Introduction

Temperate forests are important ecosystems for recharging the aquifers, as they are the source of an estimated 25 % of the national total, equivalent to 4.8 trillion m³ of water (^{Torres and Guevara, 2002}). In this respect, the Western Sierra Madre of the state of Durango is a vital region for the basins of the Pacific Ocean and for the central and northern inland of the country (^{Dueñez et al., 2006}).

Infiltration capacity is the term applied to the entry process of water through the soil surface (^{Hillel, 1981}). It is very important to estimate the infiltration rate and the accumulated sheet, as these are key components of the hydrological cycle. This estimate makes it possible to quantify the runoff, the erosion, the availability of sediments, and the recharge capacity of the aquifers, as well as to define the operation of irrigation systems and to study the effects of various land use practices (^{Grego and Vieira, 2005}; ^{Machiwal et al., 2006}).

Land uses associated with anthropic activities such as agriculture, grazing and forest management may negatively affect the biodiversity and the supply of ecosystem services in the climate change processes at a regional level (^{Sahagún-Sánchez and Reyes-Hernández, 2018}). Furthermore, they reduce the hydric contributions because the soil loses its infiltration capacity, and the aquifers lose their recharge capacity (^{Turnbull et al., 2010}; ^{Pérez et al., 2018}).

Forest management involves the execution of a program of forestry practices such as regeneration methods: seed trees, selective cutting, successive cuttings, and total or clear-cutting, as well as all the forestry activities or intermediate treatments, including thinnings, reforestation, prescribed burnings, sanitation cuttings, and trimmings that are carried out during the forest management (^{Monárrez et al., 2018}). These practices are questioned when, due to high intensity exploitation and to the supply operations, they reduce the forest vegetation, cause disturbances that expose the surface soil to the effects of rainfall, alter and modify its properties, reduce its infiltration capacity, and increase the risk of soil loss due to hydric erosion (^{Dueñez et al., 2006}).

According to ^{Pérez and Romance (2012)}, models that are fitted to the field measurements due to the different soils, climates, vegetation, and management conditions are considered in order to determine the infiltration process. Mathematical models have been developed for measuring the infiltration; in general, they are divided into three groups (^{Collis, 1977}; ^{Pérez and Romance, 2012}): 1) theoretical, 2) semi-empirical, and 3) empirical. The present study used models of the third type for the modeling of the infiltration, as they do not consider those factors that intervene in the infiltration process: the texture, or the moisture content or the soil temperature, among others.

The purpose of the study was to model the infiltration process based on the measurements performed in situ using the methodology of the double-ring infiltrometer, which were adjusted to the parameters of the Kostiakov, Horton and Lewis-Kostiakov models (^{Weber and Apestegui, 2016}) by means of the analysis of their functioning in five different forestry stands (three regeneration cuttings, a post-fire regeneration area, and a reference stand) in temperate forests of Durango State, Mexico.

Materials and Methods

Study area

The infiltration tests were carried out in the forests of La Ciudad ejido, located in the massifs of the Western Sierra Madre within the municipality of Pueblo Nuevo, Durango, where the dominant vegetation consists of Pinus duranguensis Martínez, Pinus cooperi C. E. Blanco, Pinus ayacahuite Ehrenb. ex Schltdl., Juniperis deppeana Steud., and Quercus sideroxyla Bonpl. (^{González-Elizondo et al., 2012}). The predominant soil type is Umbrisol (^{INEGI, 2005}) (Figure 1). The mean annual precipitation is 1 200 mm, and the mean annual temperature is 18 ºC, with a maximum temperature of 22 ºC and a minimum temperature of 3 ºC (^{Zúñiga et al., 2018}).

Figure 1 Study area. 

Results

The average values of initial infiltration, basic infiltration rates and accumulated infiltration for the various stands are shown in Table 2, in which the Reference stand (control) exhibited a better hydrodynamic behavior, unlike the Clear-cutting treatment, which had the lowest values for Ii, Bi and Ci. The Ii variable registered significant differences, and was therefore analyzed using the Tukey test; Bi and Ci exhibited significant differences according to the Kruskal-Wallis test.

Comparison tests allow observing highly significant differences between the Reference treatment and the other analyzed stands, particularly in variable Ii, which was reduced by 45 %, while the Bi increased slightly in the Seed Trees and Selective Cutting treatments, unlike in Clear-cutting and Post-Fire Cutting, for which decreases by 28 and 23 %, respectively, were determined. On the other hand, Ci diminished in all the stands, except for the Seed Trees area, which registered 4.7 % above the Reference stand. The initial moisture content of the soil between the stands exhibited significant differences (Kruskal-Wallis test, p<0.05); therefore, it is considered to play a significant role in the baseline and final conditions of the infiltration.

Figure 2 describes the behavior of the infiltration rate observed in the various stands. In general, there are three distinct periods: initially, the infiltration rate is high and is kept constant during a short time (<15 min); then the infiltration rate diminishes significantly (15-60 min), and this leads to a third, stabilization period known as basic infiltration rate, which may be observed in all the treatment 200 minutes after the application of the test.

Árboles Padre = Seed tres; Posincendio = Post-fire; Matarrasa = Clear-cutting; Referencia = Reference; Selección = Selective; Tiempo (minutes) = Time (minutes); Velocidad de infiltración = Infiltration rate.

Figure 2 Infiltration rate observed in forestry stands. 

The accumulated infiltration process proved that the Seed-trees and Reference stands had the highest volumes of infiltration, followed by the area exploited through Selective Cutting and those of Post-fire and Clear-Cutting. The accumulated infiltration grew constantly during the first 60 minutes; subsequently, it began to experience growth with more stable segments, and the infiltration became slower and longer after 200 minutes (Figure 3).

Árboles Padre = Seed tres; Posincendio = Post-fire; Matarrasa = Clear-cutting; Referencia = Reference; Selección = Selective; Tiempo (minutes) = Time (minutes); Infiltración = Infiltration.

Figure 3 Accumulated infiltrations observed in the forestry stands. 

Table 3 summarizes the parameters of the three fitted models, as well as the value of the determination coefficient (R²), which is a measure of the degree of goodness of the utilized equation. As may be seen in this Table, The values of R² were highest, in every case, for the Kostiakov and Lewis-Kostiakov models; furthermore, the parameters associated to the initial and cumulative infiltration (Ii and Ci) exhibited a similar tendency to that observed in all the analyzed stands.

By way of example, Figure 4 shows the behavior of the infiltration rate observed and estimated, based on the adjusted models of the third test for the Control, Selective Cutting, Clear-cutting and Post-Fire Cutting areas; it can be clearly seen that, since the initial infiltration, the Kostiakov model has a better arrangement, unlike the Horton model, which does not estimate the infiltration adequately during the first moments, and after 30 minutes tends to overestimate the infiltration. In general, this behavior was found in most tests. However, the Lewis-Kostiakov model had a correct performance in the fit, when low initial infiltration rates occurred (Ii<300 mm h^-1), unlike the Horton model, which overestimated the infiltration, and the Kostiakov models which underestimated it, as may be clearly seen in the Selective Cutting area.

Árboles Padre = Seed tres; Posincendio = Post-fire; Matarrasa = Clear-cutting; Referencia = Reference; Selección = Selective; Tiempo (minutes) = Time (minutes); Velocidad de nfiltración = Infiltration rate.

Figure 4 Adjustment of the infiltration rate based on the Horton, Kostiakov and Lewis-Kostiakov models. 

Discussion

^{Di Prima et al. (2017)} point out that opening the canopy is an important practice that influences the relationships between water and the soil. Based on the results of the present study, the differences between the initial, basic and accumulated infiltrations in the stands are determined by the type of disturbance or by the forestry treatment utilized. According to ^{Dueñez et al. (2006)} and ^{Landini et al. (2007)}, the intensity of the cutting is an important factor that determines the levels of interception of rainfall, luminosity, moisture content, depth of organic matter in the soil, etc., and, therefore, has a direct effect on the hydraulic properties of the soil.

^{Bens et al. (2007)}, ^{Wagner et al. (2011)} and ^{Archer et al. (2013)} state that the depth and amount of organic matter contribute to improve the edaphic structure and increase the capacity of infiltration, water storage and hydraulic conductivity; this can be verified based on the results for Ii, Bi and Ci, as well as on the physical characteristics of the soil and the vegetation that is prevalent in the studied stands, particularly in the Clear-cutting stand, whose properties were considerably affected by the intensity of the applied cuttings, leading to a reduction in the hydrological variables.

The values of the infiltration variables indicate that the stage of growth of the forest is a relevant factor that determines the hydrological characteristics of the soil, as suggested by ^{Hümann et al. (2011)}, ^{Marshall et al. (2014)} and ^{Archer et al. (2016)}. This agrees with the results of the study documented herein, in which the Clear-cutting and Post-Fire Cutting areas are forest masses that exhibit a similar maturity status, unlike the Seed Trees, Selective Cutting and Reference stands, which include superior forest trees.

As for the values of the statistic R², there is little variation between the Kostiakov and the Lewis-Kostiakov models, which adequately represent the evolution of the infiltrated sheet in the infiltration tests of the various assessed stands. This is confirmed by ^{Návar and Synnott (2000)}, ^{Weber and Apestegui (2016)}, ^{Sihag et al. (2017)}, according to whom the best predictions are generally obtained with the Lewis-Kostiakov model, as its parameters are more sensitive to the Umbrisol soil types, characterized by exhibiting a thick, dark horizon unsaturated in bases and rich in organic matter (^{Casanova et al., 2007}). In this regard, decreases in organic matter have an effect on the stability of the aggregates, dispersing fine texture particles and thereby favoring a reduction of the porosity and, consequently, leading to decreased infiltration (^{García-Hernández et al., 2008}).

It should be noted that information about hydrological topics and their relationship with forest management is scarce and limited. Hence, the relevance of the present study.

Conclusions

The initial (2 080 mm h^-1), basic (297.93 mm h^-1) and accumulated (16 428.29 mm h^-1) infiltration rates observed in the Referent stands evidence significant statistical differences in regard to other analyzed stands; therefore, the modifications in the forest structure cause a negative effect on the hydrological variables Ii, Bi and Ci.

The variables that make up the infiltration process are arranged in decreasing order as follows:

Characteristics like the maturity status of the vegetation, structure, composition, and the edaphic variables apparent density, thickness of the organic layer, and moisture, cause variations in the infiltration rates of the various stands analyzed.

The results of the fit of the models, based on the coefficient of determination (R²), show that both the Kostiakov and Lewis Kostiakov models are good enough for predicting infiltration in the different forest conditions studied herein; specifically, the Lewis Kostiakov model estimates the infiltration better for the Selective Cutting and Reference areas, while those of the Seed Trees, Clear-cutting and Post-fire Cutting areas are best described by the Kostiakov model.

The parameters of the infiltration models are highly important for estimating the recharge of aquifers, superficial runoffs, and soil erosion, and therefore they facilitate sustainability-based decision making.