SEARCH

SEARCH BY CITATION

Keywords:

  • atmospheric wind retrieval;
  • stratosphere;
  • radiative transfer modelling

Abstract

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Description of the measurements
  5. 3.  Description of RT-SWIFT
  6. 4.  Doppler wind determination
  7. 5.  Validation of the RT-SWIFT intensities and Doppler wind
  8. 6.  LOS wind retrieval
  9. 7.  Conclusion and recommendations
  10. Acknowledgements
  11. References

A fast forward radiative transfer model to compute the emitted limb radiances for use in recovering line-of-sight Doppler winds from thermal line emission has been developed and evaluated. This study was formulated around the Stratospheric Wind Interferometer for Transport Studies (SWIFT) instrument—a limb imaging, field widened, phase-stepping Michelson interferometer. The fast forward model is required to simulate a four-point interferogram from which line-of-sight winds may be computed. The model, RT-SWIFT (Radiative Transfer for SWIFT), is part of an effort to develop the capability of providing simultaneous measurements of horizontal wind velocity vectors and ozone concentration in the stratosphere for improving our understanding of global stratospheric dynamics and for studies in ozone transport.

Based in part on RT-MIPAS (Radiative Transfer for the Michelson Interferometer for Passive Atmospheric Sounding), RT-SWIFT uses a linear regression algorithm to parametrize the effective layer optical depths and can simulate the effect of variable ozone, nitrous oxide, water vapour and atmospheric winds. Trace gases are included as fixed climatological profiles.

The model development involved the selection of two suitable databases consisting of appropriate atmospheric absorber and wind profiles, and the accurate line-by-line modelling of their transmittances; one for generating regression coefficients and one consisting of simulated measurements for independent evaluation. The development also required selecting suitable predictors for the absorbers, winds and viewing geometry.

One-dimensional inversion results using RT-SWIFT with simulated measurements indicate that the model leads to wind and ozone error levels of about 3 to 5 m s−1 and 3 to 15% respectively for altitudes above ∼24 km. While further investment in model development and optimization is warranted, this demonstration study indicates that a sufficiently accurate fast forward model for near real-time assimilation, and inversion, of horizontal Doppler wind measurements from thermal line emission is feasible. © 2011 Crown in the right of Canada. Published by John Wiley & Sons Ltd.


1.  Introduction

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Description of the measurements
  5. 3.  Description of RT-SWIFT
  6. 4.  Doppler wind determination
  7. 5.  Validation of the RT-SWIFT intensities and Doppler wind
  8. 6.  LOS wind retrieval
  9. 7.  Conclusion and recommendations
  10. Acknowledgements
  11. References

The near real-time assimilation of radiances applied in numerical weather prediction systems requires fast and sufficiently accurate radiative transfer models to simulate radiances from available atmospheric profiles. While fast radiative transfer models for recovering temperature and constituent profiles—also referred to as fast forward models (FFMs)—are commonplace (e.g. RTTOV, Radiative Transfer model for TOVS (TOVS: TIROS Operational Vertical Sounder; TIROS: Television and Infrared Observational Satellite): Saunders et al., 1999), the need to extend the FFM capabilities to recover wind information is a recent development.

This article is oriented to determining, as a proof of concept, if a useful fast radiative transfer model is possible for recovering wind information in the context of near real-time inversion and data assimilation. The work presented here is specific to the proposed Stratospheric Wind Interferometer for Transport Studies (SWIFT) instrument (Shepherd et al., 2001; McDade et al., 2002), but could be applied to other instruments of a similar nature. The proposed SWIFT instrument relies on using Doppler interferometry to measure the wind-induced Doppler shifts of the atmospheric limb emissions of ozone from along line-of-sight paths.

A new fast forward radiative transfer model designated as RT-SWIFT and capable of simulating SWIFT radiances was developed for this study. RT-SWIFT is an adaptation of the RT-MIPAS model (Bormann et al., 2005), with a modified set of variable gases plus a newly developed parametrization for the Doppler effect. RT-MIPAS is a model developed for simulating infrared limb radiances from the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) on board the Envisat satellite (e.g. Harris, 2000). The RT-MIPAS template was chosen as it itself is a limb-viewing adaptation of RTTOV, a community model used for nadir sounders (Saunders et al., 1999).

A science impact study conducted for SWIFT relying on theoretical considerations and use of the Canadian Middle Atmosphere Model (CMAM: Beagley et al., 1997) resulted in a recommendation of desired accuracies at the level of 3–5 m s−1 for wind and 5% for ozone in the stratosphere with upper limits in error levels of 5–10 m s−1 and 10% for ozone (referred to in Lahoz et al. (2003, 2005) and Rochon et al. (2006)). Lahoz et al. (2003, 2005) conducted an observing system simulation experiment (OSSE: e.g. Atlas, 1997) study with assigned random error standard deviations of 5 m s−1 for wind in the range of 25–40 km and of 10% for ozone in the range of ∼18–50 km with a resolution of 2 km. That study suggested that SWIFT wind and ozone measurements could improve the data assimilation stratospheric analyses produced by weather forecasting systems. Rochon et al. (2006) presented an error budget scenario for SWIFT measurements with an overall 5 m s−1 total wind error level and a 5% total ozone error level for an effective vertical resolution of about 1.5 km over the 20 to 45 km altitude range with larger errors near 20 km. Measurement random errors contribute roughly 2–3 m s−1 of the total wind error in most of this region (based on recent unpublished results by the second author) and a comparatively negligible component of the total ozone errors, i.e. an uncertainty contribution of less than 0.5%. The radiative transfer model used in the aforementioned study, developed for investigating instrument designs and related error analyses, is computationally too slow for near real-time assimilation and inversion of remote-sounding radiance observations. The simulation for a single measurement using one processor requires several minutes as opposed to a fraction of a second.

In validating RT-SWIFT, attention must be given to the errors resulting from the FFM in relation to more accurate calculations. Ideally, target FFM error levels should not significantly increase the total error—FFM errors plus retrieval errors. As indicated above, in order for SWIFT measurements to have a positive impact, the total error of a retrieval should not exceed 5–10 m s−1 for wind and 10% for ozone. To this end, a target of 1 m s−1 was specified for the SWIFT wind error level at the onset of this fast forward model development. It was surmised that the ozone error level accompanying a 1 m s−1 wind error would be correspondingly small, in the neighbourhood of 1% or less, based on experiences with SWIFT retrievals.

The following report begins with a brief description of the instrument and its measurements. The next section provides a detailed description of the proposed RT-SWIFT model. This includes a brief description of the line-by-line radiative transfer model used to create measurement simulations from which the regression coefficients of RT-SWIFT are generated and which serve in the statistical performance evaluations. The next two sections describe the determination of the Doppler wind from the RT-SWIFT intensities, and a validation of its ability to simulate SWIFT measurements. In the penultimate section, RT-SWIFT is incorporated into a simple one-dimensional retrieval where its effectiveness in retrieving ozone and wind is examined. The performance evaluations include comparisons of averaged line-of-sight winds and inverted wind profiles. Finally, a summary of the results and their implications are presented.

2.  Description of the measurements

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Description of the measurements
  5. 3.  Description of RT-SWIFT
  6. 4.  Doppler wind determination
  7. 5.  Validation of the RT-SWIFT intensities and Doppler wind
  8. 6.  LOS wind retrieval
  9. 7.  Conclusion and recommendations
  10. Acknowledgements
  11. References

The SWIFT instrument extends the Wind Imaging Interferometer (WINDII: Shepherd et al., 1993) observational technique downward into the stratosphere to provide wind and ozone information for the altitude range of 20 to 55 km. WINDII made day and night-time measurements of the mesospheric and thermospheric winds, between 80 and 300 km, by observing the Doppler shifts in visible airglow emission features. SWIFT proposes to apply the same techniques to a relatively isolated ozone thermal emission line near 8.8 µm. The main objectives of SWIFT are to provide simultaneous measurements of horizontal wind velocity vectors and ozone concentration in the stratosphere for improving our understanding of global stratospheric dynamics and for ozone transport studies. The measurement principle and the instrument are further described below.

2.1.  Principle of Doppler wind measurement with a Michelson interferometer

The spectra of a group of emitting molecules in motion relative to an observer are Doppler-shifted from their rest position according to

  • equation image(1)

where equation image is the magnitude of the relative shift of a spectral feature in wave number with respect to the feature's rest position, equation image, w is the speed along the line-of-sight, and c is the speed of light.

An ordinary spectrometer operating in the infrared cannot directly observe the Doppler shift as it is very small (e.g. at 1000 cm−1 the wave number shift due to a 30 m s−1 wind is 0.0001 cm−1). However it is possible to determine the wave number shift from a Michelson interferometer's interferogram by measuring its corresponding phase shift. Figure 1 illustrates the correspondence between a wave number shift of a spectral feature and a phase shift in a Michelson's interferogram. The size of the phase shift in an interferogram, δφ, is related to the optical path difference, Δ, by

  • equation image(2)
thumbnail image

Figure 1. A wind-induced Doppler shift, equation image, (top panel) causes a phase shift, δφ, in an interferogram (middle and bottom panels).

Download figure to PowerPoint

For low-order fringes—small optical path differences (OPD)—a Doppler shift induces an extremely small phase shift (i.e. stretching or compression) in the interferogram relative to the unshifted interferogram. At higher-order fringes—larger OP—the phase shift increases. In principle, larger shifts occur at higher-order fringes, but the amplitude of the interferogram decreases with increasing OPD (see Figure 1). This imposes a constraint on which high-order fringe to measure.

As was done with WINDII, an interferogram's fringe is observed by incrementing the interferometer's movable mirror in small steps away from an initial OPD. The Doppler wind is determined by measuring the phase of an observed interferogram fringe and removing the phase shift contributions from the zero-wind phase and the phase shifts caused by the satellite's orbital motion and its motion relative to the Earth's rotation. Removal of these three phase terms within the context of this article is discussed in section 4.2. More details about phase-stepping interferometry are outlined in section 4, and a more thorough discussion can be found in Hariharan (1987, 1989).

For a limb-scanning instrument, the Doppler wind obtained from an interferogram is an average of all the contributing components of the atmospheric wind field projected along a path's line-of-sight (LOS). In the absence of strong absorption, and when there is no important decrease in concentration at lower levels, the average is heavily weighted towards the region near the tangent height which provides the largest contribution to the emission by virtue of being the lowest and longest section of the path; hence the signal is mostly representative of the tangent height winds except at the lower levels where the absorption impact is strongest. An atmospheric LOS wind profile can be estimated from a collection of limb measurements or Doppler winds using an inversion technique (e.g. Rodgers, 2000). This is illustrated in section 6 using an onion peeling approach (Russell and Drayson, 1972). By viewing the same volume of space from two orthogonal directions, two LOS wind profiles can be retrieved from which a horizontal wind field may be derived.

2.2.  Brief description of the SWIFT instrument

The SWIFT instrument concept is designed to indirectly measure horizontal wind fields using the observed shifts in an interferogram as a proxy for the LOS winds. The interferogram is formed from measurements of the thermal emission of a relatively isolated ozone line near 1133 cm−1. SWIFT, like its predecessor WINDII, is a limb imaging, field widened, phase-stepping Michelson interferometer.

SWIFT views two fields-of-view (FOVs) simultaneously. The FOVs are chosen such that the sampled volume is viewed from nearly orthogonal directions—one at 48° and one at 132°, relative to the forward direction of motion (Shepherd et al., 2001; McDade et al., 2002)—which allows a horizontal wind field to be retrieved from the derived line-of-sight winds obtained from each view. Each observational field-of-view covers a region 2° horizontally by 1° vertically (162 × 81 pixels) with vertical coverage from 15 to 65 km.

Simplistically, the atmospheric signal is passed to a detector array, via transfer optics which includes a narrow-band Fabry–Perot etalon isolating the ozone line at 1133.4335 cm−1, wide and medium-band interference filters—to eliminate the side lobes of the narrow etalon—and a field-widened Michelson interferometer to modulate the signal. The interferometer modulates the signal by adding four small increments to a fixed optical path difference of 18 cm resulting in a four-point interferogram (Figure 2). The four increments, each separated by a quarter wavelength, sample a single high-order fringe on the interferogram. The fringe is chosen from a consideration of the desired wind accuracy, constrained by the measurability of the shift. For a wind measurement of accuracy 1 m s−1, the equivalent phase shift at a fringe of order 105 is 1/16500 of a fringe. Although the shift is small, it is measurable.

thumbnail image

Figure 2. The lower four boxes are examples of the forward viewing image of radiances for four mirror steps (I1, I2, I3, I4). The upper box is an example of a four-point interferogram for a pixel—marked by a white square on each of the four images.

Download figure to PowerPoint

A more detailed description of the SWIFT instrument and similar designs may be found in Rahnama et al. (2006), Rowlands et al. (1996), Scott etal. (2001) and Gault et al. (2001). Calibration issues are discussed in Gault etal. (2003).

3.  Description of RT-SWIFT

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Description of the measurements
  5. 3.  Description of RT-SWIFT
  6. 4.  Doppler wind determination
  7. 5.  Validation of the RT-SWIFT intensities and Doppler wind
  8. 6.  LOS wind retrieval
  9. 7.  Conclusion and recommendations
  10. Acknowledgements
  11. References

At the outset it was decided that RT-SWIFT should be compatible with RTTOV (Saunders et al., 1999). This has the advantage of allowing the model to be easily plugged into existing retrieval or assimilation systems that use it. RTTOV is designed for nadir sounding and not limb-viewing measurements. RT-MIPAS (Bormann et al., 2005), which is applied to the limb-viewing MIPAS measurements, has an RTTOV heritage and is designed to be compatible with RTTOV. Like RTTOV, it has a tangent linear model and its adjoint (Bormann et al., 2005), which are generally required in assimilation or retrieval systems. RT-SWIFT is an adaptation of RT-MIPAS with a modified set of variable gases (RT-SWIFT considers N2O as an additional variable) and an added parametrization for the Doppler effect.

The core of RT-SWIFT is an iterative regression model similar to RT-MIPAS that constructs a limb emission signal from LOS transmittance and temperature profiles. As with MIPAS, the response function is implicitly imbedded within the transmittance model. The product of the SWIFT instrument is a four-point interferogram delivered from each pixel on the detector array. Each point of the interferogram is associated with a particular mirror step and its particular response function, thus RT-SWIFT requires four transmittance models in order to simulate an interferogram.

The following sections briefly describe the radiative transfer for SWIFT, the limb geometry and its unique interdependence with the wind field, followed by the transmittance/radiance model itself.

3.1.  SWIFT radiative transfer

The polychromatic clear-sky thermal infrared radiance for an observer at one end of a limb path—assuming local thermodynamic equilibrium and neglecting scattering (Li, 2002)—is the sum of the attenuated emissions from along the path, plus the attenuated emissions from sources at the far end of the path, i.e.

  • equation image(3)

where s is the distance along the path as measured from the observer; τ is the LOS transmittance from s to the observer; equation image is the Planck function evaluated at wave number equation image and temperature T, and Fi(equation image) is the instrument response function for the ith mirror step. The response function varies from pixel to pixel on the detector array. The variations are due to differences in the ray paths and variations within the instrument. The general form of the response function at mirror position i is

  • equation image(4)

where U is the instrument visibility which is related to the attenuation due to instrumental effects (i.e. imperfections). The value of 0.94 assigned to U for all pixels was taken from Rahnama et al. (2006). Δi(equation image) is the Michelson optical path difference for the ith mirror step, and τoptics(equation image) is the transmittance of the non-moving instrument optics. In this study, there is no pixel-to-pixel variation applied to Δi(equation image). More details on the optics and the response function can be found in Rahnama etal. (2006).

Neglecting the first term of Eq. (3)—negligible provided there are no significant sources within the FOV—and assuming that the variation of B over the spectral response function is small, Eq. (3) can be rewritten as

  • equation image(5)

where 〈 〉 is the averaging operator,

  • equation image(6)

Upon division of the path into a string of Ncell homogenous cells, Eq. (5) can be expressed as:

  • equation image(7)

where τj is the mean transmittance from the jth cell to the satellite (CTS) and Bj is the mean Planck function of the jth cell. The models for τj and Bj are discussed in more detail in sections 3.3 and 3.5 respectively

Multiple detector array columns (vertical slices) are used with SWIFT for the purpose of reducing the wind error contribution from measurement noise. In principle a regression model is required for each pixel on the detector array. A complete model applied to actual measurements would encompass all or most columns of both the rear and forward views. As well, since the SWIFT instrument characteristics are expected to change in flight over both short and long time-scales, e.g. temporal changes in etalon spectral alignment or in optical path difference, a final FFM would have to correctly reflect the impact of these changes. Beyond this, a gradient model version (and its adjoint) would also be needed for use with linearized solution approaches.

For simplicity, this feasibility study for a useful fast forward model was restricted to the application of a single column of pixels, as measurement noise is not being added to the simulated data. The investigation was also restricted to the recovery of the Doppler wind as opposed to the wind vector, and to temporally constant instrument characteristics. The central column of pixels of only the forward-looking FOV was arbitrarily chosen. Finally, finite differences were used for approximating gradients.

3.2.  Definition of the limb path

The atmosphere is assumed to be a set of homogeneous concentric spherical shells defined by a set of vertical profiles of altitude, pressure, temperature, volume mixing ratios and wind. For the purpose of ray-tracing the path, a supplemental profile of the atmospheric refractivity is determined from this atmosphere.

A limb path is defined by its tangent height and is approximated by a string of homogeneous cells whose boundaries are defined where the path intersects the vertical layer boundaries. For indexing purposes, the cell boundary furthest from the observer is designated with the index of the cell. The cell boundaries closest and furthest from the observer are designated as the near and far sides of the cell respectively. The space between the observer and top of the atmosphere (TOA) defines the first cell and is regarded as empty. The path through the tangent layer is physically very long compared to the other cells. For this reason the tangent layer is further subdivided into two cells, the division point being at the tangent point. The average properties of each cell are determined by an in-house ray-tracing program that determines the path length within a cell, and the absorber amount weighted pressure, temperature and volume mixing ratios of the cell. For convenience, the vertical levels are assigned such that the refracted tangent height coincides with the lower boundary of the tangent layer.

The simulations and regression coefficient determinations described in section 3.4 were applied to each of the four points of the interferogram for a group of limb paths defined by a set of fixed tangent pressures. In order to be compatible with RTTOV, the pressure levels of RT-SWIFT are coincident with the 100 pressure levels of RTTOV-9 (Saunders et al., 2008). Since the instrument's vertical field-of-view extends from about 18 to 65 km, only the upper 40 levels of the RTTOV-9 pressure grid are required. The limb paths are defined such that a refracted tangent point coincides with a pressure level as determined by ray-tracing. The model limb paths are defined as the tangent pressures which coincide with levels 8 to 40 (about 18 to 55 km) of the RTTOV levels (see Table I). The vertical spacing of the tangent heights defined by the instrument FOVs ranges from 600 to 660 m and is smaller than the spacing of the RT-SWIFT tangent heights which range from 520 to 1600 m. Most of the RT-SWIFT levels are spaced less than 900 m apart. Although the calculations are done on the RT-SWIFT levels, it is instructive to know how well the radiances would interpolate to the pixel tangent heights grid, if required. Experiments with the line-by-line radiative transfer model demonstrated that interpolation of intensities between the two grids can be done with errors of order 0.5 µW/m2/(cm−1)/sr for altitudes above 32 km and up to 7.5 µW/m2/(cm−1)/sr for altitudes below 3265 km (Turner and Rochon, 2008).

Table I. The 40 pressure levels of RT-SWIFT (hPa).
PindexPRTTOVPindexPRTTOVPindexPRTTOVPindexPRTTOV
  1. For compatibility, RT-SWIFT was chosen to operate on the upper 40 levels of the 100-level RTTOV-9 pressure grid. The 33 FFM limb paths (columns headed by Pindex) are defined by the refracted tangent heights that coincide with the RTTOV pressure levels (columns headed by PRTTOV) highlighted in bold.

 0.016041.68721411.00382435.6504
 0.038052.15261512.64922539.2566
 0.077062.70091614.45592643.1001
 0.137073.33981716.43182747.1882
 0.224484.07701818.58472851.5278
 0.345494.92041920.92242956.1259
 0.5064105.87762023.45263060.9895
10.7140116.95672126.18293166.1252
20.9753128.16552229.12103271.5398
31.2972139.51192332.27403377.2395

As the instrument only views the line-of-sight component of the Doppler shifts, the horizontal wind field must be remapped into an LOS wind representative of each cell. The remapping of the wind field to the LOS winds is tied to the viewing coordinates defined by the satellite orbit and the instrument's FOV pointing relative to the orbit. The viewing coordinate parameters used in this work are: the tangent point coordinates—latitude, longitude and geometric tangent height—and the look angle, ξ, the angle between a limb path's LOS orientation at the tangent point and north. The LOS wind, wLOS, of each cell is the average of its near and far boundary values of the zonal, u, and meridional, v, components of the atmospheric wind projected along the path's line-of-sight, i.e.

  • equation image(8)

In addition to the Doppler shifts due to the atmospheric winds, the instrument also views the additional shifts due to the forward motion of the satellite and the Earth's rotational velocity. The LOS value of these motions—designated as wsr–is assumed to be constant along the path and is assigned the value determined at the tangent point.

The look angle for an RT-SWIFT refracted tangent height is determined by interpolating between the look angles and their corresponding refracted tangent heights associated with the detector array pixels, as determined by the viewing coordinate parameters. Equation (8) uses the interpolated look angle to calculate the equation image appropriate to the RT-SWIFT tangent pressure. A value for wsr is determined in a similar manner.

Finally, the mapping of the detector pixels, with their associated refracted tangent heights, to the tangent heights of the RTTOV pressure levels is used to interpolate the instrument characteristics to the RT-SWIFT limb paths. These interpolated values are required for the transformation of the simulated radiances to the Doppler wind as described in section 4.

3.3.  Transmittance parametrization

As with RTTOV and RT-MIPAS, the RT-SWIFT total transmittance is broken into absorbing groups which are treated independently. The first three of four groups (O3, N2O and H2O) are treated as variables with respect to altitude, whereas the other absorbers (CH4, SO2, NH3, CFC-12 and HCFC-22) are treated as a single invariant group, designated as ‘fg’ for fixed gases. The total transmittance is the product of the transmittances of these four groups,

  • equation image(9)

Equation (9) assumes that the product of convolved transmittances follows Beer's Law. However, unless there is no significant overlap of spectral lines, Eq. (9) does not generally hold true. Some of the errors inherent with this assumption can be diminished by reformulating the left hand side of Eq. (9) as (McMillin et al., 1995)

  • equation image(10)

The four terms comprising the right-hand side of Eq. (10) are the effective CTS transmittances for O3, N2O, H2O and fg respectively. For convenience these four ratios are henceforth represented by equation image, equation image, equation image and equation image respectively. Thus Eq. (9) is re-expressed as

  • equation image(11)

where equation image is the effective CTS optical depth due to gaseous absorption.

In the tradition of previous work (McMillin and Fleming, 1976; Eyre, 1991; Strow et al., 2003; Bormann et al., 2005), optical depths, rather than transmittances, are parametrized. The parametrization is a recursive model that builds up the CTS optical depth by accumulating the effective cell optical depths starting from the near end of the limb path, i.e.

  • equation image(12)

where equation image is the cell's effective optical depth and is defined, for example, as

  • equation image(13)

Each component of the cell effective optical depths in Eq. (12) is represented by a recursive polynomial of the form

  • equation image(14)

where xjm are profile-dependent predictors characterizing the atmosphere state for cell j along the path, M is the number of predictors and ajm are the regression coefficients for each cell.

The regression starts at the cell nearest to the observer and indexes outward. The predictors for O3, H2O and fg (Tables II and III) are similar to those used in the RT-MIPAS model (Bormann et al., 2005). RT-MIPAS does not have N2O predictors, thus a set similar to the O3 predictors is assigned where the volume mixing ratio of N2O replaces the O3 mixing ratio.

Table II. Predictors for RT-SWIFT.
 OzoneNitrous oxideWater vapourfgLOS wsrLOS wind
  1. The table lists the predictors for each absorbing group. There are up to 17 predictors for each group for a total of 64 predictors. The predictors are defined with respect to the jth cell along the path. The profile variables are defined in Table III.

1111111
2equation imageequation imageequation imageequation imageδwjequation image
3equation imageequation imageequation imageequation image(δwj)2equation image
4equation imageequation imageequation imageequation image(δwj)3
5equation imageequation imageequation imageequation image
6equation imageequation imageequation imageequation image
7equation imageequation imageequation imageequation image
8equation imageequation imageequation imageequation image
9equation imageequation imageequation imageequation image
10equation imageequation imageequation imageequation image
11equation imageequation imageequation imageequation image
12equation imageequation imageequation imageequation image
13equation imageequation imageequation image
14equation imageequation imageequation image
15equation image
16equation image
17equation image
Table III. Profile variables used to specify the RT-SWIFT predictors.
  1. Variables are defined with respect to level j. Variables related to fg are denoted by T, those related to ozone by O, and those to water vapour by W. There are no explicit volume mixing ratio inputs for fg since they are fixed, but are implicitly represented by temperature. The nitrous oxide variables (denoted by N) are not tabulated as they are defined exactly the same way as the ozone variables, where the volume mixing ratio of N2O replaces that of O3. δsj and equation image are the refracted path length of the jth cell of the path and the reference path respectively.

equation imageequation imageequation image
equation imageequation imageequation image
equation imageequation imageequation image
equation imageequation imageequation image
equation imageequation imageequation image
equation imageequation image 
equation imageequation image 
equation imageequation imageequation image

It should be noted that the order of the ratioing (Eq. 10) is different in RT-SWIFT than in RT-TOV or RT-MIPAS where the predictor sets have been optimized. Ozone is the most significant absorber and it was thought that it should lead the ratioing sequence instead of the fixed gases as in McMillin et al. (1995). However there was no investigation as to whether this is optimal or not. In addition there was no attempt to optimize the N2O predictor set, as the focus is on the wind predictors.

Previously, other regression models have ignored winds since the wind shifts the spectra by extremely small amounts. In this work two multiplicative modifiers are introduced to account for the change in the effective optical depths due to these spectral shifts.

  • equation image(15)

where equation image is the change in the optical depth due to the spectral shift induced by the satellite motion plus the Earth's planetary rotation motion, and equation image is the change in the optical depth due to the spectral shift induced by the LOS wind. Both equation image and equation image are represented by a regression series similar to Eq. (14) with their motion-based predictors defined in Table IV.

Table IV. Doppler shift proxy predictors.
 Satellite + Earth's rotationWind
  1. The three predictors required to account for the effect of the LOS satellite plus planetary rotational speed, wsr, and the two predictors for atmospheric winds, wLOS. The variables δsj, equation image and equation image are defined in Table III.

1equation imageequation image
2equation imageequation image
3equation image 

In principle, the satellite and Earth's rotational velocities and winds could have been combined into a single velocity. However it is better to model the known and the significantly larger components separately from the smaller unknown atmospheric winds. The choice of the predictor for wsr is based on an examination of how the mean effective optical depth varies with wsr as illustrated in Figure 3. The change in the optical depth for any cell on a path (the vertical line on the plot) appears to be linear. However, closer examination of the variability with respect to wsr for any cell—and other atmosphere/path combinations—indicates that the relation is slightly nonlinear. Hence predictors involving powers of ¡checktext¿ were chosen. In addition, keeping the LOS wind component separate has the advantage of reducing the otherwise larger impact of FFM errors on the recovered LOS winds. This is described and illustrated in sections 4.2 and 5.1.

3.4.  Determination of the regression coefficients

3.4.1.  Measurement simulations

The determination of the RT-SWIFT regression coefficient values described in section 3.3 relies on having a suitable transmittance/radiance database. The required database can be generated through simulations of the atmospheric limb emissions as would be observed by the SWIFT instrument (Eqs (4) and (5)) using the Fast Line-By-Line radiative transfer model (FLBL: Turner, 1995) described below. The atmospheric states necessary for these simulations consist of the vertical profiles of pressure, temperature, the zonal and meridional wind components and the volume mixing ratios of O3, N2O, H2O, CH4, SO2, NH3, CFC-12 and HCFC-22, all initially provided as functions of altitude. Both the FLBL and RT-SWIFT models generate their limb paths in the same manner as described in section 3.2.

thumbnail image

Figure 3. The effective optical depth profile along a limb path (tangent height = 22 km) for seven values of wsr. The inset shows the variation of effective optical depth as a function for wsr for a cell at 1400 km.

Download figure to PowerPoint

The FLBL used to simulate the SWIFT measurements is a speeded-up form of a standard line-by-line (LBL) radiative transfer model (e.g. LBLRTM: Clough et al., 2005). This is achieved by replacing the computationally expensive section of an LBL code that calculates absorption coefficients directly from a spectral database with absorption coefficient look-up tables set on a wave number, pressure and temperature grid. Although the absorption coefficient does have a dependency on the amount of gas present, it is insignificant for atmospheric cases (Turner, 1995) and hence the tables only require p and T dependencies in order to be accurate. With the exception of water vapour, there is one table per absorber. The combined water vapour line spectrum and continuum has a strong absorber amount dependency, which can be removed by considering two tables formatted in the manner outlined in Turner (1995) instead of one. When compared to the in-house LBL code used to create the tables, the FLBL code is about 400 times faster and is generally within 0.1% (Turner, 1995). Consequently, the FLBL enables relatively quick processing of a large number of simulations as required by many projects. The FLBL compares favourably in intercomparison studies of nadir viewing simulations with other LBLs (Garand et al., 2001; Saunders et al., 2007). In turn, the RT-SWIFT is about 1950 times faster than the FLBL, this increase in performance being necessary for near real-time data assimilation.

Tables of absorption coefficients for O3, N2O, H2O, CH4, SO2, NH3, CFC-12 and HCFC-22 were created for the spectral region 1132.8 to 1134.0 cm−1 on a grid interval of 0.0002 cm−1. The choice of absorbers and spectral resolution is based on the earlier work of Rahnama et al. (2006) and Rochon et al. (2006) and on unpublished studies by Rochon and Turner. The N2O, H2O, CH4, and NH3 line spectra are taken from HITRAN 2000 and 2001 (Rothman et al., 2003), and the O3 and SO2 line spectra are from HITRAN 1996 (Rothman et al., 1998). The spectra for CFC-12 and HCFC-22 are equally spaced lines that were created from their respective continua. These are taken from a revised version of the ATMOS AFGL line parameter files (Brown et al., 1987) as used with the SFIT2 retrieval software (e.g. Hase et al., 2004). The H2O continuum is accounted for by CKD2.4 (Clough et al., 1989). In all cases the Voigt line shape is assumed.

The FLBL simulates atmospheric limb emission spectra on the same wave-number grid as the look-up tables and they are convolved with the appropriate instrument response function (section 3.1). The simulated radiance measurements have been validated by comparing them to corresponding results from the simulation model used in Rahnama et al. (2006) and Rochon et al. (2006). The implementation of some of the measurement configuration aspects relied on consulting a later version of the simulation software employed in the above two articles. The instrument configuration and parameter values, provided by EMS Technologies Inc. (Ottawa, Canada; now part of Com Dev Intl Ltd), are an updated version of those used in the above articles (e.g. a reference optical path difference of 16 cm instead of 18 cm).

3.4.2.  Training atmospheres

As indicated above, a suitable transmittance/radiance database is required in order to generate a set of regression coefficients for RT-SWIFT. Such a database is derived from FLBL simulations of a diverse set of atmospheres that were selected from the output of the Canadian Middle Atmosphere Model - Data Assimilation System (CMAM-DAS) described in Polavarapu et al. (2005) where only meteorological data was assimilated. The CMAM-DAS model provides global fields of geopotential height, pressure, temperature, zonal and longitudinal wind components and volume mixing ratios for H2O, O3, N2O, CH4 and CFC-12 on 71 levels from near surface to about 97 km (up to 0.001 hPa). The remaining absorbers, SO2, NH3 and HCFC-22, are filled in with climatological profiles (US Committee on Extension to the Standard Atmosphere, 1976; Anderson et al., 1986; Peterson and Margitan, 1995). For the purpose of representativeness, the model grid points (48 × 96) for 24 days—using the 16th of every month for the years 2002 and 2003—are extracted for a total of 110 592 atmospheres. In addition to the aforementioned fields, the date, location, surface pressure and surface geopotential height are provided. Hole filling was applied to some species profiles in order to remove low-value outliers related to the back-and-forth spectral–physical space conversions. This hole filling is relevant mostly to the upper mesosphere and to a lesser extent the troposphere. Use of more than one hundred thousand sets of atmospheres would require an extensive amount of computational resources, but such a large number is not required to conduct the regressions. This massive database was compacted down to a more manageable set of 94 atmospheres using a principle component analysis (PCA). The PCA method has been successfully used to create representative databases for other studies (Turner and Chouinard, 1997; Garand et al., 1999, 2001).

3.4.3.  Determination of the regression coefficients

The FLBL is used to simulate the transmittances for each absorbing group (see Eqs (10) and (11)) for all possible limb paths, all pixels of the chosen column, and all mirror step combinations. As a first step, the LOS winds are set to zero and refwsr is set to an average speed of 4850 m s−1. Next, the optical depths (equation image, equation image, equation image, equation image) are formed (Eqs (12) and (13)) and the regression coefficients, ajm, of their corresponding versions of Eq. (14) are generated.

The regression coefficients accounting for wsr are determined by repeating the calculations for the CTS transmittances and radiances of the group O3 + N2O + H2O + fg, for various values of wsr. Thirty-one values of wsr, ranging from 4000 to 5500 m s−1 in intervals of 50 m s−1, are considered. This group of effective CTS optical depths is designated with the superscript ‘osr’, where the ‘o’ indicates no wind. The group containing the reference value of wsr (4850 m s−1) is designated with the superscript ‘ooo’.

The regression coefficients, equation image, accounting for wsr for each pixel are determined through least-squares minimization of the differences between the left and right sides of

  • equation image(16)

The final group of coefficients used to account for the LOS wind of each pixel is determined by repeating the previous calculations with the LOS winds included. This group is designated with the superscript ‘wsr’ and the regression coefficients, equation image, are determined by regressing

  • equation image(17)

3.5.  Planck function parametrization

The mean Planck function of Eq. (7) follows the model described in Planet (1988) where 〈B(T)〉 is approximated by a monochromatic Planck function at an effective temperature, Teff, and a fixed wave number, equation image:

  • equation image(18)

equation image is usually defined as the centroid of the response function.

Generally a linear relationship is assumed between Teff and T. However, a plot of Teff versus T (Figure 4) for four different limb paths and 94 atmospheres over a wide range of T reveals that the relationship is not quite linear. Upon closer examination, the data separate into distinct groups, each corresponding to a limb path (inset of Figure 4). For the region around T = 260 K the spread in Teff across 33 paths is 1 K (inset of Figure 4), indicating that 〈B(T)〉 is path dependent. In addition, each sub-curve itself has some error associated with it. These errors are due to the variation of tangent height with atmosphere, and hence Teff, through the response function. These errors are sufficiently small that they can be ignored.

thumbnail image

Figure 4. Teff vs. T for four different paths Pindex (Table I) and 94 atmospheres. The inset illustrates the separation of limb paths.

Download figure to PowerPoint

Figure 5 (e.g. path 22) illustrates the residuals between Teff as determined by inverting Eq. (18), and Teff as determined by a fit to polynomials up to order 4. The assumption of linearity does not work well in this case. Consequently a higher order, a cubic, was selected for this study, i.e.

  • equation image(19)
thumbnail image

Figure 5. The residuals for path 22 of Figure 4 of the Planck function assuming Teff is linear (dashed line), quadratic (dotted line), or cubic (solid line), in T. The residuals of the quadratic and cubic are magnified by 10 and 100 times respectively.

Download figure to PowerPoint

a, b, c, d and equation image are collectively known as the band correction coefficients. The band correction coefficients were determined by fitting the data to Eq. (19) for each sub-curve of Figure 4.

4.  Doppler wind determination

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Description of the measurements
  5. 3.  Description of RT-SWIFT
  6. 4.  Doppler wind determination
  7. 5.  Validation of the RT-SWIFT intensities and Doppler wind
  8. 6.  LOS wind retrieval
  9. 7.  Conclusion and recommendations
  10. Acknowledgements
  11. References

The SWIFT instrument has been set up to take four measurements (over a fringe) of the attenuated atmospheric Doppler-shifted emissions from along a limb path across a short piece of the spectrum. The resulting measured interferogram is a superposition of many interferograms that can be regarded as equivalent to an interferogram from a single Doppler-shifted source, and is represented as (e.g. Shepherd, 2002):

  • equation image(20)

where I0 is the mean radiance of the fringe, Φ is the effective total phase (i.e. the phase for i = 0) and φi is the phase added to the initial phase when the mirror is stepped to position i. The FFM and FLBL provide our Ii's for each of the different column elements of the RTTOV-based grid.

The effective Doppler wind—the net weighted average wind along the instrument's LOS—is determined by first extracting the effective total phase of the interferogram, followed by the removal, from Φ, of the phase due to the satellite plus Earth's rotational motions, and the total phase at φ1 = 0 in the absence of any Doppler wind shift, i.e. the zero-wind phase. Details of this approach are provided in the following two subsections. This procedure is used for interferograms created by both RT-SWIFT and the FLBL.

4.1.  Determination of the total phase of the interferogram

The instrument is set up to take measurements at four nearly equidistant points across an interferogram's fringe (Figure 2) by adding three equidistant phases, φi, to the initial phase, Φ (Eq. (20) for i = 1, 2, 3, 4). The solution of the total phase from the resulting set of four equations and four measurements is

  • equation image(21)

where it is assumed that the known four phases are not equidistant.

The relationship between the wind information imbedded in the total phase and the Doppler wind phase is considered in the next section.

4.2.  Doppler wind determination

Once the total phase has been determined, the Doppler wind is found by the removal of the phase contributions due to the satellite motion, the Earth's rotational motion, and the zero-wind phase.

The total phase, Φ, of the interferogram is related to the OPD by

  • equation image(22)

where Δ is the OPD evaluated at wave number equation image. The total phase for a shifted interferogram ΦS due to w can be written as (see Eqs (1) and (2))

  • equation image(23)

Δ is wave-number dependent due to the refractive dispersion characteristics of the glass in the arms of the interferometer. This variation is accounted for by linearizing Δ across the region of interest (Thuillier and Hersé, 1988), i.e.

  • equation image(24)

where Δ0 and ∂Δ/∂λ are evaluated at equation image. Substituting Eq. (24) into Eq. (23) and neglecting the second-order term in w/c leads to

  • equation image(25)

where Δeff (= Δ0λ0Δ/∂λ) is known as the effective optical path difference (Thuillier and Hersé, 1988), and is named as such because its value, rather than Δ0, determines the phase shift.

ΦS is the sum of three phase terms: the zero-wind phase, equation image, the phase due to the satellite motion and the Earth's planetary rotation motion, φsr, and the phase due to the contributing Doppler-shifted wind, φD,

  • equation image(26)

The wind phase is determined by removing the (φ0 + φsr) component from the total phase. Ideally, the precise phase contribution due to the LOS satellite and Earth rotation velocity components would be calculated from their velocity components, and the zero-wind phase would be determined, at least partially, through calibration.

However, for this exercise the performance of the fast forward model is determined by simulating two interferograms: the measured interferogram, ΦS, and the windless, or ‘calibration’, interferogram. The latter is denoted by ΦC and is the sum of φ0 and φsr. One of the advantages of parametrizing wsr and wLOS separately in the regression model (section 3.3) is now apparent. The justification for two simulations instead of one is provided below. The effective Doppler wind phase is the difference between the measured total phase and the calibration total phase, i.e.

  • equation image(27)

which can be written as

  • equation image(28)

where

  • equation image(29)

Here, the Doppler wind wD refers to some weighted average of wind contributions along the line of sight, i.e. line-of-sight Doppler winds denoted earlier as wLOS.

Rearranging for the Doppler wind yields

  • equation image(30)

In this study, we will compare the wind phases obtained through Eq. (27) from the results of both the FFM and the FLBL. This is done to remove any errors that might result from any differences in the derived total windless phases (ΦC, i.e. for a null atmospheric wind) obtained from the two sets of simulations. This is illustrated in section 5.1.

5.  Validation of the RT-SWIFT intensities and Doppler wind

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Description of the measurements
  5. 3.  Description of RT-SWIFT
  6. 4.  Doppler wind determination
  7. 5.  Validation of the RT-SWIFT intensities and Doppler wind
  8. 6.  LOS wind retrieval
  9. 7.  Conclusion and recommendations
  10. Acknowledgements
  11. References

The accuracy of RT-SWIFT is evaluated by comparing the FFM simulations with the FLBL simulations for the dependent atmosphere set (i.e. the training set) and for a set of independent atmospheres. The only source of differences between the FFM and FLBL simulations are the errors from the limitations of the FFM regression model. The residuals, defined as the differences FLBL-FFM, characterize the errors of the fast forward model. The residuals of the above sets of atmospheres and their associated means and standard deviations have been produced for the four intensities, the total phases and the effective Doppler wind. The results are a function of tangent pressure levels but are depicted as profiles in tangent height. Residuals obtained from retrieved LOS wind profiles in altitude are presented afterwards in section 6.

5.1.  Errors for the dependent atmosphere set

Simulations of the four-point interferograms at all tangent pressures were generated for the dependent atmosphere set assuming atmospheric winds and then again assuming no winds. Each simulation is repeated 17 more times assuming a wsr ranging from 4500 to 5300 m s−1—the anticipated range of satellite plus Earth rotation speeds for the forward-looking field of view—in steps of 50 m s−1. Figure 6 plots the residuals of the four-point interferogram radiances (with wind, Iw, and without wind, I0), the derived total phase, ΦS, the simulated calibration phase, ΦC, the Doppler wind phase, and the Doppler wind as a function of tangent height. In addition the figure provides mean residuals, or biases, and standard deviations as a function of mean tangent heights. The individual points for each colour, and scattered about a mean tangent height, denote limb paths for a predefined tangent pressure.

thumbnail image

Figure 6. The upper four boxes on the left-hand side plot the distribution of residuals (µW/m2/sr/(cm−1)) between the FLBL and FFM training set radiances for each of the mirror steps (Iw1, Iw2, Iw3, Iw4). The corresponding boxes to their right are the residuals of the ‘calibration measurements’ (i.e. no wind: Ic1, Ic2, Ic3, Ic4). The residuals are plotted against tangent height (km). Each coloured band centred about a tangent height represents a path as defined by it tangent pressure. The vertical variability of a band represents the variation in the tangent height for a given tangent pressure. The 5th row of boxes plots the residuals (deg) between the FLBL and FFM determinations of Φs (differencing of Iws) and Φc (differencing of Ics) respectively. The left-hand box on the bottom row plots the residuals (deg) of the effective Doppler wind phase and the right-hand box plots the residuals (m s−1) of the Doppler wind. The bias (solid line) and standard deviation (dashed line) of the residuals are plotted in each box.

Download figure to PowerPoint

In general, the biases of the intensities are relatively constant from 15 to 35 km. They are smallest at high altitudes, increasing negatively to a peak near 40 km and then falling back towards smaller values. A similar structure can be seen in the standard deviation profiles. The source of this structure of the mean errors from the FFM is not known. However, this structure, which appears to be common to the four intensities, is mostly removed upon calculation of the total phase (Eq. (21)) through taking differences of the intensities.

The biases of the total phases (not visible on the panels) are relatively constant at about 0.02° (1/18000 of a fringe) above 23 km and increase slightly below, whereas the standard deviations are around 0.2° above 23 km and increase to 0.35° below 23 km. The smaller Doppler wind phase biases are about 0.005° and the standard deviations are about 0.04° between 20 and 35 km, increasing to 0.12° at 50 km. This shows that application of Eq. (27) to provide the Doppler wind phases ΦD for both the FFM and FLBL cancels significant regression errors common to equation image and equation image, i.e.

  • equation image

The resulting Doppler wind biases range from −0.2 to 0.4 m s−1 and the standard deviations are about 1.8 m s−1 below 35 km, increasing to 5.2 m s−1 at 50 km.

5.2.  Errors for a quasi-independent atmosphere set

A quasi-independent set of 250 atmospheres was randomly extracted from the CMAM-DA database with members of the original training set explicitly excluded. A randomly selected orbital position was assigned to each atmosphere from a database of 104 simulated orbital positions covering two circular orbits with a satellite altitude of 650 km (courtesy of C.S. Haley, previously at York University, Toronto, Canada).

Ideally, the independent set should not be compiled from the same source as the dependent set, but from an altogether different source. However, this database captures the required quantities in a self-consistent manner over the vertical range considered, which is sufficient for this demonstration study.

Figure 7 shows the residuals for the quasi-independent atmosphere set, minus the total phases, in the same manner as Figure 6. The spread of errors is slightly larger for some of the intensity panels of Figure 7. The most notable difference is the increase of bias at lower altitudes to twice the magnitude of the upper atmosphere bulge found near 40 km. The Doppler wind phase residuals (biases <0.01°, standard deviations are 0.02° to 0.03°) and Doppler wind residuals (biases <0.5 m s−1, standard deviations are 1 to 1.5 m s−1) are of the same order, but are also often smaller and more constant with height than the dependent set. Currently it is unknown why the dependent set statistics behaves as they do as compared to the independent set statistics. However, considering the results of Figure 6, the biases of Figure 7 are larger than one would expect. These might be due to the predictor choices—recalling that there was no attempt at optimizing the non-wind predictors—and possibly an inadequate training set, particularly for the lower layers.

6.  LOS wind retrieval

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Description of the measurements
  5. 3.  Description of RT-SWIFT
  6. 4.  Doppler wind determination
  7. 5.  Validation of the RT-SWIFT intensities and Doppler wind
  8. 6.  LOS wind retrieval
  9. 7.  Conclusion and recommendations
  10. Acknowledgements
  11. References

In this section, the impact of the FFM limitations on the retrieval LOS wind profiles and in the absence of other error sources is assessed from a set of FLBL simulated measurements.

thumbnail image

Figure 7. Same as for Figure 6 for the independent set of atmospheres. The plots of the residuals for Φs and Φc are excluded.

Download figure to PowerPoint

As in section 5, the SWIFT measurements are simulated using the FLBL. Unconstrained retrievals are performed using the FFM for each member atmosphere of the independent set of atmospheres. Other error sources are eliminated by furnishing the same information to both the FLBL and RT-SWIFT simulations, except for the first-guess LOS wind profile which is set to a null wind.

6.1.  LOS wind

One of the advantages of limb sounding is that the geometry of a limb measurement is such that no information comes from below the tangent point. The onion peeling retrieval algorithm takes advantage of this configuration (Russell and Drayson, 1972). In its simplest form, a profile can be retrieved by first dividing the atmosphere into a set of homogeneous shells with each shell containing one limb view tangent point. The parameter of interest is retrieved in the uppermost layer using the uppermost limb measurement. Subsequent shells are iteratively retrieved using the results from the previous shells, that is, as each shell is solved, or peeled off, a new shell is exposed, hence the term onion peeling.

The LOS winds are retrieved using the onion-peeling technique in conjunction with the Newtonian predictor

  • equation image(31)

where equation image is the ith guess of the LOS wind for the jth layer, equation image is the previous guess, equation image is the FLBL Doppler wind phase and y(x) represents the FFM simulated Doppler wind phase (ΦD; section 4.2). The local gradient, equation image, is approximated by

  • equation image(32)

where the perturbation δx is set to 1 m s−1. Some experimentation with other values of δx (e.g. 0.1 m s−1 and 10 m s−1) produced no significant effect on the results. A threshold of 0.1 m s−1 between successive solutions was found to be suitable as a convergence criterion.

The retrieval is initiated with a null wind profile. After an iteration of equation image for the highest tangent level, the LOS wind in each cell of path 1 above the highest tangent level is modified by adding the difference equation image to the current values. This is done to minimize any abrupt transition from the assumed x-profile above the first tangent layer and the derived value for x1.

Figure 8 compares the differences between the true LOS winds and those retrieved by the above method. The biases or means of the differences are less than 0.5 m s−1 for altitudes greater than 28 km and less than 1 m s−1 for altitudes greater than 22 km. The standard deviations are between approximately 2 and 5 m s−1 over the vertical range of about 23 to 48 km. Below 23 km the results deteriorate rapidly. Error standard deviations due to measurement random errors are provided in Figure 8 for comparison. Measurement random error contributes roughly 2–3 m s−1 of the total wind error for an effective vertical resolution of ∼1.5 km over most of the 20–45 km altitude region (based on more recent unpublished results by the second author). These random error standard deviations were derived using all columns of the detector array as opposed to the FFM results which are for a single column.

6.2.  Ozone and LOS wind retrieval

In the previous section, winds were retrieved assuming all other factors were well known. However, the other variables, the main ones being ozone and temperature, are not generally well known. SWIFT can be used to retrieve ozone assuming that a sufficiently accurate temperature is provided from another source (e.g. a weather prediction system). In this section the impact on the LOS wind retrieval after retrieving ozone first is briefly explored. Ozone retrieval is conducted here using the mean values of the four intensities recorded from the interferograms (I0, section 4).

thumbnail image

Figure 8. Comparison of the residuals between the true and the retrieved LOS winds (small dots), their biases (solid blue line) and standard deviations (solid red line) for the independent set of atmospheres. The colourations of the small dots have the same meaning as in Figure 6. The dashed red line included for comparison gives the error standard deviations due to measurement random error.

Download figure to PowerPoint

For the ozone retrieval, the Chahine predictor is used (Chahine, 1968, 1970), i.e.

  • equation image(33)

where x is the ozone volume mixing ratio and y is the mean of the four intensities. The initial guesses for ozone were set as the true ozone volume mixing ratio profiles; the deviations of the final solutions from the true ozone profiles are the result of the differences between the FFM and the FLBL mean intensities. A null wind profile was applied with the FFM at the ozone retrieval stage. Some experiments were performed to verify that the ozone retrieval with the FFM can be taken as insensitive to the wind profile. This is expected since the mean intensity of the interferogram is effectively equivalent to a simple radiometer measurement where tiny fluctuations due to spectral shifts are negligible.

In a manner similar to the Newtonian approach of the previous section, the abrupt transition from the assumed x-profile above the first tangent layer and the derived value at equation image is minimized by modifying those layers with the scaling factor, equation image.

The Chahine approach has been used for retrieving ozone rather than the Newtonian approach since the implemented iterative set-up of the former better contained the non-convergence problem encountered at the lower levels below 24 km. Considering the choice of initial guess for the ozone profiles, this non-convergence problem is believed to reflect a need to optimize the FFM. Although the Chahine approach contained this problem, the retrieved ozone below 24 km cannot be considered reliable. Consequently, the ozone results presented for the lower levels do not reflect the actual limitations of this FFM at these heights. The ozone results were applied as produced in order to proceed with the retrieval of winds.

Figure 9 illustrates the percentage difference between the true and retrieved ozone volume mixing ratios. The biases are less than 6% above 32 km and increase to 12% at 27 km and beyond below this altitude. Above 30 km, the standard deviations are under 5% and, at altitudes below 27 km, are greater than 10%. As previously noted, the ozone results are not reliable at levels lower than 24 km. The error standard deviations due to measurement random error are less than 0.5% (e.g. Rochon et al., 2006) and so were not included in Figure 9.

thumbnail image

Figure 9. Comparison of the residuals between the true and retrieved O3 (small dots), their biases (solid blue line) and standard deviation (solid red line) for the independent set of atmospheres. The colorations of the small dots have the same meaning as in Figure 6. Thirteen outliers (>8 std. dev.) have been removed.

Download figure to PowerPoint

Figure 10 illustrates the differences between the true LOS winds and retrieved LOS winds subject to the FFM calculations using the retrieved ozone profiles. Figure 10 looks much like Figure 8 down to 24 km. Below this level, the spread over the error profiles becomes more significant with the presence of the ozone errors. The similarity between the error structures of the wind and ozone/wind retrieval cases demonstrates that the wind errors are not significantly impacted by the ozone retrieval errors related to the FFM down to 24 km.

thumbnail image

Figure 10. Comparison of the residuals between the true and retrieved LOS winds (small dots) using the O3 profiles shown in Figure 9. The biases (solid blue line) and the standard deviations (solid red line) of the residuals are shown. The colorations of the small dots have the same meaning as in Figure 6. The dashed red line included for comparison gives the error standard deviations due to measurement random error.

Download figure to PowerPoint

A comparison of six sets of diverse LOS wind profiles in Figure 11 shows that the retrievals capture the shapes and magnitudes of the LOS wind profiles from the upper atmosphere (45–50 km) down to 24 km giving wind errors generally within 3 or 4 m s−1. The ability to capture the main features of an LOS wind profile indicates that the model performs reasonably well—at least above 24 km. However, Figure 11 also indicates that improvements to the FFM are required to better reflect the sensitivity of the radiances to the wind and certainly to the ozone at the lower levels.

7.  Conclusion and recommendations

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Description of the measurements
  5. 3.  Description of RT-SWIFT
  6. 4.  Doppler wind determination
  7. 5.  Validation of the RT-SWIFT intensities and Doppler wind
  8. 6.  LOS wind retrieval
  9. 7.  Conclusion and recommendations
  10. Acknowledgements
  11. References

The feasibility of a regression-based fast forward model for use in inversion and data assimilation of limb viewing Doppler wind measurements was investigated and evaluated using the SWIFT satellite instrument concept. This brought about the development of the RT-SWIFT fast forward model described herein. The fast forward model was developed to take advantage of the structure of RTTOV and applied the RT-MIPAS regression predictor set for constituents and introduced a new set of predictors to account for the Doppler wind. It was applied for a simplified instrument framework consisting of a single detector column and a single instrument field-of-view with temporally invariant characteristics.

thumbnail image

Figure 11. Comparison of the true LOS winds (blue), the retrieved LOS wind assuming the true O3 (green), and the retrieved LOS wind using the retrieved O3 (red), for a sample of six atmospheres taken from the set of independent atmospheres.

Download figure to PowerPoint

The evaluation was conducted by determining the wind and ozone error levels resulting from the limitations of the developed RT-SWIFT in replicating simulated measurements in the absence of other error sources. In order to retrieve Doppler wind profiles from SWIFT measurements, knowledge of the temperatures and the volume mixing ratios for ozone, and to a lesser degree other constituents, is required. Ozone profiles were extracted from the FLBL-simulated radiances using the FFM when the other profiles are known (other than the wind). The ozone errors range roughly between 3% and 15% for altitudes above 24 km with larger errors at lower levels. Given the retrieved ozone, the resulting wind error levels were found to be about 3 to 5 m s−1 for altitudes in the range 24–45 km. Both the ozone and Doppler wind error levels are larger than the targets of ∼1% and 1 m s−1 set at the onset of the study. Given the current FFM model and assuming resultant error levels from other error sources of 5 m s−1 for wind and 5% for ozone (section 1), the total error levels for SWIFT could conceivably be in the range of 6–8 m s−1 and 6–16% for altitudes in the range of 24–45 km. These are either within or somewhat over the required upper limits of 5–10 m s−1 and 10% for ozone indicated in the introduction.

The current results suggest that an investment in improving the model performance is justifiable in addition to being warranted. This assumes that wind measurements from limb observing instruments such as SWIFT are to be eventually available. The required improvement in performance for RT-SWIFT is needed mostly for the lower levels. This may be due to a need for optimization of the regression model to better reflect either the stronger self absorption of ozone or the more important signal contribution from other constituents at lower levels or both. In addition there was no optimization of any of the predictors for O3, N2O, H2O, the fixed gases or the order of ratioing set out in Eq. (10). More work on optimizing these predictors is required. Although an attempt was made to optimize the wind parameters, it was not a major effort and requires more investigation.

Acknowledgements

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Description of the measurements
  5. 3.  Description of RT-SWIFT
  6. 4.  Doppler wind determination
  7. 5.  Validation of the RT-SWIFT intensities and Doppler wind
  8. 6.  LOS wind retrieval
  9. 7.  Conclusion and recommendations
  10. Acknowledgements
  11. References

We thank Pierre Gauthier who proposed the need for this study and Louis Garand, Mohammed Shokr and the manuscript reviewers for their useful comments that helped improve the manuscript.

References

  1. Top of page
  2. Abstract
  3. 1.  Introduction
  4. 2.  Description of the measurements
  5. 3.  Description of RT-SWIFT
  6. 4.  Doppler wind determination
  7. 5.  Validation of the RT-SWIFT intensities and Doppler wind
  8. 6.  LOS wind retrieval
  9. 7.  Conclusion and recommendations
  10. Acknowledgements
  11. References
  • Anderson GP, Clough SA, Kneizys FX, Chetwynd JH, Shettle EP. 1986. AFGL atmospheric constituent profiles (0120 km).’ Air Force Geophysics Laboratory Tech. Rep. AFGL-TR-86-0110, 43 pp.
  • Atlas R. 1997. Atmospheric observations and experiments to assess their usefulness in data assimilation. J. Meteorol. Soc. Jpn 75: 120.
  • Beagley SR, de Grandpré J, Koshyk JN, McFarlane NA, Shepherd TG. 1997. Radiative-dynamical climatology of the first-generation Canadian middle atmosphere model. Atmos.-Ocean 35: 293331.
  • Bormann N, Matricardi M, Healy SB. 2005. A fast radiative-transfer model for the assimilation of infrared limb radiances from MIPAS. Q. J. R. Meteorol. Soc. 131: 16311653.
  • Brown LR, Farmer CB, Rinsland CP, Toth RA. 1987. Molecular line parameters for the atmospheric trace molecule spectroscopy experiment. Appl. Opt. 26: 51545182.
  • Chahine MT. 1968. Determination of the temperature profile in an atmosphere from its outgoing radiance. J. Opt. Soc. Am. 58: 16341637.
  • Chahine MT. 1970. Inverse problems in radiative transfer: Determination of atmospheric parameters. J. Atmos. Sci. 27: 960967.
  • Clough SA, Kneizys FX, Davies RW. 1989. Line shape and the water vapor continuum. Atmos. Res. 23: 229241.
  • Clough SA, Shephard MW, Mlawer EJ, Delamere JS, Iacono MJ, Cady-Pereira K, Boukabara S, Brown PD. 2005. Atmospheric radiative transfer modeling: A summary of the AER codes. J. Quant. Spectrosc. Radiat. Transfer 91: 233244.
  • Eyre JR. 1991. A fast radiative transfer model for satellite soundingsystems.’ Technical Memorandum No. 176, ECMWF, Shinfield Park, Reading, UK, 30 pp.
  • Garand L, Turner DS, Chouinard C, Hallé J. 1999. A physical formulation of atmospheric transmittances for the massive assimilation of satellite infrared radiances. J. Appl. Meteorol. 38: 541554.
  • Garand L, Turner DS, Larocque M, Bates J, Boukabara S, Brunel P, Chevallier F, Deblonde G, Engelen R, Hollingshead M, Jackson D, Jedlovec G, Joiner J, Kleespies T, McKague DS, McMillin LM, Moncet J-L, Pardo JR, Rayer PJ, Salathe E, Saunders R, Scott NA, Van Delst P, Woolf H. 2001. Radiance and Jacobian intercomparison of radiative transfer models applied to HIRS and AMSU channels. J. Geophys. Res. 106: 2401724031.
  • Gault WA, McDade IC, Shepherd GG, Mani R, Brown S, Gregory P, Scott A, Rochon YJ, Evans WFJ. 2001. SWIFT: An infrared Doppler Michelson interferometer for measuring stratospheric winds. Proc. SPIE 4540: 476481.
  • Gault WA, McDade IC, Rochon YJ, Scott A. 2003. Filters and calibration for the SWIFT instrument on GCOM-A1. Proc. SPIE 4881: 6066.
  • Hariharan P. 1987. Digital phase-stepping interferometry: Effects of multiply reflected beams. Appl. Opt. 26: 25062507.
  • Hariharan P. 1989. Phase stepping interferometry with laser diodes. 2: Effects of laser wavelength modulation. Appl. Opt. 28: 17491750.
  • Harris RA (ed). 2000. Envisat: MIPAS—An instrument for atmospheric chemistry and climate research. ESA SP-1229, 124 pp. Available from ESA Publications Division, ESTEC, PO Box 299, 2200 AG Noordwijk, The Netherlands.
  • Hase F, Hannigan JW, Coffey MT, Goldman A, Höpfner M, Jones NB, Rinsland CP, Wood SW. 2004. Intercomparison of retrieval codes used for the analysis of high-resolution, ground-based FTIR measurements. J. Quant. Spectrosc. Radiat. Transfer 87: 2552.
  • Lahoz WA, Brugge R, Migliorini S, Lary D, Lee A, Swinbank R, Jackson DR. 2003. SWIFTApplication of stratospheric wind measurementsto process studies and meteorology.’ Final Report, March 2003, ESTEC Contract No. 15344/01/NL/MM. Available from ESA Publications Division, PO Box 299, 2200 AG Noordwijk, The Netherlands.
  • Lahoz WA, Brugge R, Jackson DR, Migliorini S, Swinbank R, Lary D, Lee A. 2005. An observing system simulation experiment to evaluate the scientific merit of wind and ozone measurements from the future SWIFT instrument. Q. J. R. Meteorol. Soc. 131: 503523.
  • Li J. 2002. Accounting for unresolved clouds in a 1D infrared radiative transfer model. Part I: Solution for radiative transfer, including cloud scattering and overlap. J. Atmos. Sci. 59: 33023320.
  • McDade IC, Shepherd GG, Gault WA, Rochon YJ, McLandress C, Scott A, Gregory P, Rowlands N, Buttner G, Wehr T, Bezy JL. 2002. ‘Stratospheric wind measurements with SWIFT onboard GCOM-A1.’ Proc. Int. Symposium on Stratospheric variations and climate, Fukuoka, Japan, 1215 November 2002.
  • McMillin LM, Fleming HE. 1976. Atmospheric transmittance of an absorbing gas: A computationally fast and accurate transmittance model for absorbing gases with constant mixing ratios in inhomogeneous atmospheres. Appl. Opt. 15: 358363.
  • McMillin LM, Crone LJ, Kleespies TJ. 1995. Atmospheric transmittance of an absorbing gas. 5. Improvements to the OPTRAN approach. Appl. Opt. 34: 83968399.
  • Peterson DB, Margitan JJ (eds). 1995. Upper Atmospheric Research Satellite Correlative Measurement Program (UARS-CMP) Balloon Data Atlas. NASA: Washington D.C.
  • Planet WG. 1988. ‘Data extraction and calibration of TIROS-N/NOAA radiometers.’ NOAA Technical Memorandum NESS 107-Rev.1, US Department of Commerce: Washington D.C., 58 pp.
  • Polavarapu S, Ren S, Rochon YJ, Sankey D, Ek N, Koshyk J, Tarasick D. 2005. Data assimilation with the Canadian middle atmosphere model. Atmos.–Ocean 43: 77100.
  • Rahnama P, Rochon YJ, McDade IC, Shepherd GG, Gault WA, Scott A. 2006. Satellite measurement of stratospheric winds and ozone using Doppler Michelson interferometry. Part I: Instrument model and measurement simulation. J. Atmos. Oceanic Technol. 23: 753769.
  • Rochon YJ, Rahnama P, McDade IC. 2006. Satellite measurement of stratospheric winds and ozone using Doppler Michelson interferometry. Part II: Retrieval method and expected performance. J. Atmos. Oceanic Technol. 23: 770784.
  • Rodgers CD. 2000. Inverse Methods for Atmospheric Sounding: Theory and practice. World Scientific: Singapore.
  • Rothman LS, Rinsland CP, Goldman A, Massie ST, Edwards DP, Flaud J-M, Perrin A, Camy-Peyret C, Dana V, Mandin J-Y, Schroeder J, McCann A, Gamache RR, Wattson RB, Yoshino K, Chance KV, Jucks KW, Brown LR, Nemtchinov V, Varanasi P. 1998. The HITRAN molecular spectroscopic database and HAWKS (HITRAN Atmospheric Workstation): 1996 edition. J. Quant. Spectrosc. Radiat. Transfer 60: 665710.
  • Rothman LS, Barbe A, Benner DC, Brown LR, Camy-Peyret C, Carleer MR, Chance K, Clerbaux C, Dana V, Devi VM, Fayt A, Flaud J-M, Gamache RR, Goldman A, Jacquemart D, Jucks KW, Lafferty WJ, Mandin J-Y, Massie ST, Nemtchinov V, Newnham DA, Perrin A, Rinsland CP, Schroeder J, Smith KM, Smith MAH, Tang K, Toth RA, Vander Auwera J, Varanasi P, Yoshino K. 2003. The HITRAN molecular spectroscopic database: Edition of 2000 including updates through 2001. J. Quant. Spectrosc. Radiat. Transfer 82: 544.
  • Rowlands N, Buttner GJ, Raab A, Shepherd GG, Gault WA, Cann MW, Dobbie S, Sargoytchev SI, Ward WE, Mani R, Rochon YJ, Tarasick DW. 1996. Satellite instrument to measure stratospheric winds. Proc. SPIE 2830: 214.
  • Russell III JM, Drayson SR. 1972. The inference of atmospheric ozone using satellite horizon measurements in the 1042 cm−1 band. J. Atmos. Sci. 29: 376390.
  • Saunders R, Matricardi M, Brunel P. 1999. An improved fast radiative transfer model for assimilation of satellite radiance observations. Q. J. R. Meteorol. Soc. 125: 14071425.
  • Saunders R, Rayer P, Brunel P, von Engeln A, Bormann N, Strow LL, Hannon S, Heilliette S, Liu X, Miskolczi F, Han Y, Masiello G, Moncet J-L, Uymin G, Sherlock V, Turner DS. 2007. A comparison of radiative transfer models for simulating Atmospheric Infrared Sounder (AIRS) radiances. J. Geophys. Res. 112: D01S90, DOI: 10.1029/2006JD007088.
  • Saunders R, Matricardi M, Geer A. 2008. RTTOV9.1 Users Guide. NWP SAF Rep. NWPSAF-MO-UD-016, Met Office, 57 pp.
  • Scott A, Mackay B, Wang SG, Rowlands N, Shepherd GG, Gault WA, McDade IC, Rochon YJ. 2001. SWIFT instrument. Proc. SPIE 4150: 420426.
  • Shepherd GG, Thuillier G, Gault WA, Solheim BH, Hersom C, Alunni JM, Brun J-F, Brune S, Charlot P, Cogger LL, Desaulniers D-L, Evans WFJ, Gattinger RL, Girod F, Harvie D, Hum RH, Kendall DJW, Llewellyn EJ, Lowe RP, Ohrt J, Pasternak F, Peillet O, Powell I, Rochon YJ, Ward WE, Wiens RH, Wimperis J. 1993. WINDII, the Wind Imaging Interferometer on the Upper Atmosphere Research Satellite. J. Geophys. Res. 98: 1072510750.
  • Shepherd GG, McDade IC, Gault WA, Rochon YJ, Scott A, Rowlands N, Buttner G. 2001. The Stratospheric Wind Interferometer For Transport studies (SWIFT). Adv. Space Res. 27: 10711079.
  • Shepherd GG. 2002. Spectral Imaging of the Atmosphere. International Geophysics Series 82, Academic Press.
  • Strow LL, Hannon SE, DeSouza-Machado S, Motteler HE, Tobin D. 2003. An overview of the AIRS radiative transfer model. IEEE Trans. Geosci. Remote Sensing 41: 303313.
  • Thuillier G, Hersé M. 1988. Measurements of wind in the upper atmosphere: First results of the MICADO instrument. Pp 6173 in Progress in Atmospheric Physics, Rodrigo R, López-Moreno JJ, López-Puertas M, Molina A (eds). Kluwer Academic Publishers: Dordrecht.
  • Turner DS. 1995. Absorption coefficient estimation using a two-dimensional interpolation procedure. J. Quant. Spectrosc. Radiat. Transfer 53: 633637.
  • Turner DS, Chouinard CB. 1997. ‘An attempt to understand and correct some of the errors of forward radiative transfer models.’ Pp 499508 in Technical Proceedings of the Ninth International TOVS Study Conference, Igls, Austria, 2026 February 1997.
  • Turner DS, Rochon YJ. 2008. ‘Towards a fast forward model for retrievals and data assimilation for the SWIFT stratospheric wind interferometer.’ 37th COSPAR Scientific Assembly, Montreal, 1320 July 2008.
  • US Committee on Extension to the Standard Atmosphere. 1976. U.S.Standard Atmosphere, 1976. US Government Printing Office, 227 pp.