• Bauer, P. 2001. Including a melting layer in microwave radiative transfer simulation for clouds. Atmos. Res. 57:930.

  • Bauer, P. 2002. Microwave radiative transfer modeling in clouds and precipitation. Part I: Model description. Met Office NWP-SAF Rep. 5, 24 pp.

  • Bauer, P. and A. Mugnai. 2003. Precipitation profile retrievals using temperature-sounding microwave observations. J. Geophys. Res. 108.4730, doi:10.1029/2003JD003572.

    • Search Google Scholar
    • Export Citation
  • Blackwell, W J., J W. Barrett, F W. Chen, R V. Leslie, P W. Rosenkranz, M J. Schwartz, and D H. Staelin. 2001. NPOESS Aircraft Sounder Testbed-Microwave (NAST-M): Instrument description and initial flight results. IEEE Trans. Geosci. Remote Sens. 39:24442453.

    • Search Google Scholar
    • Export Citation
  • Bohren, C F. and L J. Battan. 1980. Radar backscattering by inhomogeneous precipitation particles. J. Atmos. Sci. 37:18211827.

  • Chevallier, F. 2001. Sampled database of 60-level atmospheric profiles from the ECMWF analyses. Met Office NWP-SAF Rep. 4, 27 pp.

  • Connor, M D. and G W. Petty. 1998. Validation and intercomparison of SSM/I rain-rate retrieval methods over the continental United States. J. Appl. Meteor. 37:679700.

    • Search Google Scholar
    • Export Citation
  • Deblonde, G. and S. English. 2003. One-dimensional variational retrievals from SSMIS-simulated observations. J. Appl. Meteor. 42:14061420.

    • Search Google Scholar
    • Export Citation
  • Evans, K F., J. Turk, T. Wong, and G L. Stephens. 1995. A Bayesian approach to microwave precipitation retrieval. J. Appl. Meteor. 34:260279.

    • Search Google Scholar
    • Export Citation
  • Eyre, J R. 1993. A fast radiative transfer model for satellite sounding systems. ECMWF Tech. Memo. 176, 28 pp. [Available from ECMWF, Shinfield Park, Reading RG2 9AX, United Kingdom.].

  • Gasiewski, A J., J W. Barrett, P G. Bonanni, and D H. Staelin. 1990. Aircraft-based radiometric imaging of tropospheric temperature and precipitation using the 118.75-GHz oxygen resonance. J. Appl. Meteor. 29:620632.

    • Search Google Scholar
    • Export Citation
  • Gilbert, J C. and C. Lemarechal. 1989. Some numerical experiments with variable-storage quasi-Newton algorithms. J. Math. Prog. 45:407435.

    • Search Google Scholar
    • Export Citation
  • Grecu, M. and E N. Anagnostou. 2001. Overland precipitation estimation from TRMM passive microwave observations. J. Appl. Meteor. 40:13671380.

    • Search Google Scholar
    • Export Citation
  • Grody, N C. 1988. Surface identification using satellite microwave radiometers. IEEE Trans. Geosci. Remote Sens. 26:850859.

  • Kummerow, C. Coauthors 2000. The status of the Tropical Rainfall Measuring Mission (TRMM) after two years in orbit. J. Appl. Meteor. 39:19651982.

    • Search Google Scholar
    • Export Citation
  • Kummerow, C. Coauthors 2001. The evolution of the Goddard profiling algorithm (GPROF) for rainfall estimation from passive microwave sensors. J. Appl. Meteor. 40:18011820.

    • Search Google Scholar
    • Export Citation
  • Lemaire, D., P. Sobieski, and A. Guissard. 1999. Full range sea surface spectrum in non-fully developed state for scattering calculations. IEEE Trans. Geosci. Remote Sens. 37:10381051.

    • Search Google Scholar
    • Export Citation
  • Liebe, H J., P. Rosenkranz, and G A. Hufford. 1992. Atmospheric 60 GHz oxygen spectrum: New laboratory measurements and line parameters. J. Quant. Spectrosc. Radiat. Transfer 48:629643.

    • Search Google Scholar
    • Export Citation
  • Lopez, P. and E. Moreau. 2005. A convection scheme for data assimilation: Description and initial tests. Quart. J. Roy. Meteor. Soc. 131:409436.

    • Search Google Scholar
    • Export Citation
  • Moreau, E., P. Bauer, and F. Chevallier. 2002. Microwave radiative transfer modeling in clouds and precipitation. Part II: Model evaluation. Met Office NWP-SAF Rep. 6, 20 pp.

  • Moreau, E., P. Bauer, and F. Chevallier. 2003. Variational retrieval of rain profiles from spaceborne passive microwave radiance observations. J. Geophys. Res. 108.4521, doi:10.1029/2002JD003315.

    • Search Google Scholar
    • Export Citation
  • Mugnai, A. 2003. EGPM—The proposed European contribution to the Global Precipitation Measurement (GPM) mission. Geophys. Res. Abstr. 5:12550.

    • Search Google Scholar
    • Export Citation
  • Prigent, C., W B. Rossow, and E. Matthews. 1997. Microwave land surface emissivities estimated from SSM/I observations. J. Geophys. Res. 102:867890.

    • Search Google Scholar
    • Export Citation
  • Rabier, F., A. McNally, E. Andersson, P. Courtier, P. Unden, J. Eyre, A. Hollingsworth, and F. Bouttier. 1998. The ECMWF implementation of three-dimensional variational assimilation (3D-Var). II: Structure functions. Quart. J. Roy. Meteor. Soc. 124:18091829.

    • Search Google Scholar
    • Export Citation
  • Rodgers, C D. 2000. Inverse Methods for Atmospheric Sounding: Theory and Practice. Series on Atmospheric, Oceanic and Planetary Physics, Vol. 2, World Scientific, 238 pp.

  • Saunders, R., P. Brunel, F. Chevallier, G. Deblonde, S J. English, M. Matricardi, and P. Rayer. 2001. RTTOV-7 science and validation report. Met Office Forecasting and Research Tech. Rep. 387, 51 pp.

  • Schwartz, M J., J W. Barrett, P W. Fieguth, P W. Rosenkranz, M S. Spina, and D H. Staelin. 1996. Observations of thermal and precipitation structure in a tropical cyclone by means of passive microwave radiometry. J. Appl. Meteor. 35:671678.

    • Search Google Scholar
    • Export Citation
  • Smith, E A., A. Mehta, and J M. Shepherd. 2002. Description of Global Precipitation Measurement (GPM) Mission. NASA/Goddard Space Flight Center, GPM Report Series 6, Tech Memo., 25 pp.

  • Tompkins, A M. and M. Janiskova. 2004. A cloud scheme for data assimilation: Description and initial tests. Quart. J. Roy. Meteor. Soc. 130:24952518.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Mean clear-sky weighting functions at (a) 50.3 and 118.75 ± 8.7 GHz, (b) 51.76 and 118.75 ± 4.2 GHz, (c) 52.8 and 118.75 ± 2.3 GHz, and (d) 53.75 and 118.75 ± 1.4 GHz. Solid lines are 50-GHz channels, and dotted lines are 118-GHz channels. (e)–(h) Same as (a)–(d), but after the introduction of 0.2 g m−3 liquid water cloud layer between 700 and 800 hPa.

  • View in gallery

    Flow diagram of the retrieval scheme; t, q, and w denote temperature, specific humidity, and hydrometeor content profile vectors, and tb is the brightness temperature vector. Indices “b,” “a,” and “o” refer to background (first guess), analysis (retrieval), and observation, respectively; B and R denote background and observation error covariance matrices.

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    (left) Monthly mean surface emissivities at horizontal polarization and (right) associated standard deviation retrieved from SSM/I data (Prigent et al. 1997) over (a) snow cover in Canada, (b) land in the United States, and (c) desert in Africa; (a) and (c) are in Jan 1993 and (b) is in Jun 1993. Fits are indicated by a solid line.

  • View in gallery

    Integrated content (kg m−2) of (left) liquid water, (middle) rain, and (right) snow for cases 1 (upper left rectangle in figure) and 2 (lower right rectangle in figure) on 26 Jan 2003.

  • View in gallery

    As in Fig. 4, but for case 3 (rectangle in figure).

  • View in gallery

    As in Fig. 4, but for case 4 (rectangle in figure).

  • View in gallery

    Signal variability at all channels because of radiometer noise (black), surface emissivity uncertainty (dark gray), and liquid (light gray) and frozen (white) precipitation for the Canadian snowstorm (a) area 1 and (b) area 2, (c) the North Atlantic front, and (d) the Florida convection.

  • View in gallery

    Probability density functions of the first-guess (thin dashed line) and the analysis (thick solid line) departures for each channel combination for all profiles from four cases. For channel numbers see Table 1.

  • View in gallery

    Root-mean-square departures of rain (solid), snow (dotted), and cloud water (dashed) profiles from (left to right) FG analysis using window channels (AN: 1), sounding channels (AN: 2), and sounding channel differences (AN: 3) for the (a), (b) Canadian snowstorm, (c) North Atlantic front, and (d) Florida convection.

  • View in gallery

    Histogram of (left) analysis departure occurrences and (right) accumulated occurrence from all cases and all levels using window channels for the retrieval of (a) rain and (b) snow, or sounding channels for the retrieval of (c) rain and (d) snow, respectively. Relative error limits of ±25%–100% are overplotted as dashed lines. Upper and lower numbers under the grayscale refer to left and right panels, respectively.

  • View in gallery

    Fig. A1. Example of profiles for (a) temperature, (b) specific humidity, (c) rain (solid line) and snow (dashed line), and (d) cloud water (solid line) and ice (dashed line) contents for location at 20.5463°N and 87.4799°E taken from the 12-h forecast initialized at 1200 UTC 20 Jul 2004. First 15 eigenvalues from B(w) for (e) rain and (f) snow using 100 (solid line), 500 (dashed line), and 1000 (dotted line) perturbations, respectively.

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Hydrometeor Retrieval Accuracy Using Microwave Window and Sounding Channel Observations

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  • 1 European Centre for Medium-Range Weather Forecasts, Reading, United Kingdom
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Abstract

The retrieval errors of cloud and precipitation hydrometeor contents from spaceborne observations are estimated at microwave frequencies in atmospheric windows between 18 and 150 GHz and in oxygen absorption complexes near 50–60 and 118 GHz. The method is based on a variational retrieval framework using a priori information on the cloud, atmosphere, and surface states from ECMWF short-range forecasts under different weather regimes. This approach was chosen because a consistent description of the model state and its uncertainties is provided, which is unavailable for other methods. The results show that the sounding channels provide more stable, more accurate, and less biased retrievals than window channels—in particular, over land surfaces and with regard to snowfall. Average performance estimates showed that if sounding channels are used, 80% of all retrievals are within 100% error limits and 60% of them are within 50% error limits with regard to rainfall. For snowfall, the sounding channels produce 60% of all retrievals with errors below 100% for rates smaller than 1 mm h−1, and 50%–80% of the cases have errors below 50% for more intense snowfall.

Corresponding author address: Dr. Peter Bauer, ECMWF, Shinfield Park, Reading RG2 9AX, United Kingdom. peter.bauer@ecmwf.int

Abstract

The retrieval errors of cloud and precipitation hydrometeor contents from spaceborne observations are estimated at microwave frequencies in atmospheric windows between 18 and 150 GHz and in oxygen absorption complexes near 50–60 and 118 GHz. The method is based on a variational retrieval framework using a priori information on the cloud, atmosphere, and surface states from ECMWF short-range forecasts under different weather regimes. This approach was chosen because a consistent description of the model state and its uncertainties is provided, which is unavailable for other methods. The results show that the sounding channels provide more stable, more accurate, and less biased retrievals than window channels—in particular, over land surfaces and with regard to snowfall. Average performance estimates showed that if sounding channels are used, 80% of all retrievals are within 100% error limits and 60% of them are within 50% error limits with regard to rainfall. For snowfall, the sounding channels produce 60% of all retrievals with errors below 100% for rates smaller than 1 mm h−1, and 50%–80% of the cases have errors below 50% for more intense snowfall.

Corresponding author address: Dr. Peter Bauer, ECMWF, Shinfield Park, Reading RG2 9AX, United Kingdom. peter.bauer@ecmwf.int

Introduction

The retrieval of precipitation profiles from passive microwave radiometric observations is well established and provides the foundation for a large variety of applications. With the launch of the Tropical Rainfall Measuring Mission (TRMM; Kummerow et al. 2000) the first spaceborne rain radar became available, providing combined passive–active microwave observations and, therefore, allowing for more detailed analyses of the macro- and microphysical structure of precipitating clouds (e.g., Grecu and Anagnostou 2001). However, because of the large cost of scanning radars onboard satellites, the bulk of rainfall-affected satellite observations will still be constituted by passive observations. The Global Precipitation Mission (GPM; Smith et al. 2002) concept is based on the availability of a sufficient number of wide-swath radiometric observations to achieve a temporal sampling of 3 h for every location on the earth’s surface.

The “classical” configuration of dual-polarized passive microwave window channels, as are available on the Special Sensor Microwave Imager (SSM/I) or the TRMM Microwave Imager (TMI), is designed to optimize the signal analysis over oceans. This is because water surfaces have low emissivities and polarize radiation by reflection. Over land, the depiction of information from the atmosphere is greatly affected by the large signal contribution of the surface, as well as its large variability. Over oceans, physical algorithms that involve realistic observation simulations based on combined cloud–radiative transfer models emerge as the reference (e.g., Kummerow et al. 2001). This is because they have the largest potential of improvement once sufficient microphysical constraints (from models, climatologies, other observations) are provided. Over land, the signal is too complex and the geophysical noise is too large so that constraining information will be of little benefit. This explains why purely statistical retrieval techniques remain rather successful over land (Connor and Petty 1998).

In preparation for the European contribution to GPM (EGPM; Mugnai 2003), new options for radiometer channels and new retrieval approaches are investigated that enable a better performance over land surfaces and the specific weather conditions of higher latitudes, namely, weak precipitation and snowfall. Only a few experimental studies have been carried out based on airborne measurements of microwave emission near 50 and 118 GHz over precipitating systems. Gasiewski et al. (1990) introduced the differential sensitivity between a single frequency at 53.65 GHz and several channels located near the 118.75-GHz absorption line resulting from absorption and scattering by clouds and precipitation because cloud extinction increases quadratically with frequency based on measurements of the millimeter-wave temperature sounder (MTS). Using the same instrument, Schwartz et al. (1996) retrieved the cloud cell–top altitude based on brightness temperature depressions relative to the clear-sky signal.

Recently, Bauer and Mugnai (2003) presented the first quantitative precipitation profile retrieval analysis employing temperature sounding channels in two different absorption complexes. Three major advantages of this approach are 1) the much lesser sensitivity to surface emission, 2) the possibility of cloud slicing if sets of several sounding channels are used, and 3) the distinction between clouds and precipitation from differential absorption and scattering between channels in the two absorption complexes. The EGPM concept that has been proposed to the European Space Agency (ESA), therefore, contains two sets of sounding channels in addition to window channels whose technical specifications are outlined in Table 1, according to the EGPM phase-A engineering studies.

The present study provides a quantitative retrieval accuracy estimation for the EGPM radiometer for different surface and weather conditions. Both the radiometer concept and the principles of precipitation signatures at sounding channel frequencies are introduced in section 2. The simulation and retrieval method is based on the variational retrieval method. From our experience, this methodology offers a more dynamical option for the generally underconstrained precipitation profile inversion problem. This is because the system is more open with respect to the required a priori data and the physical models that are run during the algorithm execution. Please refer to Moreau et al. (2003) for details. The variational method and its implementation for our purpose are presented in section 3. Results for both window and sounding channel radiometers are shown in section 4. The paper is concluded with a summary and a discussion in section 5. This section also contains conclusions for future instrument and algorithm design studies.

Radiometer

The radiometer has a set of window channels at 18.7, 23.8, 36.5, 89.0, and 150.0 GHz. All window channels have dual polarization, except for the 23.8-GHz channels, which only have vertical polarization. The sounding channels are located in two oxygen absorption complexes—the first set is single-band channels near 50–60 GHz, and the second set is double-side-band channels around the 118.75 GHz absorption line. The principle idea behind the combination of the two sets of sounding channels is that the higher-frequency set is more sensitive to both absorption and scattering by hydrometeors. In precipitating clouds, there will be a significant scattering signature with lower brightness temperatures (TBs) for the higher-frequency channel set than for the lower-frequency set. This will be distinctively different for nonprecipitating clouds.

For optimizing the channel combination between the two sounding channel sets, their sensitivity to clear-sky atmospheric profiles should be as similar as possible. This also minimizes the sensitivity of a retrieval algorithm to errors in the specification of the atmospheric temperature profile that is assumed for each case. The channel specification was based on fixing the 50-GHz channels and then searching for those 118-GHz channels that match best the 50-GHz-channel weighting functions averaged over a large set of profiles. Weighting functions are expressed as k(p) = ∂τ(p)/∂p, with pressure p and transmission τ.

The profile dataset consists of 55 000 profiles that were selected from European Centre for Medium-Range Weather Forecasts (ECMWF) analyses over all areas and seasons (Chevallier 2001). All simulations were carried out for a zenith angle of 53°, that is, a conically scanning radiometer. Atmospheric absorption was calculated with the millimeter-wave propagation model (MPM; Liebe et al. 1992). Calculations were performed over the frequency bandwidths that are specified in Table 1, with 100 samples per band.

The selected 50-GHz channels correspond to the lower four channels of the National Polar-Orbiting Operational Environmental Satellite System (NPOESS) Aircraft Sounder Testbed-Microwave (NAST-M) radiometer (Blackwell et al. 2001), namely, 50.3, 51.76, 52.80, and 53.75 GHz. They were chosen to cover the troposphere with average heights of weighting function peaks near 950, 800, 500, and 300 hPa, respectively (Figs. 1a–d). The corresponding 118-GHz channels show similar averaged weighting functions, with the largest differences occurring at the lower two channels as a result of their different sensitivity to moisture that significantly affects observations below 500 hPa.

If a cloud layer is introduced (liquid water content of 0.2 g m−3 between 700 and 800 hPa), the weighting function differences are clearly dominated by the cloud contribution (Figs. 1e–h). However, if the clear-sky maximum of the weighting function is located at higher altitudes, the corresponding channel pair becomes less sensitive to the cloud layer at 700–800 hPa. In the presence of clouds, different channel pairs are sensitive to different parts of the cloud. The combined use of all channel pairs in a retrieval algorithm, therefore, provides information on the vertical distribution of hydrometeor contents by reducing the sensitivity to background temperature and moisture.

Methodology

The approach for evaluating the retrieval accuracy of hydrometeor profiles over various surfaces using different channel combinations is illustrated in Fig. 2 and involves the following steps:

  • Profiles of temperature and humidity short-range ECMWF model forecasts are extracted for selected cases. The model resolution is ≈40 km, and there are 60 model levels.

  • The reference hydrometeor profiles are created by applying cloud and convection schemes. Perturbed hydrometeor profiles are created in the same way from perturbed temperature and humidity profiles. The temperature and humidity perturbations are obtained from random number generation with the characteristics of the ECMWF model’s operational background error covariances. The computation of the hydrometeor error covariance matrix B is described in section 3c.

  • Observations are simulated with a radiative transfer model using the “true” profiles. The observation error covariance matrix R contains the radiometer noise equivalent brightness temperature standard deviation (NEΔT) and the geophysical noise resulting from uncertain surface emissivities on the diagonal (see section 3c for details).

  • The retrieval method is applied to the perturbed hydrometeor profiles, and the retrieval accuracy is quantified by comparing the retrievals to the reference profiles.

Details of the individual components are outlined in the subsections to this chapter. This approach was successfully applied to clear-sky geophysical variable retrieval studies (e.g., Deblonde and English 2003) and represents a consistent testing environment, because all ingredients, that is, state variables and observables as well as their error characteristics, are defined. The method is also very well suited for the analysis of instrument performance because retrieval accuracy can be defined as a function of instrument noise, biases, channel cross correlation, and others.

Variational retrieval

Rainfall retrieval algorithms are not fully constrained. Instead, a priori information must be supplied to help derive the microphysical properties of precipitating clouds. In a physical framework, the optimum estimate of a state vector (precipitation profile) x must be obtained using an observation vector of brightness temperatures (TBs) y plus additional a priori information. Because of observation errors and errors in the observation operator H, which translates between geophysical state space and observation space, the relation between state and observation space is usually described by probability density functions (PDFs). This can be formalized with Bayes’s theorem (e.g., Rodgers 2000),
i1520-0450-44-7-1016-e1
where P(x|y) is the posteriori probability of x when y is observed; P(y|x) is the probability of making observation y when x is present, while P(x) and P(y) are the a priori probabilities of x and y, respectively. The latter may come from global statistics of state and observations. The determination of P(y|x) requires the observation operator (see following section). This operator may also be used to compute P(y) if P(x) is assumed to fully describe the a priori distribution of x. Examples of the application of the above principle are the “Bayesian” rainfall retrieval schemes that have found rather wide application in recent years (e.g., Evans et al. 1995).
One particular problem associated with these rainfall retrievals is that the model that connects states and observations, that is, y = H(x) + ϵ (where ϵ is the modeling error), is generally nonlinear. This immediately implies that the inversion of this relation is state dependent, and that the inversion must be formulated differently depending on whether (a) a first guess of the actual state xb and its error covariance B are known and are Gaussian with respect to the true state, or (b) only a PDF of state x is known from which the PDF of state y can be calculated. If situation a applies, Eq. (1) can be transformed to
i1520-0450-44-7-1016-e2
Superscripts “−1” and “T” denote inverse and transpose matrices, respectively.
The probability of P(x|y) is maximized when the first derivative of Eq. (2) vanishes. This can be solved numerically by iterative procedures, and constitutes a variational retrieval. In the minimization, the balance between the background state and the observations is weighted by their error covariance matrices and quantified by an objective cost function, defined as
i1520-0450-44-7-1016-e3
In our application, the control vector x contains vertical profiles of rain, snow, and cloud liquid water. The minimization of (3) requires the gradient of J(x),
i1520-0450-44-7-1016-e4
where HT is the adjoint operator of the radiative transfer model. The minimization module is limited-memory quasi-Newton (M1QN3) software developed by Gilbert and Lemarechal (1989). Because rain-, snow, and cloud water contents are retrieved at once, the size of the control vector [x = (wr, ws, wc)] is 3 times the number of model levels, that is, 180.

While the relative contribution of temperature and water vapor profiles to the total signal in clouds and precipitations is small, land surface emissivity will largely affect the observations in thin and semitransparent clouds. In principle, land surface emissivity could be included in the control vector as well as surface skin temperature. For this, however, a sufficiently accurate land surface module for the observation operator is required, as is an estimate of its error. Because this is not the case for the variety of surface conditions targeted in this study, climatological values were chosen.

Observation operator

The observation operator consists of a radiative transfer model that accounts for multiple scattering in the atmosphere. It represents an extension to the numerically efficient RTTOV package1 (Eyre 1993; Saunders et al. 2001) that is operationally used at many NWP centers. The extension is the inclusion of multiple scattering in the forward model as well as the tangent linear and adjoint versions of the scattering code. This will be included in the next operational version (v8). More details can be found in Bauer (2001, 2002) and Moreau et al. (2002, 2003).

All hydrometeor types, that is, rain, snow, cloud liquid water, and cloud ice, are modeled as spheres and their optical properties are taken from precalculated lookup tables to decrease numerical cost. Cloud ice and snow particles were assumed to have a constant density with size (0.9 and 0.1 g cm−3, respectively) where the permittivity calculation of the air–ice mixture follows Bohren and Battan (1980). An exponential snow particle size distribution was taken and particle melting was not accounted for because of the simplicity of the moist physical parameterizations used for this study. All hydrometeor optical properties were obtained from Mie calculations (Bauer 2002).

For an ocean surface, emissivity is modeled according to Lemaire et al. (1999) because RTTOV only provides emissivity calculations for operational and near-future satellite instruments. Land surface emissivity is particularly difficult to simulate because of the complex interaction of electromagnetic radiation with soil, vegetation, and snow cover as a function of a large number of unknown state variables. Therefore, emissivity climatologies produced from SSM/I observations and integrated NWP and satellite products (Prigent et al. 1997) were employed. The climatologies also contain information on temporal emissivity variability over the 1-month-averaging period, which is required for the perturbations in the retrieval study (see below). Data between July 1992 and June 1993 were matched with the corresponding dates of the atmospheric ECMWF model fields to ensure realistic surface conditions.

The interpolation from SSM/I frequencies to the channel frequencies that are investigated in the present study was carried out with a parametric fit developed by Grody (1988):
i1520-0450-44-7-1016-e5
where e is emissivity, ν is the frequency, and ϵ0, ϵ, ν0, and k are fitted constants. A logarithmic function was used to fit the associated standard deviation. Figure 3 shows examples of both climatological data and fits for both emissivities and emissivity variations. The example presents a snow-covered surface with dense media scattering, a vegetation-covered surface, and dry land. In all cases, emissivity decreases with frequency while emissivity variability increases. This suggests that the variability of the surface state is affecting higher frequencies (here, 89 and 150 GHz) much stronger than lower frequencies, and that, therefore, higher-frequency window channels will be quite vulnerable when used for the retrieval of atmospheric variables over land. This effect may be partially compensated by cloud particle absorption, which is also more effective at 89 and 150 GHz; however, this is quantitatively estimated in section 4.

Principally, the observation operator could also contain a cloud/convection model if the control vector would be constituted by, say, temperature and moisture profiles. This approach was chosen by Moreau et al. (2003) for the purpose of the assimilation of rain-affected passive microwave observations. However, in this study only an estimate of hydrometeor profile retrieval accuracy is carried out (instead of temperature and moisture retrieval accuracy) so that the operator can be reduced to the radiative transfer component. For the specification of the error covariances that is described in the following section, both radiative transfer and cloud/convection models are employed.

Variables

The background error covariance matrix B defines error variances and error correlations of the control variables. The estimation of the error covariances of rain-, snow, and cloud water, that is, B(wr, ws, wc), was calculated based on the error covariance matrix of temperature t and humidity q (Moreau et al. 2003), that is, B(t, q).

The matrix B(t, q) is obtained from the fields used in the operational assimilation system of the ECMWF model (Rabier et al. 1998). For the generation of B(wr, ws, wc) for each profile, 100 perturbed temperature and humidity profiles were generated with magnitudes corresponding to those of the background error variances contained in B(t, q). The ensemble of perturbed profiles is then used as input for the moist convective and large-scale condensation schemes (Tompkins and Janiskova 2004; Lopez and Moreau 2005) for producing the corresponding ensemble of perturbed rainwater and cloud liquid water profiles. From these, B(wr, ws, wc) is calculated at each grid point. The first-guess profiles are generated similarly, that is, once B(wr, ws, wc) are defined, the perturbations to x can be generated. For a discussion of the properties of B, please refer to the appendix.

Because we assume that the climatological variability of surface emissivity is an appropriate measure for surface emissivity errors in the forward modeling, artificial noise is added to the climatological values for each profile, that is, y′ = H[x, ϵ + σ(ϵ)]. The noise σ(ϵ) is also calculated from randomized numbers with zero mean and the climatological variance. The diagonal elements of the observation error covariance matrix R then contain the radiometer noise and the mean geophysical noise from surface emissivity in brightness temperature space.

Results

Sensitivity

The one-dimensional variational data assimilation (1DVAR) retrieval scheme has been applied to selected profiles from ECMWF short-range model forecasts. The meteorological events represent mainly mid- to-high-latitude conditions and weak-to-moderate precipitation intensities with significant amounts of frozen precipitation. Three out of four events were over land, and one was over the ocean:

  • case 1: western Canadian snowstorm on 26 January 2003, area 1, with heavy snowfall and light rain (n = 78);

  • case 2: same event, area 2, with heavy snowfall and moderate rainfall (n = 46);

  • case 3: northern Atlantic front on 26 January 2003, with light rain and significant snowfall (n = 88); and

  • case 4: scattered Florida precipitation on 16 June 2003, with both light/heavy rain and snowfall (n = 33).

The profiles in cases 1–3 were obtained from 6-h forecasts initialized at 1200 UTC, while case 4 was obtained from a 12-h forecast at 1200 UTC.

Figures 4, 5 and 6 display the integrated contents of cloud liquid water, rain, and snow for the four events. The first two scenes represent rather difficult observational situations because of little radiative contrast between the surface and atmosphere/clouds and rather variable surface conditions. Several 1DVAR retrievals have been performed for each meteorological event, using various channel combinations, that is, window channels, sounding channels, and sounding channel differences. The latter configuration was chosen to exploit the differential scattering and absorption signatures of clouds and precipitation.

The variational framework also provides the tools for estimating the signal variability resulting from noise and the variability of the variables to be retrieved. In our case, noise is defined by the radiometer noise and geophysical noise that originates from those parameters that are not the target of the observation, but contribute to the measurement. For the above-mentioned selection of situations, the most important source of geophysical noise is surface emissivity. For estimating the signal versus noise characteristics of all of the radiometer channels, the geophysical variability is translated into radiometric variability by applying the observation operator, that is, HBHT. In the case of hydrometeor variability, B corresponds to B(wr, ws, wc); in the case of surface emissivity variability, the diagonal elements of B contain σ2(ϵ) with the linearized observation operator H = ∂H/∂x. Here, x denotes either water/ice contents or emissivities, and emissivity uncertainties are assumed to be uncorrelated between frequencies.

Figure 7 shows the results of this sensitivity estimation for all of the channels and the four meteorological situations that are subdivided into radiometer noise, surface emissivity noise, rain, and snow signal, respectively. In case 1, none of the channels show sufficient sensitivity to rainfall because of the very small rainfall amounts. The lower three window channels and the lower four sounding channels show little sensitivity to snow, while the remaining channels have a similar sensitivity to snow and surface emissivity. The combined retrieval of sounding channels will perform better than the window channel retrieval because the lower three window channels will introduce large noise (and even biases) into the estimate.

For case 2, the situation improves, mainly for the window channels at 89 and 150 GHz, as well as for the 118-GHz channels. Over oceans (case 3), the lower window channels provide large sensitivity to rain. All of the other channels provide similar information on snow as they do over land surfaces. This suggests that being only window channels, the channels at 89 and 150 GHz provide similar skill over most surfaces with respect to snow, but have very little sensitivity to rain. As a result of the large amounts of precipitating ice in case 4, almost all channels show large sensitivity.

In summary, depending on the situation, the combination of window and sounding channels provides sufficient sensitivity to both rainfall and snowfall. However, surface contributions are large and may significantly affect the retrieval accuracy. This applies strongly to biases because an aliasing from emissivity to hydrometeor contents may occur in the retrieval. In this case, the window channels are more vulnerable because their sensitivity to surface emissivity is generally large.

Retrieval

The contribution of the observations to the retrieval can be evaluated by comparing background [or first guess (FG)] and analysis (AN) departures in terms of TBs or water contents. The AN departures represent the deviation of the 1DVAR solution to the true state in observation space (brightness temperature) and is a measure of the accuracy of the retrieval in the TB space. The FG departures represent, in the TB space, the deviation of the first-guess state from the true state and, thus, are a measure of the accuracy of the first guess. If the AN departures show improved statistics relative to the FG departures then the observations provided useful information, otherwise they degrade the a priori information.

Figure 8 shows histograms of the TB departures for the window channels (numbers 1–5), sounding channels (numbers 6–13), and the sounding channel differences (from numbers 6 minus 10 to 9 minus 13). The data represent all of the profiles from all four cases. Large background departures occur where surface contributions are large, that is, for channels 1–5, 6, and 11. Because of the nonlinear response of TBs to water and snow contents, the perturbations of hydrometeor contents may also produce biases in the FG departures. The AN departures are generally much smaller. Please note that the biases remain mainly in the window channels and even may change sign, for example, in channel 5. Interestingly, the departures from the sounding channel differences are almost bias free. Biases may be produced by the above-mentioned nonlinear relationship between perturbations in temperature and moisture, and those in water contents. They may also come from insufficient knowledge of the first-guess state in a less well constrained retrieval environment than is assumed in our study. Therefore, the use of sounding channel differences provides a means to reduce biased retrievals and, therefore, to stabilize the retrieval.

Tables 2 –4 show all TB departures depending on the meteorological situation. In case of the window channels, the analysis departures are only significantly smaller than the background departures in the presence of moderate-to-heavy precipitation or over the ocean (cases 3 and 4). Then, the AN departures almost reduce to the sensor noise level of the instrument. The departures for the sounding channels are generally lower as a result of the signal contribution of the clear atmosphere. However, almost independent of the situation, the AN departures are very small. The only exceptions are channels 6 and 11 in case 1, where the surface contribution is large relative to the weak cloud emission. As explained before, the sounding channel differences show almost unbiased histograms of FG/AN departures and values of AN departures near zero. This suggests that in the TB space, the use of differential signatures may eliminate a possible background bias.

In Fig. 9, the root-mean-square departures are shown in geophysical parameter space for each case. The magnitude of the background departures (left panels) reflects the magnitude of the perturbations. One obvious feature in all of the retrieval experiments is that cloud water is not well retrieved in the presence of rain and snow. This is because of the weak sensitivity of TBs to cloud water changes in the presence of rain and snow. Therefore, the cloud water retrieval is mainly constrained by the cloud and convection scheme. The negative side effect of this is that the cloud water retrieval becomes vulnerable to aliasing. For all radiometer configurations, the AN departures of cloud water contents are similar to the FG departures. When using window channels, the cloud water departures may even deteriorate over land surfaces. A similar performance can be observed with window channels and rain profiles. Only with respect to snow, the window channels show an improvement in departure statistics.

The sounding channels perform rather well and reduce the departures of rain and snow profiles in all situations except for case 1. Obviously, this case represents the limit of retrieval sensitivity for the chosen radiometer configurations. Interestingly, the sounding channel differences perform slightly better than the individual sounding channels in case 1, but are worse in all other cases. This can be explained by the rather small relative FG departures that do not allow a large modification of the background profiles. The minimization may, therefore, be “trapped” in a local minimum of the cost function. The better performance in case 1 is because of the small precipitation amounts and, consequently, the rather small difference between the perturbed and true profiles. Here, the dynamic signal range of the sounding channel differences is large enough to capture the total profile difference. At the same time, the channel differences are less sensitive to surface effects than the channels are themselves.

Figure 10 summarizes the retrieval uncertainty as histograms of AN departures for all profiles at all levels from the four cases. The graphs display the statistics for rain and snow as well as for window versus sounding channels. Note that for the conversion from water/ice contents, power-law conversion formulas were used (Bauer 2001). The left panels show the departure distribution while the right panels show the accumulated distributions of the absolute values. The window channel retrievals show a large scatter over the entire dynamic range, while most of the sounding channel AN departures remain below the 100% error limit (left panels of Figs. 10a,c). For rainfall, the accumulated distributions show that 80% of all sounding channel retrievals are within 100% error limits, and 60% of them are within 50% error limits. For snowfall, with both radiometer options some large departures occur for low intensities. However, the sounding channels produce 60% of all of the retrievals with error below 100% for rates smaller than 1 mm h−1, and 50%–80% of the cases have errors below 50% for more intense snowfall (Fig. 10d). Generally, the window channels have a similar performance at higher rates, but perform significantly less well for rates below 1 mm h−1 (Fig. 10c).

Conclusions

The variational retrieval framework provides a well-defined environment for determining geophysical parameter retrieval accuracy using data from existing and future earth observation instruments. In this study, the retrieval errors of rain-, snow, and cloud water profiles were quantified for various weather conditions, namely, a Canadian snowstorm, a North Atlantic front, and tropical convection and were applied to simulations employing the technical specifications of the instrumentation that was proposed for the European contribution to the Global Precipitation Mission (EGPM). This consists of a microwave radiometer with several window channels at frequencies between 18 and 150 GHz, as well as sounding channels in the 50–60- and 118-GHz oxygen absorption complexes.

ECMWF short-range forecasts of temperature and moisture and the associated operational background error statistics for these parameters were used to create reference and perturbed profiles of hydrometeors. EGPM observations were simulated with a radiative transfer model, and a one-dimensional variational retrieval method was applied to retrieve back the reference profiles. Realistic error structures for the observations were provided by estimated radiometric noise and radiative transfer modeling errors, as well as geophysical noise contributions from uncertain surface emissivity.

The main new development in this study is the application of a variational retrieval framework using operational numerical weather prediction model output for precipitation retrieval. The advantage of this approach is the fairly accurate and consistent description of the meteorological and surface conditions, including robust error statistics. This greatly reduces the limitations of existing methods that are based on mesoscale cloud model simulations that only represent very special and, in most cases, tropical situations. The requirement of an accurate and consistent description of the entire meteorological setting is, in particular, important over land surfaces where the relative signal contribution from hydrometeors is comparably small and geophysical noise is rather large.

The other new development is the proposal of temperature sounding channels for precipitation retrieval. It was demonstrated that the differential emission and scattering between collocated channels in two different absorption complexes has great advantages over window channels. While retrieval accuracy over the ocean is comparable to that of window channels, the sounding channels clearly outperform window channels for snow and cloud water retrievals and hydrometeor retrievals, in general, over land surfaces. Using sounding channel differences instead of individual channels helped to reduce biases in the retrievals that may originate from uncertain a priori information statistics. However, the smaller dynamic signal range may lead to unsatisfactory results if the first guess of the profile state is far away from the true state, because the ambiguity between states and observables is larger when using observation differences.

The EGPM mission focuses on higher latitudes and situations with weak precipitation and snowfall. From the results of this study, it is concluded that only sounding channels provide enough signal relative to geophysical noise to be useful in such conditions. The variational retrieval framework proves to be flexible enough for global application if sufficient a priori information on state and its uncertainty is available.

Acknowledgments

The authors are very grateful to three anonymous reviewers who greatly supported the publication of this work with their constructive criticism. The project was funded under contract ESTEC 18101/04/NL/GS.

REFERENCES

  • Bauer, P. 2001. Including a melting layer in microwave radiative transfer simulation for clouds. Atmos. Res. 57:930.

  • Bauer, P. 2002. Microwave radiative transfer modeling in clouds and precipitation. Part I: Model description. Met Office NWP-SAF Rep. 5, 24 pp.

  • Bauer, P. and A. Mugnai. 2003. Precipitation profile retrievals using temperature-sounding microwave observations. J. Geophys. Res. 108.4730, doi:10.1029/2003JD003572.

    • Search Google Scholar
    • Export Citation
  • Blackwell, W J., J W. Barrett, F W. Chen, R V. Leslie, P W. Rosenkranz, M J. Schwartz, and D H. Staelin. 2001. NPOESS Aircraft Sounder Testbed-Microwave (NAST-M): Instrument description and initial flight results. IEEE Trans. Geosci. Remote Sens. 39:24442453.

    • Search Google Scholar
    • Export Citation
  • Bohren, C F. and L J. Battan. 1980. Radar backscattering by inhomogeneous precipitation particles. J. Atmos. Sci. 37:18211827.

  • Chevallier, F. 2001. Sampled database of 60-level atmospheric profiles from the ECMWF analyses. Met Office NWP-SAF Rep. 4, 27 pp.

  • Connor, M D. and G W. Petty. 1998. Validation and intercomparison of SSM/I rain-rate retrieval methods over the continental United States. J. Appl. Meteor. 37:679700.

    • Search Google Scholar
    • Export Citation
  • Deblonde, G. and S. English. 2003. One-dimensional variational retrievals from SSMIS-simulated observations. J. Appl. Meteor. 42:14061420.

    • Search Google Scholar
    • Export Citation
  • Evans, K F., J. Turk, T. Wong, and G L. Stephens. 1995. A Bayesian approach to microwave precipitation retrieval. J. Appl. Meteor. 34:260279.

    • Search Google Scholar
    • Export Citation
  • Eyre, J R. 1993. A fast radiative transfer model for satellite sounding systems. ECMWF Tech. Memo. 176, 28 pp. [Available from ECMWF, Shinfield Park, Reading RG2 9AX, United Kingdom.].

  • Gasiewski, A J., J W. Barrett, P G. Bonanni, and D H. Staelin. 1990. Aircraft-based radiometric imaging of tropospheric temperature and precipitation using the 118.75-GHz oxygen resonance. J. Appl. Meteor. 29:620632.

    • Search Google Scholar
    • Export Citation
  • Gilbert, J C. and C. Lemarechal. 1989. Some numerical experiments with variable-storage quasi-Newton algorithms. J. Math. Prog. 45:407435.

    • Search Google Scholar
    • Export Citation
  • Grecu, M. and E N. Anagnostou. 2001. Overland precipitation estimation from TRMM passive microwave observations. J. Appl. Meteor. 40:13671380.

    • Search Google Scholar
    • Export Citation
  • Grody, N C. 1988. Surface identification using satellite microwave radiometers. IEEE Trans. Geosci. Remote Sens. 26:850859.

  • Kummerow, C. Coauthors 2000. The status of the Tropical Rainfall Measuring Mission (TRMM) after two years in orbit. J. Appl. Meteor. 39:19651982.

    • Search Google Scholar
    • Export Citation
  • Kummerow, C. Coauthors 2001. The evolution of the Goddard profiling algorithm (GPROF) for rainfall estimation from passive microwave sensors. J. Appl. Meteor. 40:18011820.

    • Search Google Scholar
    • Export Citation
  • Lemaire, D., P. Sobieski, and A. Guissard. 1999. Full range sea surface spectrum in non-fully developed state for scattering calculations. IEEE Trans. Geosci. Remote Sens. 37:10381051.

    • Search Google Scholar
    • Export Citation
  • Liebe, H J., P. Rosenkranz, and G A. Hufford. 1992. Atmospheric 60 GHz oxygen spectrum: New laboratory measurements and line parameters. J. Quant. Spectrosc. Radiat. Transfer 48:629643.

    • Search Google Scholar
    • Export Citation
  • Lopez, P. and E. Moreau. 2005. A convection scheme for data assimilation: Description and initial tests. Quart. J. Roy. Meteor. Soc. 131:409436.

    • Search Google Scholar
    • Export Citation
  • Moreau, E., P. Bauer, and F. Chevallier. 2002. Microwave radiative transfer modeling in clouds and precipitation. Part II: Model evaluation. Met Office NWP-SAF Rep. 6, 20 pp.

  • Moreau, E., P. Bauer, and F. Chevallier. 2003. Variational retrieval of rain profiles from spaceborne passive microwave radiance observations. J. Geophys. Res. 108.4521, doi:10.1029/2002JD003315.

    • Search Google Scholar
    • Export Citation
  • Mugnai, A. 2003. EGPM—The proposed European contribution to the Global Precipitation Measurement (GPM) mission. Geophys. Res. Abstr. 5:12550.

    • Search Google Scholar
    • Export Citation
  • Prigent, C., W B. Rossow, and E. Matthews. 1997. Microwave land surface emissivities estimated from SSM/I observations. J. Geophys. Res. 102:867890.

    • Search Google Scholar
    • Export Citation
  • Rabier, F., A. McNally, E. Andersson, P. Courtier, P. Unden, J. Eyre, A. Hollingsworth, and F. Bouttier. 1998. The ECMWF implementation of three-dimensional variational assimilation (3D-Var). II: Structure functions. Quart. J. Roy. Meteor. Soc. 124:18091829.

    • Search Google Scholar
    • Export Citation
  • Rodgers, C D. 2000. Inverse Methods for Atmospheric Sounding: Theory and Practice. Series on Atmospheric, Oceanic and Planetary Physics, Vol. 2, World Scientific, 238 pp.

  • Saunders, R., P. Brunel, F. Chevallier, G. Deblonde, S J. English, M. Matricardi, and P. Rayer. 2001. RTTOV-7 science and validation report. Met Office Forecasting and Research Tech. Rep. 387, 51 pp.

  • Schwartz, M J., J W. Barrett, P W. Fieguth, P W. Rosenkranz, M S. Spina, and D H. Staelin. 1996. Observations of thermal and precipitation structure in a tropical cyclone by means of passive microwave radiometry. J. Appl. Meteor. 35:671678.

    • Search Google Scholar
    • Export Citation
  • Smith, E A., A. Mehta, and J M. Shepherd. 2002. Description of Global Precipitation Measurement (GPM) Mission. NASA/Goddard Space Flight Center, GPM Report Series 6, Tech Memo., 25 pp.

  • Tompkins, A M. and M. Janiskova. 2004. A cloud scheme for data assimilation: Description and initial tests. Quart. J. Roy. Meteor. Soc. 130:24952518.

    • Search Google Scholar
    • Export Citation

APPENDIX

Background Errors

For a single profile the background error covariance matrix B(w) is produced from perturbations of profiles of temperature t and specific humidity q, and the subsequent application of the moist physical parameterization schemes (Tompkins and Janiskova 2004; Lopez and Moreau 2005). The perturbation statistics correspond to the background error covariance of t and q, which is calculated from the short-range forecast errors of these parameters based on the previous model analysis. The first-guess hydrometeor profiles that are used in the retrieval xb in Eq. (4) are generated by using the true profile and perturbations that reflect B(w).

The perturbations of T and q, as well as w can be calculated by using the Rodgers (2000) formulation. The (n × n) dimensional error covariance matrix B is decomposed as
i1520-0450-44-7-1016-ea1
in which λ and e denote eigenvalues and eigenvectors of B, respectively. The random perturbation for each element of x with xi = xi + σ(xi) can be determined from
i1520-0450-44-7-1016-ea2

The aj,i are produced with a Gaussian random number generator whose distribution has zero mean and unity variance, where index “i” refers to ith element of x.

For the generation of B a value of 100 for the number of perturbations has been chosen. This is used for finding a compromise between the computational effort and representativeness. The representativeness has been tested and is illustrated in Fig. A1. A profile from the 12-h short-range forecast (initialized on 7 July 2004; Bay of Bengal) of the ECMWF model was selected, which contains considerable amounts of cloud and precipitation hydrometeors. Hydrometeor contents reach 1.3 g m−3 (≈28 mm h−1) of rain near the surface and more than 2.5 g m−3 of snow above freezing level (Fig. A1c). Cloud water contents are significant and are peaking near the top of the rain layer with 0.7 g m−3. Cloud ice is less dominant, with contents below 0.2 g m−3 (Fig. A1d).

Equation (A2) was applied to the profiles of t and q that are displayed in Figs. A1a and A1b, and the moist physics schemes were applied to each perturbed profile, that is, wk = H(T, q)k, where wk denotes the hydrometeor profile from the kth perturbation and H is the observation operator. Figures A1e and A1f show the eigenvalues of the rain and snow hydrometeor content background error covariance matrices that were generated using 100, 500, and 1000 perturbations, respectively. Only the leading 15 elements are displayed. The comparison shows that the eigenvalues are almost identical, and that, therefore, 100 perturbations ensure representativeness.

Another issue is the validity of the assumption that the perturbed profiles that serve as a first guess in Eq. (4) follow a Gaussian distribution with regard to the true profiles. In principle, there are two different ways of producing the perturbed hydrometeor profiles, namely, from perturbed t and q profiles with perturbations prescribed by B(t, q), and by applying the moist parameterizations, as was done for the construction of B(w) or by producing B(w) and perturbing the reference w profiles using Eq. (A2).

In this study, the second option was chosen because the observation operator may be nonlinear, depending on the perturbations in t and q. Whether this is a valid assumption for applications of true observations and, say, global model profiles serving as first guesses has to be investigated. Because the intention of this work was more general in terms of radiometer sensitivity and theoretical retrieval accuracy, evaluation in a controlled statistical environment for this assumption seems verified.

Fig. 1.
Fig. 1.

Mean clear-sky weighting functions at (a) 50.3 and 118.75 ± 8.7 GHz, (b) 51.76 and 118.75 ± 4.2 GHz, (c) 52.8 and 118.75 ± 2.3 GHz, and (d) 53.75 and 118.75 ± 1.4 GHz. Solid lines are 50-GHz channels, and dotted lines are 118-GHz channels. (e)–(h) Same as (a)–(d), but after the introduction of 0.2 g m−3 liquid water cloud layer between 700 and 800 hPa.

Citation: Journal of Applied Meteorology 44, 7; 10.1175/JAM2257.1

Fig. 2.
Fig. 2.

Flow diagram of the retrieval scheme; t, q, and w denote temperature, specific humidity, and hydrometeor content profile vectors, and tb is the brightness temperature vector. Indices “b,” “a,” and “o” refer to background (first guess), analysis (retrieval), and observation, respectively; B and R denote background and observation error covariance matrices.

Citation: Journal of Applied Meteorology 44, 7; 10.1175/JAM2257.1

Fig. 3.
Fig. 3.

(left) Monthly mean surface emissivities at horizontal polarization and (right) associated standard deviation retrieved from SSM/I data (Prigent et al. 1997) over (a) snow cover in Canada, (b) land in the United States, and (c) desert in Africa; (a) and (c) are in Jan 1993 and (b) is in Jun 1993. Fits are indicated by a solid line.

Citation: Journal of Applied Meteorology 44, 7; 10.1175/JAM2257.1

Fig. 4.
Fig. 4.

Integrated content (kg m−2) of (left) liquid water, (middle) rain, and (right) snow for cases 1 (upper left rectangle in figure) and 2 (lower right rectangle in figure) on 26 Jan 2003.

Citation: Journal of Applied Meteorology 44, 7; 10.1175/JAM2257.1

Fig. 5.
Fig. 5.

As in Fig. 4, but for case 3 (rectangle in figure).

Citation: Journal of Applied Meteorology 44, 7; 10.1175/JAM2257.1

Fig. 6.
Fig. 6.

As in Fig. 4, but for case 4 (rectangle in figure).

Citation: Journal of Applied Meteorology 44, 7; 10.1175/JAM2257.1

Fig. 7.
Fig. 7.

Signal variability at all channels because of radiometer noise (black), surface emissivity uncertainty (dark gray), and liquid (light gray) and frozen (white) precipitation for the Canadian snowstorm (a) area 1 and (b) area 2, (c) the North Atlantic front, and (d) the Florida convection.

Citation: Journal of Applied Meteorology 44, 7; 10.1175/JAM2257.1

Fig. 8.
Fig. 8.

Probability density functions of the first-guess (thin dashed line) and the analysis (thick solid line) departures for each channel combination for all profiles from four cases. For channel numbers see Table 1.

Citation: Journal of Applied Meteorology 44, 7; 10.1175/JAM2257.1

Fig. 9.
Fig. 9.

Root-mean-square departures of rain (solid), snow (dotted), and cloud water (dashed) profiles from (left to right) FG analysis using window channels (AN: 1), sounding channels (AN: 2), and sounding channel differences (AN: 3) for the (a), (b) Canadian snowstorm, (c) North Atlantic front, and (d) Florida convection.

Citation: Journal of Applied Meteorology 44, 7; 10.1175/JAM2257.1

Fig. 10.
Fig. 10.

Histogram of (left) analysis departure occurrences and (right) accumulated occurrence from all cases and all levels using window channels for the retrieval of (a) rain and (b) snow, or sounding channels for the retrieval of (c) rain and (d) snow, respectively. Relative error limits of ±25%–100% are overplotted as dashed lines. Upper and lower numbers under the grayscale refer to left and right panels, respectively.

Citation: Journal of Applied Meteorology 44, 7; 10.1175/JAM2257.1

i1520-0450-44-7-1016-fa01

Fig. A1. Example of profiles for (a) temperature, (b) specific humidity, (c) rain (solid line) and snow (dashed line), and (d) cloud water (solid line) and ice (dashed line) contents for location at 20.5463°N and 87.4799°E taken from the 12-h forecast initialized at 1200 UTC 20 Jul 2004. First 15 eigenvalues from B(w) for (e) rain and (f) snow using 100 (solid line), 500 (dashed line), and 1000 (dotted line) perturbations, respectively.

Citation: Journal of Applied Meteorology 44, 7; 10.1175/JAM2257.1

Table 1.

Radiometer specifications.

Table 1.
Table 2.

Root-mean-square departures from FG and AN for the four studied cases and for window channels.

Table 2.
Table 3.

As in Table 2, but for sounding channel differences.

Table 3.
Table 4.

As in Table 2, but for sounding channels.

Table 4.

1

 The name RTTOV refers to its original purpose of radiative transfer modeling for the TIROS Operational Vertical Sounder (TOVS) data, but was not introduced as an acronym.

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