Meteorological Data

Two controlling seasons were recognized at Popocatépetl volcano: the wet season, with dominance of accumulation, and the dry season, with dominance of ablation (^{Delgado-Granados et al., 2007}). Summer is the rainy season (starting in May-June), characterized by precipitation of snow and hail. Snow can last until January-February before the ablation produces penitents (see for example ^{Betterton, 2001}), however, these conditions present at Popocatépetl are similar at Citlaltépetl region as shown by our data.

On September 17, 2006, two Automatic Weather Stations (AWS) began operating. One was located on the surface of Glaciar Norte (Glaciar station) at 5131 masl, and another on the lateral moraine close to the glacier at 5115 masl (Morrena station). Glaciar station was the main provider of meteorological data used in the energy balance model.

The AWS consists of temperature sensors (accuracy, ±0.5°C), a relative humidity probe (accuracy, ±5%), sensors for wind speed (accuracy, ±0.5) and direction (R.M. Young 03001-5 Wind Sentry Set), a digital barometer (accuracy, ±0.2hPa), and a NR Lite Net Radiometer (error, 3%). Daily averages of each parameter automatically calculated by the station's internal program from September 17, 2006 to October 15, 2009 are presented.

This AWS instrumentation doesn't allow obtaining the energy balance components' absolute values. However, for this study, the net radiation is compared with other data in order to recognize the main processes governing the ablation on the glacier surface.

The total radiative component was measured in the field by two sensors at Glaciar station, placed horizontally above the glacial surface. The sensor facing upwards measured the incoming direct and diffuse solar radiation, whereas the other one was facing downwards aimed towards the glacier surface. The downward aimed radiometer measured the reflected, emitted and diffused outgoing radiation. All the components were summarized in a single exiting signal: the net radiation on the glacial surface.

During times when observed wind speed was seemingly zero, these periods corresponded to low temperatures and a characteristic low valued wind direction, and thus one can interpret the data during these periods. Occasionally, some sensors were frozen, especially the moving parts of the vane and anemometer. During these periods, missing data were replaced by averages from nearby months.

No relevant gaps are present in the data, as the automatic weather station worked correctly since the startup date. However, some data gaps were replaced using daily averages and thus formed a three-year energy balance record to describe the behavior and variations of the energy balance during that period.

The energy balance model

A theoretical model has been developed for this study based on previous work (^{Paterson, 1994}; ^{Oerlemans, 2001}; ^{Francou and Puoyaud, 2004}). This model considers the glacier as an adiabatic thermodynamic system, marking an exception in the glacier-atmosphere interface where diabatic processes do occur. The equations for heat flow and water phase change (ice to liquid to vapor for instance) must take into consideration the atmosphere as a fluid or a system composed of gases.

The measured meteorological variables (temperature, solar radiation, humidity, precipitation, wind and atmospheric pressure) at the glacier fed the theoretical model. The model allowed estimating the energy exchange at the glacier-atmosphere interface at Glaciar Norte using the data obtained from the instrumentation already mentioned. The energy balance was estimated with an independent calculation of each component (latent heat, sensible heat and net radiation). The energy balance for the surface of Glaciar Norte could be approximated as:

where R is the net radiation, H and L _vE are the turbulent sensible heat flux and the turbulent latent flux respectively, L _fØ is the heat flux from precipitation, and B is the total energy flux over the surface. The energy supplied by rain is assumed negligible because the glacial surface remains at melting point, but it could be significant when rain freezes on the surface (^{Paterson, 1994}). We follow the convention to consider all fluxes towards the glacial surface as positive, while all fluxes away from the glacial surface are negative. When the surface temperature is ~0°C and the energy balance (B) is positive, melting processes are considered as natural processes on the glacial surface.

Net Radiation

The total radiative flux is the sum of the net short-wave radiation and net long-wave radiation coming from Earth and sun's emissions. Since net short-wave and long-wave radiation can be separated into incoming and outgoing radiation, the net radiation energy can be expressed by:

where S ↓ is the incoming short-wave radiation or incoming solar radiation, while S ↑ is the outgoing short-wave radiation (reflected by the Earth's surface), L ↓ is the incoming long-wave radiation emitted by the sun and the atmosphere toward the Earth's surface, L ↑ is the outgoing long-wave radiation emitted by the surface, and α is the surface albedo of the glacier. The net radiation measured at some point on the surface represents by itself an energy balance of the surface in which this is measured (^{Francou and Pouyaud, 2004}).

The turbulent heat fluxes

The water vapor transfer in a glacier is associated with the release and absorption of latent heat that dominates the water evaporation and condensation over the glacier.

On the other hand, the transport of sensible heat between the atmosphere and the glacier's surface is mainly through mechanic or thermal turbulence. The component of the vertical sensible heat flux can be expressed as /H0= ραCρdωθv¯v where ωθv¯v represents the sensible heat flux through mechanic turbulence with θ'_v being the turbulent fluctuation of the virtual potential temperature, while ρ _α represents the air density and C _pd the heat capacity of dry air (^{Singh and Singh, 2001}).

The heat transferred by convection can be treated as conduction, so H can be expressed in terms of the temperature lapse rate and as "Eddy Heat Diffusivity" (K_h ) coefficient:

here, ρ represents the air density and c _p the specific heat capacity at constant pressure. Therefore, the convective energy by the heat flux of the water vapor and the flux transferred by the precipitation are summed up to calculate the convective energy H, hence obtaining the total energy fluxes (^{Paterson, 1994}). The vertical flux of water vapor is given by E = -K _ω ∂m/∂z. So, the heat flux associated to water vapor flux is:

where L _v is the specific sensible heat of evaporation, K _ω is the eddy diffusivity of water vapor, and m the mass per unit volume of water vapor. Finally, L _fØ is the precipitation, i.e. the vertical flux of water, while L _f represents the specific latent heat of melting and Ø as the precipitation rate. As stated above, the energy supplied by rain is negligible when the surface and the air temperatures are near the melting point.

Meteorological parameterization

The equation of state for moist air as an ideal gas is:

where M _ω is the molecular weight of water, e is the pressure of water vapor in the atmosphere; while for dry air, it is given by:

with P representing the air pressure, M _α the air molecular weight and ρ the air density. Such that, m = ρeM _ω /PM_ω = (0.622) ρe/P where MωMα= (0.622). Substituting in equation (4) where m is derived just partially respect to z because the change in other direction can be neglected and the interest in focused on the vertical direction. The result is:

The heat transfer by convection depends on air turbulence and it is measured through the eddy viscosity K_m' which means that, τ= K _mρ∂ul∂z, where τ is the shear stress of dry air on the surface and u is the wind speed at height z, this equation represents the vertical flux of horizontal momentum. There is evidence, that at some height, the coefficients K _m' K_h and K _ω are approximately equal to those of a neutral atmosphere (^{Paterson, 1994}). Although this is possible only if the wind speed, temperature and water pressure are distributed logarithmically with height. This rule described by ^{Paterson (1994)} is also applied if the meteorological observations are within ~2m of the surface, and the surface is at melting point. Since these energy balance measurements were taken within the first 2m above the glacier surface, then this rule should apply over the melting surfaces studied here. Thus, it is assumed that: K _m could replace K _h and K _ω. Finally, considering that τ does not change with height,

while u_* represents the frictional velocity. This frictional velocity is related to the surface roughness (z ₀), determined by two wind speed measurements at two different heights. Thus, u _* and z ₀ for neutral atmospheres can be expressed as:

in which k ₀ is the Von Karman constant, in this case (0.4); u ₁ is the wind speed at Morrena station, and u ₂ is the wind speed at Glaciar station; z ₁ = 1.5 m and z ₂ = 16.5 m. Using the wind speed measured at both automatic weather stations to calculate z _0' then the frictional velocity ranges between 0 and 0.65 m/s, the latter value corresponds to the extreme case of Max wind speeds recorded in both weather stations. This value is higher than usual values for glacial surfaces of which the melting point is usually k ₀ ≈ 0.1 to 0.5 (^{Kuhn, 1979}) due to the high exposure to wind that represents the topography of the glacier. Equation (9) leads to ∂ul∂z = u _*/k₀z. Inserting this result into equation (8) we obtain the expression, K _m = u_*/k₀z, which can be written K _m = K_h = K_w = u_*/k₀z. Then by substituting this with the expression ρ = ρ₀(P/P₀)obtained from the state equation of ideal gases at height z and z _0' the resulting equation is:

and after integrating is obtained:

and by substituting of (9) the final expression is:

The equation (12) is obtained through a similar process

if the transfer coefficient is defined as:

The value of _^C* wills depend on measurement height and surface roughness, however previous studies have shown that the parameter depends mainly on the vertical distribution of wind speed (^{Paterson, 1994}). Applying the acquired data sets for the wind speed at the glacial surface, it is possible to calculate the z ₀ and C respectively, and this yielded an average value for _^C* equal to 0.0017. For this study, the numerical constant values given in Paterson (1994) are used: ρ ₀ = 1.29 kgm^-3 is the corresponding normal value for air density at 0°C, measured at a sea level pressure of P ₀ = 1.013 x 10⁵ Pa. These density and pressure values are used because they are a good reference for the ideal gases state equation. The heat capacity of air is c _p = 1010Jkg^-1K^-1 at these pressure conditions, and the latent heat of water vaporization of water is L _v = 2260 x 10³ J/kg. After substitution, the resulting equation yields:

At this point, it is possible to reformulate the general equation (1):

The saturation vapor pressure e was calculated using the Goff and Gratch formula

where

e is the saturation water vapor pressure (hPa)

T is the absolute air temperature in kelvins

T_S is the steam-point (boiling point at 1 atm.) temperature (373.15 K)

e_S = 611 Pa is the e _S at the steam-point pressure (1 atm = 1013.2 5 hPa)

Energy balance components

When a component of the energy balance is positive, the physical processes associated with it favor ablation. But when energy balance is negative, the associated physical processes favor accumulation if the proper temperature and precipitation conditions for accumulation are present.

In Figure 2, the components of the energy balance are plotted as independent values. The values of sensible heat are smaller than those for latent heat, although both have very similar behavior.

Latent heat is predominantly negative for the study site. This explains the presence of accumulation on the glacier. Contrary to net radiation, which is mainly considered positive, Latent heat seems to cause more ablation on the glacier. In addition, there is a greater correspondence between the energy balance and the radiative component than between the energy balance and any other component measured on this glacier. The correspondence found between the energy balance and net radiation shows a positive correlation of about 0.67 (Figure 3). From this value it can be said that the radiative components involved in net radiation mainly determine the regularity and variability of the energy balance. After discovering that fact, it is possible to conclude that the principal factor governing energy balance variability is net radiation, however, the fluxes of sensible and latent heat are very important in terms of the magnitude of the energy balance. It is possible to compare energy balance of Mexican glaciers and more tropical glaciers because the net radiative and the latent heat fluxes dominate the energy balance of these glaciers and not the sensible heat flux (^{Francou et al., 2003}; ^{Favier et al.,2004}).

So, the energy available for melting and sublimation (given by the energy balance) is determined by sensible and latent heat fluxes, while the energy variability is driven by net radiation. Figure 5 shows the annual variation behavior of temperature, relative humidity and net radiation. This behavior is essential to the formation of wet and dry seasons and its alternation along the year.

Although net radiation is the principal factor driving energy balance variations, it is important to note that the sequence of maximum and minimum balance although followed by net radiation, is opposite to that followed by sensible and latent heat. Thus, the role of latent and sensible heat fluxes appear to counter balance the effects of net radiation.

Regime and seasonality

The annual cycle of the four energy balance components was analyzed during the three years of this study (Figure 4). During all three study years, there is observed an ablation period where the values of the energy balance are high (Figure 4, d). Nonetheless, there are some periods when the energy balance values are low, which could mean accumulation periods. However, as ablation is present during almost year, the annual variation of energy balance and the energy available for melting are driven by net radiation variability, similar to what happens at tropical glaciers (^{Sicart et al., 2008}). However, from September to November the glacier experiences a strong accumulation period, and also registered the maximum annual accumulation. This phenomenon is similar to that of glaciers in the outer tropics (such as near 23^o N) where the ablation is low at the end of the balance year (^{Francou et al.,2003}).

Temperature and relative humidity have a similar behavior throughout the year. It is possible to observe an oscillation of annual regularity, where air temperature begins to descend at the end of October to early November causing the air to contain less steam water (Figure 5a and ^5b). In addition, a decrease in relative humidity begins during the same period. As a result, two seasons are defined during the year: a humid and a dry season (Figure 5, un-shaded and shaded zones respectively).

Sometimes during the summer, severe thunderstorms may occur that momentarily deposit sleet and hail on Mexican glaciers. The deposited icy material does not usually stay long, and in most cases disappears in a few days after the intense rainfall event nearby ends. This melt is fast between summer season accumulation events, when the sky is clear and the solar radiation is intense. It is common to observe that after major precipitation events, that runoff increases and the soil becomes saturated with moisture. It is important to note that although most of the snow melts and is lost as runoff, also a certain portion percolates into the glacier and may become internal accumulation or also may become superimposed ice and thus, storms may contribute slightly to reduce the energy available for melt.

It is noticeable that during the dry season, lower temperatures are recorded when low humidity is registered (Figure 5). Therefore, during the dry season it is difficult to reach a natural freezing point, since at low temperatures lower humidities are required for saturation of an ice-water-air mix. Also, during the dry season the sensible heat flux is strongly correlated with temperature, where temperature controls the interchange of sensible heat flux between glacier and atmosphere. The net radiation contains the energy available for melting and overall ablation occurs during the dry season. It is remarkable that between December-February the annual oscillations of temperature (Figure 5a), atmospheric pressure (Figure 5c), and relative humidity (Figure 5b) reach a minimum value. The low pressure registered in these months also impedes the air saturation process and reduces the effect of latent heat to sublimation. Furthermore, the net radiation reaches a maximum during those months (Figure 5d), thus causing ablation and glacier thinning. The low pressure periods shown for the summit weather station are coincident with low atmospheric pressures reported for lower altitudes, and are attributed to the passage of cold fronts. Turbulent sensible heat flux is small and its variation is low because temperatures remain low during the dry early winter season; this is the same for glaciers like Zongo (see ^{Sicart et al., 2008}). However, if sublimation is strong this partly cancels out the energy gains in H and the sum of the turbulent fluxes remains small over the glacier. For Glaciar Norte this behavior is different because H is negative and can sum to the latent heat allowing sublimation of the glacial surface. Nevertheless, net radiation is stronger than turbulent fluxes and melting is more relevant than sublimation.

Between January-March the net radiation is more intense than during the rest of the year, because the weather is often cloud free over the highest Mexican summits. However, the components corresponding to the sensible heat and latent heat fluxes also present high negative values in January (Figure 4c, and ^d). Therefore, during this period the physical processes in connection to the sensible heat and latent heat lead to accumulation and mass gain on the glacier, whereas the radiative processes lead to ablation and mass loss on the glacier. On the other hand, it can be observed that the energy balance during the same period is strongly positive but begins to decrease during about May. So, from December to May, ablation is dominant.

During the ablation period, the glacier receives energy that will be used to increase its temperature up to the melting point and from this point on the energy will be used to melt ice. It is important to notice that the ablation period coincides with the dry season, with a decrease of temperature and atmospheric pressure. So, it would be interesting to measure surface temperature of glacier in order to get better estimation of heat fluxes and to better estimate internal glacial processes, such as superimposed ice formation.

In general, the recorded temperature is so close to the melting point that the ice near the surface does not need to increase its temperature much to reach that point. This causes the component of sensible heat to be low; however, during the ablation period, the sensible heat flux is more negative than during the rest of the year. That is because when the air temperature decreases, the glacial surface needs to release energy to be in thermal equilibrium with the surrounding air.

The dry season, observed between November-May, coincides with the NH winter season when occasionally a polar air mass descends toward Mexico from the north of the continent (^{Jauregui, 2004}). These polar-type systems can spread stronger than normal winds and may cause the temperatures to abruptly drop. This increase in wind speed is the cause of the increase (in the importance) of the latent heat flux in the energy balance, due to elevated turbulent heat flux. On the other hand, the decrease in relative humidity during these frigid patterns causes a decrease in cloud cover over the glacier's surface, which contributes to the increase in registered net radiation during the wintertime dry season.

There are occasionally rare storms during winter, however, and for these cases, the internal and surficial refreezing will occur more easily. The refreezing happens more often after storms of late fall and early winter and this refreeze is the origin of the superimposed ice is usually found on the glacier as ice layers or surface covering sheets. The effect of refreezing of the storms in the energy balance is reflected by the fact that during these seasons the energy balance reaches its minimum. So we can say that storms during all seasons play a role in recharging the glacier that in the future should be evaluated so we can quantify their importance better.

It should be noted that the first year of data collection coincided with an "El Niño" winter (2006) and the beginning of "La Niña" year in March 2007 (Centro Internacional para la investigación del fenómeno del Niño, Boletín CIIFEN April 2007, available from: http://www.ciifen-int.org/images/stories/pronostico_est/Boletn_CIIFEN_April_2007.pdf, last access: 7 August 2012). The impacts of "El Niño" during the winter can be described in general as heavy rainfall and anomalously low temperatures, especially in the northern part of Mexico due the entrance of baroclinic waves and cold fronts from the north due to amplifications of the winter circulation cycle in North America (^{Magaña et al., 1999}). The winter effect of "El Niño" during the year of study is associated immediately with the possibility glacier accumulation during the winter months that still coincides with the dry season. Moreover, during November-December the lowest values in our energy balance results indicate a large accumulation of mass on the glacier during this time.

During March 2007 study period, the ocean-atmosphere climate system went into the "La Niña" phase. So, for the following months the glacier observations recorded correspond to the "La Niña" spring and summer. During "La Niña" summers, the weather tends to rain across most of Mexico. Although most rainfalls are considered normal, there are greater chances that precipitation amounts could be anomalously intense during a La Niña year. There are several factors that can result in higher rainfall than normal over southeastern Mexico, but perhaps the most important is the activity of the easterly moisture stream embedded in the ITCZ and hurricanes produced in the Caribbean and Gulf of Mexico (^{Magaña et al., 1999}). During La Niña or Neutral ENSO years hurricanes are more likely to provide extra precipitation into eastern Mexico near the study site during August through November.

Visual observations

The penitents are composed of "praying" snow peaks related to superficial ablation, that mainly form during the dry season at high altitudes in the Himalayas, Andes, Rocky Mountains, sometimes southern slopes of the Cascade volcanoes and the Alps (^{Betterton, 2001}; ^{Corripio and Purves, 2006}). During the dry season, penitents are present on Glaciar Norte confirming that ablation occurs during this period as a result of evaporation and/or sublimation, and not just melt.