The stereo-photogrammetric approach relies on the principle of parallax: the distance (or height) dependent displacement of a stationary object when observed from two or more different viewing angles or positions. The only ancillary data requirement is an accurate knowledge of the geometry of the instrument, which enables stereo reconstruction, the conversion of the displacements in the imagery (disparities) into real world observations. In comparison to radiometric cloud retrievals a number of distinct advantages are inherent.

Stereo retrievals are dependent on the geometry of the imaging system, not the radiometric fidelity. Therefore, they are calibration independent.

The pre-processing stage of the census stereo algorithm (Zabih and Woodfill, 1994) is to replace each image pixel with a vector that encodes the structure of the pixels surrounding the pixel being processed, which are referred to as the local neighbourhood and the pixel of interest, respectively. The vector is comprised of zeros and ones (a bit vector) and has the same number of elements as the local neighbourhood. A bit is set to one in this vector if its corresponding pixel in the local neighbourhood is of a lesser intensity (in this case brightness temperature) than the pixel of interest. The use of a bit vector effectively limits the influence of statistically outlying pixels on the pixel of interest during correction for radiometric dissimilarity. It is also unaffected by all radiometric distortions as long as they do not alter the pixel ordering. For any pixel x we can define the census transformation as Γx=⊗fx,n, where ⊗ is a concatenation operator that concatenates the results of the comparison function, f, to the bit vector, Γ. The comparison function takes as arguments x, the pixel of interest on which a window N is centred, and n, a pixel from the set that comprises the comparison window, i.e. n∈N. The comparison function evaluates to 1 if n<x and 0 if n≥x. The bit vector and the comparison window have the same size. Here, N is of size 7 by 7 pixels (Γ of length 49) as this was found to provide suitable discriminative power for effective stereo matching whilst not increasing computational cost significantly.

Applying Eq. (1) to every pixel in both the reference and comparison images yields two 3-D arrays of bits vectors. In order to locate the correspondences the Hamming distance metric is used to compare the bit vectors as follows, Sxi,j,ur,vr=∑Γi,jR∨Γi+ur,j+vrC, where the cost S for a given pixel x at the reference image location i,j is determined for r different across and along track displacements, u and v. This is achieved by summing the exclusive or comparisons, as determined by the exclusive or operator ∨, between the reference bit vector, ΓR, at location i,j and comparison image bit vector, ΓC, at the displaced location i+urj+vr. The costs for all disparity assessments are aggregated by a 7 pixel radius median filter to reduce noise. Following cost aggregation a simple spline interpolation routine is employed to estimate sub-pixel disparities in the along-track direction from the along-track disparities associated with the five smallest costs. Across track disparities are returned at integer level accuracy.

The disparities returned by the census algorithm are defined within the imaging coordinate system, and as such, are not physically representative of the measure of CTH. To convert from disparity to CTH, a camera model, which replicates the ATSR imaging geometry, is employed to assign each disparity estimate to an above ellipsoid elevation estimate (Denis et al., 2007). Prior to conversion to elevations, the disparities are first corrected using the AATSR co-registration correction coefficients defined in Fisher and Muller (2013). The accuracy of the elevation estimates from the Census transform varies by channel. For the 11 micron channel, employed in all cases in this study, inter-comparison studies against elevations from the GMTED2010 DEM (Danielson and Gesch, 2011) and CTH observations from CALIOP (Winker et al., 2009) return RMSE statistics of approximately 500 and 1200 m, respectively.

In order to differentiate between the surface and CTH observations the GMTED2010 DEM is used. Any pixel with an elevation that is more than 500 m above the collocated surface elevation is flagged as a cloud feature with an associated CTH.

A further check is performed on a cloudy pixel to determine if it is located over a surface covered in snow and/or ice, as the census algorithm (and most other stereo matching algorithms) tends to be confused by the textureless/homogenous nature typical of such surface types, leading to erroneous CTH retrievals. Each orbit is therefore screened for snow/ice pixels using the clear snow/ice mask developed by Istomina et al. (2010) and any flagged pixel is set to a null value. The last step in the post processing is to set all edge pixels to a null value, to remove stereo processor edge artifacts.

The CALIOP lidar has been making measurements of clouds and aerosols since 2006. The instrument is carried onboard the CALIPSO satellite, which is located in the NASA A-Train satellite constellation and therefore has an equatorial overpass time of approximately 1:30 p.m. and a 16-day orbital repeat cycle. The lidar has a ground footprint on the ellipsoid of 100 m and pulses every 333 m along track. It receives backscattered radiation in three channels, two at 532 nm with sensitivity to the backscattered intensity at orthogonal polarisations and one at 1064 nm. The vertical resolution is between 30–60 m depending on the altitude of the cloud, with 30 m resolution achievable in the troposphere (Vaughan et al., 2009). If the uppermost cloud layer has an optical depth of less than 3, then CALIOP is able to detect the presence of lower cloud layers (Vaughan et al., 2009). The cloud phase assignment is determined from the polarisation of the backscattered signal. With light backscattered from ice crystals depolarising in nature, whilst light backscattered from water clouds results in minimal depolarisation (Hu et al., 2009). The CALIOP L1 data is processed into various L2 products, of which the 1 km cloud product, CAL_LID_L2_01 kmCLay-ValStage1-V3-01, is employed here for CTH and phase analysis due to its similar resolution to the AATSR instrument. The lower limit for cloud detection for this product is a backscattered signal of greater than 1 × 10-3 km-1 sr-1 (equivalent to an optical depth of 0.01 for cirrus clouds; McGill et al., 2007, Kahn et al., 2008; Vaughan et al., 2009). The AATSR data used in this comparison is the v2.0 Rutherford Appleton Laboratory (RAL) processed data product with calibration corrections provided by D. Smith at RAL (D. Smith, personal communication, 2014). There is an updated V2.1 processing available at RAL; however these data at present have not been evaluated for co-registration accuracy between the forward and nadir view, which is critical for accurate stereo CTH retrievals. A co-registration correction is applied here using the coefficients from Fisher and Muller (2013) that were derived using v2.0 RAL processed data, and are known to improve the co-registration accuracy to pixel level or better.

The calibrated and geometrically corrected AATSR 11 micron data are first processed using the census stereo algorithm, resulting in an geometric CTH estimate in metres for each valid image pixel. Each AATSR image pixel with a geometric CTH estimate is then assigned an uncertainty (in metres) using a look-up table derived from the approach described in Sect. 4. The ORAC retrieval ingests CTP a priori estimates and therefore conversion from CTH to CTP is required. The stereo CTH and the CTH uncertainty are converted to CTP using temporally interpolated geopotential height data from the ECMWF ERA Interim reanalyses (Simmons et al., 2007) gridcell that is collocated with the AATSR observation. It should be noted that this conversion process will introduce error into the a priori estimates; however in our analysis we make the assumption that the error introduced is of similar or lesser magnitude than the errors introduced by the camera model and wind effects. The output of the ORAC, ORAC+stereo, and census stereo processing is shown for a scene over the region of interest in Fig. 2.

For the period April to October 2008, a search for collocated AATSR-CALIPSO orbits within the study region was undertaken. This resulted in a total of 70 collocated AATSR-CALIOP orbits split between the months of April, July, August, September and October (no collocations fulfilling the requirements were found for May or June). The CALIOP sampling over the ROI for the analysis is presented in Fig. 1. From these orbits, all cloud-containing 1 km CALIOP samples with a maximum of 40 min between overpasses were extracted for comparison against the AATSR retrievals. Here we make the assertion that, at least for CTH, that the impact of different sampling time on the analysis will be limited. This assertion is based on the assumption that CTH variation over scales of 200 km is well correlated (Jones, 1992), and that the cloud regime in a 200 km radius surrounding the collocation will not change within the 40 min between observations.

For each cloud-containing CALIOP sample we follow a similar approach to that used in Fisher et al. (2014) to extract the spatially and temporally collocated AATSR data. The process can be summarised as follows:

For each cloud-containing CALIOP 1 km sample, the associated latitude and longitude data are extracted and compared against the geographic grids from the temporally collocated AATSR product.

Traditional cloud retrievals tend to perform height and microphysical property retrievals separately; however, the problem with this technique is that it can be difficult to balance the LW and SW radiative effects of the clouds (Ham et al., 2009). While the visible and near-infrared channels are mostly sensitive to the effective radius and optical depth, the infrared channels provide the most information about cloud top height with all channels contributing to a lesser or greater degree to all cloud properties. Hence it is important to evaluate the effect of cloud top height a priori adjustment on the microphysical parameters within the ORAC retrieval scheme. In Sect. 5.3.1 an overview of the differences between the ORAC and the ORAC+stereo COT and RE retrievals is provided, in Sect. 5.3.2 we look at the effect of the a priori on the cloud phase retrieval and provide an inter-comparison against CALIOP to assess these changes, and in Sect. 5.3.3 we examine the effect of the inclusion of the CTH a priori on the retrieved COT and RE parameters both in the presence and absence of phase differences.

The analyses in Sect. 5.2 demonstrate that, for a number of different cloud conditions, the inclusion of stereo a priori data provides improvements in the ORAC CTH retrieval when compared to CALIOP. In the case of low clouds, such as stratocumulus, it is well known that radiative based retrieval algorithms, such as ORAC, typically exhibit CTH/CTP (cloud top pressure) retrievals which are biased too low or too high depending on whether the temperature profile is searched for a temperature match to the TOA brightness temperatures from the surface up, or the top of the profiles down, respectively. In the case of ORAC the temperature profile is searched from the top down and consequently the cloud top height is often assigned too high. These biases are caused by the fact that low-level stratocumulus clouds often occur in the presence of temperature inversions, and the atmospheric temperature profiles employed to convert between the retrieved temperature and CTP often do not effectively represent either the strength or the position of the inversion. A clear example of this is in the CALIOP profile plot in Fig. 5, where the water cloud feature detected by CALIOP at approximately 500 m between the latitudes of 68 and 69∘ latitude is poorly captured by the ORAC retrieval, which instead assigns CTHs at around 2.5 km (likely the top of the temperature inversion). The census stereo approach relies on the geometry of the instrument to assign height and therefore is completely independent of any temperature profile assumptions. In the case of boundary layer clouds, this leads to a significant reduction in bias in the retrieved CTHs as shown in the analysis in Sect. 5, and the profile plot in Fig. 5. The drawback of the stereo approach, aside from the fact that it only provides CTH, is a tendency to smooth the disparity field losing fine detail information on CTH. This effect is apparent in the following: the profile plot in Fig. 5 where the stereo heights entirely miss the fine scale detail of the cloud profile as determined by CALIOP; the census stereo output in the stereo CTH retrieval shown in Fig. 2, where the stereo algorithm misses much of the fine scale detail captured by ORAC; and the joint histogram in Fig. 4, particularly for CALIOP CTLs at altitudes between 2 and 6 km, where there is a small but significant under-estimation of the CTH by the census stereo algorithm, which is caused by the inability of the stereo algorithm to capture the finer scale CTH changes. Another potential drawback of the census stereo algorithm when applied to AATSR thermal channel is that it has a tendency to be noisy for low, particularly boundary layer, clouds, as demonstrated by the very large standard deviations (up to 4 km) in Fig. 7. This is also caused by the smoothing effect of the stereo algorithm, where stereo height retrievals from clouds above the boundary layer clouds “bleed” across the discontinuity leading to erroneous height assignments (high bias) for the boundary layer cloud. The drawbacks of the stereo algorithm, however, are somewhat mitigated (and the benefits retained), when employed as a priori in the ORAC retrieval. When combined, the accuracy of the ORAC+stereo retrieval is better for the height assignment of low-level boundary layer clouds than census stereo applied to the thermal channel due to increased sensitivity to fine detail cloud structure, and substantially better than ORAC due to the improved a priori estimates providing the necessary constraint to overcome the inversion layer degeneracy.

Cirrus and other high altitude type cloud formations, if they have low optical depth, present a challenging cloud form to assign CTH to for both radiometric and geometric type algorithms. In the presence of a low optical depth cloud, the cloud top temperature retrieved by radiative based algorithms such as ORAC corresponds to a cloud top height typically 1 optical depth into the cloud, which for many clouds may not correspond with the true CTH but rather a significant low bias, particularly for optically thin clouds with large vertical extent. For geometric type algorithms, the retrieved CTH is associated with the location within the cloud where the optical depth is sufficient to provide suitable image texture for reliable stereo image matching; this may also be some way below the true cloud top. Note that the stereo algorithm uses the dual view capability of ATSR while the ORAC retrieval uses only the nadir view. Since the forward view has twice the path length though a cloud, the penetration depth is approximately half of the nadir view. This is consistent with the results presented in the joint histograms in Fig. 4, which demonstrate for clouds above 8 km that the census stereo observations tend to have reduced low biases (approx. half) than ORAC when compared to the CTL altitude as determined by CALIOP. This observation is made more concrete in Fig. 6 and the statistical analyses provided in Sect. 5.2, where the census stereo CTH retrievals, at least for clouds less than 11 km in altitude, typically have a much reduced low bias than the ORAC retrievals. For clouds above 11 km in the inter-comparison regions, it is likely that the optical depth is too low for any of the algorithms to perform effectively. When the stereo retrievals are incorporated into the ORAC retrieval as a priori, the low bias is still present, but reduced. Further reductions in the ORAC+stereo bias could potentially be achieved by reducing the uncertainties on the stereo a priori inputs for high clouds and by using the dual view in the ORAC cloud retrieval, both of which will be examined in the future.

Similar findings to those of single-layer high ice clouds are presented for the case of multi-layer clouds where the uppermost layer is above 6 km (and therefore ice). This is to be expected, as in the instances of optically thin cloud, rather than having the surface contributing to the observed radiance, it is instead the underlying cloud feature. However, the low biases in the ORAC retrievals for multi-layer clouds, as shown in Fig. 8, are generally larger than for the single-layer cloud case. This is likely due to the assumptions of the single-layer cloud model employed by ORAC and the fact that in case of multi-layer clouds, the retrieved cloud top height is related to the effective radiance of the two layers, which will be an intermediate height. As with single-layer clouds when the stereo retrievals are incorporated into the ORAC retrieval as a priori the low biases compared to the CALIOP CTL are generally reduced, but not to the same extent as stereo alone, due to the fact that the most radiometrically consistent cloud-top height remains below the height of the upper layer cloud layer if a single cloud layer is assumed. The stereo retrieval performs similarly irrespective of the number of cloud layers, and this is a feature of the geometric approach.

The analysis in Sect. 5.3 demonstrates two situations where the inclusion of the CTH a priori has a large impact on the retrieved microphysical parameters. The first is where the inclusion of the a priori leads to a change in cloud phase. A change in cloud phase has a strong effect on the retrieved COD and RE parameters as water and ice cloud microphysics differ substantially. Changes in cloud phase occurred in ∼ 10 % of the collocated samples analysed for single cloud over water and, in comparison against CALIOP, the change in phase caused by the inclusion of the a priori is typically incorrect. However, the samples with phase changes between the retrievals are also associated with average solution costs that indicate moderate to poor/very poor quality fits for both ORAC (excluding ice clouds > 9 km, where the mean cost is ∼ 6) and ORAC+stereo. The higher mean solution costs indicate that when retrievals settle on different phases the observed conditions are not well approximated by either forward model. Causes of this poor approximation can include: multi-layer clouds (that may have been missed by CALIOP due it saturating at three optical depths), the presence of mixed phase cloud and high aerosol loading, or regions where the auxiliary data or a priori data are not appropriately defined (Sayer et al., 2011). In this instance though, an inappropriately defined CTH a priori is likely not the cause as the high costs are also present in the ORAC retrieval where it is not applied.

The second situation where the inclusion of the a priori has a significant impact is for certain water cloud retrievals. The observed discrepancies in the retrieved microphysical parameters are caused by inaccurate a priori estimates of CTH from the census stereo algorithm. The poor estimates occur where the water cloud intersects with other cloud features at higher elevations. Near the point of intersection, due to stereo algorithm smoothing effects (Zabih and Woodfill, 1994), the census stereo retrieved CTH relates to the overlying cloud feature, not the underlying water cloud, resulting in inaccurate a priori values. The ORAC+stereo retrieval is constrained against these CTH a priori values, and the degree of the constraint is dependent on the provided a priori error (Poulsen et al., 2012). In our analysis the census stereo a priori was found to be wildly inaccurate at intersections between water clouds and overlying clouds (∼ 8 km mean CTH vs. ∼ 3 km mean CTH retrieved by ORAC), in such instances the assumed error on the a priori is unsuitable, and does not provide a sensible constraint for the retrieval. In order to reproduce the observed top of atmosphere brightness temperatures the algorithm must modify other, unconstrained parameters. The inadequacy of the CTH a priori values and the provided error constraints are therefore compensated for in the COD and RE parameters, which are unconstrained in the ORAC retrieval (Poulsen et al., 2012). This results in the observed differences between the ORAC and the ORAC+stereo COD and RE retrievals for water clouds located in proximity to clouds at increased elevations. In such instances, the ORAC+stereo COD and RE retrievals are incorrect and methods for detecting when the stereo-derived a priori is inappropriate so that effective a priori estimates and errors can be applied will be investigated in future studies.

Outside of these two situations the impact of the a priori on the retrieved cloud microphysical parameters is limited. Poor agreement between the ORAC and ORAC+stereo microphysical parameters is observed in retrievals over ice (and to a far lesser degree, multi-layer cloud systems); however this is expected due to the known behaviours and limitations of the ORAC algorithm (Sayer et al., 2011). In retrieval situations where ORAC is known to perform optimally (single-layer clouds over ice-free water bodies in this instance) the mean differences between the algorithms are small. The inclusion of the a priori and the associated increase in CTH (as with high ice clouds) leads to a slight reduction in the retrieved COT and RE that is dependent on the change in CTH. The largest observed magnitude changes are for single-layer ice clouds over open water at elevations of above 9 km (which are most strongly affected by the inclusion of the a priori) with mean RE differences of 2.2 (±5.9) and mean COD differences of 0.5 (±1.8).