Uncertainty Characteristics of Total Water Path Retrievals in Shallow Cumulus Derived from Spaceborne Radar/Radiometer Integral Constraints
1. Introduction
Shallow cumulus cloud regimes are a ubiquitous feature of the subtropical atmosphere (Norris 1998). The low albedo of these regimes plays an important role in the radiative heating of the ocean and thereby in the regulation of ocean surface evaporation and the convergence of moisture into deep convective regions (Tiedtke 1989). Uncertainty in the response of the cloud feedback in this regime is largely responsible for the intermodel spread in the climate sensitivity (Bony and Dufresne 2005). Confidence in the predictions of the expected changes in the shallow cumulus regime must be predicated on an accurate model depiction of the current mean state of the regime.
Spaceborne observations offer the only globally representative dataset against which to evaluate the cloudiness in global models. However, remote sensing of the water budget of cumulus is a challenging endeavor. A requisite observation is the total water path (Wt), which is composed of a cloud (Wc) component and a precipitation (Wp) component. Standard methods for deriving Wc include passive optical and passive microwave techniques. A series of recent papers has identified large discrepancies between the two methods in regions dominated by cumulus clouds (Greenwald 2009; Seethala and Horváth 2010; Lebsock and Su 2014). Differences between the two methods in this regime are on the order of 100% and may arise due to several factors including but not limited to cloud detection errors in the optical methods, errors in the microwave emissivity and atmospheric opacity models, and ambiguity in the partitioning of the observed microwave signal between cloud and precipitation (Lebsock and Su 2014).
In addition to the passive techniques, observations from the CloudSat (Stephens et al. 2008) Cloud Profiling Radar (Tanelli et al. 2008) have provided profiles of cloud liquid water content (lc) that when integrated through depth provide the Wc (Austin and Stephens 2001). The liquid water content profiles from CloudSat have no doubt proved useful, and the continuation of this data record by the Earth Clouds, Aerosol and Radiation Explorer (EarthCARE; Illingworth et al. 2015) is essential. However, the liquid water content profiles are subject to several sources of error, including the misinterpretation of reflectivity from precipitation drops and the misdetection of hydrometeor layers (Christensen et al. 2013). Further sources of error include inaccurate assumptions regarding hydrometeor drop size distribution, which cause uncertainty in estimation of lc from the radar reflectivity (Z).
The use of observations that provide integral constraint on W has been exploited to add information to the radar-based water content retrieval algorithms with the goal of reducing bias in liquid water content retrievals. For example, the visible optical depth (τ) has been combined with the profile of Z to retrieve lc (Austin and Stephens 2001) and the path-integrated attenuation (PIA) has been used in combination with τ and the profile of Z to simultaneously estimate lc and lp (Lebsock and L’Ecuyer 2011). PIA is a useful constraint because it is approximately proportional to the mass of condensed water within the atmospheric column; however, its precision is fundamentally limited by radar sensitivity. In practice, this makes use of the PIA difficult in the case of nonprecipitating clouds with low water path and thus low signal-to-noise ratio. Optical depth is also a useful integral constraint because it is nearly insensitive to the precipitation drops, thus providing a constraint on the cloud component of the water path. However, retrievals of the optical depth are subject to several difficult biases in cumulus cloud regimes due to the impact of cloud spatial heterogeneity on three-dimensional radiative transfer (Cahalan et al. 1994; Várnai and Marshak 2002). Another potentially useful integral constraint could be provided by passive microwave brightness temperature (Tb), which is commonly used to retrieve Wc and Wp. Combinations of ground-based radar reflectivity and passive microwave brightness temperature have been used to simultaneously constrain Wc and a profile of lc (Dong and Mace 2003). Observations of Tb from the conically scanning Advanced Microwave Scanning Radiometer for EOS (AMSR-E) and its follow on (AMSR2) are coincident with CloudSat in the A-Train. However, exploitation of these Tb in combination with CloudSat has proven difficult due to large differences in instrument field of view (FOV) of the passive and active sensors.
The CloudSat project has pioneered the development of an experimental 94-GHz Tb by exploiting radar returns from cloud-free radar bins. The approach follows from the observation that the power received in cloud-free bins is the radar noise floor, which is proportional to the naturally emitted microwave Tb. Because CloudSat was not designed to act as a radiometer, careful calibration efforts were necessary to translate the received power into a physical Tb. This involved vicarious calibration against coincident 89-GHz Tb from the AMSR-E using carefully screened cloud-free pixels over well-characterized ocean surfaces in conjunction with radiative transfer modeling to translate the AMSR-E Tb to the CloudSat frequency and viewing geometry. The unique benefit of the CloudSat Tb is that it is precisely coincident with the radar reflectivity profile. The limitation of the CloudSat Tb is that it is subject to a precision of approximately 4 K on the pixel scale compared with 1.3 K for the AMSR-E on the 89-GHz channel (Kawanishi et al. 2003).
Over ocean surfaces, the CloudSat PIA is derived from the normalized radar surface cross section (σ0) by 
An example of the observed Z, σ0, and Tb from CloudSat is shown in Fig. 1. The scene is primarily composed of shallow cumulus clouds with some isolated precipitation and scattered cirrus. In pixels with significant condensed liquid water, associated increases in the observed Tb and decreases in the σ0 (increases in PIA) are observed. It is these signals that are sensitive to the integrated Wt, which are the subject of this study. Notice that the thin clouds that are not detected by the radar but are sensed by the lidar do not have a noticeable signal in either Tb or PIA. Also shown are the derived CWV and U10 from coincident AMSR-E observations using the version 6 algorithms of Remote Sensing Systems (Wentz 1997). The CWV contributes to the opacity of the atmosphere, while U10 affects the surface roughness and emissivity. The influence of these variables on the observed Tb and σ0 are subtle yet observable in the example shown. In general, their influence must be understood to derive information regarding Wt from either Tb or PIA.
An example of a primarily low-cloud, low-latitude scene from CloudSat orbit 13813. (a) The surrounding swath of MODIS 11-μm Tb. (b) The curtain of CloudSat radar reflectivity with gray areas indicating clouds detected by the CALIPSO lidar. (c) The CloudSat 94-GHz Tb. The black curve is at the native resolution, and the red curve has been smoothed with a five-pixel running mean. (d) The CloudSat normalized surface cross section σ0. (e),(f) The 100-m wind speed and CWV from AMSR-E.
Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0023.1
The observations of PIA from CloudSat have been useful as an estimate of the mean Wt over many samples; however, they are not sufficiently precise to perform pixel-scale retrievals. The purpose of this paper is to quantify errors (bias and precision) in the spatial interpolation method and to further estimate the effect of measurement precision in Tb and PIA on the retrieved Wt. The intent of the study is to influence the sensor design for next-generation cloud radars, such as the dual-frequency (W band/Ka band) scanning Doppler radar for an Aerosol–Cloud Ecosystems (ACE) mission recommended by the 2007 decadal survey (National Research Council 2007).
2. Models
a. Cloud model
A large-eddy simulation (LES) model (Matheou and Chung 2014) is coupled to a bin microphysical model (Suzuki et al. 2010) and used to produce a simulation of shallow precipitating cumulus. The simulated scenario is from the Rain in Cumulus over the Ocean (RICO) experiment (Rauber et al. 2007), using the composite atmospheric conditions outlined in vanZanten et al. (2011). Specifically, the heating profiles and soundings are the same as specified in Table 2 of vanZanten et al. (2011). This model scenario is an idealized composite of the observations during an undisturbed phase of the RICO field campaign. The makeup of cloud condensation nuclei (CCN) has a reference profile with an exponential decay scale height of 1 km and a surface value of 100 cm−3. The reference CCN size distribution follows a power-law size distribution (Junge 1955) with a −4 slope. The prognostic CCN is depleted via nucleation and replenished to the assumed reference profile and reference size spectra. Further details on the LES model used for simulations of RICO are found in Matheou et al. (2011). The domain size is 51.2 × 51.2 × 4 km3 with a spatial resolution of 100 × 100 × 40 m3. The bin microphysics scheme has 30 logarithmic bins in radius, spanning from 3 to 3000 μm.
Two important points can be made about the fidelity of the simulation and the application of instrument simulators. First, the bin microphysical scheme allows for realistic simulation of the natural variability in the observations caused by variations in the drop size distribution (DSD) that are not represented by a bulk microphysical scheme. Second, the relatively high spatial resolution of the simulation allows for the representation of the effects of heterogeneity in the field of view of the observations. This heterogeneity is referred to as nonuniform beamfilling (NUBF). Requisite assumptions related to these two factors are generally the largest sources of uncertainty in deriving cloud microphysical variables from radar reflectivity and/or passive radiometric observations.
The limitations of one realization of an LES in representing real cumulus clouds must be acknowledged. One idealized LES of undisturbed conditions should not be mistaken for being representative of cumulus clouds globally. Furthermore, the representation of NUBF effects is sensitive to the distribution of cloud horizontal sizes, which is limited by the LES resolution, domain size, and forcing conditions. To explore this limitation, we calculate the distribution of the square root of the cloud horizontal areas, which we term effective diameter. The distribution of effective diameter follows a double power-law distribution with a scale break observed between 400 and 600 m. The scaling exponent for the small clouds is −0.64 and for the large clouds it is −3.3. This behavior is in general agreement with observations (Cahalan and Joseph 1989); however, the LES scaling exponents are on the small and large sides of the average (Benner and Curry 1998). The 100-m resolution used here is relatively coarse for LES, and there is a clustering of clouds with horizontal scale at the model resolution. This scale is well below the scale of the instrument antenna patterns examined; however, the smallest scales of variability and their resultant NUBF are unresolved. Observations suggest that 50% of cloud coverage should come from clouds with chord lengths greater than about 10 km in shallow cumulus regimes (Wood and Field 2011). No clouds of this size are found in this LES, clearly demonstrating that the simulation of an unperturbed weather state does not represent the largest clouds observed in nature, which may be associated with perturbed conditions. We conclude that the results presented in this study carry the caveat that they are not necessarily representative of cumulus regimes globally. Nonetheless, the error sources explored herein will apply with varying magnitude in all cumulus regimes.
b. Radiation model
Water dielectric constant—The dielectric constants of liquid water are calculated using the parameterization described in Ray (1972). Salinity dependence is added following Klein and Swift (1977) for calculations of the sea surface optical constants.
Hydrometeor properties—The scattering and extinction properties of the hydrometeors at each model grid point are calculated from integration over the prognostic 30-bin DSD assuming spherical drops using Mie scattering theory (Bohren and Huffman 1983).
Gaseous properties—Gaseous absorption is treated using a variant of the Rosenkranz (1998) model, which is a modification of the Liebe et al. (1993) millimeter-wave propagation model.
Surface reflection—The
Radar propagation—Radar reflectivity is modeled using the time-dependent two-stream model (Hogan and Battaglia 2008). This model includes the single scattering contribution to the reflectivity and a two-stream approximation for the multiply scattered photons. However, the multiply scattered contribution is generally very small in the simulations examined here. Because this is a one-dimensional model, NUBF was accounted for in postprocessing as described in the next section.
Passive microwave propagation —Passive brightness temperatures were calculated using the two-stream Eddington approximation (Kummerow 1993). At the frequency considered here, the Eddington model is within 1.1 K of more complicated multistream models even in highly complex scattering atmospheres (Kummerow 1993).
c. Application of the radiation models to the cloud simulations
In this work one time step is analyzed from the last 10% of the LES integration to avoid the model spinup period prior to the model reaching a dynamically steady state. Profiles of thermodynamic variables were acquired from composite radiosonde observations launched from the Research Vessel Seward Johnson during the field campaign and added to the top of the LES domain to model attenuation by gasses above the model boundary. Minor scaling was required to avoid discontinuities in the thermodynamic profiles at the LES top boundary. We note that although the effect of adding gaseous attenuation above the boundary layer on the modeled reflectivities is nonnegligible, it is minor relative to the gaseous attenuation within the boundary layer.
The radiation models are applied to each column of the cloud simulations at the LES native resolution with a nadir view angle. The modeled reflectivities are then convolved with an idealized Gaussian antenna gain pattern with a 3-dB beamwidth of 1 km and a top-hat range resolution of 240 m to capture the effects of NUBF and variability in range at subresolution scales. This notional resolution is representative of current spaceborne radar capabilities and concepts. Experiments are also performed with a 3-dB beamwidth of 0.5 and 2 km to test the effect of horizontal resolution on NUBF. Unless otherwise noted, results refer to experiments with the 1-km beamwidth. Off-nadir view angles that would be provided by scanning radar are not explored here but are in principle not fundamentally different than a nadir-viewing geometry.
A key feature of the modeling framework is that the high spatial resolution of the LES and bin representation for microphysics allows for realistic representation of meteorological variability and microphysical variability that affect the relationships between the observations and the cloud microphysical parameters. In particular spatial variability introduces NUBF effects. Likewise, variability in the DSD introduces microphysical effects in the observations, which can be realistically modeled with a bin representation but not with a bulk representation of microphysics.
3. Results
a. Simulations
Figure 2 shows the simulated Wc and Wp from the LES along with the associated Tb and PIA. The scene is typical of precipitating cumulus, showing evidence of mesoscale organization, including cold pools with initiating convection at the outflow boundaries. The simulation is mostly cloud free, with a cloud cover fraction of 20%. The water path can be quite large, exceeding 1000 g m−2 even after convolution with the antenna gain pattern. However, the mean and median of the nonzero antenna-function-convolved Wt are 30 and 4 g m−2, respectively, showing that most cloudy pixels have a low water path. There is a clear association of Tb and PIA variability with the variability in cloud and precipitation. Variation of the Tb within the clear-sky region is also identifiable. Later it is shown that this variability is due to small-scale fluctuations in the column water vapor. There are hints of a saturation effect of the Tb above 280 K, whereas saturation is not apparent in the simulated PIA.
The modeled water path for cloud and precipitation, and the simulated Tb and PIA. The results are simulated at the models’ native resolution.
Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0023.1
Figure 3 shows a scatterplot of the simulated relationships between both Tb and PIA and Wt. Notice that there is natural variability in the simulated observations that is unrelated to the presence of Wt. This can be seen as the in scatter in Tb and PIA at Wt = 0 g m−2 that is caused by variation in the clear-sky CWV and U10. Additional scatter that results from variations in the hydrometer DSD is observed in the presence of clouds (nonzero Wt). The most linear relationship exists between PIA and Wt. The relationship between Tb and Wt is also fairly linear with a gradual saturation effect in the Tb signal that becomes evident as Wt increases. The nearly linear relationships of Wt with PIA and Tb are very well behaved up to reflectivity thresholds of 0 dBZ, showing little more scatter than is evident in the clear-sky CWV (i.e., Wt = 0). Above this reflectivity the pixels are associated with the largest Wp and enhanced extinction and emission from Mie behavior of large particles, which causes increased scatter in the Tb and PIA for a given Wt. This result demonstrates the fact that the ability of PIA or Tb to constrain Wt is conditioned on the presence of precipitation, which can in turn be identified and quantified via the profile of radar reflectivity.
The relationship between the total water path and (top) the PIA and (bottom) the 94-GHz Tb. Color denotes the magnitude of the precipitation component of the water path. Dashed and dotted curves represent the boundaries of the region that bounds 95% of the data for a given maximum reflectivity threshold. Notice how the area of this bounded region increases as the maximum reflectivity increases.
Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0023.1
b. Bias errors
The integral measures of PIA and Tb are potentially useful constraints for water content retrievals in shallow cumulus clouds. The utility of these integral constraints could be undermined by biases in misrepresenting the clear-sky contribution to these quantities. The clear-sky components of the Tb and PIA are a function of the CWV and U10 through its influence on the surface emissivity, and the SST. A retrieval of Wt from the observations necessitates estimating the clear-sky contribution to the observed signal. In partially cloudy cumulus scenes, the spatial interpolation method can be used to estimate the clear-sky signal via Eq. (1). In this method SST variations are expected to be minimal. Variations in U10 may in practice be large; however, they are negligible in the LES. However, there are two potential sources of uncertainty in estimating the clear-sky signal, which are discussed below: 1) misidentification of cloudy sky as clear sky and 2) systematic differences in the clear-sky and cloud-sky CWV.
The first source of bias derives from misidentification of cloudy sky as clear sky. With a radar system, the profile of reflectivity provides an explicit cloud screen subject to the minimum detectable signal of the radar. One can use cloud-free pixels (defined by the radar minimum detectable signal) to observe the clear-sky signal. To explore the effectiveness of this approach, the distribution of Tb is examined as a function of column maximum reflectivity. Figure 4 and Table 1 show the results. Table 2 shows analogous results for the PIA. The effect of increasing the radar minimum detectable signal on the estimated clear-sky signal is to bias the clear-sky estimate high, as pixels containing condensed water are misidentified as clear. Small biases (0.73 K or 0.071 dB) would be observed between the true clear-sky signal and that calculated from pixels with reflectivities below −30 dBZ. The magnitude of these biases is on the order of 5–10 g m−2 in Wt depending on the pixel-dependent sensitivity used to translate measurement error to retrieval error. It is worth noting that coincident lidar or visible reflectance observations could largely mitigate this bias entirely.
The probability distributions of the modeled 94-GHz Tb. The gray shaded distribution is for all pixels, whereas the other curves are conditioned on clear sky or various reflectivity thresholds. The dashed curve shows the cumulative distribution of Tb after weighting by the coincident water path. Note that most of the water mass is associated with Tb far larger than the clear-sky background.
Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0023.1
The mean and the standard deviation of the Tb of cloud-free pixels as determined by radar with various minimum detectable signals.
The mean and the standard deviation of the PIA of cloud-free pixels as determined by radar with various minimum detectable signals.
A second source of bias in estimation of the clear-sky signal is introduced through natural variations in the CWV. Because of these variations, there is natural variability in the clear-sky component of the Tb (Fig. 4) and PIA (not shown). Importantly, variability in CWV is not random but rather varies systematically with Wt (Fig. 5). The relationship between the CWV and the Tb is linear for clear sky with a slope of 1.5 K kg−1 m2. The analogous slope for the PIA is 0.15 dB kg−1 m2. It is evident in Fig. 5 that there is systematically greater CWV in cloudy sky than there is in clear sky. This systematic bias is quantified in Table 3 and is fairly consistent regardless of the radar minimum detectable signal. For a reflectivity threshold of −30 dBZ, the bias is 0.58 kg m−2, resulting in a 0.63-K or 0.063-dB bias in the cloudy-sky signal relative to the clear-sky signal. Interestingly, this CWV-related bias in the cloudy-sky signal approximately cancels the cloud misdetection bias of 5–10 g m−2 discussed above. The result is specific to this simulation, although to some extent the cancellation can be expected to occur more generally.
The scatter between the CWV and the modeled 94-GHz Tb. The red points represent the clear-sky pixels, and the green line is a linear fit to the clear-sky pixels with a slope of 1.5 K kg−1 m2.
Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0023.1
The mean differences between the clear-sky and cloud-sky CWV, and the associated bias in Tb and PIA for various radar minimum detectable signals.
Nonuniform beamfilling is a common source of bias error in cloud and precipitation remote sensing. NUBF results from nonlinearity in the radiative transfer that connects the observable parameter to the retrieval parameter. In this study an instrument antenna pattern with a 3-dB beamwidth of 1 km is considered, whereas the native spatial resolution of the model is 100 m. This resolution mismatch permits the exploration of the potential bias caused by NUBF. To estimate the NUBF bias, the mean relationship between Wt and each observable is calculated in 20 g m−2 bins. The mean curve for convolved observations and convolved Wt is then differenced from the analogous curve for the model native resolution. The difference between these two curves represents the average difference between a forward radar model that contains NUBF and one that considers a spatially homogenous pixel. Cloud retrievals frequently invert a spatially homogenous model; therefore, the difference between the two curves may be interpreted as the average NUBF bias caused by inverting a spatially homogenous model. The analysis procedure is repeated for beamwidths of 0.5 and 2 km. Results are shown in Fig. 6. Bias is essentially zero at Wt = 0 g m−2 and then increases monotonically with Wt. First consider the 1-km footprint. For PIA this bias increases linearly at a rate of approximately 0.5 dB per 100 g m−2, representing a potential 50% underestimate in Wt. The Tb bias, on the other hand, saturates at a value near 7 K, which would result in an approximate 30% underestimate in Wt. The footprint size has a substantial influence on the NUBF. For example reducing the footprint size to 0.5 km reduces NUBF by about 30% and increasing the footprint to 2 km increases NUBF by 10%–20%. Note that the large values of Wt are scarce as the footprint size increases to 2 km. These biases are significant relative to the biases, resulting from cloud detection and water vapor bias. Radiative transfer models that include the effects of NUBF appear necessary to mitigate retrieval bias in Wt retrievals using these integral constraints, particularly in precipitating situations. Importantly, this is true even for the relatively high-resolution observation footprint of 1 km considered here.
The bias in the relationship between the total water path and Tb and PIA. Bias is defined as the observation convolved with the antenna function minus the observation at the native model resolution. Bias curves are calculated by subtracting the mean curves for each resolution. The three curves correspond to different 3-dB footprint sizes.
Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0023.1
c. Precision error
(a) The sensitivity of the Tb calculated with a 2% perturbation of the total water path. (b) The standard deviation of Tb for a given total water path. The (c) absolute and (d) relative uncertainties in the derived water path for various measurement uncertainties (δTb) calculated using Eq. (2). (e)–(h) As in (a)–(d), but for the PIA.
Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0023.1
The expected 1σ uncertainty for Wt at about Wt = 10 g m−2 as a function of measurement uncertainty in (a) Tb and (b) surface cross section σ0. The blue arrows represent the lower bound in uncertainty, which is limited by the natural variability in the observables, caused by small-scale variation in water vapor and surface emissivity. The red arrows indicate the performance of the CloudSat measurements.
Citation: Journal of Atmospheric and Oceanic Technology 33, 8; 10.1175/JTECH-D-16-0023.1
Recall that a typical value of Wt for these simulated cumuli is 30 g m−2. For Wt at and below this typical value, the uncertainty in the observations begins to dominate the uncertainty due to natural variability. Figure 8 further examines the retrieval uncertainty for low values of Wt by specifically showing errors at Wt = 10 g m−2. In this figure it is evident that Wt cannot be retrieved to a precision much better than ~10 g m−2 regardless of instrument precision because of the natural variability in the observables. Approaching this retrieval precision requires a measurement precision of 0.3 K or 0.05 dB. In contrast, the CloudSat observation of PIA and Tb provide precision in Wt of approximately 20 and 50 g m−2, respectively, at low Wt.
4. Summary and discussion
Models of passive microwave brightness temperature and radar reflectivity were applied to an LES of shallow precipitating cumulus clouds to simulate spaceborne observations from a nadir-pointing 94-GHz radar/radiometer system. The LES permits realistic simulation of effects that often confound cloud and precipitation remote sensing, including subfield-of-view heterogeneity and microphysical variability in the hydrometeor drop size distribution. Simulated observables included the radar reflectivity, the path-integrated attenuation, and the microwave brightness temperature.
The goal of the study was to demonstrate the uncertainty characteristics of integral constraints from CloudSat or any other 94-GHz radar/radiometer on retrievals of the total water path. The integral constraints of the PIA and Tb are shown to be approximately linear with Wt. However, there is scatter in the relationships of the observables with Wt, which introduces uncertainty in the constraint. A method to derive Wt using interpolation of the clear-sky signal into the cloudy-sky pixels is considered as a basis for the uncertainty characterization.
Three sources of bias error are considered. The first is bias resulting from the misidentification of cloudy sky as clear sky, which results in errors on the order of 5–10 g m−2 for a minimum radar detectable signal of −30 dBZ. A second source of bias results from systematic differences in the cloudy- and clear-sky column water vapor, which also causes biases on the order of 5–10 g m−2, for a minimum radar detectable signal of −30 dBZ. These first two biases tend to be of opposite signs and approximately cancel in this simulation. The third and potentially largest source of bias results from NUBF. This bias increases monotonically with increasing Wt up to values of 7 K and 3 dB at 600 g m−2. This behavior is expected to be quite general to shallow cumulus scenes. The associated retrieval bias approaches 50% at these large values of Wt. The potential NUBF biases would result in an underprediction of the Wt. NUBF is significantly affected by the instrument footprint. Halving the footprint reduces NUBF by approximately 30%, whereas doubling the footprint increases NUBF by 10%–20%.
All of these potential biases might be mitigated to some extent. For example, coincident observations from a visible wavelength instrument might provide more robust cloud screening than radar would provide. Also, an analytical formulation for the spatial distribution of water vapor like those used in model parameterization would provide an estimate of the expected difference in CWV between cloudy- and clear-sky pixels. Finally, subfield-of-view heterogeneity might be parameterized in the forward radiative operator to mitigate NUBF effects.
Precision errors were considered in addition to bias errors. An analysis was performed to estimate the uncertainty in Wt for various measurement precisions in Tb and PIA. For Wt greater than 100 g m−2, a precision of 1 K or 0.16 dB is sufficient to constrain the Wt to within 30%. For low values of Wt, much greater instrument precision is required. At Wt = 10 g m−2 a precision of 0.3 K or 0.05 dB is recommended to constrain Wt to within 100%. Retrieval precision for Wt exceeding the larger of either 10 g m−2 or 30% is not likely possible due to natural variations in the Tb and PIA resulting from variance in the column water vapor. Precision is negligibly sensitive to the instrument footprint, which suggests that variability in the drop size distribution is the primary source of precision error.
It is emphasized that the uncertainty analysis is specific to the simulation of precipitating shallow cumuli considered in this study. Errors of the type reported here will exist generally; however, the magnitudes may differ with changes in cloud regime. In particular, the spatial and microphysical variability are expected to be smaller in nonprecipitating cumuli, and it follows that errors in nonprecipitating scenes will be reduced accordingly. Errors reported here should be considered an upper bound.
The potential information content and resultant uncertainty characteristics of the PIA and Tb are essentially similar and correlated for the constraint of cumulus water paths. In the case of CloudSat, this parity is not realized because the PIA precision of 0.16 dB is relatively greater than the 4-K precision of Tb. This is a natural result for an instrument that was designed to maximize radar sensitivity as opposed to radiometric precision. It is, however, feasible to imagine a design of a spaceborne cloud radar/radiometer in which the situation is reversed. Passive radiometric precision might be increased a great deal relative to that of CloudSat by increasing the spectral bandwidth of the observed radiation, thereby increasing the signal-to-noise ratio. The challenge is doing so in a careful manner that does not compromise the radar noise floor. Designing high-precision radiometric channels for combined radar/radiometer systems represents a design challenge for the next generation of spaceborne cloud radars.
Acknowledgments
The research described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration and was partially funded by the CloudSat project and the Aerosol–Cloud Ecosystems (ACE) project.
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