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}).

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.

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)

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).

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

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

where:

= Time of concentration (h)

= Length of main channel (m)

= 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.

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.

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.

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

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

For d/tp between 0.05 y 0.4

For 0.4 ≤ d/tp ≤ 2

For d/tp >2

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:

Where:

Qp= Expenditure peak.

tp= Time peak.

tb= Timebase.

tr= Delay time.

Where:

tp= Peak time.

de= Duration in excess.

tr= Delay time.

Where:

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.

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.

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.

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.

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

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

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.

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.

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.

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.

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.

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).

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).

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).