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

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  • 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-130s 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. Liebes 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 Grodys (1993) algorithm to the observations, Grodys algorithm for cloud absorption fits Rays (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...

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