Midday Boundary-Layer Collapse in the Altiplano Desert: The Combined Effect of Advection and Subsidence

Abstract

Observations in the Altiplano region of the Atacama Desert show that the atmospheric boundary layer (ABL) suddenly collapses at noon. This rapid decrease occurs simultaneously to the entrance of a thermally driven, regional flow that causes a rise in wind speed and a marked temperature decrease. We identify the main drivers that cause the observed ABL collapse by using a land–atmosphere model. The free atmosphere lapse rate and regional forcings, such as advection of mass and cold air as well as subsidence, are first estimated by combining observations from a comprehensive field campaign and a regional model. Then, to disentangle the ABL collapse, we perform a suite of numerical experiments with increasing level of complexity: from only considering local land–atmosphere interactions, to systematically including the regional contributions of mass advection, cold air advection, and subsidence. Our results show that non-local processes related to the arrival of the regional flow are the main factors explaining the boundary-layer collapse. The advection of a shallower boundary layer ($\approx -250$ m h$^{-1}$ at noon) causes an immediate decrease in the ABL height (h) at midday. This occurs simultaneously with the arrival of a cold air mass, which reaches a strength of $\approx -4$ K h$^{-1}$ at 1400 LT. These two external forcings become dominant over entrainment and surface processes that warm the atmosphere and increase h. As a consequence, the ABL growth is capped during the afternoon. Finally, a wind divergence of $\approx 8 \times 10^{-5}$ s$^{-1}$ contributes to the collapse by causing subsidence motions over the ABL from 1200 LT onward. Our findings show the relevance of treating large and small-scale processes as a continuum to be able to understand the ABL dynamics.

1 Introduction

The atmospheric boundary layer (ABL) evolves throughout the day when convection mixes air vertically, which results from mechanical turbulence and surface heating driven by the diurnal solar cycle (Min et al. 2020). When the incoming shortwave radiation begins to increase, the surface warms and turbulent eddies transport heat that cause the ABL to increase its temperature and height. When the incoming shortwave radiation starts to decline, the ABL growth slows down and reaches a quasi-steady state due to the lack of surface fluxes (Garratt and Brost 1981). This locally driven ABL evolution is canonical and it can be disrupted by non-local phenomena, such as advection and subsidence that are associated by meso- or synoptic scales, and are influenced by complex topographies. Muñoz et al. (2022) analyzed the ABL dynamics in the semi-arid valley of central Chile using meteorological data gathered at a local airport, radiosondes and reanalysis data. They found that the ABL warming is not only explained by the surface fluxes but also by an intense diurnal subsidence. Pietersen et al. (2015) quantified the contributions of heat and moisture advection, and subsidence, to the ABL height (h) in a French plateau located at the foot of the Pyrenees Mountain. Their findings showed that ignoring large-scale forcing can cause an overestimation of h of about 70%. Khodayar et al. (2008) studied the ABL diurnal variability in the Elqui Valley, in the North of Chile, and the coastal ABL nearby. They found that the ABL development in the Elqui Valley is controlled by surface fluxes during the morning, while during the late afternoon it is dominated by a cold air advection originated in the Pacific Ocean.

Although advection of temperature and moisture has been recognized has an important forcing term in the ABL development, fewer studies have considered the impact of the ABL-height- or ABL-mass advection (from hereon we will just use the term mass advection or $h_{adv}$). Mass advection is a measure of the advected volume within the mixed layer (Stull 1988; Willis and Deardorff 1976) and can be estimated from the h-gradient between two sites (Kossmann et al. 1998). It represents the displacement of an external boundary layer that can be shallower ($h_{adv}$ < 0 m s$^{-1}$) or deeper ($h_{adv}$ > 0 m s$^{-1}$) than the ABL of the point of interest. Several studies discuss mass advection as an important term in complex terrains such as urban areas and mountainous regions without quantifying it (e.g, Pal et al. 2021; Pal and Lee 2019; Angevine et al. 2003; Pal and Haeffelin 2015; De Wekker and Kossmann 2015). Only a few studies quantify the ABL mass advection tendency. One example is Kossmann et al. (1998), who include $h_{adv}$ in the prognostic equation of the ABL height for a hilly terrain between the Upper Rhine valley and the Northern Black Forest in Europe and estimate it to be $-$0.2 m s$^{-1}$ during the afternoon.

In this study we focus on the Altiplano region, where the ABL also does not follow the canonical ABL description. The Altiplano corresponds to a high plateau composed by semi-arid and endorheic basins, which are immersed in a complex mountain terrain (Fig. 1). Here, a sudden atmospheric boundary layer (ABL) collapse is observed between 1200 and 1500 LT (local time = UTC - 3 h) (-330 m h$^{-1}$, Fig. 2a). Surface observations in the Salar del Huasco (Suárez et al. 2020), an arid basin in the Chilean Altiplano in the Atacama Desert (see Fig. 1), show a sudden increase in wind speed (Fig. 2b) and a marked decrease in temperature (Fig. 2c) at the same time over the desert surface. Contradictory to the ABL collapse at 1200 LT, an increase in sensible heat flux (H) is also observed until 1500 LT (Fig. 2d). The origin of the temperature decrease, ABL collapse and rise in H is a thermally driven atmospheric flow, caused by the thermal contrast between the Pacific Ocean and the desert land surface, which arrives to the region every afternoon (Muñoz et al. 2018; Falvey and Garreaud 2005; Rutllant et al. 2003). The advection of this air mass is accompanied by a large increase in the wind and the transport of cold and dry air from the coastal desert into the Altiplano (Lobos-Roco et al. 2021; Garreaud et al. 2003). These two factors lead to enhanced mechanical turbulence and a rise in the surface-atmosphere temperature gradient, which causes H to increase until its maximum value is reached at 1500 LT, 1.5 h delayed compared to solar noon (see Fig. 17 in Appendix 2). In contrast to the more well-known surface fluxes regimes that are limited by radiation or soil moisture, the surface fluxes in the Altiplano desert are dominated by wind.

Fig. 1

General geographical localization of the Atacama Desert (dark brown), the Altiplano region (light brown), and Salar del Huasco (black box). Black lines indicate the altitude level every 250 m

Fig. 2

Surface and boundary-layer conditions over the Atacama Desert at the end of the dry season. a Potential temperature vertical profiles at 1200, 1500 and 1800 LT during 22 November 2018, a day that is representative for the end of the dry season; and diurnal variability of b wind speed at 2-m height; c temperature at 2-m height; and d surface energy balance: net radiation (RN), ground heat flux (G), sensible heat flux (H) and latent heat flux (LE). All observations were collected during a field experiment at the Salar del Huasco in the Altiplano region of the Atacama Desert (Suárez et al. 2020) and measured over the desert surface. Horizontal dashed lines on a indicate the boundary-layer height. Vertical dashed lines on b–d indicate the time when the regional air mass arrives at the Salar del Huasco, while shadows represent standard deviations of 10 days data

Although the impacts of the regional flow have been studied over temperature and wind in the Altiplano, the implications of this regional circulation on the ABL dynamics have not been systematically analyzed. Therefore, this research aims to identify the main drivers that cause the ABL to collapse at noon in the Altiplano region of the Atacama Desert, with the novelty of quantifying the mass advection and combining it with other regional forcing to analyze their independent impact over the ABL dynamics. The study will address the following question: How do local (surface-atmosphere interactions and entrainment) and non-local processes (advection and subsidence) contribute to the surface and atmospheric boundary-layer dynamics in the Altiplano region?

The Salar del Huasco, located in the Chilean Altiplano, is our study site where we performed a field experiment with surface and airborne observations. For the analysis, a conceptual land–atmosphere model will be used to identify the leading processes of the potential temperature evolution and boundary-layer tendencies over the desert surface. The strategy consists of first estimating the terms that need to be prescribed in the model (e.g. advection and subsidence) from observations and the support of a regional model. Then, we perform a suite of systematic numerical experiments with an increasing level of complexity to determine the impact of each process on the surface, the ABL average potential temperature ($\overline{\theta }$) and the ABL height diurnal evolution. The descriptions of the land–atmosphere model, the field observations, the regional model and the experiments are presented in Sect. 2. Section 3 details the approach to calculate the terms that need to be prescribed in the land–atmosphere model, and the results of their estimation. Next, Sect. 4 presents the results for the surface and ABL dynamics when systematically including the non-local processes. Finally, Sect. 5 summarizes the main conclusions and future perspectives of this research.

2 Methods

The strategy for this research consists of using the Chemistry Land-surface Atmosphere Soil Slab (CLASS) model (Vilà-Guerau de Arellano et al. 2015) to analyze the major contributors to the heat and boundary-layer tendencies. CLASS allows to break down the complexities of the land–atmosphere interactions over a given surface (in our case a desert). However, external processes to the model such as non-local phenomena need to be prescribed. For estimating the prescribed terms, we use observations gathered over the desert surface during a field experiment at the Salar del Huasco (Suárez et al. 2020) and a regional model in WRF [Weather and Research Forecasting (Skamarock et al. 2008)]. Section 2.1 presents the CLASS model, while Sect. 2.2 describes the study site and the observations, and Sect. 2.3 the WRF model. Finally, Sect. 2.4 explains the research approach by defining the experiments to be performed in CLASS.

2.1 Land–Atmosphere Conceptual Model

CLASS represents the essential processes describing the land–atmosphere interaction. It accounts for processes occurring at the surface and atmospheric forcing, as well as their feedbacks, to model the ABL dynamics. Therefore, the model allows an easy understanding of the boundary-layer main drivers (Fig. 3) to interpret observations and to break down the complexity of the land–atmosphere interactions by analyzing them term by term.

To represent the surface and ABL dynamics, CLASS estimates the radiation balance, the surface energy balance, the atmospheric surface layer and the ABL processes as follows:

• 1. Radiation balance: net radiation (RN) is estimated as the balance of longwave and shortwave components (Fig. 3). The incoming longwave radiation ($L_{in}$) and the outgoing longwave radiation ($L_{out}$) are estimated based on the Stefan–Boltzmann law. $L_{in}$ is calculated from the temperature at the top of the atmospheric surface layer (10% of h), while $L_{out}$ depends on the surface temperature. Regarding the shortwave components, the incoming shortwave radiation ($S_{in}$) is a function of latitude, longitude and time of the year, and the outgoing shortwave radiation ($S_{out}$) is dependent on the surface albedo.

• 2. Surface energy balance: CLASS represents the soil moisture and temperature transport using two soil layers and the force-restore method (Noilhan and Mahfouf 1996). The energy partitioning at the land-surface is represented using the Penman–Monteith equation (Monteith 1965). Therefore, H and latent heat fluxes (LE) are estimated by using the concept of aerodynamic resistances.

• 3. Atmospheric surface layer: the surface layer that connects the surface fluxes and the atmospheric variables is described by the Monin–Obukhov similarity theory (Monin and Obukhov 1954).

• 4. ABL dynamics: the mixed-layer theory is applied to a slab layer, which means that potential temperature ($\theta$), specific humidity (q) and wind components can be assumed constant with height (Tennekes and Driedonks 1981; Tennekes 1973; Lilly 1968). Taking $\theta$ as an example (Fig. 3), the entrainment of heat into the ABL is parameterized at the top of the mixed layer by a potential temperature jump ($\Delta \theta$), while the free troposphere conditions, which we refer to as upper layer (UL) (Fig. 3), are described by a constant lapse rate ($\gamma _\theta$).

CLASS also estimates the water and carbon exchange between the surface and the atmosphere to represent the leaf and canopy dynamics. Over the desert surface in the Altiplano region of the Atacama Desert those dynamics are irrelevant as there are no plants and little water is available in the hyper arid conditions. In our formulation of CLASS and presentation of results we will therefore only focus on the heat fluxes, the $\overline{\theta }$ evolution and the ABL growth. A more complete formulation of the coupled land–atmosphere system in CLASS can be found in Vilà-Guerau de Arellano et al. (2015) and in van Heerwaarden and Teuling (2014).

Fig. 3

CLASS conceptual model scheme for a desert surface, where the moisture budget is negligible. Main processes and variables involved in the development of the surface and ABL under the mixed-layer theory are represented, including the land–atmosphere interactions, advection processes, free troposphere conditions, entrainment fluxes and subsidence processes

In CLASS, it is possible to include the impact of both local and non-local processes on the heat and ABL height dynamics. In our case we refer to non-local phenomena as the processes acting at a regional scale ($\approx$ 150 km). The average potential temperature tendency ($\frac{\delta \overline{\theta }}{\delta t}$) is calculated as follows:

$$\begin{aligned} \frac{\delta \overline{\theta }}{\delta t} = \frac{(\overline{w'\theta '})_s-(\overline{w'\theta '})_e}{h} + \theta _{adv,ABL}, \end{aligned}$$

(1)

where $(\overline{w'\theta '})_s$ is the surface heat flux, $(\overline{w'\theta '})_e$ the entrainment heat flux, h the ABL height and $\theta _{adv,ABL}$ the ABL average heat advection. While $(\overline{w'\theta '})_s$, $(\overline{w'\theta '})_e$ and h are terms estimated internally by CLASS, $\theta _{adv,ABL}$ is a horizontal flux (Fig. 3) considered as an external term to the model that must be prescribed.

In general, horizontal advection of a generic variable can be estimated in one point by combining in a single term the wind and horizontal gradients as follows:

$$\begin{aligned} \Psi _{adv} = -\left( u \frac{\delta \Psi }{\delta x} + v\frac{\delta \Psi }{\delta y}\right) , \end{aligned}$$

(2)

where $\Psi$ is a generic variable, and u and v the horizontal wind components. We define u positive eastward and v positive northward. We will use Eq. 2 for $\Psi$ = $\theta$ and h. The strategy for estimating these advection terms is described in Sect. 3.

In the desert, we assume buoyancy is only driven by the sensible heat flux as moisture is negligible (< 1% of contribution to the buoyancy flux). Therefore, the virtual heat flux $(\overline{w'\theta '_v})$ and the virtual potential temperature jump ($\Delta \theta _v$) are approximated to $(\overline{w'\theta '_v})$ $\approx$ $(\overline{w'\theta '})$ and $\Delta \theta _v$ $\approx$ $\Delta \theta$. The surface heat flux, $(\overline{w'\theta '})_s$, is estimated from the land-surface module of CLASS. The entrainment flux, $(\overline{w'\theta '})_e$, is estimated as a fraction of the surface flux:

$$\begin{aligned} (\overline{w'\theta '})_e = -\beta (\overline{w'\theta '})_s, \end{aligned}$$

(3)

where $\beta$ is a constant usually considered with a value of 0.2 (Wouters et al. 2019; Stull 1988, 1976; Tennekes 1973).

The ABL height is estimated from its tendency ($\frac{\delta h}{\delta t}$), which is calculated as:

$$\begin{aligned} \frac{\delta h}{\delta t} = w_e + w_s + h_{adv}, \end{aligned}$$

(4)

where $w_e$ is the entrainment velocity, $w_s$ the subsidence vertical velocity and $h_{adv}$ is the mass advection (Kossmann et al. 1998).

The entrainment velocity, $w_e$, is defined by the ratio between $(\overline{w'\theta '})_e$ and $\Delta \theta$ at the inversion zone as:

$$\begin{aligned} w_e = - \frac{(\overline{w'\theta '})_e}{\Delta \theta } = \beta \frac{ (\overline{w'\theta '})_s}{{\Delta \theta }}. \end{aligned}$$

(5)

In CLASS, $\Delta \theta$ is defined by a height-dependent lapse rate ($\gamma _\theta$) in the overlying upper layer and $\overline{\theta }$ (Fig. 3). The UL represents a residual layer in the morning that afterwards blends into the free troposphere. The potential temperature jump is also influenced by the heat advection in the UL ($\theta _{adv,UL}$). Then the model estimates $\Delta \theta$ from:

$$\begin{aligned} \frac{\delta \Delta \theta }{\delta t} = \gamma _\theta w_e - \frac{\delta \overline{\theta }}{\delta t} + \theta _{adv,UL}. \end{aligned}$$

(6)

By using Eq. 1, $\frac{\delta \overline{\theta }}{\delta t}$ is internally estimated by the model. The entrainment velocity, $w_e$, is calculated from Eq. 5. The lapse rate $\gamma _\theta$ and the heat advection in the upper layer, $\theta _{adv,ABL}$, are external terms that need to be prescribed in CLASS. Section 3 presents the approach for their estimation.

The subsidence velocity, $w_s$, is defined as:

$$\begin{aligned} w_s = -Div (\vec {U_h})h, \end{aligned}$$

(7)

where h is estimated by the model (Eq. 4) and $Div(\vec {U_h})$ is the divergence of the mean horizontal wind ($\vec {U_h}$). The wind divergence is characterized by regional phenomena, and it is an external term that needs to be prescribed in CLASS (see Sect. 3). Equation 7 ensures $w_s$ equals zero at the surface and increases with height as the core of the high-pressure system at high levels is approached (Pietersen et al. 2015; Lilly 1968).

Finally, the mass advection, $h_{adv}$, is calculated by using Eq. 2 with $\Psi =h$. This term represents the displacement of an external boundary layer due to wind, which can be a shallower ABL ($h_{adv}$ < 0 m s$^{-1}$) or a deeper ABL ($h_{adv}$ > 0 m s$^{-1}$), as explained in Sect. 1. The strategy for its estimation is presented in Sect. 3. Note that, even though $\theta _{adv}$ and $h_{adv}$ are linked to the same advection event, they are different processes with different impacts on the ABL dynamics. While heat advection indirectly influences h through $w_e$ by affecting the mixed layer (Eqs. 1, 4–6), the mass advection has a direct impact on h (Eq. 4). Therefore, $h_{adv}$ is able to cause an immediate decrease in the ABL height, when $h_{adv}$ < 0 m s$^{-1}$, while for $\theta _{adv}$ it typically takes more time to influence h. Thus, the advection terms need to be estimated individually and we will evaluate their impact on the ABL dynamics independently from each other.

In summary, the surface and the ABL dynamics over a desert surface are affected by the local flux exchange between the surface and the atmosphere ($(\overline{w'\theta '})_s$), the upper free atmospheric conditions ($\gamma _\theta$), advection processes at both local and regional scale ($\theta _{adv}$ and $h_{adv}$), and by a regional wind divergence ($Div (\vec {U_h})$). While $(\overline{w'\theta '})_s$ is calculated internally by the model, $\gamma _\theta$, $\theta _{adv}$, $h_{adv}$ and $Div(\vec {U_h})$ are terms that need to be previously estimated and then prescribed in CLASS. Section 3 describes the approach for estimating these four components.

2.2 Site Description and Observations

The Salar del Huasco is a closed arid basin located between 19$^\circ$54’-20$^\circ$27’S and 68$^\circ$40’-69$^\circ$00’W in the north of Chile (Fig. 1). It has an area of $\approx$ 1470 km$^2$ and an average elevation of $\approx$ 3800 m above sea level (a.s.l). The site is highly heterogeneous with a saline shallow lake at the end of the alluvial system, surrounded by a salt flat of $\approx$ 60 km$^2$ and wetlands from which water evaporates (Lobos-Roco et al. 2021, 2022). However, as observed in Fig. 1, the dominant surface is desert. This is where the basin ABL is formed as it is the main provider of heat, with a sensible heat flux that reaches $\approx$ 500 W m$^{-2}$ around 1500 LT (Fig. 2d).

Fig. 4

Study site. a The figure shows the desert basin in the Salar del Huasco, in the north of Chile, where the surface and vertical observations were gathered over the desert surface during the E-DATA field experiment (EC station, radiosondes, UAV flights and meteorological stations). b “Virtual profiles” used to estimate advection from the WRF model. The black arrows show wind vectors at 1400 LT

Observations were gathered at the Salar del Huasco during a field campaign named E-DATA (Evaporation caused by Dry Air Transport over the Atacama Desert) (Suárez et al. 2020) between 14 and 23 November 2018. Figure 4a presents the relevant instrumentation for the surface and the boundary-layer processes analysis over the desert surface. For further details regarding the field experiment we refer to Suárez et al. (2020). Pertinent for our investigation, an eddy covariance (EC) station and a radiometer were installed to measure the energy budget (20.35$^\circ$S, 68.90$^\circ$W, 3953 m a.s.l). Fluxes were integrated using 10-min intervals after the recommended correction procedures (Fratini and Mauder 2014; Suárez et al. 2020). A transect of meteorological stations was installed in the predominant south-west wind direction observed when the regional flow arrives to the region during the afternoon (NS transect in Suárez et al. (2020)). The transect consisted of four stations installed at 2-m height, which measured temperature (T), pressure (P), relative humidity (RH), wind speed (U) and wind direction (WD). We use two of them (Met 1 and Met 3 in Fig. 4a) as they have complete data and best represent the desert surface conditions (e.g. Met 4 might be influenced by the salar). By using Met 1 and Met 3 we therefore ensure that only desert surface conditions are described. The data were collected at 5-min intervals and averaged to a 10-min interval. Also, measurements from radiosonde launches and UAV flights over the desert surface were gathered to describe the state variables in the boundary layer and the free troposphere. Vertical profiles of T, P, RH, U and WD were obtained to characterize h, the jumps at the top of the boundary layer ($\Delta \theta$, $\Delta q$) and lapse rates above the ABL ($\gamma _\theta$, $\gamma q$). Balloons were launched at 0900, 1200, 1500, 1800 and 2000 LT during 22 November 2018. UAV flights were performed every 30 min from 0900 to 1200 LT and up to 500 m above ground level (a.g.l) during the same day. The observed boundary-layer heights were estimated from these observations using the gradient method (Liu et al. 2022). The method consists of analyzing the gradient of the potential temperature profile, which is virtually zero in the mixed layer but shows a strong $\theta$ gradient at the top of the ABL due to the temperature jump in the transition zone to the free atmosphere (Marques et al. 2018; Lothon et al. 2009).

Since UAV flights and radiosondes were launched over the desert surface during 22 November 2018, and the 10 days of the field campaign were very similar to each other (see small uncertainty ranges in Fig. 2b–d), we take 22 November as a day that is representative for all days at the end of the dry season. We will therefore use 22 November 2018 data to estimate the initial and boundary conditions for the CLASS land–atmosphere model, and also to evaluate the WRF results to estimate the non-local inputs for CLASS.

2.3 Regional Model

Simplified column models like CLASS, or observations at a local scale, are not able to parameterize regional processes such as advection or subsidence. Therefore, to quantify the effect of regional forcing, the WRF model is used.

For this research, the WRF model set-up is based on the numerical settings of Lobos-Roco et al. (2021). Figure 5 shows the spatial distribution and dimensions of the four two-way nested model domains. The grid sizes are 27 km for domain D01, 9 km for domain D02, 3 km for domain D03 and 1 km for domain D04. The inner domain D04 encompasses the study area as shown in Fig. 4b and has 49 x 61 grid points. For the vertical discretization, physical parameterizations and other further details the reader is referred to Table A1 in Lobos-Roco et al. (2021). The numerical experiment was initialized on 21 November 2018 at 1200 UTC to analyze 22 November from 0900 to 1900 LT after a 24 h spin-up. The model was run using a timestep of 30 s of which 30 min fields were stored. The initial and boundary conditions were obtained from ECMWF ERA5 reanalysis data for the domains in Fig. 5, centred around 20$^\circ$S, 68$^\circ$W with a spatial resolution of 0.25$^\circ$and updates of the large-scale forcing every 6 h. A 2 K atmospheric temperature bias was corrected from the ERA5 input. Muñoz et al. (2022) attributed the temperature overestimation in the Chilean Andes region to the relatively coarse resolution of ERA5 in relation to the marked east–west topography across the country.

Fig. 5

WRF model domains D01 (27 km), D02 (9 km), D03 (3 km) and D04 (1 km) used for this study. The Salar del Huasco is located in the centre of D04 as shown in Fig. 4b (Lobos-Roco et al. 2021)

For this study, the non-local terms of mass advection, $\theta$ advection and wind divergence are calculated from the WRF model, as well as the radiation components, H, $\overline{\theta }$ and h. To obtain statistically robust estimations, the following approach was defined. First, spatial averages of 3 km x 3 km (9 km$^{2}$) are used to avoid single grid-cells with possible erratic behaviour. Second, when averaging with height the following criteria are used: (1) ABL-average: average from 50 m a.g.l up to 90% of h, and (2) UL-average: average from 50 m to 1000 m above the ABL height. Third, we express the WRF model variability for each variable as a 25–75 percentile range within the 9 km$^{2}$ area. For the 2D variables (h, H, and net radiation components) the variability is expressed over space. For the 3D variables ($\overline{\theta }$, advection and $Div(\vec {U_h})$) the variability is expressed over height after taking the spatial average.

The marked potential temperature jump is not always clearly identifiable in model simulations because it is very local and tends to be smeared out depending on the vertical resolution used. For the WRF model, the boundary-layer height is therefore estimated following the bulk Richardson number method (Vogelezang and Holtslag 1996). The method estimates the ABL height as the lowest level at which the bulk Richardson number that determines the depth and strength of mixing exceeds a critical value (R$_{ic}$= 0.25) (Li et al. 2021; Zhang et al. 2014; Vickers and Mahrt 2004). The Richardson number method has proven to be very consistent under a wide range of atmospheric conditions, and is often used for numerical weather and climate models but also in observational studies (e.g., Jeričević and Grisogono 2006; Richardson et al. 2013; Zhang et al. 2014; Bakas et al. 2020; Min et al. 2020).

2.4 Research Approach

To analyze the influence of local and regional processes, and identify the main drivers of the surface and ABL dynamics in the Altiplano, a sensitivity analysis was performed in CLASS. For this, four experiments were defined with an increasing level of complexity (Table 1):

• 1. Base case: this first experiment only includes the land–atmosphere interactions to analyze how feedback processes at a local scale influence the heat exchange between the surface and the atmosphere and, consequently, the potential temperature evolution and boundary-layer tendencies.

• 2. + Mass advection: the second experiment increases the Base case complexity by including the mass advection term ($h_{adv}$) to study the influence of this non-local process on the surface and ABL dynamics.

• 3. + $\theta$ advection: the third experiment includes the potential temperature advection to analyze the impact of this additional source of heat on the ABL. This experiment adds two components: the advection of heat in the ABL ($\theta _{adv,ABL}$) and the advection of heat in the UL ($\theta _{adv,UL}$).

• 4. + Subsidence: finally, the fourth experiment includes all the processes, local and regional, by also including the wind divergence term that describes the subsidence motions. This experiment should most closely resemble what actually happens in the Altiplano.

To be clear, the CLASS experiments results start with the Base case and then we systematically add the different terms. For instance, the last experiment“ + Subsidence”adds mass advection, $\theta$ advection and subsidence to the Base case.

Table 1 Experiments defined for the sensitivity analysis in CLASS

The CLASS model was run between 0900 and 1900 LT when the mixed-layer theory can be applied and the phenomena of interest occur. A 60 s timestep was used and results were integrated over a 10-min period to compare them with the observations. Initial and boundary conditions were estimated from the E-DATA measurements during 22 November 2018. They can be found in Table 2 (Appendix 1). Since regional processes are extremely relevant in the study site, wind was prescribed in the model from the observations (Fig. 2b).

3 Estimation of Prescribed Terms

As explained in Sect. 2.1, $\gamma _{\theta }$, the mass/cold air advection and the wind divergence, involve regional processes that are external to the model. Therefore, they need to be prescribed in CLASS. For estimating these terms, we use the E-DATA observations and the WRF model results.

3.1 Free Atmosphere Conditions

The CLASS model allows to include a height-dependant lapse rate, which we estimate from the $\theta$ vertical profiles gathered during the E-DATA field campaign. Figure 6a presents in blue colours the morning observations at 0900 LT and 0930 LT. Afternoon observations from the radiosonde launches (1200 LT to 1800 LT) are presented in red colours. The profile sections that are used for estimating $\gamma _\theta$ are presented in grey, which exclude the mixed-layer profiles and $\theta$ jumps. Two layers with different $\gamma _\theta$ characteristics are identified below and above 500 m a.g.l. Observations from the 0900 LT radiosounding and the 0930 LT drone flight are used for estimating $\gamma _\theta$ in the first 500 m a.g.l. Radiosonde launches between 0900 LT - 1800 LT are used for estimating the lapse rate above 500 m a.g.l. Figure 6b presents the height-dependent $\gamma _{\theta }$ considered for CLASS. Until $\approx$ 500 m a.g.l there is a lapse rate of 0.0015 K m$^{-1}$. The lapse rate increases to 0.003 K m$^{-1}$ at higher elevations. This has implications on the temperature jump and, therefore, on the entrainment velocity that directly affects the boundary layer (Eqs. 4, 5).

Fig. 6

a Potential temperature vertical profiles measured from drone and radiosondes over the desert surface during the E-DATA field experiment. In blue colours are the morning profiles at 0900 LT and 0930 LT. In red colours are the afternoon profiles between 1200 and 1800 LT. Indicated with grey lines are the profile sections that are used to estimate the height-dependant potential temperature lapse rate ($\gamma _\theta$); b height-dependent $\gamma _\theta$ prescribed in CLASS. The dotted lines in a and b indicate the ABL initial height, while the dashed lines indicate the 500 m a.g.l where $\gamma _\theta$ changes. Shadows in b indicate the $\gamma _\theta$ uncertainty based on the grey coloured $\theta$-profile sections shown in a

3.2 Advection

To estimate the average advection strength, observations over an homogeneous surface are required such that local heating can be assumed the same everywhere. Spatial differences between two points can therefore be attributed to advection processes only as all the other tendency terms are the same (e.g. $\theta _{adv,ABL}$ for heat in Eq. 1). By approximating Eq. 2 using finite differences, advection can be estimated from two measurement points in a transect as:

$$\begin{aligned} \Psi _{adv} = U_{1,2}^{t} \Psi _{grad_{1,2}} \end{aligned}$$

(8)

where $U_{1,2}^{t}$ is the average wind speed (u + v vector length) aligned with the transect, and $\Psi _{grad_{1,2}}$ is the gradient of a measured generic variable (e.g. $\Psi$=$\theta$) between 1 and 2 (Fig. 7). Note that we are considering the x-direction to be aligned with the wind direction, and therefore we neglect the v component contribution in Eq. 2 ($v\frac{\delta \Psi }{\delta y} \approx 0$). Following the scheme shown in Fig. 7, the aligned wind speed can be estimated using Eq. 9.

$$\begin{aligned} U_i^t = U_i cos (\alpha _i) \end{aligned}$$

(9)

where $U_i$ is the measured wind speed and $\alpha _i$ the angle between the transect and the wind direction for i = $\{1,2\}$.

The gradient is estimated from $\Psi _1$ and $\Psi _2$, and from the distance between the two points (advection distance from now on), ${r_{1,2}}$ (Fig. 7):

$$\begin{aligned} \Psi _{grad_{1,2}} = \frac{\Psi _2-\Psi _1}{r_{1,2}}. \end{aligned}$$

(10)

Fig. 7

Schematic representation for the advection approach using a generic variable $\Psi$ as an example

This approach can be applied both to observations and model results. Since an average ABL heat advection is required for the CLASS model, the advection term needs to be evaluated and subsequently averaged with height for $\Psi = \theta$. For this we use the WRF model as profiles over the desert surface were measured at one site only and higher frequency data was not available to estimate an accurate advection term. First, to validate WRF results advection at 2-m height is compared with observations. To this end, the E-DATA meteorological stations (Met 1 and Met 3 in Fig. 4a) are used to evaluate Eqs. 8-10. For the WRF model, the same two locations are used to estimate the advection term but using 9 km$^2$ average values around each site as stated in the general approach (Sect. 2.3). Since there is 10-days data available for the surface measurements, and considering that advection is a sensitive term due to its dependence on multiple variables, we take 10-days average for estimating the 2-m advection from the observations. Thus, we provide a more robust diurnal cycle to validate the WRF model results.

Figure 8 shows the wind speed and the advection results at 2-m height using field observations and the WRF model estimations. WRF correctly represents the wind speed sudden increase at noon (Fig. 8a). Also, it shows a satisfactory agreement in the negative heat advection produced by the cool air entrance at 1200 LT, which reaches up to $\approx$ -4 K h$^{-1}$ around 1500 LT (Fig. 8b). As shown by the observed and modelled wind direction (circles in Fig. 8b), this advection comes from the Pacific Ocean. A similar value, $-$2.36 K h$^{-1}$ between 1500 and 1800 LT, was reported by Lobos-Roco et al. (2021). They estimated advection as a residual term based on Eq. 1, using the same radiosondes and surface fluxes as in this study (see Appendix C in Lobos-Roco et al. 2021).

Based on the validation shown for 2-m height, we conclude that WRF can be used to estimate the average ABL heat advection following the same approach at different heights. As the horizontal advection strongly depends on the distance along the gradients are estimated (Kossmann et al. 1998), we calculate the advection distance ($r_{1,2}$ in Eq. 10) as the wind speed times the WRF model timestep (0.5 h). The distance ranges from 1 km under the lowest wind speed ($\approx$ 0.5 m s$^{-1}$) to 25 km under the highest wind speed ($\approx$ 12 m s$^{-1}$). The gradients are then estimated from a transect of virtual radiosondes defined by WRF grid points that are aligned with the south-west predominant wind direction (black dots in Fig. 4b). The virtual profile closest to closest to the salt flat is used as the reference point to calculate the gradients, while the second station is chosen depending on the advection distance estimated for each timestep. Note that over the maximum advection distance (25 km) the terrain level increases by $\approx$120 m, which gives cross-talk between vertical- and horizontal gradients if the horizontal gradients are taken with respect to the same heights a.s.l. We therefore determine the horizontal gradients with respect to the same height a.g.l. Here we implicitly assume that in the surface layer, the flow is terrain following and transitions into a horizontal flow in the mixed layer, where $\theta$ is constant with height.

Fig. 8

Diurnal variability of a wind speed at 2-m height and b advection at 2-m height estimated from observations and the WRF model results. b Also presents the observed and modelled wind direction at 2-m height (circles) in the right axis. Vertical dashed lines indicate the time when the air mass arrives at the Salar del Huasco. Shadows represent the observed standard deviations of 10 days data

Figure 9a presents the results for the heat advection estimated from WRF. It also shows the wind vectors in height and the h evolution for 22 November 2018. The heat map shows $\theta _{adv}$ at different heights. The wind vectors provide information of the horizontal wind speed and direction respect to the north (0$^\circ$). Vectors are aligned with the wind. The temporal evolution of h is given for the WRF model results (black line) and the observations from the radiosondes (black triangles) and UAV flights (circle). WRF reproduces the ABL collapse at noon and resembles quite well the observed values estimated from radiosoundings and drones. During the morning there is no heat advection influencing the ABL ($\theta _{adv}\approx 0$ K h$^{-1}$ at all heights within the ABL), which is consistent with the low values observed in wind speed. At noon, WRF correctly shows the very abrupt entrance of the cool air mass that affects the whole boundary layer. Closer to the surface the cold air advection is the strongest and it decreases at higher levels in line with the decrease in wind speed with height. Regarding the upper layer, the heat advection in the 1000 m layer above the ABL is also $\approx 0$ K h$^{-1}$ during the morning. Here wind speed is characterized by higher values and therefore the small magnitudes in heat advection can be explained by a small $\theta$-gradient in the UL (Eq. 8). Driven by the arrival of the regional flow, a cold air advection is also observed from midday in the upper layer with smaller magnitudes compared to the ABL. Figure 9b presents the average heat advection in the ABL and UL (blue and orange lines, respectively). Figure 9b also displays the observed advection at 2-m height (red dotted line) shown in Fig. 8b. The height averaged values show near zero advection for both layers until 1200 LT and then a cool air mass arrival during the afternoon that reaches a strength up to $\approx$ -4 K h$^{-1}$ around 1400 LT in the ABL and $\approx$ -1 K h$^{-1}$ around 1500 LT in the UL.

Fig. 9

a Heat advection and wind vectors as a function of height according to the WRF model results. Boundary-layer heights from WRF (black line) and observations from the E-DATA field campaign (black triangles and circle) are also shown. b Averaged ABL and UL heat advection to be included in CLASS (blue and orange lines, respectively), along with the advection estimated from observations at 2-m height shown in Fig. 8b (red dashed line). The vertical dashed lines indicate the time when the regional air mass arrives at the Salar del Huasco. Shadow in b represent WRF uncertainty range

Regarding the mass advection, the same approach was followed by approximating Eq. 8 for $\Psi =h$. The ABL average wind speed is used in Eqs. 8 and 9. Results for $h_{adv}$ are presented in Fig. 10, where a minimum value of mass advection can be found at noon ($h_{adv}$ $\approx$ -250 m h$^{-1}$). It is a negative $h_{adv}$, indicative of the advection of a shallower ABL. This mass advection is linked to the arrival of the regional airflow and due to the abrupt change in wind speed at noon a shallower boundary layer is advected towards north-east. This advection is thereby influenced by the regional topography, as the regional circulation is able to reach the Salar del Huasco thanks to the complex topography that channels a flow on the western slope of the Andes towards the salar (Lobos-Roco et al. 2021; Rutllant et al. 2003). As observed from Fig. 10, the mass advection has a larger influence on the ABL at noon. Here, $h_{adv}$ is highly variable (blue shadow) due to the variability of wind over the ABL (Fig. 9a). Although wind speed remains characterized by high values, the mass advection decreases during the afternoon. The low values in $h_{adv}$ compared to the peak value at 1200 LT can be explained by the reduced h-gradient between the local ABL and the upwind boundary layer (Eq. 8). We can interpret this as the local boundary layer approaching an equilibrium state with the upwind ABL, and therefore the mass advection has a slight impact over h during the afternoon ($h_{adv}$ < 100 m h$^{-1}$ from 1400 LT onward).

Fig. 10

Mass advection (blue line) estimated from the WRF model results and its uncertainty range given by the variability of the wind over the ABL (blue shadow). The second y-axis shows the mass advection results in m s$^{-1}$ to be able to compare them with the other terms contributing to $\delta h \delta t^{-1}$ (Eq. 4). The vertical dashed line indicates the time when the regional air mass arrives at the Salar del Huasco

3.3 Wind Divergence

Wind divergence is used to parameterize the subsidence velocity in CLASS (Eq. 7). We estimate the flow divergence from WRF by averaging the vertical motion in the layer ranging from 50 m to 1000 m above the ABL height. We also averaged the vertical wind speed over an area of 9 km$^{2}$ around the site where radiosondes were launched (Fig. 4a). As a reference, we also present divergence estimates from observational studies. Rutllant et al. (2003) studied the North coast of Chile ($\approx$ 300 km from the Salar del Huasco) in January 1997. They used observations averaged over 500-m height layers and using a budget equation (see Appendix A in Rutllant et al. 2003). They found a divergence value of 3 $\times$ 10$^{-5}$ s$^{-1}$ during the afternoon, which is an enhanced divergence compared to typical subtropical west coast values. The reported afternoon subsidence enhancement was partly associated to the solar heating of the western Andes as it allows the onshore flow to gain enough buoyancy to overcome the inversion resistance. Gálvez et al. (2005) studied the wind divergence in the Salar de Uyuni ($\approx$ 150 km from the Salar del Huasco) during November 2003 using observations at 150 m a.g.l and the method described by Davies-Jones (1993). This method consists of using polygons in balloon observations and fitting a linear wind field to calculate the divergence. They reported a strong subsidence associated with a strong onshore breeze induced by the enormous size of the Salar de Uyuni (more than 10.000 km$^{2}$).

Figure 11 presents the wind divergence comparison between the observational studies (dots), the WRF model results (in red) and the values used in this research (green line). The divergence values prescribed in the CLASS model largely fall within the WRF divergence uncertainty range indicated by the red shadow. WRF results are not strictly followed as they show very abrupt changes. For instance, the model goes from positive to negatives divergences within half an hour (e.g. from 1800 to 1830 LT) probably due to the evening transition, with changes in stability and in the mesoscale processes. Therefore, small adjustments are made within the WRF uncertainty based on the CLASS results to get the best fit with the h, $\overline{\theta }$ and $\Delta \theta$ observations. The positive values cause a negative subsidence velocity (Eq. 7) and reduces the ABL height tendency (Eq. 4).

Fig. 11

Wind divergence (red crosses) estimated from the WRF model results based on 9 km$^{2}$ averaged wind speed around the measurement site and subsequently averaged over 1000 m starting at 50 m above the ABL height. The wind divergence variability over the 1000 m above the ABL is given as a red shadow around the mean estimates. Values reported in other studies (Gálvez et al. 2005; Rutllant et al. 2003) are given in orange–and blue dots, respectively. The values prescribed in CLASS are presented as a green line. Vertical dashed line indicates the time when the regional air mass arrives at the Salar del Huasco arrives at the Salar del Huasco

4 Surface and Boundary-Layer Response to Local and Non-local Processes

Using the prescribed terms estimated on Sect. 3, results for the CLASS experiments defined in Table 1 are presented in this section. Observations and WRF model results are also presented when available. First, results for the heat exchange at the surface are presented in Sect. 4.1. Then, results for the boundary-layer dynamics are shown in Sect. 4.2.

4.1 Surface Heat Flux Evolution

The heat flux exchange between the surface and the atmosphere was obtained from the land-surface module in CLASS. Figure 12 shows the results for the experiments defined in Table 1, along with the E-DATA measurements and the WRF model results for 22 November 2018. There is a very satisfactory agreement between the observed and modelled values. There is a positive flux going from the surface to the atmosphere that warms the air during the day. In the Base case experiment, the heat flux follows a typical behaviour according to the radiation balance (Fig. 17 in Appendix 2). The heat exchange increases during the morning simultaneously to the increase of energy in the system provided by the net radiation (RN, Fig. 17a). When RN starts to decrease at 1400 LT, surface fluxes also start to decrease (Fig. 12). However, as there is still energy available in the system until 1900 LT (RN > 0 W m$^{-2}$), fluxes remain positive throughout the simulation period. When the mass advection is added to the Base case (black line), no variations are observed on the heat flux. When including the $\theta$ advection (blue line), a rise of $\approx$ 11% is obtained in the daily heat flux. Finally, when the subsidence motions are added (green line), the ABL is pushed downwards and a small decrease on the heat exchange is observed during the afternoon. In Sect. 4.2 we discuss how the changes on sensible heat flux are related to the influence of the mass and cold air advection, and subsidence, over the ABL.

Fig. 12

Surface heat flux estimated from the CLASS model experiments defined in Table 1 compared to the observed and WRF model values (black and red crosses, respectively). Vertical dashed line indicates the time when the regional air mass arrives at the Salar del Huasco. Red shadow represents WRF variability in space

4.2 Atmospheric Boundary-Layer Evolution

Figure 13 presents the ABL potential temperature results from the experiments defined in Table 1 compared to field observations and the WRF model. To interpret the results, Fig. 14 presents the main contributors to the potential temperature evolution (Eq. 1). Figure 14a presents the overall $\theta$ tendency ($\frac{\delta \overline{\theta }}{\delta t}$) estimated by the CLASS model, while Fig. 14b, c show the surface/entrainment fluxes and the heat advection contribution to $\frac{\delta \overline{\theta }}{\delta t}$, respectively.

Fig. 13

ABL potential temperature estimated from the CLASS model experiments defined in Table 1, compared to drone and radiosonde observations and the WRF model results. The vertical dashed line indicates the time when the regional air mass arrives at the Salar del Huasco. Red shadow represents WRF variability in height

When only the local land–atmosphere interactions are considered (Base case, orange dotted line), $\overline{\theta }$ is overestimated during the afternoon and exceeds the observations in $\approx$ 9 K at the end of the day. Here potential temperature increases until 1900 LT as the heat tendency remains always larger than 0 K h$^{-1}$ (Fig. 14a) thank to the continuous warming from the surface and entrainment fluxes (Figs. 12, 14b). As wind is prescribed equally in all experiments, besides the heat fluxes contribution, there is en enhancement of the mixing during the afternoon that contributes to the rise in $\theta$. Next, we add the non-local terms one by one. Note that all these terms are near zero in the morning, and only bring significant changes in $\overline{\theta }$ from 1200 LT onward. When the negative mass advection is included in the analysis (black line), no significant changes are observed in potential temperature and the tendency remains mainly the same as in the Base case (Fig. 14a). Therefore, the surface-atmosphere temperature gradient remains undisturbed and no variations are observed on the heat exchange (Fig. 12). When including the advection of cold air driven by the arrival of the regional flow, temperature decreases from noon and leads to an underestimation of $\approx$ 8 K in $\overline{\theta }$ at 1900 LT. Here the cold air advection is strong enough to counteract the warming fluxes and becomes dominant from 1300 LT (compare Fig. 14b, c). This results in an an increase in the surface-atmosphere gradient and a rise on the heat exchange as observed in Fig. 12. Finally, when subsidence is included, the ABL is pushed downwards and the surface and entrainment heating is distributed over a shallower ABL (Eq. 1). This results in an increase in the atmosphere temperature and the model is able to reproduce the observed $\overline{\theta }$ (green line). As a consequence of the temperature increase, the temperature gradient between the surface and the atmosphere decreases, and a small reduction on the heat exchange is observed during the afternoon (Fig. 12). As explained in Sect. 3.3, subsidence in this case is characterized by an adjusted wind divergence within the WRF model uncertainty (Fig. 11) to get the best fit with the observations. From these three non-local phenomena, the regional cold air advection is the dominant process in causing the temperature sudden decrease at 1200 LT. Without it, potential temperature would keep rising to $\approx$ 292 K (Fig. 13).

Fig. 14

a ABL potential temperature tendency estimated from the CLASS model experiments defined in Table 1; b surface and entrainment contribution; and c heat advection contribution. The vertical dashed lines indicate the time when the regional air mass arrives at the Salar del Huasco

Figure 15 presents the results for the ABL height dynamics. The ABL height increases quickly until noon in a similar manner in all the experiments. However, considerable differences are found during the afternoon when adding all the non-local processes. To aid the interpretation of the results shown in Fig. 15, we present Fig. 16 which depicts the main contributors to the ABL growth (Eq. 4). Figure 16a presents the boundary-layer height tendency ($\frac{\delta h}{\delta t}$) estimated by the model and Figs. 16b–f show the evolution of the terms that contribute to the ABL growth (Eqs. 3, 5-7). Figure 16b displays the subsidence velocity, Fig. 16c the entrainment velocity, Fig. 16d the entrainment flux, and Fig. 16e the potential temperature jump. The contribution of $h_{adv}$ to the tendency was already presented in Fig. 10.

Fig. 15

ABL height evolution estimated from the CLASS model experiments defined in Table 1, compared to drone and radiosonde observations estimated using the gradient method (Liu et al. 2022), and the WRF model results estimated using the bulk Richardson number method (Min et al. 2020). The vertical dashed line indicates the time when the regional air mass arrives at the Salar del Huasco. Red shadow represents WRF variability in space

Fig. 16

a ABL height tendency estimated from the CLASS model experiments defined in Table 1; b subsidence velocity; c entrainment velocity; d entrainment flux; and e potential temperature jump estimated by CLASS. The vertical dashed lines indicate the time when the regional air mass arrives at the Salar del Huasco. Triangles and circle in e represent radiosonde- and drone observations, respectively

During the morning (0900 to 1100 LT) there is a boundary-layer regime controlled by the surface- and entrainment processes. Here, h increases according to the entrainment velocity ($w_e$, Fig. 16c) as there is no contribution from the subsidence motions ($w_s$ = 0 m s$^{-1}$, Fig. 16b) and the mass advection is negligible ($h_{adv}$ < 0.01 m s$^{-1}$, Fig. 10). Around 1000 LT, the ABL height tendency peaks (Fig. 16a), which is driven by two processes. First, by an increase in the entrainment flux magnitude (Fig. 16d) that follows the surface heat flux evolution (Fig. 12). Second, by a decrease on the potential temperature jump (Fig. 16e) given the rise on $\overline{\theta }$ due to the heat fluxes warming (Figs. 12, 13). During the next hour (1000 to 1100 LT), the ABL keeps growing due to a positive contribution from $w_e$ (Fig. 16c). However, the ABL height increases at a lower rate as the tendency drops from $\approx$ 0.4 m s$^{-1}$ to $\approx$ 0.2 m s$^{-1}$ within half an hour (Fig. 16a). The sudden decrease in $\frac{\delta h}{\delta t}$ is caused by an increase in $\Delta \theta$ (Fig. 16e) due to a change in the lapse rate when the ABL height exceeds 500 m a.g.l (Fig. 6b). Therefore, the larger $\gamma _\theta$ results in a larger $\Delta \theta$ (Eq. 6) that reduces entrainment and, consequently, $\frac{\delta h}{\delta t}$ (Eq. 4).

From 1100 LT onward, there is a regionally controlled boundary-layer regime, mainly dominated by cold air advection. If regional processes are ignored, the ABL height keeps increasing up to $\approx$ 3.5 km as there is still energy available in the system (orange dotted line in Fig. 15). This is a textbook boundary-layer development as the ABL becomes deeper and the heat needs to be distributed over a bigger layer. Here the contribution from the heat fluxes (Fig. 16d) and a constrained potential temperature jump given the large $\overline{\theta }$ ($\Delta \theta$ < 2 K in Fig. 16e), lead to an entrainment velocity larger than 0 m s$^{-1}$ (Fig. 16c). In absence of non-local contributions, this causes the ABL height tendency to remain always positive and h increases until the end of the day (Figs. 15, 16a). By systematically including the contributions of the regional processes the well-known ABL is no longer observed. The advection of a shallower ABL causes $\frac{\delta h}{\delta t}$ to decrease, approaching $\approx$ 0.1 m s$^{-1}$ at 1200 LT (black line in Fig. 16a). As a result, there is a reduction of the ABL height during the afternoon and a 400-m decrease in h at the end of the day compared to the Base case (Fig. 15). The 400-m decrease in h is caused by the immediate impact of the mass advection at 1200 LT, as the tendency quickly goes back to the Base case at 1430 LT (Fig. 16a). This has two main reasons. First, the low values of $h_{adv}$ during the afternoon. In Sect. 3.2 we argued that the mass advection has a slight impact over the ABL over the ABL after midday as the local boundary layer approaches an equilibrium state with the upwind ABL after the arrival of the regional flow. Second, the small influence that the advection of a shallower boundary layer has on potential temperature (Fig. 13) and therefore on the heat exchange (Fig. 12). The mass advection does not affect the heat fluxes and $\overline{\theta }$ enough to have an impact in the entrainment velocity (Fig. 16c) and, in consequence, the tendency quickly goes back to the Base case when no other regional contribution is included (Fig. 15). When the cold air advection is added to the analysis (blue line), the ABL stops growing during the afternoon (Fig. 15). In contrast to the mass advection, $\theta _{adv}$ has a consistent influence over the ABL allowing the tendency to remain $\approx$ 0 m s$^{-1}$ until 1730 LT (Fig. 16a). The tendency remains close to zero due to an important decrease in the entrainment velocity (Fig. 16c) caused by the increase in $\Delta \theta$ when the cold air regional flow arrives (Fig. 16e). Here the warming from the entrainment and surface fluxes counteracts the decrease in the ABL height due to the cold air advection. It is only at 1730 LT that the entrainment fluxes have decreased enough following the radiation balance, and $\Delta \theta$ has increased enough as a consequence of the strong cold air advection, that $w_e$ $\approx$ 0 m s$^{-1}$ and the small but negative $h_{adv}$ causes the ABL height to shrink. Finally, when the regional subsidence is included (green line), the tendency becomes negative earlier and the ABL gradually collapses to 300 m a.g.l at the end of the day (Fig. 15). In this case the tendency becomes negative already at 1200 LT and the observations are better represented due to the adjusted wind divergence values (Fig. 11). However, subsidence does not cause the collapse by its own but the ABL height tendency remains negative thanks to the sum up of four independent processes. First, the advection of the shallower ABL that directly decreases the tendency ($h_{adv}$ < 0 m s$^{-1}$ in Fig. 10). Second, the negative wind divergence that causes subsidence motions over the ABL and also directly decreases $\frac{\delta h}{\delta t}$ ($w_s$ < 0 m s$^{-1}$ in Fig. 16b). Third, a decrease on the entrainment flux following the decrease in the radiation balance (Fig. 16d). Fourth, the strong cold advection that increases the potential temperature jump (Fig. 16e). The third and fourth processes reduce the entrainment velocity enough ($w_e$ $\approx$ 0 m s$^{-1}$ in Fig. 16c) to be exceeded by the negative contributions of subsidence and mass advection, causing the tendency to become and remain negative at midday, and the ABL to decrease already at 1200 LT.

To recap, each process on its own does not explain the ABL collapse. It is the combined effect of the mass and cold air advection plus subsidence that causes the ABL to reduce its height already at midday when there is still energy in the system to keep it growing (Fig. 17). The main responsible of the sudden temperature decrease and ABL collapse in the Altiplano region of the Atacama Desert is the cold air advection. Without it the temperature would keep rising to $\approx$ 292 K (Fig. 13) and the ABL would keep increasing to $\approx$ 3.5 km (Fig. 15). As a summary, the surface and ABL dynamics are mainly influenced by the adding of three regional forcing:

• 1. Mass advection: the mass advection of a shallower boundary layer causes an immediate decrease in the ABL height at noon as it has a direct impact over h (Fig. 15, Eq. 4). However, in this case it is not large enough to influence the potential temperature (Fig. 13, Eq. 1) and the surface flux (Fig. 12).

• 2. Cold air advection: the arrival of a cold air mass affects the mixed layer by abruptly decreasing $\overline{\theta }$ at 1200 LT (Fig. 13, Eq. 1). The cold air advection increases the heat fluxes (Fig. 12) and has an indirect but consistent influence over h during the afternoon (Fig. 15) by decreasing we through an increase in $\Delta \theta$ (Figs. 16d, f, Eqs. 4,5).

• 3. Subsidence motions: a positive wind divergence during the afternoon directly decreases the ABL height by causing a negative subsidence velocity (Fig. 15c, Eqs. 4, 7). Consequently, it causes an increase on potential temperature (Fig. 13, Eq. 1) and a slight decrease on the surface flux. Its impact remains during all the afternoon.

We repeat that this analysis is based on the study of processes that are added cumulatively in the experiments and therefore they are not investigated independently.

5 Conclusions

This research identified the main drivers of the observed afternoon ABL collapse in the Altiplano region of the Atacama Desert by integrating a land–atmosphere conceptual model, observations and a regional model. We addressed the question of how do local (surface-atmosphere interactions and entrainment) and non-local processes (advection and subsidence) contribute to the surface and atmospheric boundary-layer dynamics in the Altiplano region. During the morning, the local surface-atmosphere interactions increase the heat exchange and, together with the entrainment processes, warm the atmosphere and allow the ABL to grow. However, this regime abruptly changes at noon and turns into a boundary-layer regime mainly controlled by regional processes. First, the advection of a shallower ABL ($\approx$ -250 m h$^{-1}$ at noon) causes an immediate decrease in h at 1200 LT. Second, the arrival of a cold air mass, which reaches a strength of $\approx$ -4 K h $^{-1}$ on average over the ABL height, is strong enough to counteract the large turbulence levels driven by the high surface fluxes. As a result, cold air advection causes the ABL height to stop increasing and the ABL growth is capped already at midday. Both mass and cold air advection are linked to the arrival of a thermally driven atmospheric circulation originated by the Pacific ocean - land thermal contrast, enhanced by the steep regional topography. Finally, subsidence motions provide the additional downward push of the ABL to make it gradually collapse to 300 m a.g.l at the end of the afternoon. The subsidence velocity was characterized by a wind divergence of $\approx$ 8 $\times$ 10$^{-5}$ s$^{-1}$ after midday. Without the regional processes, the ABL would be progressively growing to 3500 m by the end of the day.

These findings show the relevance of treating large and small-scale processes as a continuum to be able to understand the ABL dynamics and recognize its main drivers. The research strategy of using a land–atmosphere conceptual model, a regional model and observations was fundamental for the aim. While the conceptual model allowed to break down the complexity of the land–atmosphere interactions, the regional model allowed to describe the processes occurring at a larger scale. The field observations were key to evaluate the models results, and to provide input parameters and tune the conceptual model. For future perspectives, other approaches to estimate advection and wind divergence in the region should be considered to validate the values assumed in this research. Collecting information in other basins within the Altiplano region to compare our results with would be also convenient to provide robust conclusions about the region behaviour. Finally, the research strategy developed in this investigation will be also used in the future to study the interaction between the ABL and the turbulent fluxes on other surface types, such as water and wet-salt surfaces. This interaction is important as it can improve water management and environmental protection.

Appendices

Appendix 1: Numerical settings for the land–atmosphere model

See Table 2.

Table 2 Initial and boundary conditions for the land–atmosphere conceptual model in CLASS

Appendix 2: Radiation analysis

Figure 17 presents the components of the radiation balance according to the E-DATA observations (Suárez et al. 2020), the WRF model and the CLASS model. Observations were treated as in Lobos-Roco et al. (2021) in which the radiation balance terms were composed from local, net total radiation and net longwave radiation measurements completed with shortwave- and longwave incoming radiation measurements at $\approx$ 8 km distance from the desert measurement site, and by using a typical albedo for dry sand soils of 0.21 (Lobos-Roco et al. 2021; Moene and Dam 2014). We find that both WRF and CLASS results agree very well with the observations. In part, this good agreement was achieved by being consistent in the used albedo (0.21) in both models and observations. In the case of CLASS the good agreement was also achieved by adjusting the default setting for the optical depth, which represents a sea-level atmosphere, to a value that better represents the atmosphere at 4 km a.s.l.

Fig. 17

Overview of the radiation balance: a net radiation; b shortwave- and c longwave net radiation; d shortwave- and e longwave in components; f shortwave- and g longwave out components estimated from the CLASS and WRF models and from observations. The vertical dashed lines indicate the time when the regional air mass arrives at the Salar del Huasco