Atmospheric stratification over Namibia and the southeast Atlantic Ocean

. We currently have a limited understanding of the spatial and temporal variability in vertically stratified 8 atmospheric layers over Namibia and the southeast Atlantic (SEA) Ocean. Stratified layers are relevant to the 9 transport and dilution of local and long-range transported atmospheric constituents. This study used eleven years 10 of global positioning system radio occultation (GPS-RO) signal refractivity data (2007-2017) over Namibia and 11 the adjacent ocean surfaces, and three years of radiosonde data from Walvis Bay, Namibia, to study the character 12 and variability in stratified layers. From the GPS-RO data and up to a height of 10 km, we studied the spatial and 13 temporal variability in the point of minimum gradient in refractivity, and the temperature inversion height, depth 14 and strength. We also present the temporal variability of temperature inversions and the boundary layer height 15 (BLH) from radiosondes. The BLH was estimated by the parcel method, the top of a surface-based inversion, the 16 top of a stable layer identified by the bulk Richardson number ( R N ), and the point of minimum gradient in the 17 refractivity (for comparison with GPS-RO data). A comparison between co-located GPS-RO to radiosonde 18 temperature profiles found good agreement between the two, and an average underestimation of GPS-RO to 19 radiosonde temperatures of -0.45 ± 1.25°C, with smaller differences further from the surface and with decreasing 20 atmospheric moisture content. The minimum gradient (MG) of refractivity, calculated from these two datasets 21 were generally in good agreement (230 ± 180 m), with an exeption of a few cases when differences exceeded 1000 22 m. The surface of MG across the region of interest was largely affected by macroscale circulation and changes in 23 atmospheric moisture and cloud, and was not consistent with BLH( R N ). We found correlations in the character of 24 low-level inversions with macroscale circulation, radiation interactions with the surface, cloud cover over the 25 ocean and the seasonal maximum in biomass burning over southern Africa. Radiative cooling on diurnal scales 26 also affected elevated inversions between 2.5 and 10km, with more co-occurring inversions observed at night and 27 in the morning. Elevated inversions formed most frequently over the subcontinent and under subsidence by high- 28 pressure systems in the colder months. Despite this macroscale influence peaking in the winter, the springtime 29 inversions, like those at low levels, were strongest. 2014; Zuidema et al., 2018). 402 Along the coast, the frequently occurring, morning and night-time inversions at low-levels may indicate the presence of the 403 weak counterpart of the low-level Benguela jet stream for which Nicholson (2010) reported a temperature lapse of 2°C between 404 850 and 700 hPa (approximately 1 450–3 000 m, ie. inversion strength of 0.13°C/100m). For the stronger counterpart, 405 of warm 440 continental air masses leads to the dissipation of cloud (Painemal et al., 2014). Our findings of higher means and high 441 variability in BLHs ( R N ) under clear sky conditions between April and August, were in good agreement with the results of 442 Davis et al., (2020). Based on these findings, we can conclude that the variability in the BLH ( R N ) over Walvis Bay is a function 443 of the origin and direction of airflow, and surface heating that, in combination with macroscale circulation, is also linked to 444 the frequency of occurrence and variability in cloud fractions.

inversion software, utilising a Radio Occultation (RO) technique. Data are provided in the "dry atmospheric 85 retrieval profiles", or "atmPrf" dataset, with a vertical resolution of approximately 50-100 m in the troposphere 86 (Guo et al., 2011;Hande, 2015). The horizontal resolution in the troposphere is between 160 and 200 km, due to 87 the occultation angle (Sun et al., 2013). In coastal regions where elevation is highly variable, the coarse horizontal 88 resolution introduces some uncertainty in estimations of BLH. 89 The Abel inversion algorithm was applied to retrieve refractivity (N) from bending angle profiles by wave optics, 90 to perform quality control, as well as correct the observations for systematic negative refractivity biases and https://doi.org/10.5194/acp-2021- 668 Preprint. Discussion started: 16 August 2021 c Author(s) 2021. CC BY 4.0 License. raster data elevation model (SRTM, 2013). To compare heights from the two datasets and across varying 172 topography, the height amsl of GPS-RO data was retained, and the radiosonde measurements in height agl were 173 converted into height amsl, considering the 91 m surface altitude at Walvis Bay airport. 174 Temperature profiles were derived from the refractivity profiles using Equation 1. The fact that these temperatures 175 are derived and not measured directly, introduces uncertainties that are largely dependent on the moisture content 176 of the atmosphere and the algorithm applied or retrieval method used (Wang et al., 2013). Equation 1 was also 177 used to calculate the saturation mixing ratio, mixing ratio, and dew point temperatures. 178 Thermal inversions are defined by an increase in temperature with height. Their strength, describing the local 179 stability of the atmosphere, was calculated as the change in temperature per 100 m interval. Inversion depth is 180 simply the vertical height through which the inversion persists. Shallow isothermal layers directly above or below 181 the inversion were not included in the calculation of the inversion depth. 182

Temperature 185
To investigate how the derived temperature from GPS-RO profiles compare to measured temperature profiles from 186 radiosondes, we show all profiles in Figure 2 that were measured on the same day and co-located within 100 km 187 of Walvis Bay (shown in Figure 1). The comparison is particularly important at low altitudes where the GPS-RO 188 retrieval may be affected by moisture and clouds, and some information may be lost that is otherwise captured by 189 the radiosonde measurements. This is evident in the inability of any of the GPS-RO profiles in Figure 2 to capture 190 the surface inversions that were seen in the radiosonde profiles. In fact, none of these co-located profiles extended 191 below 500m. Furthermore, it's important to note the higher vertical resolution of measurements made by 192 radiosonde as compared to GPS-RO signals, discussed in section 3. Despite the differences in time and resolution 193 of measurements, the temperature profiles were in good agreement in terms of temperature range and lapse rates. 194 Alexander et al. (2014) reported a relative error in the refractivity profile of -0.2 % below 8km and Wang et al. 195 (2013), an error of ± 1.6% (3% at 1000 hPa and 0.5% at 300h Pa). The greatest biases were reported for the tropics 196 under high humidity conditions (Sokolovskiy, 2003;Kuo et al., 2004). Wang et al., (2013) attributed errors between 197 2 and 10 km to the effects of signal propagation through a dry atmosphere, and an opposite bias for errors below 198 2 km due to very low Pw conditions (moist atmosphere) (Ao et al., 2003). For all the comparative profiles in Figure  199 2, the absolute error (and standard deviation) in temperatures was -0.30 ± 1.30°C below 7 km amsl for where GPS-200 RO temperatures were lower than radiosondes. In the drier portion of the atmosphere, between 7 and 10 km, 201 comparisons in Figure 2 show an error of -0.45 ± 1.25°C. The difference measured by the two methods compared 202 well with the -0.20 ± 1.50°C reported by Wang et al. (2013) for global comparisons using the "wetPrf" data and 203 several radiosonde types. The most extreme example of the differences in detected temperature with height 204 between the two methods, is on 2016/07/24 (Figure 2), where the two profiles crossed around 4.5 km. 205 https://doi.org/10.5194/acp-2021-668 Preprint. Discussion started: 16 August 2021 c Author(s) 2021. CC BY 4.0 License.

Minimum gradient of refractivity 206
A direct comparison is made between the MG height from GPS-RO and the radiosonde data. Figure 3 presents a 207 scatterplot of MG heights from radiosondes and co-located GPS-RO profiles taken within six hours and a 100 km 208 radius from Walvis Bay. The MG height estimated from the two datasets show poor agreement with overall mean 209 differences in the estimated height of 790 ± 990 m. The MG height estimated by GPS-RO generally overestimates 210 the values obtained from the radiosonde data, with only a few exceptions. Biases and observational errors in GPS-211 RO profiles (Chen et al., 2011) and radiosondes (Wang and Zhang, 2008;Wang et al., 2013), and measurement 212 resolution, have been the main reasons for a statistical difference in the retrieval of vertical atmospheric structures. 213 The differences in Figure 3 could not be explained by differences in time of measurement, which would affect 214 humidity. The location of each of these GPS-RO measurements relative to Walvis Bay is given in Figure S.2, and 215 shows that these differences are also not a direct result of spatial variability in the height of atmospheric layers. 216 Atmospheric moisture poses the greatest challenge for both GPS-RO and radiosonde sensors, especially in the 217 presence of clouds (Wang and Zhang, 2008;Wang et al., 2013). The biggest differences in MG heights above 218 1000m, were measured for all reported cases in February to May, and for two cases in September (Figure 3). 219 Considering the MG heights found, it is unlikely that the differences are explained by the inability of GPS-RO 220 signals to penetrate to the surface beyond a point of superrefraction, such as in the presence of high cloud fractions 221 in low-level clouds (Ao et al., 2012). When we exclude the six points that show differences greater than 1000 m 222 in the estimated point of MG, we find much better agreement between the GPS-RO and radiosonde datasets, with 223 mean differences of 230 ± 180 m. Although we have no explanation for the largest discrepancies, the good 224 agreement between the remaining points shows that the layer described by the MG height is likely a real 225 atmospheric discontinuity, and may be relevant to air mass transport and vertical distribution of atmospheric 226 constituents. This discontinuity is therefore treated separately from BLH as defined in the radiosonde data. 227

Boundary layer height 229
This section presents the morning BLH, estimated by the RN, VPT and surface-based inversion definitions, at 230 Walvis Bay. These measurements were made at 9 and 10 UTC in 2015, which was the most complete year-long 231 measurement record. The monthly mean and standard deviation in BLH for 2015 is summarised in Figure 4, and 232

237
The BLH, defined as the point where VPT is equivalent to that at the surface, remained stable around 320 ± 10 m, 238 as did the top of the surface-based inversion (125 ± 10 m) ( Figure 4 and Table S

Minimum gradient of refractivity 250
The MG height from GPS-RO and radiosondes (profiles limited to a minimum of 800 m, as discussed in section 251 5.2) is given in Figure 6 and summarised in Table S

261
The seasonal mean and standard deviations of the MG height over the region of interest is given in Figure 7  The diurnal variability in mean and standard deviation of the height of MG N-refractivity profiles are given in 269 Figure 8a and 8b respectively. The greatest diurnal variability in BLH was over the subcontinent, with maximum 270 heights in the daytime (9 to 20 UTC), and minimums between 21 and 8 UTC. Over the ocean, the diurnal variability 271  atmosphere, the profile will likely be super refracted (Xie et al., 2006) and no further information may be retrieved. 281 We found some similarities between these two layers, particularly in regards to the orientation of height gradients. 282 Over the ocean, the gradient towards the lowest points in these layers were in similar locations, particularly in the 283  Between these layers, we found a correlation of 0.61, which indicates a 284 moderate relationship. No spatial trends in the differences in height between the two layers were found. 285 Low-level inversions formed most frequently over the ocean, and especially between 20° and 25°S ( Table 1). The 286 low-level inversions over the ocean were situated around 1.1 ± 0.3 km amsl and over the coast around 0.9 ± 0.3 287 km, in the range of, but lower than the 850 hPa stable layer (expected around 1.4 km) described by Cosijn and 288 . Over the ocean, Figure 9 and Table 1 shows the lowest base heights near the coast and at lower 289 latitudes. The zonal variability in base heights was smallest in the summer and greatest in the winter. Over the 290 ocean and coastal margin, and towards lower latitudes, mean depths of these inversions (Table 1)  was greatest in the spring, where over the ocean, inversion strengths increased towards lower latitudes (Table 1  295 and Figure 10) and reached an annual maximum. Additionally, north of 20°S, springtime inversions were lowest 296 and deepest. 297   The seasonal variability of low-level inversion characteristics over the greater coastal region as described by GPS-302 RO data, are not representative of radiosonde measurements over Walvis Bay, as seen in Table 2. Seasonal mean 303 inversion strengths per 100 m for low-level temperature inversions measured by radiosonde data at Walvis Bay 304 (Table 1) were in the order of the 2-5°C reported for summer and 3-4.5°C reported for winter over the Benguela, 305 by Preston-Whyte et al., (1977). 306 Diurnal variability was compared between measurements made in the morning (3 to 8 UTC), noon (9 to 14 UTC), 310 afternoon (15 to 20 UTC), and night (21 to 2 UTC). On diurnal scales, this inversion layer formed more frequently 311 at night and in the early morning, as seen in Table S.2, when atmospheric stability was greatest. Diurnal variability 312 in base heights ( Figure 11) and inversion strengths ( Figure 12) was smallest along the coastal margin. 313         Table 3, were not 332 representative of radiosonde measurements over Walvis Bay given in Table 4. Mean elevated inversions at Walvis Bay were 333 highest in the spring (5940 ± 1850 m) and summer (5990 ± 1420 m) and lowest in the autumn (5260 ± 1370 m) and winter 334 (5020 ± 2070 m). We did however see a similar high winter variability in base heights along the coast in both datasets. 335 The smallest diurnal variability in GPS-RO detected base heights was along the coast over the cold, upwelling waters, and 338 towards lower latitudes (Figure 15). Variability was greatest over the subcontinent. Across the entire region, the number of 339 inversions was lowest at noon and in the afternoon (Table S.3). There was also a slightly higher incidence of deeper inversions 340 during this time, although mean depths remained around 0.2 ± 0.3 km. Inversion strengths per 100m were higher in the morning 341 and at night (Table S.3 and Figure 16). Variability in inversion strength throughout the depth was greatest along the coast and 342 smallest over the ocean (Table S.

Co-occurring inversions 345
Multiple layers of temperature inversions in the same profile were frequent over the study region. Instances of these co-346 occurring elevated inversions between 0.5-10 km, indicated as a percentage of the total number of inversions measured, are 347 summarised by time of day (Table 5) and month (Table 6). Annually, co-occurring inversions identified from GPS-RO profiles 348 were most frequently measured along the coast (16.8%), then over the ocean (14.2%) and least frequently over the subcontinent 349 (9.9%). Sixteen percent of inversions measured by radiosonde at Walvis Bay were co-occurring with another in the same 350 profile. These frequencies were less than the one in five reported by Cosijn and  for the region along the coast. 351 Over the subcontinent and along the coast, the instances of co-occurring inversions were at a minimum around noon and the 354 afternoon, whereas the maximum instances were measured in the morning and at night. Over the ocean, there was little diurnal 355 variability in the frequency of co-occurring inversions. 356 Across all three regions from GPS-RO profiles, the maximum monthly frequency of co-occurring inversions was recorded in 359 September and October (Table 6). Seasonal variability of frequencies was greatest along the coastal margin, with a maximum 360 of 22.9% in October and a minimum of 9.6% in June. The inversions measured by radiosonde data at Walvis Bay also saw an 361 increase in the frequency of co-occurring inversions between May and September. The general trend of the monthly variability 362 across all four regions showed a sharp decline after the October maximum, except for high incidences of multiple inversions 363 in the coastal margin in January. Monthly variability in co-occurring inversions was smallest over the ocean. 364  Co-occurring inversions were frequently observed between 0.6 and 1.5 km over the ocean. Along the coast, inversions were 365 co-occurring most between 0.6 and 1 km and then between 5.6 and 6.6 km. Over the subcontinent, the heights of frequently 366 co-occurring inversions were most variable, with frequent co-occurrences between 1.4 and 1.7 km, 5.4 to 5.7 km, 6 to 6.5 km 367 and 7.7 to 7.9 km. 368 6. Discussion 369

Macroscale circulation 370
Cosijn and   Low base heights of elevated inversions over the subcontinent during the winter and autumn suggests a link to the migration 388 of the high-pressure belt, which was theorised by Cosijn and . This includes the continental and SEA anticyclone 389 which adiabatically heat subsiding air and have been linked to the formation of inversions as high as 500 hPa (Preston-Whyte 390 et al., 1977; Cosijn and . Despite the increased subsidence and atmospheric stability induced by these high-391 pressure conditions, the wintertime inversions were the weakest and springtime inversions strongest. We did however see an 392 increased formation of co-occurring inversions in the colder months as compared to the warmer months ( Figure 13 and Table  393 3). The increasing frequency of co-occurring inversions between May and September coincides with the most intense 394 anticyclonic circulation over the subcontinent after which the variability decreased. The year-round cold SEA ocean and 395 subsidence under the SEA anticyclone, is responsible for higher frequencies of co-occurring inversions, than over the 396 subcontinent. The diurnal trends in stability over the subcontinent and coast were more pronounced than over the ocean, with Cool-marine air masses are transported in sea breezes and plain-mountain winds. These form most commonly in the daytime 428 and during summer (Lindesay et al., 1990). During these times, we found the steepest zonal gradients in low-level inversion 429 strengths, with strengths decreasing towards the subcontinent (Figure 10 and Figure 12). Sea-breezes have been found to inhibit 430 the noontime convective development of the coastal BLH (Davis et al., 2020), but we could not detect this in our once daily, 431 morning measurements. This effect is also not apparent in the MG height (Figure 8), but it may be responsible for maintaining 432 low noontime low-level inversion heights ( Figure 11). 433

Cloud fraction 434
The lifetime and fraction of low-cloud cover is a known modulator of the BLH over tropical coasts (Davis et al., 2020) Sc (Painemal et al., 2014), no relationship between this low-level cloud and elevated inversions could be found. 460

Biomass burning aerosols 461
This study does not attempt to study, nor suggest any causal relationships between aerosols and atmospheric stability in the 462 region. We did, however, observe some interesting correlations between pollution plumes and inversion characteristics, as well 463 as the frequency of co-occurring inversions observed. Maximums in co-occurring inversions were measured in September and 464 October across all three regions, coinciding with the maximum in radiation-absorbing aerosols over Namibia (Eck et al., 2003). 465 There also exists the potential for cloud fractions in the region to be modified by aerosols above cloud (Costantino and  The additional stratification, stabilisation and decoupling induced by multiple elevated inversions inhibit vertical motions and 472 result in the formation of both heavily polluted plumes and clean air slots, an observed but not yet clearly defined phenomena 473 over southern Africa and offshore (Hobbs, 2003). These clean air slots have been observed adjacent to plumes of pollution 474 (Hobbs, 2003) or cloud (Costantino and Bréon, 2010), and also above (Haywood et al., 2004) and below smoke layers (Wilcox,475 2010) with varying differences in the thickness and location of those gaps (LeBlanc et al., 2020). The strong and high elevated 476 inversions, and strong, deep, and low springtime low-level inversions identified in this study (Figures 9 and 10 and Table 1)

Conclusions 485
This study of 11 years of GPS-RO refractivity and temperature profiles, and three years of radiosonde data at Walvis Bay, 486 provides an in-depth look at the spatial and temporal variability of atmospheric discontinuities over Namibia and the SEA 487 Ocean. We discussed our findings in relation to the potential drivers of this variability, based on existing research specific to 488 our region of interest. The direct comparison of temperature profiles revealed that GPS-RO temperatures generally 489 underestimated those measured by radiosondes throughout the profile depth (up to 10 km). The mean differences in 490 temperatures from the two datasets decreased with distance from the surface. This is attributed to errors in refractivity related 491 to atmospheric moisture, which increases towards the surface. The identification of the point of minimum gradient in the 492 refractivity profiles compared well with radiosonde data, but not for all cases. The reason for these discrepancies could not be 493 determined, but was found to not be related to cloud top. The comparison also revealed that the MG was not consistent with 494 BLH estimated using the bulk RN definition. The BLH estimated by the bulk RN definition was consistent with the height and 495 variability in existing literature. This reaffirms the importance of identifying real structures consistent with BLH and not other 496 structures that may share similar characteristics to the BL, such as sharp moisture and temperature gradients. The sensitivity 497 of GPS-RO signal propagation to atmospheric moisture means that, despite identifying the large-scale variability, it would be 498 useful for future investigations to report variability for cloudy and cloud-free conditions separately. Unlike previous studies, 499 low-level inversions were observed over the subcontinent, although very rarely. We found links in the location and strength of 500 the nighttime low-level inversion, to the previously reported strong counterpart of the Benguela jet stream. We also found 501 similarities in the location of the mean strongest inversions over the ocean with the location of the inversion over the Sc. 502 Finally, we found correlations between seasonal maximums in low-level inversion strength and maximum occurrence of co-503 occurring inversions, to the seasonal peak in biomass burning over the subcontinent (Eck et al., 2003;Swap et al., 2003). The 504 effects of atmospheric circulation on a variety of spatial scales, as a result of latitudinal location, variability in topographic 505 features, radiative interactions over different landscapes and low-level clouds in the region, were all found to correlate with-506 and contribute to the complex character of the BLH (RN), MG height and low-level inversions. The elevated inversions were 507 also influenced by subsidence under macroscale circulation systems, and diurnally varying surface radiative effects like the 508 low-level inversions; however, no link between elevated inversions and low-level clouds were found. The high inversion 509 strengths over the ocean and subcontinent in the spring coincide with the seasonal peak in BBA over the region. Considering 510 that springtime inversions were stronger than inversions measured during the winter when subsidence under the high-pressure 511 belt exerts the greatest influence on circulation over the region (evident in the significant decrease in base heights), it might be 512 reasonable to suggest that the radiative characteristics of BBA plumes trapped within stratified layers, contribute to the high 513 inversion strengths measured in the spring. Further research is required to investigate this hypothesis.