Study area

The Tula microbasin is framed within the geographical coordinates: 19° 55’ 31.05’’ and 19° 34’ 28.74’’ north latitude and 98° 39’ 59’’ and 98° 28’ 16.39’’ west latitude (Figure 1), has an area of 103 766 ha and covers the territory of the municipalities: Calpulalpan, Sanctorum de Lázaro Cárdenas, Benito Juárez, Almoloya, Apan, Emiliano Zapata, Singuilucan, Tepeapulco, Villa de Tezontepec, Tlanalapa and Zempoala of the state of Hidalgo, Axapusco and Nopaltepec of the State of Mexico and Temacalpa of the State of Tlaxcala. In addition, it is immersed in the Panuco river basin, within the physiographic province of the Neovolcanic axis. It has an altitude range of 2 333 to 3 223 meters above sea level, the average annual rainfall is 600 mm and the predominant soil types are Feozem, Cambisol, Litosol, Regosol and Vertisol (^{INEGI, 2017a}; ^{INEGI, 2017b}; ^{INEGI, 2017c}), there are different types of vegetation, among which are the tascate forest, pine forest, oak forest, crasicaule thicket (^{INEGI, 2017d}).

Figure 1 Location of the study area. 

According to ^{López et al. (2001)}, in order to analyze the process of change of land use and coverage, it is necessary to apply three stages: a) cartographic and digital change and interpretation of change; b) analysis of land cover change and land use patterns; and c) analysis of causes of change.

Generation of land use cartographic

The generation of cartography corresponds to the first stage to perform the change process analysis. According to ^{Bautista et al. (2011)} At this stage it is necessary to select and acquire the satellite images that will be worked on, then they must be performed a standard digital treatment (geometric, radiometric and atmospheric correction). Then the image transformation follows, where the image is classified, from the association of elements observed in the image to certain thematic categories, prior to classification, the classification system must be determined and the evaluation of the geographical digital bases must be carried out (^{Rosete et al., 2008}; ^{Bautista et al., 2011}).

The generation of land cover and land use mapping in this study consisted of: a) selecting three satellite images: Landsat-5 TM (12/04/1992), Landsat-7 ETM + (02/12/2000) and Landsat -8 Oli Tirs (11/23/2017) with a resolution of 30 m and an L1TP processing level; and b) correct radiometrically and atmospheric these by means of the Atcor extension 2. Workstation of the Erdas Imagine program, to ensure a standardized comparison of data between them (^{Chander et al., 2009}; ^{Vargas-Sanabria and Campos-Vargas, 2018}); c) determine the training areas where eight study categories corresponding to land cover were established: body of water, urban area, forest area, temporary agriculture, permanent agriculture, crasicaule scrubland, secondary vegetation and area without apparent vegetation (^{Velázquez et al., 2002}); d) apply the Maximum Likelihood supervised classification algorithm to each image, in the ArcMap 10.5 software (^{Vargas-Sanabria and Campos-Vargas, 2018}); and e) validate the classification of plant cover and land use for 1992 and 2000; through its comparison against the layers of land and vegetation use of the INEGI series II and III, respectively.

While to validate the coverage of 2017, this was done by establishing control points within the study area, using Google Earth^® (^{Earth Google, 2018}) and field trips to these points, with the purpose of corroborating the type of coverage corresponding to the training site (^{Torres et al., 2018}). The pixel size of each of the land use maps was then homogenized at 30 m: 1992, 2000 and 2017 and reclassified based on the hierarchical system proposed by ^{Velázquez et al. (2002)} (Table 1) to achieve a hierarchical and homogeneous classification system.

Transition matrix construction

For the stage of analysis of patterns of change of land cover and land use, matrices of transition matrices were constructed, which are described as tables with symmetrical arrangements that contain in the rows the types of vegetation and land uses in the first year or year base and in the columns these same types but of the second year. Each cell of the main diagonal of said matrix represents the area in hectares of each kind of vegetation cover and land use that remained in the same category during the period considered, while in the rest of the cells the surface area of a given coverage or type of land use that passed to another category (Dirzo and Masera, 1996 cited by ^{López et al., 2001}) which allows to understand the dynamics of change in land cover and land use at local and regional level.

From the shapefile maps obtained from the reclassification of vegetation cover and land use of 1992, 2000 and 2017, the transition matrices were constructed, performing the following steps: a) generate transition matrices between the different categories through a cross tabulation (^{Eastman, 2012}), from the TerrSet Crosstab module, for the periods: 1992-2000 and 2000-2017; b) develop probability of belonging matrices for each class in each period with the transition matrices; these matrices are generated by dividing each of the cells of the transition matrix by the total surface area of the analyzed class (^{Vega et al., 2007}); and c) estimate the probability of belonging Pij of each class of the matrix, which is proportional to the remaining area of the same class between year 1 and year 2. Its mathematical expression (^{Sánchez et al., 2004}) is:

Pij=Sij(year 1)Sj(years 2)

Where: Sij = surface of element ij of the transition matrix of land cover and use in year 1; Sj = area of land use class j in year 2; and ∑Pij= 1 for each land use category j.

According to ^{Sánchez et al. (2004)}, the probability of belonging is interpreted as follows: 0-33% (low), 34-66% (medium) and 67-100% (high).

Exchange rates

The processes of land use change are determined with the map resulting from the cross-tabulation and are classified: unchanged, conserved, urbanization, transition, anthropic use, deforested, degraded and by productive activity (^{Rosete et al., 2008}; ^{Cuevas et al., 2011}). These were estimated using the equation proposed by (^{FAO, 1996}):

δn=S2S11n-1

Where:  δn = average annual exchange rate for class i in the nth period evaluated (to express in (%) multiply by 100); S1= total area of class i in period 1; S2= total area of class i between period 2, and n = number of years between the two periods evaluated.

Transitions of land use change

Table 3 and Figure 2 show the results obtained from the transition matrices and the probabilities of membership between categories, for the period from 1992 to 2000. The 54% 416.57+2499.89+⋯+3509.96103766.48= 53.47% of the vegetation cover of the Tula microbasin remained unchanged, while the remaining 46% presented some change (Table 3). According to Figure 3, of 100% of the agricultural area that was in 1992, 89% 31781.2135793.97= 88.79% remained in 2000 being the only category with high probability of permanence and 11% changed to zone urban 936.0535793.97= 2.62% , forest area 1213.0735793.97= 3.39% , abandoned area or without vegetation 1855.7635793.97= 5.18% and bodies of water 7.8835793.97= 0.02% .

Figure 2 Probability of permanence of land use from 1992-2000. 

In contrast, the forest area was the coverage that had the greatest change in surface area with 63% and only retained 37% of it. It should be noted that 52% 23950.446339.27= 51.68% of the forest area passed to agricultural area; which shows that agriculture is an activity that replaces other categories quickly (^{Sánchez et al., 2009}; ^{Cuevas et al., 2011}), because the population demands goods and services, plays an important role in the change of use of soil, since with increasing population the pressure on natural resources also increases generating negative impacts such as deforestation (^{Rosete-Verges et al., 2014}).

It is also important to mention that 4% of the forest area changed to urban area 1962.0546339.27= 4.23% , this is because the population went from 213 208 inhabitants in 1990 to 245 112 inhabitants by the year 2000 according to figures reported by (^{INEGI, 1990}; ^{INEGI, 2000}). Regarding the urban area, 100% only remained 40% 2499.896244.63= 40.03% , 60% change.

38% 2361.746244.63= 37.82% went to agricultural area and 16% 986.816244.63= 15.8% to area without vegetation or abandoned. This is due to the fact that the number of people increases and more goods are required to cover monetary needs, and in that decade according to ^{Cruz (2018}) there was an increase in return migration from the United States of America to the state of Hidalgo. On the other hand, areas without vegetation increase because they are abandoned due to the decline in agricultural production. During the period 2000 to 2017, 76% 367.42+2739.10+⋯+891.49103766.48= 75.67% of the total area of the basin remained unchanged, while the remaining 24% presented some change (Table 4).

According to the classification of Sánchez et al. (2003), the categories: body of water 367.42472.95= 77.68% , forest area 16253.8521023.28= 77.31% and agricultural area 58269.6366102.39= 88.15% are considered with high permanence probability; while the categories: urban area 2739.106638.49= 41.26% and areas without apparent vegetation 891.499528.66= 9.35% are considered with medium and low probability of permanence (Figure 3), respectively.

Figure 3 Probability of permanence of land use for the period 2000-2017. 

It should be noted that the agricultural area increased 83% 58269.6331781.21-1= 83.34% ; however, the forest area decreased 5.89% 16253.8517271.5-1= 5.89% , although at a lower rate compared to the 1992-2000 period. Something similar happens with the category without vegetation, it was reduced 75% 891.493509.96-1=74.6% , moving mainly to agricultural area and forest area.

As already mentioned, urban areas obtained an average probability of permanence, attributed primarily by the increase of the population in the microbasin, this being around 149% 288196115547-1= 149.41% , taking as the base year 1970 with a population of 115 547 inhabitants (^{INEGI, 1970}) and as the final year 2010 with a population of 288 196 inhabitants (^{INEGI, 2013}), the population had a growth rate of 2.3%, from 245 112 inhabitants in the year 2000 to 288 196 in the year 2010 (^{INEGI, 2000}; ^{INEGI, 2013}).

The increase in the population results in a greater demand for land to meet the productive and consumption needs of the population (^{Cuevas et al., 2011}; ^{García et al., 2012}; ^{Torres et al., 2018}).

Exchange rates

Table 5 indicates that the rates of land use change in the 1992-2000 period are higher than those recorded in the 2000-2017 period. In the case of the forestry area, it presents a negative rate for the period of 1992-2000 and positive for the period 2000-2017, which coincides with some studies carried out in Mexico, in similar periods (^{Velázquez et al., 2002}; ^{García-Barrios et al., 2009}; ^{CONAFOR-UACH, 2013}). However, the result obtained by FAO (2010) is greater than 4%. Areas without apparent vegetation have a positive exchange rate that is maintained in both periods, indicating that the eroded areas used as a mine continue to exist.

The agricultural area in the first period had a positive exchange rate that goes hand in hand with the exchange rate of urban areas, this is because the population needs goods to meet their needs. During the second period, the area of bodies of water had an increase of 24%, which is related to the increase in the agricultural area, because it increases more water, which leads the population to build more jagüeyes to retain or capture rainwater.

With respect to the 1992-2000 period, shows the processes of change of the total area that occurred in the microbasin: 37% (38 667.76 ha) did not change, 28% was deforested mainly for agricultural use purposes, which coincides with exposed by ^{SEMARNAT (2002)} in the study carried out in the period 1993-2000 at national level (^{Rosete et al., 2008}; ^{FAO, 2010}).