Degrees Of Freedom For Signal Research Articles

Atmospheric Temperature Measurements Using Microwave Hyper-Spectrum from Geostationary Satellite: Band Design, Weighting Functions and Information Content

A passive microwave instrument will be carried by China’s geostationary microwave satellite. A microwave hyper-spectral band included by the instrument ranges from 52.6 to 57.3 GHz, and totally has 89 channels in this spectral domain. The design of the hyper-spectral band is described from the aspects of scientific objectives and specifications. The weighting functions for each channel are calculated utilizing radiative transfer simulations under clear sky conditions. Then, the information content as well as the degree of freedom for signal are computed and analyzed to characterize this hyper-spectral sounding for atmospheric temperature profiling. Both the vertical distribution of the weighting functions and the width of retrieval averaging kernels indicate that the hyper-spectral band can provide more denser sampling for atmospheric temperature. The information content for the hyper-spectral band is approximately 46% higher than that of the ATMS-type channel 3 to 15, indicating that hyper-spectral measurement can improve the accuracy of retrieval. The most informative channels mainly locate near 57 GHz, having good consistency with the existing channels. The height range where the retrieval using the hyper-spectral observations is sensitive to the true profile, begins from about 800 to 1 hPa. Some channels can be considered as alternatives to each other since they have very similar information content and weighting functions. These results are expected to provide a valuable reference for future applications of the microwave hyper-spectral measurements.

Comparative Study of the Atmospheric Gas Composition Detection Capabilities of FY-3D/HIRAS-I and FY-3E/HIRAS-II Based on Information Capacity

Fengyun-3E (FY-3E)/Hyperspectral Infrared Atmospheric Sounder-II (HIRAS-II) is an extension Fengyun-3D (FY-3D)/HIRAS-I. It is crucial to fully explore and analyze the detection capabilities of these two instruments for atmospheric gas composition. Based on the observed spectral data from the infrared hyperspectral detection instruments FY-3D/HIRAS-I and FY-3E/HIRAS-II, simulated radiance data and Jacobian matrices are obtained using the Rapid Radiative Transfer Model RTTOV (Radiative Transfer for TOVS (TIROS Operational Vertical Sounder)). By perturbing temperature (T), surface temperature (Tsurf), water vapor (H2O), ozone (O3), carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and nitrous oxide (N2O), the brightness temperature differences before and after the perturbations are calculated to analyze the sensitivity of temperature and various atmospheric gas components. The Improved Optimal Sensitivity Profile (OSP) algorithm is used to select the channels for atmospheric gas retrieval. The observation error covariance and background error covariance matrices are calculated, and then the information capacity is calculated, specifically the degrees of freedom for signal(DFS) and the entropy reduction (ER). Based on this, a comparative analysis is conducted on the information capacity of atmospheric water vapor and ozone components contained in the hyperspectral detection data from HIRAS-I and HIRAS-II instruments, respectively, to explore the retrieval capabilities of the two instruments for atmospheric gas components. We selected clear-sky data from the African oceanic region and the Chinese Yangtze River Delta terrestrial region for quantitative analysis of the information capacity of HIRAS-I and HIRAS-II. The results show that FY-3D/HIRAS-I and FY-3E/HIRAS-II exhibit different sensitivities to atmospheric gas components. In different experimental regions, temperature and water vapor show the most dramatic sensitivity changes, followed by ozone, methane, and nitrous oxide, while carbon monoxide and carbon dioxide exhibit the lowest variability. Regarding channel selection, HIRAS-II identifies more gas channels compared to HIRAS-I. The experiments concluded that HIRAS-II has a significantly higher information capacity than HIRAS-I, and the information capacity of atmospheric gas components varies across different experimental regions. Water vapor and ozone exhibit the highest information capacity, followed by nitrous oxide and methane, while carbon monoxide and carbon dioxide demonstrate the lowest capacity. The H2O ER (DFS) contained in FY-3E/HIRAS-II is 1.51 (0.35) higher than that in FY-3D/HIRAS-I, the O3 ER (DFS) in FY-3E/HIRAS-II is 1.51 (0.36) higher than that in FY-3D/HIRAS-I, while the N2O ER (DFS) in FY-3E/HIRAS-II is 0.17 (0.19) higher and the CH4 ER (DFS) is 0.07 (0.04) higher than that in FY-3D/HIRAS-I.

Optimal estimation retrieval of tropospheric ammonia from the Geostationary Interferometric Infrared Sounder on board FengYun-4B

Abstract. Atmospheric ammonia (NH3) is a reactive nitrogen compound that pollutes our environment and threatens public health. Monitoring the spatial and temporal variations is important for quantifying its emissions and depositions and evaluating the strategies for managing anthropogenic sources of NH3. In this study, we present an NH3 retrieval algorithm based on the optimal estimation method for the Geostationary Interferometric Infrared Sounder (GIIRS) on board China's FengYun-4B satellite (FY-4B/GIIRS). In particular, we examine the information content based on the degree of freedom for signal (DOFS) in retrieving the diurnal NH3 in East Asia, with a focus on two source regions including the North China Plain and North India. Our retrieval is based on the FengYun Geostationary satellite Atmospheric Infrared Retrieval (FY-GeoAIR) algorithm and exploits the strong NH3 absorption window of 955–975 cm−1. Retrieval results using FY-4B/GIIRS spectra from July to December 2022 show that the DOFS for the majority ranges from 0 to 1.0, mainly depending on the thermal contrast (TC) defined as the temperature difference between the surface and the lowest atmospheric layer. Consistent with retrievals from low-Earth-orbit (LEO) infrared sounders, the detection sensitivity, as quantified by the averaging kernel (AK) matrix, peaks in the lowest 2 km atmospheric layers. The DOFS and TC are highly correlated, resulting in a typical “butterfly” shape. That is, the DOFS increases when TC becomes either more positive or more negative. The NH3 columns from FY-4B/GIIRS exhibit significant diurnal cycles that are consistent with the day–night gradient from the collocated IASI retrievals in the North China Plain and North India for the averages in July–August, September–October, and November–December, respectively. A collocated point-by-point intercomparison with the IASI NH3 dataset shows generally good agreement with a small systematic difference in the summer months that may be attributed to the slight difference in a priori profiles. This study demonstrates the capability of FY-4B/GIIRS in capturing the diurnal NH3 changes in East Asia, which will have the potential to improve regional and global air quality and climate research.

Diurnal carbon monoxide observed from a geostationary infrared hyperspectral sounder: first result from GIIRS on board FengYun-4B

Abstract. The Geostationary Interferometric Infrared Sounder (GIIRS) on board FengYun-4 series satellites is the world's first geostationary hyperspectral infrared sounder. With hyperspectral measurement collected from a geostationary orbit covering the carbon monoxide (CO) absorption window around 2150 cm−1, GIIRS provides a unique opportunity for monitoring the diurnal variabilities of atmospheric CO over eastern Asia. In this study, we develop the FengYun Geostationary satellite Atmospheric Infrared Retrieval (FY-GeoAIR) algorithm to retrieve the CO profiles using observations from GIIRS on board FY-4B, which was launched in June 2021, and provide CO maps at a spatial resolution of 12 km and a temporal resolution of 2 h. The performance of the algorithm is first evaluated by conducting retrieval experiments using simulated synthetic spectra. The result shows that the GIIRS data provide significant information for constraining CO profiles. The degree of freedom for signal (DOFS) and retrieval error are both highly correlated with thermal contrast (TC), the temperature difference between the surface and the lower atmosphere. Retrieval results from 1 month of GIIRS spectra in July 2022 show that the DOFS for the majority is between 0.8 and 1.5 for the CO total column and between 0 and 0.8 for the bottom three layers ranging from the surface to 3 km a.s.l. Consistent with CO retrievals from low-Earth-orbit (LEO) infrared sounders, the largest observation sensitivity, as quantified by the averaging kernel (AK), is in the free troposphere at around 3–6 km. The diurnal changes in DOFS and vertical sensitivity of observation are primarily driven by the diurnal TC variabilities. Finally, we compare the CO total columns between GIIRS and Infrared Atmospheric Sounding Interferometer (IASI) and find that the two datasets show good consistency in capturing the spatial and temporal variabilities. This study demonstrates that the GIIRS retrievals are able to reproduce the temporal variability of CO total columns over eastern Asia in the daytime in July. Nevertheless, the retrievals have low detectivity in the nighttime due to their weak sensitivity to the ground level CO changes limited by low information content. Model assimilation that takes into account the retrieved diurnal CO profiles and the associated vertical sensitivity will have potential in improving local and global air quality and climate research over eastern Asia.

Simulated Clear-Sky Water Vapor and Temperature Retrievals from PREFIRE Measurements

Abstract The Polar Radiant Energy in the Far Infrared Experiment (PREFIRE) mission will measure Earth’s emission at wavelengths ranging from 3 to 54 μm. The prelaunch clear-sky retrieval algorithm, evaluated with simulated test data, indicates that PREFIRE measurements will be valuable for retrieving atmospheric water vapor and temperature profiles. Far infrared measurements provide unique retrieval information, indicated by the high ranking of select FIR channels as primary contributors to the total degrees of freedom for signal (DFS). In utilizing all the PREFIRE channels, the average total DFS of 4 test regions ranges from 1.90 to 4.71. The information content increases with higher column water vapor and in the presence of near-surface temperature inversions. Using the DFS profiles for guidance, the retrieval concentrates information into 7 distinct layers to reduce the retrieval uncertainty per layer. Sensitivity tests indicate forward model error due to surface emissivity uncertainty results in about a 9% increase in column water vapor uncertainty. The clear-sky retrieval is sensitive to the presence of undetected ice clouds, especially those with optical depths larger than 0.2. Hence, in addition to a separate PREFIRE cloud mask, optimal estimation retrieval metrics are explored as possible indicators of cloudy scenes.

Satellite Aerosol Retrieval From Multiangle Polarimetric Measurements: Information Content and Uncertainty Analysis

The multi-angle polarimetric (MAP) instruments have been a focus of recent satellite missions dedicated to enhanced detection of global aerosol microphysical properties. Considering that satellite observations can hardly infer all the unknowns of atmosphere and surface, it’s crucial to know how many and which aerosol parameters can be accurately retrieved from these different MAP measurements as well as their uncertainties. In this study, we present a comprehensive insight into the information content of POLDER-3 and 3MI observations for aerosol retrievals and estimate posterior errors of corresponding parameters based on Bayesian theory. The total degree of freedom for signal (DFS) of aerosol retrievals is around 6-8 from POLDER-3, and is raised by ~1.8-3.5 with 3MI. The retrieval accuracy of volume concentration and effective radius are high (<4%) in the fine-dominant case for both POLDER-3 and 3MI, but get much lower (~8% and ~15%) in coarse-dominant conditions. Furthermore, the advanced 3MI measurements can upgrade the retrieval uncertainties of POLDER-3 by ~50%. Though additional shortwave infrared bands of 3MI provide more information regarding coarse particles, the influence of aerosols on surface BRDF leads to a decrease of the total DFS. With a prior assumption that variations of refractive index depending on wavelength, satellite retrieval accuracy of the real (<0.03) and imaginary part (<0.003) reaches close levels with that of ground-based Sun photometers. Our results can provide a fundamental reference for MAP satellite retrieval of aerosol microphysical properties.

A Comprehensive Analysis of Ultraviolet Remote Sensing for Aerosol Layer Height Retrieval from Multi-Angle Polarization Satellite Measurements

Based on the optimal estimation (OE) theory and information content analysis method, we discuss the ability to include the multi-angle satellite ultraviolet polarization channel to retrieve the aerosol layer height (ALH) for ten typical aerosol types in the China region. We also quantitatively evaluate the effects of polarization measurements and the number of viewing angles on ALH retrieval under different conditions (aerosol model, aerosol optical depth, etc.). By comparing the different degree of freedom for signal (DFS) results of ALH caused by the theoretical retrieval error changes in different microphysical parameters in the aerosol and surface model, we identify the key factors affecting ALH retrieval. The results show that the extended ultraviolet band provides important information for ALH retrieval and is closely related to the scattering and absorption characteristics of aerosol models. The polarization measurements in fine mode reduce the posterior error of ALH retrieval by 6–39%; however, this is relatively small for coarse mode. In particular, when it is applied to the transported dust and background dust aerosol types, the posterior error is only reduced by 1–8% after adding polarization measurements. For these two aerosol types with weak absorption at the ultraviolet band, increasing the number of angles observed in addition to increasing the polarization channel will more effectively improve ALH inversion. Compared with other aerosol and surface model parameters, the retrieval errors for the total volume column, effective variance, real part of the complex refractive index, and surface reflectance are the main factors affecting ALH retrieval. Therefore, reducing the theoretical retrieval error of these parameters will be helpful.

Information content and aerosol property retrieval potential for different types of in situ polar nephelometer data

Abstract. Polar nephelometers are in situ instruments used to measure the angular distribution of light scattered by aerosol particles. These types of measurements contain substantial information about the properties of the aerosol being probed (e.g. concentrations, sizes, refractive indices, shape parameters), which can be retrieved through inversion algorithms. The aerosol property retrieval potential (i.e. information content) of a given set of measurements depends on the spectral, polarimetric, and angular characteristics of the polar nephelometer that was used to acquire the measurements. To explore this issue quantitatively, we applied Bayesian information content analysis and calculated the metric degrees of freedom for signal (DOFS) for a range of simulated polar nephelometer instrument configurations, aerosol models and test cases, and assumed levels of prior knowledge about the variances of specific aerosol properties. Assuming a low level of prior knowledge consistent with an unconstrained ambient/field measurement setting, we demonstrate that even very basic polar nephelometers (single wavelength, no polarization capability) will provide informative measurements with a very high retrieval potential for the size distribution and refractive index state parameters describing simple unimodal, spherical test aerosols. As expected, assuming a higher level of prior knowledge consistent with well-constrained laboratory applications leads to a reduction in potential for information gain via performing the polarimetric measurement. Nevertheless, we show that in this situation polar nephelometers can still provide informative measurements: e.g. it can be possible to retrieve the imaginary part of the refractive index with high accuracy if the laboratory setting makes it possible to keep the probed aerosol sample simple. The analysis based on a high level of prior knowledge also allows us to better assess the impact of different polar nephelometer instrument design features in a consistent manner for retrieved aerosol parameters. The results indicate that the addition of multi-wavelength and/or polarimetric measurement capabilities always leads to an increase in information content, although in some cases the increase is negligible, e.g. when adding a fourth, near-IR measurement wavelength for the retrieval of unimodal size distribution parameters or if the added polarization component has high measurement uncertainty. By considering a more complex bimodal, non-spherical-aerosol model, we demonstrate that performing more comprehensive spectral and/or polarimetric measurements leads to very large benefits in terms of the achieved information content. We also investigated the impact of angular truncation (i.e. the loss of measurement information at certain scattering angles) on information content. Truncation at extreme angles (i.e. in the near-forward or near-backward directions) results in substantial decreases in information content for coarse-aerosol test cases. However for fine-aerosol test cases, the sensitivity of DOFS to extreme-angle truncation is noticeably smaller and can be further reduced by performing more comprehensive measurements. Side angle truncation has very little effect on information content for both the fine and coarse test cases. Furthermore, we demonstrate that increasing the number of angular measurements generally increases the information content. However, above a certain number of angular measurements (∼20–40) the observed increases in DOFS plateau out. Finally, we demonstrate that the specific placement of angular measurements within a nephelometer can have a large impact on information content. As a proof of concept, we show that a reductive greedy algorithm based on the DOFS metric can be used to find optimal angular configurations for given target aerosols and applications.

Operational assimilation of Aeolus winds in the Météo‐France global NWP model ARPEGE

AbstractThe European Space Agency's Aeolus satellite was launched in August 2018. Measurements of wind profiles are provided for the first time from space using an onboard Doppler wind lidar. The quality of Aeolus Level‐2B (L2B) wind products has been found suitable for data assimilation in the Météo‐France global model ARPEGE since April 2020, in particular, when applying a suitable bias correction method. This article describes a series of Observing System Experiments (OSEs) conducted in April–May 2020 to assess the impact of Aeolus horizontal line‐of‐sight winds (HLOSW) on Météo‐France's global numerical weather prediction analyses and forecasts. Innovation statistics and a posteriori diagnostics from a period of July–August 2019 were used to scale the random observation errors provided by the L2B processor (mostly for Rayleigh‐clear winds). Although the HLOSW data represent only 0.42% of the total amount of all observations assimilated in ARPEGE, their contribution to the reduction of the global analysis variance is up to 2.3% (measured by the Degree of Freedom for Signal). The assimilation of HLOSW showed improvement in 6 hr short‐range forecasts which is demonstrated by an overall reduction of innovations statistics for various operational observing systems. From a Forecast Sensitivity to Observations impact (FSOi) study Aeolus is found to be the third most effective observing system (per individual observation) at reducing global 24‐hour forecast errors. For longer forecast ranges, the largest positive impacts are noticed over the tropics, particularly in the lower stratosphere up to 102 hr ahead (with up to 2% root‐mean‐square error reduction for wind and temperature), but also in the troposphere up to 72 hr ahead. To a lesser extent, a similar improvement is observed over the Southern Hemisphere. This positive impact of Aeolus HLOSW in OSEs has led to their operational assimilation at Météo‐France starting in June 2020.

An Optimal Linear Transformation for Data Assimilation

AbstractLinear transformations are widely used in data assimilation for covariance modeling, for reducing dimensionality (such as averaging dense observations to form “superobs”), and for managing sampling error in ensemble data assimilation. Here we describe a linear transformation that is optimal in the sense that, in the transformed space, the state variables and observations have uncorrelated errors, and a diagonal gain matrix in the update step. We conjecture, and provide numerical evidence, that the transformation is the best possible to precede covariance localization in an ensemble Kalman filter. A central feature of this transformation in the update step are scalars, which we term canonical observation operators (COOs), that relate pairs of transformed observations and state variables and rank‐order those pairs by their influence in the update. We show for an idealized problem that sample‐based estimates of the COOs, in conjunction with covariance localization for the sample covariance, can approximate well the true values, but a practical implementation of the transformation for high‐dimensional applications remains a subject for future research. The COOs also completely describe important properties of the update step, such as observation‐state mutual information, signal‐to‐noise and degrees of freedom for signal, and so give new insights, including relations among reduced‐rank approximations to variational schemes, particle‐filter weight degeneracy, and the local ensemble transform Kalman filter.

Retrieval of Tropospheric Water Vapor From Airborne Far‐Infrared Measurements: A Case Study

AbstractWe describe studies undertaken in support of the Far‐infrared Outgoing Radiation Understanding and Monitoring mission, European Space Agency's ninth Earth Explorer, designed to investigate whether airborne observations of far‐infrared radiances can provide beneficial information on mid and upper tropospheric water vapor concentrations. Initially we perform a joint temperature and water vapor retrieval and show that the water vapor retrieval exploiting far‐infrared measurements from the Tropospheric Airborne Fourier Transform Spectrometer (TAFTS) shows improvement over the a‐priori Unified Model global forecast when compared to in situ dropsonde measurements. For this case the improvement is particularly noticeable in the mid‐upper troposphere. Equivalent retrievals using mid‐infrared radiances measured by the Airborne Research Interferometer Evaluation System (ARIES) show much reduced performance, with the degrees of freedom for signal (DFS), reduced by a factor of almost 2. Further sensitivity studies show that this advantage is decreased, but still present when the spectral resolution of the TAFTS measurements is reduced to match that of ARIES. The beneficial role of the far infrared for this case is further confirmed by performing water vapor only retrievals using ARIES and TAFTS individually, and then in combination. We find that the combined retrieval has a DFS value of 6.7 for water vapor, marginally larger than that obtained for the TAFTS retrieval and almost twice as large as that obtained for ARIES. These results provide observational support of theoretical studies highlighting the potential improvement that far‐infrared observations could bring for the retrieval of tropospheric water vapor.

Enhancing MAX-DOAS atmospheric state retrievals by multispectral polarimetry – studies using synthetic data

Abstract. Ground-based multi-axis differential optical absorption spectroscopy (MAX-DOAS) is a widely used measurement technique for the remote detection of atmospheric aerosol and trace gases. The technique relies on the analysis of ultra-violet and visible radiation spectra of scattered sunlight (skylight) to obtain information on different atmospheric parameters. From an appropriate set of spectra recorded under different viewing directions (typically a group of observations at different elevation angles) the retrieval of aerosol and trace gas vertical distributions is achieved through numerical inversion methods. It is well known that the polarisation state of skylight is particularly sensitive to atmospheric aerosol content as well as aerosol properties and that polarimetric measurements could therefore provide additional information for MAX-DOAS profile retrievals; however, such measurements have not yet been used for this purpose. To address this issue, we have developed the RAPSODI (Retrieval of Atmospheric Parameters from Spectroscopic Observations using DOAS Instruments) algorithm. In contrast to existing MAX-DOAS algorithms, it can process polarimetric information, and it can retrieve simultaneously profiles of aerosols and various trace gases at multiple wavelengths in a single retrieval step; a further advantage is that it contains a Mie scattering model, allowing for the retrieval of aerosol microphysical properties. The forward-model component in RAPSODI is based on a linearised vector radiative transfer model with Jacobian facilities, and we have used this model to create a database of synthetic measurements in order to carry out sensitivity analyses aimed at assessing the potential of polarimetric MAX-DOAS observations. We find that multispectral polarimetry significantly enhances the sensitivity, particularly to aerosol-related quantities. Assuming typical viewing geometries, the degrees of freedom for signal (DOFS) increase by about 50 % and 70 % for aerosol vertical distributions and aerosol properties, respectively, and by approximately 10 % for trace gas vertical profiles. For an idealised scenario with a horizontally homogeneous atmosphere, our findings predict an improvement in the inversion results' accuracy (root-mean-square deviations to the true values) of about 60 % for aerosol vertical column densities (VCDs) as well as for aerosol surface concentrations and by 40 % for aerosol properties. For trace gas VCDs, very little improvement is apparent, although the accuracy of trace gas surface concentrations improves by about 50 %.

Temperature and Moisture Sounding Performance of Current and Prospective Microwave Instruments under All-Sky Conditions

We provide consistent theoretical and empirical assessments of the major driving factors of the information content and retrieval performance for current and potential future microwave (MW) sounders. For the specific instrument concepts assessed, we find that instrument noise is a major driver, impacting vertical resolution as measured by the degrees of freedom for signal as much as 50%. We also observe diminished performance in the 118 GHz temperature sounding band as compared to the 50–60 GHz band, which is largely due to the increased sensor noise in the assessed 118 GHz sensor for comparable channels—a reduction in the performance gap between 118 GHz and 50 GHz bands can be obtained with a reduction of instrument noise in the 118 GHz temperature sounding channels. As expected, scene-type also significantly impacts the vertical resolution, emphasizing the importance of separating clear, cloudy, rainy, and icy conditions when evaluating instrument performance.

Improving flood forecasting using conditional bias-aware assimilation of streamflow observations and dynamic assessment of flow-dependent information content

We describe an adaptive extension of the conditional bias-penalized ensemble Kalman filter for conditional bias (CB)-aware data assimilation (DA) and comparatively evaluate with the ensemble Kalman filter (EnKF) for 6 headwater basins in Texas using the operational lumped hydrologic models from the National Weather Service. We then use CB-aware DA and the degrees of freedom for signal to assess the marginal information content of observations. We show that CB arises very frequently in varying magnitudes when assimilating streamflow observations during the catchment’s response to precipitation and subsequent drainage, and that, in general, larger discharges are associated with larger CB. CB-aware DA improves over EnKF by varying margins in times of significant flow, and the improvement is particularly large during sharp rises of the outlet hydrograph with large peak flows. For the 6 study basins, the average relative reduction in root mean square error of the ensemble mean streamflow analysis by CB-aware DA over EnKF is 31.5% for all ranges of observed flow and 32.1% for observed flow exceeding 200 cms. The flow-dependent marginal information content of the observations varies very significantly with the streamflow response of the catchment and the magnitude of CB, and tends to decrease and increase in the rising and falling phases of the hydrograph, respectively. The findings indicate that CB-aware DA with information content analysis offers an objective framework for dynamically balancing the predictive skill of hydrologic models, quality and frequency of hydrologic observation, and scheduling of DA cycles toward improving operational flood forecasting cost-effectively.

Ground-based high-resolution remote sensing of sulphur hexafluoride (SF6) over Hefei, China: characterization, optical misalignment, influence, and variability.

It is a challenge to retrieve atmospheric sulphur hexafluoride (SF6) with high resolution solar spectra because it has only one single retrieval micro window and has interfered with many factors in the retrieval. Optical misalignment is one of the key factors that affect the accuracy of SF6 retrieval. In this study, we first present a long term time series of the SF6 total column over Hefei, China, between January 2017 and December 2020, retrieved by mid-infrared (MIR) solar spectra recorded by ground-based high-resolution Fourier transform infrared spectroscopy (FTIR). The sensitivities of the total column, root mean square of fitting residual (RMS), total error budgets, degrees of freedom for signal (DOFs), and vertical mixing ratio (VMR) profile with respect to different levels of optical misalignment for SF6 retrieval were assessed. The SF6 total column is sensitive to optical misalignment. In order to avoid inconsistencies in the total column due to optical misalignment, we use the true instrumental line shape (ILS) derived from regular low-pressure HBr cell measurements to retrieve the time series of SF6. The total column of SF6 over Hefei presents strong seasonal dependent features. The maximum monthly average value of (3.57 ± 0.21) × 1014 molecules*cm-2 in summer is (7.60 ± 3.50) × 1013 molecules*cm-2 (21.29 ± 9.80) % higher than the minimum monthly average value of (2.81 ± 0.14) × 1014 molecules*cm-2 in winter. The annual average SF6 total columns in 2017-2020 are (3.02 ± 0.17), (3.50 ± 0.18), (3.25 ± 0.18), and (3.08 ± 0.16) × 1014 molecules*cm-2, respectively, which are close to each other. It indicates that SF6 total column over Hefei is stable in the past four years. Our study can improve the current understanding for ground-based high-resolution remote sensing of SF6 and also contribute to generate new reliable remote sensing data in this sparsely monitored region for investigations of climate change, global warming, and air pollution.

Can multi-angular polarimetric measurements in the oxygen-A and B bands improve the retrieval of aerosol vertical distribution?

Based on the multi-angle measurements at the top of the atmosphere including radiance and polarization in O2 A and B absorption bands simulated by forward model UNL-VRTM, the information content and posterior uncertainties about the altitude of peak aerosol extinction (Hpeak) and half-width (w) characterizing quasi-Gaussian aerosol vertical profiles are analyzed for different observation combinations. Although the information content described as degree of freedom for signal (DFS) for Hpeak and w increases with the number of angles, this increase reaches a limit when more than around six angles are used, regardless of surface type (ocean, vegetation or soil). Due to high surface reflectance of vegetation in O2 A band, the DFS of Hpeak from multi-angle measurements could be lower than 0.8, whereas the DFS > 0.9 for soil and ocean. At a single angle, polarization measurement is more sensitive to Hpeak than radiance when Hpeak is near the surface. Compared with single-angle radiance in O2 A band, adding multi-angle radiances reduces retrieval uncertainty for Hpeak by 10–20%, larger than that from only adding polarization at a single angle (< 10%), especially over vegetation. Over vegetated surface, the multi-angle radiances in O2 A and B band have comparable information, whereas for single angle, O2 B band has richer information than O2 A, especially for lower Hpeak. Multi-angle radiances and polarization in the O2 A band as well as radiances in O2 B band reduce the posterior uncertainty of w more than Hpeak, especially at large AOD, while the polarized measurements in O2 B band are more useful for Hpeak retrieval. The most significant impact of O2 B band radiances is to mitigate aerosol height retrieval uncertainties due to uncertainties in the surface parameters, whereas polarized measurements reduce errors from all error sources including measurements and forward model parameters.

Why does EnKF suffer from analysis overconfidence? An insight into exploiting the ever‐increasing volume of observations

AbstractEnsemble Kalman filters (EnKF) are empirically known to suffer from insufficient posterior spread and this issue is aggravated when assimilating a large volume of observations. This problem, commonly called analysis underdispersion or analysis overconfidence, has been well recognized, but why it occurs seems to be rather poorly understood. Inspired by the theory of the degrees of freedom for signal, this article investigates this problem by analyzing the trace of the matrix HK, where H and K represent, respectively, the observation operator and the gain matrix. A simple mathematical argument shows that tr HK for EnKF is bounded from above by the ensemble size, which entails that assimilating many more observations than the ensemble size leads automatically to tr HK underestimation, as long as the observations are of accuracy comparable to the background. Since tr HK can be interpreted as the squared spread of the posterior ensemble measured in the normalized observation space, underestimated tr HK implies overconfidence in the analysis spread, which, in a cycled context, requires covariance inflation to be applied. The theory is then extended to cases where covariance localization schemes (either B‐localization or R‐localization) are applied to show how they alleviate the analysis underdispersion. These findings from the mathematical argument are demonstrated with a simple one‐dimensional covariance model. Finally, the findings described above are used to form speculative arguments about how to interpret several puzzling features of the local ensemble transform Kalman filter (LETKF) previously reported in the literature, such as why using fewer observations can lead to better performance, when optimal localization scales tend to occur, and why covariance inflation methods based on the relaxation to prior information approach are particularly successful when observations are distributed inhomogeneously.

Aerosol profiling using radiometric and polarimetric spectral measurements in the O2 near infrared bands: Estimation of information content and measurement uncertainties

Characterization of aerosol vertical distribution in the planetary boundary layer (PBL) using passive remote sensing requires advances in the current state of the art. To quantify the performance of various passive sensor designs within a common framework we developed an aerosol climatology of the Los Angeles basin and applied observing system simulation experiments (OSSEs) to estimate the information content retrievable from a variety of sensors measuring reflected near-infrared solar radiation. In addition to simulating current and planned satellite sensors, we also characterize the sensitivity of the California Laboratory for Atmospheric Remote Sensing – Fourier Transform Spectrometer (CLARS-FTS), located at Mt. Wilson (1.67 km above sea level), which is utilized in this work as a testbed for aerosol profiling remote sensing. We estimate the impacts of spectral coverage, radiance and polarization, spectral resolution, signal to noise ratio (SNR), and number of viewing angles on the information content and retrieval uncertainties of aerosol profiles in the PBL. We found that by adding high spectral resolution (full-width half-maximum of 3 cm−1 or better), polarimetric measurements with a SNR of at least 212 to radiance measurements with SNR of 300 for both O2 A and 1∆ bands, the degrees of freedom for signal (DOFS) of a single CLARS-FTS measurement is raised from 2.1 to 2.8. This improvement is sufficient to simultaneously quantify three key parameters: aerosol optical depth, aerosol peak height, and aerosol layer thickness in the PBL. Current satellite-borne instruments (OCO-2, OCO-3, TEMPO, TROPOMI, and EPIC) and planned instruments (TEMPO, MicroCarb, SPEXone, and MAIA), individually provide a DOFS ≤ 2.25, which is insufficient to simultaneously quantify all three aerosol profiling parameters in the PBL. Joint radiometric and polarimetric measurements of the O2 A and B bands with 3 cm−1 spectral resolution, SNR of 500 for radiance and 353 for polarization, acquired at three viewing angles, can provide sufficient sensitivity to retrieve the three aerosol parameters simultaneously. The inclusion of high spectral resolution radiometric and polarimetric measurements reduces the required number of viewing angles, which is advantageous when the multiangular data are acquired with a pointable instrument. In this case a larger number of viewing angles reduces the spatial coverage that can be achieved for a given target.

Precipitation retrieval by the L1‐norm regularization: Typhoon Hagibis case

AbstractThis study examines precipitation retrieval by the L1‐norm regularization using the infrared brightness temperatures from the Himawari‐8/Advanced Himawari Imager (AHI) of the typhoon Hagibis and analyses the advantages of high temporal resolution data. The AHI data covering the entire life cycle of typhoon Hagibis are implemented and we label “precipitation” and “non‐precipitation” fields‐of‐view (FOVs) based on the variation of brightness temperature gradient in AHI channels 8–16. In the precipitation FOVs, we implement the L1‐norm regularization where contribution rate of the “input variable” in the objective functional is obtained by approximating the degree of freedom for signal. The proposed approach is an effective method to obtain sparse solutions, which can express most or all atomic information by a small amount of atomic information. Several experiments reveal that the retrieved precipitation of typhoon Hagibis exhibits good structural similarity in consistency with the global precipitation measurement (GPM) precipitation values. In particular, the proposed approach provides better structural similarity (SSIM) and peak signal‐to‐noise ratio (PSNR) value compared with the random forest method, which is beneficial in extreme precipitation.

Ground-based Fourier transform infrared (FTIR) O&amp;lt;sub&amp;gt;3&amp;lt;/sub&amp;gt; retrievals from the 3040 cm&amp;lt;sup&amp;gt;−1&amp;lt;/sup&amp;gt; spectral range at Xianghe, China

Abstract. In this study, we present O3 retrievals from ground-based Fourier transform infrared (FTIR) solar absorption measurements between June 2018 and December 2019 at Xianghe, China (39.75∘ N, 116.96∘ E). The FTIR spectrometer at Xianghe is operated with indium gallium arsenide (InGaAs) and indium antimonide (InSb) detectors, recording the spectra between 1800 and 11 000 cm−1. As the harmonized FTIR O3 retrieval strategy (Vigouroux et al., 2015) within the Network for the Detection of Atmospheric Composition Change (NDACC) uses the 1000 cm−1 spectral range, we apply the O3 retrieval in the 3040 cm−1 spectral range at Xianghe. The retrieved O3 profile is mainly sensitive to the vertical range between 10 and 40 km, and the degrees of freedom for signal is 2.4±0.3 (1σ), indicating that there are two individual pieces of information in partial columns between the surface and 20 km and between 20 and 40 km. According to the optimal estimation method, the systematic and random uncertainties of the FTIR O3 total columns are about 13.6 % and 1.4 %, respectively. The random uncertainty is consistent with the observed daily standard deviation of the FTIR retrievals. To validate the FTIR O3 total and partial columns, we apply the same O3 retrieval strategy at Maïdo, Réunion (a.k.a. Reunion Island; 21.08∘ N, 55.38∘ E). The FTIR O3 (3040 cm−1) measurements at Xianghe and Maïdo are then compared with the nearby ozonesondes at Beijing (39.81∘ N, 116.47∘ E) and at Gillot (20.89∘ S, 55.53∘ E), respectively, as well as with co-located TROPOspheric Monitoring Instrument (TROPOMI) satellite measurements at both sites. In addition at Maïdo, we compare the FTIR O3 (3040 cm−1) retrievals with the standard NDACC FTIR O3 measurements using the 1000 cm−1 spectral range. It was found that the total columns retrieved from the FTIR O3 3040 cm−1 measurements are underestimated by 5.5 %–9.0 %, which is mainly due to the systematic uncertainty in the partial column between 20 and 40 km (about −10.4 %). The systematic uncertainty in the partial column between surface and 20 km is relatively small (within 2.4 %). By comparison with other measurements, it was found that the FTIR O3 (3040 cm−1) retrievals capture the seasonal and synoptic variations of the O3 total and two partial columns very well. Therefore, the ongoing FTIR measurements at Xianghe can provide useful information on the O3 variations and (in the future) long-term trends.