The Community Cloud retrieval for Climate (CC4CL) is a cloud property retrieval system for satellite-based multispectral imagers and is an important component of the Cloud Climate Change Initiative (Cloud_cci) project. In this paper we discuss the optimal estimation retrieval of cloud optical thickness, effective radius and cloud top pressure based on the Optimal Retrieval of Aerosol and Cloud (ORAC) algorithm. Key to this method is the forward model, which includes the clear-sky model, the liquid water and ice cloud models, the surface model including a bidirectional reflectance distribution function (BRDF), and the “fast” radiative transfer solution (which includes a multiple scattering treatment). All of these components and their assumptions and limitations will be discussed in detail. The forward model provides the accuracy appropriate for our retrieval method. The errors are comparable to the instrument noise for cloud optical thicknesses greater than 10. At optical thicknesses less than 10 modeling errors become more significant. The retrieval method is then presented describing optimal estimation in general, the nonlinear inversion method employed, measurement and a priori inputs, the propagation of input uncertainties and the calculation of subsidiary quantities that are derived from the retrieval results. An evaluation of the retrieval was performed using measurements simulated with noise levels appropriate for the MODIS instrument. Results show errors less than 10 % for cloud optical thicknesses greater than 10. Results for clouds of optical thicknesses less than 10 have errors up to 20 %.

Remote sensing of clouds from satellites is vitally important for advancing our understanding of the Earth and its climate. Essential cloud parameters to retrieve are optical thickness, particle size and cloud top pressure. These parameters are critical for determining the liquid and ice water content of clouds and for evaluating both radiative and latent heating rates. Methods used to retrieve cloud properties from radiometric measurements made from satellite-based sensors abound. These methods differ in the types of measurements used, the assumptions made and the way the forward problem (the simulation of measurements given cloud properties) is inverted to obtain an estimate of cloud properties from the measurements.

The theoretical basis for retrieving cloud optical thickness and particle
size from solar reflectance measurements has been discussed by several
authors

At night the retrieval of optical thickness and effective radius is more
difficult. Past studies have focused on a split-window method

The retrieval of cloud top pressure typically relies on matching thermal
emission from a cloud in the 11

Some other retrievals using both solar and thermal channels to obtain
information on both optical thickness and/or microphysics and cloud top
pressure have been presented. In cases where a near-infrared channel is not
available, optical thickness and cloud top pressure may be retrieved with a
solar and thermal channel

The retrieval techniques discussed so far suffer from several drawbacks. First, most of them are separated into solar and thermal methods even though the measurements in these spectral regions are not independent of parameters retrieved in the other. As a result, not all of the available information may be used, i.e., solar information on the thermal optical thickness of semi-transparent clouds and thermal information on particle size. Although some methods discussed above use both solar and thermal channels, their usage is not simultaneous and, therefore, information shared between the different wavelengths may not be optimally used. In addition, the resulting retrievals may not be radiatively consistent with each other. As a consequence, forward modeling using the solar retrieved optical thickness and effective radius for a cloud with its top placed at the thermally retrieved cloud top pressure may produce simulated radiances that are significantly different than the observed radiances. This inconsistency could have significant impacts on broadband flux computations for radiation studies. Finally, except in some specific cases, these methods tend to lack a formal characterization of their uncertainties which incorporates measurement noise and the uncertainty of assumed parameters.

The optimal estimation approach to inverse problems is a statistical
inversion method based on Bayes' theorem. Application to atmospheric
retrievals was presented by

It is able to use any number of channels, where the independent information provided by each channel contributes to the retrieval, maximizing the use of the available information, whereas traditional methods are usually limited to a few preselected channels.

The parameters are retrieved simultaneously, providing a retrieval that is radiatively consistent over the wavelengths of the measurements, provided that the noise characteristics of the instruments are well known.

It is able to easily incorporate measurements from multiple sensors for synergistic retrieval algorithms, i.e., passive and active measurements.

The same framework may be applied to the retrieval of different parameters such as aerosol and cloud, providing more consistency in aerosol–cloud interaction studies, for example.

A priori information can be explicitly included in the retrieval in a way that is consistent with the measurements. This a priori information can be thought of as virtual measurements that help constrain the retrieval.

It provides a rigorous characterization of the retrieval uncertainties, including propagation of measurement noise, the uncertainty of assumed parameters and the uncertainty in the forward model.

It provides a framework to objectively evaluate the information content of the measurements in a way that is consistent across different measurement sources.

A look at the cloud retrieval literature reveals an increasing usage of
optimal estimation including application to AVHRR

This paper is Part 2 of two papers describing the Community Cloud retrieval
for Climate (CC4CL) retrieval system in the context of the Cloud_cci

The method described in this paper requires satellite imager measurements and several ancillary quantities, all of which are prepared for input in a preprocessing stage described in detail in Part 1. We will only briefly summarize here what is required. The measurements include, for each pixel, reflectance for the visible and near-infrared wavelengths and the brightness temperature for the thermal wavelengths. The method also requires the corresponding pixel geolocation (latitude and longitude) and solar and instrument geometry (solar zenith angle, satellite zenith angle and relative azimuth angle, defined as the shortest absolute difference between the solar and satellite azimuth angles). Several ancillary quantities are also required. These include meteorological profiles of pressure, temperature, water vapor and ozone, as well as surface reflectance and emissivity characteristics. In addition to the measurements and ancillary quantities, an estimate of their uncertainty characteristics is also required for an accurate estimate of the uncertainty of the retrieved quantities. Preprocessing is also responsible for cloud masking and classification and the retrieval methodology described in this paper will assume the properties of liquid water or ice cloud based on the cloud classification.

The forward model contains the physics that simulates radiances as observed
by a satellite instrument at the top of the atmosphere (TOA) given both
retrieval and assumed model parameters. In addition, derivatives of the TOA
radiances with respect to the retrieval parameters must also be computed. The
forward model can be thought of as consisting of several component models and
a radiative transfer solution that computes the radiances and associated
derivatives given the outputs of the component models and solar and
instrument geometry. The component models are

a clear-sky model including molecular (Rayleigh) scattering, absorption and emission;

a cloud layer model including cloud particle scattering, absorption and emission;

a surface reflectance model incorporating ocean and land surface bidirectional reflectance distribution functions (BRDFs).

It is important to develop a forward model that accounts for the physics to the desired accuracy of the retrieval but is also computationally efficient enough to be used for large-scale data processing. The ORAC forward model is numerically efficient by making use of both an offline component and an online component. The offline component handles the expensive particle scattering computations and the multiple scattering radiative transfer computations, the results of which are then used to produce look-up tables (LUTs) of fundamental radiative operators. These LUTs are then used in the online component, along with simple arithmetic expressions, to compute the “fast” radiative transfer solution.

Our model assumes a plane-parallel atmosphere with the levels defined by the ancillary meteorological input profiles discussed in Part 1. The required meteorological inputs are pressure, height, temperature, specific humidity and ozone mixing ratio. The surface is taken to be at the bottom level.

To account for the effects of molecular absorption and emission in a
clear-sky atmosphere, transmittances and thermal radiance profiles are
required. Specifically, the required transmittances include two profiles, one
for transmittance from each level to TOA

The transmittances and thermal radiance profiles are computed with the
Radiative Transfer for TOVS (RTTOV) model

In our case RTTOV actually only provides the transmittance

Since the clear-sky transmittance and emission profiles are independent of
cloud, their computation is considered a preprocessing task performed only
once in the preprocessing phase discussed in Part 1. The effect of the
satellite zenith angle is removed from the transmittance profiles with

In addition to the molecular absorption and emission effects, RTTOV includes
an extinction component due to molecular (Rayleigh) scattering in the
transmittance calculations. In ORAC this effect must be removed because, as
will be discussed in Sect.

For each layer bounded by upper and lower pressure levels

Note that ORAC does not take the variation of surface pressure due to terrain height or meteorology into account. Combined with the lack of polarization in the radiative transfer calculations, this means that ORAC is not currently suitable for use with instrument channels in the blue or ultraviolet, where the Rayleigh signal is much stronger and will vary significantly with terrain height. The effects due to polarization at these small wavelengths would require a full vector radiative transfer solution.

The cloud layer model accounts for particle scattering, absorption and
emission effects and is parameterized in terms of particle type (liquid water
droplets or ice crystals) and the following retrieved quantities: cloud
optical thickness at 0.55

The cloud layer model is assumed to consist of a single layer containing only
a single particle type. The cloud is assumed to be geometrically infinitely
thin and plane-parallel and is linearly interpolated into the plane-parallel
atmospheric model at a given cloud top pressure

Optical thickness

If we introduce the normalized size distribution

The effective radius

It is from these relationships and further assumptions based on particle type
that the three fundamental radiative transfer quantities required for the
multiple scattering computations discussed in
Sect.

The single-scattering albedo

The equations presented so far in this section are independent of particle
type and shape and are valid for all mediums of randomly oriented particles.
It is the source of the normalized scattering and absorption cross sections

For liquid water droplets the Mie theory code implementation presented by

As discussed, the size distribution is parameterized in terms of effective
radius, which is related to the modified-gamma distribution of
Eq. (

Ice crystal single-scattering property models provided by

The bulk single-scattering properties are computed for each wavelength by
integrating over particle size distribution and the nine ice particle habits
to produce size distribution averaged properties for a “general habit
mixture”. These are made available as a function of effective radius in 23
bins from 5 to 60

ORAC currently accepts ice crystal scattering properties up to an effective
radius of 92

The surface is characterized by a BRDF which is computed differently for
ocean and land surface. The BRDF over ocean is computed using the methodology
outlined by

The BRDF over land is a weighted sum of an isotropic kernel (unity) and two
BRDF kernels

Over snow and ice the surface reflectance is assumed to be Lambertian with
reflectance values taken from the ASTER Spectral Library Version 2.0

The next step in the forward model is the computation of reflectance,
transmission and emissivity operators which are used in the “fast” RT
solution described in
Sect.

For performance reasons, the operators are precomputed and stored in an LUT
from which the values for an arbitrary set of geometric and optical
parameters may be linearly interpolated. The LUTs are computed with the
DIscrete Ordinates Radiative Transfer (DISORT) software package

DISORT still makes approximations, which can limit its accuracy in certain
circumstances. The most important of these are as follows:

It assumes a plane-parallel atmosphere and so does not account for
the curvature of the Earth. This is important at solar and satellite zenith
angles greater than approximately

It is a one-dimensional model and so cannot reproduce the effects of horizontal gradients in the scattering medium. This is important where strong gradients exist, such as near cloud edges and/or in broken cloud fields, but this limitation is not relevant as we treat each pixel independently.

It does not model polarization effects and so cannot be used to model measurements made by instruments which are sensitive to polarization. In addition, this so-called “scalar approximation” does not take into account polarization introduced into the diffuse component of radiance by Rayleigh scattering and/or the surface, and the subsequent depolarization effect of particles.

A schematic diagram of the ORAC cloud reflectance, transmission and emission operators; surface reflectance operators; and clear-sky emission profiles. Yellow arrows indicate reflectance and transmission operators and red arrows indicate emission. Solid lines indicate beam transport and the dashed lines indicate diffuse transport.

To compute the operators DISORT must be provided with solar and instrument
geometry and the optical thickness, single-scattering albedo and phase
function for each layer. In addition to particle effects, the LUTs account
for Rayleigh scattering and therefore, even though the operators are for a
single homogeneous cloud, the computation is performed for an entire
atmospheric profile. For this we use the midlatitude summer profile provided
by

The dimensions of the ORAC LUTs used in the liquid water cloud retrieval. Note that not all LUTs are functions of all variables (for instance, atmospheric transmission terms are functions of a single zenith angle only).

The dimensions of the ORAC LUTs used in the ice cloud retrieval. Note that not all LUTs are functions of all variables (for instance, atmospheric transmission terms are functions of a single zenith angle only).

The reflectance and transmission operators represent the transfer of either
direct beam or diffuse incoming radiation resulting in either direct beam or
diffuse outgoing radiation. They are computed separately for both direct beam
and diffuse incoming sources with results for both direct beam or diffuse
outgoing radiation being produced simultaneously. In addition, an operator
representing the emissivity of the cloud is produced by including a thermal
source in the cloud layer. A total of seven operators are required (assuming
dependence on

The operators are computed for each channel across the channel's spectral
interval and then convolved with the channel's instrument response function
with

The inclusion of Rayleigh scattering effects in the reflectance and
transmission operators requires some approximation. This is because the
Rayleigh scattering parameters included are defined for each individual
atmospheric layer whereas the cloud layer is added to a single layer. This
cloud layer must be placed at a fixed top pressure within the atmosphere
(560 hPa) when producing the LUTs, since the cloud top pressure is not an
LUT variable. This is an approximation since Rayleigh scattering effects are
pressure dependent and therefore vary with height. This means that when the
retrieval places the particle layer higher than 560 hPa, the Rayleigh
scattering effects will be slightly overestimated, whereas if it is placed
lower than 560 hPa, the Rayleigh scattering will be slightly underestimated.
We have investigated the effects of this and have determined that relative to
other sources of error these effects are small at the wavelengths used in
this work but if smaller wavelength channels were to be incorporated (less
than approximately 6

Interaction with the surface is parameterized by four reflectance operators
(assuming dependence on the appropriate BRDF kernel parameters discussed in
Sect.

Schematic diagrams of each of the four ORAC surface reflectance operators. Blue represents incident radiation and red represents reflected radiation. The long arrows represent beam transport and the hemispheres with short arrows represent diffuse transport.

The first term

The “fast” radiative transfer solution uses the cloud reflectance, cloud transmission and surface reflectance operators along with clear-sky transmittances to simulate the measurements as observed by a satellite sensor at TOA. Shortwave solar reflectance computations are separated from the longwave thermal infrared brightness computations. Although not strictly required, this separation results in an efficient implementation as components such as surface reflectance or cloud top emission are specific to solar and thermal wavelengths, respectively. At thermal wavelengths, where there is a significant solar contribution, separate calculations are performed and the resulting solar reflectance is converted to brightness temperature and added to the resulting thermal brightness temperature computation.

Using the reflectance and transmission operators described in
Sect.

By gathering terms,
Eq. (

This can then be further simplified, using the appropriate series limit, to
give

Finally, the reflectance at the top of the cloud (TOC), including molecular
absorption below the cloud, is obtained by scaling the terms in
Eq. (

The observed TOA brightness temperature is given by (assuming channel dependence)

The gradient of the forward model

The gradient with respect to parameters which are to be derived from
the measurements (state parameters) is required for the inversion of the
nonlinear forward model discussed in Sect.

The gradient with respect to parameters which are considered known and are not retrieved, e.g., meteorology, surface reflectance and surface emissivity, is used to judge the sensitivity to these parameters and thus to estimate their contribution to the retrieval uncertainty.

Derivatives of the forward model may be obtained through straightforward linearization of the forward model equations already given and, as a result, the derivations will not be presented here.

The forward model introduces some assumptions and limitations that contribute
to uncertainty and may under certain conditions bias retrieval results.
Inaccuracies which result from these assumptions and limitations are termed
forward model uncertainty and do not include uncertainties in the input
atmospheric and surface parameters (termed retrieval parameter uncertainty)
or uncertainties in RTTOV (these are forward model uncertainty, but their
evaluation lies outside the scope of this paper). The assumptions and
limitations may be grouped into two lists. The first list involves
limitations related to instrument resolution and assumptions related to
limited information content:

Satellite pixels are assumed to be either completely clear or completely
overcast. Retrievals from pixels with subgrid variability, i.e., broken
cloudiness, will be biased and therefore unrepresentative of the clouds
within the pixel

Satellite pixels are assumed to be either completely of land or completely of ocean so that the BRDF and emissivity assumptions will be either for land or ocean. Retrievals from pixels with both land and ocean, such as with coastlines, islands and inland waters, will be biased since the BRDF and emissivity will be unrepresentative of at least part of the pixel.

The liquid water droplet size distribution has an assumed shape and width and only varies in effective radius. Deviations from this assumption will result in biases particularly in optical thickness and effective radius. Although it is theoretically possible to retrieve additional size distribution parameters besides effective radius, the lack of information in typical multispectral image measurements has made this impractical in the current implementation of the forward model.

Ice crystal scattering properties are computed based on shape (habit) and size. The ice cloud bulk scattering models used in the forward model must assume a size distribution and a mixture of possible habits. These assumptions are based on in-depth analysis of aircraft-based in situ measurements. Deviations from this assumption will result in biases, particularly in optical thickness and effective radius.

The forward model characterizes the cloud layer with an infinitely thin geometric thickness. Since the peak sensitivity of the thermal channels to the cloud is within the cloud itself, the cloud will be placed at a height below the top of a real cloud with finite geometric thickness.

The forward model contains only a single cloud layer. Retrievals from pixels with more than one cloud layer, where the upper cloud layer is optically thin (cirrus overlying liquid water cloud), will be the result of radiance contributions from both clouds resulting in a bias away from the properties of either cloud. For example, relative to the cirrus cloud and assuming typical cloud conditions, the optical thickness will be biased high, effective radius will be biased low and the cloud top pressure will be at a level between the cloud layers.

Each pixel is processed independently, which means that the radiative
transport that occurs in each pixel occurs independently of that in the
neighboring pixels; i.e., horizontal transport between neighboring pixels is
not accounted for. In the literature this is referred to as the independent
pixel approximation

The forward model is a scalar operator model in which radiation that is incident and reflected/transmitted from/through the cloud layer or reflected from the surface is modeled as one of two types: directional or hemispherical. This is in contrast to multi-stream models that model reflection and transmission with a range of quadrature points over the upward and downward hemispheres. The use of scalar operators is one of the primary reasons the forward model is orders of magnitude faster than a multi-stream model. Note that the operators themselves are computed with a multi-stream model to accurately account for multiple scattering effects within the cloud layer.

Finally, the assumption of a plane-parallel atmosphere and ignoring
polarization effects, both discussed in
Sect.

In this section we discuss the evaluation of the forward model with respect
to a “reference forward model”. The focus will be based on the use of
scalar operators versus a multi-stream solution while all other aspects of
the two models are essentially identical; i.e., they use the same input
parameters, both use RTTOV for gas transmittance, both use the same method to
compute Rayleigh scattering parameters and both have the same limitations and
assumptions listed in the first list of
Sect.

The reference forward model divides the atmosphere into as many layers as the
meteorological input contains. Gas transmittance is taken from the clear-sky
RTTOV computations. The Rayleigh scattering optical thickness for dry air

Fractional
differences

The comparisons that follow are presented in the form of 2-D plots of
fractional difference given by

midlatitude summer temperature, pressure and trace gas
profiles provided by

all four BRDF operators,

surface emissivity

retrieval parameters

retrieval parameter

retrieval parameter

solar zenith angle

We provide the minimum and maximum values (

In Fig.

Same as
Fig.

For the thermal wavelengths the differences remain below 0.5 % for
variation in effective radius and cloud top pressure. Interestingly, as a
function of surface temperature the difference can be much larger for a optical
thicknesses below 10 away from the base state of 290 K. This is due to the
linear approximation of
Eq. (

For ice cloud (Fig.

The ORAC retrieval algorithm is based on the optimal estimation approach for
atmospheric inverse problems described by

As with most atmospheric inverse problems, our cloud retrieval problem is
ill-posed in that noise in the measurements

In ORAC regularization is achieved with the Levenberg–Marquardt

Central to the Levenberg–Marquardt method is the regularization parameter

if, as a result of the step given by
Eq. (

if the cost function is decreased by the step given by
Eq. (

The scaling matrix

This iterative procedure, presented as a flow chart in
Fig.

Liquid water cloud scaling parameters and lower and upper retrieval limits.

Ice cloud scaling parameters and lower and upper retrieval limits.

The ORAC inversion system depicted as a flow chart. Rectangles with corners are processes, diamonds are decisions and rectangles with rounded corners are start and top terminals.

After successful convergence the retrieved state

In general, the measurement vector

The optimal estimation framework allows for explicit inclusion of
uncertainties from the measurements, the forward parameters and the forward
model itself. These uncertainties are combined into the so-called
“measurement and forward model” covariance matrix

The retrieval state vector

The a priori state vector

Liquid water cloud a priori values and associated uncertainties.

Ice cloud a priori values and associated uncertainties.

Surface temperature

It should also be noted that estimates of uncertainty do not account for systematic errors in the a priori, in particular on a regional basis. Even if the a priori inputs are unbiased globally they will have some regional bias. Users should be aware that when averaging these data, the uncertainty will not tend towards zero as the a priori uncertainty is systematic.

Our retrieval algorithm has different pathways depending on illumination
conditions: “day” (solar zenith angle

The first guess

The first guess for

Remove inversions including the tropopause from the temperature profile.

Skip past any surface inversion by searching for the lowest level at which the temperature decreases with height.

Locate inversions within the boundary layer defined as levels with
a temperature lower than that of the level above them.

If an inversion is found, locate the top of the inversion, being the next level up at which the temperature decreases relative to the previous.

Overwrite all values from the bottom of the inversion to two points above the top of the inversion (assuring the inversion has some width) by linearly extrapolating from the two levels just beneath the inversion.

Locate the tropopause as the lowest level between 500 and 30 hPa
for which the lapse rate is less than 2 K km

Overwrite all values from the tropopause up by extrapolating from the two levels just beneath the tropopause.

Interpolate the 11

If the brightness temperature is outside the range of the profile
set

Search through the profile for the first pair of levels that bound the requested temperature. For a liquid phase retrieval search from the bottom of the profile up. Otherwise, search top down.

Linearly interpolate brightness temperature between those
located levels to determine

The retrieval implementation produces a number of diagnostic fields, a few of
which will be mentioned here as they are presented later. First, the final
cost

Several products are produced that are derived from the retrieved state and
the assumed input parameters. These include cloud top height

CWP is derived from the retrieved cloud optical thickness

A “spectral cloud albedo”, a directional–hemispherical reflectance, also
referred to as black-sky albedo, defined as (with dependence on

Finally, to account for the fact that the retrieval algorithm may place the
cloud top at a location lower than the physical top, as discussed in
Sect.

As with the primary retrieval parameters, an estimate of the uncertainty in
the derived parameters is computed. For this, standard uncertainty
propagation is used:

Daytime
liquid water cloud retrieval results as a function of optical thickness

In this section we test the performance of the retrieval system just
presented. The methodology can be summarized as follows:

First, produce radiances using the “fast” forward model for a given set of parameters. These parameters include the parameters that are assumed to be known, such as meteorology and surface reflectance/emissivity to which a Gaussian variability is applied in accordance with their uncertainty. The parameters also include the set of retrieval parameters which are taken as exact.

Then, apply Gaussian noise to the radiances. For this we choose the prelaunch noise characteristics for MODIS.

Finally, perform a retrieval on the simulated radiances and compare the results to the retrieval parameters used to produce the radiances.

In the comparisons that follow we look at the fractional error of the retrieved
optical thickness

Same as
Fig.

In Fig.

Same
as Fig.

Our base state describes the parameters that are not explicitly indicated as
something else in our discussion of the results. These include the use of the
same base state values used for the forward model validation in
Sect.

Same
as Fig.

Daytime
liquid water cloud retrieval results as a function of optical thickness

Same
as Fig.

For ice cloud
(Fig.

Figures

For ice cloud
(Fig.

In Fig.

Daytime
liquid water cloud retrieval results as a function of optical thickness

Same
as Fig.

Figure

In Fig.

For ice cloud
(Fig.

This paper describes the optimal estimation component of the Community Cloud retrieval for Climate (CC4CL) based on the Optimal Retrieval of Aerosol and Cloud (ORAC) algorithm. An extensive forward model is described which includes emission, absorption and multiple scattering of radiation from both solar and thermal sources. The surface is characterized by a bidirectional reflectance distribution function (BRDF) specific to either ocean or land. The model's “fast” radiative transfer solution is separated into solar and thermal components and the model's assumptions and limitations were addressed. Validation was undertaken with a reference forward model, i.e., a more extensive forward model that attempts to eliminate some of the most important assumptions in the “fast” solution. Results show that in relation to the simple scalar operators, for optical thicknesses greater than 10, the errors are comparable to instrument noise, but it should be noted that this error is the difference between the reference forward model and the “fast” forward model and not a measure of the total errors in forward modeling. At small optical thicknesses (less than 0.1–1.0) the errors become larger, especially at optical thicknesses approaching the critical regime of unity, where the contribution of single and multiple scattering to the total shortwave signal is comparable. Fortunately, these optical thicknesses of less than unity are uncommon for most cases in cloud remote sensing.

The retrieval method is then described, including the optimal estimation approach, the input measurements and a priori quantities along with their associated uncertainties, our choice of the iteration first guess and quantities derived from the retrieved parameters. Particular attention was paid to the estimation of the retrieval uncertainty. The performance of the retrieval method was assessed theoretically by simulating measurements using a range of values for the retrieval parameters and then subsequently performing a retrieval on these simulated measurements to which Gaussian noise levels appropriate for MODIS were added. The errors are less than 10 % for optical thicknesses larger than 10 and less than 20 % for optical thicknesses larger than unity. For night our retrieval does not report cloud optical thickness or effective radius but uses the information content in these values to improve the cloud top pressure results. These results are consistent with our forward model analysis. For optical thicknesses less than unity the results become problematic, which could have implications for the retrieval of subvisible cirrus, but, as with successful aerosol retrievals over dark surfaces (such as ocean), the results are comparable to those of optical thicknesses larger than 10. Finally, compared to the actual errors our estimation of the retrieval uncertainty is comparable, again, at cloud optical thickness greater than unity.

It is worth noting that the ORAC algorithm is being extended to retrieve
properties in two cloud layers. The publication for this work is in progress
and is expected to have the citation of

ORAC/CC4CL is free and open source software and is licensed
under the GNU General Public License version 3. It can be downloaded at

The authors declare that they have no conflict of interest.

This study was funded as part of NERC's support of the National Centre for Earth Observation. This work was supported by the European Space Agency through the Cloud_cci project (contract: 4000109870/13/I-NB). Edited by: Alexander Kokhanovsky Reviewed by: three anonymous referees