1 Introduction

The spatial distribution of near-surface air temperature (hereafter simply referred to as T ns) over mountains is an important input to hydrological (Shamir and Georgakakos 2014), glaciological (Anslow et al. 2008), and ecological (Kusch 2015) studies. While free-atmosphere temperature often decreases with altitude, temperature near the surface is strongly modified by diabatic heating (e.g., absorption of solar radiation at the surface) and airflow (e.g., katabatic winds and topographic waves) which, in turn, vary strongly over complex terrain and are modulated by synoptic disturbances (e.g., Whiteman 2000). In consequence, surface temperature depends on altitude as well as other physiographical features (e.g., terrain slope and exposition) and land cover, making difficult the estimation of its spatial distribution and time evolution.

In situ measurements over mountains can be ingested into some geo-statistical models (Philippopoulos et al. 2015; Chuanyan et al. 2005; Gouvas et al. 2011) to generate the full two-dimensional distribution of temperature. However, station density is typically low over mountainous terrain given its own nature: rugged, remote, and often inaccessible. In some regions, meteorological observations are only available at stations outside the mountains, so often one attempts to estimate surface temperature distribution over the mountains using a prescribed vertical lapse rate (He et al. 2015; Hamlet and Lettenmaier 2005; Bolstad et al. 1998). In the special case of overcast, humid conditions (e.g., rainy periods), the moist adiabatic lapse rate is close to the surface temperature gradient (e.g., Ayala et al. 2015; Blandford et al. 2008); otherwise, the selection of a temperature gradient is not trivial. Table 1 includes vertical temperature gradients obtained over selected mountain ranges, with values varying from −4 to −10 °C/km. In any case, the assumption of temperature determined solely by altitude may lead to substantial errors.

Table 1 Vertical temperature gradients reported by the previous studies
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More recent studies have relied on satellite data (Kloog et al. 2016; Lin et al. 2016; Oyler et al. 2016) or outputs from numerical meteorological models (Case et al. 2016; Liu et al. 2016) to obtain the two-dimensional T ns field. In both cases, one obtains an estimate of the temperature derived from a calibration that does not necessarily represent local conditions. Radiance measurements from space-borne sensors also face the problem of missing scenes by obstructing clouds (Zhang et al. 2016) and low resolution (temporal for polar-orbiting satellites and spatial for geostationary satellites). Numerical models involve major computational efforts if one desires to achieve a high degree of spatial resolution over a long integration period.

In this contribution, we take advantage of MODIS-derived land-surface temperature and a relatively high-density meteorological network deployed over the Nahuelbuta Mountains (NM) in coastal southern Chile (centered at 38°S, 71°W; Fig. 1) to describe the spatial distribution of the near-surface temperature under different weather patterns and with an emphasis on winter, nighttime conditions. Our objectives are threefold. First, we describe two distinct nighttime temperature regimes at over NM, one of which features marked T ns differences at ridge- and sub-ridge scales and that, as commented before, are important for understanding its distinct hydrology and ecology with high degree of endemic biodiversity (Smith-Ramírez 2004; Oyarzún 1995). The second objective is to explain the heterogeneous distribution of temperature on the basis of the airflow over the mountain which we diagnose using high-resolution WRF simulations of a few cases. On a broader context, the processes shaping the T ns distribution over NM may operate in coastal mountain ranges located elsewhere in midlatitudes. As described later, NM is an archetypical coastal mountain in midlatitudes with a substantial precipitation enhancement in its upwind side and a rain shadow in its lee side (Garreaud et al. 2016). Our third objective is to make a comparison of in situ data against satellite products and numerical model outputs adding to the body of the literature on the strengths and limitations of different approaches to estimate the near-surface air temperature over complex terrain.

Fig. 1
figure 1

Location maps. Right panel shows WRF domains 1, 2, and 3. Left panel (domain 3) shows the terrain elevation of Nahuelbuta mountains (colors: height in meters) and location of AFEX stations (see details in Table 2). The line between A and B is the cross section employed in Figs. 11 and 12 and the segmented line is the border between Northwest zone (NW) and Southeast zone (SE)

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This paper is organized as follows. In Sect. 2, we provide a geographical and climatic context of the study region, as well as a description of the meteorological network, MODIS data, and WRF numerical model. Results based on in situ measurements and satellite estimates are presented in Sect. 3, where we identify cases of strong and weak nighttime temperature contrast among stations located at nearly the same altitude, as well as the southeastern and northwestern sides of the mountain. In Sect. 4, WRF is used to simulate a handful of cases with strong temperature contrasts and the model outputs are employed to understand the processes responsible for the distinct nighttime distribution of T ns under clear skies. Section 5 summarizes our main results.

2 Study region and data

2.1 Geographical context and climate background

The NM is an isolated massif located between 37° and 38°S along the coast of central Chile (west coast of South America), separated from the Andes cordillera by a central valley approximately 100-km wide (Fig. 1). The massif has a semielliptical shape about 150-km long and 100-km wide and several minor rivers draining the mountains forming narrow canyons. The mountain reaches 1300-m ASL and presents an extensive area between 1000 and 1200 m, constituting the highest elevation of the coastal mountain range to the south of 33°S. Given its accessibility, it provides an excellent location for the study of meteorological processes over isolated mountains.

The presence of the Pacific Ocean regulates the temperature of the region, producing small annual and diurnal cycles. At Concepción, a nearby coastal station (Carriel Sur airport, 36.5°S), the daily mean temperature varies from about 10 °C in winter to 15 °C in summer. At the same coastal station, the long-term (1950–2017) mean maximum and minimum temperatures are 18 and 8 °C, respectively. Atop of the mountain (Parque Nahuelbuta station, 1177-m ASL), the long-term (2002–2016) annual mean of maximum and minimum temperatures is 3 and 15 °C, respectively.

Mean annual precipitation (MAP) at the coast and the surrounding lowlands is around 1000 mm, mostly concentrated in austral winter (May–September, Viale and Garreaud 2015). The rainfall is delivered predominantly by frontal systems accompanied by northwesterly flow. The frontal precipitation is enhanced over the northwestern (windward) slope of Nahuelbuta, so that MAP reaches 2000 mm at the foothills and nearly 4000 mm atop of the mountains (Garreaud et al. 2016). Farther downstream (i.e., over the southeastern side of the mountain) MAP rapidly decreases to the background level. Given its cool, humid climate, NM is mostly covered by exotic plantations (Pinus Radiata and Eucalyptus) in its lower part and native forest over 1000 m (Debels 1999), which makes it an important forest reserve and biodiversity conservation site.

2.2 Surface observations

To better describe the rainfall distribution over NM, a network of rain gauges was installed from May to September 2011 (Fig. 1). The so-called Andes Frontal Experiment (AFEX) network was composed of 13 HOBO RG3 tipping-bucket rain gauges that also included an air thermometer built-in the HOBO Pendant event data logger. The logger/thermometers were shielded from solar radiation (with an HOBO RS1 shield) and installed at 1 m above ground (±0.1 m), recording data every 30 min (average of the past 30 min). The air thermometer has a measurement range of −20–70 °C, accuracy of ±0.47 at 25 °C, and resolution of 0.10 °C at 25 °C. A pre-deployment inter-comparison among the sensors revealed systematic differences of ≤0.4 °C, so that no bias correction was applied. The AFEX stations were installed in small clearings within the forests (at least 10 m away from major trees), preferentially along a northwest–southeast transect coinciding with the prevailing wind direction during rainstorm events, thus covering an altitude range between 137- and 1382-m ASL (Table 2).

Table 2 Weather station of AFEX network
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2.3 Satellite data

Land-surface temperature (LST) was obtained for our study period (May–September 2011) from the MOD11_L2 product (available online at http://reverb.echo.nasa.gov/). The MODIS-LST is available twice daily at about 02:00–04:00 (pre-dawn) and 11:00–13:00 (midday) local time (LT) on pixels of ~1 × 1 km2 over the study region. Validation of this product can be found in the works of Wan (2008), Wan et al. (2004), Coll et al. (2005) and Wang et al. (2008). According to these studies, the accuracy of MODIS-LST is better than 1 °C in homogeneous surfaces. On the other hand, NM is a complex terrain with variation in land cover (albeit mostly covered by forest), so we performed our own validation of MOD11_L2 against AFEX data (see Sect. 3.2).

2.4 Numerical simulations

The full three-dimensional atmospheric conditions over NM were simulated with the Weather Research and Forecasting Model (WRF model), version 3.5 (Skamarock et al. 2005). We ran WRF for 6 days of interest (June 25 and 26, July 3 and 7, and August 19 and 20, 2011). The simulations were carried out from 20 LT the day before the target dawn to 20 LT the day after. Table 3 presents the parameterizations employed in these simulations. In each case, we used a mother domain and two nested domains. A very similar model configuration was employed by Garreaud et al. (2016) in a winter-long simulation, whose precipitation fields compared favorably with the AFEX data. Furthermore, we show at the beginning of Sect. 4 that the model configuration did produce surface temperature fields in good agreement with their observational counterparts in the six analyzed cases. The inner-most domain was centered on the NM (Fig. 1) and it has a 3-km grid-spacing (75 × 75 grid points). With this horizontal resolution, some fine-scale topographic details are missed (e.g., small canyons), but the shape of the mountain, its dimensions (long-wide), main valleys, and maximum heights (about 1200-m ASL) are well captured. These are key aspects that control the pattern of mountain wave activity that we discuss in Sect. 4. In the vertical, the model has 30 sigma levels with the lower levels located at 26, 65, and 180 m above the ground. The initial and boundary conditions were obtained from the NCEP-FNL reanalysis (available online at http://rda.ucar.edu/). These reanalysis data were also employed at the synoptic characterization of the events.

Table 3 Parameterization schemes selected for WRF model runs
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3 Observational results

3.1 Local variations

We begin our analysis by showing the time series of T ns during a 2-week winter period at four stations located around 750-m ASL (Fig. 2), because these stations show distinctive features in their diurnal cycles relative to the other AFEX stations. Rainfall occurred over NM for most of the second week and T ns was very similar (typically within 1 °C) in the four stations. The modest T ns diurnal cycle is consistent with the cloudy conditions limiting the daytime heating and nighttime cooling (Dai et al. 1999). No precipitation fell during the first week and there was a marked diurnal cycle in two stations (ETA and EBA) but a much more modest cycle in the other two (TNO and CAN). The afternoon T ns values differ by less than 1.5 °C among the four stations, but after sunset ETA and EBA began to cool rapidly (~3 °C/h), while TNO and CAN cool slowly (~0.25 °C/h). By dawn, Tns at ETA/EBA can be more than 10 °C cooler than TNO/CAN. During this dry period, freezing conditions did occur every night at EBA but never at TNO.

Fig. 2
figure 2

Half-hourly time series of air temperature (°C) for a couple of weeks during winter 2011 at Torre Arauco (TNO), Escuela Trongol Alto (ETA), Torre Caramávida Norte (CAN), and El Bajo (EBA) and rainfall at EBA station (bars)

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To assess the recurrence of the contrasting periods exemplified before, Fig. 3 shows the histogram of the T ns difference between ETA and TNO at 6 a.m. (δT ns) for the winter of 2011. A multi-modal δT ns distribution is evident with a local minimum at 5 °C allowing for a regime selection. Of the 94 nights of the sample, 29 (30%) have a large thermal contrast (δT ns > 10 °C), sometimes as large as 18 °C. On the other extreme, 30% of the nights have a small thermal contrast with δT ns < 5 °C and rainfall over NM present in each of these cases.

Fig. 3
figure 3

Frequency distribution (expressed as number of days) of the air temperature (Tns) differences at 6 a.m. between stations ETA and TNO for the winter of 2011

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To further describe the local conditions using AFEX data, we averaged the temperature variations relative to 14 LT of the day before the dawn with large or small temperature differences (as defined above). Figure 4 shows the composite diurnal cycles for each station. As expected by the accompanying rainy conditions, the cases with thermal contrast less than 5 °C feature a weak and uniform evening/nighttime cooling (~−0.7 °C/h), although station EBA cools significantly more than the rest during early night. In the dry cases with large thermal contrast, most stations show a more or less similar cooling (~−1.5 °C/h) from afternoon to dusk (18 LT). In TNO and CAN, the cooling is about 1.3 °C/h until sunset when T ns becomes nearly steady for the rest of the night. ETA and EBA cool very markedly between 15 LT and sunset (−3.3 °C/h) and between sunset and midnight (−0.8 °C/h). After that, the cooling continues (albeit less intense) producing a well-defined T ns minimum at sunrise. Other stations feature a behavior intermediate between TNO/CAN and ETA/EBA.

Fig. 4
figure 4

Mean diurnal cycle of the near-surface air temperature in the AFEX stations for the group of days with a large and b small thermal contrast (defined as the dawn Tns difference between stations ETA and TNO, see Sect. 3.1 for details). For better visualization, the diurnal cycle at each station is shown relative to the temperature at 14:00 local time (LT)

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3.2 Insights from MODIS-LST

Of the 29 days with large temperature contrast at dawn (δT ns > 10 °C), only nine have unobstructed MODIS land-surface temperature fields and three of them had to be discarded due to image distortion. Using the remaining cases (see Table 4), we constructed a scatter plot between in situ T ns from the AFEX stations (average of ±15 min about MODIS transit time) and the collocated MODIS-LST (temperature interpolated to the station location). Considering the full pool of pre-dawn data, the correlation between MODIS-LST and AFEX T ns is 0.74 (Fig. 5), although the correlation varies between 0.49 and 0.73 for individual days. This indicates that MODIS-LST detects T ns variations in time quite well, but its performance decays when considering variations on space alone. MODIS-LST is, on average, 1.1 °C warmer than T ns and the root-mean-square error is 3 °C. Such values are consistent with ranges reported elsewhere (Good 2016; Yao and Zhang 2013; Lin et al. 2012; Shen and Leptoukh 2011).

Table 4 Temperature difference T TNO − T ETA and T CAN − T EBA (°C) obtained from AFEX network, land-surface temperature from MODIS, and surface temperature from WRF model considering a radius around the location of station (mean of all grid points within)
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Fig. 5
figure 5

Scatter plot of the AFEX near-surface air temperature (Tns at 1 m above ground) and land-surface temperature of MODIS (LST) interpolated to each station. Different symbols represent a specific date/time identified in the inset

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We also found that MODIS-LST did not detect the large thermal contrast between ETA/EBA and TNO/CAN. As summarized in Table 4, the LST difference is about a third of the actual values, suggesting a significant role of micro-scale (sub-pixel, ~1 km2) processes in producing the AFEX observed contrast.

A cursory examination of pre-dawn MODIS-LST during each of the 6 days selected in 2011 (e.g., Fig. 6) reveals a very recurrent pattern that is summarized by the average field, as shown in Fig. 6b (contours of terrain elevation at 500- and 1000-m ASL help to identify the NM). This pattern is also observed in other clean images during the winters of 2012 and 2013. A salient feature is a thermal inversion between 300- and 700-m ASL over the northwestern slope of the massif. In the lowlands to the north of NM, the surface temperature is around freezing, with the exception of a warmer coastal sector. Closer to the foothills, LST begins to increase to reach a maximum over 5 °C around 600-m ASL. Further up, LST decreases down to near 0 °C over the southern part of the massif’s plateau (above 1200-m ASL). Moving downhill, there is a weak increase in temperature with values just over freezing level in the lowlands to the southeast of NM. The pre-dawn pattern differs from that observed during daytime (Fig. 6a) when the LST field varies with height, but has less horizontal structure (the afternoon LST field shows a drop in temperature with altitude over the mountain, without a significant difference between the northwestern and the southeastern parts of the range).

Fig. 6
figure 6

Average MODIS land-surface temperature (LST) for six cases analyzed (see Table 4). a Average LST during daytime (June 24, 14:25 LT; June 25, 15:10 LT; July 2, 15:15 LT; July 6, 14:50 LT, August 18, 14:35 LT; and August 19, 11:00 LT). b Average LST at pre-dawn (June 25, 01:30 LT; June 26, 02:15 LT; July 3, 02:20 LT; July 7, 01:55 LT, August 19, 01:35 LT; and August 20, 02:30 LT). The contours show the 0-, 500-, and 1000-m ASL terrain elevation

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3.3 Temperature profiles

To further examine the vertical variation of temperature, we constructed the (MODIS) LST profile with height—complemented with AFEX T ns—on an NW–SE transect across Nahuelbuta (Fig. 1) for August 19 and 20, 2011 (similar profiles are seen in other dry dates). During midday (Fig. 7a), the temperature gradient in the northwestern slopes is similar to that over the southeastern slopes, both close to the dry adiabat. Notably, the temperature gradient below 700-m ASL at pre-dawn in the northwestern sector is about the same magnitude—but with opposite sign—than that over the southeastern sector (Fig. 7c). Since temperatures are near freezing on the foothills at both sides of the mountain, the contrasting temperature gradients result in a mountain-scale thermal contrast that maximizes at about 700-m ASL. The warm minus cold side temperature difference is on average 7 °C.

Fig. 7
figure 7

Vertical profiles constructed with MODIS land-surface temperature (LST) and near-surface air temperature (Tns) from AFEX stations. Yellow point: LST in the northwest sector of Nahuelbuta mountain (Fig. 1), grey point: LST at southeast sector of Nahuelbuta mountain, red point: Tns in station located in northwest sector of Nahuelbuta mountain, and blue point: Tns in station located in the southeast sector of Nahuelbuta mountain. Profiles for four representative cases (date/time in each panel) are shown: a clear-skies late morning with large temperature contrast; b overcast late morning with small temperature contrast; c clear sky dawn with large temperature contrast; and d overcast dawn with small temperature contrast. Thermal contrast defined as the dawn Tns difference between stations ETA and TNO, see Sect. 3.1 for details

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The corresponding T ns observations from AFEX stations are also plotted in Fig. 7. At pre-dawn (02:20 LT; Fig. 7c), the stations located in the northwestern sector of NM reveal an inversion (as per T ns) with strength close to that inferred from MODIS-LST. In this figure, the anomalous cold conditions in stations ETA and EBA are also evident. As commented before, days with thermal contrast less than 5 °C often present overcast, rainy conditions, precluding the use of LST. Nonetheless, as illustrated for August 16 and 17, 2011 (Fig. 7b, d), the vertical variation of T ns is very close to the moist adiabatic lapse rate under overcast conditions, regardless of the time of the day.

3.4 Synoptic conditions

The synoptic-scale patterns during nights with large (δT ns > 10 °C) or small (δT ns < 5 °C) thermal contrast are revealed by composite maps of geopotential height at 300 and 950 hPa from daily NCEP-FNL reanalysis (Fig. 8). The composite for days with large thermal contrast shows a midlatitude ridge aloft with its axis just west of the coastline, an intense anticyclone over the subtropical Pacific, and a low-level coastal trough along the Chilean coast. This configuration has been described in detail by Garreaud et al. (2002) and Garreaud and Rutllant (2003), and results in stable thermodynamic conditions and southeast low-level winds over south-central Chile. These conditions are important to define the flow regime over the mountain that explains the thermal contrasts observed. The synoptic-scale composite for days with thermal contrast less than 5 °C shows an upper level trough over the Pacific and a surface cyclone over the southern part of the continent (Fig. 8b). This is the typical large-scale environment that brings cold fronts and precipitation over south-central Chile (Falvey and Garreaud 2007; Garreaud et al. 2016).

Fig. 8
figure 8

Composite maps of geopotential height at 300 (thick contours) and 950 hPa (thin contours) from daily NCEP-FNL reanalysis for days with a large temperature contrast and b small temperature contrast. Nahuelbuta (NM) location indicated by the red point. Thermal contrast defined as the dawn Tns difference between stations ETA and TNO, see Sect. 3.1 for details

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4 Numerical simulations

The existence of a substantial thermal contrast between the northwestern (warmer) and southeastern (cooler) side of the NM during dry nights in winter calls for a physical explanation that we advance here using high-resolution numerical simulations (see details in Sect. 2.4). We performed 36-h WRF simulations of six cases during winter 2011 in which MODIS-LST and AFEX T ns reveal a marked thermal contrast (Table 4). In four cases, the simulated field of surface temperature (T s) was in good agreement with the pattern of land-surface temperature from MODIS, including the north–south thermal differences (González 2015). The best simulation (as per the highest correlation as well as the lowest root-mean-square error and bias) occurred for the night of August 20 and we selected this event for further analysis (Table 5). Nonetheless, the simulations did not capture the marked T ns difference among stations located near 750-m ASL (nor MODIS-LST), as shown in Table 4, emphasizing that the cooling process in ETA and EBA stations is a micro-scale process, whose origin is speculated about at the end of this work.

Table 5 Spatial correlation, root-mean-square error, and bias between land-surface temperature from MODIS and surface temperature from WRF model for study cases
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As typical during dry days, the T s field in the afternoon of August 19 features a nearly dry-adiabatic lapse rate regardless of the direction from which one ascends NM (Fig. 9a). The pattern of evening-to-dawn (nighttime) local temperature change features marked differences across the domain (Fig. 9b). Over the lowlands, there is widespread cooling ranging from −5 to −11 °C and the foothills (just below the 500-m contour) cool about −7 °C. Over the mountains, however, there are two-banded areas with no cooling and even slight warming (+0.5 °C from evening to dawn). The bands are oriented perpendicular to the prevailing SE low-level flow and located immediately downstream of the two peaks of NM identified in Fig. 9 by the 1000-m contour. The area with the largest warming coincides with the northwestern slope of NM in sharp contrast with the cooling over the southeastern slope. This conspicuous pattern of temperature changes during nighttime, superimposed on the rather uniform afternoon field (except for its vertical dependence), leads to the contrasting T s field at dawn simulated by WRF (Fig. 9c), with cold temperatures at lowlands, an inversion (increase in T s with height) over the northern slope of NM and much colder conditions over the southern slope. The simulated T s field is in good agreement with the MODIS-LST (Fig. 9d).

Fig. 9
figure 9

WRF-simulated near-surface air temperature in a afternoon of August 19 and c dawn of August 20, 2011. b Dawn minus afternoon difference in WRF-simulated near-surface air temperature. d MODIS land-surface temperature in the afternoon of August 19. The red line is the location of the cross section, as shown in Figs. 11 and 12

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As commented before, NM was immersed in SE low- and mid-level flow during the night of August 20 (Fig. 10). With a nocturnal Brunt–Väisälä frequency N = 0.01/s (stable thermodynamic conditions), NM maximum height h m = 1200 m, and wind speed (U) about 8 m/s over southern Chile, the inverse Froude number (N·h m/U, Reinecke and Durran 2008) is about 1.5. The values of U and N were obtained as the vertical average of the respective variables between 100–1500-m ASL in a column 50-km upstream of NM. Using the theory developed by Smith (1979, 1989) for elliptic, isolated mountains, or laboratory analogs (Baines 1987), the larger-than-one inverse Froude number suggests partial blocking of the upstream flow and low-level flow stagnation on the windward slope of the NM. Indeed, the wind vectors at 1000-m ASL show flow deflection, acceleration in the mountain’s flanks, and a prominent wake downstream (Fig. 10b). The blocking is evident by the deflection around the mountain of the near-surface wind approaching from the SE and an area of minimum wind speed (<1 m/s) near the foothills (Fig. 10a) that coincides with the maximum cooling (Fig. 9b), as calm conditions favor the cooling (Konno et al. 2013). It is possible that the development of a strong nocturnal inversion further weakens the near-surface winds, although the upstream conditions are enough to produce the near-stagnant conditions over the windward slope of NM. Conversely, the 10-m AGL wind field exhibits two bands of strong speed (>8 m/s) co-located with the areas of insignificant nighttime cooling. Indeed, the strong wind weakens the nocturnal thermal inversion near the surface by mixing warmer air downward (André and Mahrt 1982). Thus, the spatial correlation between the nocturnal 10-m wind speed and the nighttime temperature change is relatively high (0.79).

Fig. 10
figure 10

WRF-simulated wind speed (m/s, colors) wind vectors (arrows) at a 10 m above the surface and b 1000-m ASL during August 20 at 02:30 LT. Contours show the 0-, 500-, and 100-m ASL terrain elevation

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The complex distribution of nighttime cooling/warming near the surface is not only shaped by the surface wind field, but it is also reflect a deeper pattern illustrated by a vertical cross section of the temperature and its rate of change along an NW–SE transect over the NM (Fig. 11). The free tropospheric temperature during the afternoon has a large cool-ocean/warm-land contrast, but it is only slightly modified by NM (Fig. 11a). The evening-to-dawn temperature change shows a marked cooling in the lowest 1000 m over the inland valley to the SE of the massif and in the lowest 200 m over the coastal lowlands to the NW (Fig. 11b). In both sectors, the cooling increases downward signaling its radiative nature. Above 1500-m ASL, the temperature change is generally weak. Most notably, the free tropospheric air experiences a substantial warming in a layer about 500-m deep over the northwestern slope of the mountains. This vertical pattern of nighttime temperature change, superimposed on the aforementioned daytime temperature field, results in the contrasting pattern of pre-dawn temperatures over Nahuelbuta (Fig. 11c), with a marked low-level inversion downstream of NM and a weaker, elevated inversion upstream.

Fig. 11
figure 11

a Cross section of WRF-simulated air temperature at August 19, 2011 at 18 LT along the AB transect over the Nahuelbuta Mountains (see Fig. 9). b Dawn minus afternoon difference in WRF-simulated air temperature along the AB transects. c Cross section of WRF-simulated air temperature at August 20, 2011 at 02:30 LT along the AB transect

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In our case study, the nighttime warming in the lower troposphere seems partly produced by strong subsidence downstream of the highest peaks of Nahuelbuta (Fig. 12a), which in turn is produced by a mountain wave evident in the cross section of the meridional and vertical velocity (Fig. 13a). Mountain wave activity is also present during daytime (not shown), but its impact in the low-level temperature field is much weaker than at nighttime given the near-neutral stratification generated by surface heating and the much reduced low-level stability upstream of NM. Considering the mountain height, wind speed, and Brunt Väisälä frequency used previously, we obtained Fr ~ 0.7 and N·a/U ~ 100, where a ~ 80 km is the along-wind mountain length. Given these adimensional numbers, the flow is within hydrostatic regime and vertically propagating mountain waves are expected (e.g., Lin 2007) with wind acceleration along downslope, fully consistent with the pattern obtained by WRF over NM (e.g., Fig. 13a). We also calculated the Bulk Richardson number (Dörnbrack 1998) across the domain which results larger than 1.5 except very near the surface, precluding the breaking of the mountain wave over Nahuelbuta (Durran 1990). Furthermore, shear-driven turbulence in the first hundred meters above the surface (not shown) may have mixed down potentially warmer air from aloft and aid in warming of the lee slopes. Adiabatic warming due to subsidence on lee slopes has been widely documented and is associated with downslope Foehn-like winds (Gaffin 2002, 2009; Richner and Hächler 2013) and several mechanisms have been proposed to explain the formation of these winds (Elvidge and Renfrew 2016), including mountain waves (Blier 1998; Zängl et al. 2004) as identified in the present study. Accordingly, the formation of warm winds on NM would follow the model that Elvidge and Renfrew (2016) termed “isentropic drawdown”.

Fig. 12
figure 12

WRF-simulated potential temperature (K) for the six simulated cases (dates and time atop of each panel) along the AB transect over the Nahuelbuta Mountains (see Fig. 9)

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Fig. 13
figure 13

Cross section of WRF-simulated wind speed (colors) and (u, w) wind vectors for the six simulated cases (dates and time atop of each panel) along the AB transect over the Nahuelbuta Mountains (see Fig. 9)

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The adiabatic warming during nighttime over the lee (northwestern) slope of NM is restricted to elevations above 500-m ASL (e.g., Figs. 11b, 12a). Such pattern of warming is consistent with the restriction of the strong downslope flow to about 30-km downstream from the mountain peak (Fig. 13a). Farther downstream (at about 20 km in the cross section), there is a sector of strong ascending motion that resemble a hydraulic jump. Although the existence of a hydraulic jump is supported by the Froude number on both sides of NM (subcritical flow upstream and supercritical downstream), its location may be modulated by the existence of a cool marine boundary layer to the north of NM preventing the downstream propagation of the downslope flow. This hypothesis may be tested by artificially removing the marine boundary layer, but such numerical experiments are beyond the scope of this paper.

Before closing this section, let us consider the model results for the other five cases, as identified in Table 4. In all cases, there was southerly flow impinging the mountain (Fig. 13). Moreover, in five of them (those with the best spatial correlation, Table 5), there is low-level subsidence and near-surface flow acceleration over the northern, leeward side of NM between 500- and 1000-m ASL. Consistently, isentropic drawdown is seen in all six cases (Fig. 12), lending generality to the physical mechanism previously proposed to explain the ridge-scale thermal contrast over NM during dry- and clear-skies nights.

5 Conclusions

The spatial distribution of the near-surface air temperature (T ns) over a coastal mountain range in southern Chile (Nahuelbuta Mountains, 38°S) has been described here on the basis of in situ measurements in 13 stations located between 130- and 1300-m ASL, and MODIS-derived land-surface temperature (LST) on ~1 km2 pixels. Our study encompasses the austral winter (May–September) 2011, although we also used MODIS data for other winters. The way in which temperature varies in the vertical is largely determined by the time of the day (daytime/nighttime) and accompanying weather conditions (clear–dry/cloudy–rainy).

During rainy conditions (more than half of the time in winter; Garreaud et al. 2016), the vertical variation of T ns and LST is very close to the moist adiabatic lapse rate (~6.5 °C/km) regardless of the time of the day and the direction along which one moves over the mountain. This result is in agreement with observations elsewhere and consistent with vigorous mixing under stormy conditions (strong winds and near saturated conditions; Garreaud et al. 2016). Likewise, we found that T ns and LST tend to follow the dry adiabat (~9.8 °C/km) during daytime under dry- and clear-skies conditions.

LST and T ns feature a more complex pattern during nighttime under dry- and clear-skies conditions (about one third of the winter nights). These conditions often occur after a cold front has passed over the region and a migratory anticyclone dominates southern Chile, fostering intense radiative cooling of the surface after sunset. The temperature still decreases with height (at about 8 °C/km) over the windward, southeastern side of NM, but, somewhat surprisingly, the temperature increases (at about 8 °C/km) over the leeward, northwestern side of the mountains. The temperature inversion extends up to about 700-m ASL leading to an average temperature contrast of about 7 °C between the northwestern and southeastern sides of Nahuelbuta in these cases.

To illuminate the processes leading to the contrasting, mountain-scale LST and T ns distributions during dry winter nights, we performed high-resolution WRF simulations of selected cases. The simulated temperature distributions were in acceptable agreement with their observational counterparts in four out of six cases and the case of August 20, 2011, was analyzed in detail. Given the stable, anticyclonic conditions during that day, the prevailing SE winds below 1000-m ASL are blocked by the NM, producing a near-stagnant zone over the southeastern foothills of the massif. This condition favors a marked radiative cooling in this sector after sunset. The flow above 1000-m ASL can climb the mountains generating wave activity within the hydrostatic regime. The mountain wave induces subsidence and adiabatic warming in the lower free troposphere downstream of the mountain peak and intense near-surface winds in its leeward side. Both factors are important for the minimum nighttime cooling (and even a slight warming) over the northwestern slopes of NM, through downward transport of warm air, that ultimately explains the inversion and warm condition in this sector. Five (out of six) simulated cases of strong nighttime temperature contrast exhibit a wind field and thermal structure similar to the August 20, 2011, case of study, lending generality to the proposed mechanism.

In addition to the mountain-scale thermal gradient, dry nights also feature quite substantial temperature differences (>10 °C) among closely located stations at a similar altitude (~750-m ASL). These differences were undetected by MODIS-LST (~1-km resolution) and WRF—T ns (3-km resolution) indicative of their micro-scale nature. Given the limited observational data over NM, we can only speculate on these micro-scale processes. Although the two coldest stations (ETA and EBA) are in the northern, warm side of NM during dry nights, they are both confined in small, basins (a few km wide at the most) favoring the formation of cold air pools under calm winds (e.g., Clements et al. 2003). The opposite happens in CAN/TNO, both well exposed to the general, ridge-scale flow that would flush any cold air pool. A better understanding of the phenomenon described here requires observational campaigns to record temperature, wind, radiation, and turbulence. A good result at this point could turn the Nahuelbuta Mountains in a natural laboratory for the study of nocturnal cooling over isolated mountain ranges in midlatitudes.