Optimal Estimation Method Research Articles

Lunar occultation with SCIAMACHY: First retrieval results

Scanning imaging absorption spectrometer for atmospheric chartography (SCIAMACHY) is a moderate resolution imaging spectrometer on board the environmental satellite (ENVISAT) launched in March 2002. SCIAMACHY has eight channels, covering a spectral range from 240 to 2380 nm and observes the Earth’s atmosphere in nadir, limb, and occultation geometries. From SCIAMACHY lunar occultation measurements, nighttime vertical profiles of O 3 and NO 2 have been retrieved over the southern hemisphere (60°–90°S) using the optimal estimation method. The first preliminary validation of retrieved O 3 profiles with halogen occultation experiment and comparisons with stratospheric aerosol and gas experiment III (SAGE III), and Michelson interferometer for passive atmospheric sounding (MIPAS) O 3 profiles were carried out. In addition, the retrieved NO 2 profiles were compared to SAGE III and MIPAS results. The results of these preliminary validation and comparisons give confidence that reasonable scientific data products (trace gas profiles) can be derived from SCIAMACHY spectroscopic lunar occultation data.

Retrieval of stratospheric NO2 vertical profiles from ground‐based zenith‐sky DOAS measurements: Results for the MANTRA 1998 field campaign

The importance of measurements of the vertical distribution of odd nitrogen in studies of ozone chemistry and climate change has long being recognized. In this paper, we use the optimal estimation method developed by Rodgers (1976, 1990) to retrieve NO2 vertical profiles from slant column observations made with a portable ultraviolet (UV)‐visible zenith‐sky spectrometer operated on the ground during the Middle Atmosphere Nitrogen TRend Assessment (MANTRA) balloon campaign carried out at Vanscoy, Saskatchewan, Canada (52°N, 107°W), from 18 to 25 August 1998. Late summer was chosen for the campaign because the stratospheric zonal wind velocity changes sign at that time. Under such conditions the stratospheric winds are at a minimum, leaving the stratosphere in a dynamically quiescent state and closer to photochemical control (Fahey et al., 2001; Fioletov and Shepherd, 2003). The NO2 profile retrieved from the ground‐based observations is compared with the co‐located and simultaneous NO2 profile measured by a balloon‐borne UV‐visible spectrometer during sunrise on 24 August. Good agreement is observed, giving us confidence in the retrieval technique adopted. The retrieved NO2 profiles are also compared with the output of the Model for Evaluating oZONe trends (MEZON) 3D stratospheric chemical transport model. It is observed that, for altitudes below the peak concentration, the model underestimates the NO2 amount, and at the altitude of peak concentration, the model values lie between the values measured from the balloon and those retrieved from the ground‐based measurements. Nevertheless, the model reproduces the general shape of the retrieved profiles, including the altitude of the NO2 maximum, for both sunrise and sunset conditions.

A sensitivity study on spectroscopic parameter accuracies for a mm/sub-mm limb sounder instrument

The purpose of this paper is to perform a detailed error analysis for a mm/sub-mm limb sounding instrument with respect to spectroscopic parameters. This is done in order to give some insight into the most crucial spectroscopic parameters and to work out a list of recommendations for measurements that would yield the largest possible benefit for an accurate retrieval. The investigations cover a variety of spectroscopic line parameters, such as line intensity, line position, air and self broadening parameters and their temperature exponents, and pressure shift. The retrieval process is performed with the optimal estimation method (OEM). The OEM allows one to perform an assessment of the total statistical error, as well as of the model parameter error, such as the error coming from spectroscopic parameters. The instrument parameters assumed are those of the MASTER instrument studied by the European Space Agency, one of the candidate instruments for a future atmospheric chemistry mission. However, the same principle and method of analysis can be applied to any other millimeter/sub-millimeter limb sounding instrument, for instance the Japanese instrument JEM/SMILES, the Swedish instrument Odin, and the Earth Observing System Microwave Limb Sounder. We find that an uncertainty in the intensity of the strong lines give an error of similar magnitude on the retrieved species to which the lines belong. Uncertainties in the line position have overall a small impact on the retrieval, indicating that the line positions are known with sufficient accuracy. The air broadening parameters and their temperature exponents of a few strong lines dominate the error budget. On the other hand, the self broadening parameters and the pressure shifts are found to have a rather small impact on the retrieval.

Ozone column classified climatology of ozone and temperature profiles based on ozonesonde and satellite data

An updated and atmospheric dynamics oriented global climatology of ozone profiles has been derived from ozonesonde and satellite observations. The climatology, which uses total ozone to parameterize the profile shape, provides improved a priori information for ozone profile retrieval from satellite measurements using optimal estimation. It can be also used to correct the profile shape error in total ozone retrieval. Sonde data were selected from the 1990–2000 and 1988–1999 period for SAGE II excluding two years of SAGE II V6.1 data influenced by the Mount Pinatubo eruption in 1991. In addition, POAM III V3 data covering the polar region and SHADOZ ozonesonde data in the tropics were included. The ozone profile data were binned in steps of 30 DU of total ozone, 30° wide zonal bands, and into a six‐month season (winter/spring and summer/fall) in middle and high latitudes. No seasonal distinction is needed in the low‐latitude region (30°S to 30°N). Mean and standard deviation profiles for each ozone class were combined from satellites and sondes with a transition region in the range 20–26 km to merge both data sets. Temperature data from sonde, SAGE II collocated NMC, and POAM III collocated UKMO, where NMC and UKMO data are used in respective ozone retrieval, have been binned and averaged in the same manner as the ozone profiles so that for each mean ozone profile a matching temperature profile was derived. Corresponding ozone and temperature profiles help in accounting for the temperature dependence of the ozone absorption cross sections in the retrieval process. Key features of both ozone and temperature climatologies are discussed. As examples, ozone‐temperature correlation and the climatology of tropopause heights as derived from this climatology are presented, and they serve as diagnostic tools to show that the new climatology is a representative data set for global applications. Good agreement between collocated sonde profiles from Hohenpeissenberg (47.8°, 11.0°) and GOME ozone profiles, retrieved using optimal estimation method and using this climatology as constraints, was found. Also, comparison with GOME results, which were retrieved using a zonal monthly mean climatology, demonstrates the large improvements achieved by using this new climatology, particularly in the lowermost stratosphere and tropopause region.

Retrieval of nitrogen dioxide stratospheric profiles from ground-based zenith-sky UV-visible observations: validation of the technique through correlative comparisons

Abstract. A retrieval algorithm based on the Optimal Estimation Method (OEM) has been developed in order to provide vertical distributions of NO2 in the stratosphere from ground-based (GB) zenith-sky UV-visible observations. It has been applied to observational data sets from the NDSC (Network for Detection of Stratospheric Change) stations of Harestua (60° N, 10° E) and Andøya (69° N, 16° E) in Norway. The information content and retrieval errors have been analyzed following a formalism used for characterizing ozone profiles retrieved from solar infrared absorption spectra. In order to validate the technique, the retrieved NO2 vertical profiles and columns have been compared to correlative balloon and satellite observations. Such extensive validation of the profile and column retrievals was not reported in previously published work on the profiling from GB UV-visible measurements. A good agreement - generally better than 25% - has been found with the SAOZ (Système d'Analyse par Observations Zénithales) and DOAS (Differential Optical Absorption Spectroscopy) balloons. A similar agreement has been reached with correlative satellite data from the HALogen Occultation Experiment (HALOE) and Polar Ozone and Aerosol Measurement (POAM) III instruments above 25km of altitude. Below 25km, a systematic underestimation - by up to 40% in some cases - of both HALOE and POAM III profiles by our GB profile retrievals has been observed, pointing out more likely a limitation of both satellite instruments at these altitudes. We have concluded that our study strengthens our confidence in the reliability of the retrieval of vertical distribution information from GB UV-visible observations and offers new perspectives in the use of GB UV-visible network data for validation purposes.

Selection of optimal AR spectral estimation method for internal carotid arterial Doppler signals using Cramer–Rao bound

In this study, Doppler signals recorded from internal carotid artery of 80 subjects were processed by PC-computer using autoregressive method and Doppler power spectra were obtained. The parameters of autoregressive method were estimated by different estimation methods such as Yule–Walker, covariance, modified covariance, Burg, least squares, and maximum likelihood estimation. Doppler spectra were then used to compare the applied estimation methods in terms of their frequency resolution and the effects in determination of stenosis in internal carotid arteries. The Cramer–Rao bounds were derived for the estimated autoregressive parameters of the internal carotid arterial Doppler signals and the performance evaluation of the estimation methods was performed using the Cramer–Rao bound values. Finally, the optimal autoregressive spectral estimation method for the internal carotid arterial Doppler signals was selected according to the computed Cramer–Rao bound values.

Free tropospheric measurements of formic acid (HCOOH) from infrared ground‐based solar absorption spectra: Retrieval approach, evidence for a seasonal cycle, and comparison with model calculations

The seasonal variation of the free tropospheric volume mixing ratio of formic acid (HCOOH) has been derived from high‐spectral‐resolution solar absorption spectra recorded with the Fourier transform spectrometer in the U.S. National Solar Observatory facility on Kitt Peak (31.9°N, 111.6°E, 2.09 km altitude) at a typical spectral resolution of 0.005 cm−1. The spectra have been analyzed with the SFIT2 algorithm, which is based on a semiempirical application of the optimal estimation method. Absorption by HCOOH is weak in these solar spectra, but successful retrievals have been obtained with a new procedure that fits the HCOOH ν6 band Q branch at 1105 cm−1 simultaneously with a window to account for a temperature‐sensitive HDO line, which overlaps the HCOOH Q branch. After retaining only the best measurements from a database extending from June 1980 to October 2002 the retrievals show a seasonal variation, with a summer maximum and a winter minimum. Average 2.09–10 km volume mixing ratios binned in 3 month intervals range from a maximum of 792 ± 323 parts per trillion by volume (pptv), or 10−12, in July–September to a minimum of 313 ± 175 pptv in October–December, with the uncertainties corresponding to statistical means from daily averages. The results are compared with previously reported measurements and model calculations.

Implications of Stochastic and Deterministic Filters as Ensemble-Based Data Assimilation Methods in Varying Regimes of Error Growth

Accurate numerical prediction of fluid flows requires accurate initial conditions. Monte Carlo methods have become a popular and realizable approach to estimating the initial conditions necessary for forecasting, and have generally been divided into two classes: stochastic filters and deterministic filters. Both filters strive to achieve the error statistics predicted by optimal linear estimation, but accomplish their goal in different fashions, the former by way of random number realizations and the latter via explicit mathematical transformations. Inspection of the update process of each filter in a one-dimensional example and in a two-dimensional dynamical system offers a geometric interpretation of how their behavior changes as nonlinearity becomes appreciable. This interpretation is linked to three ensemble assessment diagnostics: rms analysis error, ensemble rank histograms, and measures of ensemble skewness and kurtosis. Similar expressions of these diagnostics exist in a hierarchy of models. The geometric interpretation and the ensemble diagnostics suggest that both filters perform as expected in a linear regime, but that stochastic filters can better withstand regimes with nonlinear error growth. Accurate numerical prediction of fluid flows requires accurate initial conditions. In an effort to approximate optimal estimation methods for linear problems with Gaussian error statistics, Monte Carlo methods have become a popular and realizable approach to estimating the initial conditions necessary for forecasting (e.g., Evensen and van Leeuwen 1996; Houtekamer and Mitchell 2001). Ensemble methods based on linear theory have taken two general forms: stochastic filters and deterministic filters. Both filters strive for the same result, namely to achieve the error statistics predicted by optimal linear estimation, but accomplish their goal in different fashions, the former by way of random number realizations and the latter via explicit mathematical transformations. We seek to understand the implications of these different methodologies when applied to different regimes of error growth. Through geometric considerations in a one-dimensional example and in a two-dimensional system’s state space, we formulate an interpretation of the update process for both filter types. We examine how this interpretation expresses itself in three ensemble diagnostics, root-mean-square (rms) analysis error, ensemble rank histograms, and measures of ensemble skewness and kurtosis. We then monitor filter behavior with these di

The dependence of retrieved cirrus ice‐crystal effective dimension on assumed ice‐crystal geometry and size‐distribution function at solar wavelengths

AbstractThe dependence of retrieved ice‐crystal effective dimension on assumed ice‐crystal shape and size‐distribution function is investigated at solar wavelengths (0.87, 1.6 and 3.7 µm). The dual viewing Along Track Scanning Radiometer is used to retrieve ice‐crystal effective dimension using a method of Optimal Estimation over semi‐transparent cirrus located in the tropics and mid‐latitudes. The ice‐crystal effective dimension is defined in terms of the effective diameter and it is retrieved assuming roughened hexagonal ice aggregates, pristine hexagonal ice columns, and four‐branched bullet rosettes. It is shown that if a phase function that well represents the scattering properties of cirrus is applied to each crystal type then the retrieved ice‐crystal effective diameter is only weakly dependent on ice‐crystal shape and size‐distribution function. Absolute differences between retrieved ice‐crystal effective diameter assuming hexagonal ice columns and ice aggregates combined with a representative phase function are generally well within ±5 µm. The findings of this paper have the important implication that, in climate models, simulation of cirrus cloudy radiances at solar wavelengths might be made to be independent of assumed ice‐crystal shape and size‐distribution function. © Crown copyright, 2004.

Quality assessment of ground-based microwave measurements of chlorine monoxide, ozone, and nitrogen dioxide from the NDSC radiometer at the Plateau de Bure

Abstract. A ground-based microwave radiometer dedicated to chlorine monoxide (ClO) measurements around 278GHz has been in operation from December 1993-June 1996 at the Plateau de Bure, France (45° N, 5.9° E, 2500m altitude). It belongs to the international Network for the Detection of Stratospheric Change. A detailed study of both measurements and retrieval schemes has been undertaken. Although dedicated to the measurements of ClO, simultaneous profiles of O3, ClO and NO2, together with information about the instrumental baseline, have been retrieved using the optimal estimation method. The vertical profiles have been compared with other ground-based microwave data, satellite-borne data and model results. Data quality shows: 1) the weak sensitivity of the instrument that obliges to make time averages over several hours; 2) the site location where measurements of good opacities are possible for only a few days per year; 3) the baseline undulation affecting all the spectra, an issue common to all the microwave instruments; 4) the slow drift of some components affecting frequencies by 3-4MHz within a couple of months. Nevertheless, when temporally averaging data over a few days, ClO temporal variations (diurnal and over several weeks in winter 1995) from 35-50km are consistent with model results and satellite data, particularly at the peak altitude around 40km, although temporal coincidences are infrequent in winter 1995. In addition to ClO, it is possible to obtain O3 information from 30-60km whilst the instrument is not optimized at all for this molecule. Retrievals of O3 are reasonable when compared with model and another ground-based data set, although the lowermost layers are affected by the contamination of baseline remnants. Monthly-averaged diurnal variations of NO2 are detected at 40km and appear in agreement with photochemical model results and satellite zonally-averaged data, although the amplitude is weaker than the other data sets. This NO2 result highlights the great potential of the retrieval scheme used.

Towards O 3 and NO 2 vertical profile retrieval from SCIAMACHY solar occultation measurements: first results

SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) is a space-borne instrument, which measures in the UV–Vis–IR range in nadir, limb, and occultation geometry. It has successfully been launched onboard ENVISAT (ENVIronmental SATellite) on March 1 2002. During the six month commissioning phase of ENVISAT, first test retrievals using uncalibrated Level 0 data were performed. We retrieved O 3 and NO 2 height resolved profiles with considerable accuracy and compared them to POAM III and SAGE III results. Tangent heights were calculated by O 2 and CO 2 retrievals. The retrieval is based on the optimal estimation method. The spectral fits of O 3 and NO 2 absorption spectra were analysed and the fit residues show remaining spectral inhomogeneities of the solar disk and instrumental features. An algorithm has been developed to minimise the impact of the solar inhomogeneities.

Global Ozone Monitoring Experiment ozone profile characterization using interpretation tools and lidar measurements for intercomparison

Global ozone profiles are derived from the ultraviolet and visible part of the spectra of the nadir‐viewing Global Ozone Monitoring Experiment (GOME), which is mounted on the polar orbiting second Earth Remote Sensing satellite (ERS‐2). These profiles need to be characterized, especially since the product includes a priori knowledge and so‐called averaging kernels. This additional information needs to be taken into account when comparing the profiles to correlative measurements. We perform an intercomparison between the ground‐based stratospheric lidar system in Lauder, New Zealand, and collocated GOME data. Here, the satellite profiles are retrieved with the algorithm of the Royal Netherlands Meteorological Institute (KNMI), which uses the optimal estimation method. In the comparison study significant differences are revealed which vary with season and altitude, indicating errors in the retrieval system. However, any quality assessment will just be one part of characterizing an ozone profile product that includes averaging kernels and a priori information. Data users need to be aware of the inherently complicated nature of such products that can only be fully understood when taking into account this additional information. In the second part of the study, the complex relation between the retrieved and the true profile is clarified using several interpretation tools. Applying these tools, we conclude that below 17‐km altitude the GOME profiles can only be used with appropriate use of averaging kernels (e.g., in data assimilation). Above 17 km up to 50 km the GOME spectra contain useful profile information, but the retrieved profiles have a moderate vertical resolution of about 11 km and contain a substantial fraction of a priori information of about 50%.

Validation of ground‐based observations of stratomesospheric ozone

Since January 1995, an ozone line at 110 GHz is observed with a ground‐based microwave radiometer at the Bordeaux Observatory, France (45°N), belonging to the Network for the Detection of Stratospheric Change (NDSC). Ozone profiles from 25 to 75 km are retrieved from the microwave emission spectra using the Optimal Estimation Method. Improvements on the data acquisition process and calibration procedure are presented. A comprehensive comparison with satellite (Halogen Occultation Experiment (HALOE), Microwave Limb Sounder (MLS), and Stratospheric Aerosol and Gas Experiment II (SAGE II)) and ground‐based instrument data (microwave radiometer in Bern, Switzerland, lidar at the Observatoire de Haute‐Provence, France) is given. The average profiles, using the statistically most significant data sets, deviate not more than 15% in the stratosphere and 30% in the mesosphere. We can thus assert that the Bordeaux radiometer is a well‐validated instrument providing consistent and high‐quality data.

Operational carbon monoxide retrieval algorithm and selected results for the MOPITT instrument

Measurements of Pollution in the Troposphere (MOPITT) is a new remote sensing instrument aboard the Earth Observing System (EOS) “Terra” satellite which exploits gas correlation radiometry principles to quantify tropospheric concentrations of carbon monoxide (CO) and methane (CH4). The MOPITT CO retrieval algorithm employs a nonlinear optimal estimation method to iteratively solve for the CO profile which is statistically most consistent with both the satellite‐measured radiances and a priori information. The algorithm's theoretical basis is described in terms of the observed radiances and their weighting functions, the a priori information, and the retrieval averaging kernels. Examples of actual CO retrievals over scenes with contrasting pollution conditions are demonstrated, and interpreted in the context of the retrieval averaging kernels and a priori.

Analysis of two independent methods for retrieving liquid water profiles in spring and summer Arctic boundary clouds

A large number of all‐liquid, nondrizzling stratus clouds (163 hours of measurements) were observed with a dual‐channel microwave radiometer and a colocated 35‐GHz cloud radar during the spring and summer months of the Surface Heat Budget of the Arctic Ocean (SHEBA) project. An algorithm developed by Frisch et al. [1995, 1998] to derive the liquid water content (LWC) is applied to these measurements assuming constant cloud drop number density and cloud drop size distribution breadth with height. A second algorithm developed by Löhnert et al. [2001] is specifically adapted for SHEBA clouds using a priori information from a large eddy simulation (LES) model initialized with summertime SHEBA radiosondes; about 50 soundings during nondrizzling, low‐level, all‐liquid water clouds are used. Using model‐derived drop size distributions, a relationship between simulated radar reflectivity (Z) and model LWC is derived as well as an a priori LWC profile. Once the theoretical error covariance matrix of the Z‐LWC relation is derived and the covariance matrix of the LWC profile is calculated, an optimal estimation method is applied to the SHEBA data. The Frisch et al. and Löhnert et al. methods are also applied to the LES model output, resulting in overall root‐mean‐square differences on the order of 30 to 60%. Both methods are sensitive to the assumed accuracies of the microwave‐radiometer‐derived LWP. When applied to LES model output, the Frisch et al. method shows a LWC overestimation in the lower parts of the cloud. These systematic errors are induced by the assumption of constant cloud number concentration with height.

Optimal surface temperature reconstructions using terrestrial borehole data

We derive an optimal Northern Hemisphere mean surface temperature reconstruction from terrestrial borehole temperature profiles spanning the past five centuries. The pattern of borehole ground surface temperature (GST) reconstructions displays prominent discrepancies with instrumental surface air temperature (SAT) estimates during the 20th century, suggesting the presence of a considerable amount of noise and/or bias in any underlying spatial SAT signal. The vast majority of variance in the borehole dataset is efficiently retained by its two leading eigenvectors. A sizable share of the variance in the first eigenvector appears to be associated with non‐SAT related bias in the borehole data. A weak but detectable SAT signal appears to be described by a combination of the first two eigenvectors. Exploiting this eigendecomposition, application of optimal signal estimation methods yields a hemispheric borehole SAT reconstruction that is largely consistent with instrumental data available in past centuries, and is indistinguishable in its major features from several published long‐term temperature estimates based on both climate proxy data and model simulations.

Variational assimilation of radar reflectivities in a cirrus model. II: Optimal initialization and model bias estimation

In this paper the microphysical model of cirrus clouds introduced in a related study is used to assimilate radar data. A variational approach is developed, based on a method of optimal estimation which makes use of the gradient information provided by the adjoint of the model to minimize a quadratic cost function. Multiple experiments to probe different solutions to the assimilation problem are conducted using both synthetic reflectivities and real observations. Various model and environment parameters are tested as control variables. Results indicate that specific humidity is a viable control variable at cloud levels. Even though this field is only indirectly related to the radar signal, information about the ambient humidity in which the cloud formed may be extracted from the radar reflectivities by using the cloud model in conjunction with the observations. The adjustment of the specific-humidity profile brings the model solution closer to the observed values by increasing the crystal number concentration. Systematic errors in the prognostic variables are also estimated as part of the optimization process by including a model bias term in the cost function. This is equivalent to relaxing the assumption of ‘perfect’ model, and allows for better assimilation results when both model bias evaluation and optimal initialization are performed. Copyright © 2003 Royal Meteorological Society

Retrieval and characterization of ozone profiles from solar infrared spectra at the Jungfraujoch

Vertical distributions of ozone from June 1996 to November 2000 have been retrieved from high‐resolution Fourier transform infrared (FTIR) solar absorption spectra recorded at the primary Network for Detection of Stratospheric Change station of the Jungfraujoch in the Swiss Alps (46.5°N, 8°E, 3580 m above sea level (asl). The retrievals were performed using the Optimal Estimation Method (OEM), both in a narrow spectral interval (1002.567–1003.2 cm−1) and in a broad spectral interval (1000.0–1005.0 cm−1) in the O3 9.6‐μm band. A thorough characterization of the retrievals has been performed following the lines of OEM, including an information content analysis, a study of the correlations between retrieved instrumental parameters and retrieved ozone concentrations, and an evaluation of the O3 profile error budget. It is demonstrated that the information content is significantly higher for spectra in the broad microwindow, resulting in higher vertical resolutions, on the order of 8 km, of the retrieved profiles extending up to 40 km, and less correlations between retrieved parameters. An independent statistical verification of the retrieval results and their characterization has been performed by comparison of the FTIR ozone profiles with independent measurements. These are the ozone profile measurements from balloon soundings at Payerne, from the microwave radiometer at Bern and the lidar at Observatoire de Haute‐Provence (OHP), and the total column data from the Dobson spectrophotometer at Arosa. Applying the optimum retrieval procedure in the broad spectral interval, an excellent agreement has been found between the FTIR O3 profile data and the correlative data. The largest offset of the FTIR data in comparison with the correlative data is found with respect to the lidar data in the 24‐ to 40‐km layer, and is on the order of 5%. No systematic biases have been found in the troposphere, neither in the upper troposphere‐lower stratosphere (UTLS) up to 18 km. The dispersion of the relative differences between the data sets, if any, is never larger than half of the natural ozone variability.

A consistent set of single-scattering properties for cirrus cloud: tests using radiance measurements from a dual-viewing multi-wavelength satellite-based instrument

In this paper a consistent set of single-scattering properties is presented for radiative transfer calculations and remote sensing of cirrus cloud. The single-scattering properties consist of the extinction coefficient, single-scattering albedo and phase function. A randomly oriented randomized hexagonal ice aggregate is assumed to derive the extinction coefficient and single-scattering albedo. The phase function is an extension of the Henyey–Greenstein model called the “analytic” phase function, which is generated from the asymmetry parameter at non-absorbing and absorbing wavelengths. The satellite-based dual-view along track scanning radiometer (ATSR-2) instrument is utilized to test the single-scattering properties for consistency at scattering angles between about 60° and 170°, using a method of Optimal Estimation. Optimal Estimation is applied to a set of cloud parameters and radiance measurements, which are made simultaneously at the wavelengths of 0.87, 1.6, 3.7, 11.0 and 12.0 μm , over cases of cirrus cloud located in the tropics and mid-latitudes. If the single-scattering properties and assumed model parameters were a perfect representation of the radiative properties of cirrus then the measurement residuals (i.e., differences between measurements and simulated measurements) would be identically equal to zero at each of the wavelengths for all scattering angles. It is found that the randomized ice aggregate combined with the analytic phase function minimizes the measurement residuals to generally well within ±1% (reflectance) and ±1 K (brightness temperature) at 0.87, 11.0 and 12.0 μm and to within ±3% and ±3 K at 1.6 and 3.7 μm , respectively. This compares to measurement residuals of about 8% and 10 K if the single-scattering properties are based on the randomly oriented hexagonal ice column. It is recommended that single-scattering properties based on the randomized ice aggregate combined with the analytic phase function (or a very similar phase function) should be applied to remote sensing and radiative transfer studies of cirrus cloud.

Retrieval of vertical profiles of NO3 from zenith sky measurements using an optimal estimation method

The generic optimal estimation method (OEM) developed by Rodgers [1976, 1990, 2000] for solving atmospheric data inversion problems has been successfully developed to retrieve vertical profile information of NO3 from zenith sky spectroscopic measurements of column abundance made through sunrise. The technique has been shown to be robust and yields profile information to an altitude of 20 km. The rapid photolysis of NO3 at dawn ensures that a time series of column density measurements provides significant vertical information. The method has been extensively tested and a thorough error analysis was performed. The largest source of error arises from the undersampling of the column density through sunrise, the so‐called smoothing error. The measurement errors and uncertainties in the forward model are also significant. Although a simple forward model involving only photolysis of NO3 during sunrise is able to successfully map the retrieved profile onto the column density measurements on some days, on other days systematic errors arise in the retrieval. These can be accounted for by either increased cloudiness or thermal decomposition of N2O5 in polluted boundary layer air, both effects extending the lifetime of NO3 through sunrise. The technique allows NO3 profile information to be retrieved in a variety of conditions over an extended period of time in a reliable and consistent manner.