1 Introduction

The vertical structure of the lower troposphere in sub-tropical regions is mainly characterized by sharp inversions in temperature and moisture occurring over a wide altitude range. These pronounced vertical changes are produced by different formation mechanisms such as, (i) surface-based inversions associated with radiative surface cooling during the night (Nieuwstadt 1984; Stull 1988; Seibert et al. 2000; ii) the inversion capping the marine boundary-layer (MBL) inversion associated with strong static stability and reduced vertical mixing (Busch et al. 1982; Rouault et al. 1999; Ciesielski et al. 2001; iii) the trade-wind inversion (TWI), a typical temperature inversion usually present in the trade-wind streams over the eastern portions of sub-tropical oceans (Malkus 1956; Augstein et al. 1973; Riehl 1979; Albrecht 1984; Schubert et al. 1995; Johnson et al. 1999; iv) the \(0\,^{{\circ }}\hbox {C}\) inversion layer, corresponding to an increased stability near the \(0\,^{\circ }\hbox {C}\) level, associated with the melting process within stratiform rain regions (Johnson et al. 1995, 1999; v) high-level layers of enhanced stability associated with the top of a layer of dusty, dry and warm air confined vertically in a deep mixing layer of 4–5 km in depth, as for example the Saharan Air Layer (Prospero and Carlson 1981; Dunion and Marron 2008), mainly observed in summertime. A high percentage of individual soundings in the subtropics shows multiple inversions, and almost all of these high stability layers can even be found together in particular cases, as shown in Fig. 1.

Of great importance due to the impact on weather and climate is the lowest inversion, especially below the \(0\,^{{\circ }}\hbox {C}\) inversion (generally >600 hPa), related to the formation of persistent sheets of stratocumulus and shallow cumulus clouds that significantly affect the radiation and energy balances of the atmosphere and the ocean (Hartmann et al. 1992). Several of these inversions are associated with the top of the MBL (part of the atmosphere that has direct contact and directly influenced by the ocean), which is usually identified by a sharp increase in temperature and a decrease in humidity in the transition to the free atmosphere. Other inversions are due to large-scale subsidence flow in the descending branch of the Hadley cell over the trade-wind belt. Shallower boundary layers are associated with larger cloud cover due to a moister MBL, and deeper boundary layers are associated with trade-wind cumulus and smaller values of cloud cover (Von Engeln et al. 2005).

Several efforts have been made to understand the structure of the MBL over the ocean in the last decade because the MBL is an excellent laboratory with which to study the underlying physics of air-sea interaction. The MBL plays a pivotal role in determining the atmospheric exchanges of energy, mass and momentum that occur across the ocean, which influence atmospheric and oceanic circulations over a wide spectrum of time and spatial scales (Arya 1988).

Due to its persistence, the trade-wind inversion has been the focus of numerous studies concerned with the structure of the lower sub-tropical atmosphere. The earliest work showed that these high stability layers have a marked dependence on latitude (Schubert et al. 1995; Johnson et al. 1999) and season (Dorta 1994; Marzol et al. 2006; Rémillard et al. 2012). Low inversions over the cold Atlantic Ocean currents are found near north-west and south-west Africa and a fairly flat inversion at approximately 2000 m height over most of the equatorial region. Similar features are found over the Pacific Ocean where the trade inversion slopes smoothly upward towards the equator \((0.3\hbox { m km}^{-1})\) (Schubert et al. 1995).

Fig. 1
figure 1

Sample temperature profile from Tenerife, at 0000 UTC, 17 February 08, showing extremely stable layers occurring in a wide altitude range

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One of the first studies on the frequency and height of the subsidence inversion is due to Gutnick (1958) in the Caribbean. His results showed that, during winter when precipitation is low, the inversion layer is enhanced, and during the summer the inversion weakens and rises slightly. Font Tullot (1956) used a dataset covering more than 40 years from ground-level observatories at different altitude sites in Tenerife and established the monthly average altitude of the subsidence inversion. His study reveals a clear seasonal variation, with the inversion layer typically at a height of above 1600 m m.s.l. in winter, and 1200 m m.s.l. in summer. More recent studies using regular radiosonde datasets have confirmed these findings (Cuevas 1995; Rouault et al. 1999). In the Azores, a significant seasonal variation was not observed by Rémillard et al. (2012) based on their analysis of 19-month data records.

Usually sub-tropical regions that tend to reveal TWI during most of the year show this inversion at the top boundary layer (e.g., Albrecht 1984; Schubert et al. 1995; Cao et al. 2007). Other authors, however, differentiate the TWI layer from the inversion produced at the top of the mixing layer (Johnson et al. 1995; Sempreviva and Gryning 2000) where the largest relative humidity gradient is observed (Ma et al. 1996; Philander et al. 1996; Von Engeln et al. 2005; Cao et al. 2007). This idea is mainly supported by a double structure that has been observed in stability \(({ \mathrm{d}T/\mathrm{d}z})\) in typical trade-wind soundings (Johnson et al. 1995; Rouault et al. 1999; Sempreviva and Gryning 2000; Von Engeln et al. 2005; Zhang et al. 2009; Alappattu and Kunhikrishnan 2010; Rémillard et al. 2012). Johnson et al. (1995) found high stability in layers centred near the 925-, 800- and 550-hPa levels, and suggested that the stability peak near 925 hPa represented the inversion above the mixing layer, and that the stability layer around 800 hPa was associated with the TWI. Rouault et al. (1999) also found a double inversion structure when analyzing the MBL above the Agulhas Current (Port Alfred, South Africa).

Until now all studies have paid attention to one of these two inversions focusing on changes in moisture and temperature (i.e., Grindinger 1992; Tran 1995). That is, the first detected inversion in every sounding was associated either with the top of the MBL or with the trade-wind inversion. The present study aims for a better understanding of the vertical structure of the lower troposphere over the sub-tropical ocean, specifically identifying and characterizing the differences between the TWI and the inversion associated with the top of the MBL and its latitudinal and seasonal variations, by performing a statistical analysis of long-term radiosonde datasets at Tenerife, Madeira and Azores stations.

Fig. 2
figure 2

Locations of operational radiosondes in the North Atlantic are shown in the upper side. The other two panels show the composite mean from 1980 to 2013 of geopotential height (m) (left) and vertical velocity \((\hbox {Pa s}^{-1})\) (right) at 1000 hPa

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Fig. 3
figure 3

Topographic map of Tenerife island, highlighting the location of the stations: (#60020) Santa Cruz de Tenerife and (#60018) Güimar, where the sounding balloons have been launched. The prevalent trade-wind flow and orographic lifting due to the mountains on this island is shown

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The paper is structured as follows: Sect. 2 provides an overview of the study area and corresponding climate. Datasets, methods and analysis techniques are given in Sect. 3 and in Sect. 4 results and discussion are provided. Conclusions are given in Sect. 5.

2 North Atlantic Study Area Climate Overview

The Canary, Madeira and Azores archipelagos (location given in Fig. 2) along with Cape Verde and Savage Islands make up the Macaronesian region in the Atlantic Ocean and lie between \(15^{\circ }\hbox {N}\) and \(40^{{\circ }}\hbox {N}\). The meteorological features of the Macaronesian region are governed by the strength and position of the sub-tropical North Atlantic anticyclone, the Gulf Stream and the Canaries Current (Fig. 2) and by the islands’ topography, all of which generate large differences in both weather and climate between the islands. The Cape Verde and Savage Islands were not included in our study since there are no operating radiosonde stations in these archipelagos.

Despite its proximity to the African continent (Martín et al. 2012; Mestre-Barcel et al. 2012), the climate of the Canary Islands, and specifically Tenerife (the largest and highest island of the Canary archipelago), is different from that expected for its latitude due to the strong influence of the relatively humid north-east trade winds and the cold oceanic current that surrounds the archipelago. For these trade winds, the north-easterly fetch leads to orographic lifting of air parcels as they encounter higher terrain, cooling and condensing in orographic clouds (Fig. 3).

Trade winds result in a quasi-permanent stratocumulus cloud mantle (named the “cloud of sea”), more frequent and intense in summer (Tullot 1956; Marzol 2001). The trade winds scenario is intensely disturbed under Saharan outbreaks during which we observe the Saharan Air Layer, usually above the MBL, mainly in summer (Rodríguez et al. 2011; Cuevas et al. 2013).

The North Atlantic storm track frequently crosses the Azores region during most of the year (September to March), while during late spring and summer, the Azores climate is influenced by the Azores anticyclone (Santos et al. 2004). The climate in the Madeira archipelago is largely influenced by the eastern branch of the Azores anticyclone, especially from spring to autumn. During the winter Atlantic low-pressure systems favour unstable atmospheric conditions and rainfall (Santos et al. 2004). A detailed description of the main climatological characteristics of the three archipelagos is found in Mestre-Barcel et al. (2012).

The descending branch of the Hadley cell in the sub-tropical region, which affects a part of our study region (Canary Islands and Madeira archipelagos), is associated with the constancy and frequency of the north-east trade-wind regime (Seidel et al. 2008), and consequently with the presence of an inversion indistinctly identified with the TWI and the MBL inversion.

3 Datasets, Methods and Analytical Techniques

In this study we analyzed radiosonde profiles from 1980 to 2013 at the four stations listed in Table 1. The radiosonde dataset is available at the website maintained by the University of Wyoming (http://weather.uwyo.edu/upperair/sounding.html) and was completed with the Izaña Atmospheric Research Centre dataset from the Meteorological State Agency of Spain (AEMET). Radiosonde profiles have a temporal resolution of 12 h (0000 and 1200 UTC).

Table 1 Operational radiosonde stations used in this study
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Temperature, pressure and humidity retrievals were performed with Vaisala RS80 radiosondes until 2002, and Vaisala RS92 radiosondes afterward. Wind speed and direction were measured with a Loran-C based system, which offers windfinding accuracy of aproximately \(\hbox {1 m s}^{-1}\) (Jaatinen and Kajosaari 2000), until September 1997, when Omega stations throughout the world ceased operations and were replaced by the more accurate GPS windfinding system offering \(0.1\hbox { m s}^{-1}\) accuracy (Jaatinen and Kajosaari 2000). According to the results of Loran-C and GPS windfinding comparisons, the standard deviations of the direct differences of the wind speed are within the range of the expected random error for Loran-C and GPS winds, and no significant systematic difference could be observed in the windfinding systems (Poon et al. 2000). Given that the typical ascent rate of the radiosonde balloon is \(5\hbox { m s}^{-1}\), the average vertical resolution for raw data of 30 m for temperature and relative humidity, and 150 m for wind measurements are obtained, which are good enough for our purposes.

Monthly mean values of surface pressure, sea-surface temperature (SST) and vertical velocity data were obtained from the NOAA-NCEP Reanalysis Dataset (http://www.esrl.noaa.gov/psd/cgi-bin/data/timeseries/timeseries1.pl).

3.1 Study of Homogeneities in Datasets of the Canary Stations

In October 2002, the Santa Cruz station (#60020), located in Tenerife, was moved to a new location in the municipality of Güimar (station #60018). Both stations are close to each other, approximately 21 km apart (Table 1 and Fig. 3). We used a non-parametric analysis to assess whether the Santa Cruz and the Güimar datasets can be treated as a unique dataset. Kolmógorov–Smirnov tests (Press et al. 1992; Priestly 1994) and the Mann–Whitney test (Mann and Whitney 1947), are commonly used to detect inhomogeneities. The null hypothesis is that the two datasets are from the same distribution, whereas the alternative hypothesis is that they are from different continuous distributions. An advantage of the Kolmógorov–Smirnov and Mann–Whitney tests is that no assumption is made about the distribution of data. In order to study possible inhomogeneities in temperature caused by the relocation of the radiosonde station from Santa Cruz to Güimar, we computed the tests for temperature data corresponding to five years before and after the station site change.

Statistical comparisons of air temperature at three significant pressure levels are summarized in the supplementary material (S1). The temperature variance is very high at 850 hPa, taking values of 36 and \(33\,^{{\circ }}\hbox {C}\) before and after the breaking point, respectively. This makes a difference of \(3.3^{\circ }\hbox {C}\) between the two radiosonde sites. The high value of the variance at the 850-hPa pressure level is probably due to the strong variation of the inversion layer height throughout the year. The median, however, has a similar value, 13 and \(14\,^{\circ }\hbox {C}\), before and after the breaking point, respectively, at this level. When calculating the inhomogeneity in temperature, probability values are below 0.05 in the three pressure levels. Values below 0.05 in the Kolmógorov–Smirnov and Mann–Whitney tests indicate that the series are statistically different. Therefore we rejected the hypothesis that temperature has the same mean of distribution in two series, and therefore treat both datasets (Santa Cruz and Güimar) separately. This result is expected as the soundings station was moved to a site affected by the prominent central ridge of the island, with a maximum height of 2000 m above m.s.l, which disrupts the synoptic airflow and its stratification below this level, resulting in significant changes in the vertical structure of the lower troposphere.

3.2 Sounding Analysis

Homogenization of the radiosonde station vertical interval data was necessary to perform the statistical analysis, so linear interpolation was made every 10 hPa in all of the soundings. The lapse rate of temperature, water vapour mixing ratio and wind components (u and v) was calculated at each level and for each radiosonde profile using a centred vertical difference. The centred vertical differences are defined as,

$$\begin{aligned} \varGamma _{ij} \left( {{z}_{2}+ {z}_{1}/2} \right) =\frac{\Delta {a}_{{ij}} }{\Delta {z}_{{ij}}}=\frac{{a}_{{j}} -{a}_{{i}}}{{z}_{{j}} -{z}_{{i}}} \end{aligned}$$
(1)

where \(\varGamma _{\textit{ij}} \) is the lapse rate of the “a” parameter between \({z_i}\) and \({z_j}\) altitude levels. The location of inversion layers where temperature lapse rate acquires positive values was considered. Isothermal layers were discarded.

In practice, and for present purposes, superadiabatic lapse rates in radiosonde data are frequently flagged for deletion or correction before data are used (Slonaker et al. 1996). A superadiabatic lapse rate can occur near the ground when associated with strong surface heating, and can be observed in radiosonde profiles and other techniques. However, observations of elevated superadiabatic layers are rare (Hodge 1956) and we have ensured that they are not caused by instrument artefacts. The presence of a superadiabatic lapse rate at the top of the moist layer in sub-tropical soundings might be explained by the following process: the temperature sensor becomes wet while passing through a cloud; later, when the radiosonde emerges from the cloud into the dry and warmer air above, the wet sensor experiences evaporative cooling, which results in a false superadiabatic lapse rate above the moist layer (Grindinger 1992; Cao et al. 2007). Superadiabatic lapse rates usually occur for less than 1 min, and the temperature sensor then quickly recovers and reports correct temperatures. Determination of superadiabatic gradients considered the following criteria: temperature lapse rate \(<-10\hbox { K km}^{-1}\) above layers with relative humidity >84 %; Wang and Rossow (1995) identified cloud layers as layers with a relative humidity of at least 84 %. Additionally, a strong variation in the slope of the temperature profile should be measured: a difference between the gradient above and below the cloud \(>3\hbox { K km}^{-1}\). The superadiabatic lapse rates induce fictitious inversion layers or enhanced inversions that must be removed. The results show that a small percentage (\(<\)6 %) of our dataset contains a non-surface superadiabatic lapse rate (Supplementary material S2) and less than 1 % fall in the characterization given in this study.

Statistics of the TWI and MBL inversion annual cycle were obtained calculating the monthly medians for the whole period, where the median is used instead of the mean value to minimize the outliers. The analysis is restricted to vertical profile intervals ranging from 1000 to 700 hPa, a region where the TWI and the MBL inversion are normally found.

4 Results and Discussion

4.1 Vertical Stability Structure

A detailed analysis of the stability vertical distribution was performed using the contoured frequency by altitude diagram, CFA diagram (Yuter and Houze 1995). The ordinate of the CFA diagram is the height (pressure level) and the abscissa is the value of the parameter whose distribution is being plotted with frequency contours, the gradient of temperature in our case, with a horizontal resolution of \(1\hbox { K km}^{-1}\). The calculated CFA diagram for the stations under study (Fig. 4) shows a high level of stratification, with values \(> 5\hbox { K km}^{-1}\) between 1000 and 700 hPa, above the typical moist-adiabatic lapse rate \((\approx {5}\hbox { K km}^{-1})\), which guarantees an absolute stability zone in this pressure interval (Stone and Carlson 1979; Schultz et al. 2000).

Fig. 4
figure 4

Contoured frequency by altitude diagram (CFA diagram) for stability \(({ \mathrm{d}T/\mathrm{d}z})\), divided in four intervals: Jan–Feb–Mar (a, e, i, m), Apr–May–Jun (b, f, j, m), Jul–Aug–Sep (c, g, k, o) and Oct–Nov–Dec (d, h, l, p), at Azores (a–d), Madeira (e–h) and Canary Islands: Santa Cruz (i–l) and Güimar (m–p). Isolines represent the frequency (%) of observations, at a particular level, which has stabilities in intervals of \(1\hbox { K km}^{-1}\), sized bin

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Fig. 5
figure 5

(Left) Annual variation of SST \(({}^{{\circ }}\hbox {C})\) and thermal stability \(({}^{{\circ }}\hbox {C})\). Averaged data were used in the Canary Islands to calculate SST parameters, from 27.6 to \(29.5^{{\circ }}\hbox {N}\) and 13.1 to \(16.9^{{\circ }}\hbox {E}\), in Madeira from 29.5 to \(35.2^{{\circ }}\hbox {N}\) and 15 to \(16.9^{{\circ }}\hbox {E}\) and in Azores from 35.2 to \(41.0^{{\circ }}\hbox {N}\) and 22.5 to \(30.0^{{\circ }}\hbox {E}\). The error bars represent the standard error. (Right) Annual cycle of the vertical velocity \((\hbox {Pa s}^{-1})\) has been calculated with NCEP Reanalysis Dataset. In reanalysis, values for the Canary Islands have been taken from 27.5 to \(30.0^{{\circ }}\hbox {N}\) and 12.5 to \(17.5^{{\circ }}\hbox {E}\), in Madeira from 30.0 to \(35.0^{{\circ }}\hbox {N}\) and 15 to \(17.5^{{\circ }}\hbox {E}\) and in Azores from 35.0 to \(40.0^{{\circ }}\hbox {N}\) and 22.5 to \(30^{{\circ }}\hbox {E}\). Averaged data by station for the year range under study (Table 1)

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The stability in the sub-tropical atmosphere shows a remarkable seasonal and latitudinal variation (Fig. 4), as previously mentioned. Months were grouped in four seasons (winter (January–March), spring (April–June), summer (July–September) and autumn (October–December)) to identify seasonal differences. This seasonal division has also been used in other studies over the North Atlantic (Goudie and Middleton 2001; Cuevas et al. 2013). The temperature lapse rate reveals a double structure within the high stability zone, with an enhanced stability (with positive temperature gradients -inversion layers-) close to 900- and 800-hPa levels. The peak of stability at 800-hPa level varies slightly throughout the year in all of the stations, with temperature lapse rate values corresponding to the 1.1 % contour interval in the range of \(\approx {5}\) and \(7\hbox { K km}^{-1}\). However, the peak of stability at 900 hPa shows high variability through the year, and is more intense at low latitude stations. In the Canary Islands the stability strengthening at 900 hPa during the summer months masks this observed double structure in the inversion layers.

Fig. 6
figure 6

Percentage of soundings with zero, one, two or more than two inversion layers, in the 1000- to 700-hPa pressure range, at Canary Islands (two locations), Madeira and Azores

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Fig. 7
figure 7

Annual cycle of the lapse rate \((\hbox {K km}^{-1})\), first column; gradient of mixing ratio \({ \mathrm{d}r/\mathrm{d}z}~(\hbox {g kg}^{-1}\hbox { km}^{-1})\), second column; and zonal and meridional wind speed \((\hbox {m s}^{-1})\), third and fourth columns, respectively. All of the figures have been calculated using only data from soundings with two inversions detected in the 1000–700 hPa range, at Azores (a–d), Madeira (e–h) and Canary Islands: Santa Cruz (i–l) and Güimar (m–p). Dotted lines indicate the average height of the base of the first (*) and second \((\square )\) inversion layer. Error bars represent the standard error

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Figure 5 (right) shows the annual cycle of the vertical velocity for the three archipelagos. During the summer months a strengthening of the downward flow is measured, which implies positive pressure vertical velocity \((\hbox {Pa s}^{-1})\). Owing to this intensification of the subsidence, mainly observed in the Canary Islands and Madeira, and to a lesser extent in Azores, stability is reinforced with higher values in the temperature lapse rate. This intensification of the stability during the summer months can also be observed in other parameters related to the strength of the inversion layer (Klein 1997; Wood and Bretherton 2006), such as the lower tropospheric stability, defined as the difference between potential temperature at 700 and 1000 hPa, which is represented in Fig. 5 (left).

Sounding observations show a high percentage of days with presence of thermal inversions, more than 75 % in all stations. Soundings with no inversions are around 25 % in Azores, 20 % in Madeira and 16 % in Santa Cruz. Only 8 % of the soundings from Güimar did not observe inversions in the analyzed pressure range. The percentage of soundings with one inversion layer is between 50 and 60 %, while the percentage of soundings in which two simultaneous inversion layers were detected is significant, between 17 and 33 %. The detection of two inversion layers is more frequent in the summer than during the rest of the year (Fig. 6), mainly in southern stations. However, in the Azores, significant seasonal variation is absent. Number and percentage of soundings with zero, one, two or more than two inversion layers is given in Supplementary Material (S3).

4.2 Analysis of the Double Structure Inversion

Some studies that find a double-inversion structure suggest that the first inversion \((\approx {900}\hbox { hPa})\) is the top of the mixing layer capping the MBL and limits dry adiabatic convection, while the second inversion \((\approx {800}\hbox { hPa})\), normally associated with synoptic-scale subsidence, is related to the trade wind (Johnson et al. 1995; Rouault et al. 1999; Von Engeln et al. 2005; Alappattu and Kunhikrishnan 2010). In this study, this double-inversion structure is explained in terms of parameters that differentiate inversion layers produced on the top of the mixing layer from those caused by subsidence.

The averaged height of the base of the first and the second inversion layers is shown in Fig. 7 (dotted lines), considering only soundings with two inversion layers detected simultaneously, being in Güimar, Canary Islands, about one third of all soundings (Fig. 6). It can be seen that the average of the base of the two inversion layers are located near 900- and 800-hPa levels, decreasing their heights during the summer months, in the Canary Islands and Madeira, when subsidence is most intense (Fig. 5). Values of temperature lapse rate are less than \(-5\hbox { K km}^{-1}\) below the first inversion, indicating a well-mixed moist layer, but unsaturated (Fig. 7, first column). The top of the mixing layer is usually close to the largest decrease in humidity with height and approximately coincides with the height of the first inversion layer in the four stations, mainly during summer months (Fig. 7, second column), and is located at a height \(\approx 900\hbox { hPa}\). These results confirm that the first inversion is associated with the top of the convective boundary layer, in agreement with the approach used by Von Engeln et al. (2005) for the determination of the sub-tropical planetary boundary-layer top and with criteria used by model reanalysis data (e.g. European Centre for Medium-Range Weather Forecasts- ECMWF model dataset), which determine the top of the boundary layer, at each gridpoint, as the level with maximum humidity drop provided that the temperature is above \(0\,^{\circ }\hbox {C}\).

Fig. 8
figure 8

Schematic vertical section depicting two different views of first and second inversion layer with low and high subsidence. High subsidence pressed air mass underneath. The top of the first inversion, a dry level, goes down along the dry adiabatic, however, in the base, which is at a very wet level, descends along the saturated adiabatic. This differential warming produces an enhancement of this inversion layer

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We have found that the wind shear (mainly the zonal component, u-component) is a suitable parameter for identifying the TWI. The u-component sharply changes its magnitude above the second inversion (Fig. 7, third column), except in Azores. This inversion is tied to directional wind shear, with a large gradient of the u-component just above, mainly during the summer in the Canary Islands and Madeira. The identification of the second temperature inversion with the TWI explains the finding of a higher percentage of soundings with two inversion layers during the summer months (Fig. 6). The MBL inversion behaves similarly throughout the year. However, the TWI is more common in summertime due to increased subsidence.

4.3 Seasonal Variation of Double Inversion. Conceptual Model.

Seasonal variation of the inversion base is similar in the two inversion layers (Fig. 7). A marked annual variation in its base heights is observed in the Canary Islands, as already reported in the literature (Tullot 1956; Dorta 1994; Cuevas 1995; Rodríguez 1999). In Madeira the annual variation is less pronounced, while no seasonal variation is observed in the Azores (Rémillard et al. 2012). Conventional wisdom suggests that variations in the inversion height depends on the SST, divergence, changes in the temperature and moisture above the inversion, horizontal advection and radiative cooling variations (e.g. Schubert et al. 1995). However, in our study region it is very likely that the influence of the SST is almost completely masked by the higher impact exerted by the strong subsidence. We also note that in summer, the season when we find greater subsidence and increased frequency of the two inversions, there is no SST latitudinal gradient, and the isotherms of approximately between 21 and \(24\,^{{\circ }}\hbox {C}\) are simultaneously found in Azores, Madeira and Tenerife, from July to September. Thus, in our case the heights of the two inversion layers (TWI and the MBL inversion) are basically modulated by the subsidence associated with the Hadley cell circulation.

Regarding the observed characteristics of the first and second temperature inversions, we propose a simple conceptual model to explain the reinforcement of the first inversion during high subsidence and its annual altitude variation. With high subsidence the entire layers are pushed down. The top of the first inversion layer, an area with low moisture, descends along a dry adiabatic, although the inversion base, next to saturation, descends along the saturated adiabatic. The different slopes of both adiabatics result in an enhancement of the first inversion layer, as shown in Fig. 8. Figure 8 (left) corresponds to a winter scheme with low subsidence and the summer scenario of high subsidence with two simultaneous inversion layers is depicted in Fig. 8 (right).

4.4 Spatial and Temporal Characterization of the MBL and Trade-Wind Inversion

The conceptual scheme previously described is corroborated by the analysis of the pressure, height, temperature, moisture, thickness, strength and wind direction associated with the base and the top of the TWI and MBL inversion, summarized in Table 2.

Table 2 Median values of pressure, temperature, height, mixing ratio and wind direction at the base and top of MBL inversion (MBLI) and trade-wind inversion; vertical gradients of z, T and mixing ratio, between base and top, of each inversion layer, in winter and summer, at four stations
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Table 3 Median values of pressure, temperature, mixing ratio and wind direction at the base and top of inversion layer, in soundings with one inversion measured between 1000 and 700 hPa; and thickness, strength and mixing ratio drop, in winter and summer, at four stations
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The first notable feature is the high uniformity observed in the pressure values of the base and the top for MBL and trade-wind inversion in all stations during the year, with a difference of only a few hPa in all of them (ranging from \(\approx {20}\hbox { hPa}\) in winter to 40 hPa in summer).

Although several studies have shown that the inversion-layer height increases toward the equator (Schubert et al. 1995; Johnson et al. 1999; Von Engeln et al. 2005) and its strength decreases (Karlsson et al. 2010), we observe the opposite, a decrease in altitude and reinforcement of the temperature inversion strength, mainly in summer months. Kloesel and Albrecht (1989) and Sun and Lindzen (1993) found that subsidence in the regions surrounding deep convection in the intertropical convergence zone remain relatively low inversions. However, this is not the case for the geographical domain of our study, where the subsidence seems to modulate the height of both temperature inversions. However, we must clarify that this overview on the latitudinal variation of the inversion layer height found in the literature refers to general atmospheric conditions (including land and ocean) at a hemispheric scale, and our results are limited to a short latitudinal transect (\(28^{{\circ }}\mathrm{N}\) to \(40^{{\circ }}\hbox {N}\)) over the ocean.

The height of both MBL and trade-wind inversion decreases when increasing subsidence (vertical velocity from \(-\)4 to \(8~\times ~10^{-4}\hbox { hPa s}^{-1})\) in Madeira and the Canary Islands, at a rate of \(\approx {3}~\times 10^{-5}\hbox { m hPa}^{-1}\hbox { s}\), because they are located just below the descending branch of the Hadley cell. In the Azores the influence of the subsidence is negligible due to its location in mid latitudes. The similar slopes found for MBL and trade-wind inversion suggests that both temperature inversions are modulated by the subsidence; base-inversion height of MBL and trade-wind inversion versus vertical velocity is included in the Supplementary Material (S4).

The strength of the MBL and trade-wind inversion are very similar in all stations during winter, ranging within \(1\,^{{\circ }}\hbox {C}\). However, the strength variability of the MBL inversion found in summer between the Azores and the Canary Islands is higher, within \(2\,^{{\circ }}\hbox {C}\). The TWI does not show this latitudinal dependence in summer time. These observations confirm the proposed conceptual model. The MBL inversion was identified as the layer with maximum humidity drop \(({\approx }-3\hbox { g kg}^{-1})\), which is more than double to the one associated with the TWI \(({\approx }-1\hbox { g kg}^{-1})\), except in the Azores, where the MBL inversion humidity drop is slightly higher \(({\approx }-0.7\hbox { g kg}^{-1})\) than that observed in the TWI.

4.5 Spatial and Temporal Characterization of the Single Inversion Layer

Over 50 % of the soundings show a single inversion layer within the 1000- and 700-hPa pressure range in all the stations (Fig. 6). The height of this inversion is located between the levels at which we find the MBL and trade-wind inversion when they are observed simultaneously (mainly in summer), but closer to the height of the MBL inversion as we move south (Table 3). The temperature at the base is generally slightly cooler than the one found at the MBL and trade-wind inversion bases, and at the top-inversion the temperature is intermediate to those recorded at the top of the MBL and trade-wind inversion in the Azores and Madeira, and significantly higher than those found in the two stations in the Canary Islands. The mixing ratio drop is significantly higher in the case of a single inversion and reveals an increase to the south station. The strongest single inversion is found in summer in the Santa Cruz station where the median thickness is \(\approx 390\hbox { m}\) and the inversion gradient is \(4.6~^{{\circ }}\hbox {C}\). In Güimar, the mixing ratio drop reaches \(-5.6\hbox { g kg}^{-1}\).

The main characteristics of single inversion match those associated with the MBL inversion, as there is a strong moisture gradient and, in general, no wind shear. Santa Cruz is the only station where the single inversion layer shows features of both MBL and trade-wind inversion: a clear directional wind shear (\(\approx 16^{\circ }\) wind direction at the base and \(\approx 2^{{\circ }}\) at the top) and high mixing ratio drop \((-\hbox {4.8 g kg}^{-1})\). In the other stations, only a mixing ratio drop greater than \(-\hbox {2.3 g kg}^{-1}\) is observed in all cases.

An analysis of the physical processes that modulate our finding of one or two temperature inversions was attempted. A slight relationship between the subsidence at the 700-hPa level and the number of temperature inversions in the Canary Islands stations (\(0.059\pm 0.001\hbox { Pa s}^{-1}\) for single inversion and \(0.062\pm 0.003\hbox { Pa s}^{-1}\) for two inversions) and Madeira (\(0.055\pm 0.001\hbox { Pa s}^{-1}\) for single inversion and \(0.058\pm 0.002\hbox { Pa s}^{-1}\) for two inversions) have been detected. Other atmospheric mechanisms, including dynamic flow associated with pressure patterns might be behind this dual behaviour of atmospheric stability in the lower sub-tropical troposphere. The complexity of these studies is beyond the scope of the present study and will be subject to detailed analysis at a later date.

5 Conclusions

An analysis of the lower tropospheric stability along the east side of the sub-tropical North Atlantic was performed using a long-term dataset; 43,262 upper soundings from archipelagos in the Canary Islands (Tenerife), Madeira (Madeira) and Azores (Terceira) corresponding to a period of about 30 years.

A significant percentage of the soundings reveals two simultaneous inversion layers at lower altitude (below 700 hPa), ranging from 17 % (Azores) and 33 % (Güimar, the Canary Islands), being more common in southern stations and in summer. This double structure is normally observed at about 900 and 800 hPa. We have shown, using parameters that characterize both the marine boundary layer (MBL) and the trade-wind inversion (TWI) that the first inversion is associated with the top of the MBL, close to 900 hPa, where there is a maximum vertical mixing ratio drop. This decrease at the Canary Islands and Madeira is more than double that associated with the TWI. On the other hand, the stability peak near 800 hPa is associated with the TWI, which coincides with a maximum directional wind shear, such that the wind direction turns abruptly counterclockwise when we ascend through the TWI.

Seasonal and latitudinal differences in the MBL inversion and the TWI are related with seasonal and latitudinal variations of large-scale subsidence. Consequently, increased subsidence during the summer months, especially at southern stations, produces a strengthening of the first inversion, and a similar sinking at the height of both layers with no variation in the vertical distance between the MBL and the TWI.

A simple conceptual model has been proposed that explains the strengthening of the MBL inversion during summer and the low altitude of both inversions. Greater subsidence causes a downward movement of the first inversion top along a dry adiabatic, while the base descends along a saturated adiabatic, resulting in a differential warming, and thus, a reinforcement of this inversion.

Although in previous studies the height of inversion layer increases as we approach the equator and its strength decreases, in the range of latitudes of this study (\(28^{{\circ }}\hbox {N}\) to \(40^{{\circ }}\hbox {N}\)), the opposite is observed. This result can be explained by the absence of a latitudinal gradient of the SST during the summer months in this zone, when subsidence is high, especially in the southern stations.

Over 50 % of the soundings show a single inversion between 1000 and 700 hPa. This inversion is located approximately between the levels at which we find the MBL and TWI when they are observed simultaneously, but closer to the height of the MBL inversion as we move south. In terms of temperature gradient, thickness, and mixing ratio decrease, clearly one inversion layer is associated with the MBL, except in Santa Cruz, where the single inversion layer reveals features common to both MBL and TWI.