To detect the presence of high, optically thick clouds, we infer the vertically integrated amount of methane from measurements between 2315 and 2324 nm (see Fig. ) using a radiative transfer model that neglects atmospheric scattering. The difference ΔCH4 between the retrieved CH4 column and a priori methane information coming from a chemical transport model indicates light path modification, either shortening or enhancement in comparison with the direct light path from the sun to the spectrometer via reflection at the Earth surface, due to atmospheric scattering by clouds and aerosols. Here the net effect depends on the scattering properties such as scattering height and optical depth, surface reflection and solar and observation geometry e.g.,. If the difference exceeds a certain threshold, observations are rejected. The non-scattering retrieval algorithm uses a standard least squares approach to infer the total column of CH4, CO, H2O and HDO together with a surface albedo As, its linear dependence on wavelength and a spectral offset. It is described in more detail by .

Figure  shows the probability density function (PDF) and its cumulative distribution (CPDF) of the difference ΔCH4 between a non-scattering CH4 retrieval from observations of Greenhouse Gases Observing Satellite (GOSAT, ) at the 1.6 µm band of the year 2010 over land and ocean and collocated CH4 columns from TM5 model simulations after optimization using surface measurements , relative to the model results. The maximum of the ocean and land PDF is at small differences ΔCH4, indicating a large number of scenes that are affected only little by clouds. For about 80 % of all observations, the methane abundance is underestimated by the non-scattering retrieval due to the presence of optically thick clouds. Here, the ocean PDF shows a relatively high probability for ΔCH4 between -20 and -5 % due to the presence of low stratiform clouds over ocean. For land pixels, this type of cloudiness occurs less frequently. Finally, 20 % of all cases show an overestimation of methane by the non-scattering retrieval, indicating an effective pathlength enhancement. Although the effect of light path shorting and enhancement may depend on wavelength, because of the spectral dependence of the surface albedo and the optical properties of the atmosphere, the GOSAT PDF of ΔCH4 provides a first estimate of the corresponding TROPOMI PDF of methane retrievals at 2.3 µm. As a baseline for our data selection, we accept all observations with ΔCH4≤25 %.

The physics-based retrieval of CO requires a forward model F that describes the measurement as a function of the atmospheric state including an appropriate description of atmospheric scattering, y=F(x,b)+ey. Here, vector y has the spectral measurements between 2324 and 2338 nm as its components (see Fig. ), state vector x represents the parameters to be retrieved, b describes parameters other than the state vector that influences the measurement but are not adjusted by the retrieval and ey is the measurement error. The fit window compromises about optimal CO sensitivity, little interference with water vapor and methane absorptions and small forward model errors due to the assumed cloud model. Moreover, the forward model is nonlinear in the state vector x. Therefore, the inversion problem is solved iteratively employing the Gauss–Newton method, where for each iteration step the forward model is linearized by a Taylor expansion around the solution of the previous iteration xo: F(x,b)=F(x0,b)+∂F∂x(x0,b){x-x0}+O((x-x0)2). O(x2) indicates second and higher order contributions of the expansion.

The forward model F simulates the Earth radiance measurement by a spectral convolution of the top-of-model-atmosphere radiance ITOA with the instrument spectral response function: Fi=si⋅ITOA=∫si(λ)ITOA(λ)dλ. Here, si describes the spectral instrument response of spectral pixel i with the assigned wavelength λi, and ITOA(λ) is simulated by a line-by-line radiative transfer model on a fine internal spectral grid. This model requires a solar irradiance spectrum on the internal spectral grid as input, which is inferred from the daily solar measurements of TROPOMI using the deconvolution approach by and .

State-of-the-art radiative transfer models account for multiple scattering in multiple propagation directions (streams) including the polarization of light. For our application, the computational effort of such simulations is far too large, and thus approximation methods are required to accelerate the forward model simulations. For this reason, we ignore atmospheric Rayleigh scattering, which contributes less than 0.15 % to the total signal , and use a numerically efficient two-stream scalar radiative transfer model to describe scattering by clouds and aerosols. The employed two-stream solver (2S-LINTRAN) calculates the amount of singly scattered light, whereas the diffuse radiation is approximated by two propagation directions of the radiance field, one upward and one downward. It is similar to the model by , and the numerical implementation used for the S5P CO column retrieval is described in more detail in Appendix .

In the forward model, clouds and aerosols are represented by a scattering layer with a triangular height profile in optical depth with a center height zscat and a fixed full width at half maximum of 2.5 km. Within the scattering layer we assume a constant single scattering albedo and scattering phase function. In this case, we can optimize the numerical efficiency of the two-stream solver using an aggregated vertical grid. In a first step, we calculate absorption optical depth on a 1 km vertical grid accounting for the pressure and temperature dependence of atmospheric absorption, and subsequently we combine the atmosphere layers above and below the scattering layer to one layer each by integrating the optical depth. This significantly reduces the number of vertical layers in the radiative transfer simulation (typically to less than 10), depending on the number of internal layers that are used to resolve the height profile of the scattering layer. Finally, the optical properties of the scattering layer have to be known a priori and we chose a spectrally constant single-scattering albedo ω=0.9 and an asymmetry parameter of the scattering phase function g=0.7. Moreover, we use a simplified wavelength dependence of the extinction optical thickness of the scattering layer: τ(λ)=τ(λ0)λλ0-α, where the reference wavelength λ0=2331 nm is chosen at the center of our fitting window and α=1.0 is the Ångström parameter. These a priori assumptions on the optical parameters of clouds and aerosols will be justified by the performance analysis in Sect. , which is based on measurement simulations of one TROPOMI orbit for a realistic variation of cloud and aerosol properties.

In spite of the efficiency of the radiative transfer solver, the numerical cost of the forward model has to be reduced further for operational data processing. Therefore, we pre-calculate the molecular absorption cross sections σ of CH4, H2O, HDO and CO as a function of pressure, temperature and for a spectral sampling distance of 5×10-3 cm-1 from spectroscopic databases ( for CO and CH4 respectively, and for water vapor and its isotopologues). From this data set, we derive cross sections by bilinear interpolation of the pressure and temperature for each individual retrieval layer followed by the calculation of effective cross sections σeff per species on a coarser spectral sampling ki by the generalized mean σeff(ki)=∫Ti(k)σm(k)dk∫Ti(k)dkm, with a spectral sampling of 3×10-2 cm-1. Here, k represents wavenumber and Ti(k) is a normalized symmetric triangular weighting function between spectral samplings ki-1 and ki+1 with a peak at ki. For m=1, Eq. () describes the arithmetic mean, which introduces significant forward model errors in the retrieval for the envisaged spectral sampling. We performed retrieval experiments for different values of m, where we achieved most accurate radiance simulations with CO retrieval biases < 1 % under clear sky conditions for m=0.85. Overall, the use of the effective cross sections speeds up the forward model simulations by a factor of 6 compared to line-by-line calculations on the spectral grid of the original spectroscopic database.

The SWIR measurements are sensitive to the total amount of CO along the path of the measured light. For clear sky atmospheres and within the bounds of the measurement error, only the total column of CO can be inferred from the measurement , and no information is obtained about the relative vertical distribution of CO. In the presence of clouds, the measurement loses sensitivity to the amount of CO below the cloud. To properly account for this, a regularized CO profile retrieval is required that accounts for the different sensitivity of the measurement to CO at different altitudes. For this purpose, we employ the Tikhonov regularization technique of first order embedded in the Gauss–Newton iteration scheme. For each iteration step, the least square solution x^ is given by x^=min⁡x||Sy-1/2(F(x)-y)||2+γ2||L1x||2. Here, ||⋅|| describes the Euclidean norm and Sy is the error covariance matrix of the measurement y, where we assume uncorrelated measurement errors. γ is the regularization parameter and L1=-110⋯000-110⋯0⋮⋮⋮⋮⋮⋮00⋯-11000⋯0-11 is the first-difference operator, and so the regularization favors constant solutions and penalizes the “roughness” of x. The state vector x contains the CO profile xCO, which is expressed relative to a reference profile ρref, namely xCO=ρ/ρref. For the operational implementation, TM5 model fields are used to extract an adequate CO reference profile. Besides the relative profile of CO, the state vector includes the water vapor column density for two isotopologues, cH2O and cHDO, the surface albedo As and its linear dependence on wavelength ΔAs, the effective cloud center height zcld and the effective cloud optical depth τcld. Furthermore, a spectral shift Δλ is fitted to account for spectral calibration errors of the measurement. To keep all elements of the state vector dimensionless, in addition, these entries of the state vector are normalized to a reference value. We regularize the solution in Eq. () such that 1 degree of freedom for signal of the retrieved CO profile is inferred from the measurement, bearing in mind that because of the noise the TROPOMI SWIR measurements are only sensitive to the total amount of CO along the path of the observed light through the atmosphere. For Eq. (), this corresponds to a regularization parameter γ→∞.

showed that the solution of this minimization problem is identical to an unregularized least squares approach: x^=min⁡x||Sy-1/2(F(x)-y)||2, where the state vector contains the total CO column instead of the CO profile: c=Cρ=∫ρ(z)dz, with the corresponding altitude integral operator C. All other elements of the state vector remain the same.

The solution of this least-squares problem is x^=Gỹ with ỹ=y-F(x0)+Kx0 and G=KTSy-1K-1KTSy-1.

Two important diagnostic tools can be calculated during the retrieval , the error covariance matrix Sx=GSyGT, which describes the effect of the measurement noise on the retrieved parameters including their correlations, and the column averaging kernel Acol=dc^dρtrue, which indicates the sensitivity of the retrieved column c^ to changes in the atmospheric CO profile. Here, we provide the column averaging kernel for the CO profile given by its partial columns of each model layer. In the linear approximation, the column averaging kernel relates the retrieved CO column to the true CO profile by c^=Acolρtrue+ex, with an error contribution ex. Therefore, generally c^ does not represent an estimate of the true column and the difference enull=(C-Acol)ρtrue is called the null-space error of the inversion. This error can be interpreted as the effect of the chosen reference profile on the retrieved CO column density . If the reference profile to be scaled by the inversion has the correct shape, the null space error vanishes and the retrieved column represents an estimate of the true column.

Referring to Eq. (), we characterize the retrieval accuracy for simulated measurements by the retrieval bias bCO, which is defined as the difference between the retrieved column and Acolρtrue corrected for the retrieval noise gCOey: bCO=c^-Acolρtrue-gCOeyAcolρtrue. Here gCO is the CO row vector of the gain matrix in Eq. (), and ey represents the measurement noise.

The inversion described so far focused on the regularization of the ill-posed retrieval of a CO profile from SWIR measurements. The inversion remains vulnerable to other elements of the state vector to which the measurements are insensitive for certain atmospheric circumstances. For example for a scene overcast by a optically thick cloud, the measurement is insensitive to the surface albedo. On the other hand, for a clear sky observation the adjustment of the surface albedo is required but the measurement is insensitive to the height of a possible cloud layer. Hence for these circumstances, certain eigenvalues of the normal matrix KTSy-1K approach zero, leading to singularities in the inversion. To overcome this, we apply Tikhonov regularization of zeroth order to the relevant elements of the state vector, namely x^=min⁡x||Sy-1/2(F(x)-y)||2+γ2||Wx||2, where W is a diagonal weighting matrix, of which diagonal elements are one for all elements of the state vector related to the scattering layer and the surface albedo, i.e., As, ΔAs, zcld and τcld, and zero otherwise.

The implementation of the SICOR inversion algorithm is based on the minimization problem (Eq. ). It comprises the CO profile scaling approach as a particular regularization of the CO profile retrieval in Eq. (). For the software implementation, we make use of the fact that its solution is identical to the least squares problem (Eq. ), where the atmospheric abundance of CO abundance is adjusted through scaling of a reference profile. Finally to prevent numerical instabilities, we introduce a second regularization in Eq. (), which mainly affects the inversion of cloud and surface parameters, and its effect on the retrieved CO column can be neglected. In this study, we have determined the regularization parameter γ by numerical experiments , which requires verification during the instrument commission phase.

Finally, the nonlinearity of the inversion is accounted by the Gauss–Newton iteration, where the degree of convergence is defined as the difference in the reduced chi-squared χ2 between two consecutive iteration steps, and convergence is achieved when |χn2-χn-12|<ϵ. The threshold value of ϵ can only be determined in a reliable manner using real measurements during the commissioning phase of the S5P mission. In this study, we used ϵ=0.5. For clear sky observations ignoring the retrieval of a scattering layer, the Gauss–Newton scheme shows satisfying convergence properties. However, inferring cloud properties introduces significant nonlinearity issues to the retrieval. Therefore to mitigate the risk of an unstable inversion, we reduce the step sizes of the inversion during the first few iterations as described by .

In summary, the operational S5P CO data product consists of (1) the CO vertically integrated column density c, (2) the standard deviation σ of the CO retrieval noise characterized by the retrieval error covariance matrix Sx and (3) the column averaging kernel Ac.

The forward model of our retrieval introduces errors due to the accuracy of the two-stream model, the neglect of atmospheric Rayleigh scattering and the description of clouds and aerosols by a single triangular scattering layer. To elicit the impact of these approximations, we consider three generic measurement ensembles for a clear sky atmosphere and for a cloudy atmosphere with optically thin clouds and cirrus.

Figure  shows the CO retrieval bias and the corresponding retrieval noise for simulated clear sky measurements including atmospheric Rayleigh scattering with a variable surface albedo and a variable solar zenith angle. Overall, the retrieval bias is small with -0.5 % ≤bCO≤ 0.5 %. The retrieval noise increases from values < 1 % at high sun and for bright surfaces to ≈11 % for low sun (SZA =70∘) and low albedo (As=0.03). This increase is governed by the signal strength and so by the signal-to-noise ratio of the measurement.

To investigate the effect of photon trapping between clouds and the surface, Fig.  depicts the CO bias for a cloud between 4 and 5 km altitude with a small optical depth τscat=2 as a function of surface albedo and cloud coverage. Here, the CO bias reaches 1.5 % with increasing cloud coverage. For a cirrus layer between 9 and 10 km of varying optical depth as function of the surface albedo, the light trapping effect at high surface albedo results in a CO biases bCO≤0.5 %. Similar small biases are found for an elevated dust layer and optically thin clouds (not shown).

Moreover, we investigated the implications of the retrieved cloud parameters being effective cloud parameters. These parameters differ from the truth because of the limited information available from the satellite measurements. Here, the retrieval forward model has to describe clouds in a simplified manner with a few free parameters, and all remaining cloud properties have to be fixed a priori see e.g.,. In our case, the cloud model includes several simplifications, e.g., a horizontally homogenous cloud with the triangular height distribution in optical depth, and a two-stream radiative transfer model to describe the cloud radiative properties. Considering the measured radiometric signal as a mean of a photon ensemble with different light paths through the atmosphere, the retrieval adjusts the cloud parameters and the simulated light paths such that the methane absorption features can be fitted by the forward model. This may include erroneous light paths, of which effects average out in the simulated measurement for the particular height distribution of methane. However for another trace gas with a different vertical profile, such as CO, the relevance of the individual photons for the observed signal may differ, and so the simulated light paths introduce spectral errors in the simulated CO absorption features. Subsequently adjusting the trace gas concentrations in the retrieval, CO biases are introduced for cloudy atmospheres.

Obviously, this retrieval error depends on the particular CO profile and the altitude at which the simulated light path deviates from its truth. Therefore, to characterize this inherent bias of our retrieval approach, we simulate SWIR measurements for a cloudy atmosphere adding CO abundance in a 1 km thick, vertically homogenous layer with varying layer top height zper. Here, the CO enhancement increases the CO total column by 50 %. Figure  shows the CO biases as a function of zper for scenes covered with low clouds at 1–2 km altitude with optical thicknesses of 2 and 5, and a cloud at 4–5 km covering 10 % of the scene with a cloud optical thickness of 2. In each case, the simulated measurement passes the cloud filter of Sect. . We clearly see a positive retrieval bias up to 5 % for enhanced CO concentration at the altitude of the optically thin cloud, whereas a negative bias of 7 % is found for low clouds in combination with a near-surface CO enhancements. The latter error is relevant for burning events localized in the tropospheric boundary layer. Above the cloud, the error sensitivity is only small, indicating that the light path at this altitude range is well described by our simplified radiative transfer model. Furthermore, for the optically thicker clouds the error sensitivity is below 2 %, as expected for a primarily reflecting cloud.

An important element of the CO retrieval approach is the use of methane a priori information to determine effective cloud properties from the SWIR measurements as discussed above. The SICOR retrieval relies on simulated CH4 fields from the TM5 model , which have been used in several studies (e.g., ). Via the inverse modeling technique, the sources and sinks of CH4 in the TM5 model are optimized by minimizing the residual differences between model and measurements from the NOAA-ESRL global monitoring network and deviations from the a priori surface flux distribution . In the following, we refer to these model runs as the TM5-NOAA simulations.

To test the overall accuracy of the model simulations, we compare 1 year of CH4 model fields with collocated GOSAT observations . Here, the GOSAT CH4 product is extensively validated with TCCON ground measurements with an overall root-mean-square (rms) difference of 15 ppb and a station-to-station bias of 3.5 ppb . Within these boundaries, the GOSAT XCH4 retrieval can be used to estimate the model accuracy. To this end, Fig.  shows the difference between GOSAT- and TM5-NOAA-simulated XCH4. Over China, the largest biases of up to 3 % occur because of inconsistencies in the underlying emission scenario in combination with a limited regional coverage of the NOAA-ESRL ground-based measurements. Overall biases are smaller with an rms difference between GOSAT and TM5-NOAA, amounting to 20 ppb and increasing towards southern latitudes. This latitudinal bias in TM5, relative to GOSAT, is also found in other models (see e.g., ) and is currently under further investigation. Comparisons of the modeled CH4 columns with collocated TCCON measurements are largely consistent with these findings with an rms difference between 8 and 22 ppb depending on the TCCON site.

Inherent to this analysis is the assumption that the NOAA-ESRL measurements are available in a timely manner to perform model simulation as input to the retrieval. This timeliness of the simulation needs further consideration. Commonly, inverse-modeling-derived estimates lag behind real time by approximately 1 year. This is mostly due to the availability of various types of inputs that are required, including meteorological fields, a priori emission estimates, and measurements. Due to that, we propose a modeling procedure that uses the inversion-optimized TM5 estimates of the dry air mole column mixing ratio of methane XCH4 of the previous year. Obviously, the largest error source is the variability in XCH4 caused by the year-to-year variations in meteorology and the interannual variability of the methane sources and sinks. We estimate the size of the error from results of a multi-year inversion for the period 2003–2010, calculating how XCH4 on a given day of the year (15 January, April, July and October) varied between the years. Largest variations are found over Southeast Asia, due to large regional sources of methane, but errors in the meteorology of the northern and southern hemispheric storm tracks are also present. On average, the standard deviations are well within 1 % (18 ppb) on average, regionally increasing up to 1.5 % (27 ppb). Sporadically, standard deviations up to 3 % are found, associated with biomass burning events. Acknowledging these limitations in our approach, an uncertainty of 3 % of our methane a priori knowledge seems a reasonable margin that should be achievable for most conditions encountered throughout the global domain.

For the generic clear sky measurement ensembles, Fig.  shows the PDF of the CO biases as a function of the methane model error of approximately ±3 %. A linear regression through the data points indicates a nearly one-to-one error correspondence with 1.11 % CO bias due to 1 % error in the methane model columns. Table  provides the corresponding bias sensitivity for the cloudy and cirrus measurement ensembles in Fig. . Aggregating these results, we conclude that the CO retrieval bias due to the uncertainty of the TM5-NOAA model input typically does not exceed 3 %.

Additionally to the CH4 a priori error, an erroneous surface pressure affects the inferred CO column both through a wrong conversion of the methane mixing ratio XCH4 into the total column density of methane and via an erroneous spectroscopy because of the pressure broadening of individual absorption lines. For the operational retrieval, we use pressure information from the European Centre for Medium-Range Weather Forecasts (ECMWF) with a typical accuracy of 2–3 hPa . Subsequently, ECMWF surface pressure is interpolated on the particular TROPOMI pixel by means of the digital elevation map of and , accounting for the topography of the terrain. For pressure uncertainties in the range ≤3 hPa, we obtain an error sensitivity of 0.11–0.13 % CO column error per 1 hPa surface pressure error for the clear sky and cloudy scenarios of our generic measurement ensemble. Furthermore, we evaluated the impact of uncertainties in the atmospheric temperature forecast of ECMWF, which has been estimated at a few Kelvin. Table  lists the CO retrieval sensitivities with respect to an offset of the atmospheric temperature profile in the range ±3 K, which vary between 0.17 and 0.23 % CO column error per 1 K temperature offset. Thus for the CO column product, we expect the corresponding retrieval biases due to inaccuracies in the atmospheric parameters to be well within 1 %.

Finally, we studied the CO retrieval sensitivity with respect to a set of instrument-related parameters. First, the Earth radiance spectrum may be subject to a radiometric offset Ioffset, expressed relative to the radiance level at the reference wavelength of 2315 nm, or a spectrally constant multiplicative error δIscal. Instrumental reasons for these errors can be manyfold, e.g., uncorrected stray light, detector and read-out electronics performance and an erroneous pre-flight instrument calibration. For the generic ensembles, we derived an error sensitivity of -0.47 to -0.63 % CO column error per percent radiometric offset and 0.01 to 0.02 % per percent multiplicative radiometric error. The corresponding TROPOMI observation requirement for a radiometric offset is < 0.1 %, and for a multiplicative radiometric error on the Earth radiance measurement it is < 2 % . The main reason for this robust CO retrieval performance with respect to this type of radiometric errors is the selected spectral window with relatively weak atmospheric absorption. Here, these spectral biases can be mitigated efficiently by the retrieval of an effective surface albedo and cloud properties.

To study an erroneous spectral calibration of the measurement, we assumed a correct instrument calibration λi of spectral detector i and an erroneous calibration λi′=λi+λi-λmλr-λmδs. Here, λr=2385 nm indicates the longwave edge of the SWIR band and λm=2345 nm is the spectral center. Therefore, δs characterizes the spectral calibration errors at the edges of the SWIR spectral range, whereas in the center λm the calibration error vanishes. The corresponding spectral squeeze for the CO fit windows (2315–2338 nm) is about one-third of δs. The error sensitivity of the CO column product is about 0.9 % per δs=10 pm. Due to the required knowledge of the center of all SWIR channels of <2 pm , this CO error sensitivity is not critical for a compliant instrument. Moreover, the CO retrieval has no error sensitivity to an overall offset of the spectral calibration because this parameter is adjusted by the retrieval.

Errors in the instrument spectral response function can be manyfold and are hard to quantify in a general manner. In this study, we restricted ourself to an erroneous full width at half maximum (FWHM) of the instrument spectral response function (ISRF), which may occur e.g., because of pre-flight instrument calibration errors or because of fluctuations of the instrument temperature. Table  shows the ISRF retrieval sensitivity of about 0.5 % CO error for a 1 % FWHM uncertainty of the ISRF, the latter representing the knowledge requirement for the TROPOMI instrument calibration .

Finally, we discuss the CO column error contribution originating from radiometric artifacts due to the heterogeneous illumination of the instrument entrance slit, which in turn arises from varying cloud coverage and surface reflection within a spatial sample. As discussed by and and in Appendix , this results in a distortion of the spectral response of the TROPOMI instrument. Accounting for this effect in the retrieval requires, next to detailed characterization of the instrument, a priori knowledge of the radiance heterogeneity across the instrument slit, which is not available. For future instrument development, e.g., for the succeeding Sentinel 5 mission of ESA, this instrumental effect is foreseen to be mitigated by a slit homogenizer . This is an optical device scrambling the spatial information of the incoming signal in the flight direction, and so the spectrometer is effectively exposed to a spatially homogeneous entrance signal. Because the TROPOMI instrument is not equipped with such a device, it is important to quantify potential errors on the CO data product.

For this purpose, we considered two spatial ensembles of simulated measurements. First, we investigated a MODIS Aqua cloud image over Australia, shown in Fig. , characterizing clouds by a cloud mask on a 1×1 km2 spatial grid box. For each of the samples at a spatial position (x,y), we calculated a spectral radiance field I(x,y,λ) assuming a ground albedo As=0.1 and, depending on the cloud mask, a vertically homogenous cloud between 2 and 3 km with an optical depth of τscat=20. Next, we simulated the TROPOMI observations with the instrument model in Appendix . Subsequent retrievals allow us to quantify the CO bias due to the distortion of the instrument response for the ensemble. Results of this test (right panel of Fig. ) show with a characteristic CO bias pattern at cloud edges ranging from up to +2 %, where the cloud edge enters the instrument field of view, to minimum -2 % when the field of view points mainly at clouds and the scene heterogeneity is due to a remaining contribution of clear sky radiances. Although this error contribution is significant, it has quasi-random characteristics when looking at larger spatial or temporal domains because of the quasi-random occurrence of clouds on these scales. Additionally, we investigated a measurement ensemble for spatially varying surface albedo of a 50×50 km2 wetland region in Siberia. The albedo distribution is adapted from MODIS Aqua observation at 2.1 µm with a spatial sampling of 500×500m2, with a mean albedo of 0.037 and a standard deviation of 0.017 (see Fig. ). The patchy structure of the figure is due to dark ponds of the marsh. Figure  also shows a CO bias of about ±1.5 % related to the scene heterogeneity. The mean error of the ensemble reduces to 0.05 % with a standard deviation of 0.44 %, supporting the quasi-random characteristics of this error.