Vector Radiative Transfer Code Research Articles

Polarized Radiative Transfer Simulations: A Tutorial Review and Upgrades of the Vector Discrete Ordinate Radiative Transfer Computational Tool

We present an overview and several important upgrades to the Vector Discrete Ordinate Radiative Transfer (VDISORT) code. VDISORT is a polarized (vector) radiative transfer code that can be applied to a wide range of research problems including the Earth’s atmosphere and ocean system. First, a solution is developed to the complex algebraic eigenvalue problem resulting when the b2 component of the Stokes scattering matrix is non-zero. This solution is needed to compute the V component of the Stokes vector I=[I∥,I⊥,U,V]T. Second, a significant improvement in computational efficiency is obtained by reducing the dimension of the algebraic eigenvalue by a factor of 2 resulting in a speed increase of about 23 = 8. Third, an important upgrade of the VDISORT code is obtained by developing and implementing a method to enable output at arbitrary polar angles by the integration of the source function (ISF) method for partially reflecting Lambertian as well as general non-Lambertian surfaces. Fourth, a pseudo-spherical treatment has been implemented to provide important corrections for Earth curvature effects at near horizontal solar zenith and observation (viewing) polar angles. Fifth, a post-processing single-scattering correction procedure has been developed to enhance the accuracy and speed for strongly forward-peaked scattering. With these significant improvements the results from the upgraded version of the VDISORT code match published benchmark results for Rayleigh scattering, Mie scattering, and scattering by non-spherical cirrus particles. The performance of VDISORT for a polarized incident beam source is equally satisfactory. The VDISORT vector radiative transfer code is made public and freely available for use by the growing polarimetric research community including the space-borne polarimeters on the future NASA PACE and AOS missions.

Polarized observations for advanced atmosphere-ocean algorithms using airborne multi-spectral hyper-angular polarimetric imager

Airborne measurements of the linear polarization state of light were carried out over coastal and open ocean conditions to study aerosol and water column properties and investigate the possibility of using a multi-spectral, hyper-angular imaging polarimeter for retrieving aerosol and hydrosol optical properties. The instrument, the Versatile Imager for the Coastal Ocean (VICO), is used to support the analysis of ocean color polarized observations and their implication for future space-borne polarimetry such as the polarimeters planned to be deployed with the NASA Plankton, Aerosol, Cloud, and ocean Ecosystem (PACE) mission. Several sets of images at different viewing angles from the visible to the near-infrared spectrum were collected and compared with simulations using a vector radiative transfer (VRT) code. The simulations were obtained based on measured seawater inherent optical properties from shipborne instruments and measured atmospheric parameters from the Aerosol Robotic Network (AERONET) and a shipborne sunphotometer at different locations. An uncertainty method has been derived by propagating uncertainties from the measured polarized radiances. The method demonstrates practicable uncertainty formulations that can be used to construct a measurement uncertainty budget for the polarized data products. Results from VICO and the VRT simulation are consistent for both radiance and polarization spectrum at all the measured viewing angles. The total and polarized water-leaving reflectances are retrieved at four bands and varied geometries. It is also shown that the polarized remote sensing reflectance measured at various angles could be used to distinguish between the aerosols’ and hydrosols’ optical signatures by exploiting the fact that the polarized reflectance is fairly insensitive to hydrosols for given acquisition geometries. This study thus provides an opportunity to investigate various relationships between the microphysical properties of the oceanic and atmospheric particulates such as refractive index and particle size properties. It also contributes to the development of polarization-based inverse ocean color algorithms. Finally, the provided analysis gives insights for the validation of the ocean color parameters that will be retrieved from the forthcoming polarimetric satellite missions.

Hyperspectral polarimetric imaging of the water surface and retrieval of water optical parameters from multi-angular polarimetric data.

Total and polarized radiances from above the ocean surface are measured by a state-of-the-art snapshot hyperspectral imager. A computer-controlled filter wheel is installed in front of the imager allowing for recording of division-of-time Stokes vector images from the ocean surface. This system, to the best of our knowledge, for the first time provided a capability of hyperspectral polarimetric multi-angular measurements of radiances from above the water surface. Several sets of measurements used in the analysis were acquired from ocean platforms and from shipborne observations. Measurements made by the imager are compared with simulations using a vector radiative transfer (VRT) code showing reasonable agreement. Analysis of pixel-to-pixel variability of the total and polarized above-water radiance for the viewing angles of 20°-60° in different wind conditions enable the estimation of uncertainties in measurements of these radiances in the polarized mode for the spectral range of 450-750 nm, thus setting requirements for the quality of polarized measurements. It is shown that there is a noticeable increase of above-water degree of linear polarization (DoLP) as a function of the viewing angle, which is due both to the larger DoLP of the light from the water body and the light reflected from the ocean surface. Results of measurements and VRT simulations are applied for the multi-angular retrieval of the ratio of beam attenuation coefficient (ctot) to absorption coefficient (atot) in addition to the other parameters such as absorption and backscattering coefficients retrieved from traditional unpolarized methods.

Matrix exponential in C/C++ version of vector radiative transfer code IPOL

We use only left eigenvectors to evaluate the matrix exponential in the method of discrete ordinates for the vector radiative transfer equation, which neglects circular polarization, in a plane-parallel atmosphere. This is contrary to a common practice of using the right eigenvectors to evaluate the matrix exponential combined with the left eigenvectors to avoid the inversion of the matrix of the right ones. Two numerical tests for Rayleigh and Aerosol scattering confirm our idea. For better explanation of our approach and for independent crosscheck of our results, we distribute an example in C/C++.

Variability of the reflectance coefficient of skylight from the ocean surface and its implications to ocean color.

The value and spectral dependence of the reflectance coefficient (ρ) of skylight from wind-roughened ocean surfaces is critical for determining accurate water leaving radiance and remote sensing reflectances from shipborne, AERONET-Ocean Color and satellite observations. Using a vector radiative transfer code, spectra of the reflectance coefficient and corresponding radiances near the ocean surface and at the top of the atmosphere (TOA) are simulated for a broad range of parameters including flat and windy ocean surfaces with wind speeds up to 15 m/s, aerosol optical thicknesses of 0-1 at 440nm, wavelengths of 400-900 nm, and variable Sun and viewing zenith angles. Results revealed a profound impact of the aerosol load and type on the spectral values of ρ. Such impacts, not included yet in standard processing, may produce significant inaccuracies in the reflectance spectra retrieved from above-water radiometry and satellite observations. Implications for satellite cal/val activities as well as potential changes in measurement and data processing schemes are discussed.

Assessment of Terra MODIS On-Orbit Polarization Sensitivity Using Pseudoinvariant Desert Sites

The Moderate Resolution Imaging Spectroradiometer (MODIS) is currently flying on NASA’s Earth Observing System Terra and Aqua satellites, launched in 1999 and 2002, respectively. MODIS reflective solar bands in the visible wavelength range are known to be sensitive to polarized light based on prelaunch polarization sensitivity tests. After about five years of on-orbit operations, it was discovered that the polarization sensitivity at short wavelengths had shown a noticeable increase. In this paper, we examine the impact of polarization on measured top-of-atmosphere (TOA) reflectances based on MODIS Collection-6 L1B over pseudoinvariant desert sites. The standard polarization correction equation is used in combination with simulated at-sensor radiances using the second simulation of a satellite signal in the Solar Spectrum, Vector Radiative Transfer Code (6SV). We ignore the polarization contribution from the surface and a ratio approach is used for both 6SV-derived input parameters and observed TOA reflectances. Results indicate that significant gain corrections up to 25% are required near the end of scan for the 412 and 443 nm bands. The polarization correction reduces the seasonal fluctuations in reflectance trends and mirror side ratios from 30% and 12% to 10% and 5%, respectively, for the two bands. Comparison of the effectiveness of the polarization correction with the results from the NASA Ocean Biology Processing Group shows a good agreement in the corrected reflectance trending results and their seasonal fluctuations.

Vector radiative transfer code SORD: Performance analysis and quick start guide

We present a new open source polarized radiative transfer code SORD written in Fortran 90/95. SORD numerically simulates propagation of monochromatic solar radiation in a plane-parallel atmosphere over a reflecting surface using the method of successive orders of scattering (hence the name). Thermal emission is ignored. We did not improve the method in any way, but report the accuracy and runtime in 52 benchmark scenarios. This paper also serves as a quick start user's guide for the code available from ftp://maiac.gsfc.nasa.gov/pub/skorkin, from the JQSRT website, or from the corresponding (first) author.

Effects of polarization calibration on aerosol optical depth retrieval: An ocean case sensitivity analysis

Reflectance measurements of both the visible and infrared bands of passive remote sensing sensors are widely used to retrieve aerosol optical depth (AOD) information. This is performed commonly for data obtained over both ocean and land, and these measurements allow for the off line development of a lookup table using radiative transfer models. Owing to molecular and aerosol effects, the reflected light received by the sensor is usually highly polarized. The linear polarization effect may be up to 100%, and the polarization factor of a sensor optical system will change the total intensity as well as the polarization status of the signal reaching the detector. The detector response will be different when the incident light polarization status changes, even if the total intensity remains constant. However, if the polarization calibration is neglected, it will cause obvious errors in the aerosol data retrieval. This is especially true for aerosol optical depth retrieval over an ocean. This measurement relies directly on the reflectance output of the sensor. Cases involving land surfaces are not discussed herein because the inhomogeneous properties conceal the error due to polarization. Taking the 550 and 860 nm bands as examples, the difference between the real top-of-atmosphere (TOA) reflectance and the reflectance reaching the detector is calculated using three different sensor polarization standards according to the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) and Moderate Resolution Imaging Spectroradiometer (MODIS) standards. The differences in AOD retrieval are also demonstrated using the lookup table developed previously from a vector radiative transfer code. The results reveal that under a normal situation in which the AOD is 0.15, the maximum AOD retrieval error could reach 0.04 in 550 nm but only 0.02 in 860 nm for the dust aerosol model. For the soot aerosol model, the maximum AOD retrieval error is 0.1 in 550 nm and 0.12 in 860 nm, indicating that the lack of polarization calibration will lead to large errors in aerosol retrieval over an ocean.

Considering polarization in MODIS-based cloud property retrievals by using a vector radiative transfer code

In this study, a full-vector, adding–doubling radiative transfer model is used to investigate the influence of the polarization state on cloud property retrievals from Moderate Resolution Imaging Spectroradiometer (MODIS) satellite observations. Two sets of lookup tables (LUTs) are developed for the retrieval purposes, both of which provide water cloud and ice cloud reflectivity functions at two wavelengths in various sun-satellite viewing geometries. However, only one of the LUTs considers polarization. The MODIS reflectivity observations at 0.65μm (band 1) and 2.13μm (band 7) are used to infer the cloud optical thickness and particle effective diameter, respectively. Results indicate that the retrievals for both water cloud and ice cloud show considerable sensitivity to polarization. The retrieved water and ice cloud effective diameter and optical thickness differences can vary by as much as ±15% due to polarization state considerations. In particular, the polarization state has more influence on completely smooth ice particles than on severely roughened ice particles.

The relationship between upwelling underwater polarization and attenuation/absorption ratio

The attenuation coefficient of the water body is not directly retrievable from measurements of unpolarized water-leaving radiance. Based on extensive radiative transfer simulations using the vector radiative transfer code RayXP, it is demonstrated that the underwater degree of linear polarization (DoLP) is closely related to the attenuation-to-absorption ratio (c/a) of the water body, a finding that enables retrieval of the attenuation coefficient from measurements of the Stokes components of the upwelling underwater polarized light field. The relationship between DoLP and the c/a ratio is investigated for the upwelling polarized light field for a complete set of viewing geometries, at several wavelengths in the visible part of the spectrum; for varying compositions of the aquatic environment, whose constituents include phytoplankton, non-algal particles, and color dissolved organic matter (CDOM); and for varying microphysical properties such as the refractive index and the slope of the Junge-type particle size distribution (PSD). Consequently, this study reveals the possibility for retrieval of additional inherent optical properties (IOPs) from air- or space-borne DoLP measurements of the water-leaving radiation.

Uncertainty and interpretation of aerosol remote sensing due to vertical inhomogeneity

We have built an aerosol retrieval algorithm which combines the Look Up Table (LUT) and least squares fitting methods. The algorithm is based on the multi-angle multi-wavelength polarized reflectance at the Top Of the Atmosphere (TOA) measured by the Research Scanning Polarimeter (RSP). The aerosol state parameters are the aerosol particle effective radius, effective variance, complex index of refraction, and aerosol column number density. Monomodal aerosol size distribution is assumed. The Cost Function (CF) of the least squares fitting is designed in consideration of the RSP instrumental characteristics. The aerosol retrieval algorithm inherently assumes one layer of aerosols within the atmosphere. Synthetic polarized radiance data at the TOA have been created assuming either one or two layers of aerosols using the vector radiative transfer code based on successive order of scattering method. Test cases for one-layer aerosol systems show great performance. Around 90% of the total 1200 test cases have CF values smaller than 50. For these cases, the correlation coefficients of the input and retrieved parameters are generally around or larger than 0.98. The effective variance is slightly worse with the correlation coefficient of 0.76938. On the other hand, test cases for two-layer aerosol systems show that only 50% of the total (also 1200) tested cases have final CFs smaller than 50. Among these successful cases (CF≤50), the retrieved optical depth can still be interpreted as the total column optical depth, though the correlation coefficient is decreased in comparison with the one-layer aerosol cases. We propose to interpret other retrieved aerosol parameters as the average of corresponding parameters for each layer weighted by its optical depth at 865nm. The retrieved effective radius and complex refractive index can be explained by this scheme (correlation coefficient around 0.9). The effective variance, however, shows decreased performance with the correlation coefficient of 0.46421. This may be due to the strong nonlinearity dependence of the scattering properties on the effective variance.

Numerical simulations of single and multiple scattering by fractal ice clusters

We consider the scattering model in the form of a vertically and horizontally homogeneous particulate slab of an arbitrary optical thickness composed of widely separated fractal aggregates built of small spherical ice monomers. The aggregates are generated by applying three different approaches, including simulated cluster–cluster aggregation (CCA) and diffusion-limited aggregation (DLA) procedures. Having in mind radar remote-sensing applications, we report and analyze the results of computations of the backscattering circular polarization ratio obtained using efficient superposition T-matrix and vector radiative-transfer codes. The computations have been performed at a wavelength of 12.6 cm for fractal aggregates with the following characteristics: monomer refractive index m=1.78+i0.003, monomer radius r=1 cm, monomer packing density p=0.2, overall aggregate radii R in the range 4≤ R≤10 cm and fractal dimensions D f =2.5 and 3. We show that for aggregates generated with simulated CCA and DLA procedures, the respective values of the backscattering circular polarization ratio differ weakly for D f =2.5, but the differences can increase somewhat for D f =3, especially in case of an optically semi-infinite medium. For aggregates with a spheroidal overall shape, the dependence of the circular polarization ratio on the cluster morphology can be quite significant and increases with increasing the aspect ratio of the circumscribing spheroid.

Benchmark results in vector atmospheric radiative transfer

In this paper seven vector radiative transfer codes are inter-compared for the case of underlying black surface. They include three techniques based on the discrete ordinate method (DOM), two Monte-Carlo methods, the successive orders scattering method, and a modified doubling-adding technique. It was found that all codes give very similar results. Therefore, we were able to produce benchmark results for the Stokes parameters both for reflected and transmitted light in the cases of molecular, aerosol and cloudy multiply scattering media. It was assumed that the single scattering albedo is equal to one. Benchmark results have been provided by several studies before, including Coulson et al. [22], Garcia and Siewert [7,8], Wauben and Hovenier [10], and Natraj et al. [11] among others. However, the case of the elongated phase functions such as for a cloud and with a high angular resolution is presented here for the first time. Also in difference with other studies, we make inter-comparisons using several codes for the same input dataset, which enables us to quantify the corresponding errors more accurately.

Radar polarimetry of Saturn's rings: Modeling ring particles as fractal aggregates built of small ice monomers

We analyze ground-based radar polarimetric observations of Saturn's rings at a wavelength of 12.6 cm by employing the model of a vertically and horizontally plane-parallel homogeneous slab composed of clumpy particles in the form of fractal aggregates of small ice monomers. Our model takes full account of the effects of polarization, multiple scattering, and coherent backscattering. Using efficient superposition T-matrix and vector radiative transfer codes, we perform computations of the backscattering circular polarization ratio for fractal aggregates generated with a cluster–cluster aggregation model and having the following characteristics: monomer refractive index m=1.78+i0.003; monomer packing density p=0.2; fractal dimensions D f=2.5 and 3; and overall fractal radii R in the range 4⩽ R⩽10 cm. In order to obtain physically realistic values of single-scattering properties of the aggregates we perform averaging over an ensemble of clusters generated for the same values of fractal parameters but having different geometrical configurations of the monomers. We conclude that in the framework of the above morphological model of Saturn's rings and the specific cluster–cluster aggregation procedure, it may be problematic to obtain a satisfactory and realistic agreement between theoretical computations and the observed values of the radar circular polarization ratio.

Atmospheric correction for the monitoring of land surfaces

This paper briefly describes the land surface reflectance product (MOD09), the current Moderate Resolution Imaging Spectroradiometer (MODIS) atmospheric correction (AC) algorithm and its recent updates, and provides the evaluation of the algorithm performance and product quality. The accuracy of the AC algorithm has been significantly improved owing to the use of the accurate Second Simulation of a Satellite Signal in the Solar Spectrum, Vector (6SV) radiative transfer code and a better retrieval of aerosol properties by a refined internal aerosol inversion algorithm. The Collection 5 MOD09 surface reflectance product computed by the improved AC algorithm was analyzed for the year of 2003 through the comparison with a reference data set created with the help of Aerosol Robotic Network (AERONET) measurements and the 6SV code simulations. In general, the MOD09 product demonstrated satisfactory quality in all used MODIS bands except for band 3 (470 nm), which is used for aerosol inversion. The impact of uncertainties in MOD09 upon the downstream product, such as vegetation indices and albedo, was also evaluated.

An Atmospheric Correction Algorithm for Remote Sensing of Bright Coastal Waters Using MODIS Land and Ocean Channels in the Solar Spectral Region

The present operational atmospheric correction algorithm for multichannel remote sensing of ocean color using imaging data acquired with the Moderate Resolution Imaging Spectroradiometer (MODIS) works well over clear ocean but can give incorrect results over brighter coastal waters. This is because: 1) the turbid waters are not dark for the two atmospheric correction channels centered near 0.75 and 0.86 mum; and 2) the ocean color channels (0.488, 0.531, and 0.551 mum) often saturate over bright coastal waters. Here, we describe an atmospheric correction algorithm for multichannel remote sensing of coastal waters. This algorithm is a modification of our previously developed atmospheric correction algorithm for hyperspectral data that uses lookup tables generated with a vector radiative transfer code and multilayered atmospheric models. Aerosol models and optical depths are determined by a spectrum-matching technique utilizing channels located at wavelengths longer than 0.86 mum, where the ocean surface is dark. The aerosol information in the visible spectral region is estimated based on the derived aerosol models and optical depths. Water-leaving radiances in the visible spectral region are obtained by subtracting out the atmospheric path radiances from the satellite-measured total radiances. Applications of the algorithm to two MODIS data sets are presented and compared to field measurements. The water-leaving reflectances retrieved with this algorithm over brighter shallow coastal waters compare closely with those from field measurements. In addition, the retrieved water-leaving reflectances over deeper ocean waters compare well with those derived with the MODIS operational algorithm

Diffuse and coherent backscattering of polarized light: Polarization ratios for a discrete random medium composed of nonspherical particles

For a sparse, disordered, plane-parallel particulate medium, we analyze quantitatively the effects of particle microphysical properties on the values of the linear and circular backscattering polarization ratios. Using numerically exact T-matrix and vector radiative-transfer codes, we performed computations for the following models: (1) a semi-infinite homogeneous layer composed of randomly oriented, polydisperse oblate spheroids with the real part of the refractive index equal to 1.2, 1.4 and 1.6 and the imaginary part of the refractive index equal to 0 and 0.01; (2) a semi-infinite homogeneous layer composed of randomly oriented, polydisperse, oblate circular cylinders with the refractive index 1.4; (3) finite homogeneous layers of various optical thickness composed of randomly oriented, polydisperse, oblate spheroids with the refractive index 1.55. Our computations demonstrate that the values of the polarization ratios depend substantially on particle shape, real and imaginary parts of the particle refractive index, particle size relative to the wavelength, illumination geometry and optical thickness.

Enhanced backscattering of polarized light: Effect of particle nonsphericity on the helicity-preserving enhancement factor

We analyze theoretically the effect of particle nonsphericity on the backscattering enhancement factor ζ hp in the helicity-preserving channel. Using numerically exact T-matrix and vector radiative-transfer codes, we have performed computations for optically semi-infinite homogeneous layers composed of polydisperse, randomly oriented oblate spheroids with the real part of the refractive index equal to 1.2, 1.4, and 1.6, the imaginary part of the refractive index equal to 0 and 0.01, various values of the equal-surface-area-sphere effective size parameter, and aspect ratios 1 ⩽ ɛ ⩽ 2 . Our computations demonstrate that whereas for spheres ζ hp ≡ 2 , for spheroids the helicity-preserving enhancement factor can deviate quite significantly from the value 2. The magnitude of this deviation varies substantially with particle microphysical parameters and illumination geometry.

The effect of particle shape on microphysical properties of Jovian aerosols retrieved from ground-based spectropolarimetric observations

In this paper we study potential errors in the retrieved values of the cloud particle refractive index and size that may result from the neglect of nonsphericity in analyses of ground-based spectropolarimetric observations of Jupiter. Using T-matrix and vector radiative-transfer codes, we have carried out numerous computations in the spectral range from 0.423 to 0.798μm for a plane-parallel model atmosphere comprising polydisperse ensembles of randomly oriented oblate and prolate spheroids with sizes comparable to the wavelength. The particle models were specified by a gamma size distribution with varying values of the effective radius and effective variance and by a varying refractive index. Two models of the Jovian atmosphere were considered: (i) a homogeneous semi-infinite layer composed of gas and cloud particles; and (ii) a two-layered medium with a layer of pure gas on top of a semi-infinite homogeneous layer composed of gas and cloud particles. Good agreement between ground-based observational data of the brightness and the degree of linear polarization for the center of the Jovian disk and model computations was found for the following combinations of the real part of the refractive index mR, the effective radius reff, and the effective variance veff: mR=1.45, reff=0.35μm, veff=0.40 for oblate spheroids with an axial ratio of a/b=1.3; mR=1.50, reff=0.35μm, veff=0.30 for prolate spheroids with a/b=1/1.3; mR=1.52, reff=0.40μm, veff=0.35 for oblate spheroids with a/b=1.5, and mR=1.54, reff=0.90μm, veff=0.30 for prolate spheroids with a/b=1/1.5. These values (especially the real part of the refractive index) differ quite significantly from those retrieved previously for the model of spherical cloud particles and emphasize nonuniqueness of remote-sensing retrievals based on the ground-based data alone.

Vertical ozone distribution characteristics deduced from ∼ 44,000 re-evaluated Umkehr profiles (1957-2000)

Umkehr observations taken during the 1957–2000 period at 15 stations located between 19 and 52° N have been reanalyzed using a significantly improved algorithm-99, developed by DeLuisi and Petropavlovskikh et al. (2000a,b). The alg-99 utilizes new latitudinal and seasonally dependent first guess ozone and temperature profiles, new vector radiative transfer code, complete aerosol corrections, gravimetric corrections, and others. Before reprocessing, all total ozone values as well as the N-values (radiance) readings were thoroughly re-evaluated. For the first time, shifts in the N-values were detected and provisionally corrected. The re-evaluated Umkehr data set was validated against satellite and ground based measurements. The retrievals with alg-99 show much closer agreement with the lidar and SAGE than with the alg-92. Although the latitudinal coverage is limited, this Umkehr data set contains ∼ 44,000 profiles and represent the longest (∼ 40 years) coherent information on the ozone behavior in the stratosphere of the Northern Hemisphere. The 14-months periods following the El-Chichon and the Mt. Pinatubo eruptions were excluded from the analysis. Then the basic climatological characteristics of the vertical ozone distribution in the 44–52° N and more southern locations are described. Some of these characteristics are not well known or impossible to be determined from satellites or single stations. The absolute and relative variability reach their maximum during winter–spring at altitudes below 24 km; the lower stratospheric layers in the middle latitudes contain ∼ 62% of the total ozone and contribute ∼ 57% to its total variability. The layer-5 (between ∼ 24 and 29 km) although containing 20% of the total ozone shows the least fluctuations, no trend and contributes only ∼ 11% to the total ozone variability. Meridional cross-sections from 19 to 52° N of the vertical ozone distribution and its variability illustrate the changes, and show poleward-decreasing altitude of the ozone maximum. The deduced trends above 33 km confirm a strong ozone decline since the mid-1970s of over 5% per decade without significant seasonal differences. In the mid-latitude stations, the decline in the 15–24 km layer is nearly twice as strong in the winter-spring season but much smaller in the summer and fall. The effect of including 1998 and 1999 years with relatively high total ozone data reduces the overall-declining trend. The trends estimated from alg-99 retrievals are statistically not significantly different from those in WMO 1998a; however, they are stronger by about 1% per decade in the lower stratosphere and thus closer to the estimates by sondes. Comparisons of the integrated ozone loss from the Umkehr measurements with the total ozone changes for the same periods at stations with good records show complete concurrence. The altitude and latitude appearances of the long-term geophysical signals like solar (1–2%) and QBO (2–7%) are investigated.