Two complementary and colocated instruments installed at the Savè supersite were used to provide information on the macrophysical characteristics of LLSCs (Handwerker et al., 2016): a ceilometer for the cloud base height (CBH) and a cloud radar for the cloud top height (CTH).

Through backscatter vertical profiles measured by the ceilometer from surface to 15 km a.g.l. with a 15 m vertical resolution, manufacturer software automatically provides three estimates of CBH each minute, allowing for the detection of several cloudy layers. As our focus is on LLSCs (the lowest cloudy layer), we use only the lowest value (hereafter CBHs). The LLSC top heights (CTHs) are derived from 5 min averaged radar reflectivity vertical profiles from 150 m to 15 km a.g.l. at a vertical resolution of 30 m by a methodology described in Babić et al. (2019a) and Adler et al. (2019). According to Dione et al. (2019), the LLSC top evolves overall under 1200 m a.g.l. To be consistent with this outcome, an upper limit of 1200 m a.g.l. was applied to CTHs. Unfortunately, several values of CTHs are missing particularly during the daytime for many selected cases due to the retrieval technique limitation.

The thermodynamical and dynamical characteristics of the low troposphere are retrieved from radiosondes of the MODEM radiosounding system. The MODEM radiosonde collects every second (which corresponds to a vertical resolution of 4–5 m) the air temperature and relative humidity, as well as the probe GPS localization from which horizontal wind speed components, altitude and air pressure are deduced (Derrien et al., 2016). The sensors' accuracy is 0.2 ∘C, 2 % and 0.01 m for temperature, relative humidity and GPS localization, respectively. A standard radiosonde was launched every day at 05:00 UTC and usually rose to 14 km a.g.l. On IOP days, three additional radiosondes were performed at 23:00 UTC on day-D and at 11:00 and 17:00 UTC on day-D+1. In between these soundings, so-called “reusable” radiosondes were launched more frequently at regular time intervals. At the height of 1.5 km a.g.l., the reusable radiosonde is released from its ascending balloon, falls at the surface within a reasonable distance to be easily found and used again (Legain et al., 2013). This system provided a higher temporal resolution of the conditions within the monsoon layer. During the first six IOPs of DACCIWA, the frequent soundings were performed hourly and every 1.5 h during the other IOPs. In this study, the radiosondes data were averaged at a final vertical resolution of 50 m. Additionally, measurements of an ultra-high-frequency (UHF) wind profiler are used to derive the NLLJ core height at a 15 min time interval (Dione et al., 2019).

The meteorological conditions at the surface (temperature, relative humidity and pressure of the air at 2 m a.g.l.) and some terms of the surface energy budget (net radiative, Rn0, sensible heat, SHF0, and latent heat, LHF0, fluxes at 4 m a.g.l.) were continuously acquired (Kohler et al., 2016). SHF0 and LHF0 are deduced from high-frequency (20 Hz) measurements processed with Eddy-covariance methods by using the TK3.11 software (Mauder et al., 2013).

We define some diagnostics to monitor the evolution of the LLSC layer: the fraction of low cloud coverage, the LLSC base height and cloud layer homogeneity, the link between LLSC deck and surface, and two characteristic times of LLSC evolution. The LLSC depth would also be a key diagnostic, but its monitoring is limited by the low availability of CTH cloud-radar-based estimates during daytime. In addition, the humidity and temperature sensors onboard the radiosonde were affected by water deposition during crossing of the LLSC layer, so neither is fully reliable for CTH estimates (Adler et al., 2019; Babić et al., 2019a).

The diagnostics are calculated over a time interval of 10 min with a moving window of 5 min, which is suitable for resolving the processes related to convection. Figure 2 illustrates our methodology with an example of measurements and derived diagnostics for the case of 26–27 July 2016.

Fraction of low cloud coverage. The low cloud fraction (CF) is defined as the percentage of 1 min ceilometer CBHs lower than or equal to 1000 m a.g.l. Thus, a CF greater or equal to 90 % corresponds to the presence of LLSCs. A similar methodology was used by Adler et al. (2019) but with a threshold of 600 m a.g.l. We extend the upper limit to 1000 m a.g.l. to take into account the LLSC base rising during the convective phase (Lohou et al., 2020). On 27 July 2016 (Fig. 2), the few periods between 04:00 and 11:30 UTC with CF < 90 % indicate intermittent breaks within the LLSC deck. This feature is common to many other cases.

The LWP tendency equation is based on the assumption of the horizontally homogeneous LLSCs vertically well mixed by convective turbulent mixing driven by the cloud-top radiative cooling. Following van der Dussen et al. (2014), this equation can be split into five relevant processes: 1∂LWP∂t=BASE+ENT+PREC+RAD+SUBS, in which 1aBASE=ρη(w′qt′‾b-Πγw′θl′‾b),1bENT=ρwe(ηΔqt-ΠγηΔθl-hΓql),1cPREC=-ρΔ℘,1dRAD=ρηγΔFrad,1eSUBS=-ρhΓqlws,CTH, representing the effects of turbulent moisture and heat fluxes at the cloud base (BASE), evaporation or condensation caused by the entrainment of ambient air from aloft (ENT), precipitation formation (PREC), radiative budget along the cloud layer (RAD) and large-scale subsidence (SUBS) at the cloud top.

In Eqs. (1a) to (1e), w′qt′‾b and w′θl′‾b are, respectively, the total moisture specific humidity (qt) and liquid-water potential temperature (θl) heat fluxes at the cloud base (superscript “b”), ρ is the mean air density over cloud layer, h is the cloud depth, ΔFrad and Δ℘ are the differences in net radiation and precipitation, respectively, between the cloud top and base heights (van der Dussen et al., 2014), Δθl and Δqt are the jumps of, respectively, θl and qt across the cloud layer, and we and ws,CTH are the cloud top entrainment and large-scale subsidence velocities, respectively.

The equations also introduce the following parameters: the Exner function Π=P1000RdCp; the adiabatic lapse rate of liquid water content Γql=gη(qsRdT‾-γCp); γ=LvqsRvT‾2; and η=1+LvγCp-1. In those parameters, P and T‾ are, respectively, the cloud layer pressure and temperature, qs is the saturation water vapor specific humidity at P and T‾, Rd and Rv are, respectively, the dry air and water vapor gas constant, and Lv, Cp and g correspond, respectively, to vaporization latent heat of water, specific heat of dry air at constant pressure and gravitational acceleration.

For our analysis of DACCIWA cases, we consider the LWP budget in the early morning and use the 05:00 UTC radiosounding, ceilometer and cloud-radar measurements to estimate some terms of Eq. (1). In fact, this is the optimal time for the assumption of horizontally homogeneous and vertically well-mixed LLSC layer. The PREC term is typically near zero because no significant rain was measured at the surface for the selected cases. The BASE term is not estimated because the turbulent fluxes at the LLSC base cannot be deduced from the available dataset at the Savè supersite. According to Pedruzo-Bagazgoitia et al. (2020), the BASE term is small at this time relative to the three terms RAD, ENT and SUBS. The latter are the most significant contributions in the early morning that we attempt to estimate. 2LWP=-12ρΓqlh2

The RAD term (Eq. 1d) is retrieved from the vertical profiles of upwelling and downwelling radiative fluxes which are computed using the Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART) model (Ricchiazzi et al., 1998). This software tool, which solves the radiative transfer equation for a plane-parallel atmosphere in clear and cloudy conditions, was used in the studies of Babić et al. (2019a) and Adler et al. (2019) to estimate temperature tendency due to radiative interactions during the LLSC diurnal cycle. For our simulations, the model configuration was very similar to that used in these studies. We prescribed 65 vertical input levels with a vertical resolution of 50 m below 2 km a.g.l., 200 m between 2 and 5 km a.g.l., and 1 km above 5 km a.g.l. The vertical profiles of air pressure, temperature and water vapor, density, and the integrated water vapor are based on 05:00 UTC standard radiosounding data. The cloud optical thickness, which varies with its water and ice content, is required to describe a cloud layer in the SBDART model. However, the LWP provided by the microwave radiometer deployed at the Savè supersite (Wieser et al., 2016) includes all existing cloudy layers and is not available for five of our selected cases. Therefore, the LLSC optical thickness is determined from a parameterized LWP (Eq. 2) by assuming an adiabatic cloudy layer in which the liquid water mixing ratio (ql) increases linearly (van der Dussen et al., 2014; Pedruzo-Bagazgoitia et al., 2020). The downwelling longwave radiations from potential mid-level and high-level clouds may reduce radiative cooling at the LLSC top (e.g., Christensen et al., 2013). However, the cloud layers above the LLSC (base, top and water content) cannot be precisely described in the SBDART model from the available dataset. Thus, the radiative effect of higher clouds is not directly included in our estimate of downwelling radiative fluxes but is partially taken into account through vertical profiles of temperature and relative humidity given by the radiosonde. As the shortwave radiations are zero before sunrise, only the longwave range, 4.5–42 µm with spectral resolution of 0.1 µm (Babić et al., 2019a), was selected for radiative flux calculations. For all cases, the vertical optical depth of ABL aerosol is fixed at 0.38, which corresponds to the average value of measurements performed with a sun photometer in June and July 2016 at Savè.

For the ENT term (Eq. 1b), we use the parameterization of Stevens et al. (2005) to estimate we: 3we=AΔFradΔθl, in which A is a non-dimensional quantity representing the efficiency of warming caused by the input of free tropospheric air into the LLSC layer by the buoyancy-driven eddies generated by cloud-top radiative cooling. A varies with Δθl, Δqt, wind shear at cloud top, surface turbulent fluxes and cloud microphysical processes via the buoyancy flux vertical profile (Stevens et al., 2005; Stevens, 2006). Despite the spatial and temporal variability in A, its value is generally fixed and treated as a constant parameter in several research studies (e.g., van Zanten et al., 1999; van der Dussen et al., 2014). The value of A used in the literature varies from one study to another. By considering the results of the LES developed by Pedruzo-Bagazgoitia et al. (2020) on a DACCIWA case just before sunrise with we≈4.5 mm s-1, Δθl≈4 K, a cloud-top longwave radiative cooling of around 43 W m-2, and ρ≈1.13 kg m-3 as the average value from surface to 1000 m a.g.l. (from 26 June 05:00 UTC sounding), we obtain A≈0.5. This means that the contribution of tropospheric air entrainment to heat budget at the LLSC top is around 2 times smaller than that of cloud-top radiative cooling. For the sake of simplicity and due to the lack of a precise estimate, we assume here the same behavior for all DACCIWA cases and consider A=0.5 in our analysis.

The jumps in temperature Δθl and in total water content Δqt are estimated from the soundings. We write θl=θ-1ΠLvCpql, with θ as the potential temperature, whereas qt=q+ql. We define 4Δφ≈φ+-φ-, where φ can be either θl or qt, and φ+ and φ- are in theory the values of φ just above and below the cloud top, respectively. Under the assumption of a well-mixed cloud layer, θl (qt) is conserved through the cloud layer and increases (decreases) abruptly in the warmer (drier) ambient air right above (van Zanten et al., 1999). Thus, Δθl and Δqt can be estimated from the vertical profiles of θ and q derived from the 05:00 UTC standard sounding. For θl+ and qt+, we consider the mean over the 100 m just above CTH. For θl- and qt-, we consider the sounding level just below CBH. In brief, we use the following:

5qt-=qt{belowcloudtop}=qt{belowcloudbase}=q{belowcloudbase}θl-=θl{belowcloudtop}=θl{belowcloudbase}=θ{belowcloudbase}.

For the SUBS term (Eq. 1e), we cannot accurately estimate the large-scale subsidence velocity at LLSC top. One possibility is to compute estimates from models or reanalyses. However, we decided to discard this approach because the subsidence vertical profiles from regional simulations with Consortium for Small-scale Modelling (COSMO) or from ERA-interim and ERA-5 reanalyses showed a very high temporal variability and a strong lack of coherence among the different cases. According to cloud-radar CTH estimates, the LLSC top is often stationary at the end of the stratus phases during the DACCIWA field experiment. This feature has been observed (Adler et al., 2019; Babić et al., 2019a; Dione et al., 2019) and also simulated by Pedruzo-Bagazgoitia et al. (2020). Based on the LLSC top stationarity at the time of our LWP budget analysis, ws,CTH is estimated following Lilly (1968): 6∂CTH∂t=ws,CTH+we≈0.

We first analyze the evolution of LLSC base height (CBH) and its link with the NLLJ core height and surface-based LCL along the stratus phase (Fig. 3). The CBH and LCL at the beginning of the stratus phase (Fig. 3a and b) are given by diagnostic parameters CBHm and LCLM, respectively, when the LLSC forms and the NLLJ core height is the hourly averaged value at that time. For the end of the stratus phase (Fig. 3c and d), CBH, LCL and NLLJ are averaged between 04:00 and 06:30 UTC on day-D+1.

When the LLSC forms, its base is located within the NLLJ core where cooling driven by the horizontal advection is at its maximum (Adler et al., 2019; Dione et al., 2019; Lohou et al., 2020). Both the CBH and NLLJ core heights range between 50 and 500 m a.g.l. (Fig. 3a) and are 100 m above surface-based LCL except for one case (Fig. 3b). This means that the LLSC is decoupled from the surface when it forms.

At the end of the stratus phase, we can see that the relationship between CBH and the NLLJ core height has totally changed (Fig. 3c). There is no clear linear link between both, and CBH remains mostly lower than or equal to 300 m a.g.l., while NLLJ core height is above 600 m a.g.l. in several cases. This is most likely because, during the stratus phase, the jet axis is shifted upward by the convective turbulence within the LLSC layer (Adler et al., 2019; Dione et al., 2019; Lohou et al., 2020). In addition to the jet axis rising, the averaged CBH decreases by the end of the stratus phase (Fig. 3a and c) for most cases. In some cases, CBH coincides pretty well with LCL (Fig. 3d), which indicates coupling between the LLSC layer and the surface. However, in others, CBH is still at least 100 m higher than LCL, meaning that the LLSC layer remains decoupled from the surface.

We further analyze the coupling between the LLSC deck and surface at the end of the stratus phase by using the bulk Richardson number (Stull, 1988) of the subcloud layer (RibSub). It reads as follows: 7RibSub=TSubSSubwithTSub=gθΔθCBHandSSub=ΔUCBH2. TSub and SSub are, respectively, the thermal and horizontal wind shear contributions to the Richardson number, ΔθCBH and ΔUCBH are the bulk vertical gradient of θ and horizontal wind speed (U), respectively, within the subcloud layer (from surface to cloud base) with the assumption that U is null at the surface, and RibSub is estimated with all radiosoundings available from 04:00 to 06:30 UTC on day-D+1 for each studied case. The subcloud layer height is estimated with the half-hourly median of CBHm at the radiosonde release time (Eq. 7).

Figure 4 shows RibSub (Fig. 4a), TSub (Fig. 4b) and SSub (Fig. 4c) as a function of the half-hourly median value of ΔLCLCBH at the radiosonde release time. The smaller ΔLCLCBH is, the lower RibSub will be. Interestingly, when ΔLCLCBH is smaller than 75 m, RibSub is less than or equal to 0.1 (Fig. 4a). This evidence suggests that the potential coupling between the LLSC and surface during the stratus phase is driven by underlying turbulent mixing. A similar tendency was found by Adler et al. (2019) who analyzed the soundings performed along the stratus phase of 11 IOPs.

Like RibSub, the TSub term increases with ΔLCLCBH, whereas the SSub term is nearly constant. This means that when CBH is close to LCL, the subcloud layer is well mixed, although the shear-driven turbulence is not particularly significant. Thus, the coupling between the LLSC and surface at the end of the stratus phase seems to be mostly linked to thermal stratification in the subcloud layer rather than to shear-driven turbulence.

Finally, based on Fig. 4a and b, the value of 75 m is used thereafter as a threshold for ΔLCLCBH to distinguish coupled and decoupled LLSCs at the end of the stratus phase. Through this classification, our set of 22 studied cases includes 9 LLSCs coupled with the surface (case C) and 13 LLSCs decoupled from the surface (case D) (Table A1 in the Appendix). Among the nine selected IOPs, three (nos. 5, 6 and 8) and six (nos. 3, 4, 7, 9, 11 and 14) make up cases C and D, respectively.

Based on reusable radiosoundings available for the nine selected IOPs, the temporal evolution of RibSub and its composing terms have been calculated from the start of the stratus phase up to 06:30 UTC on day-D+1 (Fig. 5). RibSub, TSub and SSub in C and D cases are similar when the LLSC forms. For C cases, TSub decreases to zero (neutral stratification) within the 3 following hours, while SSub remains almost constant, which causes a decrease in RibSub (Fig. 5a and b). In C cases presented in Fig. 5, the definitive coupling with the surface occurs within 4 h of the beginning of the stratus phase. The same behavior is observed for C cases, which are not IOPs and therefore not included in Fig. 5 (not shown). For D cases, the subcloud layer remains thermally stable along the stratus phase, and shear-driven turbulence is of the same order as for C cases. Considering these results, it appears that the shear-driven turbulence in the subcloud layer is not the main process causing the coupling of the LLSC layer with the surface during the stratus phase in the C cases.

In conclusion, the LLSC is typically decoupled from the surface at formation. Subsequently, its base lowers during the first hours of the stratus phase. In the C cases, this decrease is more important and leads to coupling between the cloud deck and the surface before sunrise. The lowering of the LLSC base was first pointed out by Babić et al. (2019a) for the 7–8 July case. They explained this feature by an additional cooling in the subcloud layer mainly due to a shear-driven turbulent mixing caused by the NLLJ. Yet, no substantial differences in wind shear below the LLSC are observed between the C and D cases, indicating that the processes related to mechanical turbulence underneath the LLSC cannot fully explain the coupling observed by the end of the stratus phase. The other relevant processes which may couple the LLSC to the surface in nighttime conditions are discussed in Sect. 4.3. In the next paragraph, we analyze the LLSC macrophysical characteristics in C and D cases at the end of the stratus phase, i.e., just before the convective phase.

The distributions of averaged LLSC base heights and depths at the end of the stratus phase are summarized in Fig. 6a and b, respectively. Only the 20 cases for which the cloud is persistent between 04:00 and 06:30 UTC on day-D+1 are considered (including 9 C cases and 11 D cases). Note that the depth could not be estimated for two of these cases because of missing CTH data. The CBH ranges from 50 to 200 m a.g.l. for C cases and within 200–400 m a.g.l. for D cases. This clear difference between coupled and decoupled LLSC explains the bimodal distribution of morning CBH observed by Kalthoff et al. (2018). In contrast, the morning LLSC depth does not depend on the state of coupling with the surface.

Figure 6c shows the LLSC base homogeneity at the end of the stratus phase by presenting statistical information about σEarly, which is the median value of diagnostic parameter σ∗ between 04:00 and 06:30 UTC on day-D+1 for each considered case. The median of σEarly is 24 m for C cases and 34 m for D cases. Their 25th percentiles and minimums are close, but the 75th percentile for D cases is more than 15 m higher than that for C cases, and the maximum is significantly larger, close to 100 m. This reveals the larger LLSC base heterogeneity found for several D cases. The coupling with the surface likely limits the fragmentation of the LLSC layer and helps to maintain cloud base homogeneity in C cases.

In brief, the coupling mechanism favors a lower CBH and a slightly more homogeneous cloud base in coupled cases. But the LLSC depth is similar in coupled and decoupled cases such that the LLSC vertical extension does not seem to be influenced by the coupling with the surface. This may be related to the negligible contribution of surface fluxes during the stratus phase (Pedruzo-Bagazgoitia et al., 2020).

In this subsection, we attempt to estimate the terms of LWP budget at the end of the stratus phase in order to answer two questions.

Using observations, do we obtain results similar to those of previous numerical simulations, particularly that of Pedruzo-Bagazgoitia et al. (2020)?

As previously seen, the most important contributions to the LWP budget are those of radiation, entrainment and subsidence. Based on available observations and by using the SBDART model, we estimate the ENT and RAD terms (Eq. 1b and d, respectively) and also give a rough order of magnitude of the SUBS term (Eq. 1e). The LLSC layer here is defined by the averaged CBHs and CTHs at the end of the stratus phase (Fig. 6a and b).

We first discuss the jumps Δqt and Δθl across the cloud top (Eqs. 4 and 5) which are involved in the ENT term. They are estimated using the 05:00 UTC (day-D+1) standard radiosoundings. The liquid water buildup on the probe sensors possibly renders some measurements suspect, especially near the cloud top. In order to evaluate the impact of this issue on our jump estimations from the 05:00 UTC standard radiosonde, we first consider a reusable sounding at a different time for which the probe has crossed the LLSC layer at both the ascent and descent. At ascent, sensors are reliable at the cloud base but may obtain incorrect data when they reach the cloud top. At descent, it is the reverse: accurate at the cloud top but possibly erroneous when reaching the cloud base. This is shown in Fig. 7 which displays the vertical profiles of θ, q and RH measured by the reusable sounding of 8 July 2016 at 06:21 UTC during both the probe ascent and descent. By analyzing the RH vertical profiles, we can see that the upper limit of the saturated layer (RH ≤ 98.5 %), i.e., the top of the LLSC layer, obtained by the descent measurements is more consistent with cloud-radar-estimated CTHs than that obtained during the ascent. Further, the descent measurements indicate warmer and drier atmospheric conditions from the CTH to around 800 m above with θ+ (q+) around 1 K (0.3 g kg-1) higher (smaller). By analyzing all reusable soundings of that kind during daytime, we find that the maximum underestimation (overestimation) of θ+ (q+) during the ascent due to wetting of the sensors is about 1.2 K (0.3 g kg-1). The overestimation of q+ by ascending sounding is within the measurement accuracy, while, compared to the 0.2 ∘C measurement accuracy, the underestimation of θ+ is significant. Consequently, we only consider a systematic error of 1.2 K on the estimates of θ+ from the 05:00 UTC standard radiosounding for which we can only rely on the ascent (the descent is too far away from the supersite).

Figure 8 displays Δqt and Δθl against q- and θ-, respectively, as estimated for 14 cases (eight C cases and six D cases) among the 20 cases in Fig. 6 for which there is evidence that the radiosonde flew through the LLSC layer. It first reveals that the thermodynamical conditions of the subcloud layer are quite steady during this summer period with only a 1.5 g kg-1 and 2 K variation range for humidity and temperature, respectively, over all cases. A similar conclusion was drawn by Adler et al. (2019). This may be due to the fact that the considered cases occurred in nearly similar synoptic conditions over SWA (Table A1).

In the C cases, q- ranges within the interval 16–17 g kg-1 with a mean of 16.8 g kg-1 and standard deviation of 0.5 g kg-1. It is lower in D cases with an average of 16.3 g kg-1 and standard deviation of 0.9 g kg-1. Thus, in the early morning, the air just below the LLSC is on average 0.5 g kg-1 moister in coupled cases. This is qualitatively true for the entire stratus phase when analyzing reusable soundings of the nine IOPs (not shown). In absolute terms, Δqt is in general lower than 3.0 g kg-1. It is smaller than or equal to 1.5 g kg-1 in 85 % of all cases. This indicates a generally weak moisture jump across the LLSC top. This is still more pronounced in the C cases for which Δqt remains lower than 1.5 g kg-1.

The parameter θ- ranges from 296 to 299 K. Beyond the same variability found in C and D cases, θ- is on average around 0.5 K cooler in C cases probably because the LLSC base is closer to the surface. The Δθl value, which varies within the interval 1–5 K, does not exhibit a clear difference between C and D cases. Thus, the fact that the LLSC base gets closer to the surface in coupled cases does not impact the temperature jump across the cloud top.

The magnitudes of Δθl and Δqt observed in SWA conditions are much smaller than those typically found for the mid-latitude stratocumulus, which can be as strong as 10 K and -10 g kg-1 (Duynkerke et al., 2004; Wood, 2012; van der Dussen et al., 2016; Ghonima et al., 2016), especially over the ocean. The vertical profile used by Pedruzo-Bagazgoitia et al. (2020) to initialize their LES had a Δθl of 4.5 K and no jump of qt across the LLSC top. This representation is consistent with what we find for the moisture jump but is on the sidelines for the temperature jump.

Table 1 compares our estimates of some parameters involved in the formulation of RAD, ENT and SUBS terms with those from the study case of van der Dussen et al. (2014), which are based on the DYCOMS-II (second Dynamics and Chemistry of Marine Stratocumulus field study) case setup (Stevens et al., 2005). Our estimates of γ, η and Γql differ from typical values used by these authors because the LLSC layer for DACCIWA cases is on average 11 K warmer and 8 g kg-1 wetter. After the analysis of SBDART model output, ΔFrad is determined from the difference of net radiative fluxes between model levels just above and below the LLSC layer, respectively. The median and standard deviation of cloud-top longwave radiative cooling are, respectively, about 55 and 5 W m-2. Our estimate of radiative cooling at the LLSC top for the 25–26 June 2016 case is 44.1 W m-2, which is in good agreement with the value of 43 W m-2 estimated by the LES of Pedruzo-Bagazgoitia et al. (2020) for the same day just before sunrise. Despite a weaker temperature and nearly absent moisture jumps at the LLSC top, the median value of our estimated cloud-top radiative cooling is around 10 W m-2 greater than that of van der Dussen et al. (2014) and falls within 50–90 W m-2, which is the typical interval range for subtropical stratocumulus (Wood, 2012). This is most likely because the LLSC of DACCIWA cases is significantly warmer.

We find only a 5 W m-2 standard deviation for radiative cooling at the LLSC top and no significant difference between C and D cases. This very low standard deviation may be due to the conditions which remained very steady from one case to the other but may also be underestimated because impacts of higher clouds are not fully included in the estimate of radiative fluxes. In order to evaluate the error due to temperature underestimation above the LLSC top, SBDART is run with both the measured and temperature-corrected profiles, while the other inputs remain unchanged. The correction of the potential temperature vertical profile consists of a linear tendency between the measured θ plus a 1.2 K correction right above the CTH and the measured θ at 800 m where we consider that the radiosonde sensors are no longer affected by the LLSC crossing. The cloud-top radiative cooling estimated by SBDART with this temperature-corrected vertical profile is greater by less than 2 W m-2.

The cloud-top entrainment velocity, we (Eq. 3), has a median value of 10.12 mm s-1, and its variability is around 25 % of the median. This median is around 2.5 times higher than the velocity obtained by Pedruzo-Bagazgoitia et al. (2020) with LES and among the highest values found by other authors (Duynkerke et al., 2004; Faloona et al., 2005; Mechem et al., 2010; Ghonima et al., 2016). Finally, we show that our estimates of RAD and ENT terms are suitable and beyond potential errors on the entrainment efficiency A and simplified settings in SBDART. As mentioned in Sect. 3.3, we approximate the SUBS term with the assumption of a stationary LLSC top at the sounding time (Eq. 6). This term must be taken with more caution than the other two due to this hypothesis.

Figure 9 presents distributions of RAD (Fig. 9a), ENT (Fig. 9b) and SUBS (Fig. 9c) terms derived from the 14 radiosoundings considered in Fig. 8 by the methodology described in Sect. 3.3. The RAD term ranges from 45 to 70 g m-2 h-1 with a median of 57 g m-2 h-1. ENT varies between -15 and 5 g m-2 h-1, indicating a smaller contribution to the LWP budget compared to RAD. The negative value of about -10 g m-2 h-1 is consistent with the study of Pedruzo-Bagazgoitia et al. (2020) with a predominant role of cloud-top temperature and moisture jumps and a drying and warming entrainment effect. Among the 14 cases, several have a smaller ENT contribution than this. One case even has a positive value for ENT, which means that the LLSC depth has more impact than temperature and moisture jumps so that the entrainment in that case favors LLSC deepening. The SUBS term ranges between -65 and -20 g m-2 h-1 with a median of around -36 g m-2 h-1. It corresponds to as much as -0.4 to -0.9 times the RAD term, which is very significant. This is also consistent with Pedruzo-Bagazgoitia et al. (2020) who found a SUBS / RAD ratio of approximately -0.4 before sunrise. Our answers to the two questions raised at the start of this subsection are as follows.

We found similar results compared to Pedruzo-Bagazgoitia et al. (2020). However, the West African inland LLSC layer, which develops within the monsoon flow (Dione et al., 2019), is characterized by weaker temperature and moisture jumps but with similar radiative cooling at its top compared to marine stratiform clouds.

From the 14 morning soundings considered in Fig. 8, we quantified the contribution of vertical shear to the production of turbulence at the LLSC top (Table A1). We find it to be generally smaller than 20×10-5 s-2, which is to say, considerably smaller than that imposed at the initialization of LES experiments performed by Pedruzo-Bagazgoitia et al. (2020). However, this contribution in the subcloud layer is mostly higher than 50×10-5 s-2 (Fig. 4c). Thus, the dynamical instability induced by the NLLJ is more important below the LLSC layer than above. This should imply that the mechanical turbulence driven by the NLLJ impacts the turbulent fluxes at LLSC base much more than entrainment of ambient air from above.

Previous studies have demonstrated that several processes may lower the LLSC base and couple the cloud deck with the surface during the stratus phase: (i) shear-driven turbulence in the subcloud layer (Adler et al., 2019; Babić et al., 2019a), (ii) cloud droplet sedimentation at the cloud base (Dearden et al., 2018), (iii) light precipitation formation (i.e., drizzle) in the subcloud layer (Wood, 2012), (iv) convective overturning driven by the cloud-top radiative cooling (Wood, 2012) and (v) large-scale advection (Zheng and Li, 2019). Section 4.1 and 4.2 allowed us to test several of these hypotheses to understand why the LLSC couples with the surface in some DACCIWA cases.

As discussed in Sect. 4.1, there is no difference in shear-driven turbulence between C and D cases, which could explain the thermally neutral stratification of the subcloud layer in C cases and the stable stratification in D cases. Therefore, the NLLJ does not appear to be responsible for the LLSC coupling in C cases.

With LES experiments based on the 4–5 July case (case D, IOP7), Dearden et al. (2018) hypothesized that the LLSC base descent during night is due to cloud droplet sedimentation at the cloud base. However, the cloud base decrease is less than 50 m before sunrise in this numerical experiment, whereas the observed LLSC base descent is larger than 100 m by the end of the stratus phase in most of our studied cases, including C and D. Thus, cloud droplet sedimentation alone cannot explain the coupling in C cases.

In all the DACCIWA cases we studied, no precipitation was recorded at the surface during the stratus phase. However, drizzle formation below the LLSC base can hardly be measured by rain-gauge sensors. Therefore, this hypothesis cannot be fully tested and remains a possibility. In terms of radiative cooling at the LLSC top, Sect. 4.2 shows that this positive contribution to the LWP budget at the end of the stratus phase is similar in the C and D cases.

The large-scale effects must be considered not only in the LLSC formation (Babić et al., 2019b) but also in its diurnal cycle. Indeed, eight of the nine C cases are observed between 26 June and 8 July 2016 (Table A1). This period corresponds to the first days of the post-onset phase characterized by a well-established and undisturbed monsoon flow over SWA (Knippertz et al., 2017). Warm air advection was observed to decouple the LLSC layer from the surface (Zheng and Li, 2019). Therefore, the reverse process, i.e., colder air advection, may produce the opposite effect. This hypothesis is all the more likely since LLSC formation during the West African monsoon season is mainly due to horizontal advection of cooler air. The reusable soundings performed during the stratus phase of the nine IOPs revealed that at 50 m a.g.l. (sounding level below the lowest CBH at the end of the stratus phase), the relative humidity remains greater than 90 % for all the cases (not shown). For C cases, a decrease in specific humidity (by around 1 g kg-1) and a slight decrease in temperature (by around 0.2 ∘C) are observed between the LLSC formation and its coupling with the surface, which maintains a constant RH. However, no clear tendency was observed in D cases. The very small tendency of temperature and humidity and the small number of studied cases do not allow us to definitively conclude an effect of cooling and drying due to the horizontal advection of maritime air. However, this advection seems to persist in C cases and could have some impact though not on LLSC base lowering (because RH is constant at 50 m a.g.l.); rather, the dry advection may have an effect on the LCL evolution. Indeed, a 1 g kg-1 decrease in near-surface specific humidity implies an elevation of surface-based LCL by 100 m which facilitates the coupling.

In summary, none of processes listed at the beginning of this subsection is solely responsible for the coupling before sunrise. We can hypothesize that it is a combination of several of those processes, each with a small impact that leads to the LLSC layer coupling with the surface. After the coupling, turbulence underneath the LLSC plays a crucial role in its maintenance during the rest of the stratus phase, as indicated by the reduction in thermal stability in the subcloud layer for C cases (Fig. 5b). Indeed, the contributions of shear-driven turbulence below the NLLJ and convective turbulence due to the cloud-top radiative cooling are important for mixing potential temperature in the subcloud layer (Dione et al., 2019; Lohou et al., 2020). In LES experiments under windless conditions carried out by Pedruzo-Bagazgoitia et al. (2020), cloud-top radiative cooling was the sole source of turbulence in the ABL until sunrise, and the coupling between cloud and surface was maintained.

The LLSC evolution during the convective phase is first analyzed according to ceilometer-derived CBH temporal change relative to surface-based LCLs. From this point of view, all C cases evolve quite similarly during this phase (scenario C), while two distinct scenarios are observed among D cases (hereafter named DC for “decoupled-coupled” and DD for “decoupled-decoupled”). Each of the three scenarios is illustrated by one typical example: the LLSC occurrence on 7–8 July (Fig. 10a) for scenario C and 25–26 June (Fig. 10b) and 4–5 July (Fig. 10c) for scenarios DC and DD, respectively.

Whether the CBH is close to LCL (Fig. 10a) or not (Fig. 10b and c), it has a low variability before 07:00 UTC in these three illustrative cases, indicating a quite horizontally homogenous base of the LLSC layer before the start of the convective phase (as seen in the previous section). The CBHs and LCLs in scenario C lift together after 07:30 UTC due to thermal convective conditions in the subcloud layer. After 09:00 UTC, σ* increases gradually, but the lower bases always fit with LCL, with ΔLCLCBH ranging between 0 and -40 m (Fig. 10a, lower panel). This can be interpreted as a progressive change in the LLSC base structure which is more and more heterogeneous at height, but the cloud layer remains coupled with the surface all along. The evolution from stratus to stratocumulus and eventually to cumulus cannot be established using CBH alone, but the ceilometer-derived CBHs already show a clear evolution from homogeneous LLSCs towards a more heterogeneous low cloud structure until the cloud deck breakup time established when CF decreases to less than 90 %, which happens at 12:00 UTC on 8 July 2016.

The LLSC in scenario DC (Fig. 10b) is decoupled from the surface at the end of the stratus phase. The LCL starts to rise at 07:00 UTC and joins the LLSC base about 1 h later, which is indicated by a decrease in ΔLCLCBH to zero (Fig. 10b, lower panel). After the coupling, scenario DC is very similar to scenario C and will be discussed further in Sect. 5.3.

The LLSC evolution in scenario DD (Fig. 10c) is quite different from the other two. The LLSC layer remains decoupled from the surface until 08:00 UTC, as shown by a significant departure between CBHs and LCL (ΔLCLCBH>120 m; Fig. 10c, lower panel) due to a similar lifting rate of both levels. After 08:00 UTC, a new cloud layer with a base very close to LCL (ΔLCLCBH<40 m) is detected 200 m below the LLSC deck. The values of σ*, much larger than 60 m after 08:30 UTC, indicate that this new cloud layer rapidly turns to shallow cumulus clouds. Unfortunately, it is not possible to distinguish both cloud layers with ceilometer-derived CBHs because they remain too close together with variable cloud bases and edges. However, we can assume that the LLSC layer forming during the night remains above the cumulus clouds during part of the convective phase. The higher CBHs detected by the ceilometer after 09:00 UTC are the overlying LLSC base (about 200 m higher). The cumulus and LLSC layers above can, however, clearly be seen on visible and infrared full-sky cameras (not shown). In the case when the two cloud layers are superimposed, two possibilities may occur: (i) the underlying surface-convection-driven cumulus clouds do not interact with the LLSC deck which remains decoupled from the surface, and (ii) the underlying cumulus clouds develop vertically, reach the LLSC layer and act to intermittently and locally couple it with the surface (Wood, 2012).

Among the 13 D cases observed at the end of the stratus phase, 8 and 5 follow scenarios DD and DC, respectively, during the convective phase (Table A1). The main difference between the three scenarios is that the first shallow convective clouds form when the LLSC layer breaks up in scenarios C and DC, whereas in scenario DD, shallow cumulus clouds form below the LLSC deck before it breaks up. Similar transitions were reported by previous observational and modeling studies on the stratiform low-level clouds (Price, 1999; Xiao et al., 2011; Ghonima et al., 2016; Mohrmann et al., 2019; Sarkar et al., 2019; Zheng and Li, 2019; Pedruzo-Bagazgoitia et al., 2020). In particular, the Sc-Cu transition of scenario DD is part of the conceptual model for marine stratocumulus (Xiao et al., 2011; Wood, 2012).

What conditions lead the LLSC either to be coupled with the surface in scenario DC or to remain possibly decoupled with the formation of an underlying cumulus cloud layer in scenario DD? No relevant differences in macrophysical characteristics of LLSC (base and depth) were found between the two scenarios at the end of the stratus phase and beginning of the convective phase (not shown). The LLSCs with low bases are not systematically those which will be coupled with the surface at the beginning of the convective phase. The four parameters presented in Fig. 8 which summarize thermodynamical conditions below and above the LLSC layer are not fundamentally different between the DC and DD scenarios either. The relative humidity in the subcloud layer at the end of the stratus phase is larger than 95 % in all D cases, and the difference between scenarios DD and DC is smaller than 2 %, which is about the measurement accuracy. Consequently, alternative approaches are needed to identify the processes involved in the LLSC coupling with the surface during the convective phase.

In conclusion, the coupling between the LLSC layer and surface during the convective phase appears to be the key factor in determining how the transition towards shallow convective clouds takes place. When the LLSC is coupled with the surface (C and DC cases), it is the breakup of the cloud deck that leads to the formation of different low-level cloud types (stratocumulus or cumulus). When the LLSC is decoupled from the surface (DD cases), the shallow convective clouds form below it. In the next subsection, we analyze the different scenarios of LLSC evolution in greater depth.

We defined two characteristic times of the LLSC evolution (see Sect. 3.2): the surface-convection influence and LLSC breakup times (Ti and Tb, respectively). Tb is determined by the diagnostic parameter CF. Ti, which indicates when the low cloud coverage is influenced by the surface buoyancy-driven turbulence, is defined differently according to the scenario. For scenario C, Ti corresponds to the time when the LLSC base starts to lift together with LCL. After sensitivity tests, Ti is defined as the first time when LCLM increases to at least 5 m above its value at 06:30 UTC. For scenario DC, Ti corresponds to the time when the rising LCL reaches the LLSC base, which is to say, when the LLSC layer is coupled with the surface (ΔLCLCBH<75 m, which is also the threshold used to differentiate C and D cases at the end of the stratus phase in Sect. 4.1). For scenario DD, Ti is the first time when new low clouds appear below the LLSC deck. As these clouds are coupled with the surface, Ti is also determined when ΔLCLCBH decreases to less than 75 m.

Figure 11 displays Tb and Ti for the 22 LLSC cases (Table A1). Ti ranges between 06:30 and 09:15 UTC. Tb varies between 07:30 and 16:00 UTC, with breakup time occurring before 12:00 UTC in 72 % of cases. The latter result is consistent with the findings of Dione et al. (2019) who used infrared sky camera images to define the LLSC lifetime. We can see that the LLSC breakup time is not linked to the time at which it starts to rise or at which underlying cumulus clouds form.

For scenario C, Ti hardly changes from one case to the other. It ranges between 06:40 and 08:00 UTC, which is not long after sunrise (06:00 UTC). The LLSC persists for at least 4.5 h and breaks up between 11:00 and 16:00 UTC. The latest breakup time, occurring at 16:00 UTC, corresponds to the 2–3 July 2016 case for which the collocated radar reveals light precipitation from higher clouds (above the LLSC layer) during the first hours of the convective phase (not shown), while nothing was recorded by the surface rain gauge. This external forcing, able to enhance the liquid water content in the LLSC layer, is certainly responsible for this late breakup. Because this case is an exception and cannot easily be compared to the others, it is not considered hereafter.

For four out of five DC cases, Ti and Tb are very close to values observed for C cases. This means that the stable stratification in the subcloud layer before the convective phase (which allowed classification of this case as decoupled during the stratus phase) is rapidly eroded after sunrise and does not seem to impact the breakup time. The case for which Tb occurred at 08:00 UTC (16–17 July 2016) is removed in the following as well because the LLSC breaks up before LCL reaches its base.

The DD scenario presents the largest variation ranges of Ti (between 06:35 and 09:00 UTC) and Tb (between 07:00 and 13:00 UTC). The most striking result is that the LLSC in scenario DD often breaks up earlier than in scenarios C and DC.

Following the LES of Pedruzo-Bagazgoitia et al. (2020), the start of the convective phase leads to three main changes in the LWP tendency equation. First, the radiative cooling (RAD term) decreases due to solar heating at the cloud top. Second, the ENT term also strongly decreases because the thermally driven convection enhances entrainment of dry and warm air from aloft into the LLSC layer. Third, the BASE term, which was close to zero during the stratus phase, comes into play during the convective phase and contributes positively to ∂LWP∂t. Despite the BASE term, the strong decrease in both ENT and RAD makes ∂LWP∂t negative 1 h after sunrise. The RAD and ENT terms cannot be estimated during the convective phase with the dataset acquired at Savè because an amount data are missing, among them the CTH.

The C and DC scenarios during the convective phase are very close to the case simulated in Pedruzo-Bagazgoitia et al. (2020), and we can expect a quite similar evolution of terms involved in the LWP prognostic equation. Conversely, the DD scenario might be very different. The LLSC breaks up earlier, mostly before or around 10:30 UTC, when it is decoupled from the surface likely due to a weaker BASE term. This hypothesis is supported by the findings of van der Dussen et al. (2014), suggesting that LLSCs coupled with the surface moisture are more resistant to cloud-thinning-related processes, such as the entrainment of dry and warm air into the cloudy layer. The stronger variability in breakup times for DD cases may come from the fact that the LLSC thinning depends on its interaction with the underlying cumulus clouds. If the latter penetrates the LLSC deck, local coupling can happen which induces a homogeneous cloud layer from the surface to the LLSC top, but, at the same time, the entrainment at the cloud top is enhanced by the vertical development of cumulus (Wang and Lenschow, 1995).

The LLSC breakup time impacts the surface radiative budget over the day, then the surface fluxes and, consequently, the vertical development of the ABL, as shown by Lohou et al. (2020). They estimated that the ABL height is about 900 m when the LLSC deck breaks up at 09:00 UTC and is 30 % lower when this breakup occurs at 12:00 UTC. Consequently, one can expect a quite different vertical development of the ABL in C/DC cases compared to DD cases.

The changes in the LLSC horizontal structure for C and DC scenarios are now further analyzed based on the evolution of the LLSC base and its standard deviation σ∗. The DD cases are excluded from this analysis because the macrophysical characteristics of associated LLSCs cannot be determined after the underlying cloud formation. As illustrated in Fig. 10a and b, the elevation rate of LCL, and consequently of the LLSC base, may change a lot from one case to the other. It is about 108 and 67 m h-1 for 8 July and 26 June, respectively. It could be expected that the higher this rate is, the higher the Rn0 and the more intense the thermally driven convection in the subcloud layer will be, as well as the corresponding BASE term. However, no clear link is pointed out between Tb and this elevation rate of the LLSC base (not shown).

Contrary to the LLSC base height, σ∗ has a common tendency among all the C and DC cases. The evolution of σ∗ with time compared to its value at Ti, σEarly, is presented in Fig. 12a. A 4 h period is considered here because it is the smallest duration between Ti and Tb for the 12 C and DC cases included in this statistic (Fig. 11). As also illustrated in Fig. 10a and b, σ∗ remains close to σEarly for at least 2 h after Ti (until 09:00 UTC for 8 July and 09:30 UTC for 26 July). Consequently, during this period, the structure of LLSC bases remains quasi-unchanged. Afterwards, σ∗ progressively increases for at least 2 h until the LLSC deck breakup. From Ti to the breakup, ΔLCLCBH remains lower than 70 m with even a slight decrease in the first 2 h (Fig. 12b) suggesting an enhancement of coupling due to the increase in thermally driven turbulence in the subcloud layer. The combination of (1) very heterogeneous LLSC base and (2) the fact that the lowest cloud bases remain close to LCL during the few hours before Tb indicates that some of the bases are coupled with the surface, but some tend to be decoupled from the surface.

Eventually, the evolution of σ∗ and ΔLCLCBH (Fig. 12) allows two periods to be defined between Ti and Tb: (1) the first 2 h after Ti during which the LLSC deck is fully coupled with the surface and the homogeneity of its base is not yet affected and (2) the few hours before Tb during which the base of the LLSC layer becomes more and more heterogeneous and intermittently decoupled from the surface. This latter tendency can be seen in Fig. 10a and b (upper and lower panels) after 11:00 and 10:15 UTC, respectively. A decoupling of the LLSC layer from the surface is also observed about half an hour before its breakup time in the LES of Pedruzo-Bagazgoitia et al. (2020).

The bottom panels of Fig. 10 present the evolution of the evaporative fraction at the surface (EF0) for the illustrative cases. Figure 12c displays the medians of this parameter over all C and DC cases. Defined as the ratio of LHF0 to (LHF0 + SHF0), an EF0 larger than 0.5 means that evapotranspiration dominates over warming. This was on average the case at Savè during the DACCIWA campaign (Kalthoff et al., 2018). Figure 12c shows that the median of EF0 decreases from around 0.75 at Ti to 0.6 at LLSC breakup. The predominance of evapotranspiration over sensible heat flux, particularly during the first 2 h after Ti, and the full LLSC coupling to the surface might contribute to maintaining this cloud layer throughout the BASE term. The LLSC base is indeed strongly homogeneous. The decrease in EF0 and its leveling at 0.6 implies a faster increase in SHF0 than LHF0. We can then expect a larger contribution of w′θl′‾b and a smaller one from w′qt′‾b in the BASE term with time. This favors the convection in the LLSC layer which enhances cloud top entrainment at the expense of cloud moistening by underlying turbulent mixing. In addition to this, the final intermittent decoupling of the LLSC layer from the surface likely contributes, together with the decrease in RAD and ENT terms (Pedruzo-Bagazgoitia et al., 2020), to the breakup of the cloud deck.

It appears that the LLSC and timing of its evolution in scenarios C and DC are very similar during the convective phase. In these scenarios, the LLSC keeps the same characteristics in terms of coupling and base homogeneity for 2 h after Ti. Afterwards and until its breakup, the LLSC becomes more and more heterogeneous and intermittently decoupled from the surface. These two steps are in phase with the evolution of EF0 that likely impacts the BASE term, which is the only positive contribution to the LWP budget during the convective phase.