Variational Quality Control Research Articles

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.

Assessing the benefit of variational quality control for assimilating Aeolus Mie and Rayleigh wind profiles in NOAA's global forecast system during tropical cyclones

AbstractIn this article, we show a “proof‐of‐concept” study to assess the utility of a variational quality control algorithm in increasing the number of assimilated Aeolus Mie‐cloudy and Rayleigh‐clear winds in National Oceanic and Atmospheric Administration (NOAA)'s global data assimilation and forecast system. The National Centers for Environmental Prediction (NCEP) Variational Quality Control (NCEP‐VQC) algorithm was tuned and applied during the minimization process. This type of quality control uses optimal control theory principles to treat outliers in the probability density function (PDF) of observational departure statistics, assuming that the observation errors follow a family of logistic distributions. In the case of Aeolus Mie‐cloudy and Rayleigh‐clear winds, the NCEP‐VQC algorithm permitted the relaxation of the gross error and one of the recommended ESA quality controls (reject Rayleigh‐clear observations below 850 hPa), assigned adaptive observation weights ranging from 0 to 1, and led to an increase in the number of retained Aeolus observations for the calculation of global analyses, which in turn improved the verification statistics on analyzed tropical storms This article discusses the advantage of implementing the NCEP‐VQC algorithm in the Aeolus data assimilation, the benefits of retaining more wind profiles that contribute to the analysis calculation, and shows improvements in the initialization and short‐term forecasts on several tropical cyclone cases.

Variational quality control of non-Gaussian innovations and its parametric optimizations for the GRAPES m3DVAR system

Variational quality control of non-Gaussian innovations and its parametric optimizations for the GRAPES m3DVAR system

Assimilation of AMSU-A in All-Sky Conditions

Abstract Radiances from microwave temperature sounders have been assimilated operationally at ECMWF for two decades, but observations significantly affected by clouds and precipitation have been screened out. Extending successful assimilation beyond clear-sky scenes is a challenge that has taken several years of development to achieve. In this paper we describe the all-sky treatment of AMSU-A, which enables greater numbers of temperature sounding radiances to be used in meteorologically active parts of the troposphere. Successful all-sky assimilation required combining lessons learned from the clear-sky assimilation of AMSU-A with the approach initially developed for humidity-sensitive microwave radiances. This concerned particularly observation thinning, error modeling, and variational quality control. As a result of the move to all-sky assimilation, the forecast impact of AMSU-A now replicates and exceeds that of the previous clear-sky usage. This is shown via trials in comparison to the current ECMWF assimilation system, judged with respect to forecast scores and background fits to independent observations. Persistently cloudy regions and phenomena such as tropical cyclones are better sampled when assimilating AMSU-A in all-sky conditions, causing an increase of about 13% in used channel-5 radiances globally. These impacts are explored, with an emphasis on tropical cyclones in the 2019 season. Independent observations provide consistent evidence that representation of humidity is improved, for example, while extratropical Z500 forecasts are improved by about 0.5% out to at least day 2. On the strength of these results, assimilation of AMSU-A moved to all-sky conditions with the upgrade to IFS cycle 47R3 in October 2021.

Variational Quality Control of Non-Gaussian Innovations in the GRAPES m3DVAR System: Mass Field Evaluation of Assimilation Experiments

The existence of outliers can seriously influence the analysis of variational data assimilation. Quality control allows us to effectively eliminate or absorb these outliers to produce better analysis fields. In particular, variational quality control (VarQC) can process gray zone outliers and is thus broadly used in variational data assimilation systems. In this study, we derived the governing equations of two VarQC algorithms that utilize different contaminated Gaussian distributions (CGDs): Gaussian plus flat distribution and Huber norm distribution. As such, these VarQC algorithms can handle outliers that have non-Gaussian innovations. We then implemented these VarQC algorithms in the Global/Regional Assimilation and PrEdiction System (GRAPES) model-level three-dimensional variational data assimilation (m3DVAR) system. Tests using artificial observations indicated that the VarQC using the Huber distribution has stronger robustness for including outliers to improve posterior analysis than that of the VarQC using the Gaussian plus flat distribution. Furthermore, real observation experiments show that the distribution of observation analysis weights conform well with theory, indicating that the VarQC is effective in the GRAPES m3DVAR system. Subsequent case study and long-period data assimilation experiments show that the spatial distribution and amplitude of the observation analysis weights are related to the mass field’s (geopotential height and temperature) analysis increments. Compared to the control experiment, VarQC experiments have noticeably better posterior mass fields. Finally, the VarQC using the Huber distribution is superior to the VarQC using the Gaussian plus flat distribution, especially at the middle and lower levels.

Correlated observation error models for assimilating all-sky infrared radiances

Abstract. The benefit of hyperspectral infrared sounders to weather forecasting has been improved with the representation of inter-channel correlations in the observation error model. A further step would be to assimilate these observations in all-sky conditions. However, in cloudy skies, observation errors exhibit much stronger inter-channel correlations, as well as much larger variances, compared to clear-sky conditions. An observation error model is developed to represent these effects, building from the symmetric error models developed for all-sky microwave assimilation. The combination of variational quality control with correlated errors is also introduced. The new error model is tested in all-sky assimilation of seven water vapour sounding channels from the Infrared Atmospheric Sounding Interferometer (IASI). However, its initial formulation degrades both tropospheric and stratospheric analyses. To explain this, the eigendeparture and eigenjacobian are introduced as a way of understanding the effect of correlated observation errors in data assimilation. The trailing eigenvalues can be problematic because they strongly amplify high-order harmonic combinations of the water vapour channels, which could have at least three consequences. First, if there are small inter-channel biases, these can be greatly amplified. Second, the trailing eigenjacobians map onto features resembling gravity waves that the data assimilation may not be able to handle. Finally, these harmonic combinations can amplify trace sensitivities, for example, revealing a strong upper stratospheric sensitivity over high cloud in what are usually mid- to upper-tropospheric water vapour channels. A likely explanation is the sensitivity to gravity wave features that are present in the observations but hard for the data assimilation to handle. After reducing the sensitivity to the trailing eigenjacobians, the new error covariance matrix gives good results in all-sky infrared assimilation.

Variational quality control of hydrographic profile data with non-Gaussian errors for global ocean variational data assimilation systems

Quality control procedures aiming at identifying observations suspected of gross errors are an important component of modern ocean data assimilation systems. On the one hand, assimilating observations whose departures from the background state are large may result in detrimental analyses and compromise the stability of the ocean analysis system. On the other hand, the rejection of these observations may prevent the analysis from ingesting useful information, especially in areas of large variability. In this work, we investigate the quality control of in-situ hydrographic profiles through modifying the probability density function (PDF) of the observational errors and relaxing the assumption of Gaussian PDF. The new PDF is heavier-tailed than Gaussian, thus accommodating the assimilation of observations with large misfits, albeit with smaller weight given to them in the analysis. This implies a different observational term in the analysis equation, and an adaptive quality control procedure based on the innovation statistics themselves. Implemented in a global ocean variational data assimilation system at moderate horizontal resolution, the scheme proves robust and successful in assimilating more observations with respect to the simpler background quality check scheme. This leads to better skill scores against both conventional and satellite observing systems. This approach proves superior also to the case where no quality control is considered. Furthermore, the implementation considers switching on the modified cost function at the 10th iteration of the minimization so that innovation statistics are based on a good approximation of the analysis. Neglecting this strategy and turning on the variational quality control since the beginning of the minimization exhibits worse scores, qualitatively similar to those of the experiment without quality control, suggesting that in this case quality control procedures are too gentle. A specific study investigating the upper ocean salinity in the Tropical Atlantic ocean is also presented and confirms the ability of the new scheme in making a better use of the in-situ observing system.

Multivariate Minimum Residual Method for Cloud Retrieval. Part II: Real Observations Experiments

Abstract In Part I of this two-part paper, the multivariate minimum residual (MMR) scheme was introduced to retrieve profiles of cloud fraction from satellite infrared radiances and identify clear observations. In this paper it is now validated with real observations from the Atmospheric Infrared Sounder (AIRS) instrument. This new method is compared with the cloud detection scheme presented earlier by McNally and Watts and operational at the European Centre for Medium-Range Weather Forecasts (ECMWF). Cloud-top pressures derived from both algorithms are comparable, with some differences at the edges of the synoptic cloud systems. The population of channels considered as clear is less contaminated with residual cloud for the MMR scheme. Further procedures, based on the formulation of the variational quality control, can be applied during the variational analysis to reduce the weight of observations that have a high chance of being contaminated by cloud. Finally, the MMR scheme can be used as a preprocessing step to improve the assimilation of cloud-affected infrared radiances.

On the use of a Huber norm for observation quality control in the ECMWF 4D‐Var

This article describes a number of important aspects that need to be considered when designing and implementing an observation quality control scheme in an NWP data assimilation system. It is shown how careful evaluation of innovation statistics provides valuable knowledge about the observation errors and help in the selection of a suitable observation error model. The focus of the article is on the statistical specification of the typical fat tails of the innovation distributions. In observation error specifications, like the one used previously at ECMWF, it is common to assume outliers to represent gross errors that are independent of the atmospheric state. The investigations in this article show that this is not a good assumption for almost all observing systems used in today's data assimilation systems. It is found that a Huber norm distribution is a very suitable distribution to describe most innovation statistics, after discarding systematically erroneous observations. The Huber norm is a robust method, making it safer to include outlier observations in the analysis step. Therefore the background quality control can safely be relaxed. The Huber norm has been implemented in the ECMWF assimilation system for in situ observations. The design, implementation and results from this implementation are described in this article. The general impact of using the Huber norm distribution is positive, compared to the previously used variational quality control method which gave virtually no weight to outliers. Case‐studies show how the method improves the use of observations, especially for intense cyclones and other extreme events. It is also discussed how the Huber norm distribution can be used to identify systematic problems with observing systems.

Validation of Two-Dimensional Variational Ambiguity Removal on SeaWinds Scatterometer Data

Abstract A two-dimensional variational ambiguity removal technique (2DVAR) is presented. It first makes an analysis based on the ambiguous scatterometer wind vector solutions and a model forecast, and next selects the ambiguity closest to the analysis as solution. 2DVAR is applied on SeaWinds scatterometer data and its merits for nowcasting applications are shown in a general statistical comparison with model forecasts and buoy observations, and in a number of case studies. The sensitivity of 2DVAR to changes in the parameters of its underlying error model is studied. It is shown that observational noise in the nadir swath of SeaWinds is effectively suppressed by application of 2DVAR in combination with the multisolution scheme (MSS). MSS retains the local wind vector probability density function after inversion, rather than only a limited number of ambiguous solutions. As a consequence, the influence of the background increases, but this can be mitigated by switching off variational quality control. A case study on an extratropical cyclone of hurricane force intensity observed with SeaWinds at 25-km resolution shows that reliable wind estimates can be obtained for wind speeds up to 40 m s−1 and more. At 25 km, the results of 2DVAR with MSS compare better with buoy measurements than with the ECMWF model. At 100-km resolution this is reversed, proving that 2DVAR retrieves small-scale features absent in the ECMWF model.

Application of Nonlinear Constraints in a Three-Dimensional Variational Ocean Analysis

Two kinds of nonlinear constraints, not previously studied in oceanography, have been adopted with the Preconditioned Optimizing Utility for Large-dimensional analyses (POpULar) in a three-dimensional oceanic variational analysis in the equatorial Pacific. One is the constraint for the variational Quality Control (QC) procedure and the other is used to avoid density and temperature inversions. Estimation of the large heat content anomaly in the upper ocean related to El Nino and La Nina phenomena is improved with the variational QC. For example, it prevents unusual but correct observation data on the thermocline deepening in the 1997/98 El Nino from being ignored. As a result, it improves the temperature field estimation in the eastern equatorial Pacific. The constraint for avoiding inversions prevents the low salinity layer at the surface and the barrier layer in the eastern equatorial Pacific in the El Nino period from being destroyed by the convective adjustment procedure performed after minimizing the cost function. Incorporating nonlinear constraints in variational analyses is thus a strong candidate for increasing the accuracy of analysis.

Three-dimensional variational data assimilation for a limited area model

A 3-dimensional variational data assimilation (3D-Var) scheme for the High Resolution Limited Area Model (HIRLAM) forecasting system is described. The HIRLAM 3D-Var is based on the minimisation of a cost function that consists of one term, Jb, which measures the distance between the resulting analysis and a background field, in general a short-range forecast, and another term, Jo, which measures the distance between the analysis and the observations. This paper is concerned with Jo and the handling of observations, while the companion paper by Gustafsson et al. (2001) is concerned with the general 3D-Var formulation and with the Jb term. Individual system components, such as the screening of observations and the observation operators, and other issues, such as the parallelisation strategy for the computer code, are described. The functionality of the observation quality control is investigated and the 3D-Var system is validated through data assimilation and forecast experiments. Results from assimilation and forecast experiments indicate that the 3D-Var assimilation system performs significantly better than two currently used HIRLAM systems, which are based on statistical interpolation. The use of all significant level data from multilevel observation reports is shown to be one factor contributing to the superiority of the 3D-Var system. Other contributing factors are most probably the formulation of the analysis as a single global problem, the use of non-separable structure functions and the variational quality control, which accounts for non-Gaussian observation errors.

Three-dimensional variational data assimilation for a limited area model : Part II: Observation handling and assimilation experiments

A 3-dimensional variational data assimilation (3D-Var) scheme for the High Resolution Limited Area Model (HIRLAM) forecasting system is described. The HIRLAM 3D-Var is based on the minimisation of a cost function that consists of one term, Jb which measures the distance between the resulting analysis and a background field, in general a short-range forecast, and another term, Jo which measures the distance between the analysis and the observations. This paper is concerned with Jo term and the handling of observations, while the companion paper by Gustafsson et al. (2001) is concerned with the general 3D-Var formulation and with the Jb. Individual system components, such as the screening of observations and the observation operators, and other issues, such as the parallelisation strategy for the computer code, are described. The functionality of the observation quality control is investigated and the 3D-Var system is validated through data assimilation and forecast experiments. Results from assimilation and forecast experiments indicate that the 3D-Var assimilation system performs significantly better than two currently used HIRLAM systems, which are based on statistical interpolation. The use of all significant level data from multilevel observation reports is shown to be one factor contributing to the superiority of the 3D-Var system. Other contributing factors are most probably the formulation of the analysis as a single global problem, the use of non-separable structure functions and the variational quality control, which accounts for non-Gaussian observation errors.

Variational quality control

Variational quality control

Variational quality control

AbstractWe describe the implementation of variational quality control in the operational four‐dimensional variational data assimilation scheme at the European Centre for Medium‐Range Weather Forecasts (ECMWF). the quality control takes place during the iterative solution of the variational analysis problem itself, rather than in a separate step prior to the main analysis. This ensures that the quality control is consistent with the analysis in terms of error statistics, background and model constraints, in particular. All observational data are used and quality‐controlled simultaneously. the probability of gross error is computed for each observation, given the preliminary analysis at each iteration. the weight of each observation is smoothly decreased with increased likelihood for gross error. the formulation, the implementation details and results from data assimilation and forecast experiments are presented.

Bayesian quality control using multivariate normal distributions

AbstractAn expression for the probability density of any distribution of observed values (given background values of known accuracy) is derived from the properties of multivariate normal distributions. This is used in the quality control of observations—‘good’ and ‘bad’ observations are assumed to have errors from a normal distribution and from a distribution giving no useful information respectively.Three Methods of quality control are presented and compared; two of these are based on the probability density derived above, and the third is based on a related maximum probability analysis. They differ in the optimality principal used: Individual Quality Control finds the most likely quality (i.e. good or bad) for each observation, given information from all the others; Simultaneous quality Control finds the most likely combination of qualities; while Variational Quality Control is based on a variational analysis which finds the most likely true values. The quality control should be considered as part of the ‘analysis’ process of using the observations; these approaches to quality control are considered as approximations to a system giving the ‘best’ analysis, based on minimizing a Bayesian loss function. Approximation are also necessary in their practical implementations; the effect of these on various operational schemes is discussed.The multi‐observation framework used includes the ‘background’ check as a special case, and it is extended to deal with observations with common sources of gross error. Applications to multi‐level checks, bias checks and checks for known error patterns are sketched.As a by‐product the standard statistical interpolation formulae are derived from the properties of normal distributions, thus demonstrating the implicit dependence of statistical interpolation on the normal distribution.