While solar eclipses are known to greatly diminish the visible radiation reaching the surface of the Earth, less is known about the
magnitude of the impact. We explore both the observed and modeled levels of change in surface radiation during the eclipse of 2017. We deployed a pyranometer and Pandora spectrometer instrument to Casper, Wyoming, and Columbia, Missouri, to measure surface broadband shortwave (SW) flux and
atmospheric properties during the 21 August 2017 solar eclipse event. We
performed detailed radiative transfer simulations to understand the role of
clouds in spectral and broadband solar radiation transfer in the Earth's
atmosphere for the normal (non-eclipse) spectrum and red-shift solar spectra
for eclipse conditions. The theoretical calculations showed that the
non-eclipse-to-eclipse surface flux ratio depends strongly on the
obscuration of the solar disk and slightly on the cloud optical depth. These findings allowed us to estimate what the surface broadband SW flux would be
for hypothetical non-eclipse conditions from observations during the eclipse
and further to quantify the impact of the eclipse on the surface broadband
SW radiation budget. We found that the eclipse caused local reductions of
time-averaged surface flux of about 379 W m-2 (50 %) and 329 W m-2 (46 %) during the ∼3 h course of the eclipse
at the Casper and Columbia sites, respectively. We estimated that the Moon's
shadow caused a reduction of approximately 7 %–8 % in global average surface
broadband SW radiation. The eclipse has a smaller impact on the absolute
value of surface flux reduction for cloudy conditions than a clear
atmosphere; the impact decreases with the increase in cloud optical depth. However, the relative time-averaged reduction of local surface SW flux
during a solar eclipse is approximately 45 %, and it is not sensitive to cloud optical depth. The reduction of global average SW flux relative to
climatology is proportional to the non-eclipse and eclipse flux difference
in the penumbra area and depends on cloud optical depth in the Moon's shadow
and geolocation due to the change in solar zenith angle. We also discuss the influence of cloud inhomogeneity on the observed SW flux. Our results not
only quantify the reduction of the surface solar radiation budget, but also advance the understanding of broadband SW radiative transfer under solar
eclipse conditions.
Introduction
On 21 August 2017, a total solar eclipse traversed the continental US from
Oregon to South Carolina (Fig. 1)
(https://eclipse2017.nasa.gov/eclipse-maps, last access: 21 August 2020). Although the path of totality
covered a small swath about 100 km wide, the penumbra extended from
the tropics to all of North America up to the Arctic polar limit, about 6400 km in diameter. Thus, the solar eclipse can cause large reductions in both
temporally averaged surface broadband shortwave (SW) flux at a given site
along the totality path and the spatially averaged global surface SW radiation budget at a given time during the eclipse. The eclipse-induced surface SW
flux reduction can lead to a decrease in sensible heat flux and associated
changes in wind speed (e.g., Turner et al., 2018). As some geo-engineering ideas suggest the blocking or reflecting of solar radiation back to space,
the testing of our quantitative understanding of solar radiation in obscured
situations is critically important (National Research Council, 2015). Thus,
quantifying and understanding the changes in the surface SW irradiances during a solar eclipse is important in this natural experiment.
The eclipse map (from https://eclipse2017.nasa.gov, last access: 21 August 2020) shows the
totality path and obscuration levels on 21 August 2017. Radiometers were
deployed to make ground-based observations at Casper, Wyoming, and Columbia, Missouri.
Several ground-based radiation experiments and modeling activities have been
carried out for understanding radiation in solar eclipse conditions in the
past. Sharp et al. (1971) reported that the sky light may be considered attenuated sunlight up to at least 99.8 % obscuration, and the effect of
multiple scattering from outside the umbral region dominates the sky
brightness close to and during totality (e.g., Mikhalev et al., 1999; Zerefos et al., 2000). Shaw (1978) developed a model to compute sky radiance
during a total solar eclipse by including first- and second-order scattering
processes that would compute the diffused light scattered into the umbra.
Emde and Mayer (2007) performed a full 3D radiative transfer model exercise
to simulate surface spectral solar radiance and irradiance change for a cloudless atmosphere during a total eclipse on 29 March 2006, providing a
benchmark for studying radiative transfer under solar eclipse conditions.
During the 21 August 2017 solar eclipse, Bernhard and Petkov (2019) made
surface spectral solar irradiance observations and performed 3D radiative
transfer simulations; Ockenfuß et al. (2019) further simulated 3D radiative transfer in more detail for understanding the impact of surface
spectral albedo, ozone vertical distribution, and surrounding mountains on surface spectral irradiance observed by Bernhard and Petkov (2019).
Estimating the impact of an eclipse on surface SW flux is a challenging
task. Though one may observe the variation of SW flux variations during an
eclipse from ground-based radiometers, it is almost impossible to obtain the
observations for the same atmospheric conditions but without a solar eclipse
because the atmosphere is often cloudy and cloud properties change rapidly
from the beginning to the end of a solar eclipse. In the past, most
observations and radiative transfer modeling studies for solar eclipse
conditions focused on spectral irradiance change during a solar eclipse.
Although there were some surface SW irradiance observations (e.g., Koepke et al., 2001; Calamas et al., 2019), there is a lack of quantification of the solar eclipse's impact on the surface SW flux, mainly because of the
complicating presence of clouds.
Clouds cover a large part of the Earth. The average global cloud cover is
about 68 % for cloud optical depth >0.1 and about 56 % for
cloud optical depth >2. Locations on the totality path are often covered by clouds. Quantifying the impact of an eclipse on
time-averaged local surface broadband SW flux in cloudy atmospheric
conditions and estimating the influence on global surface flux reduction by
the Moon's shadow from ground-based observations are the main objectives of
this study.
This ground-based measurement paper complements that of Herman et al. (2018) on the reduction of reflected spectral radiance based on DSCOVR/EPIC top of the atmosphere (TOA) observations. In this study, we
combined radiometer observations with a radiative transfer model to estimate
the impact of the solar eclipse on the temporally averaged SW flux at
Casper, Wyoming, and Columbia, Missouri. We further estimated the reduction of the global average surface SW radiation when the totality occurred at the
two sites. Since both sites were covered by clouds, this study focuses on
understanding the role of cloud in irradiance reduction during the eclipse.
In Sect. 2 of this paper, we describe the ground-based solar radiation
experiments. Section 3 describes the radiative transfer modeling experiment.
The methodology is presented in Sect. 4. The results are presented in
Sect. 5 followed by the summary in Sect. 6.
Ground-based observation experiments
Two ground sites were carefully selected from the totality path of the 21 August 2017 eclipse. They were Casper, Wyoming (at 42∘50.2′ N, 106∘19.4′ W), and Columbia, Missouri (at
38∘57.1′ N, 92∘20.1′ W); both were near
the center of the path of totality and experienced a nearly noon total solar
eclipse (local time solar time 10:38 in Casper and 12:04 in Columbia) (see Fig. 1 and Table 1 for detailed information). These two sites are
separated by a distance of about 1200 km, a typical synoptic scale, such
that the weather at these sites can be quite different, allowing us to study
the eclipse-induced surface SW changes under different atmospheric
conditions.
Parameters for the 21 August 2017 eclipse for Casper, Wyoming, and Columbia, Missouri. The first contact (C1), the moment when the Moon first touches the Sun's disk or the beginning of the partial eclipse; the second
contact (C2), the beginning of totality; the maximum of the totality (Max);
the third contact (C3), the end of totality; the fourth contact (C4), the
instant when the Moon just leaves the Sun's disk or the end of the partial eclipse. The elevation of the site (Elev.) and solar zenith angle (SZA) and
solar azimuth angle (SAA) at the totality are indicated.
Casper, WY (42∘50.2′ N, 106∘19.4′ W) Columbia, MO (38∘57.1′ N, 92∘20.1′ W) Elev. = 1560 m, SZA =36∘, SAA =143∘Elev. =227 m, SZA =27∘, SAA =181∘EventTime (UTC)EventTime (UTC)C116:22:15.6C116:45:39.9C217:42:38.0C218:12:21.4Max17:43:51.0Max18:13:39.7C317:45:04.1C318:14:57.9C419:09:25.4C419:40:13.7
The ground-based instruments include a thermal-dome-effect-corrected (TDE)
pyranometer (Ji and Tsay, 2000), a standard Pandora spectrometer instrument system (PSI) for the 280–520 nm wavelength range (with a spectral resolution of 0.42–0.52 nm) (Herman et al., 2009), and an extended-range PSI (PSI-ER) for the 280–820 nm wavelength range (with a spectral resolution of about 1 nm) (Jeong et al., 2018) at both sites. The pyranometer is a broadband radiometer that
measures solar radiation reaching Earth's surface with wavelengths
approximately from 295 to 2800 nm. Ji and Tsay (2000) found that the
fused silica dome's thermal effect on the pyranometer can introduce an error of a few W m-2 to over tens of W m-2 depending on the temperature
difference between its thermopile and glass-filter domes. Ji et al. (2011)
developed a novel non-intrusive method to correct the pyranometer's TDE and demonstrated a high level of consistency with a NIST-traceable light source maintained in a Class 10 000 clean room at the NASA Goddard Calibration
Facility. The reported accuracy of this light source for the calibration is better than 1 %. The pyranometer-observed surface broadband SW flux
without TDE correction at the totality is about -13 and -5 W m-2 at the Casper and Columbia sites, respectively. However, these unrealistic negative biases during the totality are improved with the TDE
correction (the SW fluxes are 5 W m-2 at Casper and -3 W m-2 at
Columbia). Note that according to the results of Emde and Mayer (2007),
surface spectral irradiance (and therefore broadband SW flux) for eclipse conditions is 4 orders of magnitude smaller than its counterpart for a
non-eclipse condition. Therefore, theoretical broadband SW fluxes at these
sites are less than about 0.1 W m-2. Although the TDE corrections
during the totality at both sites have largely improved the pyranometer's
instantaneous offsets, the remaining fine adjustments of SW fluxes during the eclipse can be attributed to the variabilities of sky conditions (e.g.,
distribution of scattered clouds, temperature, and wind fields near the pyranometers) coupled with radiometric performance of the sensors and
calibration uncertainties (Ji et al., 2011). We subtract the offset from the
observations such that the surface SW flux is zero at the totality for both the Casper and Columbia sites.
Both PSI and PSI-ER contain a small Avantes low stray light spectrometer.
The optical head consists of a collimator and filter wheels giving rise to a
2.2∘ field of view (FOV) for direct-Sun measurements. The
PSI is capable of obtaining NO2 and ozone total column amounts (for
details, see Herman et al., 2009, 2015). The PSI-ER has the capability to
retrieve aerosol and cloud optical depths within the given wavelength range
(Jeong et al., 2018). Note that cloud optical depth is usually much larger
than aerosol optical depth. As cloud optical depth increases, the direct
sunlight decreases exponentially, leaving a very small signal for an
instrument to detect. We used only data with a signal-to-noise ratio (SNR) of greater than 10.
The current PSI does not have an operational scheme for water vapor
retrieval. The precipitable water vapor amount observations from the nearest
AERONET stations (see Table 2) were used in radiative transfer computations
for the Columbia and Casper sites, respectively.
Atmospheric properties including aerosol optical depth (AOD) at 550 nm, ozone column amount (O3), precipitable water vapor amount
(H2O), cloud optical depth (COD) at 550 nm, and cloud top pressure
(CTP) for the Casper and Columbia sites. Note that precipitable water vapor amounts are from the nearest AERONET stations at St. Louis University, MO (38∘38.16′ N, 90∘13.9∘′ W), and Spoon
Butte, WY (42∘35.76′ N, 104∘26.58′ W), for Columbia and Casper, respectively. (The instruments for O3 and CTP observations are indicated by symbols * and ** for Casper and Columbia, respectively.)
Casper, WYColumbia, MOInstrumentAOD0.230.19PSI-ERO3313 DU*283 DU***EPIC, **PSIH2O1.4 cm4.2 cmAERONET CimelCODvariablevariablePSI-ERCTP327 mb*225 mb***MODIS, **VIIRSRadiative transfer model and model inputsThe model
The radiative transfer model used is a fast plane-parallel broadband model
for both solar shortwave and terrestrial longwave irradiances originally
developed by Fu and Liou (1992) and subsequently modified by the SARB
(Surface and Atmospheric Radiation Budget) team at NASA's Langley Research
Center (Kato et al., 2005; Rose et al., 2006). The SW portion of the model
used in this study is a delta-four-stream radiative transfer code with 18
spectral bands from 0.175 to 4.0 µm. The model accounts for
gaseous absorption by O3, H2O, O2, CO2 and CH4,
molecular scattering, aerosol and cloud absorption, and scattering. We also used the SBDART (Santa Barbara DISORT Atmospheric Radiative Transfer) model
(Ricchiazzi et al., 1998) to simulate the surface spectral flux for TOA
spectral solar irradiance for both normal and eclipse conditions to
understand the role of clouds in transmitted spectral and total shortwave flux.
The assumption of constant incident solar intensity in the 1D model is
invalid for the umbra and near the totality region because the surface
diffuse component, which depends on the 2D distribution of the TOA incident
solar irradiance, dominates under those conditions. Emde and Mayer (2007)
performed a rigorous analysis to quantify 1D errors in diffuse spectral
radiance and irradiance as a function of the time from the center of the
totality. We used their results for spectral irradiance at 500 nm as a
surrogate for estimating the error in broadband shortwave irradiance because
the solar spectrum peaks near 500 nm.
For a plane-parallel clear atmosphere, one can show that the surface diffuse
flux is about 10 % of the direct component at 500 nm for solar zenith
angles (SZAs) from 0 to 40∘. Thus, a 10 % 1D error in the diffuse component at time 150 s (about 126 km) from the center of
the totality will lead to about 1 % error in the total surface SW flux estimate. Further away from the totality, the direct component gradually
dominates, and the 1D error in the diffuse flux decreases quickly with distance (see Fig. 14 in Emde and Mayer, 2007), resulting in an even faster
decrease in the 1D error in total surface SW flux. Thus, the error in the average shortwave irradiance from the 1D model is negligible.
Additionally, cloud inhomogeneity can introduce large uncertainties into 1D radiative transfer models and is a major obstacle to computing radiative
flux for solar eclipse conditions (e.g., Koepke et al., 2001). We will discuss this issue in Sect. 4.
Model inputsTOA spectral solar irradiance during the eclipse
The change in TOA spectral solar irradiance is essential for modeling solar radiation transfer during an eclipse. For normal conditions, the
extraterrestrial solar irradiance at each wavelength is given as an average
over the whole solar disk. For eclipse conditions one needs to integrate the
limb-darkening function weighted spectral irradiance for the non-obscured part of the Sun to obtain the TOA spectral solar irradiance. Here we adopted
the analytical expression by Koepke et al. (2001) to compute the spectral
solar irradiance emitted from the non-obscured solar disk (or reduced
brightness) as a function of the distance between the centers of the disks
of the Moon and the Sun with the limb-darkening function from Neckel (2005).
The astronomical aspect of solar eclipse is well understood and the geometry
of the problem can be calculated with high accuracy (e.g., Espenak and Anderson, 2004). The parameters for the 21 August 2017 eclipse (Table 1) are calculated by Espenak (results are in the Supplement). We followed
the definition of the distance between the center of the disks of the Moon
and the Sun, normalized by the sum of the radii of the Moon and Sun in Koepke et al. (2001). To compute the reduced brightness as a function of time for
the two sites for the entire course of the eclipse event, we also used the fact that the value of the distance is linearly correlated with time (e.g., Koepke et al., 2001; Emde and Mayer, 2007).
Atmospheric and surface properties
The standard mid-latitude atmosphere is used to describe the temperature,
pressure, and trace gas profiles. Two major absorbing gases for shortwave
radiation, ozone and water vapor, are based on observations; other less
important trace gases are kept at constant levels. Column ozone amount
observations from EPIC at 15:44:50 UTC before the eclipse are used for the Casper site. The column ozone from PSI before the eclipse is used for
the Columbia site. The precipitable water vapor amounts are from nearby
AERONET stations (see Table 2). The ozone and water vapor profiles are
scaled to match the observed total column amounts. Aerosol optical depth
(AOD) was observed by PSI-ER before the eclipse and the aerosol type is
assumed to be continental aerosol with a scale height of 3 km. All trace gases and AODs are assumed constant in radiative transfer calculations.
PSI-ER was operating continuously at both sites to provide optical depth
observations. Using Beer's law for a constant TOA monochromatic direct solar
irradiance (I0), one can obtain apparent optical depth from Eq. (1):
It=I0e-τapp(t)μ0(t),
where I(t), τapp(t), and μ0(t) are the PSI-ER-observed spectral irradiance at 550 nm, the apparent optical depth, and cosine of
solar zenith angle at time t, respectively. Without considering the decrease
in TOA solar irradiance during solar eclipse, Eq. (1) will lead to a much larger apparent optical depth than it should be. Thus, one has to use the
reduced TOA spectral solar irradiance that accounts for limb-darkening effects to derive the true optical depth in Eq. (2):
It=I0,eclipse(t)e-τ′(t)μ0(t),
where I0,eclipse(t) and τ′t are the true TOA
spectral solar irradiance and eclipse-corrected optical depth. From Eqs. (1)
and (2) one can derive the eclipse-corrected optical depth as a function of apparent optical depth and the ratio of solar irradiances with and
without solar eclipse in Eq. (3):
τ′t=τappt+μ0tlnI0,eclipse(t)I0.
Subtracting the molecular scattering optical depth and aerosol optical depth
from the total optical depth, we derive cloud optical depth (τc′). Note that τc′ is not true cloud optical depth since
the instrument observes both the direct and diffuse radiation, resulting in a smaller apparent cloud optical depth than it should be. The diffuse radiation from
ice cloud has a large impact on radiation entering into the FOV of the Sun-pointing instrument due to the strong forward peak of the scattering phase function of ice crystals, resulting in a much smaller apparent cloud optical
depth than the true optical depth.
For Sun-photometer observations, Shiobara and Asano (1994) suggested the apparent optical depth τc′ can be simply related to the true
optical depth τc as
τc=kτc′
with
k=11-ωP‾ΔΩ,
where ω is the single scattering albedo and P‾ is the average
scattering phase function in the solid angle ΔΩ
subtended by the instrument FOV. Using the ice crystal scattering phase function and ω=1 at 550 nm (Baum et al., 2005) for the average ice crystal diameter of 60 µm from the Moderate-Resolution
Imaging Spectroradiometer (MODIS) product with ΔΩ of the Pandora instrument, we estimated k=1.77 and consequently the true optical depth τc at each time step. Adding the molecular optical depth and
aerosol optical depth, one can obtain the true atmospheric optical depth.
The original apparent, eclipse-corrected, and true total optical depths are presented in Fig. 2. The corrected ice crystal optical depth and aerosol
optical depth are used in the modeling calculations presented in later
sections.
Apparent (black lines), eclipse-corrected (red lines), and
diffuse-light-corrected (blue) total optical depths that correspond to
spectral radiances at 500 nm observed by Pandora systems at (a) Casper and
(b) Columbia during the solar eclipse on 21 August 2017.
From the ground, the authors at the site observed that the atmosphere over
the Casper site was mostly clear with some thin cirrus clouds. The visible
images from the GOES-16 satellite (Schmit et al., 2005) captured the eclipse and showed a fraction of cirrus cloud near the Casper site before, during, and
after the eclipse. Examples of two GOES-16 images are presented in Fig. 3a, b. The GOES-16 images and Sun-pointing PSI-observed cloud optical depth
at 550 nm suggest the presence of thin cirrus clouds not shading the direct
solar beam for some time before and during a large part of the eclipse, with
some thin cirrus fragments passing intermittently through the FOV of the
PSI. The photo taken near the totality captured a moment of the sky when the
direct solar beam was shaded by a thin cirrus cloud (Fig. 3c). The Terra satellite passed over at 17:45 UTC, the time of totality at the Casper site.
The average cloud top pressure from Collection 6 of MODIS thermal channel observations was
approximately 327 mb (Baum et al., 2012).
(a–c) For Casper, (a) and (b) are geostationary satellite (GOES-16) visible images at 16:10 and 19:15 UTC, showing thin cirrus
clouds over the Casper site indicated by the mark; (c) photo taken near the totality. Lower panels for Columbia: (d) and (e) are the thermal infrared
images with brightness temperature scale from -68 to 28 ∘C at 17:00 and 18:30 UTC, showing high-level clouds over the Columbia site indicated by the mark; (f) photo taken close to the totality.
The satellite images were downloaded from the National Center for
Atmospheric Research image archive at http://www2.mmm.ucar.edu/imagearchive/ (last access: 21 August 2020).
As observed by the authors at the site, the sky over the Columbia site was
covered by cirrus clouds above some scattered low- and mid-level cumulus clouds (Fig. 3f). The radiosonde relative humidity profile from the
nearest station before the eclipse suggests a multi-layer cloud system with
cloud tops near 200, 400, and 650 mb (Fig. 4). The GOES-16 satellite thermal
infrared images show that the Columbia site was always covered by high-level
clouds, as indicated by a very low brightness temperature (about -20 to -40∘C) (Fig. 3d, e). The Suomi National Polar-orbiting Partnership (Suomi NPP) satellite (Hillger et al., 2013) overpassed the
Columbia site at 18:30 UTC when the site was in partial eclipse. The average
cloud-top height from Visible Infrared Imaging Radiometer Suite (VIIRS) thermal infrared retrieval around the Columbia site was about 230 mb.
Radiosonde-observed vertical profile of relative humidity from Springfield, MO (at 37∘14′ N, 93∘24′ W), the nearest
station to the Columbia site, at 12:00 UTC on 21 August 2017 obtained from
http://weather.uwyo.edu/upperair/sounding.html (last access: 21 August 2020).
Because the clouds are optically thin during most of the eclipse for both
sites except the two large spikes near 17:42 and 18:30 UTC at the Columbia site (Fig. 2b), we assumed one-layer cirrus cloud between 200 and 400 mb with an effective diameter of 60 µm in the Fu and Liou (1992) radiation code
for computing the surface SW flux. We will compare the model results with
observations and discuss the error in cloud inhomogeneity not accounted for
in the 1D model in Sect. 5.
Surface spectral albedo is based on the monthly average value from the MODIS product and International Geosphere-Biosphere Programme (IGBP) albedo. We
combine MODIS surface spectral albedo at seven bands from 0.47 to 2.13 µm (Schaaf and Wang, 2015) and albedo from IGBP to get spectral
albedo for the 18 bands in the Fu–Liou model. By using these estimates of atmospheric composition and radiative algorithms, we are able to estimate
the amount of radiation reaching the Earth's surface during an eclipse.
MethodsDeriving surface irradiance for non-eclipse conditions
Koepke et al. (2001) estimated the photolysis frequencies for non-eclipse
conditions using the observed photolysis frequencies during an eclipse
divided by the normalized radiance. This method can be applied to estimate
surface spectral radiance and irradiance for non-eclipse conditions except
the area near the totality. In this section, we will show that the surface
broadband SW flux for non-eclipse conditions can be estimated from
ground-based pyranometer-observed flux during the eclipse.
The surface broadband SW flux may be expressed as
F=∫I0λT(λ)dλ,
where I0λ and T(λ) are incident TOA spectral solar irradiance and atmospheric transmittance at wavelength
λ, respectively.
We demonstrate the effect of an eclipse on the distribution of the TOA
spectral solar irradiance and influence of clouds on the transmittance in
Fig. 5. Here we define the total normalized spectral irradiance as
I0,normλ=∫I0,non-eclipseλdλ∫I0,eclipseλdλI0,eclipseλ,
where I0,eclipseλ and I0,non-eclipseλ are TOA spectral solar irradiance at wavelength λ
for eclipse and non-eclipse conditions; the spectrally integrated irradiance
of I0,normλ is always equal to the TOA total solar
irradiance for non-eclipse conditions. Figure 5a shows that there is a
red shift in TOA spectral solar irradiance as obscuration increases since the limb darkening has a much stronger effect at shorter wavelengths (e.g., Koepke et al., 2001). The peak of the spectral irradiance shifts from
0.45 µm for a non-eclipse condition to 0.50 and 0.58 µm for 90 % and 99 % obscuration of solar disk, respectively. I0,normλ is also called red-shift spectral solar irradiance. Note that the true TOA irradiance decreases by 1 order of magnitude from normal conditions to 90 % obscuration and from 90 % to 99 % of obscuration
during eclipse (see the inset of Fig. 5a).
(a) Normalized TOA spectral solar irradiance such that the
spectrally integrated total irradiances equal that for normal conditions (0 % obscuration), with the true irradiances shown in the inset. The
spectra are peaked at 0.45, 0.50, and 0.58 µm for normal
conditions (0 % obscuration) and eclipse conditions with 90 % and 99 % of obscuration; (b) spectral transmittance for clear and cloudy atmospheres for SZA =30∘ calculated from the SBDART; (c) the SBDART-modeled surface SW flux as a function of cloud optical depth for different TOA solar
spectra in (a) with the ratio of surface SW flux for the normal spectrum to that for a different red-shift spectrum in the inset; (d) the Fu–Liou radiation code modeled non-eclipse-to-eclipse surface SW flux ratios for clear atmosphere (dashed black) and cloudy atmosphere with a cloud optical depth of 2 (red) from 16:00 UTC before the eclipse to 18:11 UTC (99 %
obscuration) and from 18:16 UTC (99 % obscuration) to 20:00 UTC after the eclipse.
Clouds play a unique role in modifying spectral solar irradiance reaching
the surface. We used the SBDART to compute spectral transmittance (which is
defined as Tλ=IsλcosθI0λ, where Isλ and I0λ are the surface downward
spectral irradiance and TOA spectral irradiance at wavelength λ, respectively, and θ is the solar zenith angle) as a function of cloud optical depth for different TOA solar spectra. Figure 5b shows that an
increase in cloud optical depth leads to a relatively larger decrease in surface spectral irradiance in near-IR wavelengths compared to near-UV and
visible wavelengths. Here we examine the effect of cloud on transmitted flux
for red-shift spectral solar irradiance. For the red-shift spectrum, an
increase in cloud optical depth leads to a relatively smaller decrease in
transmitted surface flux in near-UV and visible wavelengths. There is a
relatively larger decrease in near-IR wavelengths compared to the spectrum
for the normal conditions simply because of the red shift in the TOA solar spectrum. To some extent, the larger decrease in near-IR wavelengths
compensates for the smaller decrease in visible and near-UV wavelengths,
resulting in a decrease in spectrally integrated surface SW flux similar to
that for the normal TOA spectral solar irradiance.
Figure 5c shows the change in the spectrally integrated SW flux calculated from the SBDART as a function of cloud optical depth at 0.55 µm for the
normal solar spectrum and red-shift spectral solar irradiance associated
with different obscuration levels (Fig. 5a) and shows that all curves of surface SW flux are similar in shape. For a given cloud optical depth, there
is a slightly larger decrease in surface SW flux for a larger red-shift TOA
solar spectrum associated with a larger obscuration. The ratio of surface SW
flux for the normal TOA solar spectrum to that for the red-shift solar
spectrum is presented in the inset in Fig. 5c. It is clear that the flux
ratio is not very sensitive to cloud optical depth and the ratios are
slightly larger than unity. Note that one needs to multiply a scale factor
of ∫Inon-eclipseλdλ/∫Ieclipseλdλ to obtain the true non-eclipse-to-eclipse surface SW flux ratio.
Thus, the surface SW flux ratio depends on the obscuration of the eclipse
and is not very sensitive to cloud optical depth.
Figure 5d shows the time series of the modeled non-eclipse-to-eclipse surface SW flux ratio for clear atmosphere and cloudy atmosphere with a cloud optical depth of 2 for the Columbia site. The difference between the two
ratios is less than 1 %. The difference increases slightly with cloud
optical depth. For a cloud optical depth of 10, the difference is close to
4 % near to totality at 99 % obscuration.
In this study, we assume that the non-eclipse-to-eclipse surface SW flux
ratio for realistic 3D cloudy atmospheric conditions is approximately equal
to the 1D model computed flux ratio for clear atmospheric conditions, i.e.,
Fnon-eclipse(t)Feclipse(t)≈Fnon-eclipse,model(t)Feclipse,model(t),
where Feclipse(t) and Fnon-eclipse(t) are surface SW fluxes
observed by the pyranometer and what would be observed without solar eclipse, and Feclipse,model(t) and Fnon-eclipse,model(t) are the counterparts from a 1D model for clear conditions at time t, respectively. Thus, the
surface SW flux for non-eclipse conditions can be estimated as
Fnon-eclipse(t)≈Fnon-eclipse,model(t)Feclipse,model(t)Feclipse(t).
Similar assumption was used to estimate narrowband flux from broadband flux
(Wen et al., 2013) and to compute the clear-sky reflectance enhancement in
broken cloud fields (Kassianov and Ovtchinnikov, 2008). Kassianov and
Ovtchinnikov found that the ratio between the two 1D reflectances at two
wavelengths was a good approximation to the 3D ratio of the same
wavelengths, although the two reflectances were quite different. It is
important to note that the assumption is invalid in the umbra and bordering
areas. The scattering outside of the umbra contributes to a small surface
flux Feclipse in totality area, a factor of 2.3×10-4
smaller in surface spectral flux at 500 nm compared to non-eclipse
conditions (Emde and Mayer, 2007), while the surface flux from the 1D model is zero. This 3D effect due to non-uniform spatial distribution of incident
solar irradiance at the TOA during an eclipse on surface radiation was
thoroughly studied by Emde and Mayer (2007). They show that the 1D errors
decrease quickly away from the totality. Since TOA spectral solar irradiance
is peaked near 500 nm, we use their results for 500 nm to estimate the 1D
error of broadband surface flux. At 500 nm, the 1D error for surface
irradiance decreased to less than 5 % in 200 s (or about 170 km) from the time when centers of the Moon and Sun disks coincide. Since the umbra and the bordering region cover only a tiny fraction of the whole Moon's shadow with a radius of about 3430 km on Earth, the 1D error in these areas will contribute little to the average surface flux estimates.
Estimating the impact of the eclipse on global average surface broadband
SW flux from ground-based observations
In addition to estimating the impact of the eclipse on time-averaged flux at two local sites, we also estimate its influence on the global average
surface SW radiation budget. During a solar eclipse, the Moon casts a shadow
that extends to an area greater than 3000 km in radius, significantly
reducing the global average surface SW radiation budget. Estimating the
impact of a solar eclipse on the global shortwave radiation budget from
local observations is a major goal of this research. First, we present a
method for computing the change in the global averaged surface SW flux from spatially averaged observations. Then we extend these results to global
average irradiance reduction.
First, the global average surface SW flux for an eclipse condition is the area-weighted flux inside and outside of the Moon's shadow; it can be written as
F1=(πRe2-A)F′+AFeclipseπRe2,
where Re is Earth's radius, A is the area of the penumbral shadow projected onto Earth's cross section perpendicular to the Sun–Earth line (the outermost circle in Fig. 6), F′ is the average flux outside of the Moon's shadow, and
Feclipse is the average flux in the Moon's shadow. Similarly, for a hypothetical non-eclipse condition, the global average surface SW flux is
F2=(πRe2-A)F′+AFnon-eclipseπRe2,
where Fnon-eclipse is the average surface SW flux for the Moon's shadow
area as if the eclipse were not present.
The eclipse-induced relative reduction of surface SW flux to the global
average value (ΔFr) is
ΔFr=F1-F2F2,
or
ΔFr=Feclipse-Fnon-eclipseF2AπRe2,
where F2 is the global average surface SW flux for non-eclipse
conditions.
Using the geometric information (i.e., Sun–Earth distance of 1.51×108 km and Moon–Earth distance of 3.73×105 km on 21 August 2017, radii of the
Sun, 6.957×105 km, and Moon, 1737.4 km), we calculated the radius (r0) of the Moon's shadow projected onto the plane tangent of the Earth at the totality to be about 3430 km. Note that part of the Moon's shadow falls out
of Earth's disk. For the Casper site, A=0.91πr02; for the Columbia site, A=0.97πr02. Thus, ΔF in Eq. (10b) may be
estimated by multiplying the TOA average total solar irradiance of 1360.8 W m-2 (Kopp and Lean, 2011) (with adjustment for the Sun–Earth distance) by the global average transmittance of 0.55 (Trenberth et al., 2009),
Re=6378 km, and r0=3430 km. Thus, one needs to know the
average surface SW flux for both eclipse and non-eclipse conditions to
compute the fractional reduction in global average surface SW flux.
We next show that the temporally resolved downward shortwave flux from the
pyranometers may be used to estimate the spatial average flux in the
penumbra, mainly because the ground sites are in the path of the total
eclipse; therefore, the instruments were able to sample the full course of
the eclipse.
A sketch illustrating the conversion from temporal to spatial
average. The color image has been adjusted from the images on https://epic.gsfc.nasa.gov (last access: 21 August 2020) by increasing the gamma correction (Cescatti,
2007) to bring out the region of totality over Columbia (red star) and
surrounding clouds. The green contours show the levels of obscuration from
0 % for the outmost circle with a decrement of 20 % inward. The dashed line illustrates the totality path.
First, we demonstrate this for an ideal scenario with a horizontal homogeneous atmosphere and constant surface albedo. Figure 6 shows the DSCOVR/EPIC image
acquired at 18:14:50 UTC when the Columbia site was experiencing the
totality. The average surface SW flux in the penumbra may be estimated by
averaging observations (FX1FX2,…,FXn) from a series of n
pyranometers uniformly distributed along the totality path (i.e., Feclipse=1n∑i=1nFXi). At
the Columbia site, the pyranometer observed a temporal variation of downward
flux with uniform increments of time (i.e., Ft1Ft2,…,Ftn). At time t1 when
the eclipse started, the surface radiometer sampled the downward flux
Ft1, which would be approximately the same as the
observed flux at the eastern edge (i.e., FX1) of the penumbra when Columbia was experiencing totality. Similarly, the pyranometer
observed the surface SW flux at time ti, which would be the same as
that from the pyranometer at Xi in the totality path (the white dashed line in Fig. 6) with the same phase of obscuration (i.e., FXi=Fti). Thus, the temporal average of the observed
surface SW flux from n time steps from a local site is approximately equal to the spatial average of the surface SW flux observed from a series of n
radiometers.
To estimate the surface SW flux reduction in the whole area of the penumbra, one needs to calculate the average flux in the Moon's shadow. For the assumed
homogeneous atmosphere and surface properties, the surface SW flux depends
only on the radius from the totality, and the relative reduction of the
global average flux (ΔFr) can be written as
ΔFr=∫∫Feclipser-Fnon-eclipse(r)rdφdrπRe2F2,
where the distance r is the distance from the totality and φ is
the azimuth angle. The integral is limited to the area of the shadow on the
Earth's disk only and the distance r is estimated from the linear relation
between r and t such that r=0 at the totality and r=r0 at the
beginning and end of the partial eclipse, and Feclipser=Xi=Feclipseti and Fnon-eclipse(r) are derived from Feclipse(r) (Eq. 8b). Note that we estimate r from the
linear relation with t for the time periods before and after the totality
separately because of the asymmetry of the two branches.
We emphasize that the temporal average value from one location represents
the spatial average for similar atmosphere and surface conditions in the
penumbra. The results from the Casper site represent mostly clear
atmospheric conditions. With more cloud cover over the Columbia site, the estimated shortwave irradiance change is closer to realistic atmospheric
conditions as described later.
Results
Figure 7 shows both the observed surface SW flux and its derived counterpart for non-eclipse conditions for both sites. It also shows the modeled surface SW fluxes, including the clear-sky flux for both the eclipse and non-eclipse scenarios and the flux for the one-layer cirrus with variable cloud optical
depth for non-eclipse conditions.
(a) Casper; (b) Columbia. Observed surface flux (black), derived surface SW flux for non-eclipse conditions (green), surface flux for clear
atmospheric conditions for eclipse (solid blue) and non-eclipse conditions (dashed blue); the modeled surface flux (red) uses observed cloud optical depth assuming 100 % cloud coverage. For the Casper site, the average reduction in local SW flux is 379 W m-2 or 50 % and the average reduction in global surface SW flux is 7.4 %. For the Columbia site, the average
reduction in local surface SW flux is 329 W m-2 or 46 % and the average reduction in global surface SW flux is 6.8 %.
For the Casper site (Fig. 7a), in the first period from 16:00 to 18:12 UTC before and during a large part of the eclipse, the observed surface SW flux
varies rather smoothly with time, similar in behavior to that for modeled clear-sky flux except for a few tiny dips, which is likely due to fragments of thin cirrus passing through the FOV of PSI, as indicated by small spikes
in cloud optical depth observations (Fig. 2). From 16:00 to 16:42 UTC, the observed flux exceeds the modeled one for clear atmospheric conditions by more than 20 W m-2 and by a much smaller amount as time proceeds after
16:42 UTC. This enhancement can be explained by the presence of some thin cirrus clouds not shading the direct solar beam in this time period. Thin
cirrus clouds not shading the direct solar beam have no impact on the direct
component of surface SW flux but increase the downward diffuse radiation, resulting in an increase in total surface SW flux compared to clear
atmospheric conditions. The cirrus cloud-induced surface SW flux enhancement decreases with time towards the totality as the TOA brightness
decreases. In the second time period from 18:12 to 19:12 UTC, the dips in the observed flux are much larger and last longer in time compared to the dips in the first period. This is associated with the nature of the clouds that
shade the direct solar beam, as indicated by the cloud optical depth observations (see Fig. 2).
For non-eclipse conditions, the cirrus cloud-induced enhancement and the downward dips in the estimated surface SW flux are more pronounced compared
to the eclipse scenario. In the first time period (16:00–18:12 UTC), the estimated surface SW flux exceeds that for clear atmospheric conditions by
about 20 W m-2 in the beginning of the time series to about 100 W m-2 around 17:18–17:30 UTC, much larger than the counterpart for eclipse conditions. The dips in the second period (18:12–19:12 UTC) are evidently larger than their counterparts for the eclipse conditions. The magnitude of the dips in the estimated surface flux is closely related to the observed
cloud optical depth.
In the first time period (16:00–18:12 UTC), the modeled surface SW flux (red curve) is close to the clear-sky flux (dashed blue) because of the small cloud optical depth and underestimates the surface flux accordingly.
However, the model overestimates the surface flux (green curve) in the
second period (18:12–19:12 UTC). For a given observed cloud optical depth, we expect the model to provide accurate direct surface SW flux. The discrepancy between the model and observations comes from the difference in the diffuse
component. The underestimate in the first time period is due to the fact
that the 1D model does not consider the cirrus cloud-induced enhancement by the diffuse radiation, which is a 3D effect. The overestimate in the second
time period (red curve vs. green one) is because the 1D horizontally
extended clouds produce more downward diffuse SW flux than the real cirrus
clouds that cover only a fraction of the atmosphere, as shown in GOES-16 images (see Fig. 3a, b).
Using the observed and derived surface SW flux for eclipse and non-eclipse
conditions, we estimated the average reduction of the local surface SW flux to be about 379 W m-2 or 50 %, which corresponds to a 7.4 % reduction in
the global surface SW radiation when the Moon's shadow was centered at
Casper.
Similarly, the variations of the observed surface SW flux at the Columbia
site (Fig. 7b) can be understood by comparing it with the modeled flux for clear atmosphere during the eclipse. From 16:36 to 17:06 UTC, the observed flux decreases from 800 to 460 W m-2, which is about a 340 W m-2 decrease compared to a decrease of about 60 W m-2 for clear atmospheric conditions (blue curve). This much larger decrease in the
observations is primarily due to the increase in cloud optical depth during this time period (see Figs. 2b, 8b). From 17:06 to 17:24 UTC, there is a slight increase in the observed surface SW flux compared to a continuous
decrease in the SW flux for the clear atmospheric conditions. The slight increase in the observed surface SW flux is the combination of the decrease
in the cloud optical depth and the decrease in the TOA brightness. Thus, the observed cloud optical depth combined with the TOA brightness can be used to
interpret the main features of observed surface SW flux variations. There
are time periods when observations exceed the values for clear atmosphere by
nearly 50 W m-2 in 18:39–18:48 UTC and 80–100 W m-2 in 19:12–19:36 UTC.
(a) Casper; (b) Columbia. The modeled surface SW flux variations for eclipse (solid lines) and non-eclipse (dashed lines) conditions for different cloud optical depths.
For non-eclipse conditions, the cloud effects of reducing and enhancing the
surface flux are more pronounced compared to the eclipse conditions, similar to the results for the Casper site. The derived non-eclipse flux exceeds the
value for clear atmospheric conditions by 150 W m-2 (18 %) at
18:39–18:48 UTC and near 100 W m-2 (12 %) at the end of the eclipse at 19:12–19:36 UTC. Koepke et al. (2001) suggested that when the direct solar beam is not shaded by a cloud, the additional reflection of solar radiation
from vertically extended clouds can increase the incoming surface radiation
by up to 25 % above the corresponding cloud-free values. Thus, it is not
surprising to see a large enhancement of surface SW flux in a system of
cumulus clouds under optically thin cirrus clouds.
In non-eclipse conditions, we found that the 1D model (red curve)
overestimates the surface flux (green curve) for most situations. Again, the
cloud inhomogeneity is the main cause of the overestimation. The low- and mid-level cumulus clouds that are not accounted for with the 1D model reflect
the diffuse radiation scattered by cirrus clouds above them; as a result, a
smaller amount of diffuse radiation reaches the detector, and thus a smaller total SW flux is measured compared to a 1D model. Evidently, a 1D model is
unable to simulate the enhancement induced by cloud side reflection.
From the observed surface SW flux and estimated flux for non-eclipse
conditions, we estimated the average reduction of the local average surface SW
flux as about 329 W m-2 or 46 %, corresponding to a 6.8 % reduction in the global average surface SW flux when the Moon's shadow was centered at Columbia.
To understand the role of clouds in eclipse-induced flux reduction, we modeled the surface SW flux for different cloud optical depths. Figure 8 shows that the increase in cloud optical depth leads to a decrease in surface flux
for both non-eclipse and eclipse conditions. However, at a given time during
the eclipse, the rate of decrease in surface flux to the increase in cloud optical depth for the eclipse (difference between solid curves) is smaller than the rate for non-eclipse conditions (difference between dashed curves).
This is primarily due to a smaller TOA-reduced brightness for eclipse conditions.
Figure 9 shows flux difference (i.e., Fnon-eclipset-Feclipse(t)) for different cloud optical depths. It is evident
that the flux difference is largest for clear atmospheric conditions, and the difference decreases with the increase in cloud optical depth. Thus, the eclipse has a smaller impact on surface flux under cloudy compared to clear
atmospheric conditions; the impact decreases with the increase in cloud optical depth.
(a) Casper; (b) Columbia. The modeled surface SW flux reduction (Fnon-eclipse,model-Feclipse,model) for eclipse (solid lines) and non-eclipse conditions for different cloud
optical depths.
Figures 8 and 9 show that both the time-averaged surface flux for
non-eclipse conditions (e.g., the area under the dashed curve in Fig. 8) and the average flux reduction (e.g., the area under each curve in Fig. 9)
decrease with cloud optical depth; the ratio of the two does not vary much
with cloud optical depth. In fact, Fig. 10 (blue curves) shows that the
relative reduction of the local surface flux is not very sensitive to cloud
optical depth, remaining at around 45 % at Casper and with a slightly larger value at Columbia.
(a) Casper; (b) Columbia. The modeled relative reduction of average local surface flux (blue) during the eclipse and estimated impact on
global surface SW flux budget (black).
The reduction of global SW radiation relative to climatology of surface flux
(F2 in Eq. 8b) depends on the average flux difference between
non-eclipse and eclipse conditions in the Moon's shadow area (Feclipse and Fnon-eclipse in Eq. 8b). This flux difference is proportional
to the area under each curve in Fig. 9, which always decreases with cloud
optical depth. Thus, the relative reduction of global surface radiation,
calculated using Eq. (8b), decreases with the cloud optical depth in the
Moon's shadow (black curves in Fig. 10).
Figure 10 also shows that, for a given cloud optical depth, the reduction of
the average surface SW flux for the Columbia site is larger than for the
Casper site. This difference can also be seen from Fig. 9. These differences
are mainly due to a smaller SZA at Columbia compared to Casper (see Table 1). The cosine of the SZA for the Columbia site is about 10 % larger than that for the Casper site; thus, the average TOA incident solar irradiance for the
Columbia site is also about 10 % larger than that for the Casper site. For
the same optical depth, there is a larger surface SW flux at the Columbia site compared to the Casper one for non-eclipse conditions; therefore, the impact
of the eclipse on surface flux at the Columbia site is larger than that at
the Casper one.
At Casper, the observation-based relative reduction of the local surface SW flux
(50 %) is significantly larger than the 1D modeled prediction (45 %); however, the relative reduction of global flux of 7.4 % is close to the modeled value (8.5 %) for the average cloud optical depth. At the Columbia site, the observation-based relative local reduction of the
local surface SW flux (46 %) is slightly larger than the model prediction
(45 %); on the other hand, the relative reduction of the global flux (6.8 %) is significantly smaller than the modeled one (9 %). These differences between observations and model simulations are mainly due to cloud
inhomogeneity not accounted for in the 1D radiative transfer model.
Summary
We have conducted a ground-based experiment to observe broadband shortwave
irradiance at Casper, Wyoming, and Columbia, Missouri, located in the totality path of the 21 August 2017 solar eclipse. These two sites are separated by a
distance of about 1200 km and had different atmospheric conditions. Surface shortwave flux measurements with simultaneous atmospheric observations allow
us to study the impact of the solar eclipse on the surface shortwave
radiative budget under different atmospheric conditions.
Radiative transfer calculations show that the non-eclipse-to-eclipse surface
SW flux ratio primarily depends on the obscuration of the solar disk during
eclipse and slightly depends on cloud optical depth. These results allow us
to derive non-eclipse surface SW flux under cloudy atmospheric conditions by
multiplying the observed SW flux by the modeled surface SW flux ratio.
We found that at the Casper site, the eclipse led to a decrease of 379 W m-2 (50 %) in average local surface SW flux, and the Moon's shadow caused
about a 7.4 % reduction in the global average surface SW radiation budget when the totality was at Casper; at the Columbia site, the eclipse led to a decrease
of 329 W m-2 (46 %) in average local surface SW flux, and the Moon's
shadow caused about a 6.8 % reduction in the global average surface SW radiation budget when the totality was at Columbia.
Clouds play a unique role in modifying the surface flux reduction during an
eclipse. The eclipse-induced surface flux reduction is largest when the sky is clear. For opaque clouds, the surface even without eclipse would be already
dark to begin with; thus, solar eclipse would have little impact on the
surface SW flux. The average flux reduction decreases with the increase in cloud optical depth. However, the relative reduction of local surface flux is
about 45 % and not sensitive to cloud optical depth. The relative
reduction of global average surface SW flux depends on cloud optical depth in the
Moon's shadow and geolocation due to the change in SZA.
We have discussed the 3D effect of clouds on surface radiation. We
identified that the presence of cirrus clouds not shading the direct solar
beam can significantly enhance the local surface flux; some large flux
enhancements may be explained by the reflection of solar radiation by
cumulus clouds; some discrepancies between a 1D model and observations may
be understood as cloud inhomogeneities not accounted for in a 1D model. The
mechanisms of cloud 3D effects on surface radiation enhancement have implications for surface remote-sensing research.
Data availability
Calibrated pyranometer-observed broadband flux, optical depth data and eclipse parameters are available as a Supplement, the AERONET data are publicly available at https://aeronet.gsfc.nasa.gov (NASA Goddard Space Flight Center, 2020; Holben et al., 1998), and the MODIS and VIIRS data (10.5067/MODIS/MOD06_L2.061, Platnick et al., 2017a, and 10.5067/VIIRS/CLDPROP_L2_VIIRS_SNPP.011, Platnick et al., 2017b) and DSCOVR/EPIC data (10.5067/EPIC/DSCOVR/L2_TO3_02, Marshak et al., 2018) are publicly available at https://earthdata.nasa.gov (NASA EarthData, 2020).
The supplement related to this article is available online at: https://doi.org/10.5194/acp-20-10477-2020-supplement.
Author contributions
GW wrote most of the paper and performed most of the analysis with the
help of AM. AM, SCT, JH, UJ, and NA participated in the field experiment to collect radiation measurements. RS helped with instrument management and DW
helped with data analysis.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This research was supported by NASA's
Interdisciplinary Science for Eclipse 2017 program managed by M. Guhathakurta and partly supported by NASA to the Sun-Climate research. We
thank Fred Espenak for providing eclipse parameter
calculations.
Financial support
This research has been supported by NASA-ROSES (grant no. NNX17AH67G).
Review statement
This paper was edited by Qiang Fu and reviewed by three anonymous referees.
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