New airborne retrieval approach for trade wind cumulus properties under overlying cirrus



[1] A new retrieval method is presented to derive the optical thickness τ and effective droplet radius reff of shallow cumulus in the presence of overlying thin cirrus. This new approach allows for a retrieval without a priori knowledge of the microphysical and optical properties of the overlying cirrus. The retrieval is applied to helicopter-borne solar spectral reflectivity measurements gathered by the Spectral Modular Airborne Radiation measurements sysTem (SMART-HELIOS) above trade wind cumuli near Barbados. Collocated microphysical cumulus properties (liquid water content, effective droplet radius, droplet number concentration) were measured by in situ instruments installed on the Airborne Cloud Turbulence Observation System (ACTOS). Cloud inhomogeneities lead to an underestimation of retrieved τ of up to 114%, while reff is biased by up to 27%. Moreover, misrepresentation of the overlying cirrus may cause an overestimation of the classically retrieved cumulus reff of up to 50% and an underestimation of τof up to 6%. The new retrieval, effectively correcting for the influence of overlying cirrus, enables reliable estimates of τ of the cumuli for optically thin, overcast cirrus conditions and reduces the retrieval error for reff of the cumuli by almost 50%. Agreement between in situ measured and retrieved reff is in the range of ±1 μm. The retrieval can also reproduce the wide range of in situ measured mean reff (7–18  μm), which is a result of different aerosol load and cloud top heights on the different flight days. The observed τ ranges between 5 and 36.

1 Introduction

[2] Shallow trade wind cumuli represent a common feature of atmospheric convection in the tropics. In the trade wind regime, large-scale subsidence associated with the descending branch of the Hadley circulation prevails, and clouds remain shallow under the so-called trade wind inversion [Stevens et al., 2001]. Trade wind cumuli play an important role in the transport of moisture, momentum and heat into the free troposphere [Tiedke, 1989]. Additionally, due to their high reflectivity of solar radiation and their temperature being close to the surface temperature, trade wind cumuli have a cooling effect on the Earth's radiation budget [Albrecht, 1989].

[3] Several field campaigns and observations have been performed to investigate the formation and microphysical characteristics of trade wind cumuli. These include the Barbados Oceanographic and Meteorological Extensive field campaign (BOMEX) in 1969 [Davidson, 1968; Holland and Rasmussion, 1973], the Atlantic Trade wind Experiment (ATEX) in 1969 [Augstein et al., 1973], and the Rain In Cumulus over the Ocean (RICO) campaign in 2007 [Rauber et al., 2007]. Still, open issues remain, including the relationship between aerosol particles, cloud condensation nuclei and cloud microphysical properties such as the cloud particle number size distribution and their influence on the formation of shallow cumulus convection [Xue et al., 2008]. Moreover, the impact of aerosols and microphysical properties of trade wind cumuli on precipitation, especially regarding the warm rain process, is not well understood [Kogan et al., 2012].

[4] The interpretation of the available data is complicated due to problems with regard to sampling strategy. In the past, observations of the interaction between cloud microphysical parameters and cloud reflectivity have typically been realized by two approaches: (i) either a single aircraft measured both in situ microphysical cloud parameters (inside cloud) and radiative quantities (above cloud), consecutively at different times, or (ii) two or more aircraft were employed for the in situ and the remote sensing measurements seeking to fly atop each other to sample simultaneously radiation above and microphysical properties within the cloud. Setup (i) has the disadvantage of spatial and temporal displacement of the measurements, while setup (ii) is rather difficult (due to flight restrictions) and expensive to realize. A third approach has come up recently. Closely collocated measurements of in situ and radiative quantities using a towed measurement platform dragged by aircraft or helicopter have been described by Frey et al. [2009] and Henrich et al. [2010]. The towed platforms perform in situ measurements inside clouds, while radiation data are collected above cloud by instruments installed on the airplane or helicopter. The low true air speed possible with a helicopter of about 15 m s−1 has distinct advantages over a fast-flying airplane for sampling inhomogeneous trade wind cumuli. Such cumuli typically have a horizontal extent of 1000 m or less, which requires a high spatial resolution of the measurements as provided by low flight speeds of helicopters. With a sampling rate of 5 Hz, this would yield about 250 data points per cloud. Conversely, by using a faster airplane (speed of ≥50 m s−1), lower sampling statistics are obtained. On the other hand, a helicopter is not well suited to accommodate an upward looking radiation sensor. This introduces the need for radiative transfer calculations in order to specify downward solar radiation.

[5] A major challenge in the airborne passive remote sensing of trade wind cumuli is caused by frequently observed overlying cirrus, which may have a significant impact on the retrieval of cloud properties [Chang and Li, 2005]. According to Stordal et al. [2004], the global cirrus cloud cover in the trade wind region is 10–25% with a positive trend. The overlying cirrus is not easy to handle in the retrieval due to the influence of different ice crystal habits on the radiative field as described in Wendisch et al. [2005], Wendisch et al. 2007], and Eichler et al. [2009]. Additional information from LiDAR and satellite measurements are required to appropriately consider the overlying cirrus, which often is temporally and spatially inhomogeneous, or subvisible.

[6] We present a new technique for the retrieval of optical and microphysical properties of trade wind cumuli that mitigates the effect of overlying cirrus. This new retrieval method is applied to spectral reflectivity data collected over trade wind cumuli over the Carribean Sea. The retrieval results are compared to collocated in situ measurements and the standard retrieval procedure.

2 Observations and Simulations

2.1 In Situ and Radiation Measurements

[7] The Clouds, Aerosol, Radiation, and tuRbulence in the trade wind regime over BArbados (CARRIBA) campaign took place in November 2010 and April 2011 over Barbados (13.07°N, 59.48°W). An introduction to the CARRIBA campaign is given in Siebert et al. [2012]. Thirty helicopter flights, frequently under overlying cirrus (27/30), have been performed during both time periods, although in this work, we present data from CARRIBA 2011 only. In general, flights were performed east of the island over the ocean, although in some cases (16 and 19 April), the data set was gathered partially over the island.

[8] The measurement setup is described in Siebert et al. [2006] and Henrich et al. [2010]. Two platforms were attached to a helicopter by a 160 m long rope. The Airborne Cloud Turbulence Observation System (ACTOS), positioned at the lower end of the rope below the helicopter, included instruments to collect basic meteorological variables, cloud microphysical properties and turbulence data, as well as aerosol properties within and outside the cumuli. Here we investigate measurements of the effective cloud droplet radius reff with a phase doppler interferometer (PDI), described in Chuang et al. [2008]. The PDI is a single particle spectrometer whose sample volume is created by the intersection area of two laser beams. If a droplet passes through this sample volume, the scattered light is detected by three spatially separated detectors. The droplet diameter can be derived from the phase shift between the signals of two different detectors. The PDI measures droplets in the diameter range of 3–150  μm with uncertainties in the droplet size measurements of about ±1 μm. A comprehensive compilation of the principle of operation of the PDI and further airborne instruments is given by Wendisch and Brenguier [2013].

[9] Radiation measurements were performed above the cumuli by the Spectral Modular Airborne measurement sysTem (SMART-HELIOS) installed 140m above the ACTOS payload (20 m below the helicopter). SMART-HELIOS con-tained two downward looking optical inlets for measurements of upward spectral radiance math formula (in units of W m−2 nm−1 sr−1) and upward spectral irradiance math formula(in units of W m−2 nm−1). The subscript λrepresents the wavelength. Both optical inlets were connected via optical fibers to separate pairs of plane grating spectrometers, with each pair covering the visible (wavelengths between 350 and 1000 nm and near-infrared spectral range (900–2100 nm). This configuration is similar to the SMART-Albedometer as described in Bierwirth et al. [2009]. The full width at half maximum (FWHM) of the spectrometers is between 2 and 3 nm in the visible and 8–10 nm in the near-infrared spectral range. The opening angle of the radiance inlet is 2°. Assuming that ACTOS is flying at cloud top and SMART-HELIOS 140 m above, the resulting footprint at cloud top would be a circle with a radius of 2.5 m cross-track for the math formula measurements. Along-track the footprint is defined by the flight speed and integration time of the math formula measurements (0.1–0.3 s) and ranges between 4.2 and 8.5 m. Because the helicopter could not accommodate upward-looking irradiance sensors, the downward solar spectral irradiance math formula was not measured, but simulated instead. The radiation sensors were calibrated using certified radiance and irradiance standards traceable to NIST. The wavelength calibration was performed with spectral emission lamps. Measurement uncertainties are estimated as a combination of the uncertainty in the spectrometer signal, errors during the radiometric calibration in the laboratory and the transfer calibration performed in the field, and the uncertainty of the output of the applied integrating spheres. The uncertainties of the calibration standards are the largest contributors to the overall measurement uncertainty of altogether 6% in the visible and 9%in the near-infrared spectral range.

[10] Additional instrumentation on SMART-HELIOS comprise an Inertial Measurement Unit (IMU), namely the 3DM-GX3 Attitude Heading Reference System by Micro Strain®;, and a commercial digital camera in downward-looking mode. The IMU measured the pitch and roll angles, as well as the heading of the SMART-HELIOS payload. The dynamic accuracy of the pitch, roll, and heading measurements is ±2 °. The digital camera took photographs of the underlying cloud fields every 4 s. These photos were used to identify the position of the radiation and in situ measurements.

2.2 Radiative Transfer Simulations and Standard Bispectral Retrieval (SBR)

[11] The radiative transfer library libRadtran Version 1.6-beta [Mayer and Kylling, 2005; Mayer, 2009] was used to calculate lookup tables (LUT) for the cloud property retrieval. Simulations were performed by the discrete ordinate radiative transfer solver (DISORT), version 2 by Stamnes et al. [1988]. The vertical profiles of atmospheric constituents and meteorological parameters were adopted from the standard profiles of Anderson et al. [1986] for tropical conditions, modified by measurements from ACTOS and radiosonde data. Extraterrestrial spectral irradiance data were taken from Gueymard [2004]; spectral surface albedo was applied from Wendisch et al. [2004], type Surface Albedo Sea. During instances where measurements were performed over the island, the type Surface Albedo Land is applied. The aerosol particle profiles were taken from the standard aerosol profile data for Spring/Summer conditions from Shettle [1989] for a maritime aerosol type modified by ground-based LiDAR and AErosol RObotic NETwork data. Cloud droplet scattering and absorption properties of the trade wind cumuli were derived from Mie calculations according to Wiscombe [1980]. Ice microphysical properties for the overlying cirrus were provided by Key et al. [2002], Yang et al. [2000], and Baum et al. [2005a, 2005b, 2007].

[12] The standard bispectral retrieval (SBR) was first introduced by Twomey and Seton [1980] and Nakajima and King [1990]. The SBR is performed by calculating cloud top reflectivities γλ for two different wavelengths, which are defined by:

display math(1)

and depend on τand reff. γλ values are calculated for a wavelength λ, where scattering is dominant (visible), e.g., at λ=645 nm. Here γλ shows a strong sensitivity to τ. A second γλ, where absorption is dominant (near-infrared), is calculated at, e.g., λ=1645 nm where the sensitivity is high with respect to reff. Performing γλ calculations for a multitude of τ and reff combinations yields a LUT containing model math formula for each τ and reff combination. Interpolating measured γλ values within this calculated LUT results in the retrieved τ and reff of the measured cloud.

3 Data Filter

3.1 Cloud Inhomogeneity

[13] The bispectral retrieval approach using equation ((1)) assumes a plane-parallel, homogeneous extended cloud geometry. Figure 1 shows photos of the downward-facing camera on SMART-HELIOS. Photos labeled 1–3 illustrate an exemplary traverse above a trade wind cumulus, starting at the inhomogeneous cloud edge with visible ocean surface (see 1). The cloud cover increased (2) and finally a more homogeneous part with no visible ocean surface followed (3). A second trade wind cumulus is depicted in photos 4–6. Here the cloud started with a rather homogeneous section (4). A longer period with only low opacity was adjacent (5), whereas the last section of the cumulus showed similar characteristics as in the beginning (6).

Figure 1.

Photos of the downward-facing camera on SMART-HELIOS from 23 April 2011. The numbers 1 to 6 correspond to measurement times in the time series in Figures 2e and 2f. Also visible are the 160 m long rope and ACTOS.

[14] It is very likely that three-dimensional (3D) radiative effects were a significant contributor to the radiative field at times 1,2, and 5. The clouds at times 3,4, and 6, however, were more homogeneous and one-dimensional (1D) radiative transfer seems feasible.

[15] Since the inhomogeneous parts certainly will influence the retrieval of τ and reff, a spectral measure of cloud inhomogeneity was sought to filter out data points which were measured above inhomogeneous cloud sections. Measures to discriminate cloudy from ocean surface data points have been described by Ackerman et al. [1998] and Kassianov et al. [2010], where one or several ratios of reflectivities γλ, e.g., at λ=870 nm and λ=660 nm, are used for differentiation. An optimal ratio math formula will not only determine whether the measurement was performed over a cloud or over the ocean, it will also help to identify more homogeneous cloud parts.

[16] Two time series of math formula at λ = 645 nm and at λ = 1645 nm are shown in Figures 2a and 2b, with the corresponding retrieved τ and reff illustrated in Figures 2c and 2d. Data is from 23 April 2011. A radiance-ratio math formula (black line) with λ1 = 870 nm and λ2 = 660 nm is shown for both time series in Figures 2e and 2f, respectively. The numbers 1 to 6 signal times in the time series where the photos 1 to 6 from Figure 1 were gathered.

Figure 2.

(a,b) Time series of upward spectral radiance math formula at λ=645 nm and at λ=1645 nm, (c,d) retrieved cumulus optical thickness τ and effective droplet radius reff and (e,f) radiance-ratios math formula and math formula for two measurement sections on 23 April 2011. The flight leg between 51040 and 51162 s UTC is displayed in Figures 2a, 2c and 2e. Figures 2b, 2d, and 2f are measured during 53418–53567 s UTC. For visibility reasons, in Figures 2a and 2b, math formula at λ=1645 nm is scaled by a factor of 10. In Figures 2e and 2f, the numbers 1–6 correspond to the respective photos in Figure 1.

[17] The transition from ocean surface to cloud is apparent in a sudden increase of math formula at around 51040 and 53400 s. The absolute values of math formula at λ = 645 nm and at λ = 1645 nm at points 1 and 3 are comparable and are clearly higher than for the ocean surface. The retrieved τ and reff are 10–20 and 5–10  μm larger in the more homogeneous cloud section. There is a slight dip in math formula after point 2, but the differences are small. For the second time series, math formula at λ = 645 nm and at λ = 1645 nm at times 5 and 6 are again comparable. Although opacity is quite low in the middle part of the cloud (5), retrieved τ even increase during this cloud section, while the retrieved reff are in the same range as in parts 4 and 6. From the SBR results and math formula measurements, it is hard to identify differences between the different cloud sections. math formula only dips slightly and fluctuations are slightly more frequent. Therefore, other than distinguishing clouds from the ocean surface, there seems to be little information about inhomogeneity in math formula.

[18] Looking at the ratio of several measured math formula spectra over clouds to spectra over water reveals a maximum at wavelengths where water vapor absorption is apparent (e.g., λ = 720 nm). Therefore, a second radiance-ratio math formula(grey line) with λ1 = 720 nm and λ2 = 644 nm is shown in Figures 2e and 2f. math formulaalso exhibits the step at the transition from ocean surface to cloud top measurements, visible at the beginning and end of the time series. An additional step between the inhomogeneous cloud parts (1 and 2) and the more homogeneous section (3) can be identified at around 51090 s. The area around time 3 is characterized by an increase of math formula by about 10–15%. In the second cloud case (4–6), the transition between the different cloud parts is more gradual, but still two plateaus of math formula at the beginning and end of the time series exist. The change in math formula between inhomogeneous and homogeneous cloud sections is about 18%.

[19] Both the cloud filter math formula and the inhomogeneity filter math formula are applied to every measurement flight and inhomogeneous cloud parts are excluded from the analysis.

3.2 Sensor Zenith Angle

[20] Although all cloud overpasses by HELIOS were intended to be under only small course corrections by the helicopter, the inhomogeneous structure of the cumuli fields made changes in heading and flight altitude necessary from time to time. Figure 3a shows a 30 minute time series of measured pitch and roll angles by the IMU aboard SMART-HELIOS on 18 April 2011. Positive pitch angles are defined by the nose of SMART-HELIOS going down, negative values indicate the nose going up. Positive roll angles are defined as a rotation to the right, negative angles as rotation to the left. Figure 3b illustrates the flight altitude of the SMART-HELIOS payload measured by the GPS sensor. The time series starts with the first low level leg after takeoff at around 200 m. During this time, oscillations in the roll angle are ϑ < 2°, while oscillations in the pitch angle are ϑ < 4°. At around 13.94 h, a profile from 200–2500 m yields slightly higher oscillations of the roll angle of ϑ < 4°. The nose of SMART-HELIOS follows the helicopter and an offset in the roll angle of about ϑ ≈ −7° is obvious. At the peak of the ascent, the offset is reduced, presumably due to a decrease in the vertical velocity of the helicopter as it approaches its highest point. During the following reduction in flight height, the pitch angle develops a new offset at ϑ ≈ 7°. Overall, |ϑ| < 10°.

Figure 3.

Thirty minute time series of (a) pitch (black) and roll (grey) angle measured by the IMU aboard SMART-HELIOS and (b) of flight altitude measured by the GPS sensor on 18 April 2011. (c) Bias in retrieved cumulus optical thickness τ and effective droplet radius reff as a function of sensor zenith angle ϑ. The difference between sensor azimuth angle and sun azimuth angle is 90°. (d) Same as Figure 3c, but the difference between sensor azimuth angle and sun azimuth angle is 180°.

[21] Therefore, deflections from the nadir viewing direction of the optical inlet are to be expected. If the underlying cloud is assumed to be plane-parallel and horizontally homogeneous, this results in a pure geometrical influence on reflected radiances above the cloud. Figure 3c shows the effect of increasing sensor zenith angle ϑ on the retrieval results of τ and reff. The model setup represents 22 April 2011 with a one-dimensional cloud with cloud top in 1000 m height, a geometrical thickness of 400 m, τ = 10 and reff = 10 μm. The solar zenith angle θ0 is set to the mean value during the flight on 22 April at θ0 = 30°, and the solar azimuth angle ϕ0 is set to the mean value of 270° (defined here as the sun being in the east). The sensor zenith angle ϕ is set to 0° (sensor in the north looking south), therefore, the sensor looks perpendicular to the sun.

[22] With increasing ϑ, the retrieved τare overestimated compared to the assumed input values, while the retrieved reff are underestimated, even though for ϑ < 5° the changes from the assumed τ and reff are in the range of 1%. Larger differences arise for ϑ>10°, with a maximum difference in retrieved reff of about 5% at ϑ = 16°. After that the aberration in retrieved reff is decreasing again. This is due to the exponential increase in the overestimation in τ, which offsets the smaller underestimation in reff.

[23] Figure 3d shows the same ϑ effect, but ϕis set to 270° (sensor in the west looking east into the direction of the sun). The bias in retrieved τ and reff gets as high as 13%. For ϑ < 5°, the bias in retrieved τ is about 1%, while the bias in retrieved reff is 5%. To minimize the effect of ϑ≠0 on the retrieval of τ and reff the filtered data was reduced to measurements where ϑ < 5°.

[24] The results from Figures 3c and 3d also indicate that assuming the trade wind cumuli can be represented by plane-parallel and horizontally homogeneous calculations, retrieved τ and reff should only change slightly after applying the ϑ filter.

[25] The effect from the inhomogeneity filter introduced in section 3.1 and from limiting the data to measurements where ϑ < 5° on τ and reff are summarized in Table 1. Here the percentage of data points within ϑ < 5°, the change in retrieved τand reff due to the inhomogeneity filter and the subsequent changes in filtered τ and reff due to ϑ < 5° are shown.

Table 1. The Effect of the Inhomogeneity Filter and the Requirement of Sensor Zenith Angle ϑ < 5° on Data Statistics, as Well as Retrieved Cumulus Optical Thickness τ and Effective Droplet Radius a
Date<5° (%)Δτ (%)Δreff (%)Δτ (%)Δreff (%)
  1. aColumn two shows the percentage of data points that are assumed to be cloud data (τ > 2 and reff > 2 μm) and were within ϑ < 5°. Furthermore, the changes in retrieved τand reff due to the inhomogeneity filter and due to considering data points with ϑ < 5° are shown.
14 April57+114−18−2+1
16 April79+63+1+3+2
18 April67+44−14−10−1
19 April70+6−4+3−2
22 April66+44+2100
23 April99+43+4−10
24 April65+76+2+8+2
25 April73+58+27+4+3

[26] About 2/3 or more of filtered cloud data, defined by a minimum threshold for τ and reff and filtered according to section 3.1, where gathered within ϑ < 5°. The only exception is 14 April 2011.

[27] The effect of the inhomogeneity filter was already evident in Figures 2c and 2d, where τ and reff of the more homogeneous cloud section (3) were significantly different from cloud sections 1 and 2. For every measurement flight, the transition to the filtered data set yields increased retrieved τ, with changes of 43–76%. This is understandable, since mostly data points with low optical thickness are excluded. Two days stand out: 14 April with 114% and 19 April with an increase of only 6%.

[28] The effect on retrieved reff is noticeably smaller, with differences of ≤ 4% on four of the eight measurement flights. Moreover, the sign of the change is positive in only five of the eight cases. The filter can affect the retrieved reff in either way.

[29] Reducing the filtered data to measurements with ϑ < 5° affects τ and reff comparably. The differences are ≤ 4% with a few days characterized by changes as low as 0%. This shows that after applying the inhomogeneity filter, the remaining data represents homogeneous cloud parts only. Two exceptions are 18 April and 24 April, where the τ retrieval changes from ϑ < 5° are in the range of 10%.

4 Influence of Overlying Cirrus

[30] As the helicopter-borne measurements did not allow math formula measurements, simulated math formula have to be included in the retrieval algorithm. Without knowledge of the cirrus cover and cirrus microphysical properties, this implies some uncertainties in (i) the simulated math formula and (ii) the retrieval of τand reff.

[31] The influence of overlying cirrus on the transmitted and reflected solar radiation, as well as on the SBR of τ and reff, was investigated by radiative transfer simulations adjusted to the case of 22 April 2011. The mean solar zenith angle was θ0 = 30°, while the mean solar azimuth angle was ϕ0 = 269°. A horizontally homogeneous trade wind cumulus with a cloud base at 500 m (approximated by LiDAR measurements on the island) and cloud top in 1170 m (ACTOS data) was defined as input for the radiative transfer calculations. An overlying cirrus was implemented between 13–14 km with a fixed effective radius of reff,ci = 20 μm.

[32] Downward spectral solar irradiance was calculated for cloudless conditions (math formula) and overlying cirrus conditions (math formula) at the height of the cumulus top. Figure 4a shows spectra of the ratio math formula for three values of τci. Obviously, math formula is reduced by the cirrus; the reduction is stronger the larger the cirrus optical thickness τci. The reduction is most prominent in the water vapor absorption bands indicated by the grey areas. In the spectral regions outside of these absorption bands, attenuation is approximately 2–3% for τci = 0.2 and up to 13% for τci = 1.

Figure 4.

(a) Spectral ratio of downward solar irradiance math formula under cirrus conditions to cloudless conditions for different cirrus optical thicknesses τci. Ice properties are provided by Baum et al. [2005a, 2005b, 2007]. The black arrows indicate two wavelengths were math formula is equally attenuated by a cirrus with τci = 0.2; grey arrows show such a pair for τci = 0.5. The grey shading indicates absorption bands. (b) Spectral ratio of math formula for different ice habits with ice cloud properties by Key et al. [2002] and Yang et al. [2000] (solid columns only) to bulk properties by Baum et al. [2005a, 2005b, 2007]. For all calculations, τci = 0.5. (c,d) The same as Figures 4a and 4b but for upward radiance math formula.

[33] Figure 4b illustrates the impact of different crystal shapes on math formula. The reference downward irradiance math formula was calculated assuming nonspherical bulk crystal scattering properties by Baum et al. [2005a, 2005b, 2007]. Then different ice crystal habits were assumed in the calculations of math formula, such as solid column, droxtal, plate, rosette, and rough-aggregate. Figure 4b shows spectra of the ratio math formula. Outside absorption bands the ratio math formula is in the range of only 1–2%, depending on the assumed ice crystal habit. Only a weak wavelength dependence is observed. The spectra of the ratio math formula for solid columns and ice properties by Key et al. [2002] show noticeable differences of up to 2% at wavelengths λ<700 nm and λ>1500 nm compared to the spectral ratio based on ice cloud properties by Yang et al. [2000]. The biggest differences (up to 4%) occur in the water vapor absorption bands. Altogether, the influence of different shape on math formula is small (<3%).

[34] In the following, we quantify the impact of τci and ice crystal shape on the radiance math formula reflected by the cumuli in the presence of overlying cirrus. We assume a cumulus with τ = 10 and reff = 10 μm. Figure 4c shows the spectral ratio of upward radiances math formula. The spectral behavior in the ratio math formula is similar to the decrease in the ratio math formula shown in Figure 4a, but absolute values are 1–2% smaller. The spectral ratio math formula, shown in Figure 4d, also exhibits a similar spectral behavior as the ratio math formula shown in Figure 4b. Again, the influence of ice crystal habit seems to have only a small influence on math formula. Nevertheless, taking into account the measurement uncertainty of the math formula measurements, introducing a cirrus with τci = 0.2 represents about one third of the measurement uncertainty in the near-infrared spectral range. For τci = 0.5, this translates into an additional uncertainty of one half of the measurement uncertainty in the near-infrared spectral range. Different ice crystal habits account for an additional uncertainty in the range of 1/3−1/2 of the measurement uncertainty of math formula.

[35] The uncertainties in simulated math formulamay accordingly increase the uncertainties of the retrieval of τ and reff of the cumuli. To quantify this effects, we calculated a retrieval LUT assuming cirrus-free conditions. Afterwards, the retrieval was run with input radiances math formula calculated with an overlying cirrus, thus representing a retrieval without a priori knowledge of the overlying cirrus properties. The cumulus τ was varied between 1–72, while reff of the cumuli was varied between 1–24  μm. These ranges comprise the ranges observed during the CARRIBA campaign. τci = 0.2,0.5, and 1 was assumed.

[36] Figure 5 shows the effects of overlying cirrus on the SBR results for (a) τ and (b) reff of the trade wind cumuli. Using the ice properties of Baum et al. [2005a, 2005b, 2007], the retrieved τ show an underestimation of 1–12% due to neglecting the overlying cirrus, depending on the assumed values for τ and τci. For τ < 3, the uncertainty in the retrieval is most prominent. Since the extinction efficiency of ice in the near-infrared wavelength range is higher than in the visible, the influence of overlying cirrus is higher on the retrieval of reff than of τ. Even for τci = 0.2, there is an overestimation in the retrieval results of reff of about 6%. This overestimation increases with increasing τci and reaches values of 14% and 32% for τci = 0.5 and τci = 1, respectively. The highest over-estimations occur for reff < 4 μm (40–80%). For increasing τci the retrieved reff are higher than the highest value in the retrieval LUT (24 μm). Therefore, for reff > 16 μm, there are no retrieval results for τci = 1.

Figure 5.

(a) Underestimation of retrieved cumulus optical thickness τ as a function of the assumed τ of the underlying trade wind cumulus caused by an overlying cirrus. A constant effective droplet radius of reff = 10 μm is assumed. (b) Overestimation of retrieved reff as a function of assumed reff of the underlying cumulus caused by an overlying cirrus. A constant τ = 10 is assumed. Applied cirrus optical thicknesses τci are 0.2, 0.5, and 1.0. Ice properties are provided by Baum et al. [2005a, 2005b, 2007] (circles), Yang et al. [2000] (triangles), and Key et al. [2002] (diamonds).

[37] The bias increases when using the ice scattering models from Key et al. [2002] (solid-columns), up to an underestimation of 7% for τ and an overestimation of 48% for reff. The retrieval results using the Yang et al. [2000] and Baum et al. [2005a, 2005b, 2007] scattering properties are comparable.

[38] As already shown in Figure 4d, the influence by different ice crystal habits on math formula is about 1–2%, which is in the same range as the influence by a cirrus with τci = 0.2. As an example, an overlying cirrus with solid columns or rough-aggregates only would decrease math formula even further. Misrepresentation of such an overlying cirrus in the SBR would even further increase the bias in the retrieved τand reff.

5 New Radiance-Ratio Retrieval (RRR)

5.1 Basic Idea

[39] From Figure 4c, it is obvious that the ratio math formula depends only weakly on wavelength. It is possible to find wavelength pairs, such that:

display math(2)

where λ1 and λ2 are two wavelengths outside absorption bands. This subsequently means:

display math(3)

Equation ((3)) suggests that for certain wavelength pairs λ1 and λ2, the ratio of math formula at both wavelengths is the same as the ratio of math formula for the same wavelength pairs. Therefore, on the basis of equation((3)), a new retrieval method is proposed to minimize the impact of an overlying cirrus on the retrieval of τ and reff of trade wind cumuli. Performing a radiance-ratio retrieval (RRR) with ratios math formula at two such wavelengths facilitates a retrieval that does not require a priori knowledge of the overlying cirrus properties. Similar retrieval approaches with spectral slopes have already been reported for ground-based transmissivity measurements [McBride et al., 2011].

[40] Another advantage of this retrieval is the transition from absolute to relative measurements, which yields a reduction of the retrieval uncertainty. In the SBR, γλ constitutes a semi-relative quantity. While it is a ratio of two radiative quantities, math formula and math formula, both have separate calibration procedures and uncertainties concerning the measurements and calibration. Here especially the calibration of math formula is very sensitive due to its dependence on the steradian. Moreover, math formula was not measured during the CARRIBA campaigns. The values from the radiative transfer calculations are not subject to the measurement and calibration uncertainties of measured math formula. In contrast, ratios math formula are true relative quantities by consisting of two radiances, both of which were measured and calibrated in the same way.

[41] Optimal radiance-ratios math formula need to fulfill equation ((3)). Furthermore, the sensitivity of the retrieved cumulus parameters τ and reff with respect to math formula needs to be high.

[42] Figure 6a shows the LUT grid resulting from the SBR with radiances at λ = 645 nm (sensitivity towards scattering) and λ = 1645 nm wavelength (sensitivity towards water absorption). The grey, slant lines represent isolines of constant τ (vertical lines) and reff (horizontal lines). Due to the high sensitivity of radiances in the visible wavelength range towards τ, math formula at λ = 645 nm increases with increasing τ. For a given τ, e.g., τ = 72, there is hardly any sensitivity of math formula at λ = 645 nm towards reff. In contrast, there is much higher sensitivity of math formula at λ = 1645 nm towards reff, although for decreasing τ the sensitivity of radiances at this wavelength towards τincreases. The black dot indicates a measurement point with the corresponding error bars. All solutions within the measurement error bars are possible (τ = 16–20 and reff = 7–14  μm). This is highlighted by a close-up view around the measurement point in the inlay.

Figure 6.

(a) Retrieval grid for the standard bispectral retrieval with radiances at 645 and 1645 nm. The measurement errors from the spectrometers employed during the CARRIBA campaign are illustrated by the error bars surrounding a measurement with τ =18 and reff = 10 μm. (b) Retrieval grid for the radiance-ratio retrieval (RRR) with a ratio math formula at λ1/λ2 = 1525 nm / 579 nm. The measurement point is the same as described in Figure 6a. (c) Retrieval grid for the RRR with a ratio math formula at λ1/λ2 = 1000 nm / 420 nm. The measurement point is the same as described in Figure 6a.

[43] Figure 6b shows the LUT grid for the same nonabsorbing wavelength of λ = 645 nm and a radiance-ratio math formulafor λ1 = 1525 nm, and λ2 = 579 nm. While the range of possible τsolutions is similar compared to the SBR in Figure 6a, the reff solution range is much narrower with values reff = 9–11  μm. This is due to (i) a wider retrieval grid spacing due to a different sensitivity towards reff and (ii) a reduced measurement uncertainty of math formula of 4–5% instead of 6–10% of the math formulameasurements. In the close-up, it is obvious that the possible reff solution range is now less than 1  μm in each direction. Figure 6c illustrates the LUT grid with a different radiance-ratio math formula at λ1 = 1000 nm and λ2 = 420 nm. In this case, the reff solution range is comparably larger than both the SBR, and the retrieval with math formula yielding reff = 6−−20 μm. The sensitivity of such a LUT towards reff is much lower than the SBR in Figure 6a or the LUT with math formula in Figure 6b. The choice of any math formula therefore affects the sensitivity of the resulting LUT towards τ and reff.

5.2 Systematic Search for Optimal Wavelength Pairs

[44] In this section, a measure of the wavelength-dependant sensitivity of a LUT towards the retrieval of τ and reff is established. In a first step, the general sensitivity of a LUT is analyzed, without regard to the measurement uncertainty. This sensitivity of a LUT towards the cloud parameters is merely defined by its grid spacing (see the isolines of constant τand reff in Figures 6a–6c). Subsequently, the sensitivity of the LUT towards the cloud parameters and the measurement uncertainty are combined to yield a measure of the retrieval sensitivity. This is crucial for a reliable retrieval of τ and effective droplet radius reff.

[45] A LUT that perfectly represents the measurement conditions and perfect math formula measurements (i.e., no measurement errors) yield a perfect cloud property retrieval. Retrieved τ and reff agree with the true values. Introducing a bias in one of the two math formula (for the SBR) will lead to a bias in the retrieved cloud parameters. The extent of this bias depends on the local slope LS of the LUT, which indicates the difference between two neighboring values of τ or reff as a function of differences between the respective two radiances math formula. The same holds true for the RRR with math formula.

[46] To quantify the LS of any LUT, the bias in the retrieved cloud parameter, with regard to an assumed value which indicates the true τor reff, is derived by introducing a bias in math formula(or math formula for the RRR). For the SBR and math formulasensitive towards τ, the LS thus has the form:

display math(4)

The assumed input values are denoted by the subscript “as” while the retrieval results are denoted by the subscript “ret”. A descriptive depiction of LS is illustrated in Figure 7a. Here a close-up of an arbitrary LUT is shown. As for Figures 6a–6c, the grey, slant lines represent isolines of constant τ and reff; the axis labels are omitted since the analysis holds true for the SBR and RRR, regardless of the chosen λ. Assuming a bias is introduced in math formula sensitive towards τ, the biased retrieval result is represented by τret and the assumed (i.e., unbiased) value is τas then LSis the difference between the math formula at τret and math formula at τas, relative to the math formula at τas. This is highlighted by the thick, grey line. In this example, τret<τas. reff, as<reff, ret is also possible, obviously. Since the sign of LS is of no importance, the absolute value of the difference is calculated.

Figure 7.

(a) Illustration of equation (4) in a close-up of an arbitrary lookup table. A cumulus with an assumed cumulus optical thickness τas and effective droplet radius reff, as is indicated by the black dot. A bias in math formula results in a bias in retrieved τret (highlighted by the triangle). (b) Local slopes LS as a function of differences between the retrieved and assumed reff. The grid spacing parameter for the reff retrieval sr highlights the distance between the two LS branches at the LS value representing the measurement uncertainty σ, in this case for the retrieval with math formula.

[47] Other expressions for LS, when looking at the RRR and sensitivity towards τ, math formula and sensitivity towards reff and RRR with sensitivity towards reff, are of the form:

display math(5)
display math(6)
display math(7)

In equations ((4))–((7)), always one cloud parameter is held constant.

[48] Figure 7b shows the result for LS calculations for reff and for the SBR with radiances at λ = 645 and λ = 1645 nm (solid line); radiance-ratios math formulaat λ1 = 1525 nm and λ2 = 579 nm (dashed line) and math formula at λ1 = 1000 nm and λ2 = 420 nm (dotted line) are shown additionally. In both cases, the wavelength chosen for the scattering wavelength is λ = 645 nm. For each LS two branches are visible: one for reff, ret < reff, as and one for reff, ret > reff, as. These exist due to the possibility of a positive or negative bias in math formula (for the SBR) or math formula (for the RRR). Each LS function was calculated for discrete τand reff values in the respective ranges, as described in section 5.4, and then averaged over the discrete values from the LUT. LS functions for a single τasand reff, ascan vary from the averaged values over the complete input domain.

[49] At LS=0 there is no error in the input radiances and the error in retrieved reff is 0. Each of the LS functions is characterized by a different slope. Steep slopes in each branch of LS represent math formula or math formula at wavelengths with a wide grid spacing, resulting in comparably small uncertainties in the retrieval of reff. In such a case, even a high measurement error of math formula yields retrieval results close to the assumed reff. A retrieval with low LS, conversely, represents a LUT where even minimal measurement uncertainties yield high retrieval uncertainties, indicating insensitivity to the retrieved cloud parameters at those wavelengths.

[50] To gain a quantifiable measure of the sensitivity of a LUT towards τ and reff, the measurement uncertainties need to be introduced into the analysis of a LS. This measure is the retrieval-sensitivity parameter sτ for the τ retrieval and sr for the retrieval of reff. If σ is the measurement uncertainty of math formulaor math formula, then the parameters sr and sτ represent the distance between both LS slopes at LS=σand can be calculated by:

display math

The relationship between LS and sr is also illustrated in Figure 7b.

[51] The three corresponding vertical lines show the differences in retrieved reff (in absolute values) compared to the input reffat LS=σ. Here only σ for the retrieval with math formula is illustrated by the horizontal dashed line. Of the three cases illustrated in Figure 7b, the SBR LUT has only a slightly lower slope than the LUT for the retrieval with math formula, but the higher measurement uncertainty of 9% compared to 5% yields slightly higher retrieval errors of ±2 μm compared to ±1 μm. It is apparent that the retrieval with math formula has a less favorable LS function. Although the measurement uncertainties are the same for math formula and math formula, the different slopes yield significant differences in the retrieved reff range of ±1 μm and ±7 μm, respectively. This difference in retrieval sensitivity is quantified by the retrieval-sensitivity parameters sr and sτ. For the example in Figure 7b, sryields values of 4.5,2.2, and 13.2 μm, for the retrieval using math formula at λ=1645 nm, math formula, and math formula, respectively.

[52] Figure 8 shows the result of calculations for (a) sτand (b) sr for the spectral region between 400 and 1800 nm. math formula including radiances at wavelengths below 400 nm were not included since the sensitivity of the spectrometers is not high enough in these wavelength ranges and the calibration uncertainties become too high. Dark areas in these graphs indicate wavelength combinations for math formula with low sτand srvalues, while white areas denote wavelength combinations, which are not suitable for a retrieval (sτ<8 and sr<8 μm were chosen as the threshold). While several areas with possible math formula are apparent in the τ retrieval, s r only shows s r <8 μ m for pairs with one math formula in the near-infrared spectral range. Moreover, sr does not reach values as low as sτ, which shows that the retrieval is more sensitive to τ than to reff. Looking at the uncertainties for the retrieval of both τand reff in Figure 6a, this also holds true for the SBR.

Figure 8.

(a) Retrieval-sensitivity parameter sτ for the retrieval of the cumulus optical thickness τ. (b) Retrieval-sensitivity parameter sr for the retrieval of the effective droplet radius reff. (c) sτ with an overlying cirrus with τci = 0.2. (d) sr with an overlying cirrus with τci = 0.2. The scale was cut off at sτ<8 and sr <8 μ m as only lower values are of interest.

5.3 Combining Optimal Wavelengths With Overlying Cirrus

[53] For the retrieval below cirrus, low sτ sand sr are not sufficient. As shown in Figure 4a, also math formula at these wavelengths has to be invariant with regard to the overlying cirrus. Therefore, optimal wavelengths combinations were obtained by filtering sτ and sr with the following threshold for agreement between math formula and math formula:

display math

sτ for τci = 0.2 are shown in Figure 8c, while sr with the same threshold is shown in Figure 8d. Filtered wavelength pairs are left white. Here an overlying cirrus reduces the possible solution range and only leaves a subset of wavelength pairs.

[54] Finally, combining several radiance-ratios math formula in the RRR, which Vukicevic et al. [2010] have already shown for radiances, will increase the information content of the retrieval and further improves the retrieval of τ and reff. Therefore, the retrieval was performed with three different math formula, depending on the LS at different areas within the LUT. Input values for τ and reff are set at grid areas with small reff < 5 μ m, medium 8 μ m< reff <13 μ m, and high 17 μ m< reff <24 μ m, as measured during the CARRIBA campaign. Similar analysis applies for the retrieval of τ. The favorable ratio math formula, obtained as the sum of weighted radiance-ratios math formula, subsequently will be determined by means of:

display math(8)

δi are the weighting factors determined by sτand sr. They have the form math formula. Depending on the LS at the respective position in the LUT, determined by the different math formula, the respective math formula are weighted accordingly. The math formula with the lowest srat the respective position in the LUT therefore always has the highest contribution in the retrieval.

[55] The remaining bias in the RRR due to the remaining difference between overlying cirrus and non-cirrus conditions amounts to around 1%, 2%, and 4% underestimation in retrieved τ and 1%, 4%, and 11% overestimation in retrieved refffor τci=0.2,0.5, and 1, respectively.

5.4 Comparison of SBR and RRR for CARRIBA Data

[56] Three measurement flights during the CARRIBA 2011 campaign, 16, 19, and 22 April 2011 (CARRIBA flight #23, #25, and #28), were chosen to test the RRR. Each data set ranges between 10 and 40 min with SMART-HELIOS measurements above and ACTOS dipping into trade wind cumuli. Each flight was performed under varying overcast cirrus conditions. Visible, inhomogeneous cirrus was prominent on 16 April and 22 April, while on 19 April, cirrus-free conditions were observed. Photos of the three selected cases from the forward-facing camera on ACTOS are presented in Figure 9. Retrieved reff using SBR and RRR are compared in Figures 10a–10c for each of the 3 days. Only filtered data are shown here with 1228, 735, and 609 samples. For every example, the mean relative deviation between the retrieval with the RRR and the SBR is given in the form:

display math(9)

with the number of samples N. Positive η values indicate an overestimation due to the overlying cirrus. To compare ηwith the results from Figure 5b, which were obtained for τ=10, the optical thickness range for the calculation of η is reduced to 9 < τ < 11.

Figure 9.

High contrast photos of the forward-facing camera on ACTOS from 16 April 2011 (top panel), 19 April 2011 (middle panel) and 22 April 2011 (lower panel). Instruments in the middle of each photo comprise a Sonic Anemometer and a Laser Doppler Anemometer.

Figure 10.

Scatter plots of retrieved effective droplet radius reff with the RRR over reff retrieved with the SBR for (a) 16 April 2011, (b) 19 April 2011 and (c) 22 April 2011. Each case represents the complete flight track and a 10–40 min segment above trade wind cumuli.

[57] Almost all RRR results are equal or lower than the SBR values. The biggest differences between the methods are evident in the 16 April 2011 case, Figure 10a. Here RRR values are several micrometer smaller than results from the SBR and η=12.1%. This concurs with the findings in section 5.4, with the overestimation agreeing with the case of overlying cirrus with τci≈0.5. The 19 April 2011 case in Figure 10b, with no visible overlying cirrus, results in RRR values lying close to ones from the SBR. During this flight η=0.3%. With no overlying cirrus both the SBR and RRR yield similar results. (c) The 22 April 2011 case, characterized by a thin cirrus layer, shows η=5.8. Comparing this value with the results shown in Figure 5 suggests τci ≈ 0.2.

[58] Mean values of reff,RRR are 12.1,0.3, and 5.8% below the SBR results for the 16, 19, and 22 April 2011 cases, respectively. These differences between the retrieval approaches are the result from overlying cirrus, but might also be due to differences in retrieval uncertainties between the SBR and RRR. For each measurement example the standard deviation is reduced by 44%, 40%, and 42%, for the three cases, respectively.

[59] Similar analysis for the retrieved τ shows significantly smaller differences between the SBR and RRR. This was to be expected from the results shown in Figure 5a. η calculated with respect to τ (similarly to equation ((9))) and for 9 μm< reff <11 μm is −1.9,≈0, and +0.5% for the 16, 19, and 22 April 2011 cases, respectively. For the 16 April case the underestimation of τ from the SBR due to the overlying cirrus is obvious. The overestimation for the 22 April case is most likely caused by the different retrieval uncertainties for the SBR and RRR, which offset the small underestimation due to the overlying cirrus.

[60] Although data used for the retrieval were filtered to minimize the influence of 3D radiative effects, cloud inhomogeneities and subsequently 3D radiative effects may result in different spectral signatures in cloud top reflectivity and different retrieval results. This explains the few instances where reff,RRR > reff,SBR.

5.5 Estimation of the Cirrus Optical Thickness

[61] As shown above, differences between RRR and SBR depend on the optical thickness of the overlying cirrus. Conversely, this enables the cirrus optical thickness to be estimated by analyzing the retrieval differences. Figure 11a shows the cirrus optical thickness τci derived by the overestimation of reff from the SBR, assuming the RRR yields the unbiased values. The overestimation was derived by equation ((9)) and subsequently compared with synthetic data similar to those shown in Figure 5. Here, overestimations in the SBR of reff are calculated for τci=0.2,0.5, and 1 and for solar zenith angles θ0=30° and θ0=15°. For these θ0, there is a strong linear behavior between the assumed τci and the overestimation in retrieved reff. Interpolating the η values for the three cases between these two θ0 lines (for the mean θ0value during each case) yields the respective estimates of τci. This analysis suggests τci≈ 0.5–0.6 for 16 April 2011, τci<0.1 for 19 April 2011 and τci≈ 0.1–0.2 for 22 April 2011.

Figure 11.

(a) Estimation of the mean cirrus optical thickness τci from the overestimation in effective droplet radius reff with the SBR compared to the RRR (see equation ((9))) for the 16, 19 and 22 April cases. (b) Frequency distribution of τci for the 16, 19, and 22 April cases estimated from equation ((9)).

[62] Inhomogeneities in the overlying cirrus can be analyzed in the frequency distribution of τciestimations for the complete flight track. While in Figure 11a, the mean value of η is applied, τcifor each measurement point is calculated for the normalized frequency distributions in Figure 11b. The frequency distribution for the 19 April 2011 case is much narrower than the distribution during the other two measurement days with a peak between 0−0.1. Conversely, the 16 April 2011 case shows the widest frequency distribution, with quite evenly distributed τci in the range τci= 0.3 – 0.8. Some values of τci= 0–0.3 were also observed. A peak at τci= 0.1–0.2 and a narrower distribution than for the 16 April 2011 case is prominent for the 22 April 2011 case.

6 Retrieval Results

6.1 Results and In Situ Comparison

[63] Mean values for retrieved τand reff using SBR and RRR are listed in Table 2. It becomes obvious how different each of the flights during CARRIBA 2011 was, with τ varying between 5–36 and reff varying between 7–18  μm. Even days with comparable reff, e.g., the 16 and 18 April flights, are characterized by vastly different τ. The reason for this wide range, such as different aerosol load, cloud top heights or turbulent effects on the cumuli fields will not be discussed here. Moreover, the mean liquid water path LWP for each measurement flight was determined using the relation:

display math(10)

with the density of liquid water ρ [Brenguier et al., 2011]. This relation only holds true for vertically uniform clouds. Therefore, the LWP values presented here should be considered as estimates.

Table 2. Mean Values of Cumulus Optical Thickness τ, Effective Droplet Radius reffand Liquid Water Path LWP From the SBR (τand reffOnly), RRR, and the In Situ Measurements (reffOnly) by the PDI
Flightτ SBRτ RRRreff SBR (μm)reff RRR (μm)reff In Situ (μm)LWP RRR (gm −2)
14 April21.8622.617.746.798.76102
16 April35.2535.9110.329.298.78222
18 April5.195.1310.158.439.1429
19 April8.358.356.816.806.9438
22 April13.6113.5416.0315.5016.36140
23 April13.1912.6516.3814.7213.93124
24 April19.6119.6513.5313.0612.68171
25 April16.9016.9219.2618.0917.54204

[64] Comparisons of retrieved LWP and ACTOS measurements were not performed due to the uncertainties in determining cloud height z. The cloud top height could be approximated by the ACTOS flight height (assuming ACTOS was always flying at cloud top); while the cloud base was assessed from LiDAR measurements on the island. Although the measured cloud bases were quite constant during CARRIBA 2011, these were still uncertainties due to the spatial separation between the ACTOS and SMART-HELIOS measurements and the inhomogeneous nature of the cloud fields. Therefore, a reliable cloud height z could not be derived. Comparisons of retrieved and in situ measured reff are shown in Table 2 and Figure 12a and 12b. Figure 12a shows diurnal mean values of reff for each flight during CARRIBA 2011 from the in situ measurements by the PDI and the SBR, without applying the filters discussed in sections 3.1 and 3.2. While there seems to be reasonable agreement between the in situ and retrieval results before 20 April, differences of up to 5 μm are apparent during the later flights. Applying the filters described in section 3, the RRR significantly improves the agreement between retrieved and in situ gathered reff results, shown in Figure 12b. Except for the flight on 14 April both data sets agree within ±1 μm. Moreover, the RRR results are always closer to the in situ measurements, except for 14 and 22 April.

Figure 12.

(a) Diurnal mean effective droplet radius reff measured by the PDI on ACTOS (white circles) and from the SBR from radiation measurements on SMART-HELIOS (black dots) during CARRIBA 2011. (b) Same as Figure 12a, only with filtered data according to section 3 and the addition of reff from the RRR (grey dots).

[65] The comparison shows that the new RRR yields reliable estimates of reff and that both the filter techniques and the RRR improve on the standard SBR of inhomogeneous trade wind cumuli under an overlying cirrus.

6.2 Uncertainty Discussion

[66] The retrieval uncertainties highlighted in Table 3 were derived by performing two extra retrievals with the measurement uncertainties, described in section 2, accounted for as a positive and negative bias, respectively. Subsequently, the mean absolute uncertainty was calculated. Both the in situ and retrieval results of reff agree well within the respective measurement uncertainties. The retrieval of τ is apparently more accurate than the retrieval of reff. It is obvious that the RRR yields a reduced uncertainty in the retrieval of reff and in general yields comparable uncertainties in the retrieval of τ.

Table 3. Retrieval Uncertainties for the SBR and RRR of the Cumulus Optical Thickness τand Effective Droplet Radius reff
Flight±τ SBR±τ RRR±reff SBR(μm)±reff RRR(μm)
14 April2.
16 April4.
18 April0.
19 April1.
22 April1.
23 April1.
24 April2.
25 April1.

[67] It was shown in section 3 that 3D radiative effects were a huge contributor to the overall uncertainty of the math formula measurements. The photos in Figure 1are typical examples of the overall cloud situation, with a mixture of very inhomogeneous and more homogeneous clouds. Clouds at different times in their development have been sampled. Some were in the developing stages and quite convective, while others were already dissipating, creating instances such as the ones depicted at point 5 in Figure 1. While the filter methods described in sections 3.1 and 3.2 were applied to the complete data set, 3D effects were likely still influencing the measurements. Illuminated and shadowed cloud regions are possible biases in the math formula measurements. The issues can only be solved by 3D radiative transfer calculations. Considering the multitude of cumuli sampled during the CARRIBA 2011 campaign this can certainly only be done statistically via LES calculations.

[68] The promise of truly collocated measurements with the helicopter-borne measurement setup and two payloads can only be fulfilled partially. The position of the ACTOS payload relative to cloud top, as well as relative to the SMART-HELIOS payload, introduces uncertainties when comparing the results from both data sets. The sampled trade wind cumuli during CARRIBA 2011 had a vertical extent of about 300–700 m. The possibility of ACTOS being up to 140 m below cloud top, while SMART-HELIOS was measuring math formula reflected from cloud top, cannot be excluded. This introduces a significant bias when comparing reff, since the effective radius typically increases with cloud height (see, e.g., Reid et al. [1999]). The issue of vertical photon transport in remote sensing applications has been discussed by Platnick [2000]. This analysis shows that the maximum contribution to the retrieval of reff comes from approximately the upper 60 m of the cumuli and therefore the retrieved and in situ measured reff do not necessarily come from the same cloud height. These issues can only be solved by additional instrumentation, namely the addition of a small LiDAR installed on SMART-HELIOS to asses the distance from cloud top. The second issue with positioning regards the relative horizontal displacement of the ACTOS and SMART-HELIOS measurements. Different ACTOS positions in the photos in Figure 1are obvious (e.g., position at 1 and 3). The maximum displacement of the ACTOS payload from nadir was estimated to be in range of 20 m. The SMART-HELIOS measurements, that have been accounted for in the analysis, were all performed with ϑ<5 ° (see section 3.2), which yields a maximum displacement from nadir of 12 m (assuming SMART-HELIOS is 140 m above cloud top). Therefore, the ACTOS and SMART-HELIOS results might be displaced by up to 30 m. In section 3.2, the effect of the significant cloud inhomogeneity was shown by the different retrieval results for different ϑ. The issue of both payloads gathering data from different cloud parts can only be accounted for by averaging over a sufficient time span. This of course again influences the sampling statistics. It should be kept in mind that this measurement setup is still a huge improvement on classical aircraft measurements, where the in situ and radiation measurements are performed at different times.

[69] The effect of the surface albedo is mitigated by only accounting for the filtered data (see sections 3.1 and 3.2) and τ>2, but there might still be a bias from the different albedo spectra. The ocean albedo near the coast was visibly different from the ocean albedo further offshore. Sun glint was measured occasionally and when measurements were performed over the island, the multitude of different surfaces (e.g., grass, villages, agriculture) lead to more complex surface albedo spectra.

[70] Overall, the in situ measured reff and it is reasonable to conclude that the remaining uncertainties due to 3D radiative effects and ACTOS position within the cloud are negligible.

7 Summary and Conclusions

[71] The retrieval of trade wind cumulus properties under an overlying cirrus introduces a number of challenges. Not accounting for the high inhomogeneity of the shallow cumuli affects the retrieval of the cumulus optical thickness τ and the effective droplet radius reff significantly with biases in retrieved τ of up to 114% and biases of up to 27% in retrieved reff. These biases can be mitigated by applying a radiance-ratio filter to distinguish inhomogeneous cloud layers from more homogeneous ones. In a second step, the influence of the sensor zenith angle ϑ on the retrieval of τand reff was investigated by radiative transfer calculations. The model results show that for ϑ<5° and plane-parallel, horizontally homogeneous clouds the bias in the retrieval of τ and reff is <1%. For nearly all flights during CARRIBA 2011 ϑ<5° is met by at least 67% of data points. Furthermore, the resulting bias in the retrieved cloud properties due to the threshold ϑ<5° is mostly <4%. It is reasonable to assume that the filtered measurement data can be represented by horizontally homogeneous clouds and 1D calculations.

[72] Misrepresentation of an overlying cirrus in the standard bispectral retrieval (SBR) of optical and microphysical cumulus properties leads to errors of up to 7% for the τ, and up to 50% for reff. These differences increase with the cirrus optical thickness τci and additionally depend on the ice crystal scattering properties. A new radiance-ratio retrieval (RRR) approach using ratios math formula reduces the influence of measurement uncertainties, and allows for a reliable cloud property retrieval without a priori knowledge of the overlying cirrus. Specifically, the RRR reduces the overestimation of reff from up to 50% to less than 4% for τci = 0.5. For smaller τci, these errors may be reduced to 1% for τci = 0.2.

[73] Optimal wavelength pairs λ1 and λ2 for the RRR were systematically identified introducing the retrieval-sensitivity parameters sτ and sr. Remaining uncertainties exist due to remaining differences between ratios math formula under cirrus and non cirrus conditions. The threshold used in this work is a difference of <2%.

[74] The new RRR approach was applied to derive τ, reff, and the liquid water path LWP from helicopter-borne radiation measurements gathered during the CARRIBA 2011 campaign. Three different measurement flights under thin, overlying cirrus with different τci are presented in detail to highlight the effect on retrieved τand reff from the SBR and the RRR.

[75] The CARRIBA data exhibit the same overestimation in retrieved reff values, as well as underestimations in retrieved τ, that is observed in synthetic data produced by radiative transfer calculations. Different τci for these three cases influence the results from the SBR and yield deviations in mean retrieved reff of up to 17% (up to 2.4% in mean retrieved τ). The theoretically derived reduction of the retrieval uncertainty of the reff (up to 50%) can be achieved with the CARRIBA data.

[76] Deviations between the SBR and new RRR were subsequently used to derive τci estimates of the overlying cirrus during each case and frequency distributions of estimated τci give insight into cirrus inhomogeneities during each flight.

[77] The CARRIBA data exhibit a wide range of observed τ and reff, the latter both observed in the in situ and remote sensing data. Daily mean τ vary between 5–36, while observed reff vary between 7–18  μm. These wide ranges are mainly the result of different aerosol load and cloud top heights on the different flight days and exceed the uncertainty range due to the overlying cirrus.

[78] The retrieval results for reff were compared to collocated in situ measurements performed by a Phase Doppler Interferometer. Mean reff from the RRR and the in situ measurements are well within the respective measurement uncertainties. During most days, the agreement is in the range of ±1 (μm. Remaining discrepancies are attributed to remaining 3D radiative effects introduced by the inhomogeneity of the sampled trade wind cumuli and the difficulty in assessing the ACTOS position relative to cloud top. The latter issue will be addressed by a compact LiDAR system on SMART-HELIOS in future campaigns.


[79] The authors gratefully acknowledge Deutsche Forschungsgemeinschaft (DFG) for funding this project (SI 1534/3-1 and WE 1900/18-1). We thank D. Schell and C. Klaus from enviscope GmbH for their extensive support during the CARRIBA campaigns. We are also grateful to the pilots A. Vollmer, M. Kapetanovic, and P. Archer. Special thanks to the Max-Planck-Institute in Hamburg for providing LiDAR measurements on Barbados.