Introduction

Among the four components of the planet's cryosphere (^{Williams, 2012}): floating ice, seasonal snow, glaciers and permafrost, the last three are present in the upper part of the highest Mexican volcanoes: Citlaltepetl, Popocatepetl and Iztaccihuatl [5,610, 5,500 and 5,220 masl respectively (^{INEGI, 2017})]. Throughout the world, the high mountain landscape is evolving in an accelerated manner as a consequence of climate change (^{Spehn et al., 2005}, ^{Ahumada et al, 2010}). Of their permanent ice, glaciers have dramatically retreated (^{Delgado-Granados, 2007}; ^{Herrera and Ruiz, 2009}) or have been extinct for the past decades, and permafrost (^{Williams and Smith, 2008}) has been degraded in recent years; at the same time, the permanence of seasonal snow has been progressively reduced. This together has forced the periglacial environment to experience geomorphological changes of different magnitude (^{Ahumada et al., 2010}); from the increase in areas of gelifluction (^{Janke et al., 2011}), to rock fall and landslide with catastrophic results (^{Etzelmüller, 2013}). Several investigations (^{Gruber et al., 2004}, ^{Huggel et al., 2010}, ^{Clague et al., 2012}) document that in many cases the degradation of permafrost has been the main conditioning factor.

Permafrost is a strictly thermal condition of the ground (^{French, 2007}), and it is present in circumpolar regions as well as in some high mountain areas of medium and low latitude such as the Alps and the Andes especially; there are isolated mountains in regions of the tropics that also contain it. It is composed of rock or soil with or without the presence of organic elements in its interior that remain at least two continuous years below 0 ° C (^{Trombotto et al., 2014}); Above this is the active layer that is characterized by a cyclical freezing and thawing in response to the seasons of the year (^{Osterkamp and Jorgenson, 2009}). Due to the physical-chemical characteristics of the soil and external processes such as the infiltration of water by melting and precipitation, the ice inside it may be present although it is not strictly necessary (^{French, 2007}). To indicate the general characteristics of its coverage it is designated as "continuous permafrost" when it is present in more than 90% of the surface of the land; "discontinuous permafrost" is between 65 and 90% and "sporadic" below 65% (^{Trombotto et al., 2014}).

Unlike the near-polar regions, the heterogeneity of the high mountain relief establishes the existence of microclimates among relatively small areas (^{Haeberli et al., 2010}) that often condition that air temperature and the correspondence with the presence of permafrost may differ substantially from the air-ground correlation present in circumpolar areas (^{Guodong and Dramis, 1992}). While in Canada and Alaska the lower limit of continuous permafrost generally corresponds to an annual average air temperature (AAAT) of -6°C (^{Smith and Riseborough, 2002}) and the discontinuous permafrost limit coincides with the annual isotherm of -1°C (^{Brown, 1970}; ^{French and Slaymaker, 1993}), in mountains of medium and low latitude many times the presence of permafrost can occur with a AAAT above 0°C (^{Guodon and Dramis, 1992}); such is the case of the Sierra de Telera, Spain (^{Andrés y Cía, 2006}) and the Mauna Kea volcano, Hawaii with a AAAT of + 3.6°C (^{Woodcock, 1974}, ^{Gorbunov, 1978}).

The periglacial environment in Mexico and particularly the topic of permafrost was addressed in glaciological studies at the end of the 1960s (^{Lorenzo, 1969a}, ^{Lorenzo, 1969b}) and even more so during the 1970s through the studies of ^{Heine 1973}, ^1975a, ^1975b), ¹⁹⁷⁷), as well as ^{Gorbonov (1978)}. Specifically, Heine (1975) performs a periglacial inventory on the Citlaltepetl volcano based on strictly visual descriptions, noting, in addition to other geomorphological features, that the lower limit of permafrost is located at 4,600 meters above sea level (masl). Again in the 1990s ^{Heine (1994)} reiterates the discontinuous presence of permafrost in the high Mexican mountains above the 4,600 level. During the last twenty years, most systematic works for the determination of permafrost in the country have begun, considering the thermal variable of the ground. These more recent researches have been carried out in the Popocatepetl and Iztaccihuatl volcanoes exclusively (^{Palacios et al., 2007}, ^{Andrés et al., 2010}, ²⁰¹¹, ²⁰¹²), leaving aside the Citlaltepetl volcano, the highest in the country and in North America.

In the light of the above, this work has a dual purpose: in the first instance it aims to complement the most recent studies on permafrost in the three highest mountains in Mexico and secondly, it seeks to indicate the current state of its coverage in Citlaltepetl, which, in view of the current climate change conditions should be different from the one pointed out 43 years ago. The investigation is approached by analyzing the temperatures of ground profiles at different depths and their correlation with the AAAT; the degree of incidence of solar radiation on the surface and the albedo indexes are analyzed so that together the presence and limits of permafrost are indicated. The permanent existence of ice in the subsoil and rock confirms the above.

Geographic generalities of the study area

The volcano Citlaltepetl (Star hill in Nahuatl) or Pico de Orizaba is a stratovolcano that belongs to the Neo Volcanic Axis of Mexico in its easternmost area. The center of its crater is located at coordinates 97 ° 16' N and 19 ° 02' E (^{Rossotti et al., 2006}). It has an altitude of 5,610 masl (^{INEGI, 2017}) which makes it the highest volcano in North America and the third largest mountain after Mount Denali (6,190 masl) and Mount Logan (5,959 masl). Its age is dated in ~ 650,000 years when the first stage of formation known as "Torrecillas" began, which was followed by two more phases of evolution including "El Espolón de Oro" and the current crater (^{Macias, 2005}). The most recent geological formations are a consequence of this last eruptive phase between 16,500 and 4,000 years ago (^{Macías, 2007}); these are generally composed of dacite and andesite flows that cover large extensions of the north of the cone, some parts have been buried by deposits of pyroclastic material and ash; many of these materials have been compacted and others have a looser consistency (^{Carrasco-Núñez and Rose, 1995}). The southern slope presents a significant flow of andesite from the same period and is mostly covered by pumice deposits that cover a large part of this slope with a gray-white color. The eastern and western slopes have lower amounts of lava flows that combine with deposits of pumice and ash. Above 4,000 masl the gelifraction process of the rock is noticeable, which in some cases forms conical deposits that flow according to the slope. The volcano has a clearly conical structure; the lava flows are located below the 4,900 level and above this limit its shape is markedly regular and homogeneous. On its north face and above 5,060 masl the glacier begins, extending continuously to the crater at the top of the cone; this summit divides the states of Puebla and Veracruz. In the slopes of the state of Puebla, the orography is very regular until it connects with the Central Mexican High Plateau with an average altitude of 2,200 masl; on the other hand, the relief is more rugged on the Veracruz side until it connects with the coastal plains of the Gulf of Mexico.

Figure 1 Study zone. Prepared by authors. 

Materials and methods

To understand and indicate the presence of permafrost requires the combination of models and physical observations due to the systematic variability caused by the orography of the environment, which tends to be different from one area adjacent to another (^{Gruber and Haeberli, 2009}). For this reason, in this work the current coverage of permafrost in the volcanic cone is evidenced and indicated through of a Geographic Information System (GIS) and under an empirical-statistical approach of topo-climatic variables [^{Julián and Chueca (2004)}, ^{Julián and Chueca (2005)}, ^{Abramov et al., (2008)} and ^{Serrano et al. (2009)}].

Temperature

To confirm the presence of permafrost and to delimit its coverage under the thermal criteria, five observation stations were installed for the temperature of the sub-soil and air. Four of these stations were placed at different altitudes on the northern slope of the volcano and one more on the southern slope. To the north, the first one was installed at the timberline at 4,050 masl; the second at 4,200 masl, the third at 4,584 masl and the last near the lower limit of the glacier (5,060 masl). The southern station was placed under conditions similar to that of the northern elevation of 4,200, both in altitude and in the type of substrate and orographic conditions. At each station the ground was drilled to where the substrate and tools allowed under the PACE technical manual standards (^{Harris et al., 2001}) and the ^{IPA (2008)}. In each perforation, a 2 "diameter PVC pipe was introduced, which was sealed at both ends; inside, Hobo Pendant UA-001-64 sensors were programmed and placed to log data every hour from March 22, 2015 until December 10, 2017. However, in order to avoid any uncertainty caused by considering incomplete years or seasons, the data analysis period for this work was two full years between July 1, 2015 and June 30, 2017. A sensor with the same characteristics was placed near each borehole to record the air temperature in equal periods. Figure 2 shows the position of the stations and the depths of each sensor.

Figure 2 Location of the stations and depth of the sensors. Drilling at 5,060 masl was limited to only 50 cm due to the hardness of the frozen ground that was found. Prepared by authors. 

The extraction and backup of the data was done every three months on average and during each visit the status of the batteries was tested; when they marked less than 50% of life they were replaced by new ones. The main objective of these tasks was to keep the sensors in optimal conditions for an uninterrupted temperature record and free of any alteration outside the characteristics of the weather that together would result in complete and homogeneous data series (^{Aguilar et al., 2003}, ^{OMM, 2011}, ^{Firat et al., 2012}).

The data of the two years were divided by month for each of the series and the monthly average was obtained, as well as the value of the annual average of both the air (AAAT) and the ground (AAGT) in the different depths to observe its oscillations throughout the year. In addition, monthly ground data were plotted along with their annual average value to analyze the temperature trend according to depth based on Williams and Smith (1989). At the same time the summer and winter periods were traced to further strengthen in the calculation of its temperature. Once the trend lines for the colder and warmer periods were joined at a point that manifested the absence of thermal oscillation between the two will mark the AAGT of each profile, and if this was within the range of negative temperatures would indicate the presence of permafrost (^{van Everdingen, 1985}; ^{French, 2007}; ^{Heginbottom et al., 2012}). To determine the altitudinal limit of the permafrost, the equation of the regression line resulting from the correlation between the temperatures of the ground profiles and the altitude at which they are located was used; to ensure the quality of the estimation, statistical tests were performed on the residuals of the linear regression. Additionally, the AAAT records were used to compare with the AAGT of each profile; if the AAAT was negative at an altitude with a thermal profile that indicated the presence of permafrost, there would be an ideal air-ground correlation as suggested by ^{Brown (1970)}, ^{French and Slaymaker (1993)} and ^{Smith and Riseborough (2002)}. On the other hand, if the AAAT were higher than 0 ° C with a ground profile with permafrost, it would emphasize what was pointed out by ^{Woodcock (1974)}, ^{Gorbunov (1978)}, ^{Guodong and Dramis (1992)} and Andrés y Cía (2003).

Results

The behavior of the monthly air temperature in each station shows an oscillatory pattern throughout the year that can be considered highly correlated (^{Motulsky and Christopoulos, 2003}) in relation to the altitude at which they are located [Figure 3 (f) ]. At 4,050 masl the range goes from 3.45 to 7.58°C and an AAAT of 4.97°C; at 4,200 masl, the thermal range is the lowest of all with values between 3.68 and 6.86°C and an annual average of 4.87°C. In level 4,584, the widest annual oscillation is recorded with values between -2.94 and 2.49°C with an average of 0.29°C. At 5,060 masl it varies from -2.99 to 1.06°C with an AAAT of -0.46°C. The southern station at 4,200 masl has a very similar oscillatory range, although slightly colder than its equivalent on the northern slope; their values range from 2.66 to 5.91°C with an annual average of 4.31°C. These patterns of behavior can be seen in Figure 3.

Figure 3. Monthly air and ground temperatures 2015-2017. The graph “f” indicates the correlation between the AAAT and the altitude of each station 

In the same way, the temperature profiles per altitudinal floor are shown in figure 4.

In ascending order of altitude, in the northern slope the temperatures found in the ground profiles are: at 4,050 masl, 7.80°C; at 4,200, 7.00°C; at 4,584 masl, 1.10°C and finally permafrost was located at elevation 5,060 with a temperature of -0.35°C. By using the regression equation of figure 4 (f) to determine the height at which the ground temperature is maintained at <= 0 ° C throughout the year, it is found that the lower limit of continuous permafrost is located at 4,880 masl. Figure 5 shows in summary the altitudinal estimate (shaded in black) and its statistical analysis.

Figure 5 Regression analysis by means of residuals and estimation of the lower altitudinal limit of permafrost. 

A higher AAGT in the profile of the southern station is due to a greater amount of ISR [see figure 7 (a)]; it shows a value of 7.80°C at 4,200 masl. Considering the 0.80°C difference between the north and south profiles at 4,200 masl, it is assumed that the lower limit of the continuous permafrost is located above the corresponding limit on the north side. In this way, if we use the previous regression equation once more to identify at what altitude the line crosses the -0.80°C we obtain as a result 4,963 masl as seen in figure 5. That is, while in the north the lower limit of continuous permafrost with a TMAS <= 0°C is located at 4,880 masl, in order to match that temperature in the south it would be necessary to ascend 83 meters more in vertical; so the permafrost cover, given the conical geometry of the volcano, would represent a concentric and at the same time elliptical shape (see figure 11). On the other hand, concerning the temperature of each profile and the value of the air temperature at the altitude at which they are located, there is an almost perfect correlation (^{Motulsky and Christopoulos, 2003}) with R² = 0.99; this relationship is summarized in Figure 6.

Figure 6 Air-ground correlation on the northern slope of the volcano. In this analysis, the southern slope station was not considered because, despite having an AAGT greater than that of its northern equivalent in response to a greater ISR, it has (as noted above) an AAAT 0.56°C lower. 

Figure 7 ISR (a) and albedo (b) maps. The highest albedo portion to the north of the crater belongs to the body of the glacier, while the rest are due to the reflectivity of the pumice deposits (^{Dobos, 2003}, Ahrens, 2006). Prepared by authors. 

Figure 8 Buried ice in the northern slope. The image was taken at 4,810 masl, just below the “El Espolón de Oro”; it shows two isolated patches (a and b) of glacial ice buried by debris with a diameter of 2 to 12 cm. The linear section of exposed ice of patch b has a thickness of 60 cm and a length in the direction of the slope of approximately 65 meters. Photograph (c) shows in detail an exposed portion of solid ice below fine sediments and gravel. 

Regarding the characteristics of the relief and its determining role on the ISR throughout the year, it can be seen in the map of figure 7 (a). In the same way, the particularities of reflection of the deposits determine the albedo indexes shown in the resulting map of Figure 7 (b).

The prospecting carried out along with the data mining allowed to identify large portions of ice buried by debris flows and deposits of finer materials above 4,700 masl. The location of these portions of buried ice suggest that they are remnants of the glacier which extended to this level during the year of 1975 (^{Cortés-Ramos and Delgado-Granados, 2015}).

Additionally, ice outcrops are common through the rocky walls; many of these have remained throughout the time this work lasted, particularly those that are above 4,700 masl. The series of images shown in figure 9 provides an example of this.

Figure 9 Interstitial and intrusive ice. The sequence of previous photographs was taken at mid-day on May 31, 2016. The photo (a) was taken at 4,780 masl in the rocky portion known as “Los laberintos” and is visible through the cavities of the rock the lenticular ice agglomerations of 1 to 2 cm in diameter. Photo (b) shows a larger portion of ice that has formed in the middle of the separation of blocks of dacite from the flow of “Los laberintos” at 4,730 masl; it can be noticed the diagonally shaped 60 x 20 cm expanded between the spaces of the rock. The photograph (c) was taken close to 4,800 masl; the external part of approximately 90 x 40 cm of a solid portion of ice that covers the entrance of a rock cavity is clearly visible. 

Figure 10 Protalus rampart on the northern slope. The photograph (a) shows the rich ice content by the recrystallization of the snow; in the background a part of the group of snow-debris channels can be seen. The exposed portion of massive ice shows a lobular shape that extends from the middle of the geoform to the upper part of it (photograph b). The photograph (c) was taken from an altitude of 4,700 masl; it exhibits the whole of the geoform that starts at 4.765 masl with an almost angular aspect close to the middle of its shape, product of the debris bearing above it that turn in the direction of the small valley downhill. In the background the summit of the “El Espolón de Oro” can be observed. 

There is also another type of geoform composed of detritus and cryoclasts with ice developed inside just below the set of nivodentritic channels at the foot of the remains of "El Espolón de Oro". The rich ice content in its interior could be the product of snow accumulation that has been covered by debris over time; it is suggested, according to ^{Trombotto et al., (2014)} that it could represent a phase in the evolution of a debris glacier.

Therefore, it can be assumed that at least one hundred meters below the limit of continuous permafrost a parallel strip with a discontinuous and isolated presence of permafrost is located, which overall looks in accordance with figure 11.

Figure 11 Schematic distribution of permafrost in the volcanic cone. The image has been made without considering scales. Prepared by authors. 

Finally, the value of the areas of continuous and discontinuous permafrost cover, considering the orography, were estimated at 5.52 km² [this value does not consider the area of 0.61 km² (^{Cortés-Ramos, 2016}) occupied by the glacier] and 2.06 km² respectively.

After the combination of variables, factors and elements analyzed in this paper, we can obtain the final map of permafrost distribution in the Citlaltepetl volcano (figure 12).

Figure 12 Map of distribution of permafrost in the Citlaltepetl volcano. Prepared by authors. 

Discussion

After 43 years, when Heine (1975) pointed out the presence of permafrost in the volcano, it is still present in the Citlaltepetl. Although the author did not have prolonged temperature records to determine the permanence of the ground under freezing over at least two continuous years as is currently indicated in the specialized literature, this work confirmed its presence from the thermal perspective. The isolated and discontinuous portions that Heine found from 4,600 masl today are 180 meters above, an area we have identified as the discontinuous permafrost strip with an area of 2.06 km². On the other hand, the continuous permafrost cover is positioned at an average of 4,920 masl, considering the north and south slopes with an area of 5.52 km². The homogeneous characteristics of the relief and the material deposited above this level condition the continuous presence of permafrost.

The degradation of permafrost in the Citlaltepetl, although it is remarkable, has been presented more slowly compared to the retreat of its glacier. If we consider the northern slope where Heine (1975) indicates its beginning at 4,600 masl and that for that same year the lower limit of the glacier was calculated at 4,700 masl (^{Cortés-Ramos and Delgado-Granados, 2015}), to compare it against our estimate of the discontinuous permafrost from 4,780 masl and currently at the beginning of the glacier at 5,060 masl, we obtain a retraction of 360 meters in the glacier against 180 meters of variation in the permafrost limit; in other words, the glacier has retreated at a rate of 8.6 meters per year compared to 4.3 meters per year of permafrost since 1975. These circumstances indicate the persistence of permafrost before the possible extinction of the glacier.

The large portions of ice found in the subsoil have remained at least for decades and are likely to remain even after the glacier has disappeared; on the other hand, the smaller fragments embedded in the rock walls may last only a few years due to the high rate of thermal conductivity offered by the rock (^{Vosteen and Schellschmidt, 2003}).

Although the surface of the south slope receives more ISR throughout the year compared to the north, its higher albedo index would balance its temperature to some extent. In spite of the fact that there is a warmer temperature of 0.56°C in the profile of the southern ground with respect to the north at 4,200 masl, the higher index of albedo above 4,800 masl compared to that of the northern slope at the same elevations and near the top it becomes equal or slightly higher than the one that presents the glacier ice of the north, it would come to "soften" the degree of ISR.

The regression model applied for the estimation of the lower limit of permafrost shows an acceptable level of certainty and is based on the high correlation existing (^{Motulsky and Christopoulos, 2003}) between the AAGT of each profile and its corresponding altitude (R² = 0.91).

The AAAT and the AAGT in the north are perfectly matched (R² = 0.99). The case of the southern slope, at least for elevation 4,200 where the soil is warmer in response to the aforementioned ISR, the ground-air relationship deserves special attention and should be addressed in subsequent studies because its AAAT could be influenced for other micro-climatic factors.

The presence of permafrost in the station located at 5,060 masl and its corresponding value of air temperature (-0.35°C and -0.45°C respectively), as well as the AAGT-AAAT correlation indicated above indicate that at least for this mountain the permafrost interacts with an air temperature also below zero and at the same time make assume a balance between them.

The temperature conditions found in the permafrost classify it as "warm permafrost" (Noeztli et al., 2003) and coincide very closely with those found by ^{Andrés et al., (2010)}, ²⁰¹¹) and ^{Yoshikawa (2013)} in the tropical Chachani volcano (16 ° south latitude) of the Peruvian Andes and with the most of the high and low latitude permafrost in which its thermal conditions, always close to the thawing point, could allow them to be classified as "committed" and potentially unstable as suggested by ^{Fischer et al., (2006)}.

Conclusions

The permafrost at Citlaltepetl is still present, but the degradation and retreat of its coverage is latent; this process is relatively similar to that of the retreat of its glacier in response to climate change as expressed by ^{Wiliam and Smith (2008)} and ^{Ahumada et al., (2010}). Notwithstanding the above, the rise of the lower limit of permafrost has been slower in comparison, as pointed out on a global scale by ^{Fischer et al., (2006)} due to its hiding and protection characteristics provided by the surface and are contrary to direct exposure to the elements experienced by glacial ice. This suggests that of these two indicators of high mountain climate change, permafrost will remain at least a few decades after the glaciers are extinct.

This work updates the information provided in 1975 by Heine and complements the series of more systematic studies on permafrost coverage for the three highest mountains in the country.

Recommendations

Given its importance as an indicator of climate change, a continuous and uninterrupted monitoring of the permafrost temperature in the highest volcano in Mexico and North America, including, among other actions, the expansion of observation stations with records at a greater depth, is highly necessary in order to have a more complete and accurate database that serves as a basis for climate studies and subsequent geological risks.