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Clouds represent a critical factor in regulating the Earth's atmosphere and its energy balance. Satellite instruments can measure the energy balance and global atmospheric properties only through an accurate knowledge of the vertical profile of cloudiness, which is as yet one of the key shortages in atmospheric science. The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) on-board the ENVISAT satellite, designed to infer the amount of atmospheric trace-gases, demonstrated also sensitivity to the radiation emitted from clouds. In order to model the effect of the geometrical extent of a cloud on MIPAS measurements, we developed a retrieval model capable to simulate cloud effects on broad spectral intervals accounting for the two-dimensional (2-D) variability of the atmosphere in the satellite orbit plane. The 2-D analysis revealed a sensitivity of MIPAS spectra to both the vertical and horizontal extents and the position of clouds along the instrument line of sight. One-dimensional models were found to underestimate Cloud Top Height (CTH) by approximating clouds as an infinite horizontal layer with a finite vertical extents. With the 2-D approach, we showed it is possible, for optically thin Polar Stratospheric Clouds (PSCs), to retrieve both CTH and horizontal dimension by analyzing simultaneously all the limb observations that come across the cloud with their field of view. For a selected case study we found a very good agreement for both PSC CTH and horizontal extents retrieved from MIPAS measurements and those retrieved from coincident CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarisation) measurements.
©2011 Optical Society of America
1. Introduction
Clouds play a key role in climate by directly influencing dynamics, chemistry and radiation, and acting as a complex interface among atmospheric components. In particular, clouds influence both the amount of solar radiation that reaches the ground and that is reflected back to space. Thus they affect the thermal radiation trapped within the troposphere and largely contribute to the atmospheric energy balance.
Several studies (e.g [1].) have stressed that the knowledge of vertical profiles of cloudiness is necessary for deriving radiative fluxes and have discussed the influence of vertical extent, overlap and coverage of clouds on the Earth radiation budget. An accurate knowledge of the Cloud Top Height (CTH) is therefore essential to understand the impact of clouds on the Earth's radiation budget. However to date most of the standard cloud data sets, derived from satellite measurements and used to infer radiative fluxes and heating rates, ignore cloud overlap [2]. For this reason in case of multiple cloud layering the retrieved CTH represents an “effective” value of the altitude of the existing cloud layers but does not correctly describe the real cloud multiple configuration.
The most commonly detected situation for multilayer clouds corresponds to a semitransparent cirrus cloud overlapping a lower level cloud of moderate optical thickness [3]. Small-scale cloud structures like thin cirrus layers of a few hundred metres and sub visible cirrus clouds are also not uncommon in the atmosphere and their radiative impact is expected to be significant. In addition, thin Polar Stratospheric Clouds (PSC), formed under low stratospheric temperature conditions, are a common feature of vortex region in polar winter. These clouds are known to play a key role in ozone depletion providing the surfaces for heterogeneous chemical activation of chlorine compounds that are responsible of ozone reduction in the stratosphere.
The thin and sub visible cirrus clouds as well as multi layered clouds are undetectable by passive nadir looking instruments. However, they can be detected exploiting the capability of nadir active sensors to retrieve the cloud profile as performed by the recently launched lidar instrument on the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) satellite. The limb viewing geometry is particularly sensitive to clouds of small optical thickness and therefore appropriate for these situations as instruments like the Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere (CRISTA) [4,5], the Stratospheric Aerosol and Gas Experiment II (SAGE II) [6] and the Cryogenic Limb Array Etalon Spectrometer (CLAES) [7] have highlighted. It is therefore important to have a robust algorithm to retrieve the cloud extents from limb viewing observations.
The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) [8], operating on-board European Space Agency (ESA) sun-synchronous Environmental Satellite (ENVISAT), is a limb sounding Fourier Transform spectrometer developed for the measurement of high-resolution atmospheric emission spectra in the thermal InfraRed (IR) from 680 to 2410 cm−1. For about 80% of its measuring time, MIPAS sounds the stratosphere and the upper troposphere regions in its “nominal” observation mode, with backward looking lines of sight approximately lying into the orbit plane. Although the instrument was designed to measure the distribution of atmospheric trace-gases, its measurements are sensitive to the radiation emitted from clouds [9], as shown in some studies on PSC cases [10,11] and thus can be used to derive cloud properties (i. e. CTH retrievals described in [12]).
Most limb IR forward models adopted to retrieve cloud properties to date, model the cloud as an infinite shell delimited in altitude by a cloud top and a cloud bottom, therefore assuming that the whole optical path between these two altitudes lays within the cloud itself. However, real clouds have a finite geographical extent so that only a fraction of the optical path may cross the cloud. In these cases, modelling the cloud as an infinite shell can produce relevant errors on the simulated radiances. By comparing CTHs retrieved from MIPAS to the Cloud-Aerosol Lidar with Orthogonal Polarisation (CALIOP) coincident products in the case of PSCs, in [13] they have identified as an important error source the impact of a Field Of View (FOV) partially filled by the cloud in its horizontal extension.
The correct treatment of real cases, in which the instrumental FOV can be partially filled by the cloud, requires a 2-Dimensional (2-D) model of the atmosphere and of the cloud. Several forward models included in 2-D retrieval schemes [14–17] have the capability of modelling the horizontal variability of the atmosphere. For the MIPAS experiment the Geo-fit algorithm [18] turned out to provide retrievals with improved accuracy with respect to conventional 1-D retrievals (see [19]) confirming the best performances of a 2-D approach. Based on the forward model internal to the Geo-fit code we developed the BroadBand-Clouds2D (BB_Clouds2D) forward model with the additional capability of simulating broad band spectra with a full 2-D model of both the atmosphere and clouds [20]. The capability of BB_Clouds2D of modelling partially cloudy FOV (both in the horizontal and vertical directions) led to an improvement in the forward model accuracy and opened the possibility to retrieve both CTH and cloud horizontal dimensions in the orbit plane. In this paper we present the fully developed BB_Clouds2D retrieval system and we give a detailed description of its functionalities. Since our intent is to describe the methodology used for the 2-D retrieval of the cloud geometrical extent we limit this analysis to PSC cases that can be reproduced using the single scattering approach based on Mie theory.
The structure of the paper is as follows: in Sect. 2 we describe the main characteristic of BB_Clouds2D and of the 2-D modelling of cloud in the MIPAS FOV; in Sect. 3 we present the results of test retrievals performed on simulated spectra, to determine CTH and cloud horizontal extent. In Sect. 4 we compare CTH and horizontal cloud extent retrieved for a PSC by our retrieval system with those by the CALIOP experiment on board of the CALIPSO satellite. Conclusions are given in Sect. 5.
2. The BB_Clouds2D forward model
Within the MIPAS spectral bands, clouds show features over broad frequency regions. For this reason we updated the forward model internal to the Geo-fit code for broad band spectral calculations. Actually, in order to speed up the computation, Geo-fit computes spectral radiances on small spectral regions called Micro-Windows (MWs) where the gas cross sections are obtained by interpolating pre-computed look-up tables at the Curtis-Godson [21] equivalent values of pressure and temperature. While retaining this and all the geometrical features of the Geo-fit code (that is the modelling of the elliptic Earth’s shape, the 2-D ray tracing, and the exploitation of the Curtis-Godson integrals) we have modified the forward model in order to reproduce the full MIPAS spectrum at reasonable computational cost. This forward model, called Broad Band Forward Model (BBFM) [22], has been earlier exploited for spectroscopic investigations that led to the identification of H15NO3 in MIPAS spectra [23]. Then, for the purpose of correctly model the cloud contribution in MIPAS spectra we have implemented the capability to model the cloud effects in BBFM; the resulting code has been called “BB_Clouds2D”. Next subsections thoroughly describe the implemented cloud model and the computational optimizations made.
2.1 Cloud modelling
In order to model the effects of a cloud in MIPAS spectra, we took into account the scattering and absorption processes contributing to the radiative transfer originated by the cloud in the MIPAS FOV. For the representation of these processes we adopted a discretized form of the single scattering approximation for unpolarized light (derived from Eq. (4).122 of [24]):
where s is the path along the limb view, I is the intensity at frequency ω in the direction n; B(s,ω) is the Plank function at frequency ω; ka is the total absorption coefficient including both cloud (kac) and gaseous (kag) contributions and ke is the extinction coefficient given by ka + ks, where ks is the scattering coefficient. We calculated the cloud parameters such as absorption (kac) and scattering (ks), coefficients and phase function (a1) using the Mie scattering subroutine given by [24]. The last term of Eq. (1) represents the Scattering Source Function (SSF) that is the radiation scattered into the instrument LOS from the cloud. The SSF is calculated using the single scattering phase function a1 (function of ω and of the incident and scattered directions), and the incoming radiances from different directions surrounding the cloud. To speed up the calculations, some assumptions were necessary in calculating the incoming radiances in SSF: i.e. we assumed a spherical atmosphere locally homogeneous in the horizontal direction. Furthermore for the computation of the intensity I inside the integral representing the SSF, Eq. (1) is used considering only the absorption by the cloud (that is setting ks = 0 in last term of Eq. (1)). This approximation is consistent with the previous studies [11] and [25]. In our model the contribution given by scattered solar radiation is not considered since, as shown in [11], this contribution does not produce significant effects below 1400 cm−1 (while it can become relevant above 1800 cm−1) and all the calculations reported in this study refer to the 790-1300 cm−1 spectral region. To properly represent the cloud contribution in a spectrum several correlative data are also needed: the refractive index of the species the cloud is made of (ice, water, Nitric Acid Trihydrate (NAT) etc.) at the considered frequency, the average size of the particles, the size distribution, the number density of the particles. All these parameters are externally provided to the code.To validate the implemented approach, we compared BB_Clouds2D spectral simulations to those produced by KOPRA and reported in [25], (see their Figs. 1 and 2 ) assuming in our code a horizontally homogeneous atmosphere and an infinite cloudy shell. The comparison was made for five different scenarios with ice cloud particles of 4 μm radius and number density ranging from 0.01 to 100 cm−3. An example of the performance of the BB_Clouds2D FM with respect to the KOPRA FM (green) is reported in Fig. 1. In the figure we show a detail of Fig. 1 of [25] superimposed with the spectra computed using BB_Clouds2D FM (in light grey) for the clear sky case, and for the scenarios from 1 to 3. Figure 1 shows a good agreement between the two codes with differences below 5%.
Fig. 1 Comparison between limb spectra for 11 km tangent altitude in case of strong absorption (single scattering albedo = 0.24) extracted from Fig. 1 of [25] with superimposed spectra calculated using the BB_Clouds2D FM in light grey for the different scenarios.
Fig. 2 Left panel: Atmospheric discretization into cloves and cloud representation as a group of cloudy cloves (dark grey) and as a shell (light grey). Right panel: Atmospheric discretization and cloud representation as an ensemble of cloudy cloves (dark grey) and as a shell (light grey) in a representation where the Earth’s atmosphere is flattened. The three black lines represent the pencil beams at the centre and at the edges of MIPAS instrumental FOV. The irregular symbols along the line of sight represent the intersection between the pencil beams and both altitude levels (not shown in the figure) and radii. See text for further details.
We have verified that the single scattering approximation used in our code produces results that are comparable to those obtained with multiple scattering for optically thin (optical depth in the limb direction, see Table 1 in [25] for optical depth values) clouds such as PSCs or thin cirrus. For the treatment of clouds such as thick cirrus (but also of high tropospheric clouds, both not considered in our study) the multiple scattering calculation is necessary (e. g. As shown in [26] for cirrus clouds). Moreover the spherical particles assumption used in our FM can be no longer valid for cirrus clouds composed by non spherical particles. The non sphericity of cirrus particles was taken into account in other FM used for modelling cirrus effects in MIPAS spectra (e.g. in [26] and [27]). However, it has been demonstrated that, if the particles forming the PSC are not spherical, the scattering and absorption parameters can still be described using the Mie approximation if the size parameter (2πr/λ, with r effective radius and λ wavelength) is less than 30 (condition that is fulfilled using MIPAS spectral range and PSC particle dimensions). The BB_Clouds2D FM can therefore be used to correctly model all PSCs (as already performed, e.g. in [10]) and thin cirrus clouds for which the sphericity assumption is valid.
Table 1. Retrieval Tests on Cloud Extent from Multiple Limb Viewsa
2.2 2-D modelling of clouds
Into the BB_Clouds2D (as in the Geo-fit FM [18]) the atmosphere is discretized in the vertical domain using altitude levels, and in the horizontal domain using lines perpendicular to the Earth’s surface (radii). The atmospheric region delimited by two consecutive radii and levels is called “clove” (see Fig. 2). The same 2-D atmospheric discretization adopted for the ray tracing can be exploited to model the cloud horizontal and vertical extent. We modelled the cloud as a group of contiguous cloudy cloves, and calculated cloud scattering and absorption parameters only for the cloves crossed by the instrument FOV.
An example of how a cloud is represented in BB_Clouds2D is shown in the left hand panel of Fig. 2. In this panel, the grid represents the 2-D discretization of the atmosphere and the cloud is represented by the dark-grey shaded area. An expanded and flattened view is shown in the right hand panel of Fig. 2. We represent the 2-D discretization as a function of the Orbital Coordinate (OC, defined as the polar angle originating at the North Pole and spanning the orbit plane over its 360 deg. extent) and of the altitude with respect to the Earth’s surface. In the right panel of Fig. 2 the area sampled by one MIPAS limb view is identified by three lines that represent pencil beams at the centre and at the edges of the instrumental FOV. The cloud is again represented by the dark-grey shaded area. In both panels of Fig. 2 the light-grey shaded areas indicate the atmospheric regions that would be used in a 1-D model to represent the cloud occupying the dark-grey cloves of the 2-D model.
2.2.1 Modelling of a partially cloudy FOV in the vertical dimension
In the original Geo-fit FM, the effect of the finite instrument’s FOV is accounted for by convolving the FOV instrumental function (i.e. the response of the instrument to the angular displacement from the central pointing direction) with the atmospheric radiance represented by a polynomial function of the pointing angle. In the left panel of Fig. 3 the FOV function is represented in arbitrary units (in green) and the radiance (calculated at the sample frequency of 947.5 cm−1) for three pencil beams in clear sky conditions is represented with blue dots. As reported in the previous Section and shown in Fig. 2, in the BB_Clouds2D code the cloud is modelled assuming a flat cloud top. This assumption is consistent with previous works exploiting MIPAS data, e.g [28], and implies that the used CTH is an effective value that is used to represent the effect of the observed cloud. When a cloud partially fills the instrument FOV, the atmospheric radiance shows a jump in correspondence of the edge of the cloud within the FOV (dashed in the left panel of Fig. 3). An accurate modelling of this jump is not possible using a single interpolating polynomial. A solution could be to simulate a very large number of pencil beams and to use a linear interpolation between them (e.g. 11 beams calculation shown in orange left panel of Fig. 3). However this approach can be very demanding in terms of computing time. In order to avoid such an heavy procedure we have adopted the following strategy: we calculate two separate radiative transfers for the same number (3) of pencil beams, one assuming clear sky condition (blue dots in left panel of Fig. 3) and one assuming a fully cloudy FOV (red dots in top left hand panel of Fig. 3). This last simulation is obtained by artificially extending in vertical the cloud until the FOV is completely filled.
Fig. 3 Left panel: FOV function in arbitrary units (green) and radiances at 947.5 cm−1 calculated for 3 pencil beams in clear sky (blue) or completely cloudy FOV (red) together with 11 pencil beams calculation (orange) and two polynomials approach (purple) for partially cloudy FOV (cloud top position given by dashed line). Right panel: Difference between simulated MIPAS spectra after convolution with FOV calculated using 11 pencil beams and our approach (orange) and 11 pencil beams and single polynomial approach (grey) together with noise level (green). The dotted line marks the 947.5 cm−1.
For each spectral point we then use two second order polynomials to represent the synthetic radiances as a function of the pointing angles (purple dashed line in left hand panel of Fig. 3). The convolution with the FOV function is applied using the polynomial in clear sky case for angular displacement outside the cloud edges and the polynomial calculated in cloudy conditions inside the cloud. This approach enables to accurately model the discontinuity in the spectral intensity originated by the cloud at low computational cost. The differences between our approach and the 11 beams calculation is shown in orange in the right hand panel of Fig. 3. In the same figure we also show the difference obtained when using a single interpolating polynomial (grey line). The difference between the spectrum calculated with our approach and the spectrum computed with a high number of pencil beams is of the order of the corresponding noise level (in green) while the use of a single interpolating polynomial produces significant deviations from the high resolution calculation.
2.2.2 Modelling of a partially cloudy FOV in the horizontal dimension
The 2-D atmospheric discretization of BB_Clouds2D allows an accurate modelling of cases with partially cloudy FOV in horizontal that are not uncommon in MIPAS measurements scenario. A preliminary assessment of the sensitivity of MIPAS spectra to the horizontal finite dimension of a cloud using BB_Clouds2D was reported in [20], where it is shown that simulated spectra are sensitive to variations of the horizontal fraction of the FOV occupied by the cloud.
In order to furtherly test the sensitivity of MIPAS measurements to the horizontal position of the cloud, in the present study we introduced a cloud in the instrument FOV composed by a log-normal size distribution with mean radius of 4 μm, and distribution width of 0.3 of ice particles (the used refraction index is from [29]). A number density of 0.1 cm−3 (same characteristics of [25]) was assumed. We considered two cases where the cloud enters the FOV from opposite sides with respect to the tangent point. In both cases, the simulated radiances increase in function of the fraction of FOV occupied by the cloud (Fig. 4 and Fig. 5 ).
Fig. 4 Upper panels: cloud entering MIPAS FOV from satellite’s side with respect to the tangent point. Lower panel: BB_Clouds2D simulated spectra for different cloud amount into MIPAS FOV as in upper panels.
Fig. 5 As Fig. 4 but for cloud entering MIPAS FOV from satellite opposite side respect to the tangent point.
In order to evaluate the sensitivity of the measured radiance with respect to the horizontal position of the cloud along MIPAS optical path, we simulated two cases using the same cloud mass (calculated in terms of cloudy area intercepted by the FOV) but at different positions along the FOV (as in top panels of Fig. 6 ). We found that the background radiance assumes lower values when the cloud is encountered far from the satellite, labelled as case a), than when the cloud is located along the portion of limb view near the satellite, labelled case b) (bottom panels of Fig. 6). The radiance reaches the highest value for a saturated FOV (cyan layer and spectrum in Fig. 6).
Fig. 6 Top left: Case a): Cloud entering the MIPAS FOV from the satellite opposite side with respect to the tangent point (dark grey) and cloudy shell (cyan). Top right case b): Cloud entering the MIPAS FOV from the satellite side with respect to the tangent point (dark grey) and cloudy shell (cyan). Bottom: Simulated spectra in case of a cloudy shell, in case a) and b) and difference between case b) and a) respect to the noise level.
We also investigated the impact of the cloud density by varying the number density from 0.01 cm−3 to 1 cm−3 (see top panels of Fig. 7 ) and simulating a similar cloudy area placed along the limb view far from (case a) and near to (case b) the satellite. In the bottom left panel of Fig. 7, spectra simulated for the two cases with the number density equal to 0.01 cm−3 are plotted together with their difference compared to the corresponding noise level.
Fig. 7 Top left panel: Case a) Cloud entering the MIPAS FOV from the satellite opposite side respect to the tangent point. Top right panel: Case b) Cloud entering MIPAS FOV from the satellite side with respect to the tangent point. Bottom: Simulated spectra in case b) and a) and their difference with respect to the noise level for N = 0.01 cm−3 (left), N = 0.1 cm−3 (middle) and N = 1 cm−3 (right panel).
Analogous plots are reported Fig. 7 for number densities of 0.1 cm−3 (central panel) and 1 cm−3 (right panel). Even if in case a) the cloudy area intercepted by the FOV is 15% larger than in case b), once more, in all the three cases, the radiances simulated with the cloud placed near the satellite point reach higher values than the radiances obtained when the cloud is located far from the satellite. Similar results were found by [27] for a different cloud scenario. This behaviour can be explained considering that the signal coming from the cloud located far from the satellite (after the tangent point) is attenuated by the longer path length through the atmosphere with respect to the one obtained for the cloud placed near the satellite.
The difference in the radiances for cases a) and b) changes both in value and spectral shape as a function of the cloud density. While for low density clouds the difference is higher at 800 cm−1 than at 950 cm−1, for denser clouds the difference appears to be very similar at all wavenumbers. At higher density the dependence on the wavelength is therefore saturated.
2.2.3 Modelling a partially cloudy FOV in both horizontal and vertical dimensions
Exploiting the 2-D potentialities of BB_Clouds2D, we have investigated the influence on simulated spectra of a FOV which is partially cloudy in both the vertical and horizontal dimensions. As a baseline, we simulated a spectrum assuming a cloud located on the satellite side with respect to the tangent point, in an altitude range of about 2 km, with the cloud top coinciding with the tangent altitude (case a of Fig. 8 ). We then simulated a cloud with the same horizontal extent and extended vertically to completely fill the instrument FOV (case b of Fig. 8) and a cloud as an infinite shell with the same vertical extension (case c of Fig. 8). Comparison of the corresponding simulated radiances (Fig. 8 bottom left and central panels) shows that extending the size of the cloud in the horizontal or in the vertical dimension implies, as expected, an increase in radiance. The increment of vertical or horizontal cloud dimension causes similar increments of the radiance (see Fig. 8), therefore highlighting the difficulty in discriminating the two effects. A quantitative analysis of the negligible difference between these two effects is shown in the bottom right panel of Fig. 8: the difference between the spectra simulated with a FOV completely cloudy in vertical (case b) or in horizontal (case c) is below the noise level estimated for the limb view. Note that in this case the cloudy area intercepted by the FOV is not the same for case b) and c).
Fig. 8 Top left panel: Case a) FOV partially cloudy in both horizontal and vertical (CTH = 21 km). Top middle panel: Case b) FOV partially cloudy in horizontal (CTH = 23.6 km). Top right panel: Case c) FOV completely cloudy in horizontal and partially cloudy in vertical (CTH = 21 km). Bottom left panel: Simulated spectra in case c) and a), their difference and corresponding noise level. Bottom middle panel: Simulated spectra, their difference and corresponding noise level for cases b) and a). Bottom right panel: Simulated spectra, their difference and corresponding noise level for cases c) and b).
3. Simulated retrieval of cloud dimension
The sensitivity of MIPAS spectra to cloud extent explored in the previous Section suggests that BB_Clouds2D can be exploited to retrieve the geometrical dimensions of the clouds. In [20], the sensitivity of MIPAS spectra to the altitude of the cloud top was used to retrieve CTH, as already done in [28,30] and [13] with 1-D algorithms. The sensitivity study performed in Sect. 2.2.2 highlights the sensitivity of MIPAS spectra to the horizontal position of a cloud, although with the limitations shown in Sect. 2.2.3 when retrieving the CTH together with the horizontal extent of the cloud.
In order to retrieve cloud extent parameters we included the BB_Clouds2D into a non-linear least squares retrieval system that finds the best estimate of the target parameters through a Gauss-Newton iterative procedure. In this procedure, the state vector x, that includes the value of all the retrieval targets, at iteration i + 1, is calculated through the expression:
In Eq. (2) vector n contains the differences between each observation and the corresponding simulation, Sn is the Variance-Covariance Matrix (VCM) of the observation and K is the Jacobian, i.e. the matrix of the (numerical in our study) derivatives of the spectra with respect to the retrieval parameters. In this first approach, systematic errors were not taken into account and the VCM of the observations only accounts for the measurement noise. Systematic errors such as those introduced by forward model simplifications, in our case form the largest contribution to the total error, however, they are very difficult to quantify. Thus the reported errors are representative of only the random error component due to measurement noise.
In the present retrieval simulation the retrieved parameters are CTH and the horizontal position of the cloud in the orbit plane through its horizontal limits towards and opposite to the satellite (named hereafter X1 and X2).
3.1 Retrieval set up
Test retrievals were performed on synthetic spectra simulated with BB_Clouds2D representing real MIPAS limb views affected by clouds. The atmosphere adopted in the retrieval test was obtained from MIPAS2D database products [31] and measurement noise from real MIPAS observations was added to the synthetic spectra.
The clouds seen by MIPAS can be of a wide variety of types such as cirrus clouds, cumulus clouds, PSCs and also volcanic plumes. In our study we considered PSCs as composed by β-NAT (refraction index by [29]). In a similar fashion as in [27] for cirrus clouds, the retrieval was performed over three MWs (828-832 cm−1, 940-950 cm−1, 1295-1300 cm−1). All the calculations reported in the next sections are relative to PSC cases. As already shown in previous works on MIPAS data (e. g [10], [13].) the single scattering approach for spherical particles can be safely used to model the PSC influence on MIPAS spectra. In this paper our main purpose is to describe a new method for the retrieval of the geometrical cloud extents. Therefore, in order to reduce the errors due to the use of non-spherical particles and of the single scattering approximation we limit our analysis to PSC cases. In the reported retrieval approach (based on the use of limb sounding measurements) the cloud is considered homogeneous over the distance covered by at least one LOS and all the microphysical parameters are representative of the whole cloud. Therefore, restricting the analysis to PSC cases, we also reduce the impact of the errors due to the assumption of a homogeneous cloud. When analysing tropospheric or convective clouds, the homogeneity assumption can be no longer valid, while it can be exploited for cirrus and PSCs as in ([26], [10]).
3.2 Simulated retrieval with a single limb view
As a starting point we performed several tests retrieving cloud geometrical parameters from a single MIPAS limb view. The results obtained from these tests show that, as seen in Sect. 2.2.3, the effect of changing the vertical or horizontal extent of a cloud produces a very similar effect in the computed radiances. This implies that CTH and the horizontal extent of a cloud are highly correlated parameters. We then conclude that they cannot be retrieved simultaneously from a single limb view.
We therefore used a single limb view to investigate the relationship of the two geometrical parameters by evaluating the error on CTH produced by wrongly assuming a completely cloudy FOV in horizontal in the case of partially filled FOV conditions. The reference spectra were produced using a β-NAT PSC cloud that only partially fills the FOV in horizontal (from 21° to 25° as in Fig. 8), then wrongly assumed as a cloudy atmospheric infinite layer in the retrieval. Under this configuration, the retrieval reaches convergence with a final CTH (21.58 ± 0.03 km), that is 0.87 km lower than the one used to produce the synthetic observation (22.45 km). This error is due to the fact that the wrong representation of the cloud horizontal extent produces an overestimation of the radiance values. With no further information available, this radiance overestimation is compensated by the retrieval with a lower CTH value rather than reducing the horizontal fraction of the FOV covered by the cloud (see also [13]). For this reason, when analysing real measurements and performing the retrieval over a single limb view, a safe strategy is to retrieve the CTH only and obtain the cloud horizontal extent from external data in order to improve the forward model accuracy and reduce the error on the CTH.
The possibility of retrieving both CTH and cloud horizontal extent without the need of external information was explored using simultaneously multiple limb views crossing the same cloud.
3.3 Simulated retrieval with multiple limb views
In the Geo-fit 2-D approach [18], the information about a retrieval parameter referring to a given clove is inferred from all MIPAS limb views that sound the clove itself. Exploiting a similar approach for the cloudy atmospheric parcels we attempt to retrieve information about both the cloud horizontal and vertical extent from different MIPAS scans whose limb views cross the same cloud. An example is reported in Fig. 9 , where the cloud is sounded by three different limb views belonging to contiguous MIPAS scans. The simulated case reproduces limb views of scans 29, 30 and 31 of MIPAS orbit 4198 acquired on 19 December 2002. The β-NAT PSC is centred around the central scan while the limb views of the two adjacent scans are only partially filled by the cloud (Fig. 9 in grey).
Fig. 9 Simulated MIPAS limb views for scan 29, 30 and 31 of orbit 4198 for the 19 December 2002. The simulated cloud used to produce the synthetic spectra (grey shade) partially fills in horizontal domain the FOV for scans 29 and 31. The cloud used as initial guess for our retrieval tests is also shown (red shade).
In the retrieval we assumed a cloud with fixed microphysical parameters (e.g. refraction index, mean radius, number density) and adjustable geometrical extent (red area in Fig. 9). To avoid the shortages of a single limb view discussed in the previous section, we used the limb view of the central scan, that has a completely horizontally cloud filled FOV, to retrieve the CTH value. We then adopted this value to retrieve the latitudinal cloud extent from the limb views of the other two scans (X1 from scan 29 and X2 from scan 31). We then performed a joint retrieval where we simultaneously retrieved the three parameters exploiting all the three scans. Table 1 reports the retrieval results in the case of sequential fit and in the case of joint fit. The table shows how in both cases convergence is reached with the retrieved estimates correctly matching the real values within the given uncertainties.
Although the results look very encouraging, suggesting that it is possible to use MIPAS spectra to infer both the vertical and horizontal extent of a cloud, the test was performed assuming as perfectly known all cloud microphysical characteristics, an unlikely situation when using real observations. Therefore, we performed several tests to assess the impact of the assumed cloud refraction index, particle radius and number density, on the retrieval of cloud dimension parameters. Even in the case of very different cloud characteristics the retrieval procedure reaches the convergence with a maximum difference on CTH of about 1.5 km, and about 0.5° on the latitudinal cloud dimension (against a vertical resolution of MIPAS measurements of about 3 km and a horizontal resolution of about 5° in latitude) due to the errors on the cloud microphysical parameters.
A refinement in our retrieval strategy can then be introduced considering that in our approach the cloud extent is retrieved assuming to have the same CTH for all the three scans. We thus assume that the CTH is constant for a large latitude range. In real measurement scenarios this approximation may fail. For this reason, we first studied the systematic errors introduced by this assumption and then an alternative retrieval strategy. In Fig. 10 we show in black the observation geometries of the highest limb view of two contiguous scans (scan 24 and scan 25 of orbit 35681) that sound a β-NAT PSC with a finite latitudinal extent and a CTH that varies with latitude (grey shaded area in Fig. 10). If we use the method previously described to retrieve the value of the CTH jointly to the value of the latitudinal extent X2 we obtain the results summarised in Table 2 and shown by the red shaded area in Fig. 10. The retrieved value of the CTH is in good agreement with the CTH used to simulate the limb view of scan 24 and is 1.25 km higher than the one used to simulate scan 25 limb view, while the value of X2 is smaller than its reference value. The error on the X2 determination is due to the wrong CTH used for scan 25.
Fig. 10 Cloud contaminated limb views for MIPAS scan 24 and 25 of orbit 35681 and simulated cloud following coincident data from CALIPSO (grey). The cloud extent retrieved (in terms of CTH and X2) using higher limb views of scan 24 and 25 is marked in red (see text for details).
Table 2. Retrieval Tests on Cloud Extent from Multiple Limb Views Using Two Different Retrieval Approachesa
In order to reduce these systematic errors, we have developed an alternative approach. When a MIPAS scan sounds a cloud, more than one limb view can be affected by the cloud itself. Therefore we can exploit not only the topmost cloudy view but also the ones with lower tangent altitudes. For example the vertical FOV of the second (lower) cloudy limb view can be completely saturated by the cloud, reducing to nearly zero the sensitivity of the corresponding spectrum to the CTH variation. This spectrum can then be used for the retrieval of X2. However, in real measurement scenario, the CTH can lay also into the lower limb view’s FOV. As an example of this, in Fig. 10 we have plotted in light grey the second cloudy limb view of scan 25. Even in these cases, despite the cloud doesn't fully cover the vertical FOV of the lower scan, the fraction of the vertical FOV occupied by the cloud is relevant. Therefore the sensitivity of the corresponding spectrum to the CTH is still reduced with respect to the spectrum of the upper limb view. Repeating the previous test using the second cloudy limb view of scan 25 (grey line in Fig. 10), to determine X2 we retrieved a cloud latitudinal extent (X2) only 0.2° smaller than the reference value. Fixing X2 to the retrieved value we used the highest cloudy limb view of scan 25 to retrieve the CTH. The retrieved CTH now agrees well with the reference one (see Table 2) supporting the adopted approach.
In all the approaches described above, we have always assumed that the Cloud Bottom Height (CBH) lies outside the considered limb view FOV and therefore its influence on the simulated spectra is negligible. This is almost always a good approximation when we consider the highest cloudy limb view. However, when using also the lower cloudy views, the CBH can lie into the FOV varying the fraction of the FOV occupied by the cloud. In these cases the error due to the uncertainty in the CBH should be taken into account or, if available, correlative data can be used to determine the CBH position. In the case considered here, the variation of the CBH position from 20 to 22 km has effects of the order of the noise on the spectra of the second limb view of scan 25.
The tests reported in this Section show the feasibility of retrieving cloud geometrical extents from MIPAS spectra. This can be obtained, as in the Geo-fit approach, using information from different limb views that sound the same cloud. At the same time these tests highlight the difficulties that can be faced in real cases, because for every cloud a dedicated strategy has to be developed.
An example of application to the real MIPAS data is reported in the next Section.
4. Applications to real data
4.1 Selection of a case study
To verify the possibility of retrieving CTH and cloud horizontal extent from MIPAS real measurements with the new retrieval system based on BB_Clouds2D we have selected scans 24 and 25 of MIPAS orbit 35681, measured on 26 December 2008 (18:40 UTC). We selected this case study because of the existence of coincident measurements by the CALIOP lidar [32] that can be used to validate our results.
4.2 Retrieval strategy
Cloud detection is performed by the level 2 processor used by the ESA to routinely analyse MIPAS spectra [33] using the Cloud Index (CI) method proposed in [34]. The CI value is the ratio of the integrated spectral radiances in the 788–796 cm−1 range (where gas absorption is dominant) and in the 832–834 cm−1 range (where clouds effect dominates). In our algorithm we used the CI method to identify the cloudy spectra, considering as cloudy all spectra having a CI value smaller than the threshold value of 4.5 (as also used in [35] for detection of PSCs). These cloudy spectra have been used for a real retrieval test.
To obtain the best result, considering that we only retrieve the cloud geographical extents, we simulated the cloud contaminated spectra used for the retrieval test using atmospheric and cloud microphysical parameters as close as possible to the real ones. Information about the PSC composition and mean radii can be obtained exploiting the NAT PSC signature at 820 cm−1 [30]. In case of MIPAS, this method was applied in [35] to MIPAS observations using synthetic spectra, and also on real data [13] highlighting good agreement with CALIPSO PSCs classification [36]. Using the method proposed in [13], we classified the PSC considered in the present study as composed by NAT particles with mean radius lower than 3 μm. Then, following [35], the best representation of MIPAS broad band spectra was obtained using β-NAT clouds with mean radius equal to 0.5 μm and number density of 5 cm−3. Preliminary considerations about the observed cloud latitudinal extent can be made exploiting the CI analysis for different scans. In the selected case, the CI analysis showed that scan 26 was cloud free, while scans 23, 24, and 25 contained cloudy limb views. From geometrical considerations we considered the limb views of scan 23 and 24 as horizontally completely cloudy due to the fact that their spectra are labelled cloudy at the same tangent altitudes. Therefore, scan 25 should have a limb view only partially filled in horizontal by the cloud. Following the results reported in Sect. 3.3, we retrieved CTH values for scan 24 and both CTH and horizontal extent for scan 25.
4.3 Retrieval results
We retrieved the CTH value and X2 using the highest cloudy sweep of scan 24 and the second cloudy limb view for scan 25. The CTH retrieved for scan 24 was 24.27 ± 0.02 km, while the retrieved X2 value was 70.13 ± 0.02 ° latitude. Finally, we used the highest cloudy spectrum of scan 25 for the scan 25 CTH retrieval, obtaining a value of 23.35 ± 0.03 km.
The results of this retrievals are summarised in the right hand panel of Fig. 11 : the cloud extent retrieval performed with BB_Clouds2D retrieval system for scans 24 and 25 of orbit 35681 shows the presence of a PSC with CTH value from about 24.3 km at lower latitude to about 23.5 km at higher latitude (about 70 degrees) where the PSC event terminates.
Fig. 11 Left panel: MIPAS scan 24 and 25 of orbit 35681 on the 26 December 2008 and coincident CALIOP data. CTH in km for PSC layer is plotted using a colour code, while black crosses represents clear sky part of MIPAS FOV and the black line represents clear sky CALIOP measurements. Horizontal lines represent the latitude-longitude position of the intersections between MIPAS LOS for scan 24 and 25 and CTH level. Right panel: MIPAS limb views of scans 24 and 25, retrieved BB_Clouds2D CTH and cloud extent (light blue) and coincident CALIOP data (red for aerosol-PSCs and orange for cloud data).
We repeated the exercise simulating the performance of 1-D retrieval of CTH (with the cloud simulated as an infinite cloudy atmospheric layer) for scan 25. The 1-D CTH retrieval provides a value of 23.05 ± 0.03 km. Note that all the tests reported in our manuscript were carried-out using a non automated retrieval prototype which prevented the application to large data set.
4.4 Validation
The CALIOP instrument was specifically developed to measure high resolution vertical profiles of aerosols and clouds. The high resolution spatial grid of CALIOP data (5 km horizontal and 180 m vertical resolution for PSCs analysis [36]), produces an accurate determination of PSCs extent. For this reason its measurements have been selected for the evaluation of the quality of the BB_Clouds2D retrieval results.
For the comparison of the retrieved cloud extent from scans 24 and 25 of MIPAS orbit 35681 we selected the CALIPSO granule recorded the 26 December 2008 at 22:34 UTC. This granule fulfilled the matching criteria identified in [13] for MIPAS-CALIOP comparisons (maximum time mismatch of 6 h and distance of 200 km). All the selected MIPAS scans satisfy the time constrain (4 hours), while the spatial constrain is fully satisfied for scan 25 (119.5 km distance) while is slightly off for scan 24 (273 km) as shown in the left hand panel of Fig. 11.
The reported CALIOP data for the top and bottom altitudes of the aerosol layer highlight the presence of a PSC layer between approximately 20 and 25 km in altitude extending from the lower latitudes of 69.4 ° (red dots in right hand panel of Fig. 11) with CTH that lowers northward (from 25 to 23.5 km see colour coded points in left hand panel of Fig. 11).
In the right hand panel of Fig. 11, the cloud scenario is represented in an altitude/latitude map. The map includes CALIOP information on aerosol-PSCs layer (red dots) and cloud layer (orange dots) top and bottom altitudes. The BB_Clouds2D retrieved cloud extent is reported in light blue. The cloud top altitude observed by CALIOP exhibits some oscillations, reflecting the high spatial resolution of these measurements. These oscillations cannot be reproduced by BB_Clouds2D results as the cloud is modelled as a single box. We averaged CALIOP data inside each MIPAS FOV, and compared them to the BB_Clouds2D CTH results. The overall agreement between the two instruments is very good: the CTH difference between MIPAS and CALIOP for scan 24 is −220 m and for scan 25 is + 90 m. The cloud latitudinal extent difference is about + 0.75 latitude degrees (about 80 km). Considering that the average distance between two consecutive MIPAS scans is about 400 km (about 4-5 latitude degrees) the 80 km (0.75 latitude degrees) difference between CALIOP and MIPAS retrieved cloud latitudinal extent can be considered a good agreement.
In the case of scan 25, the comparison between MIPAS CTH retrieved in 1-D mode, with the cloud modelled as a cloudy atmospheric layer (that overestimate by at least 3 degrees the latitudinal extent of the cloud) and the averaged CALIOP layer top altitude data produces a difference of −210 m.
The fact that MIPAS CTH retrieved with a 1-D cloud model is underestimated with respect to CALIOP, is in line with the findings of [13] (see Fig. 5 of the referred paper) that suggest that one of the major reasons for the underestimation of the CTH is the modelling of the cloud as an infinite shell. The fact that the CTH retrieved using a 2-D approach produces a result in better agreement ( + 90 m in 2-D retrieval compared to −210 m in 1-D retrieval) with CALIOP data supports this hypothesis and stresses the importance of a correct latitudinal cloud extent evaluation for CTH retrieval from limb scanning measurements.
5. Conclusions
We developed the 2-D BB_Clouds2D (Broad Band_Clouds 2D) retrieval system with the aim of retrieving cloud dimensions from MIPAS measurements with a tomographic approach. The code is based on the 2-D discretization of the atmosphere introduced by Geo-fit with the addition of single scattering and absorption processes relevant to thin cloud simulation. This configuration is particularly suited for PSCs.
The new code allowed the evaluation of the impact of a correct modelling of the cloud on CTH retrieval. Our results show that CTH can be significantly underestimated with 1-D codes that impose the representation of the cloud as an infinite shell, sometimes overestimating its real horizontal extent, consistently with what suggested in previous studies (e.g [13].).
We showed the sensitivity of the BB_Clouds2D retrieval system to the cloud portion sampled by MIPAS observations and to the cloud position with respect to the tangent point. When retrieving from a single limb view, the correlation existing between CTH and horizontal cloud dimension prevents to distinguish between a cloud placed between tangent point and the satellite and the opposite situation with a cloud further away from the satellite, as well as distinguishing between a cloud filling the FOV in the vertical or in the horizontal directions. The adopted 2-D simultaneous use of multiple limb views sounding the same cloud to retrieve cloud extent parameters is therefore needed and was shown to be a successful strategy both with simulated and real measurements. We also investigated the impact of sources of errors and found that microphysical parameters remain one of the largest uncertainties.
As an example of practical application we investigated a PSC event using multiple MIPAS limb views crossing the cloud and compared results to high resolution CALIOP measurements in close coincidence. In the reported case the 2-D approach allows the retrieval of the cloud horizontal extent. This retrieval, not possible in common 1-D inversions, allows to determine a CTH which is in better agreement with the CALIOP data compared to the 1-D modelling of the cloud as an infinite shell. It should be stressed how remarkable the comparison with lidar data is considering that the two satellite instruments have completely different measurements approaches.
These preliminary results show that, for PSC cases, the 2-D approach leads to a significant improvement in the retrieval of cloud parameters both in terms of increased accuracy (e.g. of CTH) and in terms of retrieving additional parameters (e.g. the horizontal extent). The application of this approach to future satellite limb measurements acquired with closer separations between the scans with respect to the MIPAS instrument (e. g. the PRocess Exploration through Measurements of Infrared and millimetre-wave Emitted Radiation (PREMIER) mission [17]), could be used to retrieve “effective cloudiness parameters” geophysically useful for the scientific community. Actually, given the importance of determining cloud properties for both energy balance and climate studies, and for improving the retrieval of chemistry measurements under cloudy conditions, these results further encourage a broader adoption of the 2-D approach. The validation of the BB_Clouds2D retrieval on a solid statistical basis will be performed in a future work. Further developments will also investigate the possibility to retrieve additional cloud parameters from limb spectra. Moreover, we plan to investigate the application of this method to larger data sets and quantify the improvements generated by the inclusion of the BB_Clouds2D in Volume Mixing Ratio (VMR) retrievals.
Acknowledgments
E. Arnone and E. Papandrea acknowledge support by ESA within the framework of the Changing Earth Science Network Initiative. The authors acknowledge ECMWF for having granted direct access to their archives of atmospheric data. CALIOP data were obtained from the NASA Langley Research Center Atmospheric Science Data Center.
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