Optimal Estimation Retrieval Research Articles

A Flexible, Multi-Instrument Optimal Estimation Retrieval for Wind Profiles

Abstract Instruments such as Doppler lidars, radar wind profilers, and uncrewed aircraft systems could be used in observation networks to fill in the temporal and spatial gap that exists for low-level wind observations. These instruments, however, do not directly observe the wind and require a retrieval to be used to obtain wind estimates from their observations. Also, the depth and uncertainty of observations collected by these instruments vary depending on the environment that they are sampling. Optimal estimation is a variational retrieval method that combines information from a prior dataset and observations to retrieve an atmospheric state. This technique can be beneficial to use when observations have large uncertainties or provide insufficient information to obtain the atmospheric state by themselves. A new optimal estimation retrieval for obtaining wind profiles from typical lower atmospheric wind profiling instrumentation has been developed. This retrieval allows for more observations from wind profiling instrumentation to be used when retrieving wind profiles, increases the depth of retrieved profiles, and eliminates vertical data gaps. This retrieval can also be used to easily combine observations from different instruments or even with model data to create combined data wind retrievals that leverage the strengths of the different data sources to retrieve a wind profile that is superior to those obtained by the individual observations or data sources. It is envisioned that this retrieval will be continued to be developed and maintained as community software as lower atmospheric wind observing capabilities further develop and expand.

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.

Optimal Estimation Inversion of Ionospheric Electron Density from GNSS-POD Limb Measurements: Part I-Algorithm and Morphology

GNSS-LEO radio links from Precise Orbital Determination (POD) and Radio Occultation (RO) antennas have been used increasingly in characterizing the global 3D distribution and variability of ionospheric electron density (Ne). In this study, we developed an optimal estimation (OE) method to retrieve Ne profiles from the slant total electron content (hTEC) measurements acquired by the GNSS-POD links at negative elevation angles (ε < 0°). Although both OE and onion-peeling (OP) methods use the Abel weighting function in the Ne inversion, they are significantly different in terms of performance in the lower ionosphere. The new OE results can overcome the large Ne oscillations, sometimes negative values, seen in the OP retrievals in the E-region ionosphere. In the companion paper in this Special Issue, the HmF2 and NmF2 from the OE retrieval are validated against ground-based ionosondes and radar observations, showing generally good agreements in NmF2 from all sites. Nighttime hmF2 measurements tend to agree better than the daytime when the ionosonde heights tend to be slightly lower. The OE algorithm has been applied to all GNSS-POD data acquired from the COSMIC-1 (2006–2019), COSMIC-2 (2019–present), and Spire (2019–present) constellations, showing a consistent ionospheric Ne morphology. The unprecedented spatiotemporal sampling of the ionosphere from these constellations now allows a detailed analysis of the frequency–wavenumber spectra for the Ne variability at different heights. In the lower ionosphere (~150 km), we found significant spectral power in DE1, DW6, DW4, SW5, and SE4 wave components, in addition to well-known DW1, SW2, and DE3 waves. In the upper ionosphere (~450 km), additional wave components are still present, including DE4, DW4, DW6, SE4, and SW4. The co-existence of eastward- and westward-propagating wave4 components implies the presence of a stationary wave4 (SPW4), as suggested by other earlier studies. Further improvements to the OE method are proposed, including a tomographic inversion technique that leverages the asymmetric sampling about the tangent point associated with GNSS-LEO links.

Applying machine learning to improve the near-real-time products of the Aura Microwave Limb Sounder

Abstract. A new algorithm to derive near-real-time (NRT) data products for the Aura Microwave Limb Sounder (MLS) is presented. The old approach was based on a simplified optimal estimation retrieval algorithm (OE-NRT) to reduce computational demands and latency. This paper describes the setup, training, and evaluation of a redesigned approach based on artificial neural networks (ANN-NRT), which is trained on >17 years of MLS radiance observations and composition profile retrievals. Comparisons of joint histograms and performance metrics derived between the two NRT results and the operational MLS products demonstrate a noticeable statistical improvement from ANN-NRT. This new approach results in higher correlation coefficients, in addition to lower root-mean-square deviations and biases at almost all retrieval levels compared to OE-NRT. The exceptions are pressure levels with concentrations close to 0 ppbv (parts per billion by volume), where the ANN models fail to establish a functional relationship and tend to predict 0. Depending on the application, this behavior might be advantageous. While the developed models can take advantage of the extended MLS data record, this study demonstrates that training ANN-NRT on just a single year of MLS observations is sufficient to improve upon OE-NRT. This confirms the potential of applying machine learning to the NRT efforts of other current and future mission concepts.

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.

Can DSD Assumptions Explain the Differences in Satellite Estimates of Warm Rain?

Abstract Satellite-based oceanic precipitation estimates, particularly those derived from the Global Precipitation Measurement (GPM) satellite and CloudSat, suffer from significant disagreement over regions of the globe where warm rain processes are dominant. GPM estimates of average rain rate tend to be lower than CloudSat estimates, due in part to GPM being less sensitive to shallow and/or light precipitation. Using coincident observations between GPM and CloudSat, we find that the GPM_2BCMB product misses about two-thirds of total accumulated warm rain compared to the CloudSat 2C-RAIN-PROFILE product. This difference becomes much smaller when products are compared at 1000 m above the surface (mitigating surface clutter issues) and when forcing the frequency of rain from CloudSat to match the frequency from GPM (mitigating sensitivity issues). However, even then a gap of about 25% remains. Using an optimal estimation retrieval algorithm on the underlying data, we retrieve a similar result, but find that the remaining difference between the GPM and CloudSat retrieved rain rates can be almost entirely accounted for by inconsistent assumptions about the shape of the drop size distribution (DSD) that are made in the two retrievals. We conclude that DSD assumptions contribute significantly to the relative underestimation of warm rain by GPM compared to CloudSat. Because the choice of DSD model has such a large effect on retrieved rain rates, more work is needed to determine whether the DSD models assumed by either the GPM_2BCMB or 2C-RAIN-PROFILE algorithms are actually appropriate for warm rain.

Emissivity retrievals with FORUM's end-to-end simulator: challenges and recommendations

Abstract. Spectral emissivity is a key property of the Earth's surface, of which only very few measurements exist so far in the far-infrared (FIR) spectral region, even though recent work has shown that the FIR is important for accurate modelling of the global climate. The European Space Agency's 9th Earth Explorer, FORUM (Far-infrared Outgoing Radiation Understanding and Monitoring) will provide the first global spectrally resolved measurements of the Earth's top-of-the-atmosphere (TOA) spectrum in the FIR. In clear-sky conditions with low water vapour content, these measurements will provide a unique opportunity to retrieve spectrally resolved FIR surface emissivity. In preparation for the FORUM mission with an expected launch in 2027, this study takes the first steps towards the development of an operational emissivity retrieval for FORUM by investigating the sensitivity of the emissivity product of a full spectrum optimal estimation retrieval method to different physical and operational parameters. The tool used for the sensitivity tests is the FORUM mission's end-to-end simulator. These tests show that the spectral emissivity of most surface types can be retrieved for dry scenes in the 350–600 cm−1 region, with an absolute uncertainty ranging from 0.005 to 0.01. In addition, the quality of the retrieval is quantified with respect to the precipitable water vapour content of the scene, and the uncertainty caused by the correlation of emissivity with surface temperature is investigated. Based on these investigations, a road map is recommended for the development of the operational emissivity product.

Are elevated moist layers a blind spot for hyperspectral infrared sounders? A model study

Abstract. The ability of the hyperspectral satellite-based passive infrared (IR) instrument IASI to resolve elevated moist layers (EMLs) within the free troposphere is investigated. EMLs are strong moisture anomalies with significant impact on the radiative heating rate profile and typically coupled to freezing level detrainment from convective cells in the tropics. A previous case study by Stevens et al. (2017) indicated inherent deficiencies of passive satellite-based remote sensing instruments in resolving an EML. In this work, we first put the findings of Stevens et al. (2017) into the context of other retrieval case studies of EML-like structures, showing that such structures can in principle be retrieved, but retrievability depends on the retrieval method and the exact retrieval setup. To approach a first more systematic analysis of EML retrievability, we introduce our own basic optimal estimation (OEM) retrieval, which for the purpose of this study is based on forward-modelled (synthetic) clear-sky observations. By applying the OEM retrieval to the same EML case as Stevens et al. (2017), we find that a lack of independent temperature information can significantly deteriorate the humidity retrieval due to a strong temperature inversion at the EML top. However, we show that by employing a wider spectral range of the hyperspectral IR observation, this issue can be avoided and EMLs can generally be resolved. We introduce a new framework for the identification and characterization of moisture anomalies, a subset of which are EMLs, to specifically quantify the retrieval's ability to capture moisture anomalies. The new framework is applied to 1288 synthetic retrievals of tropical ocean short-range forecast model atmospheres, allowing for a direct statistical comparison of moisture anomalies between the retrieval and the reference dataset. With our basic OEM retrieval, we find that retrieved moisture anomalies are on average 17 % weaker and 15 % thicker than their true counterparts. We attribute this to the retrieval smoothing error and the fact that rather weak and narrow moisture anomalies are most frequently missed by the retrieval. Smoothing is found to also constrain the magnitude of local heating rate extremes associated with moisture anomalies, particularly for the strongest anomalies that are found in the lower to mid troposphere. In total, about 80 % of moisture anomalies in the reference dataset are found by the retrieval. Below 5 km altitude, this fraction is only of the order of 52 %. We conclude that the retrieval of lower- to mid-tropospheric moisture anomalies, in particular of EMLs, is possible when the anomaly is sufficiently strong and its thickness is at least of the order of about 1.5 km. This study sets the methodological basis for more comprehensively investigating EMLs based on real hyperspectral IR observations and their operational products in the future.

Retrieval and evaluation of tropospheric-aerosol extinction profiles using multi-axis differential optical absorption spectroscopy (MAX-DOAS) measurements over Athens, Greece

Abstract. In this study, we report on the retrieval of aerosol extinction profiles from ground-based scattered sunlight multi-axis differential optical absorption spectroscopy (MAX-DOAS) measurements, carried out at Athens, Greece. It is the first time that aerosol profiles are retrieved from MAX-DOAS measurements in Athens. The reported aerosol vertical distributions at 477 nm are derived from the oxygen dimer (O4) differential-slant-column-density observations at different elevation angles by applying the BRemen Optimal estimation REtrieval for Aerosol and trace gaseS (BOREAS) retrieval algorithm. Four case studies have been selected for validation purposes; the retrieved aerosol profiles and the corresponding aerosol optical depths (AODs) from the MAX-DOAS are compared with lidar extinction profiles and with sun-photometric measurements (Aerosol Robotic Network, AERONET, observations), respectively. Despite the different approach of each method regarding the retrieval of the aerosol information, the comparison with the lidar measurements at 532 nm reveals a very good agreement in terms of vertical distribution, with r>0.90 in all cases. The AODs from the MAX-DOAS and the sun photometer (the latter at 500 nm) show a satisfactory correlation (with 0.45 < r < 0.7 in three out of the four cases). The comparison indicates that the MAX-DOAS systematically underestimates the AOD in the cases of large particles (small Ångström exponent) and for measurements at small relative azimuthal angles between the viewing direction and the sun. Better agreement is achieved in the morning, at large relative azimuthal angles. Overall, the aerosol profiles retrieved from MAX-DOAS measurements are of good quality; thus, new perspectives are opened up for assessing urban aerosol pollution on a long-term basis in Athens from continuous and uninterrupted MAX-DOAS measurements.

Linking rain into ice microphysics across the melting layer in stratiform rain: a closure study

Abstract. This study investigates the link between rain and ice microphysics across the melting layer in stratiform rain systems using measurements from vertically pointing multi-frequency Doppler radars. A novel methodology to examine the variability of the precipitation rate and the mass-weighted melted diameter (Dm) across the melting region is proposed and applied to a 6 h long case study, observed during the TRIPEx-pol field campaign at the Jülich Observatory for Cloud Evolution Core Facility and covering a gamut of ice microphysical processes. The methodology is based on an optimal estimation (OE) retrieval of particle size distributions (PSDs) and dynamics (turbulence and vertical motions) from observed multi-frequency radar Doppler spectra applied both above and below the melting layer. First, the retrieval is applied in the rain region; based on a one-to-one conversion of raindrops into snowflakes, the retrieved drop size distributions (DSDs) are propagated upward to provide the mass-flux-preserving PSDs of snow. These ice PSDs are used to simulate radar reflectivities above the melting layer for different snow models and they are evaluated for a consistency with the actual radar measurements. Second, the OE snow retrieval where Doppler spectra are simulated based on different snow models, which consistently compute fall speeds and electromagnetic properties, is performed. The results corresponding to the best-matching models are then used to estimate snow fluxes and Dm, which are directly compared to the corresponding rain quantities. For the case study, the total accumulation of rain (2.30 mm) and the melted equivalent accumulation of snow (1.93 mm) show a 19 % difference. The analysis suggests that the mass flux through the melting zone is well preserved except the periods of intense riming where the precipitation rates were higher in rain than in the ice above. This is potentially due to additional condensation within the melting zone in correspondence to high relative humidity and collision and coalescence with the cloud droplets whose occurrence is ubiquitous with riming. It is shown that the mean mass-weighted diameter of ice is strongly related to the characteristic size of the underlying rain except the period of extreme aggregation where breakup of melting snowflakes significantly reduces Dm. The proposed methodology can be applied to long-term observations to advance our knowledge of the processes occurring across the melting region; this can then be used to improve assumptions underpinning spaceborne radar precipitation retrievals.

Harmonization of Space-Borne Infra-Red Sensors Measuring Sea Surface Temperature

Sea surface temperature (SST) is observed by a constellation of sensors, and SST retrievals are commonly combined into gridded SST analyses and climate data records (CDRs). Differential biases between SSTs from different sensors cause errors in such products, including feature artefacts. We introduce a new method for reducing differential biases across the SST constellation, by reconciling the brightness temperature (BT) calibration and SST retrieval parameters between sensors. We use the Advanced Along-Track Scanning Radiometer (AATSR) and the Sea and Land Surface Temperature Radiometer (SLSTR) as reference sensors, and the Advanced Very High Resolution Radiometer (AVHRR) of the MetOp-A mission to bridge the gap between these references. Observations across a range of AVHRR zenith angles are matched with dual-view three-channel skin SST retrievals from the AATSR and SLSTR. These skin SSTs act as the harmonization reference for AVHRR retrievals by optimal estimation (OE). Parameters for the harmonized AVHRR OE are iteratively determined, including BT bias corrections and observation error covariance matrices as functions of water-vapor path. The OE SSTs obtained from AVHRR are shown to be closely consistent with the reference sensor SSTs. Independent validation against drifting buoy SSTs shows that the AVHRR OE retrieval is stable across the reference-sensor gap. We discuss that this method is suitable to improve consistency across the whole constellation of SST sensors. The approach will help stabilize and reduce errors in future SST CDRs, as well as having application to other domains of remote sensing.

Sea Ice and Atmospheric Parameter Retrieval From Satellite Microwave Radiometers: Synergy of AMSR2 and SMOS Compared With the CIMR Candidate Mission

AbstractResearch on improving the prediction skill of climate models requires refining the quality of observational data used for initializing and tuning the models. This is especially true in the polar regions where uncertainties about the interactions between sea ice, ocean, and atmosphere are driving ongoing monitoring efforts. The Copernicus Imaging Microwave Radiometer (CIMR) is an European Space Agency (ESA) candidate mission which promises to offer high resolution, low uncertainty observation capabilities at the 1.4, 6.9, 10.65, 18.7, and 36.5 GHz frequencies. To assess the potential impact of CIMR for sea ice parameter retrieval, a comparison is made between retrievals based on present AMSR2 observations and a retrieval using future CIMR equivalent observations over a data set of validated sea ice concentration (SIC) values. An optimal estimation retrieval method (OEM) is used which can use input from different channel combinations to retrieve seven geophysical parameters (sea ice concentration, multi‐year ice fraction, ice surface temperature, columnar water vapor, liquid water path, over ocean wind speed, and sea surface temperature). An advantage of CIMR over existing radiometers is that it would provide higher spatial resolution observations at the lower frequency channels (6.9, 10.65, and 18.7 GHz) which are less sensitive to atmospheric influence. This enables the passive microwave based retrieval of SIC and other surface parameters with higher resolution and lower uncertainty than is currently possible. An information content analysis expands the comparison between AMSR2 and CIMR to all retrievable surface and atmospheric parameters. This analysis quantifies the contributions to the observed signal and highlights the differences between different input channel combinations. The higher resolution of the low frequency CIMR channels allow for unprecedented detail to be achieved in Arctic passive microwave sea ice retrievals. The presence of 1.4 GHz channels on board CIMR opens up the possibility for thin sea ice thickness (SIT) retrieval. A combination of collocated AMSR2 and SMOS observations is used to simulate a full CIMR suite of measurements, and the OEM is modified to include SIT as a retrieval parameter. The output from different retrieval configurations is compared with an operational SIT product. The CIMR instrument can provide increased accuracy for SIC retrieval at very high resolutions with a combination of the 18.7 and 36.5 GHz channels while also maintaining sensitivity for atmospheric water vapor retrieval. In combination with the 1.4 GHz channels, SIT can be added as an eighth retrieval parameter with performance on par with existing operational products.

Aerosol retrieval study from multiangle polarimetric satellite data based on optimal estimation method

Based on the optimal estimation (OE) theory, an inversion framework for aerosol retrieval from multiviewing polarimetric satellite measurements, is presented. The retrieved parameters include the wavelength-independent volume concentration and spectral aerosol optical depth (AOD). An OE-iteration approach is proposed to implement the framework. Polarization data from the polarization and directionality of the Earth’s reflectance sensor over the Chinese Beijing–Tianjin–Hebei region are selected to test the proposed algorithm. The validation against aerosol robotic network products produces high correlation coefficients (R) of 0.85, 0.9, and 0.86 for the fine-mode volume concentration, fine-mode AOD, and total AOD at 500 nm, respectively. These results indicate that the OE retrieval framework is practical and useful in the quantitative retrieval of AOD and fine-mode volume concentration from the multiangle polarization data.

The Observed Structure and Precipitation Characteristics of Southeast Atlantic Stratocumulus from Airborne Radar during ORACLES 2016–17

AbstractDuring the Observations of Aerosols above Clouds and Their Interactions (ORACLES) 2016 and 2017 field experiments, the Third Generation Advanced Precipitation and Cloud Radar (APR-3) flew aboard the NASA P-3 aircraft taking over 10 million profiles of stratocumulus clouds in the southeast Atlantic Ocean. This study documents cloud structure, precipitation frequency and intensity, and atmospheric stability for each flight during both field experiments. A larger cloud fraction was estimated for 2016, likely due to a larger estimated inversion strength (EIS) in the experiment area (between 6 and 10 K) compared to 2017 where EIS was on average 4–6 K lower. We used an optimal estimation retrieval to derive precipitation rates for all measurable clouds during both experiments. Over 30% of clouds observed during the 2016 experiment exhibited precipitation reaching the surface, but retrieved drizzle rates were below 0.01 mm h−1 in all but 40% of these profiles. This is in sharp contrast to the 2017 campaign where over 53% of precipitating profiles had rainfall rates larger than 0.01 mm h−1. The differences in cloud and rain fractions between the two years are most likely due to differences in the sampling environments; however, enough variations in cloud, virga, and rain fraction exist for similar environmental conditions such that additional analysis of cloud and aerosol interactions—specifically their effect on precipitation processes—needs further exploration. The extensive APR-3 sampling of drizzling stratocumulus under similar thermodynamic conditions provides a rich dataset for examining the influence of biomass burning aerosols on cloud fraction, morphology, and precipitation characteristics in this climatically important region.

Two decades observing smoke above clouds in the south-eastern Atlantic Ocean: Deep Blue algorithm updates and validation with ORACLES field campaign data

Abstract. This study presents and evaluates an updated algorithm for quantification of absorbing aerosols above clouds (AACs) from passive satellite measurements. The focus is biomass burning in the south-eastern Atlantic Ocean during the 2016 and 2017 ObseRvations of Aerosols above CLouds and their intEractionS (ORACLES) field campaign deployments. The algorithm retrieves the above-cloud aerosol optical depth (AOD) and underlying liquid cloud optical depth and is applied to measurements from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS), Moderate Resolution Imaging Spectroradiometer (MODIS), and Visible Infrared Imaging Radiometer Suite (VIIRS) from 1997 to 2017. Airborne NASA Ames Spectrometers for Sky-Scanning, Sun-Tracking Atmospheric Research (4STAR) and NASA Langley High Spectral Resolution Lidar 2 (HSRL2) data collected during ORACLES provide important validation for spectral AOD for MODIS and VIIRS; as the SeaWiFS mission ended in 2010, it cannot be evaluated directly. The 4STAR and HSRL2 comparisons are complementary and reveal performance generally in line with uncertainty estimates provided by the optimal estimation retrieval framework used. At present the two MODIS-based data records seem the most reliable, although there are differences between the deployments, which may indicate that the available data are not yet sufficient to provide a robust regional validation. Spatiotemporal patterns in the data sets are similar, and the time series are very strongly correlated with each other (correlation coefficients from 0.95 to 0.99). Offsets between the satellite data sets are thought to be chiefly due to differences in absolute calibration between the sensors. The available validation data for this type of algorithm are limited to a small number of field campaigns, and it is strongly recommended that such airborne measurements continue to be made, both over the southern Atlantic Ocean and elsewhere.

Retrievals of Riming and Snow Density From Vertically Pointing Doppler Radars

AbstractRetrievals of ice and snow are made from Ka‐ and W‐band zenith‐pointing Doppler radars at Hyytiälä, Finland, during the snow experiment component of the Biogenic Aerosols: Effects on Clouds and Climate (2014) field campaign. In a novel optimal estimation retrieval, mean Doppler velocity is exploited to retrieve a density factor parameter, which modulates the mass, shape, terminal velocity, and backscatter cross sections of ice particles. In a case study including aggregate snow and graupel we find that snow rate and ensemble mean ice density can be retrieved to within 50% of in situ measurements at the surface using dual‐frequency Doppler radar retrievals. While Doppler measurements are essential to the retrieval of particle density, the dual‐frequency ratio provides a strong constraint on particle size. The retrieved density factor is strongly correlated with liquid water path, indicating that riming is the primary process by which the density factor is modulated. Using liquid water path as a proxy for riming, profiles classified as unrimed snow, rimed snow, and graupel exhibit distinct features characteristic of aggregation and riming processes, suggesting the potential to make estimates of process rates from these retrievals. We discuss the potential application of the technique to future satellite missions.

The Community Cloud retrieval for CLimate (CC4CL) – Part 2: The optimal estimation approach

Abstract. The Community Cloud retrieval for Climate (CC4CL) is a cloud property retrieval system for satellite-based multispectral imagers and is an important component of the Cloud Climate Change Initiative (Cloud_cci) project. In this paper we discuss the optimal estimation retrieval of cloud optical thickness, effective radius and cloud top pressure based on the Optimal Retrieval of Aerosol and Cloud (ORAC) algorithm. Key to this method is the forward model, which includes the clear-sky model, the liquid water and ice cloud models, the surface model including a bidirectional reflectance distribution function (BRDF), and the "fast" radiative transfer solution (which includes a multiple scattering treatment). All of these components and their assumptions and limitations will be discussed in detail. The forward model provides the accuracy appropriate for our retrieval method. The errors are comparable to the instrument noise for cloud optical thicknesses greater than 10. At optical thicknesses less than 10 modeling errors become more significant. The retrieval method is then presented describing optimal estimation in general, the nonlinear inversion method employed, measurement and a priori inputs, the propagation of input uncertainties and the calculation of subsidiary quantities that are derived from the retrieval results. An evaluation of the retrieval was performed using measurements simulated with noise levels appropriate for the MODIS instrument. Results show errors less than 10 % for cloud optical thicknesses greater than 10. Results for clouds of optical thicknesses less than 10 have errors up to 20 %.

Optimal Estimation Versus MCMC for $$\mathrm{{CO}}_{2}$$ CO 2 Retrievals

The Orbiting Carbon Observatory-2 (OCO-2) collects infrared spectra from which atmospheric properties are retrieved. OCO-2 operational data processing uses optimal estimation (OE), a state-of-the-art approach to inference of atmospheric properties from satellite measurements. One of the main advantages of the OE approach is computational efficiency, but it only characterizes the first two moments of the posterior distribution of interest. Here we obtain samples from the posterior using a Markov Chain Monte Carlo (MCMC) algorithm and compare this empirical estimate of the true posterior to the OE results. We focus on 600 simulated soundings that represent the variability of physical conditions encountered by OCO-2 between November 2014 and January 2016. We treat the two retrieval methods as ensemble and density probabilistic forecasts, where the MCMC yields an ensemble from the posterior and the OE retrieval result provide the first two moments of a normal distribution. To compare these methods, we apply both univariate and multivariate diagnostic tools and proper scoring rules. The general impression from our study is that when compared to MCMC, the OE retrieval performs reasonably well for the main quantity of interest, the column-averaged $$\mathrm{{CO}}_{2}$$ concentration $$X_{\mathrm{{CO}}_{2}}$$ , but not for the full state vector $$\mathbf {X}$$ which includes a profile of $$\mathrm{{CO}}_{2}$$ concentrations over 20 pressure levels, as well as several other atmospheric properties.Supplementary materials accompanying this paper appear on-line.

Optimal Estimation of Sea Surface Temperature from AMSR-E

The Optimal Estimation (OE) technique is developed within the European Space Agency Climate Change Initiative (ESA-CCI) to retrieve subskin Sea Surface Temperature (SST) from AQUA’s Advanced Microwave Scanning Radiometer—Earth Observing System (AMSR-E). A comprehensive matchup database with drifting buoy observations is used to develop and test the OE setup. It is shown that it is essential to update the first guess atmospheric and oceanic state variables and to perform several iterations to reach an optimal retrieval. The optimal number of iterations is typically three to four in the current setup. In addition, updating the forward model, using a multivariate regression model is shown to improve the capability of the forward model to reproduce the observations. The average sensitivity of the OE retrieval is 0.5 and shows a latitudinal dependency with smaller sensitivity for cold waters and larger sensitivity for warmer waters. The OE SSTs are evaluated against drifting buoy measurements during 2010. The results show an average difference of 0.02 K with a standard deviation of 0.47 K when considering the 64% matchups, where the simulated and observed brightness temperatures are most consistent. The corresponding mean uncertainty is estimated to 0.48 K including the in situ and sampling uncertainties. An independent validation against Argo observations from 2009 to 2011 shows an average difference of 0.01 K, a standard deviation of 0.50 K and a mean uncertainty of 0.47 K, when considering the best 62% of retrievals. The satellite versus in situ discrepancies are highest in the dynamic oceanic regions due to the large satellite footprint size and the associated sampling effects. Uncertainty estimates are available for all retrievals and have been validated to be accurate. They can thus be used to obtain very good retrieval results. In general, the results from the OE retrieval are very encouraging and demonstrate that passive microwave observations provide a valuable alternative to infrared satellite observations for retrieving SST.

Retrieval of volcanic SO<sub>2</sub> from HIRS/2 using optimal estimation

Abstract. We present an optimal-estimation (OE) retrieval scheme for stratospheric sulfur dioxide from the High-Resolution Infrared Radiation Sounder 2 (HIRS/2) instruments on the NOAA and MetOp platforms, an infrared radiometer that has been operational since 1979. This algorithm is an improvement upon a previous method based on channel brightness temperature differences, which demonstrated the potential for monitoring volcanic SO2 using HIRS/2. The Prata method is fast but of limited accuracy. This algorithm uses an optimal-estimation retrieval approach yielding increased accuracy for only moderate computational cost. This is principally achieved by fitting the column water vapour and accounting for its interference in the retrieval of SO2. A cloud and aerosol model is used to evaluate the sensitivity of the scheme to the presence of ash and water/ice cloud. This identifies that cloud or ash above 6 km limits the accuracy of the water vapour fit, increasing the error in the SO2 estimate. Cloud top height is also retrieved. The scheme is applied to a case study event, the 1991 eruption of Cerro Hudson in Chile. The total erupted mass of SO2 is estimated to be 2300 kT ± 600 kT. This confirms it as one of the largest events since the 1991 eruption of Pinatubo, and of comparable scale to the Northern Hemisphere eruption of Kasatochi in 2008. This retrieval method yields a minimum mass per unit area detection limit of 3 DU, which is slightly less than that for the Total Ozone Mapping Spectrometer (TOMS), the only other instrument capable of monitoring SO2 from 1979 to 1996. We show an initial comparison to TOMS for part of this eruption, with broadly consistent results. Operating in the infrared (IR), HIRS has the advantage of being able to measure both during the day and at night, and there have frequently been multiple HIRS instruments operated simultaneously for better than daily sampling. If applied to all data from the series of past and future HIRS instruments, this method presents the opportunity to produce a comprehensive and consistent volcanic SO2 time series spanning over 40 years.