Future Changes in the Free Tropospheric Freezing Level and Rain–Snow Limit: The Case of Central Chile

The freezing level in the free troposphere often intercepts the terrain of the world’s major mountain ranges, creating a rain–snow limit. In this work, we use the free tropospheric height of the 0 ◦C isotherm (H0) as a proxy of both levels and study its distribution along the western slope of the subtropical Andes (30◦–38◦ S) in present climate and during the rest of the 21st century. This portion of the Andes corresponds to central Chile, a highly populated region where warm winter storms have produced devastating landslides and widespread flooding in the recent past. Our analysis is based on the frequency distribution of H0 derived from radiosonde and surface observations, atmospheric reanalysis and climate simulations. The future projections primarily employ a scenario of heavy greenhouse gasses emissions (RCP8.5), but we also examine the more benign RCP4.5 scenario. The current H0 distribution along the central Chile coast shows a gradual decrease southward, with mean heights close to 2600 m ASL (above sea level) at 30 ◦C S to 2000 m ASL at 38◦ S for days with precipitation, about 800 m lower than during dry days. The mean value under wet conditions toward the end of the century (under RCP8.5) is close to, or higher than, the upper quartile of the H0 distribution in the current climate. More worrisome, H0 values that currently occur only 5% of the time will be exceeded in about a quarter of the rainy days by the end of the century. Under RCP8.5, even moderate daily precipitation can increase river flow to levels that are considered hazardous for central Chile.


Introduction
Most of the precipitation falling on the ground can be traced back to ice crystal formation in the subfreezing environment of the middle and upper troposphere when enough moisture is provided by tropical or extratropical weather systems [1]. As the ice crystals grow, they descend and eventually cross the 0 • C isotherm at a height H 0 above sea level (ASL) and begin to melt. The melting layer depth is highly variable, depending on the air temperature profile and the hydrometeors population (size, type, density), but it generally ranges between 100 and 300 m [2,3]. Over the terrain, the delimitation of sectors receiving rain or snow during a storm is also related to the position of the near surface 0 • C isotherm, although rain can occur with temperatures as cold as −1.5 • C and snow can occur with temperatures as high as +1.5 • C (e.g., [4,5]). The height of the 0 • C level over the terrain is closely tied to the nearby free tropospheric 0 • C isotherm height (H 0 ) during precipitation events, but the surface level tends to be several hundred meters below its free tropospheric counterpart [6,7]. This offset is driven by the forced ascent of moisture-laden air parcels over the mountainous terrain that caused

Study Region
The Andes cordillera runs close to the western side of South America from north of the equator (10 • N) down to Tierra del Fuego (53 • S). Along its subtropical portion (30 • -38 • S), its crest level reaches more than 5000 m ASL, well above the mean freezing level during winter storms (∼2400 m ASL; see Figure 1a). Central Chile, the narrow strip of land to the west of the subtropical Andes, is home to more than 12 million inhabitants with a large concentration (>7 million) in the metropolitan area of Santiago that sits right at the Andean foothills. Annual mean precipitation in this region varies between 200-2000 mm (Figure 2), depending on latitude and height [23].
Precipitation is largely concentrated in the austral winter (May-September) and is mostly caused by cold fronts [24]. The Andes cordillera enhances precipitation by a factor of 2-3 between the upstream lowlands and the upper part of the mountains [23]. Between 10 to 20 precipitation events occur every winter lasting 1-3 days, with storm accumulations that are highly correlated with the amount of water vapor impinging against the Andes [24]. Indeed, extreme events (>50 mm per day) occur when intense atmospheric rivers ahead of cold fronts make landfall in this region [25,26]. Major storms generally result in marked, sudden increases in the flow of the rivers descending from the Andes [27], leading to flooding in central Chile. These events are a significant threat in central Chile, damaging infrastructure and causing loss of lives with a recurrence of 5-10 years [28]. Although the magnitude of the flooding is primarily controlled by the amount of the precipitation falling over the region, the elevation of the freezing level during the storms modulates the hydrological response [9]. During winter storms, H 0 ∼2200 m ASL over the upper Maipo river basin (area: 5500 km 2 ) east of Santiago, but some precipitation events feature an H 0 in excess of 3500 m ASL, tripling the pluvial area relative to mean conditions, and thus increasing the risk of hydrometeorological hazards [9]. This was the case in 3 May 1993 when a moderate precipitation event occurred under warm conditions (H 0 ∼4000 m ASL), resulting in multiple landslides and downstream flooding on the city of Santiago that caused more than 80 fatalities and major damage in public and private infrastructure [14,29,30].

Observations
Quality-controlled daily rainfall and average temperature is available from 1999 to 2017 for eight surface stations across central Chile (30 • -38 • S, Figure 2) operated by the National Weather Service (DMC). In each station, we define a wet day as one with more than 5 mm accumulation and dry days as those with no precipitation. In this work, we only consider the winter semester (May to September) for central Chile and the rest of the Southern Hemisphere (SH). Santo Domingo, a coastal site at 33.65 • S, 71.61 • W (75 m ASL), is the only radiosonde station operated by DMC in this region (black start in Figure 2), with launches twice daily at 12:00 and 00:00 UTC. In all cases, there is only one level in which the air temperature profile crosses the 0 • C, even if there is an inversion in dry days because they are warm and low [10], so the free tropospheric H 0 was obtained unambiguously from direct interpolation using the temperature and geopotential height of the levels just above and below 0 • C. On a given day, a mean value of H 0 was calculated using the 00:00 UTC (8:00 PM of the previous day), 12:00 UTC (8:00 AM of the current day) and 00:00 UTC (8:00 PM of the current day) values, and then pooled into the wet or dry groups according to the concurrent rainfall data at Santo Domingo. In stations with surface data only (surface air temperature, SAT), we estimated the freezing level during rainy days using a moist adiabatic lapse rate (Γ moist ≈ 6.5 • C/km) as H 0s f c = SAT/Γ moist + H G , which proved to be a good approximation in this region [10,31]. In Section 4.3, the ETOPO2v2 elevation data [32] was used to determine hypsometric curves (basin area below a given height) of Andean selected basins in central Chile. Catchment boundaries are obtained from the CAMELS-CL dataset [33], where basin outlets are defined according to the location of available streamflow gauges and following topographic-driven limits.

Reanalysis
To supplement the reduced number of stations from where we can derive H 0 in central Chile and obtain a global perspective, we also employed the Climate Forecast System Reanalysis (CFSR, version 1) described in detail by Saha et al. [34]. Atmospheric variables from this state-of-the-art reanalysis system are available from 1979 to 2010 for every 6 hr on a global 0.5 • × 0.5 • lat-lon grid. As with the Santo Domingo sounding, the vertical profiles of air temperature and geopotential height were used to obtain H 0 in each grid point and time step. We then calculate the daily mean H 0 from the five values centered at 12:00 UTC (00:00, 06:00, 12:00, 18:00, 00:00 UTC) for every day. A comparison between observed H 0 at Santo Domingo and those obtained from CFSR is shown on Figure 3. There is a notable correspondence between daily averages of H 0 for both wet and dry days, with correlation coefficients exceeding 0.9. However, the relative error in the percentiles of the distribution does not exceed 3% in both cases. In Section 4.1, we provide further evidence that H 0 derived from CFSR is a good approximation of the actual H 0 distribution all along central Chile.

Models
To project the freezing level in the future, we use results from five models included in the Coupled Model Intercomparison Project Phase 5 (CMIP5, [35]) listed in Table 1. The variables used were daily averages of geopotential height, temperature (both at standard isobaric levels) and total precipitation at the surface. This allows us to obtain the daily freezing level grouped into wet and dry days at any given location for their respective winter season (May-September in the Southern Hemisphere and October-April in the Northern Hemisphere). Although the CMIP5 database includes results from more than 50 GCM, differing in their subgrid schemes (parameterizations) and spatial resolution, our analysis is restricted to those models with available surface and upper-air daily data and a grid spacing of ∼2 • × 2 • (or finer) to obtain at least three grid points in latitude and a minimum representation of the Andes cordillera. The five selected models (from independent research centers) in the group conform to a good representation of the central Chile climate [36] and have resolution ranging from 0.75 • to 1.86 • . Even so, the position of the coastline and Andes ridge of each model can differ substantially from their actual locations, so particular caution was taken in considering the topographic features of each model.  [35] used to characterize the future condition of the H 0 distribution. The variables T and Z correspond to temperature and geopotential height at isobaric levels. The variables pr and sftlf represent precipitation rate and fraction of land area, respectively.

Model
Institution Variables Spatial Resolution (lat × lon) The present climate distribution of H 0 considers the period between 1976 and 2005 from the historical runs. Based on the previous works [37], the CMCC-CM model has the least errors representing H 0 in central Chile in the present climate, being used as our reference model. For the rest of the 21st century, we use primarily the simulations under the RCP8.5 scenario [38], representing a negative prospect in terms of greenhouse gases emission and atmospheric concentrations [39] in which CO 2 -equivalent reaches about 1000 ppm by the end of the century. In this sense, our work illustrates that changes that could occur in a worst-case scenario. Some key analysis, however, were repeated with climate simulations under the more benign RCP4.5 scenario (CO 2 -equivalent ∼500 ppm by the end of the century) to illustrate the sensitivity of the predicted changes in H 0 to the greenhouse gases concentrations.

The Freezing Level in Present Climate
Given the nearly two-dimensional nature of the Andes cordillera, extending almost straight north-south along its subtropical portion, and its proximity to the Pacific shoreline (Figure 2), most of the subsequent analyses are performed using the along-coast (latitudinal) profile of H 0 . We acknowledge that the coastal, free tropospheric value of H 0 during a particular storm can differ from the actual snow line over the western slope of the Andes [7,10] but any coast-to-Andes difference is likely to exist both in present and future climates, so it will not preclude exploring the climate change impact upon the freezing level. Figure 4 shows the latitudinal variation of the mean freezing level (H 0 ) along the coast of central Chile using the CFSR values for wet and dry days during the winter semester (May-September). In the case of the wet days, we also included the surface-based H 0 and the Santo Domingo H 0 distribution. There is a good agreement between the mean values derived from CSFR and the observations along the full transect, except for a ∼100 m offset in the mean value that was subsequently removed from the whole latitudinal profile. The mean freezing level during wet days (H 0wet ) gradually decreases southward, from about 2600 m ASL at 30 • S to 2000 m ASL at 38 • S. Except in the southernmost part of our study region, the mean freezing level is below the Andean crest, and at the latitude of Santiago and Santo Domingo (33 • S), H 0wet ∼2400 m ASL, about half of the altitude of the mountain peaks that reach ∼6000 m ASL. The interquartile range of H 0 during wet days is close to 800 m all along central Chile, and extreme high values (95% percentile) can reach up to 3500 m ASL, showing a high variability of the freezing level among winter storms, consistent with previous findings in Garreaud [9]. The mean freezing level for dry days during winter months (about 90% of the total) also decreases from north to south along the Chilean coast, and it is 800-1000 m higher than H 0wet . The standard deviation of H 0 under dry conditions is about 700 m, so the freezing level distribution during rainy and dry days have little overlap (see Figure 3). Since both samples are obtained from the winter semester, the lower H 0 values during wet days reflect an actual drop of the air temperature in the lower and middle troposphere in connection with the postfrontal nature of precipitation in central Chile. There, the bulk of the precipitation falls in the first 12-24 h after the front passage cold front in the majority of the winter storms [9,24,37]. The H 0 depression during wet days-relative to dry conditions-also occurs near the west coast of other continents as evidenced in the reanalysis maps ( Figure 1b) and documented over the Sierra Nevada in the United States of America [11] and the Iberian Peninsula [40]. Notably, H 0 tends to rise during winter storms over the east side of the continents (most markedly in North America and East Asia) and the midlatitude oceans.

Future Changes
Let us begin our description of the future change in the freezing level by considering the frequency distribution of H 0 during winter wet days over Santo Domingo (33 • S) from the CMCC-CM model (Figure 5a). For present climate, the simulated H 0 distribution fits well with the observations in terms of the central value and spread. By the end of the century (2071-2100), under the RCP8.5 scenario, the shape of the distribution is preserved, but there is a substantial shift toward higher values (∼600 m in the mean), consistent with the expected tropospheric warming. The shift in the H 0 distribution under the RCP4.5 scenario is similar to that in RCP8.5, but the increase in the mean value is about ∼400 m. Figure 5b synthesizes the north-south distribution of H 0 (mean value and interquartile range) during wet days for different decades in the 21st century, showing a progressive rise as time progresses. Note that toward the end of the century, H 0wet is close to, or higher than, the upper quartile of the H 0 distribution in the current period, and the increase in H 0 seems to be slightly greater in the north. Near the southern limit of our domain (37 • -38 • S), H 0wet in the current climate nearly coincides with the Andean ridge level, so the upper part of the mountains receive snow in about half of the winter storms, allowing the formation of a seasonal snowpack. By the end of the century, however, the mean freezing level during wet days is expected to be several hundred meters above the top of the southern Andes, so snowfall might be quite uncommon even over the highest terrain with a detrimental impact on water availability during the summer months [41]. The projected rise of H 0 toward the end of the century under the RCP4.5 scenario is about 70% of its RCP8.5 counterpart across the whole region.
To place changes throughout central Chile in a global context, Figure 6 shows the change in the mean freezing level (∆H 0 ) for wet days between the end of century (2071-2010, under RCP8.5) and the historical period (1976-2005) using the CMCC-CM model. There is an increase in H 0 worldwide, most marked over the subtropical and tropical oceans (∆H 0 close to 1000 m) but rather small at higher latitudes in both hemispheres. The pattern and magnitude of ∆H 0 is similar during dry days, but the projected rise tends to be ∼100-200 m higher across much of the subtropics and midlatitudes (not shown). In central Chile, for instance, ∆H 0 is close to 600 m ASL and 750 m ASL for wet and dry days, respectively.
Next, we examine the changes in freezing level in central Chile using results from the 5 GCM with high spatial resolution and daily data (Section 3.3). Except for CMCC-CM, the simulated H 0 distribution in current climate exhibits biases as large as ±10% [37]; therefore, we use the so-called delta approach here to analyze future changes [42,43]. For each model, we calculate the future (end-of-the-century under RCP8.5) minus present difference in H 0 (mean value and selected percentiles), and then we average the five results. The multimodel mean ∆H 0 is then added to the observed (CFSR) profile of H 0 in the current climate as shown in Figure 7a for the wet and dry winter day groups, along with an indication of the model spread. For the wet days, ∆H 0 is about 400 m (250-600 m range among the models), while for days without precipitation the mean change is close to 600 m (400-800 m range). The values of ∆H 0 have little variation along the profile. Similar increases were found when considering the median and the lower and upper quartiles, suggesting an overall shift of the H 0 frequency distribution while preserving its shape, as we showed for the specific case of CMCC-CM (Figure 5a). The latitudinal profiles of ∆H 0 for wet and dry days under the RCP4.5 scenario are also included in Figure 7a. When considering the multimodel mean, the rise in mean freezing level is about half of that obtained under RCP8.5, suggesting a linear behavior of the projected changes of the free tropospheric temperature in central Chile, in line with results from Zazulie et al. [44] for surface temperatures over the subtropical Andes.  As noted in the introduction, winter storms with higher than average H 0 greatly increase the risk of flooding and landslides along central Chile, so particular attention must be placed in the change of extreme events. To gauge those changes, here we consider the variation in the 95% percentile value under wet conditions (H 095wet ). At the latitude of Santiago, H 095wet ∼3300 m ASL in the present climate, nearly 1 km above the mean value. For each model, we obtained H 095wet in the present-climate simulation, as a function of latitude, and then we calculated the frequency of the time in which this value will be surpassed in the last decades of the 21st century. The multimodel mean change in frequency is shown in Figure 7b. The mean frequency in which future freezing levels (during wet days) will equal or exceed the present climate H 095wet is about 20% between 38 • -34 • S and up to 30% in the northern part of the domain. Thus, what is now labeled as an extreme event will be a condition 4-6 times more frequent by the end of the century (under RCP8.5 scenario), a worrisome projection whose hydrological consequences will be discussed in the next section. Even in the case of the more benign RCP4.5 climate scenario, the frequency of extreme events (5% of the time in the current climate) could double (Figure 7b).

Hydrological Impact
Here, we provide a rough estimate of the hydrological impact of the H 0 changes during wet days over central Chile contingent of the occurrence of the RCP8.5 heavy emission scenario. Such impact varies with latitude since both H 0wet and the terrain elevation decrease toward the south. Indeed, one may expect less acute impacts in the southern part of the domain because even in the current climate, the Andean basin mostly receives rainfall (H 0wet ∼ H G ). Figure 8a shows the area of the terrain above 1000 m ASL and below the present climate mean freezing level (during wet days) for selected Andean basins of central Chile (A p ). The baseline was chosen close to the base of the Andes foothills. We then recalculated the A p , keeping the baseline but changing the upper limit to H 0wet in the future (2071-2100; RCP8.5) and H 095wet in the present and future climates. For selected basins, Figure 8b shows the areal increment factors, defined as the ratio of A p obtained with the new upper limits to the area defined with the present H 0wet . Considering the rise of the mean freezing level during winter storms, the most affected basins would those between 33 • S and 35 • S. Particularly, the pluvial area in the upper Maipo River (that drains into the central valley just south of Santiago) almost doubles because of the projected rise in H 0wet from present to future. Further south A p would be almost unaffected since most of the increase in H 0 occurs over the maximum height of the terrain. However, the basins north of 33 • S would be less affected since their average slope is gentler. In present climate, the pluvial area also increases markedly when considering the 95% percentile H 0 relative to the mean value. Continuing our focus on the Maipo basin, we found that the pluvial area increases by a factor of 3 when considering the 95% percentile of H 0 in the present and by a factor of 4.5 when considering the 95% percentile events in the future. The increment factor in other basins is lower, but future warm storms might have a pluvial area 2-3 times larger than average storms in the present climate. The large increase in the projected pluvial area for the Maipo basin, along with its closeness to the large city of Santiago, calls for further analysis. In Figure 9, we present contours of H 0 for mean and extreme cases under wet conditions, superimposed on a topographic map. Note, for instance, that nearly the entire basin would receive rainfall in the 5% of warmer winter storms of the future, a conditions that in the present climate has a probability of approximately less than 0.5%. Of course, the river flow on a given storm is also dependent on the amount of precipitation and soil moisture (which dictate the infiltration rate), but an upper bound of the river flow can be easily obtained as Q max = PB × A p , where PB is the basin averaged rainfall and A p depends directly from H 0 [24]. The right panel of Figure 9 shows Q max as a function of the precipitation for selected values of H 0 . We have marked the value Q max = 500 m 3 /s, which is considered dangerous to this area based on the work of Bustos [45], and also include the frequency distribution of the daily precipitation for this basin. For the mean freezing level in the present, at least 50 mm/day is required for the Maipo River to reach a dangerous level, a daily accumulation that happens in about 5% of the time (Figure 9b). In the future, however, flooding might be caused by a 25 mm/day storm, considering the mean freezing level, and by just 10 mm/day if the storm happens under warm conditions (95th percentile of H 0 ). This last value is even lower than the average daily accumulation, so such a hazardous combination of precipitation and freezing level leading to flooding may occur rather frequently despite the annual mean precipitation decrease over central Chile predicted for the rest of the 21st century by numerical models [46]. Indeed, projections based on the CMCC-CM model show that daily precipitation rate would change to lower values ( Figure 10) and the number of wet days (≥5 mm/day) nearly halves from the current condition to the end of the century. Nonetheless, the number of days in which the combination of H 0 and precipitation results in a upper Maipo river flow ≥500 m 3 /s decreases marginally (from 107 to 92 days per 30 years), thus doubling the frequency in which hazardous condition occurs if precipitation is taking place. The increase in such conditional frequency is even more striking considering higher river flow values. For Q max ≥ 2000 m 3 /s, not only does the conditional frequency triple but the total number of days increases toward the end of the century under the RCP8.5 scenario, considering the CMCC-CM model results and the simple hydrological model described before.  The projected increase in H 0 during wet days also implies a reduced amount of water stored in the Andean snowpack that forms every winter and releases fresh water during spring/summer when this resource is most needed for agriculture and other uses in central Chile [41]. As before, we provide a rough estimate of these changes here by considering the partition between liquid and solid precipitation during winter in the Maipo river basin. For each storm, the liquid and solid volumes were calculated by multiplying the basin mean daily precipitation for the pluvial and snow areas, defined by the part of the basin below or above the freezing level, respectively. We then added all those volumes during the present  and future (2070-2100, under RCP8.5) periods. Solid precipitation (forming the snow pack) accounts for about 75% of the total in current climate but such contribution decrease to 57% in the far future. The total precipitation over the Maipo River basin also decreases by about 35% (relative to present day), considering the CMCC-CM model results [37]; that figure that is in line with multimodel estimates [46]. The combined effects of warmer storms and less precipitation thus result in future (end of the century, RCP8.5) winter snow accumulation halving present climate values, ensuing a dramatic decrease in summer-fall river flow, an effect documented in other basins in central Chile by Vicuña et al. [47].

Conclusions
The distribution of H 0 along central Chile (30 • -38 • S) was obtained from the CFSR reanalysis for the present climate and five climate models for the rest of the 21st century under the RCP8.5 and RCP4.5 scenarios. In this highly populated region, variations of the freezing level within precipitation events and between storms can produce substantial differences in the pluvial area, affecting runoff generation and the discharge of rivers draining the Andes cordillera.
Relative to present day conditions, the mean H 0 in the future (RCP8.5) would be approximately 400 m higher for days with precipitation and 600 m for days without precipitation. In general, we found a progressive increase of the H 0 distribution while preserving its shape. Toward the end of the century, the mean value under wet conditions is close to or higher than the upper quartile of the H 0 distribution in the current climate, and the increase in H 0 seems to be slightly greater in the north. By the end of the century, however, the mean freezing level during wet days could be several hundred meters above the top of the southern Andes, so snowfall will likely become quite uncommon even over the highest terrain with detrimental impact for the water availability during the summer months. The more benign RCP4.5 scenario also results in a shift of the H 0 distribution toward higher values but with an amplitude about half of its RCP8.5 counterpart.
Regarding the occurrence of particularly warm storms, H 0 values that currently occur in only 5% of the days with precipitation (H 0 > 3300 m ASL) might be concurrent with nearly 25% (10%) of the future winter storms throughout central Chile under RCP8.5 (RCP4.5). The projected changes in H 0 translate into an increase in the pluvial area and, therefore, in the volume of water available for all the basins of central Chile during storms, except in the southernmost basins where the current freezing level is generally above the Andes ridge, at the expense of the water stored in the seasonal snowpack. The basins most affected would be those around 34 • S. The upper Maipo River, draining just to the south of the city of Santiago, might experience an increase in its pluvial area by a factor 4 to 5 times the pluvial area during future warm storms relative to mean current conditions. Keep in mind that our inferences are rough estimates of the hydrological response to changing freezing level and contingent to the negative RCP8.5 climate scenario. In this condition, even moderate daily precipitation could increase the river flow to levels that are considered hazardous for central Chile. Thus, even under the prospect of drying along central Chile, warmer winter storms in the future possess a substantial risk of landslides, flashfloods and widespread flooding along the foothills of the subtropical Andes, calling for more comprehensive studies in this subject.