The Spinning Enhanced Visible and Infrared Imager (SEVIRI) sensor, mounted on the geostationary Meteosat Second Generation (MSG) satellites, is ideally suited to provide spatiotemporally coherent observations of clouds. It features a spatial resolution of 3 km at nadir and scans its full disk every 15 min 96 hemispheric scans per day;. In the context of this study, 14 years (2004–2017) of SEVIRI data are used to continuously detect FLCs with the algorithm developed by . The algorithm relies mostly on a channel difference in the thermal infrared (12.0–8.7 µm), and in an extensive validation against surface observations this technique has shown a good performance (97 % overall correctness of the classification). The 14-year FLC data set used here has already been applied to study spatial and temporal patterns of FLC occurrence along the southwestern African coast in . It should be noted that this satellite technique does not discriminate between fog and other low clouds.

The focus of this study is on FLCs in the central Namib, from which the majority of historical and present-day station measurements stem e.g.,. To provide a representative measure of the overall FLC cover in the central Namib on a daily basis, FLC occurrence is averaged between 03:00 and 09:00 UTC (local time is UTC +2 h) in the region between 22 and 24∘ S and up to 100 km inland. Only pixels with at least a 5 % FLC occurrence frequency in the climatology as in are used. A specified averaging time period is needed to avoid statistically mixing two separate FLC events occurring on successive nights, which would be the case in a daily average FLC occurrence data set. The specific time period is chosen to include all periods of the diurnal cycle, with FLC occurrence rising, peaking, and starting to dissipate during this time. The spatial and temporal averaging is illustrated for an exemplary day in Fig. a. While the specific day shown here is arbitrary, the general feature of maximum FLC cover in the early morning hours and rapid decline shortly after sunrise is typical of the region . For further analyses, the data set is divided into “FLC days” with mean regional FLC cover exceeding 50 % between 03:00 and 09:00 UTC and “clear days” with mean FLC cover below 3 %. These thresholds are chosen to represent two clearly separated parts of the FLC cover distribution that occur with similar frequencies. The resulting distribution of daily average FLC cover and the number of cases in each class are shown in Fig. b. As the time of sunrise varies by season, the constructed data set is likely to feature a seasonal bias in FLC occurrence. It should be noted that this has no effect on the separation of FLC days and clear days within seasons, the analysis of which is the main purpose of this data set. The resulting monthly average FLC cover in the central Namib (Fig. c) should not be used in a quantitative sense but rather to illustrate the general seasonal cycle of FLCs in this region. It is interesting to note that the seasonal cycle of FLCs is not necessarily coupled to the seasonal cycle of fog occurrence due to the seasonal cycle in the vertical position of the low-cloud layer. For example, at coastal locations fog peaks in the central Namib between April and August , while marine fog over the adjacent Atlantic has been found to peak between March and May, with a minimum occurrence between June and August .

To investigate the large-scale meteorological conditions associated with FLCs in the central Namib, ERA5 reanalysis data from the European Centre for Medium-Range Weather Forecasts (ECMWF) are used. ERA5 is the new generation of reanalysis and follow-up of ERA-Interim . In comparison to ERA-Interim, it features higher spatial (0.25∘) and temporal (hourly) resolutions, along with other improvements .

In the context of this study, 14 years (2004–2017) of meteorological fields are analyzed. To characterize large-scale dynamic and thermodynamic conditions, fields of mean sea level pressure (MSLP), geopotential height at 500, 700, 850, and 925 hPa (Z500, Z700, Z850, and Z925), 2 m air temperature (T2m), sea surface temperature (SST), total columnar water vapor (TCWV), specific humidity (Q), as well as winds at 10 m and at all ERA5 pressure levels between 1000 and 500 hPa, and lower tropospheric stability LTS; computed as the difference between potential temperature at 700 hPa and T2m, are used. To represent the morning conditions for which FLC is averaged, 06:00 UTC fields of ERA5 data are selected. While, for additional analysis, T2m fields are also used at nighttime (01:00 and 03:00 UTC), the 06:00 UTC fields are used if no specific information on time is given.

The 24 h backward trajectories are calculated using the Lagrangian analysis tool LAGRANTO;. The three wind components needed for the trajectory calculations are taken from ERA5 on a regular 0.5∘ latitude–longitude grid, at 137 model levels in the vertical, and at a 3-hourly temporal resolution. The spatial resolution is used to reduce the data volume and computational cost. While the native resolution would be preferable, the general patterns of the trajectories are not expected to be affected, as tests with lower-resolution ERA-Interim data showed comparable results. The trajectories are started daily at 06:00 UTC for the periods April, May, June, September, October, and November 2004–2017. Their starting points are located in the central Namib, close to Gobabeb at 23∘ S, 15∘ E, 25 hPa above the surface (at ≈940 hPa), which corresponds roughly to 200 m above ground level. By doing so, the back trajectories represent air masses for the levels where fog and low clouds in the region are typically observed . In order to obtain insights about the physical properties of the air masses, the temperature, potential temperature, specific humidity, and relative humidity are tracked along the trajectories. The location is chosen, as it is the main site of both historic and present-day scientific activity in the region .

The atmospheric variability in the South Atlantic Ocean and southern African region is characterized by means of a principal component analysis (PCA; see). PCA solves the eigenvalues of the data covariance matrix and projects data variability onto an orthogonal basis, i.e., decomposes data variability into independent variability modes. Each mode explains a fraction of the total variance and is represented by a spatial anomaly pattern and a standardized time series (namely, the principal components, PCs) accounting for the amplitude of the anomaly pattern. Here, the PCA is used to analyze daily fields of the zonal and meridional components of 10 m wind at 06:00 UTC in a domain centered on the Namib (0∘–40∘ E, 40∘ S–0∘ N). In the context of this study, the main modes of the wind variability are used to understand possible linkages between atmospheric circulation at the synoptic scale and the daily occurrence of FLCs in the Namib region. The wind fields are first remapped onto a 1∘ regular grid (PCAs are computationally expensive; ). Then daily 06:00 UTC anomalies are computed by subtracting the 14-year climatological average wind components at each grid point. The PCA is applied to the covariance matrix of both components in the domain. Remapping to 1∘ resolution allows not only an accurate description of the atmospheric variability at synoptic scale but also a smoothing out of the variability associated with small-scale effects. The sensitivity of the PCA to the spatial resolution is tested by conducting the analysis based on wind fields remapped to a 2∘ resolution. The results of the two PCAs at the different resolutions are very similar, demonstrating their robustness. Daily anomalies are computed with respect to the 14-year sampling of the FLC data set, in order to compare wind and FLC variability over a homogeneous climatology.

Statistical modeling of fog or low clouds is typically done by using local fields of a set of predictors, i.e., relevant meteorological fields and aerosol properties e.g.,. The circulation-induced variability can be captured by spatial patterns of pressure fields . A major challenge when using pressure fields (denoted X, as an n×p matrix of n samples and p predictors located on a grid) to predict a target variable is, however, that the number of (strongly correlated) predictors can quickly outgrow the number of observations. This typically leads to high-variance problems (overfitting) in classical statistical models. The issue can be overcome with shrinkage methods, as, e.g., regularized linear models . These provide an extension of linear regression techniques that shrink the regression coefficients of a model by penalizing their size, thereby addressing the aforementioned high-variance issues . Ridge regression is a specific example of a regularized linear model where the shrinkage is controlled by a value λ that shrinks the coefficients of the model towards zero using the L2 penalty (the squared magnitude of the coefficient value is added as a penalty term to the loss function). This method is well suited for cases with a large number of correlated predictors that are all relevant (coefficients >0) . The method can be used for classification and regression .

Here, the statistical learning method is used in a classification setting. That is, a binary response variable (FLC day or clear day) is modeled using logistic regression regularized with the ridge penalty. In logistic regression with a binary response variable, the “odds ratio”, log⁡Pr(FLC day|X=x)Pr(clear day|X=x), is estimated as a linear function of the predictors for any given day as follows: 1log⁡Pr(FLC day|X=x)Pr(clear day|X=x)=β0+βTx, with β0 the intercept and βT the model coefficients. From the odds ratio, the estimated probabilities and the corresponding class (FLC day or clear day) are determined for each sample. The ridge regression penalty based on the L2 norm, i.e., R(λ)=λ∑i=1pβi2, is then incorporated as a constraint on the size of the regression coefficients in the objective function that is minimized to fit the model. The tuning parameter λ directly trades off between a more flexible regression model (small penalty, i.e., low λ value) that, however, possibly suffers from high-variance issues and a less flexible regression model. Accordingly, a larger value of λ enforces smaller (but nonzero) regression coefficients, and a smoother spatial map of regression coefficients is obtained as a result. The optimal λ value is derived through 10-fold cross-validation. For a more complete description of regularized (logistic) regression, the reader is referred to and the ElasticNet vignette for a hands-on tutorial (https://web.stanford.edu/~hastie/glmnet/glmnet_alpha.html, last access: 5 October 2019). Model estimation and cross-validation was performed using the scikit-learn package in Python .

The ridge regression method is used to predict FLC and clear days over the complete 14-year time series, using spatial patterns of 06:00 UTC (representative of averaging time of FLC cover; see Sect. 2.1) ERA5 MSLP fields in a large spatial domain centered on the central Namib (0–45∘ S, 8∘ W–38∘ E; shown in Fig. ). The ERA5 pressure fields feature a spatial resolution of 0.25∘×0.25∘ and as such lead to 33 485 predictor fields.

Figure  shows a climatology of the dynamic and thermodynamic characteristics of the southeastern Atlantic and southern African region based on 14 years (2004–2017) of ERA5 data. Two seasons are shown in the figure that are representative of two different fog regimes described in the next paragraph;: September, October, and November (SON) in Fig. a and c and April, May, and June (AMJ) in Fig. b and d. At this spatial scale, the South Atlantic High and the continental high control the characteristic near-surface flow patterns during both seasons. During SON, the South Atlantic High is more prominent and, in combination with the thermal contrast between land and ocean, results in the formation of a low-level jet during this time . This alongshore coastal jet intensifies the upwelling of cold water, which feeds back to amplify the jet by increasing the thermal land–ocean contrast . On a local scale, the near-coastal winds that drive the upwelling are additionally modulated by the coastal topography . While more prominent during SON, when the more pronounced South Atlantic High produces stronger winds, coastal upwelling water of the Benguela Current is apparent in the relatively low SSTs along the southwestern African coastline during both seasons (Fig. c and d) and throughout the year . During AMJ, continental high-pressure situations are the most prominent circulation pattern . This is visible in the more pronounced continental high-pressure system and leads to a marked amplification of the easterly flow over the southern African continent. In the Namib Desert, thermally and topographically induced local wind systems within the boundary layer modulate these synoptic air-flow patterns, and the significance of the induced diurnal oscillations can exceed that of the synoptic scale . The combination of large-scale subsidence and low SSTs along the coastline produces high-LTS conditions in the coastal marine regions adjacent to the Namib, specifically during SON (LTS contours in Fig. c and d). In the adjacent marine regions downwind of the central Namibian coast, these stable conditions promote the formation of the southeastern Atlantic stratocumulus cloud deck and controls its seasonal cycle , where the SST component is responsible for most of the LTS seasonality. One should note that MSLP and LTS are both affected by the high elevation of the central plateau in southern Africa (see Fig. ) and are not likely to be a perfect representation of near-surface pressure conditions and lower-tropospheric stability in this region. However, due to the joint consideration of regions in southern Africa with high topography, the low-lying central Namib, and marine regions, no one specific pressure level of geopotential height can adequately summarize near-surface conditions throughout this large domain. Additional analyses show that patterns obtained from MSLP fields in southern Africa are similar to those at 925 and 850 hPa (not shown).

As outlined in the introduction, distinct seasonal fog and FLC patterns have been identified in the central Namib . During SON, described as “high FLC season” in , FLCs frequently occur in the central Namib as a low stratus or high fog (cloud base height on average ≈400 m a.s.l. – above sea level) that touches the ground inland, whereas during the “low FLC season” in AMJ, FLCs occur less frequently, do not extend as far inland, and are typically lower, at ≈200 m a.s.l., and thus register as fog termed “advection fog” in at locations closer to the coastline . While the FLC occurrence in the central Namib peaks in austral summer and is lowest during winter, fog peaks at coastal locations in AMJ and at inland locations during SON due to the seasonal cycle in the vertical position of the cloud layer . For these reasons, this study focuses on mechanisms determining FLC variability within these two characteristic fog seasons.

It has been assumed that the occurrence of FLCs in the Namib region and their variability on diurnal to seasonal scales is driven by the position and strength of large-scale pressure systems, as this would affect occurrence and advection of low-level clouds, atmospheric stability, and SSTs . Coastal upwelling, which has been shown to determine marine sea fog patterns along the Namibian coastline , in combination with the presence of a coastal low that drives the onshore advection of foggy air masses has been found to be a major driver of fog occurrence in southern Namibia during austral summer . One should note though that the relationship between SSTs and fog in the Namib region is complex; point out that too large an upwelling extent can also lead to less fog in southern Namibia. Based on these insights and also on knowledge from related coastal upwelling systems , it is clear that the Atlantic anticyclone, the SSTs, and the large-scale subsidence are main drivers of this coastal FLC system. While all of these links play a role in FLCs in the Namib, the influence of synoptic-scale variability has not been explored, and a more in-depth analysis is needed to estimate the importance of the different mechanisms for the day-to-day variability in FLCs in the Namib region.

Figure  shows large-scale patterns of averaged monthly mean differences in (a) MSLP and 10 m winds, (b) Z500 and winds at the same pressure level, (c) T2m, (d) LTS, (e) SST, and (f) TCWV on FLC versus clear days (as defined in Sect. ) in the central Namib (marked with a star) during the investigated 14-year period (all months are considered here). The average of monthly mean differences is chosen rather than the overall mean differences to account for the distinct seasonal cycle of FLC occurrence in the Namib (Fig. c). In each pixel, an independent two-sided t test is computed to identify significant differences between the two classes (contours show p values <0.01). It is apparent that the dynamical conditions (Fig. a and b) on FLC days differ significantly on the synoptic scale. On FLC days, MSLP over continental southern Africa is systematically lower by about 3–5 hPa. This anomaly of lower MSLP extends over the southeastern Atlantic ocean at about 30∘ S. In a smaller oceanic region along the coastline north of 23∘ S, MSLP is significantly higher, leading to an overall anomalously high land–sea pressure gradient in this region and an onshore flow anomaly of near-surface winds in the central Namib on FLC days. The land–sea contrast in MSLP indicates a heat low over land, where the heat anomaly (Fig. c) could be driven by northerly advection ahead of the trough or enhanced surface warming. As discussed in Sect. , MSLP and 10 m winds may not be a good representation of near-surface level characteristics where topography is high; however, additional analyses of geopotential height at 850 and 925 hPa corroborate observed MSLP patterns. Differences exist in winds north of the central Namib, where at 925 and 850 hPa (not shown), a stronger onshore flow anomaly is observed than at 10 m, possibly indicating a topographical blocking of the onshore flow below the inversion. Z500 on FLC days (Fig. b) is significantly lower over the southeastern Atlantic between 30 and 40∘ S. This pattern is an indication of upper-level waves disturbing the mean tropospheric circulation of the southeastern Atlantic and southern Africa . In combination, MSLP and Z500 show a weakly baroclinic structure with the mid-level trough shifted to the west (see Fig. ). While a coastal low, which has been described in as a local feature that can determine onshore flow, may still be present on FLC days, the composite differences between FLC days and clear days do not provide a clear indication of an increase in its presence on FLC days on average. However, as describe, the coastal low is frequently followed by a frontal passage, which is a synoptic-scale signal observed here (Fig. ).

There is a coherent pattern of slightly lower SSTs (≈0.5 K; Fig. e) along the coastline on FLC days; however, the difference between SSTs on FLC and clear days is not significant at the 0.01 level (and also not at the 0.05 level). It is interesting to note that SSTs tend to be lower on FLC days, although the coast-parallel, near-surface wind that partly governs the upwelling is slightly weaker in these cases (Fig. a), potentially hinting at a time-lag response of SSTs. This is to be expected, as Ekman transport produces a steady-state situation only after a few pendulum days , although an initial upwelling response can be expected earlier . It appears likely that effects of SST patterns on FLC variability are most pronounced on longer timescales (i.e., seasonal to interannual) that feature higher SST variability , as also observed in the Chilean Atacama Desert . Differences in TCWV on FLC and clear days are pronounced (Fig. f). A coherent region of a significantly dryer column stretches from the central Namib over the coastal Atlantic, where the anomaly is strongest. This is likely the dry slot or dry air intrusion of the synoptic-scale disturbance, which leads to increased longwave cooling at cloud top in case of FLC presence and has been shown to be a main determinant of cooling within the marine boundary layer . This enhanced cooling can increase FLC cover, which has been observed to be a significant mechanism for stratocumulus clouds over the southeastern Atlantic . A substantial moist anomaly is visible over the southern African continent, likely driven by large-scale free-tropospheric moisture transport from the northwest (Fig. b). These moist air masses may contribute to the observed T2m heat anomaly via greenhouse warming (Fig. c). This effect of free-tropospheric moisture on surface temperatures has been observed in the Kalahari Desert and other arid or semi-arid regions before . Along the coastal strip that is typically overcast with FLCs , T2m is significantly lower by about 4 K, which is likely a feedback of FLCs reflecting solar radiation and slowing down the surface heating in the early morning or due to air-mass differences. The observed difference patterns in LTS (Fig. d) between FLC and clear days match those of T2m so that they can be assumed to be mostly driven by its surface component (Pearson correlation coefficient is -0.90 for land pixels).

The observed anomaly patterns indicate that different mechanisms are triggered by the observed synoptic-scale disturbances and may contribute to FLC occurrence in the central Namib in two main ways:

increased FLC cover due to increased longwave cooling under the dry anomaly close to the coast;

Figures  and  show seasonally averaged differences between FLC and clear days of all analyzed parameters during the two seasons SON and AMJ. During both seasons, MSLP (Fig. a and b) and Z500 (Fig. c and d) indicate synoptic-scale disturbances on FLC days. However, seasonal differences exist, as the disturbance is more pronounced during AMJ. The negative continental MSLP anomalies on FLC days are larger during AMJ, likely amplified by the more pronounced T2m anomalies and subsequent effects on a continental heat low during this time (see Fig. c and d). As noted above, the continental heat anomaly can be caused by northerly warm air advection or enhanced warming due to changes in the radiative balance. The observed seasonal MSLP and 10 m wind anomalies (Fig. a and b) that result in a transport of warm air from the northeast into the anomaly region (see Fig. ), as well as the TCWV anomalies (Fig. a and b), suggest that during SON, the heat anomaly on FLC days is mostly due to northerly advection of warm air, whereas during AMJ, TCWV is significantly increased over the southern African continent. Here, the T2m anomalies closely follow those of TCWV (Pearson correlation coefficient of 0.75 in continental regions, with significantly higher T2m on FLC days than clear days), suggesting that the increased moisture causes an additional surface heating due to greenhouse warming as discussed in Sect. . It is likely that the TCWV anomaly is caused by a large-scale free-tropospheric moisture transport from the tropics, which is supported by the marked wind anomalies at 500 hPa (Fig. d) that show a northwesterly anomaly and the absolute wind and moisture fields at 700 hPa during this time (Fig. ). It should be noted that a Lagrangian transport of moisture at this scale takes time and as such is likely to occur when the disturbance is relatively stationary or if two consecutive systems pass within a short timeframe .

While the yearly averaged composites show that over land, LTS is driven to a large extent by T2m (Fig. c and d), this is not quite as pronounced during SON (correlation coefficient =-0.57; Fig. c and e). Over continental southern Africa, the differences in T2m (Fig. c) are frequently compensated for by similar differences in potential temperature at 700 hPa (not shown). The most pronounced LTS feature during both seasons, however, is the coastal anomaly of increased LTS (over land and weaker over the adjacent ocean), which is driven by T2m. As this anomaly is also apparent during nighttime (01:00 and 03:00 UTC, not shown), it is likely that this pattern is mainly due to the relatively warm subsiding continental outflow that is apparent on clear days, rather than a radiative effect of FLCs as found in California . During AMJ, LTS is significantly lower over a large marine region south of 25∘ S, which is likely caused by the synoptic-scale disturbance.

During both seasons, SSTs in the coastal upwelling region are slightly lower on FLC days than on clear days, although these differences are not significant at the 0.01 level for the most part (very localized regions at ≈28∘ S are significantly lower during AMJ). In isolated patches further south, upwind of the study area, SSTs tend to be significantly higher on FLC days. This could lead to increased surface latent heat fluxes, increasing the moisture content of the marine boundary layer, particularly during AMJ when stronger near-surface winds are also apparent. A few 100 km to the west and south of the Namibian coastline, SSTs could similarly add to the increased moisture within the marine boundary layer. It is not clear yet, however, what exactly drives the observed anomaly patterns of SSTs. As upwelling reacts to the time-integrated wind field forcing over longer timescales than analyzed here , the SST response to the instantaneous winds that are considered here is expected to be relatively weak. However, in the case of a relatively stationary disturbance as discussed above, the upwelling patterns could indeed reflect an SST response to a synoptic forcing. While the seasonally varying TCWV and SST anomalies (Figs. e, f and a, b, respectively) illustrate the seasonal variability in the mechanisms that can contribute to FLC occurrence in the central Namib, during all months, the outlined systematic patterns of significant negative MSLP anomalies over continental southern Africa and the localized coastal high-pressure anomaly are apparent. It can be concluded that a low-pressure anomaly in continental southern Africa and the associated onshore advection of marine boundary-layer air masses facilitate FLC occurrence in the central Namib during the entire year.

To better understand the characteristics of the observed moisture transport and its relevance for FLC occurrence in the central Namib, information on the vertical patterns of moisture and wind anomalies is needed. Figure  shows average seasonal differences in Q and winds on FLC versus clear days at different pressure levels during (a) SON and (b) AMJ (averaged between 20 and 25∘ S). During both seasons, a complex vertical structure of Q anomalies is apparent, which is assumed to be disturbance-induced. During both seasons, the marine boundary layer features an onshore flow anomaly and is more humid on FLC than on clear days, especially during AMJ, when this is a synoptic-scale feature, likely related to the cold front of the disturbance. These differences are caused by the subsiding dry continental easterly air masses that dominate on clear days, whereas on FLC days, a slight onshore flow of the more humid marine boundary-layer air is observed in the central Namib. Over land, these marine air masses flow against the dominant continental easterly winds , producing a northerly wind flow at ≈15∘ N (not shown) that has been found to be associated with fog occurrence in the central Namib . Above the moist marine boundary layer, the free troposphere is relatively dry on FLC days during both seasons, a feature which is not as clearly visible in the columnar TCWV composites during AMJ, as it is masked by the moist anomaly in the marine boundary layer (Fig. a). It is interesting to note that the marine dry anomaly peaks between December and February (not shown), the season with maximum FLC cover in the central Namib, with TCWV anomalies exceeding 10 kgm-2. The seasonal difference in the free-tropospheric Q anomalies over the continent is clear, and the vertical distribution of Q anomalies during AMJ corroborates the assumption that the observed positive TCWV anomalies are due to free-tropospheric moisture transport (Fig. b). Expressed in relative terms, Q is approximately halved within the dry anomaly region on FLC days during both seasons, suggesting that radiative cooling is an important factor for FLC cover, especially over marine regions where the dry anomaly is most pronounced. During AMJ, the free-tropospheric relative moisture difference between FLC days and clear days is observed to be as high as 220 %. This substantial increase in free-tropospheric moisture in this otherwise dry central plateau region induces a substantial surface heating, contributing to the formation of the observed heat low, which modulates regional wind systems and leads to the onshore flow anomaly.

It should be noted that in a comparable upwelling system (coastal California), also find a positive relationship between T2m over land and coastal low-level cloudiness, with the T2m anomaly shifted poleward by about 5∘ latitude from the cloud field. They propose that the T2m–cloud relationship is due to spatially offset associations between coastal low-level cloudiness and stability (potential temperature at 700 hPa), which is strongly correlated to T2m over land, thereby resulting in the T2m anomaly, rather than T2m driving the onshore advection. While in the central Namib the anomaly patterns between potential temperature at 700 hPa and T2m are similar in that they are also positively correlated during SON (and therefore compensate each other in terms of LTS; Fig. c and e), they are uncorrelated during AMJ (and also in the annual averages), when T2m over land is strongly correlated to TCWV. Also, during all times of year, the T2m and MSLP anomalies are directly inland from the cloud field, suggesting an influence on onshore advection.

Air-mass back trajectories, initiated in the central Namib, close to Gobabeb at 23∘ S, 15∘ E (indicated by the star in Fig. ), 06:00 UTC, and 25 hPa above ground level (approximates 200 m above ground level), are computed for the 14-year observational period. Figure  shows the back trajectories for FLC days (a, b) and clear days (c, d) for the two seasons SON (a, c) and AMJ (b, d). During both seasons, air masses on FLC days nearly exclusively stem from the marine boundary layer and have traversed over the cool upwelling ocean water along the coastline for the time span of 24 h. This is in agreement with findings from , which noted that a marine origin of air masses is critical, and potential mixing with continental air masses along the trajectory that would lead to a warming and drying. While the number of FLC days during SON is higher than during AMJ, following the general seasonality of FLCs in the region (see Fig. c), no clear seasonal differences in air-mass dynamics can be observed in such situations. This suggests that during both seasons, similar local dynamic conditions drive FLCs or air masses that develop into FLCs inland into the Namib Desert but that due to seasonal differences in large-scale dynamics, these situations occur with varying frequency during different seasons.

On clear days, air-mass histories are more diverse and show distinct seasonal differences but are frequently characterized by subsiding continental air masses. While on clear days during SON a considerable fraction of the air masses is still transported from the marine boundary layer, during AMJ, subsiding northeasterly continental air masses dominate. This seasonal shift in air-mass dynamics is likely driven by the seasonality of the two dominating high-pressure systems of the region that is shown in Fig. . During AMJ, the continental high-pressure system is enhanced and leads to the stronger easterly flow. These observations support the hypothesis by that the seasonality of fog in the central Namib is to some extent controlled by the southern African high-pressure system, as the associated easterly winds are likely to inhibit large-scale onshore advection of cloudy marine boundary-layer air masses. The results also suggest that aerosols from the biomass burning season in continental southern Africa are unlikely to play a large role for fog formation by acting as cloud condensation nuclei, as biomass burning aerosols within the boundary layer are mostly associated with continental air masses in this region . However, biomass burning aerosols may influence FLCs in the Namib region by absorbing solar radiation and modifying the thermodynamic conditions, which has been modeled and observed to influence the Namibian stratocumulus deck .

While systematic differences in air masses exist between FLC days and clear days, clear days may still feature air masses that are advected from the marine boundary layer (see Fig.c). To understand the differences between the FLC days and clear days in such situations, these are isolated and analyzed in the following. Figure  shows the average Q, relative humidity (RH), air temperature (T), potential temperature (pot. T), and pressure (P) along all of the back trajectories that are advected from the marine boundary layer (here, P>900 hPa over ocean). It is apparent that these air masses contain significantly more moisture and feature significantly lower pot. T on FLC days than on clear days, which explains most of the difference in RH. The back trajectories of FLC days feature a stronger cooling during the last 10 h of advection (hours 0–10), resulting in an additional increase in RH. The deviation in T between FLC and clear days seems to be driven by the vertical movement of the air masses, rather than differences in radiative cooling, as no changes in pot. T are apparent. At 10 h before initialization, air masses on clear days are located ≈20 hPa higher than on FLC days, not cooling off as they are advected due to their simultaneous subsidence. Other potential factors that may drive the observed deviation in T, such as the free-tropospheric moisture content and the surface temperature along the back trajectories, were not found to be systematically different on FLC and clear days (not shown). These findings highlight that FLCs Namib in the region are dependent on dynamics and also that marine boundary-layer moisture content and temperature changes during advection are important controls as well.

It is likely that the computed air-mass back trajectories do not fully capture thermally and topographically induced local air-flow patterns seefor a review that contribute to local FLC occurrence patterns and possibly formation. However, the larger-scale patterns of air-mass history of marine boundary-layer air masses versus the subsiding continental air masses from the free troposphere are clearly evident from the analysis presented and offer a consistent physical explanation of the large-scale FLC occurrence patterns. The observations suggest that FLCs in the Namib region are either advected after forming over the cool adjacent ocean or condensation takes place during advection of the marine boundary-layer air masses over land due to higher humidity levels, lower temperatures or radiative cooling, though a mix of these processes is likely.

The analysis of air-mass back trajectories shows that the discrimination between FLC and clear days is not possible using dynamics alone and that seasonal differences exist in the link between the probability of FLC days and advection patterns. To further investigate the role of different dynamical regimes for FLC occurrence, a PCA is conducted on spatial patterns of synoptic-scale near-surface winds (see Sect.  for details on the method). Figure a shows correlations between daily FLC cover in the central Namib and the PCs associated with the first six modes of variability in near-surface winds during all months of the year. All PCs are significantly correlated to FLC cover during some months of the year. Clear correlation patterns are evident; PCs 1, 2, 4, and 5 show negative correlations with FLC cover, while PCs 3 and 6 feature positive correlations. These PCs that facilitate FLC occurrence (3 and 6) show westerly or northwesterly wind anomalies in the central Namib, while PCs that are negatively associated with FLC cover in the Namib region feature anomalously strong continental easterly winds, consistent with results presented in Sect.  and . Figure c and d show the spatial patterns of near-surface wind anomalies of PCs 3 (explained variance: 11 %) and 4 (explained variance: 6 %) as examples for PCs that promote and impede FLC occurrence, respectively. A seasonal dependence of the correlations on PCs and FLC cover is apparent and seems to be related to the seasonality of FLC cover (Fig. b); PCs associated with onshore circulation in the central Namib feature the strongest positive correlations during winter when FLC cover is generally lowest over the Namib, especially evident for PC 3. This appears plausible, as during winter, the typical dynamical setting is less conducive to FLCs (see Fig.  for fall/early winter conditions during AMJ), and consequently, FLC occurrence is dependent on a stronger dynamical disruption during this time. During summer, when FLCs frequently occur in the central Namib, dynamical conditions associated with PCs 4 and 5 (dominance of continental easterlies) seem to impede the occurrence of FLCs. The results underscore that the advection of marine air masses is crucial for the occurrence of FLCs in the central Namib.

Based on the evidence presented above, showing that FLC occurrence is tightly connected to synoptic-scale patterns, it can be assumed that FLC occurrence can be predicted to some extent with a statistical learning technique that utilizes spatial patterns of dynamical information. Here, a ridge regression is applied to classify FLC days and clear days based on MSLP fields in a region spanning 45∘×45∘ that is centered on the central Namib (see Sect. 2.4). MSLP fields are used, as their anomaly patterns on FLC days are similar during the different analyzed seasons and thus summarize the controlling mechanisms of onshore advection of marine boundary-layer air masses. Figure a shows the resulting coefficients, i.e., regression slopes, of the statistical model. The sign and spatial patterns of the coefficients are similar to the observed MSLP anomalies shown in Fig. , where coefficients (and anomalies) are negative in the inland region of Namibia and positive along the northern part of the Namibian coastline. It should be noted that the statistical model seems to mostly rely on regional MSLP fields, resulting in low coefficients at the synoptic scale, e.g., the Atlantic high-pressure system. It can be concluded that the synoptic-scale pressure patterns set the stage for more localized pressure and wind modulations that determine FLC occurrence and that regional MSLP fields contain information on both.

Figure b gives a summary of statistical measures of the skill of the model to classify between FLC and clear days in the central Namib. Using MSLP fields at 06:00 UTC on the day of the FLC cover information, the ridge regression model has a probability to correctly detect FLC days of 94 %, with 17 % of the reported FLC days being false alarms, leading to an overall correctness of the model of 86 % and a positive bias of 14 %. The critical success index (CSI: 0.79) and the Heidke skill score (HSS: 0.72) combine these scores and show that the model is skillful in distinguishing between the defined fog and clear days. As MSLP fields in southern Africa may not be representative due to the high topography, the model was additionally run based on Z850 and Z925 fields. The model performances were nearly the same (overall PC of 84 % in both cases), suggesting that it is adequate to use MSLP in this context. The colored dots in Fig. b illustrate the progression of the model skill when the training is carried out based on MSLP fields of 1, 2, 3, or 4 d prior to the FLC observation. While, as expected, the model skill deteriorates with an increasing temporal gap between the MSLP predictors and the time of FLC occurrence, the model is capable of predicting fog occurrence fairly well 1 d in advance, as the time series of day-to-day FLC occurrence features a significant autocorrelation of some days. To some extent, this may be connected to the strong persistence of synoptic-scale dynamics in the subtropics. Even though the model only uses MSLP fields, ignoring, e.g., effects of radiative cooling due to moisture anomalies, surface temperatures, and seasonal characteristics, which have been shown to modify FLC occurrence, the results still illustrate the potential of a dynamics-based statistical fog forecast in this region. It should be noted that changes in circulation additionally influence upwelling intensity, e.g., such that some of the explained variability may also be attributed to factors influencing FLC formation rather than advection. However, due to the longer time scale of SST responses, and due to the marked contrasting differences in air mass history on FLC and clear days, the latter is thought to be the first-order mechanism leading to the high model skill.

It should be noted that the distinction between FLC and clear days is based on spatially and temporally averaged FLC occurrence (see Sect. 2.1) and that days are omitted that feature an FLC cover between 3 % and 50 %. Also, the exact location and time of FLC occurrence is likely to be dependent on local temperature gradients and topography that lead to local modulation of winds . Still, the model produces promising results that may be built upon in future studies by testing a similar model setup to predict the timing and duration of FLCs at specific locations.