Hydraulic Analysis and Cold-Air Pool Interaction of the Raco Gap Wind

Ricardo C. Muñoz aDepartment of Geophysics, University of Chile, Santiago, Chile

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Laurence Armi bInstitute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, La Jolla, California

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Abstract

Raco is a local wind occurring in central Chile where the Maipo River Canyon exits into the Santiago valley. The intensification of the easterly down-canyon flow starts at any time during some cold season nights, accompanied by increases in temperature and drops in humidity. The hypothesis of the raco being a gap wind controlled by the narrowest section in the 12-km canyon exit corridor is tested with data from two events in July 2018 and July 2019. The data are analyzed in the framework of hydraulic theory, and a subcritical-to-supercritical transition is documented to occur at the narrows of the gap where the Froude number is close to unity, confirmed by radiosondes launched in the narrows in 2019. For the raco flow, the sum of potential and kinetic energy is conserved upstream of the narrows, while the acceleration occurring farther downstream loses a large fraction of energy to frictional dissipation. The raco events occur under the influence of regional subsidence, but a differential nocturnal warming of the in-canyon air mass is responsible for a pressure gradient driving the raco. In the 2019 case, a ceilometer mounted on an instrumented pickup truck documented the structure and movement of the interface between the raco air and the cold-air pool (CAP) existing over the valley to the west. Together with a radiosonde launched near the CAP–raco surface front, the observations reveal the intense shear-driven mixing taking place at the interface and the factors supporting the establishment of a stationary front.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ricardo C. Muñoz, rmunoz@dgf.uchile.cl

Abstract

Raco is a local wind occurring in central Chile where the Maipo River Canyon exits into the Santiago valley. The intensification of the easterly down-canyon flow starts at any time during some cold season nights, accompanied by increases in temperature and drops in humidity. The hypothesis of the raco being a gap wind controlled by the narrowest section in the 12-km canyon exit corridor is tested with data from two events in July 2018 and July 2019. The data are analyzed in the framework of hydraulic theory, and a subcritical-to-supercritical transition is documented to occur at the narrows of the gap where the Froude number is close to unity, confirmed by radiosondes launched in the narrows in 2019. For the raco flow, the sum of potential and kinetic energy is conserved upstream of the narrows, while the acceleration occurring farther downstream loses a large fraction of energy to frictional dissipation. The raco events occur under the influence of regional subsidence, but a differential nocturnal warming of the in-canyon air mass is responsible for a pressure gradient driving the raco. In the 2019 case, a ceilometer mounted on an instrumented pickup truck documented the structure and movement of the interface between the raco air and the cold-air pool (CAP) existing over the valley to the west. Together with a radiosonde launched near the CAP–raco surface front, the observations reveal the intense shear-driven mixing taking place at the interface and the factors supporting the establishment of a stationary front.

© 2024 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ricardo C. Muñoz, rmunoz@dgf.uchile.cl

1. Introduction

Topographic gaps refer to well-defined openings cutting through terrain barriers extending on their sides (Jackson et al. 2013; Whiteman 2000). The barriers can be large mountain chains, such as the Alps, coastal topography as in the case of straits, or the lateral sides of a valley constriction. In turn, gaps can also have various shapes and different geometrical parameters like width, length, and depth. Gap winds refer to relatively strong winds that are occasionally observed along gaps. Their presence largely affects the local meteorology, with reported impacts on human well-being (Ohashi et al. 2018), air pollution (Li et al. 2023), aerosol transport (Green et al. 2008), fires (Wagenbrenner et al. 2018; Garner and Kovacik 2023), wind energy (Wilczak et al. 2019), coastal upwelling (Hong et al. 2018), and even tropical cyclone formation (Holbach and Bourassa 2014). Jackson et al. (2013) provided a thorough review of gap wind observations, modeling, and forecasting. The scales of gap winds vary widely, closely tied to the scales of the topographic elements defining the gap and the barrier. In the larger scale, gap flows extending over hundreds of kilometers and reaching above 20 m s−1 have been documented over straits along the northwestern coast of the United States and Canada (Lackman and Overland 1989; Colle and Mass 2000). In the smaller scale, the Hijikawa-arashi gap wind in western Japan has peaks around 10 m s−1 and occurs along a 10-km corridor connecting the inland Ozu basin with the Hijikawa River mouth (Ohashi et al. 2015; Ito et al. 2019). Another small-scale wind with similarities to our case of interest is the “mini-foehn” in Germany’s Isar Valley documented by Hornsteiner (2005) and Hornsteiner and Zängl (2006).

The gap flows that develop along the Wipp Valley pass in the central Alps have received much scientific attention (Mayr et al. 2007 and references therein). In terms of the forcing of gap winds, these studies conclude that horizontal pressure differences developing between the air masses (or reservoirs) upstream and downstream of the barrier are their main drivers and, in turn, that these differences often arise hydrostatically due to both air masses having distinct potential temperatures (Mayr and Armi 2008). Jackson et al. (2013) described four mechanisms by which these temperature differences may arise: 1) differential synoptic-scale advection of temperature; 2) formation of distinct air masses over different surfaces under anticyclonic conditions; 3) mesoscale terrain-induced differential warming by subsidence and diabatic processes; and 4) differential cloudiness on the opposing sides of the gap. Additionally, Mayr et al. (2007) emphasized the asymmetry shown by gap winds: upwind of the barrier the flow is deep and slow, while downstream it is shallow and much faster. The potential to kinetic energy conversion suggested by such asymmetry has motivated the use of hydraulic theory to investigate the dynamics of gap winds, in analogy to a subcritical-to-supercritical transition of water flow in a channel with a constriction in its cross section (e.g., Henderson 1966). The hydraulic approach has proven useful to develop theoretical models (e.g., Drobinski et al. 2001), diagnose numerical model results (e.g., Flamant et al. 2002; Zängl 2004), and interpret field observations of gap winds (e.g., Ohashi et al. 2015).

Raco is the local name of a relatively strong, warm, and dry wind observed occasionally at the exit of the Maipo Canyon as it flows into the Santiago valley in central Chile (Fig. 1). In contrast to foehn-type winds in South America like the zonda (Norte 2015) and the puelche (Montecinos et al. 2017), which generally cross the Andes barrier and have an effect in a large region downwind, the raco is more local in nature, and most of the times, its easterly direction is opposite to flow with a westerly component existing at the Andes top level (Rutllant and Garreaud 2004). Muñoz et al. (2020, hereinafter M2020) presented a 7-yr climatology of the raco wind characteristics together with results of a 4-day intensive observational period (IOP) carried out in July 2018, in which 6-hourly radiosondes were launched from the two extremes of the 12-km Maipo Canyon exit corridor. They hypothesized the raco to be a gap wind developing downwind of a topographic constriction existing in the middle of the corridor, which on occasions may act as a hydraulic control forcing a nocturnal valley exit jet to descend and accelerate toward the corridor exit producing the raco wind at the surface. In the present contribution, we show and analyze results from a field campaign carried out in July 2019 with the aim of gathering additional observations to further test the gap wind hypothesis. In particular, a third radiosonde launching site was operated in the middle of the exit corridor, about 2 km downwind of the topographic constriction. Additionally, we apply a hydraulic analysis to the 2018 and 2019 observations to verify the hydrodynamic transition taking place along the corridor.

Fig. 1.
Fig. 1.

(a) Regional topography of the Santiago valley and surroundings. Santiago city is shown as a gray area. SCL marks the Santiago airport. The red and black line shows the boundary of the Maipo basin as defined in the text. The red section and points N and S refer to elements in Fig. 6. The black box shows the region of the Maipo Canyon gap enlarged in (b). The inset shows the location of the region in southern South America (red box), with gray shading for altitudes above 3000 m MSL. (b) Zoom view of the exit corridor of the Maipo basin. Colored circles mark the position of measurement sites: ALM, LOB, CAN, and MAN. An X mark near ALM shows the location of a fixed thermometer installed at a CRN. Colored lines show the trajectory of the radiosonde balloons launched on 0600 LT 24 Jul 2019. Numbers near the trajectories indicate the altitude (m MSL) of major direction changes. Gray altitude contours are shown every 500 m.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

We also address the interaction of the raco wind with the cold-air pool (CAP) that rapidly develops over the Santiago valley during clear-sky winter nights. The dynamics of nocturnal foehn and gap winds interacting with CAPs has received observational (Haid et al. 2022; Lareau and Horel 2015) and modeling (Umek et al. 2022) attention, as it ultimately determines the extent of the impact that these winds can have at the surface. Moreover, as CAPs are sensitive to external conditions (Sheridan et al. 2014) and are commonly associated with air pollution problems (e.g., Baasandorj et al. 2017), their modulation by gap winds can have a significant effect on local air quality conditions.

The paper is organized as follows. Section 2 describes the climatological and topographic setting of the raco wind and the data available for the analysis. Section 3 presents the observations during the 2019 raco event and its synoptic environment. We present a hydraulic analysis of the observations in section 4. Section 5 examines the interaction between the raco and the CAP existing over the Santiago valley. Section 6 provides conclusions.

2. Climate, site, and data

The region of interest is located in central Chile at about 33.5°S and 70.5°W. Its climate is largely controlled by the subtropical southeast Pacific anticyclone providing a very stable lower troposphere, with rain events concentrated in winter when midlatitude weather systems are able to reach the region (Falvey and Garreaud 2007). In-between rain events, the weather in central Chile is strongly modulated by subsynoptic coastal lows that travel from north to south along the coast inducing at a fixed point a quasi-weekly alternation between very stable and clear-sky conditions followed by a reduction of the stability and the intrusion of the humid marine boundary layer into inland valleys like that of Santiago (Garreaud et al. 2002). The raco events are typically observed in the stable phase of this modulation, in association with regional warming of the lower troposphere and the concomitant occurrence of air pollution events in the Santiago valley (Rutllant and Garreaud 2004; Muñoz et al. 2023).

The raco wind is perceived in the southeasterly portion of the valley (Fig. 1a) where the Maipo River exits the Andes mountains into the valley through a 12-km zonally oriented corridor (Fig. 1b). Of particular importance for this study is the presence of a V-shaped topographic constriction located in the middle of the corridor, about 2 km east of the Canelo town (Fig. 2). The topographic area draining through the gap will be subsequently referred to as the Maipo basin and is outlined with a bold line in Fig. 1a. A more quantitative orographic description of this basin is presented in section 4a.

Fig. 2.
Fig. 2.

View of the topographic constriction as seen from CAN (in Fig. 1) looking up canyon to the east. Photograph by Patricio Aceituno.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

In terms of observations, automatic weather stations at La Obra (LOB) and Almenar (ALM) provide continuous monitoring of near-surface meteorology (Fig. 1b and Table 1). The IOP documented here took place from 22 to 25 July 2019 in which 6-hourly radiosondes (model iMet-4; InterMet Systems) were launched from three sites along the Maipo Canyon exit corridor: at ALM, Canelo (CAN), and Manzano (MAN) (Fig. 1b). The Almenar and Manzano sites were also used in the 2018 IOP reported in M2020, with the Canelo site added in 2019 to measure conditions closer to the narrowest section of the gap. The trajectories plotted in Fig. 1b during raco conditions show that three distinct regions of the easterly flow leaving the Maipo Canyon below 3000 MSL are probed: the region upstream of the narrows by the MAN radiosonde, that downstream by the CAN radiosonde, and that at the corridor exit by the ALM radiosonde. Above the easterly flow layer, the southward movement of the balloons is due to persistent northerly winds existing between 3000 and 5000 m MSL that have been explained as a barrier effect of the Andes on the westerly flow aloft (Rutllant and Garreaud 2004; Scaff et al. 2017).

Table 1.

Sites and measurements in the 2019 IOP.

Table 1.

As in 2018, a mobile ceilometer system (Flores et al. 2020) measured the horizontal and vertical distribution of boundary layer aerosols and surface temperature and humidity along the exit corridor. Finally, one additional fixed thermometer was installed at a crane site (CRN) between Almenar and La Obra sites to better track the passing of the raco front (section 5).

To supplement the local observations, we use vertical profiles of temperature and winds derived from commercial airplanes operating from the Santiago airport (SCL point in Fig. 1a). These data are available through the Aircraft Meteorological Data Relay (AMDAR) program of the World Meteorological Organization (Moninger et al. 2003) and have been shown to represent well meteorological conditions over the Santiago valley (Muñoz et al. 2022). Additionally, we make use of ERA5 reanalysis data (Hersbach et al. 2020) to describe the large-scale meteorological conditions prevailing during the IOP.

3. The 24 July 2019 raco event

During the IOP, central Chile was affected by a midtropospheric cutoff low as shown in Fig. 3. Garreaud and Rutllant (2006) mentioned cutoff lows as one of the synoptic variants leading to the formation of surface warm-core coastal lows, which in turn have been associated with raco events (Rutllant and Garreaud 2004; M2020). Indeed, Fig. 3a shows a coastal trough in the sea level pressure field of 1200 UTC 24 July. This day, the coastal surface pressure at Santo Domingo (100 km west of Santiago) decreased 5 hPa from 0000 to 0900 UTC, while the 500-hPa geopotential height of the Santo Domingo operational radiosondes rose about 30 m in 12 h, revealing a general warming of the lower troposphere during the night. A factor for this warming is subsidence in the lower troposphere, which according to the ERA5 reanalysis prevailed above the Santiago valley from 0600 UTC 23 July to 1200 UTC 25 July, peaking in the first half of 24 July.

Fig. 3.
Fig. 3.

Sea level pressure (colored contours are labeled in hPa) and 500-hPa geopotential heights (bold black contours are labeled in m) derived from the ERA5 reanalysis for the region of South America and the southeast Pacific. Fields are shown for 1200 UTC (a) 24 and (b) 25 Jul 2019. Red dots mark the location of the Santiago valley.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

The only raco event during the IOP began at La Obra station in the first hours of 24 July and reached Almenar station around 0600 LT = UTC − 4 h (Fig. 4a), producing at both sites northeasterly winds with gusts (maximum of 5-s measurements) between 8 and 12 m s−1, much larger than the 0–2 m s−1 gusts prevalent during nonraco nighttime hours. The increases in wind speeds were accompanied by rapid increases in temperature and decreases in the water vapor mixing ratio (Figs. 4b,c). In contrast, wind, temperature, and humidity evolve with no prominent jumps during the night in the upwind station of Manzano (not shown). The raco event ended at Almenar at around 1200 LT 24 July and about 1 h later at La Obra, with attendant changes in the wind direction to the western sector, drops in temperature, and increases in the mixing ratio, marking the gradual penetration of the daytime near-surface westerly flow into the Maipo Canyon. This pattern of surface meteorology conditions during the 24 July event puts it well within the typical variability of raco events described in M2020.

Fig. 4.
Fig. 4.

Time series of 5-min surface variables measured at LOB (blue) and ALM (red) stations during 23–24 Jul 2019. (a) Gust intensity (continuous; left axis) and wind direction (dots; right axis). (b) Air temperature. (c) Water vapor mixing ratio. Nighttime periods are marked with a gray background. Black dashed lines indicate the times of radiosondes shown in Fig. 8.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

The 23–24 July evolution of the vertical profiles of zonal wind and temperature above Manzano, Canelo, and Almenar is shown in Fig. 5, together with the evolution of the same variables derived from the AMDAR database for the Santiago airport, which represents conditions over the valley not directly affected by the raco wind. In terms of zonal wind, we distinguish at all sites two layers. An upper layer (e.g., Z > 3000 m MSL at Manzano) of easterly flow is associated with the midtropospheric cutoff low described earlier. In this layer, negative zonal winds are restricted to the night between 23 and 24 July, peaking around 0000 LT 24 July. The ERA5 reanalysis data are consistent with these observations, showing also that the cutoff low–associated easterly flow at 500 hPa maximizes further south (∼35°S) on 1200 UTC 24 July. In any case, the cutoff low weakened rapidly (Fig. 3b) and this easterly flow aloft is not considered essential for the occurrence of raco wind events as proved by its absence in other cases (Rutllant and Garreaud 2004; M2020) and the fact that midtropospheric cutoff lows are only one of several synoptic configurations conducive to surface coastal lows and raco events (Garreaud and Rutllant 2006).

Fig. 5.
Fig. 5.

Vertical and time evolution of (left) zonal wind and (right) temperature for 23–24 Jul 2019. Vertical dashed lines indicate midnight. Stars indicate radiosonde launching times. (a) Zonal wind at Manzano. Contours are every 2 m s−1, and the white contour marks the zero value. (b) Difference between the temperature at Manzano and that above the Santiago valley as represented by the AMDAR data. Contours are every 1°C, and the white contour marks the zero value. (c) As in (a), but for CAN. (d) As in (b), but for CAN. (e) As in (a), but for ALM. (f) As in (b), but for ALM. (g) Zonal wind of AMDAR data taken as representing Santiago valley conditions. Contours are every 2 m s−1, and the white contour marks the zero value. (h) As in (g), but for temperature. Contours are every 2°C. White boxes in (e) and (f) are due to a truncated radiosonde at ALM.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

A bottom layer (e.g., Z < 3000 m MSL at Manzano) of easterly flow occurs both nights at all sites. In the upstream site of Manzano, it had maximum speeds of about 6 m s−1 around 0600 LT in both nights, but the altitude of this maximum is around 1500 m MSL on 23 July and around 2800 m MSL on 24 July. In the two stations downwind of the narrows (Canelo and Almenar), the zonal wind profiles in the bottom layer show strikingly different characteristics during the two nights. While on 23 July, the easterly flow above Canelo and Almenar is similar to that above Manzano in terms of intensity (6–8 m s−1) and altitude of the maximum speed (1500–2000 m MSL), on 24 July, the easterly flow downwind of the narrows intensifies dramatically and the level of maximum speed descends significantly as compared to the zonal wind profile upwind of the gap above Manzano. In turn, the descent and intensification of the zonal flow downwind of the narrows explain the appearance of the raco wind at Almenar around 0600 LT 24 July (Fig. 4a). The zonal wind above the valley (Fig. 5g) has a vertical–temporal structure similar to that above the stations inside the Maipo Canyon, although the intensity of the easterly flow in the bottom layer is much weaker.

The right panels in Fig. 5 describe the evolution of the vertical temperature structure above all sites. To better appreciate the differences between them, the full temperature evolution is presented only for the valley (Fig. 5h), while for the sites inside the Maipo Canyon, we show their temperature anomalies with respect to the valley (Figs. 5b,d,f). All stations show a substantial nighttime warming of the lower troposphere occurring between 1800 LT 23 July and 0600 LT 24 July, consistent with the increase of the 500-hPa geopotential height and decrease in surface pressure described at the beginning of this section. The warming, however, is not the same at all sites, but it shows significant differences in the easterly flow bottom layer. In the upper portion of this layer, a cool anomaly is observed over the stations inside the Maipo Canyon, increasing to the east and reaching up to about 3°C about 2500 m MSL above Manzano. In the lower portion of the layer, a warm anomaly exists, which increases to the west, reaching up to about 5°C around 1000 m MSL above Almenar. As will be argued later, these temperature anomalies are significant for the dynamics of the raco wind: the cool anomaly above Manzano drives a pressure gradient forcing the air to leave the canyon, and the shallow near-surface positive anomaly at Almenar reflects that this exit flow is warmer than the valley air mass, probably due to the forced descent it experienced on its exit path.

4. Hydraulic analysis

The simplest hydraulic analysis of a steady stratified flow is based on the conservation of discharge or volumetric flow rate D and energy per unit mass E by an incompressible inviscid fluid layer moving below a less dense quiescent fluid:
D=SU=constant,
E=12U2+g(e+h)=constant,
where S is the cross-sectional area of the moving layer, U is its average velocity, h is its depth, e is the bottom elevation, and g′ = gΔρ/ρ is the reduced gravity computed based on the acceleration of gravity g, the density difference between both layers Δρ, and a reference density ρ (cf. Flamant et al. 2002). In this section, we analyze our measurements at the three sites along the Maipo Canyon exit corridor during raco events in light of these conservation principles. Additionally, we check whether the raco wind results from the hydraulic phenomenon of a subcritical-to-supercritical transition triggered at the topographic constriction existing in the exit corridor.

a. Mass conservation

The easterly wind at Canelo during a raco event corresponds to the outflow of the air mass inside the Maipo basin as defined in section 2 and shown in Fig. 1a. The principle of mass conservation, together with the topographic characteristics of the basin, shed light on the inflow needed to sustain the raco outflow, which is the matter of this subsection. Figure 6a shows the altitude of the basin edge in an 80-km stretch across the topographic constriction near Canelo. While the total length of the basin edge is about 450 km, the part not included in Fig. 6a is everywhere above 3000 m MSL, varying mainly between 4000 and 5000 m MSL and with peaks up to about 6000 m MSL in the eastern flank of the basin. The only open lateral section of the basin below 3000 m MSL is, therefore, restricted to the zone shown in Fig. 6a (see also Fig. 1), and below 2200 m MSL, it is further constrained in the constriction. Thus, the Maipo basin below 3000 m MSL can be considered as a confined topography with only one main lateral opening around the gap, and the air mass leaving the basin through the latter must necessarily be compensated by mean subsidence occurring over the basin.

Fig. 6.
Fig. 6.

(a) Surface elevation of points along the edge of the Maipo basin as defined in section 2. The abscissa axis shows the horizontal distance measured clockwise along the basin edge with 0 at the gap. Only 80 km around the gap are shown (red section of the basin edge in Fig. 1a). The points S and N are reference points marked in Fig. 1a. Height annotations for MAN and CAN are discussed in section 4c(1). (b) Schematics of topographic parameters of a semienclosed basin as a function of altitude z: lateral exit cross-sectional area L, horizontal drainage area A, and enclosed volume V. (c) Values of the parameters for the Maipo basin.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

The schematics in Fig. 6b illustrate the topographic parameters needed to relate the required subsidence to the gap outflow, namely, the lateral exit area L, the horizontal drainage area A, and the enclosed volume V of the basin. Their values as a function of altitude are shown in Fig. 6c. Between 800 and 2200 m MSL, the V-shaped constriction produces a parabolic increase of L with altitude. Above 2200 m MSL, the topography south of the gap levels off defining a lateral ridge about 25-km wide. Consequently, L increases much faster with altitude, defining two distinct regions for the lateral opening of the basin below 3000 m MSL: below 2200 m MSL, it is confined to the gap, and above that level, it opens into a ∼35-km total wide cross section. This confined topography can be compared to that of the Sinbad basin in Colorado, in which a similar mass budget analysis was performed by Whiteman et al. (1996). The V-shaped constriction in their case has a depth of about 600 m, as compared to 1400 m in our case. The values of the basin perimeter and of L, A, and V at the top of the gap are in our case between 7 and 12 times larger than the corresponding values in the Sinbad case, pointing to the much larger extension of the confined topography considered in the present work.

For the raco event of 0600 LT 24 July, Fig. 7a shows the zonal wind vertical profile measured at Canelo station. Integrating this wind profile over the lateral exit area shown in Fig. 6a provides an estimate of the volumetric airflow discharge rate D, leaving the Maipo basin (Fig. 7b). Demanding that this exit flow rate be compensated by vertical subsidence crossing the horizontal area A at each level (Fig. 6b) produces the vertical velocity profile shown in Fig. 7c, in which mean subsidence values between 5 and 10 cm s−1 are estimated inside the basin below 2200 m MSL. However, the wind speed vertical profile measured near the axis of a valley is an overestimation of the average speed in the valley cross section, as has been discussed by various authors (King 1989; Rucker et al. 2008). Indeed, Whiteman et al. (1996) applied a 0.7 factor to the measured exit wind speed profile when performing the mass budget of the Sinbad basin. The shading in the profiles in Fig. 7 represents the variation of the estimates when the mean wind in the exit cross section ranges from 70% to 100% of the zonal wind speed measured at Canelo. The bulge in the subsidence profile between 2200 and 3000 m MSL is associated with the widening of the exit area at 2200 m MSL described previously, for which the wind speed profile measured at the gap axis is less representative and a smaller correcting factor should probably be applied, as compared to the region below 2200 m MSL. With the 70% correction factor, the mean subsidence intensity below 2200 m MSL is between 4 and 6 cm s−1, which is still about double the values reported for the Sinbad basin. The airmass turnover time below 2200 m MSL, computed as the volume V (Fig. 6b) divided by the exit flow rate D (Fig. 7b), is between 1.5 and 2 h, which is about half of that reported for the Sinbad basin. Interestingly, despite the Maipo basin being much larger than the Sinbad basin, the turnover circulation associated with the raco wind in the former appears significantly more intense than that in the latter, which is driven mostly by radiative cooling.

Fig. 7.
Fig. 7.

(a) Zonal wind measured at CAN at 0600 LT 24 Jul 2019. (b) Discharge rate through the lateral opening of the basin. (c) Mean subsidence needed to compensate the outflow rate. Shading marks the variation of each parameter if the mean outflow velocity through the lateral opening ranges from 70% to 100% of the actual zonal wind measured at CAN.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

As mentioned earlier, raco events tend to occur during periods of regional lower-tropospheric warming, which in the case under study is manifested by the isotherms around 3 km MSL steadily rising in the period between 1800 LT 23 July and 0600 LT 24 July (Fig. 5h). If this warming were solely due to subsidence, the same figure can be used to estimate a value of vertical velocity between −3 and −5 cm s−1, which is similar to the range of the subsidence estimated above with mass conservation arguments. Of course, radiation and horizontal advection may also play a role in the temperature evolution, but we postulate that synoptically driven regional subsidence acting over the semiconfined Maipo Valley plays a main role in the intense turnover circulation during raco events suggested by our mass conservation analysis.

A last comment related to the topography of the Maipo basin is the role of the lateral ridge existing at ∼2.2 km MSL (Fig. 6a) in limiting the maximum intensity of the raco wind. Indeed, M2020 (their Fig. 6b) showed that maximum hourly wind speeds at La Obra during raco events increase with the duration of the event, but they never surpass about 9 m s−1 in the longest events. Our hypothesis is that the lateral ridge acts as a spillway weir of a hydraulic dam, limiting the maximum depth that can be attained by the upstream air mass, considered as the source reservoir or driver of the raco wind.

b. Hydraulic transition

To analyze the change of flow depth and speed along the Maipo Canyon exit corridor during raco events, we consider a steady hydraulic flow conserving mass and energy [Eqs. (1) and (2)] as it moves along a corridor with a varying cross-sectional shape. To simplify the analysis, we consider a rectangular-shaped cross section of width b(x) varying in the flow direction x so that S = bh. To emphasize the energy conversion aspect of the solution, we introduce in Eqs. (1) and (2) a specific kinetic energy, K = (1/2)U2, and a specific potential energy, P = g′(h + e), with which they can be written as
D=bh2K,
E=K+P.
Differentiating these equations with respect to x, we obtain
0=1bdbdx+1h(1gdPdxdedx)+12KdKdx,
0=dKdx+dPdx.
Solving for the rate of change of the individual energy components, we get
dPdx=dKdx=2K1Fi2(1bdbdx1hdedx),
where Fi=U/gh is the internal Froude number. Equation (7) is equivalent to Eq. (A7) in Armi (1986) but posed here in terms of energy components.

The paramount importance given to the Froude number in hydraulic analyses is accounted for by Eq. (7). For a flow subject to a change in its cross section (prescribed by db/dx or de/dx), the energy conversion occurs from potential to kinetic or in the opposite direction, depending on the value of Fi2 compared to unity. In particular, for a subcritical flow (Fi2<1) approaching a horizontal-level gap (db/dx < 0 and de/dx = 0), Eq. (7) predicts that potential energy is converted to kinetic energy, resulting in the flow becoming shallower and faster as it approaches the narrowest section of the gap. In doing so, however, the Froude number increases and the possibility exists that it goes to unity. For the energy conversion rates in Eq. (7) not to become infinite, this critical condition can only occur where db/dx = 0, i.e., at the narrows. When this happens, the flow keeps accelerating beyond the gap, as Eq. (7) indicates that when db/dx > 0, supercritical flow (Fi2>1) also transforms potential into kinetic energy. This situation is called a hydraulic transition, in which a subcritical flow evolves into a supercritical flow in passing through a contraction in which Fi2=1. The resulting flow is asymmetric through the narrows: deep and slow upstream, but shallow and fast downstream. The observation of an asymmetric flow through a gap implies that a hydraulic transition must have occurred at the narrowest point in the topography, where Fi2=1, which is the condition tested next for the raco wind.

In our case, the parameters needed to compute Fi2 are best visualized with the help of vertical profiles of zonal wind and potential temperature for selected times, as shown for the 2019 IOP in Fig. 8. For the sake of extending the analysis to more than just one case, in Fig. 9, we also include profiles obtained in the 2018 IOP (M2020), although in this earlier campaign no radiosondes were launched from the intermediate Canelo site, close to the narrows. The top of the out-flowing layer is generally well defined by a potential temperature jump Δθ. The bottom of the layer is either the top of the CAP or surface inversion when it exists or the surface itself otherwise. The parameter U is estimated based on the approximate mean zonal wind speed in the layer. Figures 8a and 8d illustrate the way in which the different parameters to compute Fi2 were estimated for 0600 LT 24 July 2019. The first step was to use the vertical profiles of potential temperature to locate the flowing layer between the top of the CAP and the base of the temperature inversion aloft. In the case of Fig. 8d, this procedure produced depth estimates h for the flowing layer of 1300, 900, and 700 m for MAN, CAN, and ALM, respectively. Next, the vertical profiles of zonal winds were used to estimate the mean wind speed U in the flowing layer, as illustrated by the dashed colored lines in Fig. 8a. In this example case, U values of 6, 11, and 13 m s−1 were estimated for MAN, CAN, and ALM, respectively. For all the profiles considered, the estimated parameters and the resulting Fi2 are shown in Table 2. In all the cases in which raco wind was observed at Almenar, there is indeed a hydraulic transition along the exit corridor between Manzano and Almenar. At Manzano, Fi2 is in all cases much smaller than 1, due to the deep and slow-moving flowing layer. In contrast, Fi2 at Almenar is always larger than 1 when the raco wind is present and the exit flow is fast and shallow. In the 2019 IOP, the Fi21 obtained at Canelo in the 0600 and 0900 LT soundings confirms that the hydraulic subcritical-to-supercritical transition occurs near the narrows located close to this site. Without radiosondes launched west of Almenar, however, it is not possible to address the subsequent supercritical-to-subcritical transition that is often associated with a hydraulic jump (Drobinski et al. 2001).

Fig. 8.
Fig. 8.

Vertical profiles of (a)–(c) zonal wind, (d)–(f) potential temperature, and (g)–(i) pressure anomalies during selected hours of the 2019 IOP [pressure anomalies discussed in section 4c(2)]. Blue profiles marked as “valley” correspond to AMDAR observations representing conditions above the Santiago valley. The shaded rugged line around 2.2 km MSL in each panel represents the level of the lateral ridge existing south of the gap. Dashed and arrowed lines in (a) and (d), respectively, illustrate the estimation of hydraulic parameters in Table 2.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

Fig. 9.
Fig. 9.

Vertical profiles of (a)–(c) zonal wind, (d)–(f) potential temperature, and (g)–(i) pressure anomalies during selected hours of the 2018 IOP [pressure anomalies discussed in section 4c(2)]. Blue profiles marked as “valley” correspond to AMDAR observations representing conditions above the Santiago valley. The shaded rugged line around 2.2 km MSL in each panel represents the level of the lateral ridge existing south of the gap.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

Table 2.

Hydraulic scales for 2019 and 2018 raco cases.

Table 2.

c. Energy conservation

We take in this subsection two approaches to assess conservation of energy of the raco flow based on our data (Figs. 8 and 9). First, we address the energy conservation for the entire out-flowing layer considered as a hydraulic flow by checking Eq. (2). Then, we perform an energy analysis for the air parcel leaving the Maipo Canyon exit corridor at the level of maximum zonal wind speed at Almenar, for which we apply a classic Bernoulli analysis, although with an explicit consideration of a possible altitude drop of the parcel as it moves along the corridor and across the gap (see the appendix).

1) Hydraulic energy analysis

The values of E in Eq. (2) were computed using the same hydraulic parameters with which the Froude number was calculated, and the results are also included in Table 2. The assessment of energy conservation is performed by comparing the changes in K and P occurring between two sites, which we denote as ΔK and ΔP, respectively. If E is conserved between the two sites, then ΔK = −ΔP and the loss of potential energy (ΔP < 0) associated with the flowing layer descending and becoming more shallow translates into a corresponding increase in kinetic energy (ΔK > 0) related to its increase in speed. For the six cases of Figs. 8 and 9 and for all possible site pairs, the scatter between ΔK and ΔP is shown in Fig. 10. As compared to the perfect energy conservation line, all points fall on it or below it. In the latter case, the reason is the loss of energy to friction, as suggested by the fact that in 2019, when it was possible to distinguish between the MAN–CAN and CAN–ALM parts of the corridor, the part upwind of the narrows (squares in Fig. 10) shows remarkably little energy loss, in contrast to the large energy loss experienced in the part downwind (triangles in Fig. 10), related to the raco wind in contact with the ground. Of course, when assessing the total energy conservation along the full corridor (circles in Fig. 10), the result is a clear energy loss (between 20% and 50% of ΔP), in the 2019 and 2018 cases. Another conclusion to be drawn from the 2019 cases in Fig. 10 is that most of the potential energy drop takes place downwind of CAN, reflecting the marked asymmetry of the flow depth with respect to the narrows.

Fig. 10.
Fig. 10.

Scatter of changes in specific kinetic energy ΔK and specific potential energy ΔP between pairs of sites: ALM–MAN (big circles), ALM–CAN (triangles), and CAN–MAN (squares). Colors refer to the times of the comparison: 0600 LT (blue), 0900 LT (yellow), and 1200 LT (red). Dotted symbols correspond to 2018 cases. Black diagonal lines correspond to perfect (ΔK = −ΔP) and partial energy conservation.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

The combination of energy conservation [Eq. (2)] and the Fi2=1 condition leads to the well-known result that when the gap acts as a hydraulic control of the flow, the depth of the flow layer at the gap is 2/3 of the upstream reservoir depth measured with respect to the gap floor (e.g., Henderson 1966, p. 36). Considering Canelo and Manzano as representing the gap and the upstream reservoir, respectively, we can then expect that
hCANhMAN+eMANeCAN23.
For the 0600 and 0900 LT 24 July 2019 cases, when a clear hydraulic transition occurred at the narrows, the left-hand fractions computed with the values in Table 2 result as 0.69 and 0.73, respectively, close enough to the theoretical 2/3 value. Part of the discrepancy may be due to the Canelo site not being exactly at the critical point and that the Manzano site has some kinetic energy and is not a stagnant reservoir based on its low but not zero internal Froude number. The 2/3 ratio of layer depths annotated in Fig. 6 shows that the elevation of the lateral ridge existing south of the gap controls the maximum depth that the upstream cold air reservoir may attain, which is what is observed in Figs. 8 and 9 when comparing the extent of the cooler air over Manzano and the annotated elevation of the lateral ridge.

2) Parcel energy analysis

Equation (A12) or (A15) is used next to estimate the increase in wind speed observed between Manzano and Almenar, focusing on the parcel with the highest velocity at the latter site. First, however, we describe our computation of the pressure anomaly profiles shown at the bottom of Figs. 8 and 9 and which are needed in Eqs. (A12) and (A15). Based on the pressure and temperature profiles of the radiosondes, we integrated the hypsometric equation to get a p(z) relationship at each site and time. The starting point of the integration was defined aloft: a pressure of 555 hPa was set at 5000 m MSL for all sites, keeping in mind that they are separated by just a few kilometers (see trajectories in Fig. 1b). After the integration, a vertical profile p(z) is available for all sites. At each time, the mean pressure profile p¯(z) is the average of the profiles at Almenar, Canelo, and Manzano (only Almenar and Manzano in the 2018 case), and the pressure anomaly at each site is simply p(z)=p(z)p¯(z). Not surprisingly, the pressure anomaly profiles (bottom panels in Figs. 8 and 9) increase in the layer where the temperature of the soundings differs significantly (middle panels in Figs. 8 and 9).

To apply Eq. (A12) or (A15) to explain the maximum wind speed observed above Almenar in our raco cases (Figs. 8 and 9), we must estimate the altitude drop experienced by the parcels leaving the canyon at the jet nose, which can be done by looking at the potential temperature profiles, considering the latter to be a conservative variable. For the 0600 LT 24 July 2019 case (left column panels in Fig. 8), the jet at Almenar and Canelo is located around 1500 m MSL, and the potential temperature at this altitude is almost the same at the three sites, from which a near-horizontal path for the parcels can be estimated and Eq. (A12) is applicable. From Fig. 8g, we estimate a pressure anomaly difference between Manzano and Almenar at 1500 m MSL of about 1 hPa, which together with ρo ∼ 1 kg m−3 produces an increase in kinetic energy of about 100 m2 s−2. The zonal wind speed at Manzano in this case was about 5 m s−1, from which the speed at Almenar would be around 15 m s−1, very close to the observed maximum wind speed at this site.

At 0900 LT 24 July 2019 (center column panels in Fig. 8), the jet at Almenar is still around 1500 m MSL, but the potential temperature profile at Almenar is separated from the Canelo and Manzano profiles, suggesting that the jet nose parcel at Almenar may have descended about 500 m between Canelo and Almenar and, therefore, Eq. (A15) is used to estimate the increase in speed of the parcel. The pressure anomaly difference between Manzano (at 2000 m MSL) and Almenar (at 1500 m MSL) is still around 1 hPa, and the wind speed estimates are similar to those at 0600 LT. At 0900 LT, the maximum wind speeds at Almenar and Canelo look very similar (around 14 m s−1 at 1500 m MSL) and one may wonder whether there was indeed acceleration between Canelo and Almenar. We note, however, that if the parcel descended 500 m between these two sites, then its velocity at Canelo was about 9 m s−1 (at 2000 m MSL), in between the 5 m s−1 Manzano speed and the 14 m s−1 Almenar speed. In turn, the jet nose parcel at Canelo (at 1500 m MSL) may have continued its descending and accelerating downwind path, but in doing so, it must have felt the strong surface friction suggested by the 500-m shear-driven mixed layer present at Almenar (Fig. 8e), and therefore, for it, energy conservation is not applicable and boundary layer dissipation needs to be included.

The 1200 LT 24 July 2019 profiles (right column panels in Fig. 8) are close to the end of the raco event. Consequently, the pressure anomalies are about half of those in the previous profiles, although it is difficult to distinguish in the potential temperature profiles the possible vertical displacement that the parcel leaving the canyon may have experienced. Nonetheless, using a pressure anomaly difference of about 0.5 hPa between Manzano and Almenar and a speed of about 3 m s−1 at the entrance site, the exit speed would be about 10 m s−1, near the observed jet velocity at Almenar. The 2018 cases (Fig. 9) share characteristics of the 0900 LT 24 July 2019 case: potential temperature profiles separated between Almenar and Manzano suggesting a significant descent of the exit parcels and a mixed layer at the surface indicative of important friction. Despite the pressure anomalies being larger than in the 2019 case, the maximum wind speed at Almenar remains at about 15 m s−1. In 2018, the exit jet is located much closer to the surface than in 2019 and at the top of the shear-driven mixed layer, suggesting that surface friction is playing an important role in its dynamics.

5. Interaction with the cold pool

The hydraulic analysis of the previous section accounts for the acceleration and descent of the flow after passing through the narrows and heading toward the canyon exit. To be felt at the surface, however, the flow must erode and displace the CAP that developed over the valley during the night and which is evident by the strong surface inversion present at Almenar in the 0600 LT radiosonde (Fig. 8d). Indeed, as described by M2020, at a fixed surface point, the appearance of the raco wind occurs many times accompanied by a sudden increase in temperature and a decrease in absolute humidity, signaling the replacement of the cold and humid CAP by the dry and warm upper air that was forced down by the gap flow. The abrupt changes in temperature at the surface measured at three fixed sites (ALM, CRN, and LOB) together with those detected in the various mobile ceilometer transects allow the tracking of the CAP–raco front position in the period between 0200 and 1300 LT 24 July 2019, as shown in Fig. 11. During the night, the front moves westward from La Obra to Almenar with a speed around 0.25 m s−1, reaching about 1 km west of Almenar. After sunrise, the front becomes stationary for a couple of hours until 1100 LT when it recedes to the east at about 0.5 m s−1. This is the time also in which the MAN–LOB pressure difference begins to decrease (bottom panels in Fig. 8), due to the Maipo Canyon daytime warming. In this section, we address consecutively the mixing and erosion at the CAP top, the displacement of the CAP by the raco wind, and the equilibrium behind the stationary front that is eventually attained.

Fig. 11.
Fig. 11.

Position of the raco front at different times (red circles) for 24 Jul 2019. ALM, CRN, and LOB correspond to points with fixed temperature measurements. Other points are obtained from the mobile ceilometer measurements. The shaded area marks the nighttime period. The letters “S” and “C” mark times of soundings and ceilometer transects shown in Fig. 8 and Figs. 13 and 14, respectively. The abscissa coordinate is the distance along the route followed by the mobile ceilometer as shown in the inset.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

As seen in Fig. 11, the 0600 LT radiosonde at Almenar was launched around the time the raco wind arrived at the site (see also Fig. 4a), providing a unique opportunity to examine in more detail the complex mixing dynamics occurring at the CAP–raco frontal interface. The near-surface instability observed in the 0600 LT Almenar potential temperature profile (20°C above 21°C around 900 m MSL in Fig. 8d) hints to the active overturning taking place at this moment. In Fig. 12, we have used the raw 1-s radiosonde thermodynamic and position data of the 0600 LT Almenar radiosonde to plot instantaneous profiles measured in the lowest 200 m AGL. Figure 12a shows the instantaneous profiles of potential temperature and water vapor mixing ratio. The loops in the profiles are caused by the balloon being caught in a descending flow around 850 m MSL, which is clear in Fig. 12b where the computed vertical velocity of the sonde is shown. Despite the nominal 5 m s−1 buoyancy-driven ascending speed of the balloon, it descends instantaneously at a rate of up to 10 m s−1, pointing to the intense vertical motions occurring at the CAP–raco interface. After exiting the descending flow, the balloon ascends at about 10 m s−1 up to around 1200 m MSL, marking now a layer of intense (∼5 m s−1) flow ascent. Above that, the vertical velocity of the sonde stabilizes around its nominal value of 5 m s−1 (shown in Fig. 13a), leaving behind the region of strong vertical velocities of the flow. The large vertical velocities inferred for the flow from the sonde ascending speed are probably an instantaneous expression of the 15-min averages of vertical velocities exceeding 1 m s−1 during raco conditions measured by a sodar instrument in the 2018 IOP (M2020).

Fig. 12.
Fig. 12.

Instantaneous 1-s radiosonde data over ALM for 0600 LT 24 Jul 2019. (a) Potential temperature (red) and water vapor mixing ratio (blue) profiles. Circles at the bottom show surface values measured in the cold pool by the mobile ceilometer system. (b) Instantaneous vertical velocity of the sonde. The dashed vertical line marks the nominal 5 m s−1 ascent rate of the sonde. (c) Joint (θ, q) diagram of the profiles in (a). The q axis has been inverted to leave near-surface conditions at the bottom of the figure. (d) 10-s wind speed (bold line) computed by the sounding system and the instantaneous wind speed of the sonde (fine line). The oscillations in the latter are probably affected by the pendular movement of the sonde below the balloon.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

Fig. 13.
Fig. 13.

Cross sections along the raco front around 0635 LT 24 Jul 2019. (a) Reflectivity field measured with the mobile ceilometer in arbitrary units; high (low) reflectivity is mapped into cold (warm) colors. The horizontal axis s corresponds to the distance measured along the road, positive eastward and negative westward from ALM station. Vertical and horizontal axes are plotted with a 1:1 scale. Black bold lines depict the trajectory followed by the 0600 LT radiosonde launched at ALM: dashed line starts at the ALM site; the continuous line is shifted 300 m to the west (see text). Vertical velocities w annotated in the figure refer to those of the sonde (see also Fig. 12b). (b) Surface potential temperature (red; left scale) and water vapor mixing ratio (blue; right scale) measured together with the mobile ceilometer.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

The flow dynamics underlying the strong vertical velocity fluctuations of the 0600 LT radiosonde described above can be further visualized in Fig. 13a, where a cross section of the mobile ceilometer data is plotted for a transect performed across the raco front about 35 min after the radiosonde launch. The s coordinate in the abscissa is defined as the distance along the route followed by the truck, with s = 0 at the route point with the same longitude as Almenar station, positive values are to the east of Almenar, and negative values to the west where the CAP is located. The zonal extent of the plot is restricted to about 1500 m west of Almenar, so that the frontal region can be visualized using a 1:1 scale. To better convey the thermal contrast existing in the domain, the high ceilometer reflectivity of the polluted and humid CAP air has been mapped into blue colors, while the low reflectivity values of the clean raco air have been assigned warm colors. The surface potential temperature and water vapor mixing ratio measured concurrently with the ceilometer are shown in Fig. 13b. They allow the surface raco front at this time to be located at about s = −200 m. The type of ceilometer used in these measurements does not measure aerosols well in the layer very close to the surface (Kotthaus et al. 2016) missing the leading edge of the CAP air mass reaching the front, but from s = −400 m and westward, the ceilometer vividly depicts the large perturbations of the CAP–raco interface. The dashed black line shows the trajectory of the 0600 LT radiosonde when the front was near Almenar. The solid black line is the same trajectory but moved westward 300 m, accounting roughly for the different times of the sounding and the ceilometer transect. The ups and downs of the radiosonde trajectory in the first 300 m AGL appear to follow the CAP–raco interface, before leaving the perturbed zone around 1200 m MSL and acquiring the steady ascent rate provided by its buoyancy. In turn, the interface perturbations visualized by the ceilometer data resemble Kelvin–Helmholtz instabilities, and even a possible breaking wave can be appreciated at s = −800 m.

Returning attention back to the perturbed layer around 850 m MSL in Fig. 12a, large excursions of the potential temperature θ and water vapor mixing ratio q are measured there by the sonde. As in this setting these two variables can be considered conservative, the (θ, q) plot shown in Fig. 12c provides insight on the mixing taking place (Betts and Albrecht 1987). Indeed, the (θ, q) points of the perturbed region (loops in Fig. 12a) fall along a well-defined straight mixing line, suggesting that the various parcels probed by the sonde in this layer result from the mixing of two distinct air masses. Moreover, the mixing line appears to join conditions existing at around 900 m MSL (θ ∼ 22°C, q ∼ 1 g kg−1; see Fig. 12a) with those measured at the surface inside the CAP by the mobile ceilometer unit (θ ∼ 9°C, q ∼ 3 g kg−1; see Fig. 13b), showing that the strongly perturbed flow in the frontal zone is actively mixing the cool and humid surface CAP air with the warm and dry raco airmass aloft.

The possibility of mixing across a stably stratified flow layer of depth ΔZ in which potential temperature and wind speed changes are Δθ and ΔU, respectively, can be diagnosed with a Richardson number (Ri) computed as
Ri=gθΔθΔZΔU2,
where θ is the mean potential temperature and g is the acceleration of gravity. We use the vertical profiles in Figs. 12a and 12d to estimate Δθ ∼ 5 K and ΔU ∼ 5 m s−1 as values representing the differences between conditions above and below the mixing layer existing around 850 m MSL. The depth of the latter is estimated as ΔZ ∼ 50 m, which together with g = 9.8 m s−2 and θ ∼ 290 K produces an Ri ∼ 0.3. This value is close to the commonly used critical Richardson value of 0.25 allowing for the development of shear instabilities of a stably stratified fluid, which explains the vigorous perturbations of the CAP–raco interface observed at this time.
While the Richardson number analysis may account for the turbulent erosion of the CAP top, the actual removal of the CAP needs to consider the energy required to displace the dense air and replace it by the warmer and fast-moving air coming from aloft. To this aim, we follow Lareau and Horel (2015), who, in their idealized numerical simulations of CAP interaction with winds above it, examined the possibility of CAP removal by evaluating a so-called CAP Froude number as
Fr=UBH,
where U is the maximum wind speed above the CAP and BH is an integral measure of the buoyancy deficit of the CAP computed as
BH=g0H[θ(z)θ(H)]θ(H)dz,
where H is the CAP depth. They find that Kelvin–Helmholtz waves develop at the CAP top when Fr increases above unity and that for Fr > 2, these waves break down leading to rapid CAP erosion and removal. For the 0600 LT Almenar temperature sounding (Fig. 8d), we estimate BH ∼ 12 m2 s−2 for a 200-m-deep CAP layer. As the wind speed at the top of this layer was around 10 m s−1 (Fig. 8a), the computed CAP Froude number is about 3, consistent with the intense and effective CAP removal occurring in Almenar, as shown by the slow but steady westward movement of the CAP–raco front at this time (Fig. 11).

An expanded view of the CAP–raco interaction is shown in Fig. 14, which presents two ceilometer transects that crossed the frontal zone around 0800 and 0920 LT: the first turning north after the zonal stretch of the route west of Almenar (green path in Fig. 14c) and the second turning south and then west again (blue path in Fig. 14c). At the times of these transects, the front had moved westward and was quasi-stationary around s = −1.1 km (Figs. 11 and 14b,e). In both ceilometer cross sections (Figs. 14a,d), a clear distinction of the CAP structure can be noticed: a perturbed zone in the region directly confronting the Maipo Canyon exit corridor and a more quiescent CAP layer on the sides and farther away from the exit. The locations of the transition points along both paths have been marked with orange lines in the panels, while the location of the raco front is marked with a red line. Furthermore, it is clear in the ceilometer transects how the CAP deepens to the west, as a result of the topography sloping down in this direction. In light of the previous discussion, this deepening will increase the CAP buoyancy deficit, with the probable consequence that the further west the raco front moves, the harder it is for it to displace the CAP. This effect could explain that raco is much more frequent at La Obra than at Almenar (M2020) and that only few raco events are perceived farther west in the southeastern portion of the Santiago valley.

Fig. 14.
Fig. 14.

Cross sections of (a),(d)aerosol backscatter and (b),(e) surface potential temperature and water vapor mixing ratio for mobile ceilometer transects performed west of ALM around 0800 LT in (a) and (b) and 0920 LT in (d) and (e) on 24 Jul 2019. (c) The paths of the transects are shown in the map, together with the approximate locations of the raco front (red line and circle) and the boundaries between the perturbed and unperturbed CAP (orange lines).

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

The stationary front observed during 2–3 h after sunrise around s ∼ −1000 m (Fig. 11) can be envisioned as an equilibrium between the eastward pressure gradient force resulting from the CAP–raco density difference and the inertial force associated with the rapid easterly raco flow impinging into the front. The front speed c of a density current moving into a stationary environment is given by
c=2gHΔρρ,
where H is the depth of the density current, Δρ is the difference in densities of the flows, and ρ is the mean density (Markowski and Richardson 2010, p. 144). Alternatively, c can be interpreted as the speed of the environmental flow supporting a stationary front, which is approximately the raco situation. From Figs. 14a, 14b, 14d, and 14e, we estimate scales H ∼ 100 m and Δρ/ρ ∼ Δθ/θ ∼ 10/300, resulting in c ∼ 8 m s−1, which is comparable to a typical intensity of the raco wind near the surface. Thus, the establishment of a stationary raco front similar to that observed for a few hours in the current case is probably frequent.

6. Conclusions

Figure 15 shows a cartoon with the elements that our analysis suggests are relevant for the occurrence of the raco wind at the exit of the Maipo Canyon. In terms of topography, we showed that the Maipo basin is very much confined below 3000 m MSL, except on its western flank where a narrow gap is the only opening below 2200 m MSL. Between these two altitudes, a lateral ridge existing to the south of the gap widens the opening of the basin substantially. Synoptically, raco events are usually associated with enhanced regional subsidence, which produces a steady warming of the lower troposphere. This warming is, however, less marked inside the basin, and a pressure gradient results that forces air westward out of the basin. Enhanced radiative cooling or weaker subsidence inside the basin could explain this differential warming, which contrasts with the typical argument of differential cooling driving nocturnal valley exit jets (Zardi and Whiteman 2013).

Fig. 15.
Fig. 15.

Cartoon (not to scale) with elements deemed important in the development of raco winds (see text). The color palette, similar to that in Figs. 13 and 14, highlights the potential temperature difference between raco and CAP air masses. The top of the flowing layer is marked by a capping inversion, whereas its bottom may be the topographic surface or the top of the surface inversion layer.

Citation: Journal of Applied Meteorology and Climatology 63, 4; 10.1175/JAMC-D-23-0193.1

In passing through the gap, the exit flow may transition from subcritical-to-supercritical conditions, descending and accelerating as it moves further west into the southeastern portion of the Santiago valley. Near the surface, the raco wind encounters the cold-air pool existing over the valley defining what we call the raco front, where the strong shear induces intense mixing as attested by the Kelvin–Helmholtz-like perturbations observed in the ceilometer transects and the large vertical velocity perturbations derived from the radiosonde movement in Fig. 12b.

The conceptual model of the raco wind as a transitional hydraulic gap flow, first suggested by M2020, accounts for many of its characteristics: 1) The initial time of the raco at La Obra station does not show any preference during the night, which can be explained because the occurrence of the critical condition at the gap is controlled by multiple factors affecting the temperature difference between the Maipo Canyon and the Santiago valley; 2) the onset of raco at one site is commonly accompanied by temperature increases and drops in humidity, as the raco is able to erode and displace the cold-air pool (CAP); 3) the intensity of the raco is directly related to a pressure gradient developing along the exit corridor (M2020), which arises from differences in the temperature and depth of air masses across the gap; 4) soundings during raco events reveal the large asymmetry of the flow along the gap, a hallmark signature of hydraulic transitional flows; 5) the frequency of raco winds maximizes around La Obra and diminishes to the west, as only the stronger raco events are able to push the westerly deepening CAP sufficiently to the west; and 6) the raco wind intensity at a fixed site appears to be capped, which may be related to the southern lateral ridge in Figs. 6a and 15 precluding the in-basin cold air mass from becoming much deeper than the altitude of the ridge. Still, there remain open questions which may deserve further study. For example, supercritical flows downwind of a gap commonly end with a hydraulic jump (e.g., Drobinski et al. 2001), for which we have no evidence in the raco case. Perhaps the observations have simply not detected the jumps or the expansion of the raco wind upon leaving the Maipo Canyon atop the Santiago valley CAP makes a hydraulic jump unnecessary. Another pending issue is the nature of the mechanism(s) producing the differential warming mentioned above as the source of the pressure difference driving the raco wind. Future observational and modeling work may address these questions. Drobinski et al. (2001) attributed the small number of observational studies of gap flows to the “difficulty of being at the right time and in the right place” to observe them. The regularity of the raco wind and its high frequency of occurrence in the cold season (M2020) make it an ideal study case for improving the understanding of gap flows.

Acknowledgments.

We thank three reviewers, Georg Mayr, and C. David Whiteman for suggestions that improved the paper and Dale Durran for clarifying for us the application of Eq. (A2) under hydrostatic conditions. We thank Mark Falvey for his help in producing Fig. 1 and him, Andrés Arriagada, and Andrés Martínez for the deployment of the mobile ceilometer. We thank the several students taking part in the IOP and the Almenar and Manzano schools and Canelo fire station that made their facilities available for the measurements. RM acknowledges the support of FONDECYT Grants ANID-Chile 1170214 and 1221511. LA acknowledges the support of the Scripps Institution of Oceanography and Lucky Larry’s Auto Repair.

Data availability statement.

The data are available from the authors upon request.

APPENDIX

Parcel Energy Conservation

Conservation of energy for an air parcel can be expressed in terms of the Bernoulli function:
B=cpT+K+gz,
where K= (1/2)(u2 + υ2 + w2) is the kinetic energy per unit mass of the parcel (u, υ, and w are the Cartesian components of its velocity), T is its temperature, z is its altitude, cp is the specific heat at constant pressure of air, and g is the acceleration of gravity (cf. Gaberšek and Durran 2004). In steady and inviscid conditions, parcels conserve B so that
dBds=0=cpdTds+dKds+gdzds,
where the derivatives are made with respect to a curvilinear distance coordinate s, measured along the parcel trajectory (identical to a streamline in steady conditions). If the parcel conserves also potential temperature, it can be readily shown that
dTds=1cpρdpds,
where ρ is the parcel density.
Combining Eqs. (A2) and (A3), we can solve for the rate of change of the kinetic energy of the parcel as a function of its altitude and pressure change:
dKds=gdzds1ρdpds.
In a hydrostatic environment, there is a large amount of cancellation between the two terms in the right-hand side of Eq. (A4): as a parcel descends (dz/ds < 0), its pressure increases (dp/ds > 0). The pressure rate of change can be computed with the help of partial derivatives as
dpds=pxdxds+pzdzds=pxdxdsρgdzds,
where the hydrostatic condition was used in the last step and we assumed that the parcel moves only in the (x, z) plane. Replacing Eq. (A5) in Eq. (A4), the altitude change terms cancel out and we obtain
dKds=1ρpxdxds,
where the partial derivative is taken at constant z. At this point, it is convenient to decompose the pressure field in an average profile varying only with z and an anomaly part allowing for the change of pressure in the flow direction x:
p(x,z)=p¯(z)+p(x,z),
so that Eq. (A6) is now
dKds=1ρpxdxds.
In turn, the rate of change of p′ along the trajectory can be evaluated as
dpds=pxdxds+pzdzds,
from which Eq. (A8) is transformed into
dKds=1ρ(dpdspzdzds),
which has the advantage of explicitly including the effect of altitude variations in the change of the kinetic energy of the parcel. If the trajectory is horizontal, then dz/ds = 0 and
dKds=1ρdpds,
which can be integrated between an initial condition (subscript i) and a final condition (subscript f) to get
KfKi=1ρo[pi(z)pf(z)],
where a constant reference density ρo has been considered, and the pressure perturbations are computed at the constant altitude z of the parcel. Equation (A12) is equivalent to Eq. (11) of Gaberšek and Durran (2004), who emphasized its validity just for horizontal flow.
In the raco flow, air parcels may have an altitude drop along their trajectories, so that we seek now an extension of Eq. (A12) for such a case. When the parcel varies its altitude along the trajectory, the second term in the parenthesis of Eq. (A10) is not necessarily zero, and to compute the kinetic energy change, one needs to know the spatial structure of the pressure anomaly and the path followed by the parcel. From our observations (bottom panels in Figs. 8 and 9), we consider a simple spatial structure for the pressure anomalies described by
p(x,z)=PoxL(1zH),
where x is a horizontal coordinate with origin at the gap (near Canelo in our case) and increasing downwind (westward in our case), Po is the near-surface pressure anomaly difference between upstream and downstream points (Manzano and Almenar sites, in our case) separated by a distance L, and H is the depth of the flowing layer. Replacing Eq. (A13) in Eq. (A10), we obtain
dKds=1ρ(dpdsPoLHdzdsx).
To integrate Eq. (A14), we still need to know the variation of the trajectory slope dz/ds, along the parcel path, for which we have no information. In the case of a rectilinear path, dz/ds is constant and the integral of the second term in the right-hand side of Eq. (A14) vanishes when computed between points symmetric across the gap (x = −L/2 and x = +L/2). In this case, the change in the kinetic energy of the parcel is
KfKi=1ρo[pi(zi)pf(zf)],
where now, as compared to Eq. (A12), the pressure anomalies are those at the initial and final altitudes of the trajectory. The constant trajectory slope is probably not a very realistic assumption, as the asymmetry of the gap flow suggests that parcels may descend faster downwind of the gap. In this case, Eq. (A15) would be an overestimation, but we still will use it as a simple first approximation to the increase in kinetic energy of the parcels crossing the gap.

REFERENCES

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    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
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    • Search Google Scholar
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    • Search Google Scholar
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  • Armi, L., 1986: The hydraulics of two flowing layers with different densities. J. Fluid Mech., 163, 2758, https://doi.org/10.1017/S0022112086002197.

    • Search Google Scholar
    • Export Citation
  • Baasandorj, M., and Coauthors, 2017: Coupling between chemical and meteorological processes under persistent cold-air pool conditions: Evolution of wintertime PM2.5 pollution events and N2O5 observations in Utah’s Salt Lake Valley. Environ. Sci. Technol., 51, 59415950, https://doi.org/10.1021/acs.est.6b06603.

    • Search Google Scholar
    • Export Citation
  • Betts, A. K., and B. A. Albrecht, 1987: Conserved variable analysis of the convective boundary-layer thermodynamic structure over the tropical oceans. J. Atmos. Sci., 44, 8399, https://doi.org/10.1175/1520-0469(1987)044<0083:CVAOTC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Colle, B. A., and C. F. Mass, 2000: High-resolution observations and numerical simulations of easterly gap flow through the Strait of Juan de Fuca on 9–10 December 1995. Mon. Wea. Rev., 128, 23982422, https://doi.org/10.1175/1520-0493(2000)128<2398:HROANS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Drobinski, P., J. Dusek, and C. Flamant, 2001: Diagnostics of hydraulic jump and gap flow in stratified flows over topography. Bound.-Layer Meteor., 98, 475495, https://doi.org/10.1023/A:1018703428762.

    • Search Google Scholar
    • Export Citation
  • Falvey, M., and R. Garreaud, 2007: Wintertime precipitation episodes in central Chile: Associated meteorological conditions and orographic influences. J. Hydrometeor., 8, 171193, https://doi.org/10.1175/JHM562.1.

    • Search Google Scholar
    • Export Citation
  • Flamant, C., and Coauthors, 2002: Gap flow in an Alpine valley during a shallow south föhn event: Observations, numerical simulations and hydraulic analogue. Quart. J. Roy. Meteor. Soc., 128, 11731210, https://doi.org/10.1256/003590002320373256.

    • Search Google Scholar
    • Export Citation
  • Flores, F., A. Arriagada, N. Donoso, A. Martínez, A. Viscarra, M. Falvey, and R. Schmitz, 2020: Investigation of a nocturnal cold-air pool in a semiclosed basin located in the Atacama Desert. J. Appl. Meteor. Climatol., 59, 19531970, https://doi.org/10.1175/JAMC-D-19-0237.1.

    • Search Google Scholar
    • Export Citation
  • Gaberšek, S., and D. R. Durran, 2004: Gap flows through idealized topography. Part I: Forcing by large-scale winds in the nonrotating limit. J. Atmos. Sci., 61, 28462862, https://doi.org/10.1175/JAS-3340.1.

    • Search Google Scholar
    • Export Citation
  • Garner, J. M., and C. E. Kovacik, 2023: Extreme wildfire environments and their impacts occurring with offshore-directed winds across the Pacific coast states. Wea. Climate Soc., 15, 7593, https://doi.org/10.1175/WCAS-D-22-0043.1.

    • Search Google Scholar
    • Export Citation
  • Garreaud, R., and J. Rutllant, 2006: Meteorological factors of the air pollution in Santiago (in Spanish). Critical Episodes of Air Pollution in Santiago, R. Morales, Ed., Universitaria, 36–53.

  • Garreaud, R., J. Rutllant, and H. Fuenzalida, 2002: Coastal lows along the subtropical west coast of South America: Mean structure and evolution. Mon. Wea. Rev., 130, 7588, https://doi.org/10.1175/1520-0493(2002)130<0075:CLATSW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Green, M. C., J. Xu, and N. Adhikari, 2008: Transport of atmospheric aerosol by gap winds in the Columbia River gorge. J. Appl. Meteor. Climatol., 47, 1526, https://doi.org/10.1175/2007JAMC1561.1.

    • Search Google Scholar
    • Export Citation
  • Haid, M., A. Gohm, L. Umek, H. C. Ward, and M. W. Rotach, 2022: Cold-air pool processes in the Inn Valley during föhn: A comparison of four cases during the PIANO campaign. Bound.-Layer Meteor., 182, 335362, https://doi.org/10.1007/s10546-021-00663-9.

    • Search Google Scholar
    • Export Citation
  • Henderson, F. M., 1966: Open Channel Flow. Prentice Hall, 522 pp.

  • Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 19992049, https://doi.org/10.1002/qj.3803.

    • Search Google Scholar
    • Export Citation
  • Holbach, H. M., and M. A. Bourassa, 2014: The effects of gap-wind-induced vorticity, the monsoon trough, and the ITCZ on east Pacific tropical cyclogenesis. Mon. Wea. Rev., 142, 13121325, https://doi.org/10.1175/MWR-D-13-00218.1.

    • Search Google Scholar
    • Export Citation
  • Hong, X., M. Peng, S. Wang, and Q. Wang, 2018: Simulating and understanding the gap outflow and oceanic response over the Gulf of Tehuantepec during GOTEX. Dyn. Atmos. Oceans, 82, 119, https://doi.org/10.1016/j.dynatmoce.2018.01.003.

    • Search Google Scholar
    • Export Citation
  • Hornsteiner, M., 2005: Local foehn effects in the upper Isar Valley, part 1: Observations. Meteor. Atmos. Phys., 88, 175192, https://doi.org/10.1007/s00703-003-0073-4.

    • Search Google Scholar
    • Export Citation
  • Hornsteiner, M., and G. Zängl, 2006: Local foehn effects in the upper Isar Valley, part 2: Numerical simulations. Meteor. Atmos. Phys., 91, 6383, https://doi.org/10.1007/s00703-004-0107-6.

    • Search Google Scholar
    • Export Citation
  • Ito, J., T. Nagoshi, and H. Niino, 2019: A numerical study of “Hijikawa-arashi”: A thermally driven gap wind visualized by nocturnal fog. J. Appl. Meteor. Climatol., 58, 12931307, https://doi.org/10.1175/JAMC-D-18-0189.1.

    • Search Google Scholar
    • Export Citation
  • Jackson, P. L., G. Mayr, and S. Vosper, 2013: Dynamically-driven winds. Mountain Weather Research and Forecasting: Recent Progress and Current Challenges, F. K. Chow, S. F. J. D. Wekker, and B. J. Snyder, Eds., Springer, 121–218.

  • King, C. W., 1989: Representativeness of single vertical wind profiles for determining volume flux in valleys. J. Appl. Meteor., 28, 463466, https://doi.org/10.1175/1520-0450(1989)028<0463:ROSVWP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kotthaus, S., E. O’Connor, C. Münkel, C. Charlton-Perez, M. Haeffelin, A. M. Gabey, and C. S. B. Grimmond, 2016: Recommendations for processing atmospheric attenuated backscatter profiles from Vaisala CL31 ceilometers. Atmos. Meas. Tech., 9, 37693791, https://doi.org/10.5194/amt-9-3769-2016.

    • Search Google Scholar
    • Export Citation
  • Lackman, G. M., and J. E. Overland, 1989: Atmospheric structure and momentum balance during a gap-wind event in Shelikof Strait, Alaska. Mon. Wea. Rev., 117, 18171833, https://doi.org/10.1175/1520-0493(1989)117<1817:ASAMBD>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Lareau, N. P., and J. D. Horel, 2015: Dynamically induced displacements of a persistent cold-air pool. Bound.-Layer Meteor., 154, 291316, https://doi.org/10.1007/s10546-014-9968-5.

    • Search Google Scholar
    • Export Citation
  • Li, X., K. Zhao, S. Zhong, X. Yu, Z. Feng, Y. Zhong, A. Maulen, and S. Li, 2023: Evolution of meteorological conditions during a heavy air pollution event under the influence of shallow foehn in Urumqi, China. Adv. Atmos. Sci., 40, 2943, https://doi.org/10.1007/s00376-022-1422-x.

    • Search Google Scholar
    • Export Citation
  • Markowski, P., and Y. Richardson, 2010: Mesoscale Meteorology in Midlatitudes. Wiley-Blackwell, 407 pp.

  • Mayr, G. J., and L. Armi, 2008: Föhn as a response to changing upstream and downstream air masses. Quart. J. Roy. Meteor. Soc., 134, 13571369, https://doi.org/10.1002/qj.295.

    • Search Google Scholar
    • Export Citation
  • Mayr, G. J., and Coauthors, 2007: Gap flows: Results from the Mesoscale Alpine Programme. Quart. J. Roy. Meteor. Soc., 133, 881896, https://doi.org/10.1002/qj.66.

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  • Fig. 1.

    (a) Regional topography of the Santiago valley and surroundings. Santiago city is shown as a gray area. SCL marks the Santiago airport. The red and black line shows the boundary of the Maipo basin as defined in the text. The red section and points N and S refer to elements in Fig. 6. The black box shows the region of the Maipo Canyon gap enlarged in (b). The inset shows the location of the region in southern South America (red box), with gray shading for altitudes above 3000 m MSL. (b) Zoom view of the exit corridor of the Maipo basin. Colored circles mark the position of measurement sites: ALM, LOB, CAN, and MAN. An X mark near ALM shows the location of a fixed thermometer installed at a CRN. Colored lines show the trajectory of the radiosonde balloons launched on 0600 LT 24 Jul 2019. Numbers near the trajectories indicate the altitude (m MSL) of major direction changes. Gray altitude contours are shown every 500 m.

  • Fig. 2.

    View of the topographic constriction as seen from CAN (in Fig. 1) looking up canyon to the east. Photograph by Patricio Aceituno.

  • Fig. 3.

    Sea level pressure (colored contours are labeled in hPa) and 500-hPa geopotential heights (bold black contours are labeled in m) derived from the ERA5 reanalysis for the region of South America and the southeast Pacific. Fields are shown for 1200 UTC (a) 24 and (b) 25 Jul 2019. Red dots mark the location of the Santiago valley.

  • Fig. 4.

    Time series of 5-min surface variables measured at LOB (blue) and ALM (red) stations during 23–24 Jul 2019. (a) Gust intensity (continuous; left axis) and wind direction (dots; right axis). (b) Air temperature. (c) Water vapor mixing ratio. Nighttime periods are marked with a gray background. Black dashed lines indicate the times of radiosondes shown in Fig. 8.

  • Fig. 5.

    Vertical and time evolution of (left) zonal wind and (right) temperature for 23–24 Jul 2019. Vertical dashed lines indicate midnight. Stars indicate radiosonde launching times. (a) Zonal wind at Manzano. Contours are every 2 m s−1, and the white contour marks the zero value. (b) Difference between the temperature at Manzano and that above the Santiago valley as represented by the AMDAR data. Contours are every 1°C, and the white contour marks the zero value. (c) As in (a), but for CAN. (d) As in (b), but for CAN. (e) As in (a), but for ALM. (f) As in (b), but for ALM. (g) Zonal wind of AMDAR data taken as representing Santiago valley conditions. Contours are every 2 m s−1, and the white contour marks the zero value. (h) As in (g), but for temperature. Contours are every 2°C. White boxes in (e) and (f) are due to a truncated radiosonde at ALM.

  • Fig. 6.

    (a) Surface elevation of points along the edge of the Maipo basin as defined in section 2. The abscissa axis shows the horizontal distance measured clockwise along the basin edge with 0 at the gap. Only 80 km around the gap are shown (red section of the basin edge in Fig. 1a). The points S and N are reference points marked in Fig. 1a. Height annotations for MAN and CAN are discussed in section 4c(1). (b) Schematics of topographic parameters of a semienclosed basin as a function of altitude z: lateral exit cross-sectional area L, horizontal drainage area A, and enclosed volume V. (c) Values of the parameters for the Maipo basin.

  • Fig. 7.

    (a) Zonal wind measured at CAN at 0600 LT 24 Jul 2019. (b) Discharge rate through the lateral opening of the basin. (c) Mean subsidence needed to compensate the outflow rate. Shading marks the variation of each parameter if the mean outflow velocity through the lateral opening ranges from 70% to 100% of the actual zonal wind measured at CAN.