Correlated Observation Errors Research Articles

Global atmospheric state analysis using objective Gaussian probability density functions

Atmospheric state analysis is a difficult scientific problem due to the chaotic nature of the atmosphere. Data assimilation is a framework for generating an accurate state analysis of a physical system using probability density functions (PDFs) describing uncertainty of information on the state of the physical system. However, since PDFs cannot be deduced theoretically, those used in data assimilation of atmospheric state analysis are based on empirical tunings. This PDF uncertainty limits the theoretical consistency and accuracy of atmospheric state analysis and that of all atmospheric sciences. In this study, we constructed a highly accurate and theoretically consistent atmospheric state analysis by objectively estimating the PDFs of all datasets (forecasts and observations) under the Gaussian approximation. We show that an ensemble of data assimilations with 192 members using the four-dimensional variational method and sample statistics obtained with the data assimilation theory (Desroziers’ method) can generate more accurate objective Gaussian PDFs, including flow-dependent forecast error structures. Numerical experiments of atmospheric state analysis and forecasts using objective PDFs were conducted and compared with those using conventional empirical PDFs. The objective PDFs had smaller error variances for most data (about 34% of those of CNTL on average) and larger observation error correlations for satellite radiances, where the strongest correlation was greater than 0.8. The analysed atmospheric states are systematically different, such as a cooler (exceeding 1.2 K) and wetter (exceeding 1.2 g/kg) low troposphere in regions characterized by low-level clouds off the west coast of the continents. The theoretical consistency evaluated by the chi-square-based tests showed a clear improvement from 16 to 95%. The forecast accuracy was improved globally up to 9%, with 95% statistical significance. The tropical cyclone track forecast accuracy was also improved about 20%.

A Novel Localized Fast Multipole Method for Computations With Spatially Correlated Observation Error Statistics in Data Assimilation

AbstractSeveral observation types (e.g., geostationary satellite and Doppler radar observations) have recently been found to exhibit strong spatial error correlations. Including these error statistics in data assimilation for numerical weather prediction can improve analysis quality and forecast skill. Moreover, it allows for increases in the spatial density of observations assimilated, which is needed for the provision of information on appropriate scales for high‐resolution forecasting. However, introducing correlated error statistics may increase the computational complexity and parallel communication costs of matrix‐vector products involving observation precision matrices (inverse observation error covariance matrices). Without new approaches, we cannot take full advantage of new observation uncertainty estimates. We develop a new numerical approximation method based on a particular type of fast multipole method and a domain localization approach. The basic idea is to divide the observation domain into boxes and then separate calculations of matrix‐vector products according to the partition. These calculations can be done in parallel with very low communication overheads. The new method is easy to implement and parallelize, and it is applicable to a wide variety of observation precision matrices. We applied the new method to a simple variational data assimilation problem and found that the computational cost of the variational minimization was dramatically reduced while preserving analysis accuracy across a range of scales. The new method has the potential to be used as an efficient technique for practical applications where a large number of observations with mutual error correlations need to be assimilated quickly.

Multiscale model diagnostics

I consider the problem of model diagnostics, that is, the problem of criticizing a model prior to history matching by comparing data to an ensemble of simulated data based on the prior model (prior predictions). If the data are not deemed as a credible prior prediction by the model diagnostics, some settings of the model should be changed before history matching is attempted. I particularly target methodologies that are computationally feasible for large models with large amounts of data. A multiscale methodology, that can be applied to analyze differences between data and prior predictions in a scale-by-scale fashion, is proposed for this purpose. The methodology is computationally inexpensive, straightforward to apply, and can handle correlated observation errors without making approximations. The multiscale methodology is tested on a set of toy models, on two simplistic reservoir models with synthetic data, and on real data and prior predictions from the Norne field. The tests include comparisons with a previously published method (termed the Mahalanobis methodology in this paper). For the Norne case, both methodologies led to the same decisions regarding whether to accept or discard the data as a credible prior prediction. The multiscale methodology led to correct decisions for the toy models and the simplistic reservoir models. For these models, the Mahalanobis methodology either led to incorrect decisions, and/or was unstable with respect to selection of the ensemble of prior predictions.

Sampling and misspecification errors in the estimation of observation‐error covariance matrices using observation‐minus‐background and observation‐minus‐analysis statistics

AbstractSpecification of the observation‐error covariance matrix for data assimilation systems affects the observation information content retained by the analysis, particularly for observations known to have correlated observation errors (e.g., geostationary satellite and Doppler radar data). A widely adopted approach for estimating observation‐error covariance matrices uses observation‐minus‐background and observation‐minus‐analysis residuals, which are routinely produced by most data assimilation systems. Although this approach is known to produce biased and noisy estimates, due to sampling and misspecification errors, there has been no systematic study of sampling errors with this approach to date. Furthermore, the eigenspectrum of the estimated observation‐error covariance matrix is known to influence the analysis information content and numerical convergence of variational assimilation schemes. In this work, we provide new theorems for the sampling error and eigenvalues of the estimated observation‐error covariance matrices with this approach. We also conduct numerical experiments to illustrate our theoretical results. We find that this method produces large sampling errors if the true observation‐error standard deviation is large, while the other error characteristics, including the true background‐error standard deviation and observation‐ and background‐error correlation length‐scales, have a relatively small effect. We also find that the smallest eigenvalues of the estimated matrices may be smaller or larger than the true eigenvalues, depending on the assumed and true observation‐ and background‐error statistics. These results may provide insights for practical applications: for example, in deciding on appropriate sample sizes and choosing parameters for matrix reconditioning techniques.

Impact of Assimilation of the Tropical Cyclone Strong Winds Observed by Synthetic Aperture Radar on Analyses and Forecasts

Abstract A few high-wind observations have been obtained from satellites over the ocean around tropical cyclones (TCs), but the impact of data assimilation of such observations over the sea on forecasting has not been clear. The spaceborne synthetic aperture radar (SAR) provides high-resolution and wide-area ocean surface wind speed data around the center of a TC. In this study, the impact of data assimilation of the ocean surface wind speed of SAR (OWSAR) on regional model forecasts was investigated. The assimilated data were estimated from SAR on board Sentinel-1 and RADARSAT-2. The bias of OWSAR depends on wind speed, the observation error variance depends on wind speed and incidence angle, and the spatial observation error correlation depends on the incidence angle. The observed OWSAR is screened using the variational quality control method with the Huber norm. In the case of Typhoon Hagibis (2019), OWSAR assimilation modified the TC low-level inflow, which also modified the TC upper-level outflow. The propagation of this OWSAR assimilation effect from the surface to the upper troposphere was given by a four-dimensional variational method that searches for the optimal solution within strong constraints on the time evolution of the forecast model. Statistical validation confirmed that errors in the TC intensity forecast decreased over lead times of 15 h, but this was not statistically significant. The validation using wind profiler observations showed that OWSAR assimilation significantly improved the accuracy of wind speed predictions from the middle to the upper level of the troposphere. Significance Statement The purpose of this study was to demonstrate the impact of the assimilation of ocean surface wind speed by synthetic aperture radar (SAR) on regional model predictions. In the case of tropical cyclones, ocean surface wind speed assimilation modified inflows in the lower layer and outflows in the upper layer. The results indicate that the SAR assimilation improves the accuracy of wind speed forecasts in the middle to upper troposphere.

An Adaptive Channel Selection Method for Assimilating the Hyperspectral Infrared Radiances

Abstract Hyperspectral infrared (IR) satellites can provide high-resolution vertical profiles of the atmospheric state, which significantly contributes to the forecast skill of numerical weather prediction, especially for regions with sparse observations. One challenge in assimilating the hyperspectral radiances is how to effectively extract the observation information, due to the interchannel correlations and correlated observation errors. An adaptive channel selection method is proposed, which is implemented within the data assimilation scheme and selects the radiance observation with the maximum reduction of variance in observation space. Compared to the commonly used channel selection method based on the maximum entropy reduction (ER), the adaptive method can provide flow-dependent and time-varying channel selections. The performance of the adaptive selection method is evaluated by assimilating only the synthetic Fengyun-4A (FY-4A) GIIRS IR radiances in an observing system simulation experiment (OSSE), with model resolutions from 7.5 to 1.5 km and then 300 m. For both clear-sky and all-sky conditions, the adaptive method generally produces smaller RMS errors of state variables than the ER-based method given similar amounts of assimilated radiances, especially with fine model resolutions. Moreover, the adaptive method has minimum RMS errors smaller than or approaching those with all channels assimilated. For the intensity of the tropical cyclone, the adaptive method also produces smaller errors of the minimum dry air mass and maximal wind speed at different levels, compared to the ER-based selection method. Significance Statement Assimilating satellite radiances has been essential for numerical weather prediction. Hyperspectral infrared satellites provide high-resolution vertical profiles for the atmospheric state and can further improve the numerical weather prediction. Due to limited computational resources, and correlated observations and associated errors, efficient and effective ways to assimilate the hyperspectral radiances are needed. An adaptive channel selection method that is incorporated with data assimilation is proposed. The adaptive channel selection can effectively extract the information from hyperspectral radiances under both clear- and all-sky conditions, with increased model resolutions from kilometers to subkilometers.

Including the Horizontal Observation Error Correlation in the Ensemble Kalman Filter: Idealized Experiments with NICAM-LETKF

Abstract Densely observed remote sensing data such as radars and satellites generally contain significant spatial error correlations. In data assimilation, the observation error covariance matrix is usually assumed to be diagonal, and the dense data are thinned or spatially averaged to compensate for neglecting the spatial observation error correlation. However, in theory, including the spatial observation error correlation in data assimilation can make better use of the dense data. This study performs perfect model observing system simulation experiments (OSSEs) using the nonhydrostatic icosahedral atmospheric model (NICAM) and the local ensemble transform Kalman filter (LETKF) to assess the impact of assimilating horizontally dense and error-correlated observations. The condition number of the observation error covariance matrix, defined as the ratio of the largest to smallest eigenvalues, is important for the numerical stability of the LETKF computation. A large condition number makes it difficult to compute the ensemble transform matrix correctly. Reducing the condition number by reconditioning is found effective for stable computation. The results show that including the horizontal observation error correlation with reconditioning makes the analysis more accurate but requires 6 times more computations than the case with the diagonal observation error covariance matrix. Significance Statement It is important to effectively utilize observations in data assimilation for more accurate weather prediction. Spatially dense observations are known to have an error correlation that is ignored in the data assimilation. This study explores assimilating dense observations by explicitly including observation error correlations with an idealized experiment. The results shows that the analysis is improved by including the observation error correlations. Also, the condition number of the observation error covariance matrix is essential for stable computations.

A Machine Learning Augmented Data Assimilation Method for High‐Resolution Observations

AbstractThe accuracy of initial conditions is an important driver of the forecast skill of numerical weather prediction models. Increases in the quantity of available measurements, particularly high‐resolution remote sensing observational data products from satellites, are valuable inputs for improving those initial condition estimates. However, the traditional data assimilation methods for integrating observations into forecast models are computationally expensive. This makes incorporating dense observations into operational forecast systems challenging, and it is often prohibitively time‐consuming. Additionally, high‐resolution observations often have correlated observation errors which are difficult to estimate and create problems for assimilation systems. As a result, large quantities of data are discarded and not used for state initialization. Using the Lorenz‐96 system for testing, we demonstrate that a simple machine learning method can be trained to assimilate high‐resolution data. Using it to do so improves both initial conditions and forecast accuracy. Compared to using the Ensemble Kalman Filter with high‐resolution observations ignored, our augmented method has an average root‐mean‐squared error reduced by 37%. Ensemble forecasts using initial conditions generated by the augmented method are more accurate and reliable at up to 10 days of forecast lead time.

Impacts of radar forward operator on convective-scale data assimilation and short-term forecasts

The current study utilizes the operational data assimilation system of Deutscher Wetterdienst (DWD) to investigate the impacts of improved radar forward operator. First of all, it is shown that for experiments in which both conventional and radar data are assimilated and the latent heat nudging (LHN) is applied, the one with improved operator (i.e., with improved Mie-scattering scheme and accounting for beam broadening effect and etc.) exhibits neutral impacts on short-term forecasts. However, in subsequent experiments, in which conventional data are not assimilated and the LHN is switched off, the one with improved operator not just reduces representation error during data assimilation cycles but also enhances the short-term forecast skills. In addition, it is found that the subsequent experiments result in much shorter observation error correlation length scales for radar reflectivity data, indicating that the application of the LHN or assimilation of conventional data may increase the length scales.

A Regional multi-Air Pollutant Assimilation System (RAPAS v1.0) for emission estimates: system development and application

Abstract. Top-down atmospheric inversion infers surface–atmosphere fluxes from spatially distributed observations of atmospheric composition in order to quantify anthropogenic and natural emissions. In this study, we developed a Regional multi-Air Pollutant Assimilation System (RAPAS v1.0) based on the Weather Research and Forecasting–Community Multiscale Air Quality (WRF–CMAQ) modeling system model, the three-dimensional variational (3D-Var) algorithm, and the ensemble square root filter (EnSRF) algorithm. This system can simultaneously assimilate hourly in situ CO, SO2, NO2, PM2.5, and PM10 observations to infer gridded emissions of CO, SO2, NOx, primary PM2.5 (PPM2.5), and coarse PM10 (PMC) on a regional scale. In each data assimilation window, we use a “two-step” scheme, in which the emissions are inferred first and then input into the CMAQ model to simulate initial conditions (ICs) of the next window. The posterior emissions are then transferred to the next window as prior emissions, and the original emission inventory is only used in the first window. Additionally, a “super-observation” approach is implemented to decrease the computational costs, observation error correlations, and influence of representative errors. Using this system, we estimated the emissions of CO, SO2, NOx, PPM2.5, and PMC in December and July 2016 over China using nationwide surface observations. The results show that compared to the prior emissions (2016 Multi-resolution Emission Inventory for China – MEIC 2016)), the posterior emissions of CO, SO2, NOx, PPM2.5, and PMC in December 2016 increased by 129 %, 20 %, 5 %, 95 %, and 1045 %, respectively, and the emission uncertainties decreased by 44 %, 45 %, 34 %, 52 %, and 56 %, respectively. With the inverted emissions, the RMSE of simulated concentrations decreased by 40 %–56 %. Sensitivity tests were conducted with different prior emissions, prior uncertainties, and observation errors. The results showed that the two-step scheme employed in RAPAS is robust in estimating emissions using nationwide surface observations over China. This study offers a useful tool for accurately quantifying multi-species anthropogenic emissions at large scales and in near-real time.

Impact of correlated observation errors on the conditioning of variational data assimilation problems

SummaryAn important class of nonlinear weighted least‐squares problems arises from the assimilation of observations in atmospheric and ocean models. In variational data assimilation, inverse error covariance matrices define the weighting matrices of the least‐squares problem. For observation errors, a diagonal matrix (i.e., uncorrelated errors) is often assumed for simplicity even when observation errors are suspected to be correlated. While accounting for observation‐error correlations should improve the quality of the solution, it also affects the convergence rate of the minimization algorithms used to iterate to the solution. If the minimization process is stopped before reaching full convergence, which is usually the case in operational applications, the solution may be degraded even if the observation‐error correlations are correctly accounted for. In this article, we explore the influence of the observation‐error correlation matrix () on the convergence rate of a preconditioned conjugate gradient (PCG) algorithm applied to a one‐dimensional variational data assimilation (1D‐Var) problem. We design the idealized 1D‐Var system to include two key features used in more complex systems: we use the background error covariance matrix () as a preconditioner (B‐PCG); and we use a diffusion operator to model spatial correlations in and . Analytical and numerical results with the 1D‐Var system show a strong sensitivity of the convergence rate of B‐PCG to the parameters of the diffusion‐based correlation models. Depending on the parameter choices, correlated observation errors can either speed up or slow down the convergence. In practice, a compromise may be required in the parameter specifications of and between staying close to the best available estimates on the one hand and ensuring an adequate convergence rate of the minimization algorithm on the other.

Including observation error correlation for ensemble radar radial wind assimilation and its impact on heavy rainfall prediction

AbstractAn assumption of uncorrelated observation errors is commonly adopted in conventional data assimilation. For this reason, high‐resolution data are resampled with strategies such as superobbing or data thinning. These strategies diminish the advantages of high temporal and spatial resolutions that can provide essential details in convection development. However, assimilating high‐resolution data, such as radar radial wind, without considering observation error correlations can lead to overfitting and thus degrade the performance of data assimilation and forecasts. This study uses a radar ensemble data assimilation system that combines the Weather Research and Forecasting model and Local Ensemble Transform Kalman Filter (WRF‐LETKF) to assimilate radar radial wind and reflectivity data. We present a strategy to include the error correlation of the Doppler radar radial wind in the WRF‐LETKF radar assimilation system and examine its impact on the accuracy of short‐term precipitation predictions based on a heavy rainfall event on June 2, 2017 in Taiwan.For radial wind, the horizontal error correlation scale is approximately 25 km according to the innovation statistics. The introduction of observation error correlation for radar radial wind assimilation produces more small‐scale features in wind analysis corrections compared to the experiment using an independent observation assumption. Consequently, the modification of wind corrections leads to stronger convergence accompanied by higher water vapor content, which enhances local convections. This results in more accurate simulations of reflectivity and short‐term precipitation. In particular, this advantage is identified for extreme heavy rainfall thresholds at small scales according to probability quantitative precipitation forecasts and fractions skill score.

Development of the Real‐Time 30‐s‐Update Big Data Assimilation System for Convective Rainfall Prediction With a Phased Array Weather Radar: Description and Preliminary Evaluation

AbstractWe present the first ever real‐time numerical weather prediction system with 30‐s update cycles at a 500‐m grid spacing for the prediction of convective precipitation in the subsequent 30 min using a new‐generation multi‐parameter phased array weather radar. The system comprises a regional atmospheric model known as the SCALE and the local ensemble transform Kalman filter (LETKF). To accelerate the SCALE‐LETKF system, data transfer between the two aforementioned components is performed using a memory copy instead of a file I/O. A complete real‐time workflow including domain nesting and observational data transfer is constructed. A real‐time test in July and August 2020 showed that the system is fast enough for a real‐time application of 30‐s forecast‐analysis cycles and 30‐min prediction. The development includes a new thinning method considering the spatially correlated observation errors in the dense radar data. This new thinning method is effective in two past case studies in the summer of 2019.

Effects of Flow Dependency Introduced by Background Error in Frequent and Dense Assimilation of Radial Winds Using Observation Error Correlated in Time and Space

Abstract We investigated the effect of flow dependency in the assimilation of high-density, high-frequency observations. Radial winds from a Doppler radar are assimilated using a regional hybrid four-dimensional variational data assimilation (4D-Var) scheme with a flow-dependent background error covariance. To consistently assimilate 5 km × 5.625° cell-averaged radial winds at an interval of 10 min, the spatial and temporal correlations of the observation error are statistically diagnosed to be incorporated into the hybrid 4D-Var. The spatial correlation width is larger than that expected from instrument error, suggesting a contribution from representation error whose propagation is also considered to lead to temporal correlation, the width of which is diagnosed to increase with forecast time. The background error covariance also has an important role in incorporating observational information into the analysis. Single observation experiments show that the hybrid 4D-Var has more small-scale structure in its flow-dependent background error correlation than the 4D-Var limited from the climatological background error covariance mainly in the former part of the assimilation window. This suggests the higher potential of the hybrid 4D-Var to allow more higher-wavenumber components in the increment. A case study shows that the hybrid 4D-Var makes better use of the dense and frequent observations, reflecting more detailed representation of flow throughout the assimilation window, leading to promising results in the forecast. Sensitivity experiments also show that it is important to use the optimal observation error correlation. It is suggested that the flow-dependent background error becomes necessary to effectively use high-resolution, high-frequency observations.

Information content in 4D seismic data: Effect of correlated noise

Several types of data used in history matching for subsurface reservoir characterization have errors that are spatially or temporally correlated. Although it is often assumed that correlated observation errors decrease information content, using a simplified flow problem, we show that for data that are spatially dense (such as 4D seismic data), correlated observation errors result in higher information content than data with similar levels of errors, but without correlation. Unfortunately, correlations in the observation error are often unrecognized and difficult to estimate, especially if the correlation scale of the errors is similar to a characteristic length of the signal. In addition, many history matching algorithms are incapable of accounting properly for correlated observation error, so data are either thinned or the observation error is inflated to partially account for the lack of proper treatment. We show that neglecting correlations in the observation errors or inflating the variance, result in loss of information content. Finally, we show that it is possible to iteratively estimate the correlated observation errors through analysis of residuals after history matching. • Measurement errors in seismic data are generally correlated. • Correlated errors can increase information content when measurements are dense. • Neglecting correlations during model calibration results in information loss. • Correlations in seismic data can be estimated from data mismatch after calibration.

Efficient computation of matrix–vector products with full observation weighting matrices in data assimilation

AbstractRecent studies have demonstrated improved skill in numerical weather prediction via the use of spatially correlated observation error covariance information in data assimilation systems. In this case, the observation weighting matrices (inverse error covariance matrices) used in the assimilation may be full matrices rather than diagonal. Thus, the computation of matrix–vector products in the variational minimization problem may be very time‐consuming, particularly if the parallel computation of the matrix–vector product requires a high degree of communication between processing elements. Hence, we introduce a well‐known numerical approximation method, called the fast multipole method (FMM), to speed up the matrix–vector multiplications in data assimilation. We explore a particular type of FMM that uses a singular value decomposition (SVD‐FMM) and adjust it to suit our new application in data assimilation. By approximating a large part of the computation of the matrix–vector product, the SVD‐FMM technique greatly reduces the computational complexity compared with the standard approach. We develop a novel possible parallelization scheme of the SVD‐FMM for our application, which can reduce the communication costs. We investigate the accuracy of the SVD‐FMM technique in several numerical experiments: we first assess the accuracy using covariance matrices that are created using different correlation functions and lengthscales, then investigate the impact of reconditioning the covariance matrices on the accuracy, and finally examine the feasibility of the technique in the presence of missing observations. We also provide theoretical explanations for some numerical results. Our results show that the SVD‐FMM technique can compute the matrix–vector product with good accuracy in a wide variety of circumstances and, hence, has potential as an efficient technique for assimilation of a large volume of observational data within a short time interval.

Assimilation of ASCAT Sea Surface Wind Retrievals with Correlated Observation Errors

Data assimilation systems usually assume that the observation errors of wind components, i.e., u (the longitudinal component) and v (the latitudinal component), are uncorrelated. However, since wind components are derived from observations in the form of wind speed and direction (spd and dir), the observation errors of u and v are correlated. In this paper, an explicit expression of the observation errors and correlation for each pair of wind components are derived based on the law of error propagation. The new data assimilation scheme considering the correlated error of wind components is implemented in the Weather Research and Forecasting Data Assimilation (WRFDA) system. Besides, adaptive quality control (QC) is introduced to retain the information of high wind-speed observations. Preliminary experimental results suggest that analyses from the new data assimilation scheme are more reasonable compared to those from the conventional one, and could improve the forecasting of Typhoon Noru.

The Impact of Assimilating Satellite Radiance Observations in the Copernicus European Regional Reanalysis (CERRA)

The assimilation of microwave and infrared (IR) radiance satellite observations within numerical weather prediction (NWP) models have been an important component in the effort of improving the accuracy of analysis and forecast. Such capabilities were implemented during the development of the high-resolution Copernicus European Regional Reanalysis (CERRA), funded by the Copernicus Climate Change Services (C3S). The CERRA system couples the deterministic system with the ensemble data assimilation to provide periodic updates of the background error covariance matrix. Several key factors for the assimilation of radiances were investigated, including appropriate use of variational bias correction (VARBC), surface-sensitive AMSU-A observations and observation error correlation. Twenty-one-day impact studies during the summer and winter seasons were conducted. Generally, the assimilation of radiances has a small impact on the analysis, while greater impacts are observed on short-range (12 and 24-h) forecasts with an error reduction of 1–2% for the mid and high troposphere. Although, the current configuration provided less accurate forecasts from 09 and 18 UTC analysis times. With the increased thinning distances and the rejection of IASI observation over land, the errors in the analyses and 3 h forecasts on geopotential height were reduced up to 2%.

The importance of simulated errors in observing system simulation experiments

Observing System Simulation Experiments (OSSEs) for numerical weather prediction rely on simulated observations that should include simulated observation errors in order to realistically represent the behaviour of real data. Real observations include many types of error, such as instrument error, representativeness error, and observation operator error, with some portion of this error being correlated in time and space or possibly between data types. Data assimilation systems are designed to account for random, uncorrelated errors, but are not yet adept at handling correlated errors; as a result, the correlated errors are more readily incorporated into the analysis increment by the data assimilation system than uncorrelated errors. In this work, the role of correlated observation errors in modifying the behaviour of the National Aeronautics and Space Administration Global Modeling and Assimilation Office (NASA/GMAO) OSSE framework is investigated. The effects on analysis increment, analysis error, forecast errors and observation impacts of including or neglecting correlated simulated errors is explored. The use of correlated observations for calibration and validation of the OSSE is also discussed.

Assimilation of Satellite Microwave Observations over the Rainbands of Tropical Cyclones

AbstractA novel Bayesian Monte Carlo integration (BMCI) technique was developed to retrieve geophysical variables from satellite microwave radiometer data in the presence of tropical cyclones. The BMCI technique includes three steps: generating a stochastic database, simulating satellite brightness temperatures using a radiative transfer model, and retrieving geophysical variables such as profiles of temperature, relative humidity, and cloud liquid and ice water content from real observations. The technique also provides uncertainty estimates for each retrieval and can output the error covariance matrix of selected parameters. The measurements from the Advanced Technology Microwave Sounder (ATMS) on board Suomi National Polar-Orbiting Partnership (Suomi NPP) and the Global Precipitation Measurement (GPM) Microwave Imager (GMI) were used as input. A new technique was developed to correct the ATMS and GMI observations for the beam-filling effect, which is due to small-scale variability of precipitation and clouds when compared with the instrument footprint and also the nonlinear relation between the brightness temperature and precipitation. In addition, the assimilation of the BMCI retrievals into the NASA GEOS model is discussed for Hurricane Maria. The results show that assimilating the BMCI retrievals can influence the dynamical features of the cyclone, including a stronger warm core, a symmetric eye, and vertically aligned wind columns. Two possible factors that may limit the impact of the BMCI retrievals include 1) the resolution of the model (about 25 km), which was too coarse to show the potential of the BMCI data in improving the representation of tropical storms in the model forecast, and 2) the data assimilation system not being able to consider vertically correlated observation errors.