# Retrieval of temperature and tangent altitude pointing from limb emission spectra recorded from space by the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS)

## Abstract

[1] Retrieval of abundances of atmospheric species from limb infrared emission spectra requires accurate knowledge of the pointing of the instrument in terms of elevation, as well as temperature and pressure profiles. An optimal estimation-based method is presented to infer these quantities from measured spectra. The successful and efficient joint retrieval of these largely correlated quantities depends strongly on the proper selection of the retrieval space, the selection of spectral microwindows, and the choice of reasonable constraints which force the solution to be stable. The proposed strategy was applied to limb emission spectra recorded with the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) on board the Envisat research satellite in order to validate the instrument pointing information based on the satellite's orbit and attitude control system which uses star tracker information as a reference. Both systematic and periodic pointing calibration errors were detected, which meanwhile have been corrected to a major part. Furthermore, occasional pitch jumps were detected, which could be assigned to parameter uploads to the satellite's orbit and attitude control system. It has been shown that in general, it is justified to assume local thermodynamic equilibrium below 60 km for these purposes. The retrieval method presented has been proven to be suitable for independent monitoring of MIPAS line-of-sight pointing.

## 1. Introduction

[2] The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) is a limb emission spectrometer designed for measurement of trace species from space [*Endemann and Fischer*, 1993; *Endemann et al.*, 1996; *Fischer*, 1992; *Fischer and Oelhaf*, 1996]. It is part of the core payload of the Environmental Satellite (ENVISAT) which was successfully launched into its Sun-synchronous polar orbit on 1 March 2002. As for all limb sounders, precise knowledge of the pointing of the line of sight in terms of elevation is crucial for successful data analysis. In particular, for emission spectroscopy, retrieved mixing ratios of any species depend considerably on the assumed temperature profile.

[3] A wealth of literature exists on how to infer temperature and/or pressure from space-borne limb emission measurements [see, e.g., *Gille and House*, 1971; *Abbas et al.*, 1984; *Kumer and Mergenthaler*, 1991; *Mertens et al.*, 2001]. The retrieval algorithm used by the European Space Agency (ESA) for so-called operational near-real time data processing with the requirement to deliver pressure, temperature, and volume mixing ratio profiles of H_{2}O, O_{3}, HNO_{3}, CH_{4}, N_{2}O, and NO_{2} within 3 hours after measurement has been documented by *Ridolfi et al.* [2000]. Complementary to this, an off-line data processor of different specification has been developed at the Institut für Meteorologie und Klimaforschung (IMK) and complemented by components relevant to treatment of non–local thermodynamic equilibrium (non-LTE) at the Instituto de Astrofisica de Andalucia (IAA). The purpose of this complementary IMK-IAA processor, which is presented here, is, besides cross validation issues, to derive atmospheric parameters beyond the ESA operational data product. This comprises an extension in altitude of the operational products, the extension of the number of species retrieved, and application to special (nonstandard) modes of observation.

[4] For MIPAS, line-of-sight pointing information is available, which relies on the Envisat orbit and attitude control system which uses a star tracking system as reference. The angular calibration of the MIPAS scan mirror relative to the platform is inferred from the observation of stars moving through the instantaneous field of view of MIPAS [*Endemann*, 1999; *Nett*, 2003]. On the basis of spacecraft position and viewing angle, ray tracing calculations are performed for a model atmosphere to generate the tangent altitude information, which is the geometrical parameter provided to the data user. These data henceforth are called “initial pointing data.” Since higher accuracy of pointing information is desirable for retrieval of abundances of atmospheric constituents, and in order to have the possibility of independent monitoring of the MIPAS line-of-sight pointing information, it was decided to develop a strategy to retrieve the tangent altitudes directly from the MIPAS spectra. Since response of the measured signal depends on pointing information and temperature in a correlated manner, and on none of these quantities perfect a priori knowledge is available, both are retrieved simultaneously.

[5] The retrieval of temperature and line of sight pointing is the third step in the IMK-IAA processing sequence; it follows after cloud detection and correction of spectral shift and precedes retrieval of the abundances of atmospheric constituents. Abundances of some of the additional species are supposed to be close to the MIPAS detection limit. Improved knowledge on instrument pointing, as well as atmospheric pressure and temperature profiles is desirable in order to minimize the propagation of errors of these quantities to the abundances of the hard-to-detect species. This led to a retrieval strategy quite distinct from that chosen for the operational near-real time data processor. In this paper we emphasize the ability of the processor to provide accurate pointing information (altitude registration). First, the retrieval processor used is described and the parameter settings relevant to retrieval of temperature, pressure and pointing information are discussed. Then, the robustness and accuracy of the proposed retrieval scheme is analyzed on the basis of simulated measurements. Finally, this method is, as part of the MIPAS calibration/validation activities, used to validate the initial MIPAS instrument pointing information. Although the IMK-IAA processor supports the analysis of non–local thermodynamic equilibrium (non-LTE) emissions, the standard processing of temperature and line of sight pointing as presented in this paper assumes LTE for reasons of efficiency. As it will be shown in section 4, this assumption is justified up to altitudes of approximately 60 km.

## 2. Retrieval Processor

*Rodgers*, 2000, and references therein] and leads, after linearization of the radiative transfer problem and after writing the solution into the context of Newtonian iteration in order to take nonlinearity into account, to the following estimators of state parameters:

*m*

_{max}×

*n*

_{max}Jacobian, containing the partial derivatives of all

*m*

_{max}simulated measurements

**y**under consideration with respect to all unknown parameters

**x**, superscript

*T*denotes a transposed matrix,

**x**is the

*n*

_{max}-dimensional vector of unknown parameters,

**x**

_{a}the related a priori information. The term

**y**

_{max}is the

*m*

_{max}-dimensional vector of measurements under consideration,

**y**(

**x**

_{i}) is the forward modeled spectrum using parameters

**x**

_{i}from the

*i*th step of iteration.

**R**is an

*n*

_{max}×

*n*

_{max}regularization matrix, and

**S**

_{y}is the

*m*

_{meas}×

*m*

_{max}covariance matrix of the measurement. The optional term λ

**I**(tuning scalar times unity) damps the step width

**x**

_{i+1}−

**x**

_{i}, bends its direction toward the direction of the steepest descent of the cost function in the parameter space and prevents a single iteration from causing a jump of parameters

**x**beyond the linear domain around the current guess

**x**

_{i}[

*Levenberg*, 1944;

*Marquardt*, 1963].

**S**

_{random}of the retrieved quantity

**x**is calculated as

**x**

_{j}of the uncertainty Δ

*b*

_{j}of parameter

*b*

_{j}is

[8] The critical points in the detailed implementation of a retrieval processor remain as follows: The forward model for the solution of the radiative transfer problem, the appropriate numerical representation of the unknown parameters to be retrieved, the selection of an appropriate subset of the entire spectral measurement data which carries the required information on the target parameters (so-called microwindows), the selection of reasonable constraints to keep the solution of the typically ill-posed inverse problem stable, and the adequate numerical treatment.

### 2.1. Forward Model

[9] The IMK-IAA processor uses the Karlsruhe Optimized and Precise Radiative Transfer Algorithm (KOPRA) [*Stiller*, 2000] for the forward solution of the radiative transfer equation. This radiative transfer model provides analytical derivatives along with the radiance spectra [*Höpfner*, 2000] and supports all relevant physics such as non-LTE [*Funke and Höpfner*, 2000], line coupling [*Funke*, 2000], and horizontal inhomogeneities of the atmosphere. Instantaneous field-of-view effects [*Hase*, 2000] and atmospheric refraction [*Hase and Höpfner*, 1999] are taken into account. KOPRA has been thoroughly cross-validated against other radiative transfer codes [*Glatthor et al.*, 1999; *von Clarmann et al.*, 2002, 2003b; *Tjemkes et al.*, 2003].

### 2.2. Retrieval Parameters

[10] For the application of the retrieval processor discussed here, the parameters to be retrieved are (1) temperature (*T*), (2) absolute tangent altitudes, (3) so-called “continuum,” and (4) radiometric zero level calibration correction (so-called “offset”). Pressure, temperature, and altitude are related by the hydrostatic equation, where in our implementation temperature and altitude are the independent variables, while pressure is the dependent variable.

[11] 1. Temperature is represented and retrieved on a fixed altitude grid, which does not depend on the actual tangent altitudes. As global reference frame the World Geodetic System 1984 (WGS84) is used. The use of a fixed altitude grid avoids postdifferentiation and resampling, which is required when the tangent altitudes, which are retrieval parameters themselves and thus change during the retrieval, define the altitude grid. The grid width has been chosen quite fine (4–44 km: 1 km; 44–70 km: 2 km; 70 km–80 km: 5 km; 80 km–100 km: 10 km; 100 km–120 km: 20 km; gridding for non-LTE reference calculations even finer) which allows comfortable diagnostics, such as averaging kernels on a sub–tangent altitude grid, and avoids degradation of the vertical resolution beyond the loss of resolution due to regularization.

[12] 2. MIPAS is a limb scanning instrument where the measurement geometry is varied by angular movement of an elevation scan mirror, contrary to a detector array instrument with fixed angular distances between different lines of sight. This means that in case of MIPAS not only the absolute altitude of the tangent altitude pattern is variable but also the relative distances between adjacent tangent altitudes. The scheme presented here formally retrieves each single tangent altitude as an absolute quantity, while information on the relative tangent altitudes, i.e., vertical distances between adjacent tangent altitudes, are retrieved implicitly. A hydrostatic pressure profile is then calculated (see below). This retrieval scheme is distinct from usual schemes, which retrieve pressure and relative tangent altitudes, and then either assign the altitudes via the hydrostatic approximation or just report retrieved species abundances as a function of pressure rather than altitude [see, e.g., *Ridolfi et al.*, 2000]. First, ray path geometry is calculated correctly in each iteration. Second, the compensation of altitude mispointing by pressure correction neglects the altitude dependence of all other atmospheric state parameters, in particular the abundances of species. Furthermore, since a priori knowledge on the instrument pointing is given in geometric coordinates, retrieval of tangent pressure rather than tangent altitude would require an update of the constraint term in equation (1) in each step of iteration. This delicate complication is avoided by using geometric coordinates. However, the main advantage of the retrieval of tangent altitude instead of pressure is computational efficiency: While the calculation of the partial derivatives of spectral radiances with respect to pressure requires extensive radiative transfer calculations, the evaluation of the partial derivatives with respect to tangent altitudes requires only incremental variation of the boundaries of integration of precalculated pencil beam radiances over the field-of-view function of the instrument. Certainly, many of these arguments depend on the actual instrument specification, the nature of available a priori data, and the data structure of the forward model used. Therefore the choice of geometric altitude as pointing variable may not be appropriate for other instruments.

[13] 3. The KOPRA radiative transfer model includes continua of H_{2}O [*Clough et al.*, 1989, version CKD 2.4; *Clough*, 1995], N_{2} [*Lafferty et al.*, 1996], O_{2} [*Thibault et al.*, 1997] and CO_{2} [*Echle and Höpfner*, 2000], based on CO_{2} χ factors by *Menoux et al.* [1987, 1991] to account for the non-Lorentzian shape of the line wings. However, it is common experience that in emission spectroscopy the calculated continuum often does not fit the actual background radiation perfectly. Therefore an additional locally wave number-independent background continuum component is fitted to the measurement in order to prevent errors in modeled continua from being propagated into the retrieval of target parameters. This empirical additional absorption coefficient, which does not depend on any physical continuum model, compensates for atmospheric contributions of weak wave number dependence not reproduced by the radiative transfer forward model. Such effects may include continua due to superimposed wings of far-off transitions, uncertainties of H_{2}O, O_{2} and N_{2} continua, and, most important, signal from aerosols and clouds. As for high tangent altitudes no such continua have been observed, this quantity is set to zero for altitudes higher than 32 km. For altitudes below, the fit parameter formally is the abundance of a locally (i.e., within a microwindow) grey absorbing/emitting constituent. In order to allow for variations of background continuum with wave number, an individual parameter is retrieved for each microwindow, constrained to smoothness in both the altitude and the wave number domains (see below).

[14] 4. As zero-offset calibration is not perfectly known, this quantity is also retrieved directly from the spectra. While in lower altitudes the offset information in the spectra is largely correlated with the continuum, unambiguous offset information is contained in high altitude spectra with tangent altitudes above 32 km, where the continuum is zero. The zero offset calibration error is constant with tangent altitude for each limb scan. The partial derivative of the spectrum with respect to zero offset is unity, since the offset is additive.

_{2}, O

_{2}, H

_{2}O, Ar, CO

_{2}, O) as provided by the extended Mass Spectrometer Incoherent Scatter (NRLMSISE-00) atmospheric model [

*Picone et al.*, 2002]. The variation of the gravitational acceleration

*g*(ϕ,

*z*) with latitude ϕ and altitude

*z*is calculated as

*R*

_{e}(ϕ) the local distance to the Earth's center,

*R*

_{c}(ϕ) the distance to the

*y*axis of the ellipse along the ellipse's normal, ω the Earth's angular velocity, and

*g*

_{0}(ϕ) the gravitational acceleration on ground in m/s

^{2}, which is calculated as

[16] The standard treatment of a limb scanning sequence is to assume horizontal homogeneity of each atmospheric state parameter, i.e., to define state parameters as functions of altitude but constant in latitude and longitude. Since this simplification can trigger systematic errors, the algorithm is coded to handle latitudinal and longitudinal variation of state parameters. Approaches of different level of sophistication are supported: The simplest way is just to include horizontal gradient information on state parameters from external sources in the radiative transfer forward model and to keep the gradients fixed while the parameters themselves are retrieved. Also retrieval of horizontal gradient information from the spectra is supported, which needs sufficient regularization [*von Clarmann et al.*, 2000; *Steck*, 2000]. The most rigorous approach supported by the code is direct retrieval of 2-D fields in an optimal estimation scheme which uses a series of successive limb scans in a tomographic approach rather than single limb scans (T. Steck, personal communication, 2003). However, none of these options has been activated for processing of data presented in this paper.

### 2.3. Microwindow Selection

[17] Since retrieval of tangent altitudes and temperature precedes the retrieval of species abundances, no reliable information on atmospheric state parameters is available from a previous retrieval step. This implies that, in order to avoid error propagation caused by unknown species abundances, only transitions of species should be used whose abundances change only slightly and are well known. Traditionally, both in absorption and emission spectroscopy, small spectral regions (so-called “microwindows”) which contain only CO_{2} lines are used for this purpose [see, e.g., *Abbas et al.*, 1984; *Rinsland et al.*, 1992; *Stiller et al.*, 1995]. Errors caused by variations of CO_{2} mixing ratios are discussed in sections 3 and 4. In order to obtain independent information on tangent altitudes and temperature, spectral lines of different temperature dependence are needed. The IMK-IAA retrieval does not explicitly force the microwindow selection toward CO_{2} transitions, but uses an objective method to find optimal microwindows which minimize the propagation of retrieval noise, uncertainties in species abundances and certain instrumental uncertainties to retrieved temperatures and tangent altitudes [*von Clarmann and Echle*, 1998; *Echle et al.*, 2000]. This optimization approach leads to microwindows which exclude spectral grid points where the gain of additional information is overcompensated by uncertainties of model parameters, such as the unknown abundances of atmospheric species other than CO_{2}, O_{2}, or N_{2}.

[18] Since, for reasons of efficiency, the standard setting of the IMK-IAA retrieval scheme assumes LTE and neglects line coupling, also microwindows where these effects are important are avoided. The MIPAS performance data assumed for the microwindow optimization in terms of nominal noise equivalent spectral radiance (NESR_{0,requirement}), noise equivalent spectral radiance after apodization (NESR_{APO,requirement}), and radiometric errors in terms of gain and offset are listed in Table 1. The selected microwindows used for pointing and temperature retrievals, the most prominent CO_{2} transitions, and the main interfering species are listed in Table 2. These microwindows all fall in the MIPAS A band. However, in case of corrupted data in band A, the microwindow selection scheme will automatically fall back to spectral transitions in other MIPAS bands. Coregistration uncertainties of the MIPAS bands in terms of pointing direction have been estimated by means of actively scanning the field of view across Mercury used as a bright infrared source [*Nett*, 2003]. Since no evidence of any asymmetries of the field-of-view shapes have been found, these data suggest that tangent altitudes of bands A, AB, B and C coincide by better than 12 m, while effective band D tangent altitudes are lower by about 46 m. This excellent altitude alignment of the MIPAS spectral bands is explained by the fact that the field of view is determined by a field stop within the telescope which is common to all detectors, and detectors are all mounted in the same orientation with respect to the incident beam (M. Birk, personal communication, 2003). Band-dependent atmospheric refraction contributes by only 0.3 m in the worst case (between bands A and D at 6 km tangent altitude) and thus is negligible. As a consequence, tangent altitudes retrieved from MIPAS band A radiances are valid also for the bands AB, B and C, while a correction by −46 m could be considered for channel D.

MIPAS band | A | AB | B | C | D |
---|---|---|---|---|---|

Spectral Coverage, cm^{−1} |
685–970 | 1020–1170 | 1215–1500 | 1570–1750 | 1820–2410 |

Spectral Sampling, cm^{−1} |
0.025 | 0.025 | 0.025 | 0.025 | 0.025 |

NESR_{0,requirement}^{a} |
50 | 40 | 20 | 6 | 4.2 |

NESR_{0,in flight}^{a} |
38.62 | 21.56 | 14.91 | 3.92 | 3.91 |

NESR_{APO,requirement}^{a} |
30.35 | 24.28 | 12.14 | 3.64 | 2.549 |

NESR_{APO,in flight}^{a} |
23.44 | 13.09 | 9.05 | 2.38 | 2.37 |

Gain error,% of true radiance | 2 | 2 | 2 | 2 | 2 |

Offset error^{a} |
100 | 80 | 40 | 12 | 8.4 |

- a
In nW (cm
^{2}sr cm^{−1})^{−1}.

^{a}

Spectral Coverage, cm^{−1} |
Number of Spectral Points | Nominal Altitudes, km | Prominent Transitions | Main Interfering Species |
---|---|---|---|---|

687.175–692.125 | 7–17 | 33–42; 52–68; | 02201←01101 R24-28 | O_{3}, NO_{2}, H_{2}O |

11101←10001 Q10-38 | ||||

01101←00001 R26-30 | ||||

693.500–693.650 | 7 | 47 | 01101←00001 R32 | O_{3}, NO_{2} |

737.525–741.300 | 7–42 | 6; 21–30; 36–68 | 10001←01101 R21-25 | O_{3}, NO_{2} |

746.350–746.500 | 7 | 6; 9; 47; 68 | 11101←02201 R5 | O_{3} |

780.850–781.000 | 7 | 9; 42; 47–60 | 11101←02201 R54 | O_{3}, NO_{2} |

12201←03301 R30 | ||||

801.450–801.625 | 7–8 | 12–18; 33; 39–52; 68 | 11101←01101 R12 | O_{3}, NO_{2}, ClONO_{2} |

968.900–969.100 | 7–8 | 6–12 | 00011←10001 R10 | O_{3}, COF_{2} |

- a Not all spectral grid points within a microwindow are used for analysis at all altitudes. Some spectral grid points where the signal is significantly contaminated by interfering species are disregarded for analysis.

[19] While the IMK-IAA processor supports dedicated microwindows for different latitude bands (polar, midlatitudinal, tropic), as well as latitude-dependent initial guess profiles of atmospheric constituents, these early results shown here have been generated with microwindows optimized for midlatitudinal conditions and a midlatitudinal profile of CO_{2} mixing ratios. Estimated errors due to assumed one sigma differences of 2 ppmv between the actual and the assumed mixing ratios of CO_{2} are below or equal 0.1 K and 26 m for temperature and tangent altitude, respectively.

[20] In order to achieve the best possible trade-off between noise-induced random error and systematic errors due to unknown state parameters, both the microwindow selection and the detailed microwindow definition (boundaries, grid point selection within each microwindow) are altitude dependent.

[21] Both offset and continuum are assumed to vary only slowly with wave number. For practical reasons, this behavior is taken into account in the retrieval processor by assuming that these quantities do not vary within a microwindow but can take different values in different microwindows.

### 2.4. Constraints

[22] Because of the representation of the retrieved atmospheric state parameters on an altitude grid finer than the vertical distance of tangent altitudes of the measurements, the correlations of partial derivatives of the measurements with respect to temperature and with respect to the line-of-sight pointing, and due to the large number of fit variables, the inverse problem is ill-posed and needs regularization. The regularization matrix **R** is set up as a block diagonal matrix with one block for temperature (**R**_{T}), tangent altitudes (**R**_{LOS}), continuum (**R**_{c}), and offset (**R**_{o}), each. No correlation constraints between these blocks are introduced in this matrix, i.e., off-diagonal blocks are all zero.

**L**

_{1}is a first-order differences operator weighted by the actual grid width, and γ a scalar which controls the strength of regularization. For this application, γ has been chosen as 1.059 K

^{−2}(at 1-km altitude sampling), such that the number of degrees of freedom of the retrieved temperature profile (typically about 15) is only slightly smaller than the number of tangent altitudes of the limb sequence (up to 17, depending on cloud contamination) [

*Steck*, 2002]. This corresponds to the expected achievable altitude resolution of a measurement where all altitude information is given by measurement geometry while the information content of pressure broadening is quite limited due to limited spectral resolution.

[24] All-inclusive accuracies of the initial line of sight pointing information in terms of tangent altitude errors are specified as 1800 m (absolute, above ground), 900 m (relative error between first and last measurement of a limb scan), and 300 m (relative error between two successive tangent altitudes (each 95% confidence limit).

*Rodgers*, 2000]. While the specified tangent altitude accuracy does not follow a Gaussian distribution, a pointing covariance matrix has been approximated as (K. Ressel, personal communication, 1996)

**U**is a

*n*×

*n*transformation matrix of the type

*n*is the number of tangent altitudes within a limb sequence, and

**S**

_{LOS}is a diagonal matrix where the first

*n*− 1 diagonal entries are (150 m)

^{2}, while the last diagonal element is (900 m)

^{2}. This approach approximates one-sigma uncertainties as uncertainties at 95% confidence limit scaled down by a factor of 2. This slightly overestimates relative pointing uncertainties, since it assumes random accumulation of relative pointing errors, which ends up in a top-to-bottom one-sigma uncertainty of 600 m instead of 450 m as specified. Since the star tracking system based pointing data is independent from the spectral measurements, its use as a priori information in the sense of optimal estimation seems adequate for routine data analysis and similar applications except validation of the initial pointing information itself. For the latter purpose, i.e., to detect biases of the initial line-of-sight pointing data, the variance of the absolute pointing a priori information is set to infinity, while the variances of the relative tangent altitudes remain unchanged. Using the first order equivalence of a pure smoothing constraint and optimal estimation for this particular case, which has been pinpointed by

*Steck and von Clarmann*[2001],

**R**

_{LOS}can be expressed using the Tikhonov formalism (see, e.g., equation (4)) for this purpose. No significant difference in the results due to these different regularization approaches has been found for cases analyzed so far.

[26] The continuum is set to zero above 32 km (hard constraint). This is justified, because none of the physics which causes any signal to be parameterized and compensated by the empirical continuum, such as far wing radiation, aerosol, or water vapor continuum, has any significant effect in these high altitudes. Below 32 km the regularization approach of the continuum in the altitude domain is the same as for temperature, i.e., a Tikhonov-type first-order smoothing constraint with γ = 10^{10} km^{2} (at 1 km altitude sampling). In order to force the continuum character of the empirically fitted continuum, additional first-order smoothness regularization is applied in the wave number domain (i.e., between microwindows) (γ = 2.5 × 10^{7} km^{2} at 1 cm^{−1} spectral distance).

[27] Since there is no atmospheric continuum above 30 km, all radiance offset in these high altitude spectra carries information on the (altitude independent) zero calibration correction. Therefore this quantity does not need to be constrained, i.e., **R**_{o} = 0. The regularization of the offset calibration correction in the wave number domain may be worthwhile consideration of but has not been implemented, since there has not been any evidence of necessity. Certainly, the assumption of altitude-constant offset is an implicit constraint in itself, but not in the formal sense of equation (1). This issue falls rather in the definition of the retrieval parameter space.

## 3. Preflight Processor Functionality Test

[28] The capability of our data processing scheme to retrieve temperature and line of sight from limb emission measurements has been proven in a retrieval study on the basis of simulated measurements. The rationale of this test was to show that the actual temperature and pointing data indeed are retrieved within the estimated error margins. For this purpose, a chemically and dynamically self-consistent atmospheric model atmosphere was generated for one certain date and geolocation (80°N latitude, 1200 LT). For this atmospheric situation vibrational temperatures for all relevant species were generated. Radiative transfer calculations under consideration of non-LTE, line coupling and strong atmospheric aerosol loading were performed for a typical MIPAS-like limb sequence. Rigorous accuracy driving parameters far beyond the parameter setting which is typically used in a retrieval applications were chosen with respect to rejection of weak spectral lines, discrete integration of the radiative transfer equation through the inhomogeneous atmosphere, and integration of pencil beam radiances over the MIPAS field of view, in order to generate simulated spectra as realistic as possible. These spectra were superimposed with spectral noise and zero-offset calibration error according to the MIPAS instrument specification. These calculated spectra then were used for test retrievals, where neither the atmospheric state parameters chosen for generation of the synthetic measurements nor the true tangent altitudes were fed into the retrieval. Instead, climatological data were used as initial guess and a priori information, and elevation pointing information differing from the true data by approximately one standard deviation of the specified MIPAS initial pointing uncertainty. Since this processor functionality study was performed as a blind test in a sense that the input data used for generation of the simulated measurements were not available to the scientists in charge of the retrievals, this test can be considered as a test under fairly realistic conditions. Further details of this blind test retrieval experiment, which included also retrieval of atmospheric constituents and in which several European research groups participated, are given by *von Clarmann et al.* [2003a].

[29] Results of retrieved tangent altitudes and temperatures from this blind test are presented in Figures 1 and 2 respectively. A detailed error budget is reported in Tables 3 and 4 for a typical MIPAS temperature and line-of-sight retrieval. Error components under consideration are measurement noise as reported in Table 1; uncertainty of the actual CO_{2} mixing ratio (assumed as 3 ppmv); climatological uncertainties of the mixing ratios of all other species contributing to the infrared spectrum; spectroscopic data uncertainties; spectral shift, i.e., frequency calibration uncertainty (assumed 0.001 cm^{−1}); gain calibration uncertainty (assumed 1%, because values as specified in Table 1 seem too pessimistic). Neither the temperature smoothing error, which describes the difference between the smoothed retrieved profile and a possibly higher structured true profile is included, nor the uncertainty of tangent altitudes due to imperfect knowledge of an altitude-pressure reference point to build up the hydrostatic atmosphere. Furthermore, errors due to assumption of LTE instead of non-LTE are not included in the error budget. The correlation coefficients (covariance divided by the product of standard deviations) of temperature at a certain altitude and the closest retrieved tangent altitude are reported in the last column of Table 3. Temperatures were retrieved with an accuracy of typically better than 1 K for stratospheric altitudes (0.58 K standard deviation). This is consistent with the estimated total retrieval errors, which are 0.5–1.0 K for stratospheric altitudes, which is quite encouraging. Correlation coefficients are all positive, which is not surprising, since a tangent altitude assumed too high typically implies, due to lower CO_{2} density, a lower signal, which can be partly compensated by higher temperatures. For unconstrained retrievals with microwindows based on an ad hoc selection, correlations were found much more compact [*von Clarmann et al.*, 1995].

^{a}

Height, km | Total Error | Spectral Noise | Systematic Components | Variability CO_{2} |
Variability Other Gases | Spectroscopic Data | Spectral Shift | Gain Calibration | Correlation Coefficient |
---|---|---|---|---|---|---|---|---|---|

9.0 | 0.9 | 0.4 | 0.8 | 0.1 | 0.6 | 0.2 | 0.1 | 0.3 | 0.18 |

12.0 | 0.7 | 0.4 | 0.6 | <0.1 | 0.3 | 0.3 | 0.2 | 0.3 | 0.35 |

15.0 | 0.6 | 0.4 | 0.4 | <0.1 | 0.2 | 0.2 | 0.1 | 0.3 | 0.51 |

18.0 | 0.5 | 0.4 | 0.4 | <0.1 | 0.3 | 0.1 | <0.1 | 0.3 | 0.46 |

21.0 | 0.6 | 0.4 | 0.5 | <0.1 | 0.3 | 0.1 | 0.2 | 0.2 | 0.35 |

24.0 | 0.5 | 0.4 | 0.4 | <0.1 | 0.1 | <0.1 | 0.1 | 0.3 | 0.33 |

27.0 | 0.6 | 0.4 | 0.4 | <0.1 | <0.1 | <0.1 | 0.1 | 0.4 | 0.27 |

30.0 | 0.7 | 0.4 | 0.5 | 0.1 | <0.1 | 0.1 | 0.4 | 0.4 | 0.14 |

33.0 | 0.9 | 0.4 | 0.8 | 0.1 | 0.1 | 0.2 | 0.7 | 0.4 | 0.15 |

36.0 | 0.7 | 0.4 | 0.5 | 0.1 | 0.1 | 0.2 | 0.2 | 0.4 | 0.17 |

39.0 | 0.7 | 0.4 | 0.6 | 0.1 | 0.1 | 0.3 | 0.1 | 0.4 | 0.23 |

42.0 | 0.9 | 0.4 | 0.8 | 0.1 | 0.1 | 0.4 | 0.3 | 0.5 | 0.06 |

46.0 | 1.0 | 0.5 | 0.8 | <0.1 | 0.1 | 0.4 | 0.5 | 0.4 | 0.15 |

52.0 | 0.7 | 0.5 | 0.4 | <0.1 | 0.1 | 0.1 | 0.1 | 0.4 | 0.00 |

54.0 | 0.7 | 0.5 | 0.5 | 0.1 | 0.1 | 0.3 | 0.1 | 0.4 | ^{b} |

56.0 | 0.9 | 0.5 | 0.7 | 0.1 | 0.2 | 0.4 | 0.2 | 0.4 | ^{b} |

58.0 | 1.0 | 0.5 | 0.9 | 0.1 | 0.1 | 0.5 | 0.5 | 0.5 | ^{b} |

60.0 | 1.2 | 0.6 | 1.0 | 0.1 | 0.1 | 0.5 | 0.5 | 0.6 | 0.58 |

68.0 | 1.7 | 1.1 | 1.3 | 0.1 | 0.6 | 0.8 | <0.1 | 0.9 | 0.44 |

- a In K.
- b Not applicable, since there were no tangent altitudes near these altitude grid points.

^{a}

Height, km | Total Error | Spectral Noise | Systematic Components | Variability CO_{2} |
Variability Other Gases | Spectroscopic Data | Spectral Shift | Gain Calibration |
---|---|---|---|---|---|---|---|---|

9.244 | 0.26 | 0.094 | 0.24 | 0.020 | 0.20 | 0.052 | 0.065 | 0.006 |

12.236 | 0.25 | 0.070 | 0.24 | 0.022 | 0.19 | 0.082 | 0.018 | 0.009 |

15.231 | 0.19 | 0.072 | 0.18 | 0.024 | 0.14 | 0.086 | 0.039 | 0.009 |

18.233 | 0.16 | 0.071 | 0.14 | 0.025 | 0.10 | 0.078 | 0.052 | 0.01 |

21.233 | 0.13 | 0.074 | 0.10 | 0.026 | 0.071 | 0.068 | 0.004 | 0.005 |

24.233 | 0.13 | 0.073 | 0.11 | 0.026 | 0.049 | 0.094 | 0.021 | 0.004 |

27.234 | 0.15 | 0.073 | 0.13 | 0.026 | 0.027 | 0.12 | 0.044 | 0.002 |

30.235 | 0.17 | 0.068 | 0.16 | 0.024 | 0.042 | 0.14 | 0.060 | <0.001 |

33.235 | 0.15 | 0.065 | 0.14 | 0.023 | 0.034 | 0.13 | 0.013 | 0.005 |

36.235 | 0.18 | 0.057 | 0.17 | 0.021 | 0.076 | 0.15 | 0.022 | 0.009 |

39.235 | 0.16 | 0.057 | 0.15 | 0.020 | 0.025 | 0.15 | 0.016 | <0.001 |

42.237 | 0.19 | 0.050 | 0.18 | 0.015 | 0.013 | 0.17 | 0.053 | 0.009 |

47.237 | 0.19 | 0.051 | 0.19 | 0.013 | 0.022 | 0.16 | 0.095 | 0.003 |

52.240 | 0.17 | 0.058 | 0.16 | 0.018 | 0.022 | 0.16 | 0.018 | 0.017 |

60.245 | 0.19 | 0.077 | 0.18 | 0.022 | 0.027 | 0.16 | 0.051 | 0.042 |

68.357 | 0.19 | 0.089 | 0.17 | 0.022 | 0.025 | 0.15 | 0.033 | 0.055 |

- a In km.

[30] The retrieved relative tangent altitude spacing differs from the true data by less than 50 m within the upper stratosphere, and less than 150 m for all tangent altitudes above 15 km. Since the reference point for setting up the hydrostatical atmosphere has been taken from a climatology instead from meteorological analysis data, the initial pointing offset of 0.9 km could be corrected only partly in this simulated retrieval. The residual pointing offset of approximately 300 m is fully explained by the 3% difference in pressure at the reference point between the climatological values used as a priori information in this test retrieval and the actual values used for generation of the simulated measurements. Use of actual meteorological analysis data for this purpose is expected to improve results considerably when applying the processor to real measurement data. Assuming a perfect pressure-altitude reference point, tangent altitude errors are estimated at 130 to 260 m, whereby uncertainties of abundances of interfering species is the leading error source below approximately 20 km. Between 20 and 24 km the random error due to spectral noise is dominating, while for higher tangent altitudes the error budget is dominated by uncertainties of spectroscopic data. In particular, this simulated retrieval proves the validity of the chosen approach to avoid the problem of non-LTE by careful selection of appropriate CO_{2} transitions instead of the more time-consuming explicit treatment of non-LTE during the retrieval.

## 4. MIPAS Pointing Assessment

[31] In order to both demonstrate its applicability to real MIPAS measurement data, and to assess the characteristics of the initial MIPAS pointing information, the algorithm presented in this paper was applied to MIPAS measurements taken on July 24, 2002 (Envisat orbits 02081-02083). During this time MIPAS was operated in its standard measurement scenario with approximately 3 km tangent altitude spacing from 6 to 47 km and additional tangent altitudes at 52, 60 and 68 km. Geolocations are shown in Figure 3. The actual in-flight NESR values, averaged over tangent altitudes and, within each MIPAS band, over wave number, are listed in Table 1. Retrieved temperatures and tangent altitudes for orbit 02081 are shown in Figure 4. Estimated retrieval errors from various sources are compiled in Table 3 and 4 for limb scan 1 of orbit 2081, which is considered representative.

[32] Since validation of retrieved temperatures is a major issue in itself, requiring large amounts of MIPAS data and correlative measurement data, it is reported in a dedicated paper [*Wang et al.*, 2003], while this paper is focused on the assessment of line-of-sight pointing. However, since temperature and line-of-sight pointing data are correlated by their retrieval errors, we shortly discuss also retrieved temperature distributions. The along-orbit temperature cross section shows all expected features, such as cold tropical tropopause, extreme cold southern polar stratosphere and very warm stratopause above. Where no tangent altitudes are plotted, e.g., limb scans 38–40, below 25 km, related spectra have not been used for the retrieval due to cloud contamination. For a more quantitative analysis, results have been plotted relative to ECMWF analysis data (resampled on a geometrical altitude grid from the original data which were provided on geopotential altitude grid) for temperature and nominal ESA-provided tangent altitudes for pointing (5, 6–7). Mean temperature differences are shown in (Figure 8). Retrieved temperatures differ from ECMWF analysis by typically less than 2 K, except for altitudes above 50 km and regions in the Southern hemisphere. In these regions of larger differences (occasionally more than 10 K) ECMWF temperatures are known to be of limited accuracy, due to the limited number of atmospheric observations available. Also the estimated retrieval errors increase at these altitudes but justify only deviations below 2 K in the MIPAS measurement range. Measurement noise is the leading error source there. Furthermore, MIPAS temperatures seem biased high with respect to ECMWF analysis data in an altitude band around 40 km. As pointed out by A. Simmons (private communication, 2003), the differences at the upper heights could be explained by a bias in the ECMWF analyses. Above 30 km, the ECMWF loses the radiosonde data and model biases become larger. Moreover, the AMSU-A (Advanced Microwave Sounding Unit) data the analyses rely on at these levels are prone to biases also. A recent SPARC comparison of climatologies [*Randel et al.*, 2002] compared a number of stratospheric climatologies, including one derived from a few years of the ECMWF ERA-40 reanalysis. The ECMWF reanalysis stood out as the coldest of all data sets between 30 and 45 km. Mean temperatures at 3hPa from ERA-40 for the years in question (1992–1997) are not very different from what the ECMWF have produced in recent years operationally.

[33] In order to assess systematic errors introduced by the neglect of non-LTE, additional to the LTE standard processing non-LTE retrievals were performed for MIPAS measurements taken during Envisat orbit 2081. The non-LTE processing [*Funke et al.*, 2002; *von Clarmann et al.*, 2003c; *Stiller et al.*, 2003] uses a generic non-LTE model that calculates the non-LTE populations of the relevant species in an online mode in each iteration of the retrieval using kinetic parameters currently known from all previous experiments and mostly reported by *López-Puertas and Taylor* [2001]. Apart from the inclusion of non-LTE, all processor settings have been kept as for to the standard processing. The differences of retrieved temperatures in non-LTE and LTE operation modes of the processor are shown in Figure 9. The non-LTE modeling for CO_{2} uses the fast collisional rate of CO_{2}(*v*_{2}) by atomic oxygen, opposite to the moderate value used in previous studies [*Lopez-Puertas et al.*, 2002]. The results show that non-LTE induces kinetic temperature differences smaller than 1 K below ∼60 km. The temperatures retrieved under consideration of non-LTE are cooler than those retrieved under LTE by ∼1–2 K for daytime around 70 km. In contrast, non-LTE temperatures are warmer by 3–7 K for the polar night (scans ∼35–45). These results are in agreement with expectations. The cooler daytime temperatures retrieved under non-LTE are due to the larger non-LTE populations of the *v*_{2} states involved in the measured transitions obtained after the relaxation of solar absorption at 4.3 and 2.7 μm. The warmer temperatures in the polar night mesosphere result from the under-LTE populations of the CO_{2}(*v*_{2}) levels (see Figure 10) that occur for this warm region (see Figure 9).

[34] Retrieved tangent altitudes differ considerably from the initial pointing information. Pointing differences of up to 3 km have been detected (e.g., limb scans 60–78 in orbit 02082; limb scans 0–10 in orbit 02083), as well as pointing discontinuities (e.g., between limb scans 10 and 11 in orbit 02083). These by far exceed deviations which can be explained by the estimated retrieval errors, which are below 260 m. In order to exclude artefacts in the pointing retrieval, several parameter settings and baseline decisions of the retrieval strategy were thoroughly assessed. In particular, (1) different microwindow selections were used; (2) the hydrostatic constraint was deactivated for dedicated test runs; (3) correlations between horizontal temperature gradients and differences between ECMWF analysis and retrieved temperatures was searched for; (4) the a priori constraint on the instrument pointing was varied; (5) low tangent altitudes with possible undetected cloud contamination were excluded; and (6) non-LTE as candidate explanation was assessed. None of these investigations has given evidence of an artefact in our retrievals. While results differed in minor details, they reproduced, in particular, the large pointing discontinuity observed for orbit 02083, regardless which parameter setup or retrieval baseline was chosen. This is considered as an indication of the robustness of the results.

[35] After having been informed of these results, ESA finally could attribute the pointing discontinuities (pitch jumps) to updates of the onboard orbit model coefficients sent to the satellite's attitude and orbit control system (H. Nett et al., personal communication, 2002). Furthermore, a bias as well as harmonic correction has been applied to the nominal pointing calibration. For measurements taken on 2 December 2002 (orbit 3959) MIPAS pointing as inferred with the upgraded ESA pointing scheme has been investigated (Figure 11). There is some indication of overcompensation, since now there is a bias of the ESA pointing data of −780 m with respect to the IMK-retrieved pointing data. However, the remaining differences between corrected nominal pointing and retrieved pointing are within the accuracy specification of the star tracker based pointing system.

## 5. Discussion and Outlook

[36] The proposed retrieval strategy proved robust and reliable both when applied to simulated as well as real MIPAS data. While this paper intends to prove the applicability and robustness of the retrieval scheme, thorough validation of retrieved temperature profiles against collocated measurements has been initiated. First results are published by *Wang et al.* [2003]. Currently, the application of the IMK-IAA processor with respect to the retrieval of temperature and line-of-sight pointing in an extended altitude range up to 100 km from special upper atmosphere mode data is tested. This application requires a rigorous non-LTE approach, since information on temperature above 60 km is mainly given by 1st and 2nd CO_{2} hot bands at 4.3 μm strongly affected solar absorption.

[37] It has been shown that the assumption of LTE in the standard processing is valid below 60 km in general. However, at polar winter conditions non-LTE induced systematic errors in the retrieved temperatures may exceed 1 K above 55 km. These non-LTE effects are caused by the lower populations (with respect to LTE) of the CO_{2} 15-μm levels in the lower mesosphere that are predicted to occur when this region is very warm. The LTE retrieval tends to underestimate these warm temperatures.

[38] Further investigations refer to the inclusion of horizontal structures (T. Steck, personal communication, 2003), use of the generalized covariance matrix [*von Clarmann et al.*, 2001] which transposes uncertainties of nonfit parameters in the radiance domain and adds them to the **S**_{y} covariance matrix, or constraining the temperature retrieval with ECMWF analysis data as a priori instead of Tikhonov-type smoothing. However, while the potential to add further sophistication to the data processing scheme is large, no evidence has been found that this is needed for routine processing of MIPAS spectra in the nominal tangent altitude range from 6 to 68 km.

## Acknowledgments

[39] Part of this work has been funded under EC contract EVG1-CT-1999-00015 (AMIL2DA), ESA contract 15530/01/NL/SF (INFLIC), BmBF contracts 07 ATF 43/44 (KODYACS), 07 ATF 53 (SACADA) and 01 SF 9953 (HGF Vernetzungsfonds). The IAA team was also partially supported by Spanish projects PNE-017/2000-C and REN2001-3249/CLI. B. Funke has been supported through an European Community Marie Curie Fellowship. The authors like to thank H. Nett for making MIPAS spectra accessible in the early commissioning phase, B. Schimpf, F. Schreier, K. Ressel, and M. Birk for useful discussions, as well as an anonymous reviewer for many detailed suggestions to improve the paper. Meteorological analysis data have been provided by ECMWF.