1 Introduction

The diurnal cycle of atmospheric convection is governed by solar insolation over interior coastal plains in moist sub-tropical zones during summer season. Weak synoptic pressure gradients and ‘col’ airflow in the saddle between two lows promote the formation of sea breezes that can penetrate inland hundreds of kilometers. Surface observations (Rouault et al. 2012) and satellite measurements (Nesbitt and Zipser 2003; Dai et al. 2007) show a late afternoon peak of rainfall as land-sea temperature gradients relax (Kikuchi and Wang 2008). These form a global diurnal pressure wave following the sun with thermal circulations that amplify over sub-tropical highlands (Huang et al. 2010).

Studies of the diurnal climatology in convection and temperature (Yang and Slingo 2001; Nesbitt and Anders 2009; Biasutti et al. 2012) make clear that differences in land-sea thermal responses amplify rainfall especially where moisture converges over large islands and peninsulas. Operational models can accurately portray the turbulent heat fluxes that precede diurnal convection (Dai and Trenberth 2003; Tadross et al. 2006) and produce accurate forecasts of onset whose timing depends on terrain elevation and roughness.

Short-lived thermally forced airflow can be evaluated from ΔU = gH/θv (dθv/dx) dt, where H is the surface layer thickness, θv is the virtual potential temperature, and dx is the coast-inland distance (Pielke & Segal 1986). A scale analysis yields 10 m/s2(300 m)/300 K (1.5/105 K/m) 4 × 104 s ~ 6 m/s. Sea breezes penetrating over topographic slopes of 1/100 km produce vertical motion of > 0.06 m/s and afternoon rainfall in the absence of synoptic forcing, given sufficient atmospheric moisture. On semi-arid west coasts with upwelling, humidity is absent, while along east coasts with warm currents, humidity is plentiful, so sea breezes tend to generate deep convection during summer.

Koseki et al. (2018) advanced our knowledge of the diurnal cycle over southeast Africa via WRF numerical simulations, following earlier work by Pohl et al. (2014). Their high-resolution simulations with realistic topography reproduced mean features of the diurnal circulation and convection. Different model schemes gave minor changes in the location and timing of diurnal rainfall over the Drakensberg escarpment. Afternoon sea breezes were well simulated over the coastal plains but opposing airflows from the Kalahari were weak. Therefore moisture penetrated too far inland and induced diurnal rainfall ~ 3 h early and ~ 30% above satellite–gauge verifications.

The objective of this research is to analyze the diurnal cycle of convection over southeast Africa and to understand its kinematic and thermodynamic forcing using high-resolution reanalysis, multi-satellite products, and in-situ observations. The datasets and analysis methods that reflect a diurnal cycle are described in Section 2. Section 3 offers results of in-situ — observed and reanalysis — assimilated weather and satellite diurnal rainfall from seasonal to hourly time-scale, as overall statistics and a case study in January 2014; a summary is given in Sect. 4.

2 Data analysis

Initial data explorations cover southeast Africa 12–36°S, 10–39°E (Fig. 1A) in the period Oct–Mar 2000–2023. cMorph multi-satellite rainfall is employed to quantify diurnal rainfall (Joyce et al. 2004; Janowiak et al. 2005) at 3-hourly 25-km resolution and depend on Meteosat geostationary radiance measurements. Regional conditions are evaluated using satellite IR surface temperature and vegetation color fraction at 10-km resolution. Diurnal temperature range (max–min) was analyzed from gridded station records interpolated by the Climate Research Unit (CRUv4; Mitchell and Jones 2005) and from numerical simulations from the coupled model intercomparison project v6 (CMIP6; Eyring et al. 2016). Details of the 27 CMIP6 models interpolated to 1 × 1° and averaged to an ensemble mean are given in < climate-scenarios.canada.ca/?page = cmip6-technical-notes > . Hourly weather station reports from the South African Weather Service (SAWS) are relatively dense across southeast Africa, so interpolated products such as the European Reanalysis v5 (ERA5; Hersbach et al. 2020) that blend satellite measurements via model physics are employed to characterize the diurnal weather conditions and detect airflow that triggers convection. Parameters include horizontal wind, vertical motion, latent and sensible heat flux, net solar radiation, specific humidity, rainfall, surface air, and dewpoint temperature at hourly 25-km resolution. ‘Residual’ winds and rainfall were calculated by subtracting the average for all hours from 3-hourly mean values with a focus on summer afternoons.

Fig. 1
figure 1

Trend of A CRU4 station (shaded) and ensemble CMIP6 model-simulated (contour ≥ 0.2 °C/year) diurnal temperature range and B satellite vegetation color fraction 1980–2023 with accelerating sea breeze (arrows over southeast coast) and elevation contours. Afternoon (14–20:00) minus all-hour ‘residual’ over multiple summers Oct–Mar 2000–2023: C surface wind and D rainfall. Dashed box is eSA index area; dots refer to station wind roses. E and F Oct–Mar afternoon-only wind roses on the southeast coast, based on 14–17:00-h observations 2000–2023 N ~ 4000. Gray squares in A refer to 2nd-order stations of the SAWS

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Motivation for this work came from a linear trend analysis of monthly diurnal temperature range and vegetation color fraction 1980–2023. When mapped over southern Africa, the eastern plains exhibit significant upward trends. Further geographic context derived from an empirical orthogonal function (EOF) analysis of 3-hourly multi-satellite (cMorph) rainfall in the period 2000–2023. EOF mode-2 (explaining 12% field variance) formed a land-sea dipole with afternoon rainfall over eastern South Africa (eSA) 25–32°S, 26–30.5°E during austral summer (Oct–Mar). The EOF mode-2 loading pattern aligns SW-NE to the Drakensberg escarpment, whereas EOF mode-1 (22% variance) reflects NW–SE cloud bands.

The mode-2 dipole time-score was averaged to monthly interval and ranked to find the composite group with highest land > sea rainfall: Jan 2006, Dec 2007, Jan 2008, Jan 2010, Jan 2011, Jan 2012, Dec 2014, Jan 2016, Dec 2016, and Jan 2017, all occurring in austral summer. Top-10 composite height sections along 29S were constructed to determine whether sea breezes are part of a larger atmospheric circulation that sustains diurnal eSA rainfall. Point-to-field associations were analyzed by regressing the mode-2 dipole time-score >  − 0.1σ onto monthly fields of sea level air pressure and 850-hPa specific humidity in the period Oct–Mar 2000–2023. These methods reveal the ‘climate envelope’ supporting high diurnal amplitude.

Statistical analysis included afternoon wind roses at Maputo (26°S, 32°E) and Umtata (32°S, 29°E) airports and E-W sections of air temperatures and diurnal range along 29°S and over the annual cycle. Scatterplot cross-correlations of daily time series 2000–2023 were calculated for eSA area-averaged 850-hPa specific humidity, diurnal temperature range, surface zonal inflow (along 30°E), latent heat flux, 600-hPa vertical motion, river discharge, and global climate influences from the El Niño–Southern Oscillation as defined by Nino3 SST. Daily time series have N = 8126, but serial persistence requires │r│ > 0.40 for 95% confidence. These methods uncover seasonal and synoptic influences on diurnal amplitude.

The daily dipole time-score tended to crest in the period Oct 13–Mar 14 and afternoon rainfall was aligned SW-NE to the Drakensberg escarpment, so this summer was selected for detailed analysis. Box-whisker plots of the repetitive diurnal cycle for multi-satellite 3-hourly rainfall was compared with ERA5 sensible heat flux and hourly rainfall. Meteorological conditions during a period of large diurnal amplitude 17–23 Jan 2014 were studied via hourly time series of eSA net solar radiation and rainfall, and synoptic observations of the SAWS. Durban airport METAR and radiosonde measurements were obtained and E-W sections of surface air temperature, air pressure, and zonal wind along 29°S were extracted at 2-hourly intervals 10–16:00 on 19 Jan 2014. Thermal forcing of onshore airflow convergence and afternoon rainfall was estimated by scale analysis. Forward and backward airflow trajectories were calculated for 18–19 Jan 2014 using the HYSPLIT method (Stein et al. 2015) which led to further work on the inertial oscillation, nocturnal winds, and roughness length over the interior plateau.

3 Results

3.1 Trends and diurnal features

A map of linear trends in CRU4 station and CMIP6 model-simulated diurnal temperature range 1980–2022 is given in Fig. 1A. Upward trends > 0.03 C/year emerge over eSA in the station record, while values > 0.02 C/year appear over Botswana and Zambezi zone (15–23°S, 18–32°E) in the numerical ensemble. Thus southeastern Africa has experienced an increase in diurnal temperature range that could accelerate continental scale land-sea breezes. The map of vegetation color trend (Fig. 1B) shows a marked increase along the southeast facing coastal plains 20–34°S, 24–36°E. There is little change in vegetation color fraction over the interior plateau, but the Namib desert facing the cold Atlantic shows a decline. Surface wind trends (arrows in Fig. 1B, adapted from Jury 2022) show increasing onshore airflow near Durban (30°S, 31°E). Although trends here are evaluated across the year, seasonal analyses (not shown) suggest that much of the signal derives from an increase of maximum temperature during summer.

Diurnal residual winds and rainfall during summer afternoons 14–20:00 Oct–Mar 2000–2022 are illustrated in Fig. 1C, D. Clearly there is a continental scale 3-m/s sea breeze that penetrates ~ 200 km inland along the coast of Namibia (20°S, 15°E) and east South Africa (30°S, 30°E; cf. larger vectors Fig. 1C). Over the southern plateau (25–30°S, 20–30°E) there is a westerly afternoon wind that converges onto the Drakensberg escarpment, opposing the sea breeze from KwaZuluNatal. These airflows drive afternoon residual rainfall over eSA. There is no convective response to sea breeze forcing over the western Kalahari (25–33°S, 17–22°E) due to coastal upwelling and near-zero heat flux in the Benguela Current; however, afternoon rainfall is enhanced over northern Namibia (13–23°S, 14–21°E) due to tropical inflow from Angola and Zambia.

Focusing on the afternoon airflow over eSA, wind roses near the coast at Umtata and Maputo (Fig. 1E,F) show frequent southeasterly winds of 4–7 m/s during austral summer Oct–Mar 2000–2022. Airflow from other directions is nearly absent, suggesting that thermal forcing overpowers synoptic-scale coast-parallel winds. Table 1 identifies that the inland gradient of maximum temperature (adjusted for elevation) is ~ 3 °C/100 km at 31°E and that mean diurnal range exceeds 12 °C over the interior plateau (24–29°E) during summer. This response can be understood from thermodynamic scale analysis: ΔT = Qh dt / M Cp, where dt ~ 4 × 104 s, M airmass ~ 103 kg, Cp ~ 103 J/kg K, and daytime sensible heat flux Qh ~ 300 W/m2. Table 2 indicates a mean diurnal temperature range of 11–15 ± 2 °C with higher amplitude in September and lower amplitude in February.

Table 1 Mean Oct–Mar 2000–2023 maximum and minimum temperatures and diurnal range along 29°S latitude
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Table 2 Mean annual cycle and quintiles of monthly diurnal temperature range (Tx-Tn) averaged over eSA
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3.2 Dipole links to summer climate

The EOF mode-2 rainfall dipole loading pattern and its time-score (reduced to monthly) are given in Fig. 2A, B. As noted earlier, there is a SW-NE axis over the Drakensberg escarpment and opposing values over the Agulhas Current. The time-score is jagged and exhibits little multi-year variability. Peak values occur in austral summer Dec–Jan and refer to land > sea rainfall associated with onshore airflow. Regression of the time-score above − 0.1σ onto fields of sea level air pressure and 850-hPa specific humidity during summer 2000–2023 (Fig. 2C, D) are instructive. There is a weak South Atlantic anticyclone, but no Mascarene anticyclone. Two low pressures appear over the Kalahari plateau and Mozambique Channel which induce the col airflow that promotes diurnal sea breezes. The humidity regression reveals enhanced tropical moisture linked to the southeast coast and Mozambique Channel and anomalous dry conditions over the ocean, inferring source–sink areas.

Fig. 2
figure 2

Satellite rainfall PC-2 representing the sea > land dipole: A standardized spatial loading pattern with elevation contours and B monthly standardized time-score with threshold dashed. C and D Regression of PC-2 time-score >  − 0.1 onto fields of sea level air pressure and 850-hPa specific humidity Oct–Mar 2000–2023

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Top-10 composite wind anomalies (Fig. 3A, B) reflect weak synoptic forcing. An upper high and surface low appear over the Mozambique Channel, evicting the Mascarene anticyclone. SSTs illustrate the well-known warm-east/cool-west pattern (Fig. 3C), so humidity is available along the southeast facing coast. The top-10 composite E-W height section along 29°S (Fig. 3D) reveals westward airflow in the 1000–850-hPa surface layer that rises over the highlands, only to return eastward above 500 hPa. Moisture anomalies penetrate into the Kalahari plateau 24–29°E. The N-S height section on 28°E (Fig. 3E, F) shows Hadley cell over-turning which exports tropical moisture toward eSA. Uplift is narrowly focused on the Drakensberg escarpment (29°S) during summers with land > sea rainfall dipole. Yet the sub-tropical jet is near normal (> 30 m/s at 35°S, 200 hPa) and even promotes zonal over-turning and sea breeze penetration.

Fig. 3
figure 3

Top-10 dipole months composite wind anomalies: A 200–300-hPa upper and B 850–925-hPa lower level. C Top-10 composite surface temperature field and d E-W height section on 29°S of zonal circulation vectors and anomalous specific humidity contours (g/kg) with elevation profile, E top-10 composite N-S height section on 28°E of meridional circulation vectors, and F zonal wind contours with elevation profile. Vertical motions are exaggerated. Only A and B represent anomalies; sections are dashed in C

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3.3 Temporal analysis

Statistical analysis of continuous daily eSA time series 2000–2023 is conducted to understand synoptic influences on thermal circulations. Scatterplots (Fig. 4A–C) illustrate that area-wide humidity is inversely related to diurnal temperature range and zonal wind on the eastern boundary. As expected, a westward moist inflow suppresses diurnal temperature range via cloud cover limiting solar radiation. Yet within the scatterplots there are cases with moderate easterlies (U − 5 m/s) and high diurnal temperature range (Tx-Tn + 15 °C) having 850-hPa specific humidity > 10 g/kg. The scatterplot regression of latent heat flux and 850-hPa humidity is positive and has a regression fit that is higher (r2 0.40) than for U wind (r2 0.28), suggesting that moisture budgets depend more on transpiration than inflow. Figure 4D is a time series of these variables over the summer of 2013–2014. Therein we note that Oct–Nov are dry (5 g/kg) and exhibit diurnal range ~ 20 °C. In mid-Jan 2014 there is a spell of high humidity and high diurnal range that supports thermally forced sea breezes. A box-whisker plot of 3-hourly rainfall time-scores (Fig. 4E) shows rainfall increasing through the afternoon. Peak values from 14 to 20:00 reach 0.2 mm/h while upper percentiles exceed 0.5 mm/h similar to Roy and Balling (2007). Box-whisker plots of the mean diurnal cycle of ERA5 sensible heat flux and rainfall over the summer 2013–2014 (Fig. 4F, G) illustrate thermal forcing rising in Gaussian fashion then declining around 16:00 as rainfall crests by 18:00. The reanalysis is consistent with satellite, so inferring that diurnal weather diagnostics follow reality.

Fig. 4
figure 4

Temporal analysis of eSA area-averaged data: A–C scatterplots of daily 850-hPa specific humidity vs. diurnal temperature range and zonal wind on 30°E and latent heat flux, 2000–2023. D Daily time series of diurnal temperature range and 850-hPa specific humidity Oct 13–Mar 14. Arrows point to cases of interest. E Box-whisker plot of mean diurnal cycle of 3-hourly multi-satellite rainfall dipole time-score Oct 13–Mar 14. F and G Box-whisker plots of mean diurnal cycle of ERA5 hourly sensible heat flux and rainfall (local time) Oct 13–Mar 14 averaged over eSA. Sensible heat flux is converted to mm/h for comparison

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Table 3 summarizes the cross-correlations of continuous daily time series 2000–2023 in the eSA area which highlight seasonal and synoptic weather influences. The expected negative association between moisture parameters and diurnal range stand out. The weak correlation between sensible heat flux and Tx-Tn occurs because SHF leads by 2–3 months over the annual cycle. The 600-hPa vertical motion associates with humidity but little else. River discharge is naturally related to both latent heat flux and 850-hPa moisture but Niño3 exerts little influence on most variables, as the sea breeze occurs under weak synoptic forcing. Even when filtered for inter-annual variability, the Niño3 correlation with eSA diurnal temperature range and land > sea rainfall remains insignificant, suggesting that thermally forced circulations and convection are decoupled from the large-scale climate.

Table 3 Correlation of daily time series averaged over eSA area except U30°E is surface zonal wind on eastern boundary, 2000–2023
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3.4 Jan 2014 case study

Weather conditions surrounding a spell of high diurnal amplitude in the period 17–23 Jan 2014 are presented in this section. Satellite rainfall and daytime land surface temperature maps over eSA (Fig. 5A, B) show convection over the southeastern escarpment reaching 100 mm and thermal gradients ~ 25 °C between land and sea. Over the southwest Indian Ocean SST were homogeneous ~ 26 °C and marine rainfall was < 20 mm during the week. Back-trajectories arriving at 28.5°S, 29.5°E, 18–19 Jan 2014 (Fig. 5C) derive from the warm Agulhas Current. The trajectories are westward over the sea, northwestward over the coastal plains, and up the Tugela Valley. Time series of eSA hourly ERA5 net solar radiation and rainfall (Fig. 5D) reveal peak values of 800 W/m2 at noon and 0.2–0.6 mm/h at 17:00. Sunshine exhibited little change during the week while rainfall varied in amount but not phase.

Fig. 5
figure 5

IR satellite measured: A sum of rainfall and B mean daytime land surface temperature both 17–23 Jan 2014 with elevation contours. C Near-surface 2-hourly back-trajectories reaching VanReenen’s Pass (28.5°S, 29.5°E) on 18–19 Jan 2014 from the warm Agulhas Current. D Time series of hourly net solar radiation (right axis) and rainfall averaged over eSA area 17–23 Jan 2014

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Figure 6A, B are the profiles via 11:00 radiosonde at Durban and ERA5 over eSA on 19 Jan 2014. Observations reflect a moist layer up to 800 hPa with light winds and dewpoint depression > 15 °C above 600 hPa. The lapse rate followed the moist adiabat so CAPE was near-zero. Durban winds swung to southwest at 700 hPa then westerly aloft (500 hPa). The ERA5 profile of q × W indicates that humid uplift occurred between 800 and 600 hPa over eSA, 1–2 km above the Drakensberg escarpment and interior plateau. The synoptic chart of 14:00 19 Jan 2014 (Fig. 6C) illustrates an anticyclone to south and cyclone to east with diffluent onshore flow supporting sea breeze penetration. Over the Orange River Valley a warm dry westerly wind occurred (Td < 10 °C). Station plots at Durban indicate a counter-clockwise (inertial) rotation of airflow and afternoon sea breeze under partly cloudy skies. An E-W slice of reanalysis temperatures and zonal winds along 29°S (Fig. 6D, E) reveals the sharp ∂T/∂x gradient at 31°E reaching 5 °C between 12 and 14:00. In consequence the − U wind accelerates 14–16:00 with a ∂U/∂x gradient of ~  − 4 × 10−5 s−1 yielding convergence and afternoon convection at 30°E.

Fig. 6
figure 6

A Durban radiosonde skew-T profile 11:00 19 Jan 2014 with CAPE < 10 J/kg. B ERA5 profile of q × W averaged over eSA 19 Jan. C Synoptic weather chart 14:00 19 Jan 2014 with dry line dashed. D Durban synoptic reports 08–16:00 19 Jan. E and F E-W sections on 29°S of surface air temperature and zonal wind at four times during mid-day on the 19th; dot is Durban, and icon is diurnal rain ~ 30 mm. Wind barbs with stars in C are satellite tracked winds

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Using the ∂T/∂x in scale analysis (cf. Section 1 above) a sea breeze of ~ 5 m/s rises over the coastal plains 1/100 (cf. Fig. 3D) producing vertical motion of 0.05 m/s and ~ 30 mm of diurnal rainfall according to dP/dt = ∫z ρ(W)Δqs(ef), where the integral over cloud depth includes ρ air density, W vertical motion, Δqs 10−4 increase of saturated specific humidity, and ef 20% convection efficiency.

The most significant finding here (Fig. 7A) is a zonal over-turning circulation on 19 Jan 2014 comprised easterly winds below 800 hPa from 29 to 34°E and westerlies above 700 hPa from 24 to 32°E on 29°S. This atmospheric rotor appears regularly under diurnally amplified col airflow and draws humidity westward over and around the Drakensberg (Fig. 7B) during afternoon hours. Moist Agulhas air (O3 < 45 ppb) displaces semi-arid conditions typified by high ozone concentration (> 57 ppb). Changes in the air pressure along 29°S on 19 Jan 2014 are presented in Fig. 7C. A thermal low (1007 hPa) develops over the Kalahari plateau, while pressure over the Indian Ocean remains steady. The pressure gradient ∂P/∂x strengthens from 10:00 to 16:00 (~ 8 hPa/5° longitude) but is maintained only a few hours, so moist airflow is drawn westward and fuels afternoon thunderstorms over the maize belt of South Africa.

Fig. 7
figure 7

A E-W height section on 29°S of zonal circulation vectors (largest 10 m/s) and specific humidity (shaded g/kg) on 19 Jan 2014 with elevation profile and sea level air pressure icons. B Maps of surface specific humidity (shaded > 11 g/kg inland from coast) 11–14:00 (left) and 17–20:00 19 Jan (right). Dashed line (at left) is section, with near-surface ozone (red contours, ppb). C Sea level air pressure along 29°S during the daytime

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Surface airflow over the semi-arid western plateau experiences low surface roughness (0.1 m) in comparison with the (0.8 m) eastern escarpment and tropical forests (Fig. 8A). The smooth land surface enables winds from the Namibian highlands to sweep into the Orange River Valley. Forward trajectory analysis 18–19 Jan 2014 (Fig. 8B) exhibits counter-clockwise looping and eastward airflow from Bloemfontein. The residual wind hodograph 17–23 Jan 2014 (Fig. 8C) rotates counter-clockwise according to the 24-h inertial oscillation at 30°S. With daytime heating the airflow is northeastward. Nocturnal cooling induces southwestward airflow in a low-level core (875–800 hPa 26–28°E) near sunrise (Fig. 8D). This feature is unlike channeled trade-winds in the Limpopo Valley (Spavins-Hicks et al. 2021), and relies on low friction and cool-west/warm-east nocturnal temperatures.

Fig. 8
figure 8

A Land surface roughness. Triangle is Bloemfontein for B near-surface 3-hourly forward trajectories 18–19 Jan 2014. C Residual wind hodograph 17–23 Jan 2014 exhibiting 3-hourly airflow rotation at Bloemfontein (nocturnal blue, diurnal red). D E-W height section on 29°S of meridional wind residual 03–06:00 17–23 Jan 2014 with elevation profile and nocturnal surface temperature residual labelled

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4 Summary

This study has explored the structure, modulation, and impacts of the mean diurnal climate of southeastern Africa using high-resolution reanalysis, multi-satellite, and in-situ datasets. The work was motivated by a trend of increased diurnal temperature range, which CRU4 shows over eSA and CMIP6 spreads across Botswana (cf. Fig. 1A). EOF analysis revealed a land–sea dipole pattern for rainfall whose temporal amplitude peaks during summer afternoon when heating of the sub-tropical plateau initiates sea breeze moisture convergence. Point-to-field regressions (Oct–Mar 2000–2023) identified climatic conditions favoring the rainfall dipole: col airflow between adjacent sub-tropical low-pressure cells (30°S, 20°E/22°S, 37°E) and a weak mid-latitude anticyclone (40°S, 10°E).

Diurnal residual and case study analysis of hourly data demonstrated that an ~ 6-m/s sea breeze below 800 hPa penetrates ~ 200 km inland during the day, as part of a zonal over-turning circulation (cf. Fig. 7A) that features westerlies above 700 hPa. The sea breeze lifts Agulhas moisture over the Drakensberg escarpment fueling convection. Further work could include harmonic analysis (cf. Silva et al. 2011, Nikulin et al. 2012), and evaluation of the diurnal cycle in coupled general circulation model simulations under climate change scenarios (Eyring et al. 2016).