatica (2016) page, which is shown in Figure 2.

Source: Own elaboration with information from Source: Instituto Nacional de Estadistica, Geografia e Informatica (2016) and Servicio Metereologico Nacional (2022).

Figure 2 Delimitation of the watershed and climatological stations near the watershed. 

Subsequently, it was performed the analysis of the pluviometric information. For this purpose, a 30 km buffer was made to the basin watershed previously obtained, which corresponds to those that have an impact on the basin. Of these stations, 14065 and 14169 were selected because they are the closest to the basin and are in operation. In this way, the daily information was processed. Tables 2, 3, and 4 and Figures 3 and 4 information for station 14065, and tables 5, 6, and 7, and figures 5 and 6, for station 14169. This analysis was carried out for the purification of pluviometric data. It should be mentioned that those months and years with less than 90% of information were discarded from the study.

Table 2 The number of days with recorded precipitation height at station 14065. 

Year 01 02 03 04 05 06 07 08 09 10 11 12 Days/year Month/year
1882 0 0 0 30 31 30 31 31 30 31 30 0 244 8
1883 31 28 31 30 31 0 31 0 0 0 30 31 243 8
1884 31 29 31 0 0 30 0 0 0 0 0 0 121 4
1890 31 0 31 30 31 30 31 31 30 31 0 31 307 10
1891 0 28 0 0 0 0 0 0 0 0 0 0 28 1
1894 0 0 0 0 0 0 0 0 30 0 0 0 30 1
1895 0 0 0 30 31 30 0 0 0 0 30 0 121 4
1896 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1897 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1898 0 28 0 0 0 0 0 0 0 0 0 0 28 1
1899 0 0 0 0 31 30 0 0 0 0 0 0 61 2
1919 0 0 0 0 0 0 0 0 0 31 0 0 31 1
1925 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1943 0 28 31 30 31 30 31 31 30 31 30 31 334 11
1944 31 29 31 30 31 30 31 0 0 31 30 31 305 10
1945 31 28 31 30 31 30 31 31 30 31 30 0 334 11
1946 31 28 31 0 0 30 31 31 30 31 30 31 304 10
1947 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1948 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1949 31 28 0 30 0 0 0 0 0 0 0 0 89 3
1951 0 0 0 0 0 0 0 0 0 0 0 31 31 1
1952 1 0 31 30 1 30 31 31 30 31 30 31 277 9
1953 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1954 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1955 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1956 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1957 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1958 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1959 31 28 31 30 31 30 31 31 30 31 0 31 335 11
1960 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1961 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1962 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1963 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1964 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1965 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1966 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1967 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1968 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1969 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1970 31 28 31 0 0 30 31 31 30 31 30 31 304 10
1971 31 28 31 0 31 30 31 31 30 31 30 31 335 11
1972 0 29 31 30 0 30 31 31 30 31 30 31 304 10
1973 31 28 31 30 31 30 0 31 0 0 30 31 273 9
1974 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1981 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1982 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1983 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1984 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1985 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1986 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1987 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1988 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1989 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1990 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1991 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1992 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1993 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1994 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1995 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1996 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1997 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1998 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1999 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2000 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2003 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2004 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
2005 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2006 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2007 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2008 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
2009 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2010 31 28 31 30 31 30 31 31 30 31 30 31 365 12

*Leap year

Source: Own elaboration based on information from the Servicio Metereologico Nacional (2022).

Table 3 Monthly accumulated precipitation heights at station 14065. 

Year 01 02 03 04 05 06 07 08 09 10 11 12 Annual
1896 0 0 0 0 0 0 0 0 111.5 0 0 0 111.5
1897 0 0 0 0 0 0 0 0 0 0 0 0 0
1925 0 0 0 0 0 0 0 0 0 0 0 0 0
1947 0 0 0 0 0 0 0 0 0 29.4 0 0 29.4
1948 0 0 0 0 0 0 0 0 0 0 0 0 0
1953 0 0 0 0 0 0 0 0 0 0 0 0 0
1954 0 0 0 0 0 0 0 0 0 0 0 0 0
1955 0 0 0 0 0 0 0 0 0 0 0 0 0
1956 0 0 0 0 115.7 0 0 0 0 0 0 0 115.7
1957 0 0 0 0 0 0 0 0 0 0 0 0 0
1958 0 0 0 0 0 0 0 0 0 0 33.9 0 33.9
1960 0 0 0 0 0.9 0 303 0 0 0 0 31.5 335.4
1961 27.3 0 0 0 0 0 0 0 0 0 0 0 27.3
1962 0 0 0 0 0 0 0 0 0 0 30.7 0 30.7
1963 0 0 0 0 0 0 0 0 0 0 0.2 0 0.2
1964 0 0 0 0 0 0 0 0 173.7 0 0 0 173.7
1965 0 0 0 0 0 0 0 0 0 0 0 0 0
1966 0 0 0 0 0 0 0 0 133.5 86.8 0 0 220.3
1967 0 0 0 0 0 0 0 0 212.8 0 0 11.9 224.7
1968 0 0 0 0 0 137 0 0 0 0 0 0 137
1969 0 0 0 0 0 0 0 0 0 0 0 0 0
1974 0 0 0 0 0 0 0 0 0 0 0 0 0
1981 1.9 0.5 0.1 0.3 0.1 12.3 9.6 3.8 3.6 2 0.8 0.6 35.6
1982 0 0 0 0 0 50 53.4 235.1 10.2 5.6 84 3.4 441.7
1983 22.5 0 0 8 51.2 165.1 58.7 28.6 136.8 26.3 3.1 0 500.3
1984 19 8.2 81.7 0 4.7 305.7 200.2 148.2 29 53.7 17.8 1.6 869.8
1985 4.1 0 0 0.6 4.8 55.7 184.4 220 110.3 80.2 13.8 3.2 677.1
1986 0 4.1 0 5.9 3 38.8 43.1 41.7 152.6 8.4 42 0.2 339.8
1987 3.8 1.3 0.2 0.4 6 42.5 250.9 42.1 28.2 32.2 6.5 0.1 414.2
1988 29.6 0 0.1 0 0 32.2 6.9 15.5 3.8 0.5 4 2.6 95.2
1989 0 4 23 0.2 0 40.4 52.2 304.8 163.8 47.5 2.2 38.1 676.2
1990 1.9 83.3 0 0 31.7 34.7 353.7 201.7 205.9 133.6 0 0 1046.5
1991 1 11.6 0 38.6 0 35.5 389.3 167.8 58.7 10.1 0.8 10.7 724.1
1992 254.2 9.6 1 6.2 16.8 85 284.9 64.3 114.1 91.6 20.5 15.7 963.9
1993 16.3 0 0 0.5 0.6 181.8 18 50.2 21.7 7.2 0 0 296.3
1994 0 0 0 0 1.4 262.3 172 314 238.5 104.9 2 6.6 1101.7
1995 1.5 6.5 0 0 35.8 228 22.9 272.5 164.4 29.2 2.6 18.4 781.8
1996 0 0.8 0 0.4 7.2 60.8 204.3 227.4 198.1 58.4 11.9 2.6 771.9
1997 0.9 3.5 56.6 61.3 59.3 209.1 0 213.3 43.3 72.9 19.8 7.9 747.9
1998 0 0.1 0 0 0 63.3 235 341.4 75.4 15.1 0 2.7 733
1999 0 0 0 0 7.5 251.3 195.2 255.1 26.8 47.9 0 0 783.8
2000 0 0 0 0 8.9 49.5 62.9 81.5 199.2 21.8 0 1.1 424.9
2003 5.4 0 0 0 6.9 81.7 300.5 156.4 234.3 34.4 25.2 0 844.8
2004 0 0 4.2 0 78.8 469.5 0 119.7 359.6 14.6 0 7.1 1053.5
2005 2.4 3.5 10.8 0 17.2 71.3 336.7 92.2 307.5 80.6 2.2 0 924.4
2006 0 0 8.5 0 6.4 146.9 146.9 348.6 132.8 156.8 24.6 11.5 983
2007 17.7 6.9 0 0 0.4 188.5 325.6 183 206.6 20.3 16.5 17.9 983.4
2008 0 0 0 1.1 1.8 299 245.2 163.3 270.7 88 0 0 1069.1
2009 14.5 0 0 8.5 33.7 112 234.8 125.5 198.2 71.6 0 3.9 802.7
2010 21.9 142.1 0 0 27.4 208.6 454.1 166.1 239.6 0 0 0 1259.8
2013 51 0 0 0 35.2 110.9 301.7 208 247.5 40.7 24.3 56.9 1076.2
2014 10.1 0 0.4 0 24.6 132.7 150 234.8 171.9 76.4 19.6 1.8 822.3
2015 0.6 17.4 84.8 15.8 24.2 263.8 197.2 205.9 139.1 96.4 3.1 26.4 1074.7
2018 34.4 13.1 0 0.3 60.9 365 269.7 300.6 336.1 79.2 38.4 2.1 1499.8
Average 10.04 5.86 5.03 2.74 12.46 88.72 112.28 102.46 101.11 31.93 8.34 5.31

Source: Own elaboration based on information from the Servicio Metereologico Nacional (2022).

Table 4 Monthly maximum precipitation heights at station 14065. 

Year 01 02 03 04 05 06 07 08 09 10 11 12 Maximum annual rainfall
1896 0 0 0 0 0 0 0 0 5.9 0 0 0 5.9
1897 0 0 0 0 0 0 0 0 0 0 0 0 0
1925 0 0 0 0 0 0 0 0 0 0 0 0 0
1947 0 0 0 0 0 0 0 0 0 10 0 0 10
1948 0 0 0 0 0 0 0 0 0 0 0 0 0
1953 0 0 0 0 0 0 0 0 0 0 0 0 0
1954 0 0 0 0 0 0 0 0 0 0 0 0 0
1955 0 0 0 0 0 0 0 0 0 0 0 0 0
1956 0 0 0 0 46.5 0 0 0 0 0 0 0 46.5
1957 0 0 0 0 0 0 0 0 0 0 0 0 0
1958 0 0 0 0 0 0 0 0 0 0 17.7 0 17.7
1960 0 0 0 0 0.9 0 57.2 0 0 0 0 25.6 57.2
1961 15 0 0 0 0 0 0 0 0 0 0 0 15
1962 0 0 0 0 0 0 0 0 0 0 26.9 0 26.9
1963 0 0 0 0 0 0 0 0 0 0 0.2 0 0.2
1964 0 0 0 0 0 0 0 0 50.8 0 0 0 50.8
1965 0 0 0 0 0 0 0 0 0 0 0 0 0
1966 0 0 0 0 0 0 0 0 29.8 30.3 0 0 30.3
1967 0 0 0 0 0 0 0 0 25.5 0 0 9.4 25.5
1968 0 0 0 0 0 39.3 0 0 0 0 0 0 39.3
1969 0 0 0 0 0 0 0 0 0 0 0 0 0
1974 0 0 0 0 0 0 0 0 0 0 0 0 0
1981 0.8 0.4 0.1 0.2 0.1 1.7 2 0.9 0.8 0.6 0.8 0.6 2
1982 0 0 0 0 0 16.4 9.9 33.8 3.1 1.4 68.1 1 68.1
1983 14.5 0 0 8 19.4 33 11.1 6.2 56.4 14.9 1.5 0 56.4
1984 9.3 6.2 68 0 1.6 43.1 54.1 39.6 5 30 17.8 1.6 68
1985 3.5 0 0 0.6 3.2 12.1 52.2 77.5 35.3 31.1 12.8 1.5 77.5
1986 0 4.1 0 5.7 1.6 5 6.6 10.8 45.7 4.2 31.6 0.2 45.7
1987 1.7 1 0.2 0.4 3.7 15.8 34.2 5.3 12.3 32.2 3.2 0.1 34.2
1988 29.6 0 0.1 0 0 12.2 4.5 3.6 3.4 0.5 2.7 1.6 29.6
1989 0 4 23 0.2 0 9.6 10.1 44.2 41.1 25.6 1.3 15.9 44.2
1990 1.2 71 0 0 17 7.8 40 31.7 30.2 32.5 0 0 71
1991 1 10.7 0 38.6 0 7.5 51.1 27.4 12 5 0.3 4.1 51.1
1992 58.2 9.2 1 4.5 6.2 21.6 29.3 12.8 31.6 38.1 20 13.6 58.2
1993 16.3 0 0 0.5 0.6 36.3 12.3 8.2 5.4 2.7 0 0 36.3
1994 0 0 0 0 1.3 70 40.2 56.5 57.1 27.9 2 6.6 70
1995 1.5 6.5 0 0 14.9 61 4.9 60.5 22.1 25.5 1 12.5 61
1996 0 0.8 0 0.4 2.7 23.5 43.9 30.6 47 42 7.6 2.6 47
1997 0.9 2.3 26.5 27.3 36 51.4 0 54.4 12.6 27.5 19 4.2 54.4
1998 0 0.1 0 0 0 24.6 30.2 67.9 15.8 7.5 0 2.7 67.9
1999 0 0 0 0 4.8 85.2 41.7 42.7 22.6 38.4 0 0 85.2
2000 0 0 0 0 8.7 18.5 17 20.6 51.6 12.1 0 0.5 51.6
2003 3.4 0 0 0 6 41.4 35.4 32.1 58.3 17.6 24.2 0 58.3
2004 0 0 2.7 0 33.6 45.8 0 54.3 71.2 7.1 0 5.3 71.2
2005 2.4 2.7 9 0 15 40.3 50.2 35.2 60 30.6 2.2 0 60
2006 0 0 8.5 0 3.6 37 23.4 63.2 26.3 48.2 24.6 8.2 63.2
2007 8.5 4.5 0 0 0.4 53.1 68.8 26.9 40.6 12.8 7.5 13.9 68.8
2008 0 0 0 1.1 1.7 42 42.4 27.8 79.3 46.4 0 0 79.3
2009 10.9 0 0 7.3 18.9 23.7 42.2 30.2 73.3 40.2 0 2.2 73.3
2010 13.8 51.8 0 0 15.8 56.1 63.6 38.5 76.2 0 0 0 76.2
2013 40.6 0 0 0 17 22 49.9 35.6 51.4 14.3 10.5 29.9 51.4
2014 4.3 0 0.4 0 14.7 25.8 47.2 41.1 39.6 37.7 9.8 1.8 47.2
2015 0.4 9.2 44 13.8 13.4 68.2 52.3 38.7 47.8 48 1.9 26.4 68.2
2018 20.6 9 0 0.3 30.6 56.9 54.8 70.8 48.6 28.7 26.2 1.6 70.8
Average 4.79 3.58 3.40 2.02 6.29 20.52 20.05 20.92 23.99 14.29 6.32 3.59

Source: Own elaboration based on information from the Servicio Metereologico Nacional (2022).

Source: Own elaboration based on information from the Servicio Metereologico Nacional (2022).

Figure 3 Monthly accumulated precipitation heights, station 14065. 

Source: Own elaboration based on information from the Servicio Metereologico Nacional (2022).

Figure 4 Maximum monthly precipitation heights, station 14065. 

Table 5 The number of days with recorded precipitation height at station 14169. 

Year 01 02 03 04 05 06 07 08 09 10 11 12 Days/ Year Months/ Year
1941 0 0 0 0 0 0 31 31 30 31 30 31 184 6
1942 31 28 31 30 0 30 31 31 30 31 30 31 334 11
1943 31 28 0 30 31 0 0 0 0 0 0 0 120 4
1944 0 0 0 0 0 0 17 31 0 0 0 0 48 1
1945 0 0 31 30 31 30 31 31 30 31 0 31 276 9
1946 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1947 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1948 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1949 31 28 31 30 31 30 31 31 30 0 0 0 273 9
1954 0 0 0 0 31 30 31 31 30 31 30 31 245 8
1955 31 28 31 0 31 30 31 31 30 31 30 31 335 11
1956 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1957 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1958 31 28 31 30 31 26 31 31 30 31 30 31 361 11
1959 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1960 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1961 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1962 31 28 31 30 31 12 31 31 30 31 30 31 347 11
1963 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1964 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1965 31 28 31 30 31 30 31 31 29 31 30 31 364 12
1966 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1967 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1968 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1969 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1970 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1971 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1972 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1973 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1974 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1975 31 0 31 30 31 30 31 31 0 31 30 31 307 10
1976 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1977 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1978 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1979 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1980 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1981 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1982 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1983 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1984 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1985 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1986 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1987 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1988 31 29 31 30 31 30 31 0 30 31 30 31 335 11
1989 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1990 31 28 31 30 0 0 0 0 0 0 0 0 120 4
1991 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1992 31 0 0 0 0 0 22 31 30 31 30 31 206 6
1993 31 28 29 30 31 30 0 0 0 31 30 31 271 9
1994 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1995 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1996 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
1997 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1998 31 28 31 30 31 30 31 31 30 31 30 31 365 12
1999 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2000 31 29 31 30 31 30 31 31 29 31 29 0 333 11
2001 31 28 31 30 31 30 30 31 30 31 30 31 364 12
2002 31 28 31 30 31 0 31 31 30 31 30 31 335 11
2003 0 28 31 30 31 30 31 0 30 31 30 31 303 10
2004 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
2005 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2006 31 28 31 30 31 30 31 31 30 31 30 0 334 11
2007 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2008 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
2009 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2010 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2011 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2012 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
2013 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2014 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2015 31 27 31 30 31 30 31 31 30 31 29 31 363 12
2016 31 29 31 30 31 30 31 31 30 31 30 31 366* 12
2017 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2018 31 28 31 30 31 30 31 31 30 31 30 31 365 12
2019 31 28 31 30 0 0 0 0 0 0 0 0 120 4

*Leap year

Source: Own elaboration based on information from the Servicio Metereologico Nacional (2022).

Table 6 Monthly accumulated precipitation heights at station 14169. 

Year 01 02 03 04 05 06 07 08 09 10 11 12 Annual
1946 15.1 9 0 8.9 20.2 361.6 211.3 192.5 95.7 186 48.2 40 1188.5
1947 50 6.5 0 0 22 140.4 228.5 205.5 177 57.5 0.5 5.5 893.4
1948 69.1 0 1 33 13.5 228.5 169.7 142.7 49 38 12.5 3.5 760.5
1956 0 0 0 0 98 123 242.4 208.1 105.3 4 0 0 780.8
1957 0 0 0 0 10 32.5 131.5 127.7 65.1 39.5 0 2.5 408.8
1959 8 0 0 14.9 14.2 174.9 308.2 223.6 113.3 67.2 0 5 929.3
1960 8.2 0 0 0 40 26 258 302 50 17 8 30 739.2
1961 16 0 0 0 30 212 264 143 145 28 0 0 838
1963 0 8.6 0 5 55.7 229.3 334.9 197.4 115 24 1.6 104.3 1075.8
1964 62 0 0 0 10.8 175.1 251.7 317.2 109.7 38 39.7 100.5 1104.7
1965 1.3 94.1 0 4.4 33.3 179.1 269 290.4 95.5 50.2 0 24.4 1041.7
1966 8.8 35.5 35.8 52.2 83.2 219.3 241.7 269.9 147.5 77.5 0 0 1171.4
1967 79.8 0 3.5 0.3 31 227 295 253.5 226.7 109.9 56 10.2 1292.9
1968 1.6 37.5 125.4 20.9 10.9 181.6 267.8 183.5 166.7 9.2 0.7 33.9 1039.7
1969 0.6 0 1 0 9.7 96.3 128.9 140.4 148.5 48.5 0 5.9 579.8
1970 1 25.6 0 0 0 294.7 275 182.3 130.8 48.2 22.3 0 979.9
1971 7.2 0 0 0 48.8 297.7 196.1 231.4 224 66 0.5 0.8 1072.5
1972 3.3 0 0 0 30.2 274.9 237.1 221.7 164 4 27.4 0.3 962.9
1973 13.4 7.1 0 0.4 10.1 127.8 355.5 378.4 134 80.1 0 0 1106.8
1974 1.6 0 0 11.6 67.5 177 253.9 202.4 214.3 11.9 1.3 14.9 956.4
1976 0.5 0.3 1.8 4.1 10.8 60.6 408 224.2 113.4 55.5 69.7 2 950.9
1977 1.4 0 0 14.9 37.8 243.8 271.6 191.7 192.6 85.3 26.3 3.5 1068.9
1978 0 13.8 0 0 14.9 200.5 292.9 175 231.7 143.8 39.2 2.4 1114.2
1979 1.8 15 0 0 11.5 73 255.3 260.6 75.7 0 0 37.1 730
1980 24.8 1.2 0 3.4 3.7 181 250.7 279 211.3 64.8 32.2 34.1 1086.2
1981 59 15.5 3.5 15.5 6.7 364.2 286.1 94.9 116 57 22.7 14.7 1055.8
1982 0 0 0 2.3 15.5 89.4 319 244.1 69.5 30.5 92.9 46.8 910
1983 20.9 0 0 0 48.7 71.8 375.8 162.3 100.1 31.2 26.5 0 837.3
1984 21.9 13.1 1.5 0 10.6 311.1 193.9 119.7 154.8 48.2 0 11.9 886.7
1985 18.9 0 0 0 14.5 321.4 172.4 133.7 115.3 86.4 18 2.8 883.4
1986 0 5.5 0 4.8 10 240 156 212.3 130.3 64.2 30.5 0.4 854
1987 4.2 28.5 4.4 9 34.3 282.2 243.3 249.1 223.4 0 3.5 2.1 1084
1989 0 9.8 0 0 0 52.2 289.7 253.8 166 51.6 10.5 48.7 882.3
1991 0.5 12.8 0 0 0 156.7 465.2 131.9 108.9 34.6 17 11.7 939.3
1994 0.2 0 0 1.5 0 160 184.5 214.5 322.5 90 4.5 0 977.7
1995 2 0 0 0 32 257 156.5 316 153.5 18 7 20.3 962.3
1996 0 0 0 0 12.6 192 213 256.5 166 56 10 0 906.1
1997 1 2 58.5 58 20.5 190.5 399 196 122.5 108.5 27 3 1186.5
1998 0 0 0 0 0 121.5 363 307 231 99 0 0 1121.5
1999 0 0 0 0 5 303.5 293 184.5 91.5 36 3 0 916.5
2001 0 0 2.5 0 59 212.5 331 218 92.5 37.5 0 0 953
2004 40.5 0 1.5 0 55 425.1 141.5 239.5 441 27 0 6.5 1377.6
2005 4 0 0 0 12 25.3 364 113.5 226.6 95.2 3.5 0 844.1
2007 17.5 13 0 0 1.5 178.5 283.5 232 185.5 40.7 12.5 3 967.7
2008 0 0 0 0 2.5 434.8 315.8 221.9 221.5 81.1 0 0 1277.6
2009 15.5 0 0 0 60.3 173.7 244.2 132.2 196.9 56.5 0 3 882.3
2010 48.5 137.8 0.1 0 18.4 236.5 353.8 125.1 311.5 0 0 0 1231.7
2011 10 0 1 0 24 75.3 399 239.8 118.5 97 0 0 964.6
2012 0 88 0 0 1.5 194 246 321.5 132.5 29 0 0 1012.5
2013 62 0 0 0 53.5 162.5 341 169.5 302.5 42.5 25.5 75 1234
2014 4.5 0 0 0 63 161.5 178.5 269 202.5 52.5 28 5 964.5
2015 3.5 24 70.5 21 23 259 314 130 186 107 2 28.5 1168.5
2016 0 6.5 13 0 17.5 246 377 182 149.9 15.5 42.5 0 1049.9
2017 0 1 0 0 10 162.5 163.5 218.8 227 22.5 0 30 835.3
2018 27.5 18.5 0 5 58 249.5 148 269.8 267 44 32.5 8 1127.8
Average 13.41 11.46 5.91 5.29 25.23 197.23 267.45 212.78 164.26 52.97 14.65 14.22

Source: Own elaboration based on information from the Servicio Metereologico Nacional (2022).

Tabla 7 Maximum monthly precipitation heights at station 14169. 

Year 01 02 03 04 05 06 07 08 09 10 11 12 Maximum annual precipitation
1946 11 9 0 7.2 12 100 52 35 35 72 23.5 10 100
1947 16 6.5 0 0 14.5 40 83.5 62 68 16.5 0.5 3 83.5
1948 51.5 0 0.5 24.5 6 60 35 38 19 15 6.5 1 60
1956 0 0 0 0 34.1 37.5 30.2 41 24.5 4 0 0 41
1957 0 0 0 0 10 26.5 35.5 38.5 12.5 25 0 2.5 38.5
1959 8 0 0 5 8 25 40 42.3 25.4 9.3 0 3 42.3
1960 3 0 0 0 8.3 9 37 50 18 8 8 18 50
1961 7 0 0 0 9 32 45 42 25 15 0 0 45
1963 0 8.6 0 3.8 26.5 42.6 48.3 58.6 39.6 10.1 1.4 62.4 62.4
1964 24.7 0 0 0 10.8 32.5 43.5 52.5 38.3 20 18.3 24.8 52.5
1965 1.3 51.4 0 4.2 33.3 62.2 41.2 50.5 25.4 22.4 0 17.7 62.2
1966 5.5 34.1 32.7 19.1 38.2 52.7 48.3 58.8 24.8 25.2 0 0 58.8
1967 49.5 0 3.5 0.3 16 52.6 53.1 39.2 54.8 33.1 56 9.7 56
1968 1.6 23.5 81 14.3 10.9 31.4 38.5 37.5 38.2 3 0.7 13.1 81
1969 0.6 0 0.8 0 8.1 43.7 48.5 41 30 40 0 3.6 48.5
1970 1 11.7 0 0 0 72.1 68.5 34.3 22.5 47.3 17.5 0 72.1
1971 5.7 0 0 0 29.3 53.5 26.3 48.2 31 23.4 0.5 0.8 53.5
1972 2.4 0 0 0 14.7 44.4 53.7 67.9 39.8 3 14.5 0.3 67.9
1973 9.4 4.2 0 0.4 5.2 35.2 52.8 51 23.8 22.3 0 0 52.8
1974 1.3 0 0 9 24.8 31.2 46.8 36.1 76.8 10.3 1.3 7.9 76.8
1976 0.5 0.3 1.8 3.1 10.8 15 64 48.5 38.9 30 19.2 0.8 64
1977 1 0 0 7 26 72.2 54.5 29.5 60.5 32 9.9 2.5 72.2
1978 0 8.5 0 0 8.9 55.2 43 28.1 38 41.7 32.5 2.4 55.2
1979 1.8 7.8 0 0 11.5 21 41.8 47.5 18 0 0 22 47.5
1980 7.2 1.2 0 1.8 2.7 35.2 28 66 49.4 44 19.5 16.9 66
1981 21.5 10.5 3 6.9 5.2 74.9 56.2 12.6 40 22 22.7 13.3 74.9
1982 0 0 0 2.3 11.4 24.8 62.9 43.8 25.6 11 78 15.8 78
1983 13.2 0 0 0 21.5 14.2 48.8 26.8 23.3 18.4 9 0 48.8
1984 13.5 10.8 1.5 0 6 50.5 50.2 26.2 38 24.8 0 10.1 50.5
1985 15.8 0 0 0 13.5 72 30.2 20 42 25.5 16.9 1.5 72
1986 0 5.5 0 4.8 2.8 35.6 29 42 23.1 32.2 20.5 0.4 42
1987 3 17.1 4.2 6.4 18 96 43 49.3 56.5 0 3.5 1.2 96
1989 0 9.8 0 0 0 17.7 45.7 46.5 49.3 42.4 10 16.8 49.3
1991 0.5 12.8 0 0 0 72.7 65.1 27.3 46.5 16 16.8 4.8 72.7
1994 0.2 0 0 1.5 0 33.5 32 34.5 66 30.5 4.5 0 66
1995 2 0 0 0 21.5 53 28.5 53 40.5 18 7 14 53
1996 0 0 0 0 6.5 54 51 50 39 32.5 6.5 0 54
1997 1 2 24 24 10 48 62 38 36 33.5 26 3 62
1998 0 0 0 0 0 45 68 85 72 43 0 0 85
1999 0 0 0 0 2.5 88 40 29 26 20.5 3 0 88
2001 0 0 1.5 0 29 48 35 29 17 15 0 0 48
2004 13 0 1.5 0 24 63 42 57 91 15 0 5 91
2005 4 0 0 0 12 16 42 38 45.5 59 3.5 0 59
2007 10.5 11.5 0 0 1.5 34 74.5 43 48.5 15 8.5 3 74.5
2008 0 0 0 0 2.5 56 54 32 34.7 39 0 0 56
2009 15.5 0 0 0 34 32 56.5 37.5 50 22.5 0 2 56.5
2010 21 45 0.1 0 18.4 70 49 20 91 0 0 0 91
2011 10 0 1 0 24 29.5 57 41 30.5 29 0 0 57
2012 0 30 0 0 1.5 42 44 42 62 20 0 0 62
2013 50 0 0 0 40 35.5 57 32 60 21 9 35 60
2014 3.5 0 0 0 46 31 36 50 51 26 10.5 2.5 51
2015 3.5 13.5 46 16 15 84 68 44 35.5 49.5 2 28.5 84
2016 0 6.5 9.5 0 9.5 42 66 32 48 12 17 0 66
2017 0 1 0 0 10 71 32 51 33 14 0 17 71
2018 13.5 13 0 5 31 42 32 37.5 48 12.5 24 8 48
Average 7.73 6.47 3.87 3.03 14.49 46.52 47.57 42.07 40.85 23.50 9.61 7.35

Source: Own elaboration based on information from the Servicio Metereologico Nacional (2022).

Source: Own elaboration based on information from the Servicio Metereologico Nacional (2022).

Figure 5 Monthly accumulated precipitation heights, station 14169. 

Source: Own elaboration based on information from the Servicio Metereologico Nacional (2022).

Figure 6 Maximum monthly precipitation heights, station 14169. 

Through analyzed data, it was observed that station 14169, also known as "Zapopan", has a higher quality of data, as it has a greater tendency towards the average. In this way, we proceeded to data cleansing and analysis, then, we proceeded to the analysis using different probability distributions to get a better fit. The standard errors obtained by each of the distributions analyzed are shown in Table 8. It can be seen that the distribution with the best fit is the Double Gumbel function, which is why it was used and the parameters were chosen in Table 9.

Table 8 Standard error analysis 

Function Periods Maximum Likelihood
2 parameters 3 parameters 2 parámetros 2 parameters
Normal 3.374 ------- Normal 3.374
Lognormal 1.997 1.998 Lognormal 1.997
Gumbel 1.936 ------- Gumbel 1.936
Exponential 3.314 ------- Exponential 3.314
Gamma 2.310 1.900 Gamma 2.310
Double Gumbel 1.398

Source: Own elaboration (2020).

Table 9 Summary of standard errors. 

Parameter Alpha 1 Beta 1 Alpha 2 Beta 2 p
Valor 0.11315 51.311 0.11227 81.235 0.82

Source: Own elaboration (2020)

Subsequently, to obtain the daily precipitation heights and their respective conversions to 24-hour precipitation heights using the factor 1.13, as well as the 1-hour precipitation ( table 10 )from the Secretaria de Comunicaciones y Transportes (2019) isohyet maps.

Table 10 Precipitation heights for different return periods. 

Recovery period, Tr (years) Precipitation (mm per day) Precipitation (mm 24h) Precipitation, mm 1 hr (SCT)
10 85.5 96.62 50
25 95.1 107.46 60
50 101.7 114.92 75
100 108 122.04

Source: Own elaboration based on information from Secretaría de Comunicaciones y Transportes (2019).

The results of the parameters used in Chen's formula can be seen in table 11.

Table 11 R, F, a, b, and c parameters for use in Chen's formula 

Parameter
Weather station R Weather station R Weather station R
14169. Zapopan 0.5762 14169. Zapopan 0.5762 14169. Zapopan 0.5762

Source: Own elaboration based on Campos-Aranda (2008).

Once the parameters of the previous table were obtained, the precipitation intensities of climatological station 14169 were obtained (Table 12 and Figure 7).

Table 12 Intensities for different durations and Tr of climatological station 14169. 

Intensities (mm/hr) for station 14169, Zapopan.
  Duration (min)
Tr (years) 5 10 15 25 30 45 60 80 100 120 1440
2 135.91 108.11 90.20 68.33 61.13 46.75 38.10 30.74 25.88 22.42 2.77
5 153.35 121.98 101.78 77.10 68.97 52.75 42.99 34.69 29.21 25.30 3.13
10 166.54 132.48 110.53 83.73 74.90 57.29 46.69 37.67 31.72 27.48 3.40
20 179.74 142.97 119.29 90.37 80.84 61.83 50.38 40.66 34.23 29.65 3.66
25 183.98 146.35 122.11 92.50 82.75 63.29 51.57 41.62 35.04 30.35 3.75
50 197.18 156.84 130.86 99.13 88.68 67.83 55.27 44.60 37.55 32.53 4.02
100 210.37 167.34 139.62 105.77 94.61 72.37 58.97 47.58 40.06 34.71 4.29

Source: Own elaboration based on Campos-Aranda (2008).

Source: Own elaboration based on Campos-Aranda (2008).

Figure 7 Intensity-Duration-Frequency curves, station 14169. 

The length and slope of the main channel were obtained using the model previously made in Qgis. The latter through the average slope method, whose length of the channel was 16,494.2479 m and the slope was 0.0209 (m/m). The concentration-time was 2.54 hours by Kirpich. Subsequently, the Curve Number was obtained for each of the conditions to be analyzed. Satellite images from the EarthExplorer platform of United States Geological Survey (2022) were used on May 27, 2008, and February 19, 2022, the first of which was obtained by the LANDSAT 5 satellite and the second by LANDSAT 9. Obtained results are shown in Figures 8 and 9. The curve numbers proposed by Chow-Ven (1994) were used for this procedure.

Source: Own elaboration based on data obtained from United States Geological Survey (2022).

Figure 8 Land cover for May 27, 2008. 

Source: Own elaboration based on data obtained from United States Geological Survey (2022)

Figure 9 Land cover for February 19, 2022. 

The Curve Number (CN) weights the background land conditions, the cover, and the type of soil where runoff occurs to determine the effective runoff produced by a given event. This methodology is usually the most widely used "to transform total precipitation into effective precipitation, arose from the observation of the hydrological phenomenon in different soil types in various states and for different antecedent humidity conditions" (Lavao-Pastrana & Corredor-Rivera, 2014).

In this context, the edaphology of the study area was obtained using the Edaphology charts with scales 1: 250,000 and 1: 1,000,000 dated 2001 (Comisión Nacional para el Conocimiento y uso de la Biodiversidad, 2001). Figure 10 shows the soils of the basin along with the texture of each of the polygons obtained.

Source: Own elaboration based on data obtained from Comisión Nacional para el Conocimiento y uso de la Biodiversidad (2001).

Figure 10.  Edaphology of the basin. 

It is important to note that this analysis was carried out with photographs with a pixel size of 30 meters, so it is a large-scale analysis and could vary if photographs with a higher pixel quality were used. In this sense, once the data from the previous illustrations were obtained, we proceeded to merge both the coverages and the edaphology of each of the polygons for both scenarios to obtain the results shown in Figures 11 and 12, and Table 13.

Source: Own elaboration based on data obtained from United States Geological Survey (2022)

Figure 11 Number Curve for May 27, 2008. 

Source: Own elaboration based on data obtained from United States Geological Survey (2022).

Figure 12 Curve number for February 19, 2022. 

Table 13 Curve number for normal humidity conditions. 

Use Area (km2) NC (Area) X (Curve number)
27/05/2008 19/02/2022 27/05/2008 27/05/2008
Forest with canopy in good condition, with B-grade soil 18021366.03 18021366.03 55 Forest with canopy in good condition, with B-grade soil 18021366.03
Residential, average plot size 1/8 acre or less, A-grade soil 4196205.18 7084438.05 77 Residential, average plot size 1/8 acre or less, A-grade soil 4196205.18
Residential, average plot size 1 acre or less, A-grade soil 8442541.28 5556037.46 51 Residential, average plot size 1 acre or less, A-grade soil 8442541.28
Residential, average plot size 1 acre or less, B-grade soil 3850573.16 3850573.16 68 Residential, average plot size 1 acre or less, B-grade soil 3850573.16
Σ 34510685.65 34510685.65 Σ 34510685.65

Source: Own elaboration based on United States Department of Agriculture (1986)

From the above analysis, it was possible to obtain a Curve Number of 58.15 for the conditions in 2008 and 60.32 for 2022. Subsequently, stream peak flows for antecedent wet conditions (CN, III) were obtained for both scenarios (May 27, 2008, and February 19, 2022), which are shown in Tables 14 and 15, respectively.

Tabla 14.  Caudales pico para diferentes duraciones de tormenta y condiciones antecedentes húmedas (CN, III) para el 27 de mayo del 2008 

d (horas) Tr CN i (cm/hr) P (cm) Pe (cm) X tr (horas) d/tr Z Q (m³/s)
0.60 10 58.15 6.66 4.00 0.01 0.01 1.99 h 0.301 0.228 0.226
0.80 10 58.15 5.48 4.38 0.03 0.03 1.99 h 0.401 0.302 1.002
1.00 10 58.15 4.67 4.67 0.05 0.05 1.99 h 0.501 0.383 1.950
1.20 10 58.15 4.08 4.89 0.08 0.07 1.99 h 0.602 0.452 2.836
1.40 10 58.15 3.63 5.08 0.10 0.07 1.99 h 0.702 0.512 3.613
1.60 10 58.15 3.27 5.24 0.13 0.08 1.99 h 0.802 0.567 4.280
1.80 10 58.15 2.99 5.37 0.15 0.08 1.99 h 0.903 0.616 4.847
2.00 10 58.15 2.75 5.50 0.17 0.08 1.99 h 1.003 0.661 5.334
2.20 10 58.15 2.55 5.60 0.19 0.08 1.99 h 1.103 0.703 5.734
2.40 10 58.15 2.38 5.70 0.21 0.09 1.99 h 1.204 0.742 6.096
2.60 10 58.15 2.23 5.79 0.22 0.09 1.99 h 1.304 0.779 6.395
2.80 10 58.15 2.10 5.87 0.24 0.09 1.99 h 1.404 0.813 6.656
3.00 10 58.15 1.98 5.94 0.25 0.08 1.99 h 1.504 0.846 6.878
3.20 10 58.15 1.88 6.01 0.27 0.08 1.99 h 1.605 0.877 7.075
3.40 10 58.15 1.79 6.08 0.28 0.08 1.99 h 1.705 0.907 7.234
3.60 10 58.15 1.71 6.14 0.30 0.08 1.99 h 1.805 0.935 7.390
3.80 10 58.15 1.63 6.19 0.31 0.08 1.99 h 1.906 0.962 7.513
4.00 10 58.15 1.56 6.25 0.32 0.08 1.99 h 2.006 1.000 7.717
4.20 10 58.15 1.50 6.30 0.33 0.08 1.99 h 2.106 1.000 7.628
4.40 10 58.15 1.44 6.35 0.35 0.08 1.99 h 2.206 1.000 7.537
4.60 10 58.15 1.39 6.40 0.36 0.08 1.99 h 2.307 1.000 7.459
4.80 10 58.15 1.34 6.44 0.37 0.08 1.99 h 2.407 1.000 7.359
5.00 10 58.15 1.30 6.49 0.38 0.08 1.99 h 2.507 1.000 7.272
5.20 10 58.15 1.26 6.53 0.39 0.07 1.99 h 2.608 1.000 7.182
5.40 10 58.15 1.22 6.57 0.40 0.07 1.99 h 2.708 1.000 7.099
5.60 10 58.15 1.18 6.60 0.41 0.07 1.99 h 2.808 1.000 7.004
5.80 10 58.15 1.15 6.64 0.42 0.07 1.99 h 2.909 1.000 6.928
6.00 10 58.15 1.11 6.67 0.43 0.07 1.99 h 3.009 1.000 6.827
6.20 10 58.15 1.08 6.71 0.44 0.07 1.99 h 3.109 1.000 6.756
6.40 10 58.15 1.05 6.74 0.44 0.07 1.99 h 3.209 1.000 6.668
6.60 10 58.15 1.03 6.77 0.45 0.07 1.99 h 3.310 1.000 6.592
6.80 10 58.15 1.00 6.81 0.46 0.07 1.99 h 3.410 1.000 6.533
7.00 10 58.15 0.98 6.83 0.47 0.07 1.99 h 3.510 1.000 6.441

Fuente: Elaboración propia, 2022.

Table 15 Peak flows for different storm durations and wet antecedent conditions (CN, III) for February 19, 2022. 

d (hrs) Tr CN i (cm/hr) P (cm) Pe (cm) X tr (hrs) d/tr Z Q (m³/s)
1.00 10 60 4.67 4.67 0.10 0.10 1.99 h 0.501 0.383 3.585
1.20 10 60 4.08 4.89 0.13 0.11 1.99 h 0.602 0.452 4.769
1.40 10 60 3.63 5.08 0.16 0.12 1.99 h 0.702 0.512 5.754
1.60 10 60 3.27 5.24 0.19 0.12 1.99 h 0.802 0.567 6.570
1.80 10 60 2.99 5.37 0.22 0.12 1.99 h 0.903 0.616 7.241
2.00 10 60 2.75 5.50 0.25 0.12 1.99 h 1.003 0.661 7.804
2.20 10 60 2.55 5.60 0.27 0.12 1.99 h 1.103 0.703 8.253
2.40 10 60 2.38 5.70 0.29 0.12 1.99 h 1.204 0.742 8.655
2.60 10 60 2.23 5.79 0.31 0.12 1.99 h 1.304 0.779 8.976
2.80 10 60 2.10 5.87 0.33 0.12 1.99 h 1.404 0.813 9.253
3.00 10 60 1.98 5.94 0.35 0.12 1.99 h 1.504 0.846 9.482
3.20 10 60 1.88 6.01 0.37 0.12 1.99 h 1.605 0.877 9.682
3.40 10 60 1.79 6.08 0.38 0.11 1.99 h 1.705 0.907 9.837
3.60 10 60 1.71 6.14 0.40 0.11 1.99 h 1.805 0.935 9.989
3.80 10 60 1.63 6.19 0.42 0.11 1.99 h 1.906 0.962 10.103
4.00 10 60 1.56 6.25 0.43 0.11 1.99 h 2.006 1.000 10.328
4.20 10 60 1.50 6.30 0.44 0.11 1.99 h 2.106 1.000 10.164
4.40 10 60 1.44 6.35 0.46 0.10 1.99 h 2.206 1.000 10.003
4.60 10 60 1.39 6.40 0.47 0.10 1.99 h 2.307 1.000 9.860
4.80 10 60 1.34 6.44 0.49 0.10 1.99 h 2.407 1.000 9.696
5.00 10 60 1.30 6.49 0.50 0.10 1.99 h 2.507 1.000 9.550
5.20 10 60 1.26 6.53 0.51 0.10 1.99 h 2.608 1.000 9.404
5.40 10 60 1.22 6.57 0.52 0.10 1.99 h 2.708 1.000 9.268
5.60 10 60 1.18 6.60 0.53 0.10 1.99 h 2.808 1.000 9.121
5.80 10 60 1.15 6.64 0.54 0.09 1.99 h 2.909 1.000 8.999
6.00 10 60 1.11 6.67 0.55 0.09 1.99 h 3.009 1.000 8.850
6.20 10 60 1.08 6.71 0.56 0.09 1.99 h 3.109 1.000 8.737
6.40 10 60 1.05 6.74 0.57 0.09 1.99 h 3.209 1.000 8.606
6.60 10 60 1.03 6.77 0.58 0.09 1.99 h 3.310 1.000 8.491
6.80 10 60 1.00 6.81 0.60 0.09 1.99 h 3.410 1.000 8.397
7.00 10 60 0.98 6.83 0.60 0.09 1.99 h 3.510 1.000 8.266

Source, Own elaboration (2022).

The peak flow obtained is highlighted in green shading and in bold. In both scenarios, stream peak flows were obtained for a 4 hours storm, with values of 7,717m3/s and 10,328 m3/s, respectively. Finally, synthetic hydrographs were obtained for both scenarios, which are shown in Figure 13. These hydrographs were made using the methodology described by Aldama-Rodríguez & Ramírez-Orozco (1998) and using a peak time of 3.99 hours and a base time of 11.98 hours. In them we could observe that the volume of direct runoff for May 27, 2008, was 169121.27 m3 and 226345.656 m3 for February 19, 2022, thus having an increase between them of 57224.39 m3. It would be necessary to court them with the measures currently used by the municipality and carry out a simulation with the existing infrastructure and the runoff volumes to observe the reaction of the system in the event of an eventuality.

Source, Own elaboration (2022).

Figure 13 Number Curve for February 19, 2022. 

Based on the above results, a visit in situ was made, and the infrastructure was found to be in deteriorated condition and inadequately implemented. Since a hydraulic subsystem that emulates the behavior of storm regulating basins does not allow the water to evacuate in a considerable time. This leads to entropic conditions within the subsystem itself (Figure 14).

Source, Own elaboration (2019).

Figure 14 Canal of Patria and Colomos avenues after several days without a storm. 

There was also considerable dragging of sand, weeds, and solid urban waste along the canal. These reach the retention basins, sewers, and manholes (Figure 15).

Source, Own elaboration (2019).

Figure 15 Sewers and manholes inside the Patria Avenue canal. 

From the results obtained, it is possible to observe that runoff has increased considerably in recent years. This increase in runoff flow is around 33.84% considering the Chow-Ven (1994) method in wet soil conditions, for the flow estimated in 2008; that is, it went from 7.72 m3/s to 10.33 m3/s. This modification has caused a systemic disorder increased urban social entropy, as reported by Bascuñan-Walker et al. (2011), due to the transformation and disorder of the soil, and in concordance with Gordillo & Castillo (2017), confirming that migration has extended the urban stain, altering natural processes of infiltration-runoff and consequently flooding.

Figures 8 and 9 show the spread of urbanization, a significant decrease in the lower density residential area (1 acre), for the passage to a densification of the same (residential with plots size less than or equal to 1/8 acre). Thus, we have a decrease in the residential area with an average lot size of 1 acre from 8.44 km2 to 5.56 km2, causing greater land consumption and greater demand for urban services, which, according to Aguirre-Nuñez (2011), tends to extinguish the ecosystem services provided by the watershed.

In this context, it is necessary to build a model that contemplates the existing rainwater infrastructure and also to contrast them in future research with the capacity of the system, since maybe it does not have enough to contain stream flows. Nevertheless, it is possible to affirm that in the metropolis of Guadalajara the urbanization process is occurring and increasing regardless of the knowledge, structural and thermodynamic functioning of the systems. In other words, this phenomenon is occurring without planning, or under non-systemic planning premises. This conceptual category (non-systemic planning) refers to factors related to an absence of the fundamentals of systems theory, a lack of knowledge of the causes of entropy, and a lack of implementation of negentropy with long-term effects. In sum, the homeostasis of this urban system is the result of the action of entropies of anthropic origin identified in the critical and hypercritical phase, with morphological conditions that are difficult to reverse (Table 16).

Table 16 Considerations in the application of the EHN model 

Entropy Homeostasis Negentropy
Land development tends to replace the original surfaces with impervious coverings (concrete pavements, asphalt, cobblestones, stone, platforms for horizontal serial housing, etc.). These reduce the infiltration rate and increase the velocity and volume of runoff. A higher concentration of fine material is identified adjacent to the mouths of circular channels and in open channels. Water flows exceed the free edge and consequently cause flooding in the surrounding areas. It is a priority to determine exclusive use zones for phreatic recharge, through hydraulic infrastructure for rainwater detention and retention, to rethink horizontal housing, and to prioritize sustainable urban mobility.
There are limitations, omissions, permits, or violations of the regulatory frameworks for real estate and land use. Likewise, regarding the management and final disposal of water resources and/or urban solid waste. Excessive urban-housing growth, insufficient and deficient hydraulic infrastructure. In addition, obstruction and clogging of subway conduits (pipes) and surface conduits (canals and/or sewers). Establishment of public policies under a systemic conception, and implementation of citizen awareness programs for land use, care of hydraulic infrastructure, and the management and final disposal of rainwater runoff and domestic waste.

Source: Own elaboration based on González-Pérez (2018).

Conclusions

According to the EHN model, anthropic forces have destabilized the homeostasis of the city and its environment. Entropy, in this case, results from urbanization, and negentropy refers to the set of reactions that have not been able to minimize the levels of entropy generated by the urban-habitat growth and consequently in the increase of the streamflow.

In hydraulic matters, the volumes of water inflow and outflow at different time intervals experienced in this area of the metropolis of Guadalajara exceed the storage and transport capacity of the urban pipelines. Therefore, it is imperative to control the quality, quantity, and magnitude of rainwater discharges into the receiving bodies and to avoid affecting houses and the population. However, the in situ inspection showed quantities of fines and flow rates above the reception capacities. In this sense, the current sizing and conditions in this specific area no longer meet the requirements for receiving, detaining, retaining, and transporting rainwater together with household discharges. In other words, the increase in urbanization has led to a greater number of discharges and consequently greater entropy in the system.

Urban-housing growth is unsustainable in the face of excessive demand for land and housing, where systemic premises are not considered in watershed management. In this sense, it is inadequate to omit or allow areas that are sensitive to the infiltration of rainwater runoff to be urbanized. Likewise, it has become a modus operandi to evacuate rainwater runoff in the shortest possible time, without taking into account the various surrounding subsystems. This exercise does not solve the underlying problem, but rather displaces it downstream.

Land cover change and runoff management imply a multidisciplinary and transdisciplinary exercise. The thermodynamics of urban systems, through anthropic pressure, is increasing entropy levels, with often irreversible effects in the main urban centers. The contribution of this work lies in the qualitative and quantitative measurement of current conditions, identifying the cause of these conditions, and the magnitude of possible interventions to minimize systemic entropy. In the case study, over 14 years, there have been increases in the residential area with a higher density of more than 2,886,503.82 m3, thus increasing the volume of runoff produced. Hence, the need to consider systemic land planning and integrated watershed management; that is, the initial assumption that relates non-systemic urban-territorial planning with an increase in the entropy phase is confirmed to the extent that the original conditions of land cover are affected.

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Received: June 19, 2021; Accepted: July 04, 2022; Published: August 31, 2022

*Corresponding Author: Mario Guadalupe González-Pérez. Dpto de Estudios del Agua y la Energía. Universidad de Guadalajara. Av. Nuevo Periférico, 555, Ejido San José Tateposco. C.P 45425, Tonalá, Jalisco, México. Teléfono (33) 31342276. E-mail: mario.gperez@academicos.udg.mx

Contribution of the authors

Conceptualization of the study, GPMG; SFM; methodology development, RHJA; software management and experimental validation, RHJA, FVF; results analysis, FVF, GPMG; data management, FVF writing and preparation of the manuscript, GPMG, SFM; writing, proofreading and editing, GPMG. “All authors of this manuscript have read and accepted the published version of it."

Conflict of interests

"The authors declare no conflict of interest."

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