airborne radiometric observations of cloud liquid-water emission at 89 and 157 ghz: application to...

24
QUARTERLY JOURNAL ROYAL METEOROLOGICAL SOCIETY OF THE ~~ ~~ VOl. 121 OCTOBER 1995 Part A No. 527 Q. J. R. Meteorol. SOC. (199S), 121, pp. 1501-1524 Airborne radiometric observations of cloud liquid-water emission at 89 and 157 GHz: Application to retrieval of liquid-water path By S. J. ENGLISH* Meteorological Ofice, UK (Received 29 September 1994; revised 27 March 1995) SUMMARY Measurements of the microwave brightness temperature of stratocumulus cloud at 89 and 157 GHz using the Microwave Airborne Radiometer Scanning System on the UK Meteorological Research Flight's C-130 aircraft have been analysed. Comparisons of observed and calculated brightness temperature using models available in the literature have given good agreement for sea-surface emission and atmospheric attenuation in clear and cloudy skies. A nonlinear retrieval scheme has been applied to the observations to retrieve cloud liquid-water paths for comparison with the in situ measurements. Validation of the retrieved liquid-water paths to within SO g m-2 has been achieved. Ambiguities between cloud retrievals and water vapour and surface parameters are discussed. The observed differences between the retrieval and the in situ measurement are not found to correlate strongly with cloud temperature, but a higher than expected correlation is found with the drop-size distribution. It is demonstrated that the scheme is applicable to satellite soundings of cloud, and that a similar level of accuracy should be achieved. KEYWORDS: Airborne observations Cloud liquid water Microwave radiometry Remote-sensing retrieval Satellite sounding 1. INTRODUCTION Since 1978 a passive microwave radiometer, the Microwave Sounding Unit (MSU), has been operating on the NOAAt polar orbiting platform as part of the TOVS (TIROS' Operational Vertical Sounder) suite. The MSU was designed to provide a limited back up to the infrared instruments for temperature sounding in the presence of cloud by taking advantage of the low absorption of clouds below 60 GHz. In the mid-1990s a major upgrade of the microwave sounding capability will take place with the introduction of the Advanced Microwave Sounding Unit (AMSU). The AMSU will comprise a temperature sounder (AMSU-A) and a humidity sounder (AMSU-B) whose channel details are listed in Table 1. In addition to the sounding channels there are window channels at 23.8,31 and 50.3 GHz on AMSU-A and 89 and 150 GHz on AMSU-B. The purpose of the window channels is to identify fields of view contaminated by precipitation and, in the absence of very dense or precipitating clouds, to retrieve cloud and surface parameters. If maximum advantage is to be obtained from the new technology an improved understanding of the radiative transfer is required, particularly for the new AMSU-B instrument. Measurements of non-resonant gaseous absorption, cloud absorption and sea-surface reflectance are required. * Corresponding address: Remote Sensing Instrumentation, Meteorological Office, Building Y70, D.R.A., Farn- borough, Hampshire GU14 6TD, UK. * Television Infra-Red Observation Satellite National Oceanic and Atmospheric Administration 1501

Upload: s-j-english

Post on 06-Jul-2016

225 views

Category:

Documents


0 download

TRANSCRIPT

Q U A R T E R L Y J O U R N A L

R O Y A L M E T E O R O L O G I C A L S O C I E T Y O F T H E

~~ ~~

VOl. 121 OCTOBER 1995 Part A No. 527

Q. J. R. Meteorol. SOC. (199S), 121, pp. 1501-1524

Airborne radiometric observations of cloud liquid-water emission at 89 and 157 GHz: Application to retrieval of liquid-water path

By S. J. ENGLISH* Meteorological Ofice, UK

(Received 29 September 1994; revised 27 March 1995)

SUMMARY Measurements of the microwave brightness temperature of stratocumulus cloud at 89 and 157 GHz using the

Microwave Airborne Radiometer Scanning System on the UK Meteorological Research Flight's C-130 aircraft have been analysed. Comparisons of observed and calculated brightness temperature using models available in the literature have given good agreement for sea-surface emission and atmospheric attenuation in clear and cloudy skies. A nonlinear retrieval scheme has been applied to the observations to retrieve cloud liquid-water paths for comparison with the in situ measurements. Validation of the retrieved liquid-water paths to within SO g m-2 has been achieved. Ambiguities between cloud retrievals and water vapour and surface parameters are discussed. The observed differences between the retrieval and the in situ measurement are not found to correlate strongly with cloud temperature, but a higher than expected correlation is found with the drop-size distribution. It is demonstrated that the scheme is applicable to satellite soundings of cloud, and that a similar level of accuracy should be achieved.

KEYWORDS: Airborne observations Cloud liquid water Microwave radiometry Remote-sensing retrieval Satellite sounding

1. INTRODUCTION

Since 1978 a passive microwave radiometer, the Microwave Sounding Unit (MSU), has been operating on the NOAAt polar orbiting platform as part of the TOVS (TIROS' Operational Vertical Sounder) suite. The MSU was designed to provide a limited back up to the infrared instruments for temperature sounding in the presence of cloud by taking advantage of the low absorption of clouds below 60 GHz. In the mid-1990s a major upgrade of the microwave sounding capability will take place with the introduction of the Advanced Microwave Sounding Unit (AMSU). The AMSU will comprise a temperature sounder (AMSU-A) and a humidity sounder (AMSU-B) whose channel details are listed in Table 1. In addition to the sounding channels there are window channels at 23.8,31 and 50.3 GHz on AMSU-A and 89 and 150 GHz on AMSU-B. The purpose of the window channels is to identify fields of view contaminated by precipitation and, in the absence of very dense or precipitating clouds, to retrieve cloud and surface parameters. If maximum advantage is to be obtained from the new technology an improved understanding of the radiative transfer is required, particularly for the new AMSU-B instrument. Measurements of non-resonant gaseous absorption, cloud absorption and sea-surface reflectance are required. * Corresponding address: Remote Sensing Instrumentation, Meteorological Office, Building Y70, D.R.A., Farn- borough, Hampshire GU14 6TD, UK.

* Television Infra-Red Observation Satellite National Oceanic and Atmospheric Administration

1501

1502 S. J. ENGLISH

TABLE 1 . AMSU CHANNEL CHARACTERISTICS BASED ON ACTUAL INSTRUMENT BUILD FROM THERMAL-VAC DATA (TAKEN FROM SAUNDERS et al. 1994)

Channel Centre frequency No. of number of channel pass Bandwidth Polarization

designation ( G W bands (MHz) angle?

AMSU-A2 1 23.8 f 0.0725 2 125 90 - 6 2 31.4 f 0.050 2 80 90 - e

AMSU-A1 3 50.3 f 0.050 2 80 90 - e 4 52.8 f 0.105 2 190 90 - 0 5 53.596 f 0.115 2 170 e 6 54.40 f 0.105 2 190 e 7 54.94 f 0.105 2 190 90 - 8 8 55.50 f 0.0875 2 155 e 9 ~1 f 0.0875 2 155 e

10 ~1 f 0.217 2 78 e 11 UI f 0.3222 f 0.048 4 36 e 12 ~1 f 0.3222 f 0.022 4 16 e 13 UI f 0.3222 f 0.010 4 8 e 14 ~1 f 0.3222 f 0.0045 4 3 0 15 89.0 f 1.0 2 1000 90 - e

AMSU-B 16 89.0 f 0.9 2 1000 90 - 0 17 150.0 & 0.9 2 1000 90 - e 18 183.31 f 1.00 2 500 90 - e 19 183.31 f 3.00 2 lo00 90 - e 20 183.31 f 7.00 2 2000 90 - 9

Values for AMSU-A1 are from the engineering model, and for AMSU-A2 and AMSU-B from first flight models.

t The polarization angle is defined as the angle from horizontal polarization (i.e. electric field vector parallel to satellite track) where 0 is the scan angle from nadir.

UI = 57.290 344 GHz.

The UK Meteorological Office has procured and operated a dual-frequency radi- ometer on a C-130 aircraft since 1990. The Microwave Airborne Radiometer Scanning System (MARSS) has channels at 89 and 157GHz, close to the AMSU-B windows at 89 and 150 GHz. The MARSS has flown on over 130 sorties of between 3 and 10 hours duration collecting data over open sea, sea ice and land for a wide variety of weather conditions. These data have been used to validate available models of sea-surface emissivity (Guillou et al. 1995) and the results led to the selection of Liebe (1989a) as the best available gaseous-absorption model (English et al. 1994). Guillou et al. (1995) found that a simple geometric sea-surface emissivity model using the Cox and Munk (1955) roughness spectrum gave an overall bias of less than 1 K for both channels. It was found, however, that the surface model did tend to underestimate the surface emission, especially at high sea surface temperature, and the possible effect of this on liquid-water path (LWP) retrievals is investigated. English et al. showed the Liebe (1989a) model to give brightness temperatures for the near zenith view of within 2-3 K for most atmospheres but larger departures were observed for very moist or very dry atmospheres. In this paper, detailed comparisons are presented of a retrieved LWP product from the MARSS with in situ measurements from the C-130’s cloud microphysics instrumentation. The retrieval of LWP is currently restricted to

CLOUD LIQUID-WATER-PATH RETRIEVAL 1503

cases over the open sea. It is assumed that there are no ice particles or that the ice particles present have no radiative significance, a valid assumption for the cases studied. Generally ice can occur in stratocumulus, but these ice crystals are not of radiative importance at these frequencies. The retrieval scheme is tested using aircraft data, as this supplies the closest matching of radiometer data with in situ data. However, the scheme can readily be extended to satellite-based retrievals. This is considered in the discussion.

2. AIRCRAIT INSTRUMENTATION

The MARSS radiometer is fully described by Jones (1991). In 1992 and 1994 slight upgrades were made to the radiometer and these are described by Guillou et al. (1995). In brief, it is a two-channel radiometer operating at 89 and 157 GHz measuring a single polarization which rotates with view angle. At the nominal nadir position the radiometer views close to horizontal polarization. Recently the 157 GHz channel has had a polar- izer added which rotates the vector through about 45". Using this polarizer the 157 GHz polarization varies from horizontal in the backward view to vertical in the forward view. By rotating the polarizer in the other direction, the polarization can be made to go from vertical to horizontal. During each scanning cycle, which takes just under 3 seconds, nine upward views, nine downward views and two calibration targets are observed. The nine views are nominally at intervals of lo" from -40" to +40" viewing along track. The cali- bration uses a hot target (at 334 K) and a cold target which is allowed to remain at ambient temperature (230-300 K). The radiometer is calibrated linearly in temperature such that the definition of brightness temperature given by Stogryn (1975) is used. When flying in cloud it is possible that liquid water may collect on the reflecting mirror although no conclusive evidence of this was observed. In any case runs in cloud and runs immediately after leaving cloud are rejected.

The C-130's instrumentation is able to measure all parameters of importance to the radiative environment for comparison with the observed brightness temperatures. Wind speed is calculated using an inertial navigation system calibrated using the Global Positioning System (Offiler et al. 1994). The surface wind speed can then be calculated using a boundary-layer model (Ezraty 1985). The surface skin temperature is measured using a PRT-4 infrared radiometer which is accurate to about 0.3 K. Cloud liquid-water content (LWC) is measured by a Johnson-Williams (JW) hot-wire probe. This requires some interactive calibration to remove the effects of icing and residual water on the sensor (Moss et al. 1993). The JW probe is inefficient at collecting large droplets (radii greater than 30 pm). The error in estimation of the LWC arising from this can be approximately quantified using a modified 'Cl' cloud droplet distribution (Deirmendjian 1969). For a cloud with effective radius, re, less than 12 pm, droplets with radii greater than 30 p m have a negligible contribution to the LWP. The contribution of droplets with radii greater than 30 pm rises to 2% at re = 15 p m and 11% at re = 19 pm. The LWC can also be estimated from drop-size counters: the C-130 has an FSSP (Forward Scattering Spectrometer Probe) to measure small droplets and a 2-dimensional laser shadowing instrument (the '2DC') to measure large droplets. The JW probe is believed to give a more representative LWC than integrating the drop-size distribution from the FSSP and the 2DC. These instruments can, however, give an indication of the presence of large droplets likely to be missed by the JW probe. In addition, a further measure of the cloud microphysics can be obtained from the effective-radius retrieval (Taylor 1993) from the combined visible and infrared multi-channel radiometer on the aircraft. The in situ LWP is estimated by integrating the LWC against height during an aircraft profile through cloud.

1504 S. J. ENGLISH

3. THE RADIATIVE-TRANSFER MODEL

The gaseous-absorption model was validated in clear-air conditions using upward views. The observations were compared with various empirical models by English et al. (1994) and the best agreement was given by the model of Liebe (1989a) except for very moist and very dry atmospheres. Liebe’s model is used for all gaseous absorption in this paper.

The microwave emissivity of the surface depends on surface type, frequency and viewing geometry. A geometric sea-surface emissivity model using a Gaussian slope dis- tribution (Cox and Monk 1955) is used to represent emission from the wind-roughened ocean. Only one scale of roughness is considered, such that the reflection from each facet can be written in terms of Fresnel reflection coefficients, following Wilheit (1979). The dielectric model of Klein and Swift (1977) is adopted. The Gaussian facet-slope distribu- tion depends on the surface-stress vector which can be related to a wind speed at a standard height (e.g. 12.5 m). At an incidence angle of 53” the emissivity depends more strongly on wind speed for horizontal than for vertical polarization. Wentz et al. (1986) and others have shown that it is possible to retrieve the surface wind speed and the surface tempera- tGe from the dual polarized Special Sensor Microwaveflmager (SSMD). However, for the AMSU only a single polarization is measured, and this is a mix of vertical and horizontal polarization dependent on view angle. For a single-polarization radiometer there is less information to retrieve wind speed, and it is unlikely that these retrievals will be as useful as those from a dual-polarized radiometer. However, it is still necessary to parametrize the surface correctly. Wentz (1992) has also shown that the bidirectional nature of the sea-slope roughness gives a weak wind-direction dependence. This effect is neglected in this paper.

For liquid clouds the scattering coefficient is negligible so the total extinction coef- ficient K,, x K , (the Rayleigh absorption coefficient). The extinction can then be calcu- lated using the Rayleigh approximation. At frequencies above 100 GHz the accuracy of the Rayleigh approximation can be in error by several per cent for large droplets (2% for an effective radius of 20 p m at 157 GHz). This is a smaller error than the inefficiency in the collection for large droplets by the JW probe. Both would give an overestimate of the retrieved cloud with respect to the JW probe.

We can calculate the dielectric constant using a single-Debye relation (Ray 1972) or a double-Debye relation (Liebe 1989b), the latter being more appropriate for high-frequency calculations. The sensitivity to choice of dielectric model is discussed in section 6. In this paper we compare Grody’s (1993) algorithm to the observations, Grody’s algorithm for cloud absorption fits Ray’s (1972) dielectric formula for the Rayleigh approximation such that the dimensionless optical depth, a, is given by:

C 0 . 0 2 4 1 ~ ~ ~ 0 ( T )

a = u2 + uo(T)2

where uo(T) = 160 exp {7.2(1 - 287/T)}, C is the cloud LWP in millimetres (1 mm = 1000 g m-’ = 0.1 g cm-’), T is temperature in K, and u is frequency in GHz. The relax- ation frequency, uo(T), is between 100 and 140 GHz at temperatures of 270-285 K. As a result the temperature dependence of the optical depth is different at 89 and 157 GHz.

The radiative-transfer equation is solved for a non-scattering atmosphere using microwave brightness temperature as defined by Stogryn (1975) as the radiative vari- able. The atmosphere is divided into 40 levels. These 40 pressure levels are not fixed but are optimized for each profile (see English et al. 1994). Each level is determined such that all significant changes in the temperature and water-vapour profiles are represented.

CLOUD LIQUID-WATER-PATH RETRIEVAL 1505

4. THE RETRIEVAL METHOD

Newtonian iteration is used for the retrieval scheme following Rodgers (1976). In general an optimum solution can be found using this method for weakly nonlinear cases. The n + lth guess can be calculated from the nth guess and the background, G.

xn+1 - xo = WnIY - Y n - Kn(xo - (2) where W, = SK:(K,SK: + E + F)-l, K,, = dy,/dx,, x , + ~ is the solution on then + lth iteration, x, is the solution on the nth iteration, xo is the apriori information vector, S is the error covariance matrix of the background field, y is the observed brightness-temperature vector, yn is the calculated brightness-temperature vector on the nth iteration, E is the error covariance matrix of the observations, F is the error covariance matrix of the forward model, and superscript T denotes transpose.

If the model is linear then the solution can be found in one step. For weakly nonlinear cases the derivative matrix, K, has to be recalculated at each step in the iteration. The value of x,,~ - x, is a suitable convergence criterion.

The covariance of the solution is given by Rodgers (1976) for the converged solution as

where K is evaluated for the final value of S. The appropriate value of S depends on whether we have prior knowledge about the clouds being observed. With no apriori knowledge the diagonal term of S would have to be set large enough to represent the whole population of clouds. For both aircraft and satellite retrievals of cloud the maximum cloud amount for which retrievals are possible depends on the water-vapour burden (WVB) and to a lesser extent temperature. It also depends on the range of channels. Low-frequency channels are less sensitive to cloud and can, therefore, make measurements through deeper cloud than high-frequency channels. For the MARSS instrument it is possible to retrieve LWPs up to 1000 g m-2 (for very dry atmospheres) though more generally the LWPs will become unreliable above 500 g m-2. For cloud with LWP greater than 500 g m-2 the radiative- transfer model becomes highly nonlinear as the channels lose sensitivity. If we view cloud with a true LWP of 1000 g m-2, then the uncertainty on the solution will be 850 g m-2 (for nadir view) assuming a background uncertainty of 1000 g m-2. This shows there is little information available when the cloud becomes this deep (2 km assuming LWC = 1 g m-3 at cloud top). There are very few sources of apriori data to initiate the iteration. In this study the apriori consists of initially assuming all areas to be cloud free, with an uncertainty on the cloud of 250 g mP2. The retrieval scheme then fits the cloud to the observed brightness temperatures. The uncertainty on the solution from Eq. (3) , using h4ARSS data, is then calculated to be 30-50 g mP2 depending on WVB and LWP.

The MARSS radiometer only has two window channels and is therefore limited in its ability to retrieve many variables. For this experiment the cloud LWP is the only free parameter for upward views and the background is taken as being zero cloud with an error variance of 250 g mP2 (i.e. it is assumed thin stratocumulus is being observed). The temperature and water-vapour profiles measured by the aircraft are used and are not allowed to change during the retrieval. The cloud is distributed between a cloud top and cloud base. The choice of cloud top and base can be made carefully using observations from the profile through cloud. In the absence of a valid cloud top or base a useful retrieval is still possible for runs above or below cloud if all the cloud is assumed to be in the lowest 3 km of the atmosphere. The impact of errors in cloud top or cloud base were investigated, and inaccurate placing of the cloud increased or decreased the cloud retrieval by no more than f12%.

s,=, = (s + K ~ ( E + F ) - ~ K ) - ~ ( 3 )

1506 S. J. ENGLISH

For downward views the cloud liquid water in the path from the aircraft to the surface, and the surface wind speed are the free parameters. The sea surface temperature measured by the C-130’s PRT-4 infrared radiometer whilst flying at a height of 30 m is used and is a constant in the retrieval scheme. Non-diagonal terms in the covariance matrix are neglected, and the diagonal terms are set to 250 g m-2 for cloud and 5 m s-l for wind speed. The cloud LWP along the reflected paths is constrained to be equal to the sum of the cloud viewed above the aircraft and that viewed between the aircraft and the surface. The background nadir cloud is also taken to be zero, and a background wind speed is used equal to that measured at the base of the aircraft profile.

These constraints are appropriate for thin stratocumulus cloud and for a reasonable background wind speed. The amount of information available for wind-speed retrievals using these two channels is very small. However, by allowing wind speed to vary in the retrieval it should be possible to distinguish between changes in wind speed and changes in cloud. The scheme is, however, primarily designed for the retrieval of a realistic cloud LWP.

If the scheme is extended to satellite data then the temperature and water-vapour profiles would also be retrieved. This requires numerical weather prediction (NWP) to provide an a priori data product (e.g. Prigent 1994). In this case S is the error covariance of the forecast-model variables. Again the uncertainty on the solution can be calculated using Eq. (3). The uncertainty on the solution is also about 50 g ma2 using this scheme for satellite-based retrievals. For satellite soundings a cloud top can be inferred from other satellite instruments (e.g. AVHRR*, HIRSt) in the absence of higher cloud. For the AMSU or SSMD, which have lower-frequency channels than the MARSS, L W s up to 4000 g m-2 can potentially be retrieved. In practice, cloud with such high water content would never fully fill the field of view of these instruments.

Similar iterative schemes have been used by Prigent (1994) on SSMA data and by Peter (1994) on ground-based radiometric data from 23.87 to 54.95 GHz. Prigent showed it was possible to retrieve integrated water-vapour content, surface wind speed and LWP from the SSM/I channels and compared the results with a number of statistical algorithms. Good agreement was achieved for wind speed and water-vapour content, and the Weng and Grody (1994) scheme gave reasonable agreement for L W . Prigent emphasized that the iterative nonlinear approach is similar to the assimilation scheme for NWP models and the scheme is initiated with N W P data. This approach is consistent with the aim of direct assimilation of satellite radiances into N W P models. Peter’s results showed that a multifrequency ground-based radiometer can retrieve integrated water vapour to a standard deviation of 0.5 kg m-2 and a bias of just 0.2 kg m-’, but that L W can only be retrieved to a standard deviation of 60-80 g m-2 and a bias of 10-20 g m-2 (Note: throughout this paper we express cloud LWP in g m-’ and WVB in kg m-’)). It can be observed that the standard deviations found by Peter are slightly higher than the uncertainty predicted by Eq. (3). Peter and Prigent both included precipitation in their retrievals. In this paper it is assumed that a preprocessing scheme has removed precipitating systems with the exception of light drizzle from stratocumulus.

5. CASE STUDIES

It can be seen from the discussion in section 4 that the optimum type of cloud for verifying the retrieval scheme and the cloud model is homogeneous stratocumulus of

* Advanced Very High Resolution Radiometer High-resolution Infra-Red Sounder

CLOUD LIQUID-WATER-PATH RETRIEVAL 1507

LWC 50-250 g m-'. Some inhomogeneous cases may still be useful if there is a very good match between the C-130 flight path above or below the cloud and the location of the profile through the cloud. Alternatively, the variability of the measured cloud during a run in cloud can be taken as representative of the variability through the whole depth of the cloud and the results compared.

The case studies used are taken from the Atlantic Stratocumulus Transition Experi- ment (ASTEX) based in the Azores during June 1992 (Albrecht 1993), the First ATSR (Along-Track Scanning Radiometer) Tropical Experiment (FATE) based at Ascension island in November 1991, one flight over the Gulf of Bothnia during the Surface and Atmospheric Airborne Microwave Experiment (SAAMEX) (from March 1990), and sev- eral around the British Isles. During these experiments the MARSS had two roles: firstly to be able to observe the variability of the stratocumulus at night; and secondly, the main pur- pose, to measure the microwave radiative properties of stratocumulus in the homogeneous cloud. The varying locations have provided examples of cloud with varying temperature, altitude and drop-size distribution. A series of straight and level runs of about ten minutes duration are flown below, in, and above the cloud. Before each set of level runs a profile is flown at an ascent or descent rate of 2.5 m s-'. Occasionally additional orbit runs are included at the end of the straight and level runs. These are runs where the aircraft holds a constant bank of between 30" and 45", thus flying a circle (diameter 1-2 km) over the same area of cloud.

(a) ASTEX During the ASTEX the h4ARSS was operated on 14 of the C-130's 16 sorties and

collected about 100 hours of data flying below, in, and above the stratocumulus. This experiment was primarily designed to study the breakup of stratocumulus on the edge of an extensive stratocumulus sheet during the diurnal cycle. Detailed study was made of the diurnal cycle of stratocumulus which was not previously well represented in numerical models (e.g. Albrecht ef al. 1995). North-easterly winds on the eastern side of the Azores high periodically bring large amounts of aerosol from continental Europe, increasing the cloud-condensation-nuclei population and substantially modifying the stratocumulus. The stratocumulus varied from a maritime type with large droplets and occasional drizzle, large effective radius (Taylor 1993) and low droplet-number concentrations, to a continental type with high droplet-number concentrations, small droplets and no drizzle. The cloud also varied from homogeneous layer stratocumulus where the droplet size and LWC increase from the base of the cloud to the top, to a cumuliform type where mixing gives a more homogeneous vertical profile of both LWC and droplet size. By the nature of the experiment the cloud was often not ideal for validating radiative-transfer code but it did have the advantage that by careful monitoring the temporal and spatial variability of the cloud was known. Six flights from the ASTEX provided adequate conditions for model validation. These are listed in Table 2.

Figure 1 shows two vertical profiles of LWC plotted against pressure height for flight A209. It can be observed that the L W from the two profiles is very different (100 g m-2, 200 g m-'). Although the stratocumulus cloud used in this study is fairly homogeneous it still displays natural variability, and the radiometer data (from straight and level runs) has to be carefully matched to the appropriate aircraft profile through the cloud. The run mean LWC from the straight and level runs between the profiles are used to check the match. In Fig. 1 it can be observed that for the ASTEX flight A209 the run means follow profile 2 better than profile 3. Also the cloud top for profile 3 is nearly 100 m higher than profile 2, the latter being consistent with that observed during the vertical stack of straight and level runs. Figure 1 thereby shows that profile 2 is more representative for this stack of runs.

1508 S. J. ENGLISH

TABLE 2. RUNS USED FROM THE ASTEX CAMPAIGN

Flight

A203 A204 A205 A205 A206 A208 A209 A209

Date

1 June 1992 2 June 1992 4 June 1992 4 June 1992 5 June 1992 7 June 1992 8 June 1992 8 June 1992

Liquid-water path

(g m-7

51 25 46 4

80 32

100 200

Cloud type (Sc and Cu)

Variable Continental Maritime Maritime Maritime Maritime Maritime Maritime

Mean cloud temperature Runs below Runs above

(K) ail cloud all cloud

281 .O 282.8 284.3 284.3 284.7 281.3 286.4 286.4

Liquid water con ten t gm-J

Figure 1. Cloud liquid-water content for profile P2 and profile P3 from flight A209. The mean liquid-water content for the level runs through cloud at 130 m, 170 m, 310 m and 470 m are denoted by the dark circles where

the cross bars denote the standard deviation along the run.

This is the method adopted to select which profile is most representative for particular runs from all the flights. As a further check on the LWP, the value calculated from combining the FSSP and 2DC measurements was compared with the JW value. The agreement was usually well within the quoted error for the JW instrument. In this paper we compare the microwave brightness temperature and retrieved L W with measurements by the JW hot- wire probe. The FSSP and 2DC data are used to help separate maritime profiles, where the LWP may be underestimated, from continental profiles where we expect the JW accuracy to be within 5-20% (Moss et al. 1993). The error characteristics of JW probes are discussed in detail by Walter Strapp and Schemenauer (1982). In this paper it is assumed the error on the in situ data is within 20%, ignoring collocation errors.

CLOUD LIQUID-WATER-PATH RETRIEVAL 1509

(6) FATE In contrast to the ASTEX, the air in the tropical south Atlantic was always clean

during the FATE and the stratocumulus was maritime with an effective radius of between 10 and 15 pm. Drizzle was observed on many occasions. The runs used are listed in Table 3. There were no useful runs below cloud during the FATE.

TABLE 3. RUNS USED FROM THE FATE CAMPAIGN

Liquid-water Mean cloud path Cloud type temperature Runs above

Flight Date (g m-2) (Sc and Cu) (K) all cloud

A140 2 Nov. 1991 A140 2 Nov. 1991 A142 6 Nov. 1991 A142 6 Nov. 1991 A142 6 Nov. 1991 A142 6 Nov. 1991 A142 6 Nov. 1991 A146 1 1 Nov. 1991

140 154 59 65 78 22 17

101

Maritime Maritime Maritime Maritime Maritime Maritime Maritime Maritime

289.4 289.4 288.4 288.4 288.4 288.4 288.4 288.3

(c) SAAMEX One flight during the SAAMEX campaign over snow and ice gave homogeneous

cloud. Flight H986 was in the region of the Gulf of Bothnia in March 1990 and the stratocumulus was associated with a frontal system with very deep cloud (LWC about 700 g m-'). This case is slightly different to those presented above, as the underlying surface was sea ice rather than open sea water. No runs were possible under cloud and no retrieval from the nadir view is attempted. As these data could not be used for retrievals they are only used in section 6(a) where the model is validated by comparing brightness temperatures from model and calculation.

(d ) British Isles frights The cloud conditions around the British Isles are highly variable. Whilst no semi-

permanent stratocumulus sheet such as that observed during the ASTEX or FATE is present it is not uncommon for extensive stratocumulus to form for short-lived periods. The data used are listed in Table 4.

6. RESULTS

(a) Cloud-model validation Figures 2(a)-2(f) show zenith brightness temperatures plotted as functions of altitude

for flights H986 (SAAMEX), A140 (FATE) and A209 (ASTEX). In each case five model lines are plotted. The continuous line is the brightness temperatures predicted by Liebe's gaseous-absorption model and Grody 's cloud model. The four dashed lines represent the predicted brightness-temperature profile with no cloud, 50%' 150% and 200% of observed cloud from left to right. For H986 the mean temperature of the cloud was about -5 "C and some ice crystals were present. The effect of these small ice crystals is neglected. The cloud was ice-free for A209 and A140, the mean cloud temperature being 13.1 "C

000 L

OS6

008

I,, , , , , , , , , , , , , , , , , , , , , , , , (q;\

ozo 1

026 V 2

028 5 v)

5 Ti

OZL

029

OSL 021 06 09 OE 0

320 I

000 L

086 ~p

096 2 ID u1 Ln

T T

OP6 0

016

006

OZOL

026

? u) v)

028 5 5 Kl

3z1

129

OTSl

CLOUD LIQUID-WATER-PATH RETRIEVAL 1511

TABLE 4. RUNS USED FROM THE UK FLIGHTS

Liquid-water Mean cloud path Cloud type temperature Runs below Runs above

Flight Date (g m-') (Sc and Cu) (K) all cloud all cloud

A109 19 July 1991 45 A112 8 Aug. 1991 26 A164 10 Jan. 1992 93 A164 10 Jan. 1992 156 A164 10 Jan. 1992 188 A164 10 Jan. 1992 215 A165 17 Jan. 1992 226 A169 5 Feb. 1992 59 A169 5 Feb. 1992 37 A169 5 Feb. 1992 97 A292 21 Oct. 1993 158 A292 21 Oct. 1993 115

* Orbit runs (left wing down by 30").

Continental Continental Continental Continental Continental Continental Continental Continental Continental Continental Variable Variable

278.2 278.8 275.2 275.2 275.0 275.0 274.3 278.8 278.8 278.8 271.3 271.3

3 0 0 4 1* 0 1* 0 0 1 0 1 0 1 1 1 1 1 0 1 1 1 0 2'

and 16.1 "C respectively. The cloud LWPs for Figs. 2(a)-2(f) were 700 g m-2 for H986, 167 g m-2 for A140 and 200 g m-' for A209. All three flights represent moderately thick stratocumulus associated with a subsidence inversion for A140 and A209 but with an unstable frontal zone for H986. The cloud modifies the zenith brightness temperatures by between 0.1 K (g m-')-' and 0.3 K (g m-')-l depending on the WVB, cloud temperature and cloud amount. By observing the dashed lines it can be seen that the rate of increase of brightness temperature with cloud LWP falls as LWP rises for H986 where the cloud was very deep. For A140 and A209, however, the rate of increase remains almost linear as the LWP rises. This weakly nonlinear behaviour justifies the use of damped Newtonian iteration as a retrieval method. In many instances the retrieval will be linear.

The observed brightness temperatures in Figs. 2(a)-2(f) are typical of the range ob- served. For H986 and A209 the brightness temperature rises monotonically with falling altitude, and the results agree well with the model, albeit with a small offset at 157 GHz for A209. In clear air the results agree well with those presented by English et al. (1994). For A140 the agreement is good at cloud top (i.e. the clear-air model is agreeing well). The first run below cloud top lies on the 200% line for both channels, the next on the clear-air line for both channels. The two runs below cloud base both fall near the 50% line. It is apparent that the cloud in this stack was too inhomogeneous to distinguish model errors and unrepresentivity of the cloud profile. Differences which are systematic with height (such as that for A209) are more likely to be significant, although again care must be taken. On occasion the water-vapour profile above cloud is not representative. This can lead to a difference between model and observation at all levels despite the cloud being modelled accurately. Zenith views for runs above cloud are only sensitive to water vapour so should have similar observed and modelled brightness temperatures, as the clear-air model has been shown to be accurate throughout the troposphere (English et al. 1994). If poor agreement is found, or two runs above cloud give very different results in the zenith view, this has to be due to mesoscale variability of the water-vapour profile. In order to be able to associate differences in the final analysis solely with the cloud model and retrieval problem these cases are not included in the overall analysis. The objective is to obtain a quality controlled data set where the profiles are representative of the runs, the mesoscale variability is low and the water-vapour absorption is accurately represented.

1512 S. J. ENGLISH

Figure 3. Zenith brightness temperature below cloud at 89 GHz (diamonds) and 157 GHz (circles). Cross bars denote the standard deviation of the observations.

The model can be carefully validated for cloud radiative transfer by modelling the cloud layer only. It is possible to fly above the cloud top and measure the downwelling brightness temperature. The modifying effect of the cloud layer on the downwelling bright- ness temperatures can then be calculated using the radiative-transfer model. The resulting downwelling brightness temperature below cloud can be compared with an actual air- craft run below cloud. This method relies on a homogeneous and unvarying cloud layer. In practice it is not possible to ensure that the cloud is not varying with time. Even the semi-permanent sheets of stratocumulus found in areas such as the Azores have a diurnal fluctuation (Albrecht et al. 1995). Aircraft stacks were therefore used from both night and day flights to avoid biasing the data set.

The results for both channels are shown in Fig. 3. The calculated brightness temper- atures below cloud are plotted against the observed brightness temperatures. The best-fit line for both channels has a gradient less than unity, substantially so at 89 GHz. However, at 89 GHz the gradient is close to unity for zenith brightness temperature less than 90 K, and at 157 GHz the results are similarly impressive for brightness temperature less than 150 K. Overall the standard deviation is 16 K with a 5 K bias at 89 GHz. The figures are similar at 157 GHz. The root mean square (r.m.s.) and bias (observed-calculated) are shown in Table 5.

Table 5 also shows the difference between observed and calculated brightness tem- peratures if no cloud had been included in the radiative-transfer model. The bias confirms the trend observed in Fig. 3: that the runs where the 89 GHz zenith brightness tempera- ture exceeded 90 K give a substantial model underestimate (18.6 K and 24.3 K at 89 and 157 GHz respectively). This contrasts strongly with the bias for the runs with 89 GHz zenith brightness temperature less than 90K where the bias is less than 2 K for both

CLOUD LIQUID-WATER-PATH RETRIEVAL 1513

TABLE 5. BRIGHTNESS-TEMPERATURE COMPARISON FOR ZENITH VIEWS

Channel Bias Standard deviation Root mean square (GH4 Set Number of runs (K) (K) (K)

89 JW cloud used 24 5.0 15.8 16.2 157 JW cloud used 24 7.8 18.6 19.6 89 No cloud used 24 26.0 23.7 34.8

157 No cloud used 24 34.4 31.2 46.1 89 8 9 G H z S 9 0 K 16 -1.8 5.6 5.7

157 8 9 G H z s 9 0 K 16 -1.3 7.5 7.4 89 8 9 G H z 3 90K 8 18.6 20.9 26.9

157 89 GHz 2 90 K 8 24.3 22.9 32.4

JW is Johnson-Williams hot-wire probe.

channels. Overall the bias is about 5 K and the r.m.s. about 16 K at 89 GHz, slightly higher than this at 157 GHz. These values are compared with the model calculation where cloud is neglected in Table 5. The bias is much higher, about 30 K, when the cloud emission is ignored but the r.m.s. error is only halved by including the cloud in the model. It was found that the cases which gave the worst agreement not only had high brightness temper- atures but also very variable figures. The calculated brightness temperatures were in fact usually within one standard deviation of the mean observed brightness temperature, albeit the standard deviation could be as high as 40 K. This can be observed in Fig. 3. Two pos- sible explanations exist: firstly that as the cloud becomes thick and variable the radiative transfer through the cloud is no longer well represented by the model. Alternatively the cloud LWP measured during the aircraft profile is unrepresentative of the cloud during the runs for high LWP where the mean LWP is dominated by embedded cumulus. Either way good validation is impossible when the natural variability is this high. Encouragement can, however, be taken from the excellent agreement for cases where the standard deviation of the observed brightness temperatures are low.

(b) Cloud retrievals using a nonlinear retrieval scheme In the previous section it has been shown that for homogeneous and thin clouds the

model shows very small bias but a significant r.m.s. error. For thicker and less homogeneous clouds the agreement was poorer. In the context of the AMSU it is not the quality of agreement in the window channels which is of primary concern, but whether the model and sensitivity are good enough to retrieve cloud accurately enough to sound through clouds. Also, Guillou et al. (1995) have shown that the surface model can be validated to within 1-3 K, depending on surface conditions. But can we represent the surface accurately enough to sound through clouds over the ocean when both cloud and surface parameters are not well known? The nonlinear scheme has been applied to data from the ASTEX and FATE campaigns and also a number of flights around the UK.

Examples of LWP retrievals from straight and level runs are shown in Fig. 4. Figure 4(a) shows a retrieval from flight A209, described in detail in Fig. 1. This run was a low-level run below all cloud and is associated with the second profile which had a JW LWP of 200 g m-2. It is possible to retrieve the LWP above the aircraft directly from the upward- looking (zenith) view and also by modelling the reflection of the cloud on the sea surface from the downward-looking (nadir) view. The reflectivity of the ocean surface at 89 and 157 GHz is about 0.4 and 0.3 respectively. Therefore when flying under cloud the LWP can either be derived from looking up at the cloud or looking down at the reflection of

1514 S. J. ENGLISH

0, 300 3

0 2 0 40 60 Distance km

(0) A209'89 GHz' . '

' ' '

1

n

E CT

a 5

L Y

L m ._

0 100 200 300 400 LWP gm-'

........ Nadir - Zenith

f! 350

+

al CL

2 3 0 0 -

Y

ffl 01 100 2

(h) A206 15; GH; '

.-.-. __: . :-.. .~ '.L.--JL;. ....-, .....".......

-.. .-.---L--.-.

: 2 0 0 - Y

.K cn .-

0 20 40 60 Distance km

........ Nadir

E

.. n-.- .-I"- -----._ ,--- .~ ,__,-_- a

250

0 20 40 60 Distance km

0 20 40 60 Distance krn

w 45.0 0 V C

3 0 V 0

0

33.8

22.5 L

L

11.3 E

= 0.0

300 Y F E

c

g 20c

al Y

[d) A206

0 200 400 600 800 1000 1200 LWP gm-'

1

........ Nadir -Zenith I

0 20 40 60 Distance km

Figure 4. Retrieved liquid-water path ( L W ) for flights A209 and A206. (a)-@) The retrieved L W as a function of distance for zenith view and nadir view using the reflected signal. (cHd) Histograms of LWP corresponding to (a)-@). ( e x f ) The 89 GHz brightness temperatures for zenith and nadir view. (g)-(h) The 157 GHz brightness

temperatures for zenith and nadir views.

CLOUD LIQUID-WATER-PATH RETRIEVAL 1515

the cloud from the sea surface. If the model predicting the reflectivity of the sea surface is exact there should be no systematic bias between the two retrievals along a run. For A209 the zenith retrieval is fairly homogeneous, varying from 110 g mP2 to 300 g m-2 and averaging 208 g m-2. The nadir retrieval is systematically higher, ranging from 160 g mP2 to 360 g m-2 and averaging 269 g m-2. Figure 4(c) shows a histogram of the probability density for different LWPs from this run. It follows quite closely a Gaussian distribution. On average we would expect the aircraft profile to be representative with no bias compared with the retrieved product. This bias in the nadir view implies that the sea-surface model is underestimating the apparent brightness temperature of the sea, and the retrieval scheme is having to add more cloud to compensate. This is consistent with the measurements of sea-surface emissivity presented by Guillou et al. (1995) where the model used was shown to underestimate the surface emission by between 1 K and 3 K depending on sea surface temperature and wind speed.

By contrast Fig. 4@) shows the LWP from flight A206 plotted against distance. This is a low-level run similar to the one presented from A209, with retrievals from both the zenith and nadir view of the cloud above the aircraft. The stratocumulus was much more variable, mostly due to small-scale cumulus embedded in the stratocumulus sheet. This type of cloud was commonly observed during the ASTEX. The LWP in these cumulus intrusions was 500-1500 g m-’. It can be observed that for the cumulus features the retrieval from the zenith view is not consistently below that from the nadir view but there is a large random error. This is because the zenith and nadir views of the cloud are slightly offset, and where the cloud is inhomogeneous the LWP on two adjacent paths can be very different. In the areas of more homogeneous stratocumulus it can be observed that again the LWP from the nadir views is systematically about 50 g mP2 higher than that from the zenith views, as was the case for A209, again consistent with an underestimate by the surface-emissivity model. It should be noted that for downward-looking views above cloud the sensitivity to the surface model is smaller, and the error in the surface model consequently less important. In Fig. 4(d) a histogram of the LWP from A206 is plotted and this can be compared with Fig. 4(c) for A209. The distribution for A206 is clearly not Gaussian with a large peak at about 30-100 g rn-’ and a long tail of LWPs from 100-1200 g mF2. The aircraft profile flew through stratocumulus with a LWP of 67 g m-2. The distribution shown in Fig. 4(d) is, therefore, a combination of a Gaussian-type distribution of LWP from stratocumulus with a mean of about 70 g m-2 and the long tail at high LWP from cumulus intrusions. The mean retrieved LWP along this run was 213.4 g m-2 from the zenith views and 232.9 g m-2 from the nadir views. The length of the run was 60 km which is comparable with the field- of-view size for the largest fields of view of the SSM/I and AMSU-A. Such sensors would therefore detect the total LWP in both stratocumulus and cumulus. However most profiles taken by the aircraft are through the stratocumulus so a LWP of about 70 g m-2 is the most likely to be measured. If the profiles are biased towards measuring stratocumulus then the retrievals will show an overestimate with respect to the profiles. The same applies to SSM/I or AMSU-A retrievals. Even if the profile data set is not biased the distribution of Fig. 4(d) would require a large number of independent comparisons to represent the cloud adequately (30 for a 10% error). About 30 profiles (each with several runs) were used in this study after the quality control discussed in the previous section. Therefore the r.m.s. difference between the in situ and retrieved LWP has enough independent data points to take account of the difficulty in obtaining a meaningful LWP adequately in an inherently noisy data set. The brightness temperatures for the cases in Figs. 4(a)-4(d) are shown in Figs. 4(e)-4(h).

By comparing a retrieval of cloud LWP using nadir views with the in situ cloud LWC measurement at the top of the cloud we can verify that the variability along the run does

1516 S. J. ENGLISH

arise predominantly from changes in cloud L W . In Fig. 5 such a comparison is taken from flight A146 of the FATE. The cloud had a typical stratocumulus profile such that the total LWP was inferred from the LWC at cloud top. This was then compared with the MARSS retrieval along the 30 km length of the run. The absolute agreement is fair and the structure of the cloud is very similar from the retrieval and the in situ data except in the regions of very high LWP (cumulus) where the MARSS appears to overestimate. This figure shows that the variation along the run is dominated by changes in LWP. It also highlights that the present scheme will be inappropriate for very thick cloud.

Figure 6 shows a summary of retrieved L W s from the three principal sources plotted against the LWP observed by the aircraft. The points represent both upward and downward views but only from runs completely clear of cloud at the flight altitude. The nadir views are exclusively from runs above cloud and the zenith runs from below cloud. Overall the agreement is mostly within f50 g m-* although some runs, notably from the ASTEX, give poorer agreement. The data are summarized in Table 6. Overall there is little difference between the nadir and zenith views in absolute accuracy. Assuming Gaussian statistics the expected uncertainty on the retrieved LWP, assuming no forward model error and realistic instrument-error characteristics, was shown to be 3650 g m-2. These results are, therefore, close to the theoretical value, and confirm that even a simple cloud model is giving adequate performance. For some flights the assumption that all the variance in brightness temperature is due to either wind speed or LWP changes may be invalid.

Although overall the agreement was good there were notable occasions when some runs gave much poorer agreement. There could be a variety of reasons for this, but it was investigated to see if the difference correlated with cloud microphysics or tempera- ture. The cloud type was divided into drizzling (maritime) or non-drizzling (continental) stratocumulus. For some runs drizzle was observed but the cloud physics (2DC and FSSP)

500 I I I I

LWP from MARSS 0 I I I I I

0 5 10 15 20 25 30 Distance krn

Figure 5. Retrieved liquid-water path (LW) from nadir views flying above cloud and L W extrapolated from the Johnson-Williams (JW) probe for flight A146.

CLOUD LIQUID-WATER-PATH RETRIEVAL 1517

- 0 - - 250 - -

- 200 - -

-

-

- -

100 - -

- A ASTEX (zenith) 0 ASTEX (nadir) FATE (nadir)

OUK (zenith)

- - - - - -

300a

0 50 100 150 200 250 300 JW LWP gm-’

Figure 6. Retrieved MARSS liquid-water path (LWP) plotted against JW LWP for ASTEX, FATE and UK flights, The agreement is usually within 50 g m-*. Exceptions do occur, notably for ASTEX where a significant

overestimate occurs in the retrieval and the UK flights where the nadir runs show a retrieval underestimate.

TABLE 6. MEAN STATISTICS OF LIQUID-WATER-PATH RETRIEVALS USING AN ITERATIVE METHOD

Subset Bias Standard deviation Root mean square

Number of runs (g m-’) (g m-2) (g m - 9 ASTEX zenith views ASTEX nadir views FATE nadir views UK zenith views UK nadir views All zenith views All nadir views Drizzle No drizzle Mean cloud temperature c 280 K 280K 9 MCT S 285 K Mean cloud temperature z 285 K All data

17 9

15 8

13 25 37 34 20 14 27 21 62

-34.9 -27.7 -9.7 -3.8 20.5

-25.0 -4.0

-39.6 6.7

12.7 -35.9 -31.6 -14.6

47.1 66.5 55.5 38.6 40.3 46.2 56.1 81.0 43.7 44.3 64.8 82.3 50.7

57.5 68.9 54.3 36.3 43.8 51.7 55.5 72.3 43.5 43.4 55.6 77.5 54.0

suggested the cloud was continental whereas on other occasions no drizzle was observed in maritime stratocumulus. These are neglected. Table 6 lists the bias, r.m.s. error and standard deviation of the two cloud categories. A very much higher r.m.s. was found for the drizzling cases. This arose both from an increased standard deviation and a significant overestimating bias in the retrieval of nearly 40 g m-*. It is likely that this high r.m.s. for drizzling cases arises both from errors in the JW LWC measurement and in the use of the Rayleigh approximation for cloud droplets. However, both these effects are too small to explain fully the observed difference, and it is possible that some other aspect of the radiative environment is not being properly represented in the model.

1518 S. J. ENGLISH

In addition to comparing the retrieval data with the in situ microphysical data it is also possible to compare them with effective-radius retrievals from the VIS/IR radiometer on the aircraft (Taylor 1993). Unfortunately this multi-channel radiometer did not operate on many flights with the MARSS when conditions passed the quality control. Only five runs are currently available from four flights. However, the two runs with effective radii over 15 p m gave poor agreement, and the three runs with low effective radii (less than 12 pm) gave good agreement. As drizzle from stratocumulus occurs when the droplets are large, the poor agreement for large effective radius is consistent with the results presented in Table 6.

Another potential source of error is the dielectric model used in the cloud model. The most likely error from the dielectric model concerns the temperature dependence at high frequency (Klein and Swift 1977). In Table 6 the differences are averaged for three temperature ranges. Both the r.m.s. and the standard deviation rise sharply with increasing temperature. The bias is low for clouds of temperature less than 280 K but similar for warmer clouds. All the low-temperature clouds come from UK flights where the air has a high cloud-condensation-nuclei count and the clouds form a non-drizzling continental stratocumulus. The two warmer cloud categories are composed of runs from the ASTEX and FATE where usually the air was clean and the clouds composed of a low number density of large droplets. The change of bias with cloud temperature could, therefore, be due to the correlation of cloud microphysics with cloud temperature. In any case comparing retrievals using the dielectric model of Liebe (1989b) and Ray (1972) shows an increased LWP from the Liebe model at high temperature. This would increase the temperature dependence of the difference between retrieval and observations and worsen the overall r.m.s. difference. The change of r.m.s. and standard deviation is difficult to interpret. We would not anticipate an error in the dielectric model to give an increased random error at high temperature. One possible explanation is that the increased SST gives an increased boundary-layer depth. This in turn decouples the surface from the air at flight altitude, giving an increased uncertainty in both wind speed and water vapour at low altitude. It appears unlikely that increased inhomogeneity of the cloud is responsible as the standard deviation of the retrieved LWP has no correlation with cloud temperature.

(c) The sensitivity of L WP retrievals to surface wind speed In the previous subsection it was suggested that errors in the surface wind speed may

affect the random error of the retrieval. For a dual-polarized radiometer it is possible to distinguish LWP and wind-speed changes whereas for AMSU and MARSS, which measure a single polarization, there is an ambiguity between wind speed and LWP changes. Wind speed was included as a free parameter in the retrieval scheme for the MARSS retrievals, for the downward-looking views. The uncertainty on the background cloud field (which is set to zero) is much larger than the uncertainty in wind speed, and the cloud retrieval uses most of the available information in the MARSS data. For example, if the apriori uncertainty in the cloud retrieval is 250 g mP2 and wind speed is 5 m s-l for an instrument error of 2 K the uncertainty in the cloud is reduced to about 35 g m-* but the wind speed only to 4.3 m s-'. A polarizer was added to the 157 GHz channel to increase polarization information at the edge of the scan by rotating the polarization vector by 45". This significantly improves the quality of the retrieval at the scan edge. The wind-speed uncertainty falls to 3.2 m s-* and the cloud LWP uncertainty also falls to 25 g mP2. An example of this is shown in Fig. 7, where the true and retrieved wind speed and the true and retrieved LWP are plotted as functions of scan position. At the edge of the scan the retrieved LWP and wind speed are different from the other views, and are closer to the in situ values. The error characteristics of the retrieval then become scan-position (i.e. swath position for a satellite system) dependant.

CLOUD LIQUID-WATER-PATH RETRIEVAL 1519

6 E 2 0 1

D

Windspeed \ 200 I - 150

'E

5 0

a

2 4 6 8 10 Scan Position

Figure 7. Cloud liquid-water path (LWP) and wind speed as functions of scan position. The continuous line denotes the retrieved value and the dotted line the in sia measurement made by the C-130's instrumentation.

This is undesirable. In effect it would create unreal gradients of wind speed or cloud (by creating larger errors in the centre of the scan than at the edge). To avoid this it is better to retain the same polarization for all channels and to minimize the change of emissivity with view angle. The AMSU will have matching polarizations for all window channels (Table 1 in the introduction lists the AMSU channels) and the polarization vector will rotate with view angle from nominal vertical at nadir. The proposed polarizations for the AMSU radiometer is therefore an optimum design. The only improvement is to adopt a dual polarized conical scan (used for example by the SSM/I) where cloud and wind speed can be properly distinguished at all scan positions.

(d ) Cloud and water-vapour retrievals using a simple regression scheme An alternative approach to including cloud as a free parameter in a nonlinear retrieval

scheme is to devise a simple regression scheme to retrieve the LWP based on either an empirical or model data set. A simple scheme has been devised to retrieve both zenith and nadir LWP and WVB from the MARSS channels (89 and 157 GHz) based on regression from a simulated data set. The radiative-transfer model (Eq. (1)) assumes a linear relation- ship between optical depth and LWP. This method, therefore, works out an optical depth and then calculates the LWP by a linear regression between optical depth and LWP. This is similar to the approach of Grody and Ferraro (1992) and Karstens et al. (1995). Penney (1994) compared different empirical algorithms, and estimated the minimum error on the retrieved LWP for S S W was 50 g m-2. For the MARSS the sensitivity to LWF' is greater but the ambiguity with water vapour and surface parameters is also more difficult to handle in a simple algorithm. For SSMD a statistical and iterative scheme have similar error char- acteristics but an iterative scheme is preferable from the point of view of data assimilation. For AMSU-B a physical iterative scheme is again more appropriate for data assimilation. In this subsection we investigate whether it is also more accurate. An atmospheric mean radiating temperature (TMR) is required to calculate optical depth; but it was found that the retrieval was only weakly sensitive to the choice of this temperature so a mean value of 280 K was used for all runs. A linear relationship is also used for water vapour, neglecting the second-order term associated with the anomalous absorption. The LW, C , and WVB,

1520

0

S . J. ENGLISH

0 Retrieval tram Observations

A Retrieval from model TBo

I

E E

L 3 0 a a >

CLOUD LIQUID-WATER-PATH RETRIEVAL 1521

be producing misleading results. The regression scheme retrieves similar amounts of LWP for the synthetic data and the observed data and can successfully retrieve zero cloud for the cloud-free case to an r.m.s. of 32.3 g m-' and a bias of just 12 g m-2. The retrieval of LWP from the observations is noisy and gives an r.m.s. difference of 114.3 g m-2 compared with the measured LWP, although the bias is only 22.1 g m-'. These are significantly worse error characteristics than the iterative scheme for cloud. We do not claim in this paper that the simple regression scheme could not be improved upon. It could use an infrared cloud-top temperature such as Liu and Curry (1993) and the choice of TMR could be more appropriate. It seems unlikely, however, that this could reduce the r.m.s. of over 114 g m-2 to the value of just 46 g m-' achieved with the iterative scheme for zenith views. This appears to justify the assertion that a physical iterative scheme is not only more appropriate but also considerably more accurate than a statistical regression scheme for these channels.

It is apparent that for zenith views such a simple scheme can give us some infor- mation on both WVB and LWP even for these two channels where WVB and LWP do not have orthogonal gradient vectors (i.e. they are not independent variables in the retrieval). Additional channels would be required to do a similar exercise for downward views.

7. DISCUSSION

The MARSS channels have been shown to be capable of retrieving cloud LWP to an r.m.s. accuracy of about 50 g m-2, assuming that a reasonable temperature and humid- ity profile and some prior knowledge about the height of the cloud and the cloud type is available. There appears to be little difference in retrieval performance for nadir and zenith views. The r.m.s. is slightly higher for nadir views but overall the bias is lower. We would have anticipated that the bias would have been larger for nadir views owing to the known error characteristics of the emissivity model (Guillou et al. 1995). However, the boundary-layer model used to extrapolate flight-altitude wind speed will overestimate the surface wind speed when the surface layer becomes decoupled under stratocumulus. This would compensate for model errors and could also lead to an increased random error. The ambiguity problem reduces with view angle, especially with the polarization vector rotated by 45". For the AMSU view it would give an almost systematic error in LWP across the scan. Ambiguities also exist with water vapour, although it has proved surprisingly easy to distinguish water vapour and cloud changes using even a simple regression scheme.

The agreement between observed and retrieved LWP is usually close to the retrieval error given by Eq. (3). The results confirm that the model used is adequate for thin strato- cumulus, and the LWP can be retrieved to an accuracy of about 50 g m-2 and that the overall bias of the retrieval is very small (15 g m-2). However, for drizzling stratocumulus there is an overestimation of the retrieved product compared with the JW LWP for both nadir and zenith views. This was also observed when comparisons were made of observed and calculated brightness temperatures where very good agreement for thin clouds (89 GHz brightness temperature less than 90 K) contrasted strongly with a model deficit for deep clouds (89 GHz brightness temperature greater than 90 K). The results have been shown to be weakly sensitive to inaccuracy in the cloud height. For thin stratocumulus it is, therefore of limited importance where the cloud is placed in the profiles. Also there is little evidence that there is an error correlating with cloud temperature.

It has been shown that often the mean LWP for stratocumulus sheets is dominated by small-scale deep embedded cumulus. These clouds are relatively unlikely to be sampled by aircraft or other means of obtaining ground truth for satellite measurements. This may lead to an apparent overestimate in satellite retrievals of cloud LWP by comparison with other

1522 S. J. ENGLISH

methods, particularly for large field-of-view instruments such as the MSU. On occasion large cloud amounts have been reported. For example, Spencer (1993) used MSU data to estimate precipitation, though he acknowledges the primary signal in the MSU data is from cloud. The MSU data show a higher climatological precipitation accumulation than existing data sets in many areas. It is possible that this arises from undersampling by other methods, although it is equally possible that the rainfall relation used could not be extended to global use. This emphasizes the value of model and retrieval validation from an aircraft capable of measuring the microwave brightness temperature and in situ cloud data to a finer horizontal resolution.

The retrieval accuracy of 50 g m-2 tells us we have a potentially useful retrieval of cloud but does not tell us whether this is adequate for the sounding channels. Assuming the cloud to be in the 700-1000 hPa region the AMSU sounding channels most affected by cloud are the AMSU-A channels 4,5 and 6 (see Table 1 for a list of AMSU channels) for temperature sounding and AMSU-A channels 1 and 15 and AMSU-B channels 19 and 20 for humidity sounding. The temperature-sounding channels show a sensitivity to cloud errors of 50 g mP2 of 0.9 K, 0.6 K and 0.1 K for channels 4,5 and 6. Equation (3) can be used to determine the impact of cloud errors on the retrieval of temperature and humidity. If we include cloud LWP as a free parameter in Eq. (3) with temperature and humidity then in principle we can retrieve LWP to an accuracy of under 30 g mP2. As we achieved an r.m.s. difference comparable with the theoretical value for the aircraft studies it is reasonable to assume that the same scheme using the same model could fare equally well for retrievals from satellites such as AMSU. The problem is essentially identical. However, the primary products from AMSU are the temperature and water-vapour retrievals. It is important to demonstrate that sounding is possible though thin cloud. The addition of a cloud layer only reduces the temperature-retrieval accuracy by a maximum of 0.06 K. If the information for cloud retrieval of the AMSU-A channels is ignored then the 50 g mP2 LWP error would still only reduce the retrieval accuracy by 0.1 K. Of course this figure would be much larger if we were not restricting this study to stratocumulus. The impact on humidity retrievals is slightly greater. The uncertainty on the retrieved WVB is about 6 5 % higher with the cloud included than for clear-air cases. The validation of the radiative-transfer model and retrieval methodology suggest that temperature and humidity information will be easily obtained from AMSU in areas of stratocumulus cloud, with only a slight degradation on clear-air regions. Data will only be unavailable in areas of precipitating cloud (other than light drizzle), representing a significant improvement in sounding capabilities compared with the current TOVS series. Evidence has also been presented that significant differences between retrieved and in situ LWP may also occur when light drizzle is present. It is, however, very difficult to attribute this difference to the retrieval or the in situ data as it occurs for stratocumulus cases when the LWP becomes dominated by small-scale cumulus intrusions. Overall the aircraft studies confirm that LWP can be handled by a retrieval scheme for AMSU and a useful cloud parameter can be retrieved to about 50 g m-’.

ACKNOWLEDGEMENTS

The effort of the Royal Air Force, ground crews and all the staff of the Meteorological Research Flight, particularly Jon Taylor, Doug Johnson, Gill Martin and Roger Saunders for organizing most of the UK, ASTEX and FATE flights, is gratefully acknowledged. The MARSS radiometer was jointly developed by the Laboratoire Mktkorologie Dynamique de Centre National de la Recherche Scientifique (CNRS) and the staff of the Remote Sensing Instrumentation branch of the UK Meteorological Office. The author thanks his colleagues from these establishments, in particular Dave Jones for calibrating and operating

CLOUD LIQUID-WATER-PATH RETRIEVAL 1523

the MARSS, and Tim Hewison and Andy Kirkman for operating the MARSS. Useful dis- cussion with Graeme Penney (UK Meteorological Office) and Catherine Prigent (CNRS) is also acknowledged.

REFERENCES

Albrecht, B. A.

Albrecht, B. A., Bretherton, C. S., Johnson, D. W., Schubert, W. H. and Frisch, A. S.

Cox, C. and Munk, W.

Deirmendjian, D.

English, S. J., Guillou, C., Prigent, C. and Jones, D. C.

Ezraty, R.

Grody, N. C.

Grody, N. C. and Ferraro, R. R.

Guillou, C., English, S. J.,

Jones, D. C. Prigent, C. and Jones, D. C.

Karstens, U., Simmer, C. and

Klein, L. A. and Swift, C. T. Ruprecht, E.

Liebe, H. J.

Liu, G. and Curry, J. A.

Moss, S. J., Brown, P. R., Johnson, D. W., Lauchlan, D. R., Martin, G. M., Pickering, M. A. and Spice, A.

Offiler, D., Brown, P. R., Grant, A., Jackson, N. and Johnson, D.

Penney, G.

1993

1995

1955

1969

1994

1985

1993

1992

1995

1991

1995

1977

1989a

1989b

1993

1993

1994

1994

‘The Atlantic Stratocumulus Transition Experiment (ASTEXF an overview’. Proceedings of the spring meeting of the Amer- ican Geophysical Union

The Atlantic Stratocumulus Transition Experiment-ASTEX. Bull. Am. Meteorol. SOC., 76, No. 6,899-904

Some problems in optical oceanography. J. Marine Res., 14(1), 63-78

Electromagnetic scattering on spherical polydispersions. Elsevier, New York

Aircraft measurements of water vapour continuum absorption at millimetre wavelengths. Q. J. R. Meteorol. Soc., 120, 603- 625

I’Etude de l’algorithme d’estimation de la vitesse de la frottement a la surface de la mer. IFREMER, No. 85.2.42.5000 ESA Contract 6155/85/NL/BI

Remote sensing of the atmosphere from satellites using microwave radiometry. Pp. 259-334 in Atmospheric remote sensing by microwave radiometry. Ed. M. A. Janssen. John Wiley and Sons

A comparison of passive microwave rainfall retrieval methods. Pp. 60-65 in Proceedings of the sixth conference on meteorology and oceanography. American Meteorological Society, Atlanta GA

Passive microwave airborne measurements of the sea surface re- sponse at 89 and 157 GHz. J . Geophys. Res., in press

‘Microwave Airborne Radiometer Scanning System: Calibration and initial performance assessment’. Met. O(RS1) Branch Memorandum No. 3. (Available from the National Meteo- rological Library, Bracknell, UK)

Remote sensing of cloud liquid water. Meteorol. Atmos. Phys., 54,

An improved model for the dielectric constant of sea water at microwave frequencies. IEEE J. Ocean. Eng., OE-2, 104- 111

MPM-An atmospheric millimeter wave propagation model. Inf. J . Infrared and Millimeter Waves, 10(6), 631450

Millimeter wave attenuation and delay rates due to fog and cloud conditions. IEEE Trans. Antennas and Prop., 37(12), 1617- 1623

Determination of characteristic features of cloud liquid water from satellite microwave measurements. J. Geophys. Res., 98, D3,

‘Cloud microphysics measurements on the MRF C-130 working group report’. MRF Technical Note No. 12. (Available from the National Meteorological Library, Bracknell, UK)

157-171

5069-5092

‘Report of the aircraft wind working group’. MRF Technical Note No. 17. (Available from the National Meteorological Library, Bracknell, UK)

‘A sensitivity study of S S W statistical and physical liquid water path algorithms using a radiative transfer model’. FR- Div. Technical Report No. 110. (Available from the National Meteorological Library, Bracknell, UK)

1524 S . J. ENGLISH

Peter, R. 1994

Prigent, C. 1994

Ray, P.

Rodgers, C.

1972

1976

Saunders, R. W., English, S. J. and 1994

Spencer, R. W. 1993

Stogryn, A. 1975

Taylor, J. P. 1993

Walter Strapp, J. and 1982

Weng, F. and Grody, N. C. 1994

Jones, D. C.

Schemenauer, R. S.

Wentz, F. J. 1992

Wentz, F. J., Mattox, L. A. and 1986 Peteherych, S.

Wdheit, T. T. 1979

‘The retrieval of tropospheric water vapour and cloud liquid with an iterative non-linear algorithm’. Specialist meeting on microwave radiometry and remote sensing of the environ- ment, Rome, Italy, 14-17 February

‘Physical retrieval of geophysical parameters from S S W : re- quirements for radiative transfer models’. From Progress in electromagnetic research symposium, Noordwijk, Nether- lands, 11-15 July

Broadband complex refractive indices of ice and water. Appl. Optics, 11,18361844

Retrieval of atmospheric temperature and composition from re- mote measurements of thermal radiation. Revs. Geo. Space Phys., 14(4), 609424

‘AMSU-B a new tool for atmospheric research’. SPIE 2313,9% 107, Rome, Italy, 2%30 September

Global oceanic precipitation from the MSU during 1979-1991 and comparisons to other climato1ogies.J. Climate, 6,1301-1326

A note on brightness temperature at millimeter wavelengths. IEEE Trans. Geosci. Electron., GE-13(2), 8 1 4 4

‘The remote retrieval of stratiform water cloud radiative and microphysical properties’. PhD Thesis, University of Reading

Calibrations of Johnson-Williams liquid water content meters in a high speed icing tunnel. J. Appl. MeteoroL, 21(1), 98-108

‘Retrieval of liquid and ice water in atmosphere using Special Sensor MicrowaveDmager (SSMD) data. Specialist meeting on microwave radiometry and remote sensing of the environ- ment, Rome, Italy, 14-17 February

Measurement of oceanic wind vector using satellite microwave radiometers. IEEE Trans. Geosci. andRemoteSensing, 30(5), 960-972

New algorithms for microwave measurement of ocean winds: Applications to SEASAT and the Special Sensor Micro- wavenmager. J. Geophys. Res., 91(C2), 2289-2307

A model for the microwave emissivity of the ocean’s surface as a function of wind speed. IEEE Trans. Geosci. Electron., GE- 17,244-249