[1,2]Victor J. H. Trees

1]R&D Satellite Observations, Royal Netherlands Meteorological Institute
(KNMI), de Bilt, The Netherlands

2]Geoscience and Remote Sensing, Delft University of Technology, Delft, The
Netherlands

3]Meteorology and Air Quality Group, Wageningen University & Research,
Wageningen, The Netherlands

# Clouds dissipate quickly during solar eclipses as the land surface cools

<EMAIL_ADDRESS>Stephan R. de Roode  Job I. Wiltink  Jan Fokke Meirink
Ping Wang  Piet Stammes  A. Pier Siebesma  [  [  [

###### keywords:

Solar Eclipses, Clouds, Satellite Measurements, Large-Eddy Simulations, Solar
Geoengineering

## Abstract

Clouds affected by solar eclipses could influence the reflection of sunlight
back into space and might change local precipitation patterns. Satellite cloud
retrievals have so far not taken into account the lunar shadow, hindering a
reliable spaceborne assessment of the eclipse-induced cloud evolution. Here we
use satellite cloud measurements during three solar eclipses between 2005 and
2016 that have been corrected for the partial lunar shadow together with
large-eddy simulations to analyze the eclipse-induced cloud evolution. Our
corrected data reveal that, over cooling land surfaces, shallow cumulus clouds
start to disappear at very small solar obscurations ($\sim$15%). Our
simulations explain that the cloud response was delayed and was initiated at
even smaller solar obscurations. We demonstrate that neglecting the
disappearance of clouds during a solar eclipse could lead to a considerable
overestimation of the eclipse-related reduction of net incoming solar
radiation. These findings should spur cloud model simulations of the direct
consequences of sunlight-intercepting geoengineering proposals, for which our
results serve as a unique benchmark.

## Introduction

Blocking part of the solar radiation incident on the Earth’s (lower)
atmosphere and surface is one of the proposed strategies to counteract the
current and future global temperature rise, which may be inevitable if climate
change mitigation efforts prove to be insufficient [1, 2, 3, 4]. This type of
(solar) geoengineering is based on placing sun shields or reflecting particles
in space between the Earth and the Sun [5, 6, 7, 8, 9, 10], or on the
injection of aerosols into the stratosphere [11, 12]. General circulation
models (GCMs) suggest that an insolation reduction of 3.5-5.0% can largely
undo the global temperature rise and intensified hydrological cycle associated
with a quadrupled pre-industrial CO2 concentration [13, 14, 15, 16]. However,
those GCMs also predict latitudinal variations in temperature response, and an
extra reduction of precipitation in the tropics. Moreover, although clouds
play a vital role in the Earth’s radiation balance [17], the impact of solar
dimming on clouds is still poorly understood [18, 19, 20, 21]. GCMs modeling
the response to (extraterrestrial) dimming of sunlight are based on idealized
scenarios [22]. They inherently suffer from uncertainties [23], mainly focus
on the long-term impact, and highly parameterize short-term and small-scale
processes such as cloud formation [23, 20]. Twice a year on average, for a few
hours the opportunity arises to take measurements of the Earth experiencing
gradual insolation reductions from 0 to nearly 100%, during the partial phase
of a solar eclipse. Although the time scales involved with solar
geoengineering will most likely not be equivalent to those of solar eclipses,
these measurements can help to better understand (and test models that
predict) the immediate cloud response to the deployment of sunlight
intercepting material.

Figure 1: SEVIRI images of the annular solar eclipse on 3 October 2005. (a)
The original and (b) the eclipse corrected TOA VIS reflectance over East
Africa (in the West) and Indian Ocean (in the East), at 09:37, 10:37, 11:37
and 12:37 UTC (from top to bottom). The colored contour lines indicate the
solar obscuration fraction and the white squares over land mark the study
area. (c) The corresponding eclipse corrected cloud optical thickness zoomed-
in on the study area.

Ground-based meteorological observations during solar eclipses have primarily
focused on fast drops in air temperature, winds and turbulence, and on
changing (photo)chemistry [24, 25]. Weather publications contain anecdotal
descriptions of dissipating low-level cumulus clouds right before totality,
while mid- and high-level clouds survived [26, 27]. The timing of the eclipse-
induced effect on cumulus clouds is difficult to quantify with ground-based
measurements due to the chaotic nature of cumulus cloud evolution and the
missing observation of the non-eclipse state, and atmospheric model studies of
eclipses did not yet analyze the cumulus cloud sensitivity [28, 29, 30, 31].
Additionally, the precise locations of the affected clouds can be hard to
predict and are sometimes inaccessible for ground-based observers. Earth
observation satellites in geostationary orbit can continuously monitor clouds
in large geographical areas [32, 33, 34] and hints of dissipating cumulus
clouds have been observed by comparing satellite images before and after a
total solar eclipse, without estimating the non-eclipse state [26, 35].
However, during solar eclipses, satellite images show spatio-temporally
varying darkening [35, 36] and satellite retrievals of cloud cover and cloud
optical thickness (COT) are biased. This bias is caused by not taking into
account the insolation reduction in the calculation of the top-of-atmosphere
(TOA) reflectance from which cloud properties are derived. Hence, it has
remained unknown how fast clouds are modified by various solar obscuration
fractions.

Here, we present geostationary satellite measurements of clouds during three
solar eclipses between 2005 and 2016 that have been corrected for the
insolation reduction. Our corrected measurements reveal that shallow cumulus
clouds start to dissipate at a solar obscuration of $\sim$15% over cooling
land surfaces, which would have been hidden in the partial lunar shadow
without insolation reduction correction. Using large-eddy simulations we
explain the timing of the cloud dissipation and demonstrate that the rising
air parcels in the atmospheric boundary layer are already affected by the
solar eclipse at even smaller obscurations. We calculate that neglecting the
dissipating cloud behaviour in the simulations would result in an
overestimation of 20 W m-2 of the eclipse-related reduction of net incoming
shortwave radiation at the top-of-atmosphere. Finally, we discuss that the
high cloud sensitivity to rather small insolation reductions should spur cloud
model simulations of the short-term impact of sunlight-intercepting
geoengineering concepts.

## Results

### Satellite observations

Figure 1 shows the uncorrected and corrected TOA visible (VIS) reflectance
over East Africa and part of the Indian Ocean, at four subsequent hours during
the annular solar eclipse on 3 October 2005, obtained by the Spinning Enhanced
Visible and InfraRed Imager (SEVIRI) instrument (see Methods). In the first
hour, cumulus clouds were present over land. They are better visible in the
corrected high resolution images of the COT zoomed in on the specific area
over land at 3∘-7∘ latitude and 27∘-31∘ longitude (Fig. 1c), which we call the
study area. The derived COT in the cloudy pixels was $\lesssim$ 5 and SEVIRI
estimated a cloud top altitude of $\sim$2 km (see Supplementary Figure 1),
indicating that they were shallow and located in the planetary boundary layer.
Similar large-scale daytime shallow cumulus cloud fields over land can be
found in central Africa and the Amazonian rainforest throughout the year, and
in northeast America and Siberia during the boreal summer [37, 38]. When the
obscuration increased in the second hour, the cloud cover in the study area
diminished, although remnants of the cloud pattern of the previous hour are
still recognizable. In the third hour, the insolation increased again, but the
shallow cumulus clouds stayed away while the clouds that survived had grown in
size and COT. It was only during the final stage of the eclipse that shallow
cumulus clouds returned throughout the study area. Over ocean, the cumulus
clouds did not disappear. In Supplementary Figures 2 and 3, we provide two
more examples of vanishing shallow cumulus clouds over land during solar
eclipses.

Figure 2: Time series of cloud and land surface parameters in the study area
(i.e., the white square in Fig. 1). (a) The retrieved cloud cover by SEVIRI.
(b) The cloud optical thickness (COT) retrieved by SEVIRI. (c) The spatial
mean land surface temperature (LST) retrieved by SEVIRI. (d) The modeled cloud
cover with DALES. (e) The COT simulated with DALES. (f) The sensible and
latent heat fluxes modeled with DALES. The black solid lines are for the day
of the solar eclipse (3 October 2005). The grey dashed lines in (a), (b) and
(c) are for the comparable days but without solar eclipse. The black dashed
lines in (d), (e) and (f) are the results of the modeled reference case. The
blue solid lines illustrate the spatial average obscuration fraction, with
error bars in (a), (b) and (c) representing the standard deviation of the
spatial variation. The blue vertical dotted lines indicate the start, maximum,
and end of the eclipse (from left to right). The missing observations between
9 and 10 UTC in (b) are caused by COT retrieval errors at that scattering
geometry due to the cloud bow. The insets show the time series zoomed in on
09:00 to 10:00 UTC. Local noon occurred at 10:04 UTC.

The disappearance of shallow cumulus clouds only occurred on the day of the
solar eclipse. Figure 2a shows the time series of the cloud cover in the study
area, compared to that during 11 comparable days which we selected based on a
similar type of cloud pattern before the eclipse started (see Methods). Also
depicted in Fig. 2 is the obscuration fraction on the eclipse day. The time
series shows that the increasing cloud cover in the morning already halted at
low obscuration fractions ($\sim$0.15), happening at around 09:30 UTC which
was 30 minutes after the start of the eclipse. Secondly, there was a $\sim$50
minutes time lag with respect to the instant of maximum obscuration at 10:52
UTC before the clouds started to return. During the increase in cloud cover
between 12:00 and 12:30 UTC, the mean COT in the cloudy pixels decreased (see
Fig. 2b), which can be attributed to the contribution of the newly formed
shallow clouds. This decrease is absent in the time series of the comparable
days.

Because shallow cumulus clouds in the boundary layer are generated by rising
thermals originating from air close to the surface [39], we collected land
surface temperature (LST) measurements from space by SEVIRI, derived from
infrared radiation emitted by the shallow land surface layer (see Methods).
Figure 2c shows the spatially averaged LST in the study area on the eclipse
day and the comparable days. The maximum LST on the comparable days was two
hours delayed with respect to local noon at 10:04 UTC, which could possibly be
explained by the smaller heat flux into the ground due to the warmed
subsurface layer in the afternoon [40]. On the eclipse day, the LST drops
instantly with the obscuration fraction, due to the direct response of the
shallow land surface layer temperature to net radiation forcing [40]. We
estimate a maximum LST drop of 5.8 K induced by the eclipse at 11.00 UTC (see
Methods). Comparable fast drops in satellite LST measurements have been found
in a study over Europe during the total solar eclipse of 20 March 2015 by Good
[41] who showed dependencies of the drop magnitude on the eclipse duration and
time of the day (earlier eclipses gave larger drops), vegetation, surface
height and distance to the coast. We did not detect a time lag in the LST
minimum with respect to maximum solar obscuration: a time lag of $\sim$1.5
minutes as reported in literature [41] is not resolved in our LST data at 15
minutes intervals. Hence, the measured time lag of $\sim$50 minutes before
clouds return in Fig. 2a cannot be explained by a time lag in the LST. Over
ocean, we found no sea surface temperature drop when the eclipse passed (see
Supplementary Figure 4), due to the large heat capacity of water and the
efficient heat transport from the sea surface to deeper water layers through
turbulent mixing [40].

### Large-eddy simulations

In order to explain the land-cloud interaction in the study area, we simulated
the evolution of shallow cumulus clouds during a solar eclipse with the Dutch
Atmospheric Large-Eddy Simulation (DALES) model [42]. Figures 2d and 2e show
the time series of the simulated cloud cover and mean COT, respectively, as
would be measured from space (see Methods), and Supplementary Figure 5
contains snapshots of the spatially resolved cloud fields. We present the
results for the solar eclipse case, using the measured LST as input, and a
reference case without eclipse-induced LST drop (see Methods). Indeed, in the
solar eclipse case, our simulations show a substantial decrease in cloud cover
with respect to the reference case. The cloud cover already differed $\sim$15
to $\sim$20 minutes after the start of the eclipse when the obscuration was
still smaller than $10\%$. As in the observations (Fig. 2a), there is a time
lag in the instant of minimum cloud cover with respect to mid-eclipse, after
which the cloud cover rapidly increases. We note that the simulated cloud
cover right after the eclipse is even larger than in the reference case, while
the simulated COT is lower. A larger cloud cover after the eclipse compared to
the hypothetical non-eclipse scenario is difficult to prove with our
observations, due to the large variability of the cloud cover on the
comparable days in the afternoon (cf. Fig. 2a). During the rapid increase in
cloud cover, the simulated COT also increases, which is not in agreement with
the observations, but can be attributed to the absence of the deeper
convective clouds in the south part of the study area due to the horizontally
averaged input settings in our simulations (see Methods).

Figure 3: Large-eddy simulation results from DALES for the solar eclipse and
reference case. (a) Time-varying vertical profiles of the horizontal mean
liquid water specific humidity $q_{\mathrm{l}}$ and (b) the buoyancy flux
$\overline{w^{\prime}\theta_{\mathrm{v}}^{\prime}}$ for the solar eclipse
case. (c) The vertical updraft velocity $w_{\mathrm{3\%}}$ of the 3-percentile
fastest rising parcels at various altitudes and (d) the travel time $\Delta t$
of the 1- to 5-percentile fastest rising parcels from the surface to lifting
condensation level (LCL) and to the cloud top (indicated with brown and grey
color shades, respectively), for the solar eclipse case. Similar for Figs.
(e), (f), (g) and (h), but then for the reference case. In Figs. (a), (b), (e)
and (f), the LCL and level of minimum buoyancy flux (LMBF) are indicated with
a dashed and dotted line, respectively.

The disappearing clouds during a solar eclipse can be explained by the drop in
sensible (thermal) and latent (moisture) heat fluxes from the surface to the
lowest atmosphere layer (Fig. 2f), as a result of the dropping LST (see Eqs. 1
and 2). Those heat fluxes drive the buoyancy flux (Figs. 3b and f) of
relatively warm and moist air parcels from the surface, through the well-mixed
boundary layer, up to the level of minimum buoyancy flux (LMBF) where the
parcels are capped by a temperature inversion (see Supplementary Figure 6).
The rising parcels are cooled through adiabatic expansion which increases the
parcel relatively humidity (RH) up to 100% at the lifting condensation level
(LCL) where shallow cumulus clouds are formed that can extend to higher
altitudes (Figs. 3a and e). During a solar eclipse, this process is
suppressed, which is clear from the overall drop in buoyancy flux. The drop in
surface and buoyancy fluxes is consistent with the diminished boundary layer
turbulence during solar eclipses found in other studies [43, 44, 31]. It
should be noted that the LMBF is still higher in our model than the LCL, but
with smaller upward parcel velocities (Fig. 3c) which are controlled by the
surface buoyancy flux, fewer parcels reach the LCL.

The $\sim$15 to $\sim$20 minutes delay of the simulated vanishing cloud cover
with respect to the dropping LST can be related to the $\sim$16 to $\sim$24
minutes travel time around 09:00 UTC of the fastest rising parcels from the
lowest atmospheric layer to the cloud top as shown in Fig. 3d, after which the
first individual clouds could fully disappear. We note that the vertical
updraft velocity of the lowest layer responded within 5 minutes to differences
in surface fluxes. The travel time depends on the cloud top height and
vertical updraft velocities (see Figs. 3c and g and Methods). Thus, the cloud
response was initiated when the parcels affected by the eclipse started
rising, at even smaller obscuration fractions than at which this response
could be observed. The $\sim$18 minutes time lag of the simulated cloud cover
minimum with respect to mid-eclipse can be related to the relatively long
travel time around 11:10 UTC of $\sim$13 to $\sim$19 minutes to LCL at which
the newly formed clouds started influencing the cloud cover. Furthermore, we
note that the LCL and cloud base remained slightly lower after the eclipse
compared to the reference case, due to the continued colder air near the
surface (see Supplementary Figure 7 and Eq. 4). In Fig. 4 we provide a
conceptual model in which we summarize the most important processes
responsible for the shallow cumulus cloud behavior during a solar eclipse.

Figure 4: Conceptual model of shallow cumulus cloud evolution during a solar
eclipse. The time progresses in the horizontal direction to the right.
Background color shading indicates the virtual potential temperature of the
atmosphere and land surface in our simulation. The red and blue arrows are the
sensible and latent heat fluxes, respectively, which depend strongly on the
temperature difference between the surface and the atmosphere just above the
surface. The yellow arrows represent the amount of incoming solar radiation,
which is largest around noon but is reduced during a solar eclipse as
illustrated by the lunar disk covering the solar disk. When the growing
atmospheric boundary layer height (dotted line) intersects with the lifting
condensation level (dashed line), clouds are formed, but they are diminished
when the updrafts are slowed down during a solar eclipse, as indicated by the
smaller inclination of the black arrow.

The disappearance of the shallow cumuli during the solar eclipse has a notable
feedback on the solar radiative fluxes. This can be understood from Fig. 5,
which shows the simulated reflected and net incoming shortwave (SW) radiative
flux at TOA, for both the reference and solar eclipse cases. As a result of
the solar eclipse the net incoming SW flux started to decrease at 09:00 UTC.
However, this change, which has solar dimming as its main cause, is also
affected by the decrease of SW radiation reflected back into space due to the
clearance of the sky. Indeed, the latter indirect effect causes an opposing
increase in the net incoming SW flux at TOA. Neglecting the solar eclipse-
induced cloud disappearance in our simulations (as illustrated by dotted line
in Fig. 5), resulted in an overestimation of 20 W m-2 of the eclipse-related
reduction of net incoming SW flux at TOA at 11:22 UTC. We note that this error
would further increase with longer time lags of the cloud return with respect
to mid-eclipse, such as found in the satellite observations (Fig 2a), because
then more sunlight illuminates the cloud-free scenes.

## Discussion

The observed response of shallow cumulus clouds to a solar eclipse at already
$\sim$15$\%$ obscuration, initiated at even smaller obscurations due to the
parcel travel time, reveals the potential direct consequence of deploying
sunlight intercepting material in the stratosphere or in space. We note that
the duration of the cloud response is expected to depend on the speed and
magnitude of the local obscuration variations, as the altered difference
between the near-surface air and surface temperature, which causes the
response, may possibly restore after a certain period. Diminished shallow
cumulus clouds would partly oppose the objective of solar geoengineering which
is to decrease the amount of net incoming solar radiation, and could prevent
the growth into deeper convective and possibly precipitating clouds [45].
While solar geoengineering proposals aim to reduce the solar radiation
reaching the (lower) atmosphere and surface globally by only a few percent
(depending on the required compensation), the use of non-uniform reductions to
achieve this goal could increase the locally experienced variations in
obscuration [10]. Space-based examples are the deployment of solar reflectors
in Earth orbit [8, 9] or in orbit around the 1st Lagrange point [10], offering
daily and seasonally varying shading, respectively. Injected stratospheric
aerosols can also exhibit spatio-temporally varying patterns due to seasonally
changing global stratospheric circulation, depending on the injection location
[46] and strategy employed (whether constant or step-wise) [47, 48].
Consequently, aerosol optical depths of 0.4-0.6 could be attained locally [47,
46, 48], causing up to $\sim$45% of the local direct sunlight to be scattered
or absorbed by the aerosols before it reaches the lower atmosphere. Our
results should spur model simulations investigating the response of shallow
cumulus clouds to those geoengineering concepts, particularly for scenes over
land where the surface temperature can adjust quickly. Additionally, our
measurements provide an opportunity to validate these models, enhancing their
reliability in predicting cloud behavior under natural conditions and in a
world influenced by solar geoengineering.

Figure 5: Simulated radiative fluxes at the top-of-atmosphere (TOA). (a) The
reflected and (b) the net incoming shortwave (SW) radiation (note the
different scales of the vertical axes). The solid line is for the solar
eclipse case, the dashed line is for the reference case, and the dotted line
is for reference case multiplied by (1 - $f_{\mathrm{o}}$), with
$f_{\mathrm{o}}$ the solar obscuration fraction. The bottom panels show the
deviation of the latter from the solar eclipse case.

## Methods

Cloud measurements

The primary data set used in this research consists of measurements from the
Spinning Enhanced Visible and InfraRed Imager (SEVIRI) on board the Meteosat
Second Generation (MSG) series of geostationary satellites operated by
EUMETSAT. We used data from Meteosat-8 and Meteosat-10, for the 2005-2006 and
2016 cases, respectively. SEVIRI measures TOA radiances over the full Earth
disk centered at 0∘ latitude and 0∘ longitude every 15 minutes in twelve
channels across the visible and near-infrared part of the spectrum [49].
Eleven channels have a narrow bandwidth at low spatial resolution (3 x 3 km2
at sub-satellite point) and one channel has a broad bandwidth (0.6 - 0.9
$\mu$m) at high spatial resolution (1 x 1 km2), the latter being referred to
as the HRV channel. Shortwave channel reflectances were obtained from the
observed radiances and the calculated solar irradiance, and were calibrated
with MODIS following Meirink et al. [50]. For the longwave channels, the
operational calibration from EUMETSAT was used.

For the surface temperature analyses at low spatial resolution (see Surface
temperature measurements), cloud masks were calculated using the EUMETSAT
Nowcasting and Very Short Range Forecasting Satellite Application Facility
(NWC SAF) v2021 cloud algorithm [51]. The NWC SAF software also provided the
cloud top height at low spatial resolution. For the cloud analyses at high
spatial resolution, we used the low-resolution NWC SAF cloud mask as a basis
and improved the spatial resolution of the cloud mask using the HRV TOA
reflectances by comparing with a HRV TOA reflectance climatology, which was
generated for each pixel with HRV TOA reflectance measurements in a 16-day
period centered at the day of the eclipse, following the method of Bley and
Deneke [52]. The TOA reflectances of the 0.6 and 1.6 $\mu$m channels were
paired to simultaneously retrieve the COT and effective droplet radius [53,
34], which were downscaled to high spatial resolution using the HRV channel as
described in more detail in [54, 55]. The COT of the pixels that were not
masked as cloudy was set equal to zero. For the study area (3-7∘ N latitude,
27-31∘ E longitude on 3 October 2005) and between 06:00 and 09:00 UTC, pixels
with a TOA reflectance value larger than 1.0, originating from the sunglint in
the rivers, were removed from the cloud product.

Solar eclipse correction

We corrected the TOA reflectance for its reduction during a solar eclipse,
that was due to the ignorance of the reduced solar irradiance in its
calculation, through a division by 1 - $f_{\mathrm{o}}$, with $f_{\mathrm{o}}$
the solar obscuration fraction. In previous work [56], we validated this
approach with the TROPOMI satellite instrument, which allowed for accurate
monitoring of aerosols in the partial lunar shadow up to
$f_{\mathrm{o}}=0.92$. Recently, Wen et al. [57] applied a similar type of
correction to images of the Earth Polychromatic Imaging Camera (EPIC)
instrument on the Deep Space Climate Observatory (DSCOVR), to quantify the
measured TOA reflectance error without eclipse correction of the sunlit side
of the Earth during the annular solar eclipse on 21 June 2020. The value of
$f_{\mathrm{o}}$ is different for every pixel as it depends on measurement
time, surface height, latitude and longitude, which are provided with the
SEVIRI data. The so-called Besselian elements describing the temporal
variation of the Moon shadow’s geometry were taken from Espenak and Meeus
[58]. The value of $f_{\mathrm{o}}$ also depends on wavelength through the
wavelength dependent limb darkening of the solar disk [59]. For the
corrections of the TOA reflectances in the HRV channel and 0.6 $\mu$m, 0.8
$\mu$m and 1.6 $\mu$m channels, we used the limb darkening coefficients of
Pierce and Slaughter [60] and Pierce et al. [61] at 0.7 $\mu$m and the central
wavelengths 0.635 $\mu$m, 0.81 $\mu$m and 1.64 $\mu$m, respectively. We refer
to Trees et al. [56] for more details about the solar eclipse correction of
the TOA reflectance. Applying the cloud algorithms to the corrected TOA
reflectance yielded the corrected cloud mask and COT.

Surface temperature measurements

For the measurements of land surface temperature (LST), we used the LST
product of the Land Surface Analysis Satellite Application Facility (LSA SAF)
[62] derived from the 10.8 $\mu$m and 12 $\mu$m SEVIRI channels [63] with an
uncertainty of 1 to 2 K [64] which is expected to be stable within the time
scales of solar eclipses [41]. We computed the horizontal average LST in the
study area in every 15 minutes time step, after replacing the cloudy pixels by
interpolated nearest neighbour values using the corrected SEVIRI NWC SAF cloud
mask (see Cloud algorithm and Solar eclipse correction). The maximum LST drop
due to the eclipse was estimated with respect to the average LST of comparable
days (see Selection of comparable days). For the measurements of the sea
surface temperature (SST), we used the hourly SST product of the Ocean and Sea
Ice Satellite Application Facility (OSI SAF) [65] derived from the 10.8 $\mu$m
and 12 $\mu$m SEVIRI channels with an uncertainty well below 1 K [66].

Selection of comparable days

The selection of days without solar eclipse that are comparable to our study
case on 3 October 2005 in East Africa was done by first selecting 100 days
from September and October in 2004, 2005 and 2006 with the smallest
differences with respect to our study case in the sums of the predicted
sensible and latent heat fluxes by ERA5 [67] (which does not take into account
the solar eclipse effect) in the complete diurnal cycle. Subsequently, we
refined the selection by removing the days for which the mean of the absolute
differences in high spatial resolution cloud cover with respect to our study
case between 06:00 and 09:00 UTC was larger than the threshold of 0.1. In this
way, we obtained 11 days for which we find the cloud cover comparable in the
morning before the lunar shadow reached the study area: 2004-09-10,
2004-10-24, 2005-09-03, 2005-09-19, 2005-09-25, 2005-09-29, 2005-10-04,
2006-09-01, 2006-09-04, 2006-09-08, 2006-10-06. We visually inspected the HRV
TOA reflectance and COT for those comparable days and indeed found between
06:00 and 09:00 UTC similar types of shallow cumulus clouds throughout the
scene, with low COTs ($\lesssim$ 5) as shown in Fig. 2b.

Cloud simulations The cloud simulations were performed with the Dutch
Atmospheric Large-Eddy Simulation (DALES) model [42]. The setup was a
horizontally cyclic domain of 50 by 50 km2 with horizontal cell sizes of 100
by 100 m2 and 209 vertical layers between 0 and 14 km altitude. The vertical
extent of each layer was stretched by a factor 1.01 with respect to the layer
just below, and it was 20 m in the lowest layer. The ground surface was
assumed flat. The atmosphere variables in the domain were initialized with
horizontally homogeneous vertical profiles of the liquid potential
temperature, total water specific humidity, and horizontal wind speed and
direction. Those profiles were the horizontal mean profiles at 02:00 UTC in
the study area (3∘-7∘N latitude, 27∘-31∘E longitude on 3 October 2005), taken
from ERA5 [67]. The pressure profile was determined with the use of the
thermodynamic profiles, the gas law and mean hydrostatic balance. After 02:00
UTC, the simulation freely propagated those variables, until 15:00 UTC when
the simulations ended. The time and altitude dependent mean horizontal
advective tendencies of heat and moisture, in addition to the geostrophic
winds, were all diagnosed from ERA5 and prescribed in the DALES runs. That is,
we neglect the horizontal in- and outflow of eclipse-induced atmospheric
changes at the boundaries of the domain, e.g. due to short-term disturbances
in the horizontal pressure gradient [68]. At the top boundary during the
simulation, we imposed large-scale subsidence, also taken from ERA5.

The surface fluxes of heat and moisture were computed according to the
vertical difference of potential temperature $\theta$ and the water vapor
specific humidity $q_{\mathrm{v}}$ between the ground surface and the lowest
atmospheric model layer (indicated by the subscript ’bot’), respectively. With
the appropriate conversion of potential temperature to temperature the
sensible and latent fluxes can be expressed as

$\displaystyle F_{\mathrm{SH}}=\frac{\rho
c_{\mathrm{p}}}{r_{\mathrm{a,T}}}(T_{\mathrm{sfc}}-T_{\mathrm{bot}}-\frac{gz_{\mathrm{bot}}}{c_{\mathrm{p}}})$
(1) $\displaystyle F_{\mathrm{LH}}=\frac{\rho
L_{\mathrm{v}}}{r_{\mathrm{a,q}}}(q_{\mathrm{sat}}(T_{\mathrm{sfc}})-q_{\mathrm{v,bot}})$
(2)

where $\rho$ is the air density in kg m-3, $c_{\mathrm{p}}=1004$ J kg-1 K-1
the heat capacity of dry air, $g=9.81$ m s-2 the gravitational acceleration,
$L_{\mathrm{v}}=2.5\cdot 10^{6}$ J kg-1 the latent heat for vaporization of
water, and $q_{\mathrm{sat}}$ the temperature dependent saturation specific
humidity. The aerodynamic resistance coefficients for heat and moisture,
$r_{\mathrm{a,T}}$ and $r_{\mathrm{a,q}}$, respectively, depend on the
atmospheric stability near the surface following Monin-Obukhov similarity
theory [42]. The dependencies of the $r_{\mathrm{a}}$ values on the surface
roughness length and the actual soil water content, which for land conditions
will typically be much lower than the saturated value $q_{\mathrm{sat}}$, were
taken into account by multiplying them with constant correction factors. This
calibration step was made to obtain sensible and heat fluxes that were
consistent with the ECMWF model for the reference case. As a consequence, the
surface heat fluxes were not parameterized as functions of net incoming
radiation, to avoid unnecessary complexity and uncertainties. Instead, the
surface temperature $T_{\mathrm{sfc}}$ was prescribed using the SEVIRI LST
measurements in the study area (see Satellite measurements), and shifted to
the ERA5 skin temperature at 02:00 UTC through a positive offset of 2.0274 K
applied to the complete LST time series, for consistency with the initial
atmospheric profiles. In the simulation without eclipse and until 09:00 UTC,
$T_{\mathrm{sfc}}$ was identical to that in the simulation with eclipse, but
after 09:00 UTC it was the average of the LST time series of the comparable
days shifted to the ERA5 skin temperature at 02:00 UTC.

The simulated cloud cover in the study area was computed as follows. First, we
regridded the DALES output liquid water specific humidity $q_{\mathrm{l}}$ in
kg kg-1 to a grid with cell sizes of 1 x 1 km2, for a fair comparison with the
SEVIRI observations. Secondly, we computed the COT by evaluating the following
integral from the surface ($0$) to TOA ($z_{\mathrm{TOA}}$) [69]:

$\displaystyle\mathrm{COT}(x,y)=\int_{0}^{z_{\mathrm{TOA}}}\frac{\frac{3}{2}\rho_{\mathrm{air}}(z)q_{\mathrm{l}}(x,y,z)}{\rho_{\mathrm{liq}}r_{\mathrm{eff}}}dz$
(3)

where $\rho_{\mathrm{air}}$ is the air density in kg m-3,
$\rho_{\mathrm{liq}}=1000$ kg m-3 is the density of liquid water, and
$r_{\mathrm{eff}}$ is the droplet effective radius which we assumed to be
constant and equal to 10-5 m. Thirdly, the columns ($x,y$) with a COT larger
than 1 were flagged as a cloudy column. The cloud cover was computed as the
number of cloudy columns divided by the total number of columns in the domain.
For the mean COT time series, we computed the horizontal average COT
considering the cloudy columns only.

The lifting condensation level (LCL) in m was computed from the DALES output
of air temperature $T_{\mathrm{bot}}$ in K and relative humidity RHbot in $\%$
of the bottom atmospheric layer (at 10 meter altitude), using the suggested
formula by Lawrence [70]:

$z_{\mathrm{LCL}}=\left(20+\frac{T_{\mathrm{bot}}-273.15}{5}\right)\cdot(100-\text{RH}_{\mathrm{bot}})$
(4)

The level of minimum buoyancy flux (LMBF) was computed as the altitude at
which the buoyancy flux $\overline{w^{\prime}\theta_{v}^{\prime}}$ was
minimum, where $\theta_{\mathrm{v}}$ is the virtual potential temperature
which depends on specific humidity $q_{\mathrm{v}}$ in kg kg-1, temperature
$T$ in K, pressure $p$ in Pa, reference pressure $p_{0}=10^{5}$ Pa,
$c_{\mathrm{p}}$, the gas constant for dry air $R_{\mathrm{d}}=287.0$ J kg-1
K-1, and the gas constant for water vapor $R_{\mathrm{v}}$ = 461.5 J kg-1 K-1
[71]:

$\theta_{\mathrm{v}}=T\left(\frac{p_{0}}{p}\right)^{\frac{R_{\mathrm{d}}}{c_{\mathrm{p}}}}\left(1+\left(\frac{R_{v}}{R_{d}}-1\right)\cdot
q_{\mathrm{v}}\right)$ (5)

and $\overline{w^{\prime}\theta_{\mathrm{v}}^{\prime}}$ was defined as:

$\overline{w^{\prime}\theta_{\mathrm{v}}^{\prime}}=\frac{\sum^{N_{x}}_{i=1}\sum^{N_{y}}_{j=1}w_{ij}(\theta_{\mathrm{v,}ij}-\overline{\theta}_{\mathrm{v}})}{N_{x}N_{y}}$
(6)

in which $N_{x}$ and $N_{y}$ are the number of grid cells in the horizontal
$x$\- and $y$ directions, and the overbar indicates a horizontal mean value.
The mean updraft virtual potential temperature,
$\overline{\theta}_{\mathrm{v,up}}(z)$, was computed as the mean of
$\theta_{\mathrm{v}}(z)$ of the updrafts only (i.e., the grid points at a
certain altitude $z$ for which $w_{ij}>0$). The velocities of the fast rising
parcels were defined by the $p$-percentile velocities $w_{\mathrm{p\%}}$ (with
$p=1$, $3$ and $5$), which were the vertical velocities at a certain altitude
$z$ for which a percentage $p$ of the $w$-distribution contained grid points
with $w_{ij}>w_{\mathrm{p\%}}$ (see [72]). The travel time $\Delta t$ of the
fast rising parcels from the surface to a certain altitude $z_{*}$, using
vertical velocity $w_{\mathrm{p\%}}$, was computed by numerically evaluating

$\Delta t=\int_{0}^{z_{\mathrm{*}}}\frac{dz}{w_{\mathrm{p\%}}(z)}$ (7)

with $z_{\mathrm{*}}=z_{\mathrm{LCL}}$ for the travel time to LCL and
$z_{\mathrm{*}}=z_{\mathrm{CT}}$ for the travel time to the cloud top. The
cloud top was defined as the highest altitude for which $q_{\mathrm{l}}>0$.

DALES uses the Rapid Radiative Transfer Model for Global climate model
applications (RRTMG) radiation scheme [73, 74] to compute the shortwave (SW)
and longwave (LW) radiative fluxes through the atmosphere, emitted and
reflected by the surface, and emerging from TOA during the simulation. In the
solar eclipse case, the SW radiation incident at TOA was multiplied by
($1-f_{\mathrm{o}}$), where $f_{\mathrm{o}}$ was the horizontal mean
obscuration fraction in the study area taken at 0.635 $\mu$m (see Solar
eclipse correction). We used vertical profiles of the ozone mass mixing ratios
in the study area from ERA5 [67]. The surface albedo was the horizontal mean
white-sky albedo in the study area measured by MODIS [75].

Supplementary information

This article has accompanying supplementary videos of the corrected SEVIRI TOA
VIS reflectance and cloud optical thickness during the solar eclipses of 3
October 2005, 29 March 2006, and 1 September 2016 (corresponding to Fig. 1 and
Supplementary Figures 2 and 3, respectively) at 15 minutes temporal
resolution.

Acknowledgments The authors thank Richard Bintanja (KNMI) for the discussions
during manuscript preparation and David Donovan (KNMI) for reading the
manuscript before submission. VT acknowledges funding by the User Support
Programme Space Research (GO), project number ALWGO.2018.016, of the Dutch
Research Council (NWO). SdR acknowledges funding by the Refreeze the Arctic
Foundation for research on geoengineering techniques at TU Delft.

Competing interests The authors declare no competing interests.

Author contributions VT wrote the manuscript with contributions from SdR, JW
and JFM. VT computed the solar obscuration fractions. SdR did the DALES
computations. JW and JFM prepared the SEVIRI observations and JW converted the
observations to high spatial resolution. VT, SdR, JW, JFM, PW, PS and APS
reviewed the manuscript and were involved in the analysis and selection of the
presented results.

Data availability The data required to replicate the timeseries presented in
this article, as well as the input and boundary conditions for our model
simulations, are available in the public repository Zenodo
(https://doi.org/10.5281/zenodo.10371414).

Code availability The Dutch Atmospheric Large-Eddy Simulation (DALES) software
used for this research is publicly available under the terms of the GNU GPL
version 3 on https://github.com/dalesteam/dales.

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Supplementary Figure 1: Cloud top height above geoid in the study area on 3
October 2005 measured by SEVIRI. The surface height above geoid in this area
varies between 300 and 1700 m. Supplementary Figure 2: Similar to Fig. 1, but
for the total solar eclipse of 29 March 2006 passing over West Africa (in the
North-East) and the Atlantic ocean (in the South-West) at 07:37, 08:37, 09:37
and 10:37 UTC (from top to bottom). The white squares in (b) indicate the zoom
area for the cloud optical thickness in (c). Supplementary Figure 3: Similar
to Fig. 1, but for the annular solar eclipse of 1 September 2016 passing over
Middle Africa and the Indian Ocean (in the East) at 07:50, 08:50, 09:50 and
10:50 UTC (from top to bottom). The white squares in (b) indicate the zoom
area for the cloud optical thickness in (c). Supplementary Figure 4: SEVIRI
images of the land and sea surface temperature and their anomaly over East
Africa and part of the Indian Ocean during the annular solar eclipse on 3
October 2015. (a) The land surface temperature measurements at five subsequent
hours (from top to bottom) and (b) the deviation from the mean of the
comparable days. The white square indicates the study area. The negative
deviation over land at 10:07, 11:07 and 12:07 UTC was caused by the solar
eclipse. Supplementary Figure 5: Simulated cloud optical thickness (top view)
with DALES for (a) the solar eclipse case and (b) the reference case, at
08:00, 09:00, 10:00, 11:00 and 12:00 UTC (from top to bottom). Supplementary
Figure 6: Vertical profiles of atmospheric horizontal mean quantities
simulated by DALES at 11.00 UTC. (a) The virtual potential temperature taking
all columns (black solid line) and columns with updrafts only (red solid
line), and (b) their normalized difference, for the solar eclipse case. (c)
The liquid water specific humidity for the solar eclipse case. Similar for
(d), (e) and (f) but then for the reference case. Positive values in (b) and
(e) indicate positive buoyancy. In (b), (c), (e) and (f), the level of neutral
buancy (LNB), lifting condensation level (LCL), level of minimum buoyancy flux
(LMBF), level of free convection (LFC) and limit of convection (LOC) are
indicated. Supplementary Figure 7: (a) Simulated horizontal mean air
temperature and (b) relative humidity by DALES of the bottom atmospheric layer
(at 10 meter altitude) for the study area in the solar eclipse case (solid
line) and reference case (dotted line).