Estimating aerosol emission from SPEXone on the NASA PACE mission using an ensemble Kalman Smoother: Observing System Simulation Experiments (OSSEs)

We present a top-down approach for aerosol emission estimation from SPEXone polarimetric retrievals related to the aerosol amount, size, and absorption using a fixed-lag ensemble Kalman smoother (LETKS) in combination with the ECHAM-HAM model. We assess the system by performing Observing System Simulation Experiments (OSSEs), in order to evaluate the ability of the future multi-angle polarimeter instrument, SPEXone, as well as a satellite with near perfect global coverage. In our OSSEs, the Nature Run (NAT) is a simulation by the global climate aerosol model ECHAM-HAM with altered aerosol emissions. The Control (CTL) and the data assimilation (DAS) experiments are composed of an ensemble of ECHAM-HAM simulations, where the default aerosol emissions are perturbed with factors taken from a Gaussian distribution. Synthetic observations, specifically Aerosol Optical Depth at 550 nm (AOD550), Angstrom Exponent from 550 nm to 865 nm (AE550-865) and Single Scattering Albedo at 550 nm (SSA550) are assimilated in order to estimate the aerosol emission fluxes of desert dust (DU), sea salt (SS), organic carbon (OC), black carbon (BC) and sulphate (SO4), along with the emission fluxes of two SO4 precursor gases (SO2, DMS). The synthetic observations are sampled from the NAT according to two satellite observing systems, with different spatial coverages. The first is the sensor SPEXone, a hyperspectral multi-angle polarimeter with a narrow swath (~100 km), that will be a part of the NASA PACE mission. The second is an idealized sensor that can retrieve observations over the whole globe even under cloudy conditions. The prior emission global relative Mean Absolute Error (MAE) before the assimilation ranges from 33 % to 117 %. Depending on the species, the assimilated observations sampled using the idealized sensor, reduce this error to equal to or lower than 5 %. Despite its limited coverage, the SPEXone sampling bares similar results, with somewhat larger errors for DU and SS (both having a MAE equal to 11 %). Further, experiments show that doubling the measurement error, increases the global relative MAE to 22 % for DU and SS. The emission estimation of the other species is not affected as much by these changes. In addition, the role of biased meteorology on emission estimation was quantified by using two different datasets (ERA-5 and ERA-interim) to nudge the U and V wind components of the model. The results reveal that when the wind of DAS uses a different reanalysis dataset than the NAT the estimated SS emissions are negatively affected the most, while the estimated emissions of DU, OC, BC and SO2 are negatively affected to a smaller extent. If the DAS uses dust or sea salt emission parametrisations that are very different from the NAT, posterior emissions can still be successfully estimated but this experiment revealed that the source location is important for the estimation of dust emissions. This work suggests that the upcoming SPEXone sensor will provide observations related to aerosol amount, size and absorption with sufficient coverage and accuracy, in order to estimate aerosol emissions.

A fast, single-iteration ensemble Kalman smoother for sequential data assimilation

Ensemble-variational methods form the basis of the state-of-the-art for nonlinear, scalable data assimilation, yet current designs may not be cost-effective for reducing prediction error in online, short-range forecast systems. We propose a novel, outer-loop optimization of the ensemble-variational formalism for applications in which forecast error dynamics are weakly nonlinear, such as synoptic meteorology. In order to rigorously derive our method and demonstrate its novelty, we review ensemble smoothers that appear throughout the literature in a unified Bayesian maximum-a-posteriori narrative, updating and simplifying some results. After mathematically deriving our technique, we systematically develop and inter-compare all studied schemes in the open-source Julia package DataAssimilationBenchmarks.jl, with pseudo-code provided for these methods. This high-performance numerical framework, supporting our mathematical results, produces extensive benchmarks that demonstrate the significant performance advantages of our proposed technique. In particular, our single-iteration ensemble Kalman smoother is shown both to improve prediction / posterior accuracy and to simultaneously reduce the leading order cost of iterative, sequential smoothers in a variety of relevant test cases for operational short-range forecasts. This long work is thus intended to present our novel single-iteration ensemble Kalman smoother, and to provide a theoretical and computational framework for the study of sequential, ensemble-variational Kalman filters and smoothers generally.

Aerosol formation and growth rates from chamber experiments using Kalman smoothing

Bayesian state estimation in the form of Kalman smoothing was applied to differential mobility analyser train (DMA-train) measurements of aerosol size distribution dynamics. Four experiments were analysed in order to estimate the aerosol size distribution, formation rate, and size-dependent growth rate, as functions of time. The first analysed case was a synthetic one, generated by a detailed aerosol dynamics model and the other three chamber experiments performed at the CERN CLOUD facility. The estimated formation and growth rates were compared with other methods used earlier for the CLOUD data and with the true values for the computer-generated synthetic experiment. The agreement in the growth rates was very good for all studied cases: estimations with an earlier method fell within the uncertainty limits of the Kalman smoother results. The formation rates also matched well, within roughly a factor of 2.5 in all cases, which can be considered very good considering the fact that they were estimated from data given by two different instruments, the other being the particle size magnifier (PSM), which is known to have large uncertainties close to its detection limit. The presented fixed interval Kalman smoother (FIKS) method has clear advantages compared with earlier methods that have been applied to this kind of data. First, FIKS can reconstruct the size distribution between possible size gaps in the measurement in such a way that it is consistent with aerosol size distribution dynamics theory, and second, the method gives rise to direct and reliable estimation of size distribution and process rate uncertainties if the uncertainties in the kernel functions and numerical models are known.

Batch seismic inversion using the iterative ensemble Kalman smoother

An ensemble-based method for seismic inversion to estimate elastic attributes is considered, namely the iterative ensemble Kalman smoother. The main focus of this work is the challenge associated with ensemble-based inversion of seismic waveform data. The amount of seismic data is large and, depending on ensemble size, it cannot be processed in a single batch. Instead a solution strategy of partitioning the data recordings in time windows and processing these sequentially is suggested. This work demonstrates how this partitioning can be done adaptively, with a focus on reliable and efficient estimation. The adaptivity relies on an analysis of the update direction used in the iterative procedure, and an interpretation of contributions from prior and likelihood to this update. The idea is that these must balance; if the prior dominates, the estimation process is inefficient while the estimation is likely to overfit and diverge if data dominates. Two approaches to meet this balance are formulated and evaluated. One is based on an interpretation of eigenvalue distributions and how this enters and affects weighting of prior and likelihood contributions. The other is based on balancing the norm magnitude of prior and likelihood vector components in the update. Only the latter is found to sufficiently regularize the data window. Although no guarantees for avoiding ensemble divergence are provided in the paper, the results of the adaptive procedure indicate that robust estimation performance can be achieved for ensemble-based inversion of seismic waveform data.