4D-Var System Research Articles

Estimating Forecast Error Covariances for Strongly Coupled Atmosphere–Ocean 4D-Var Data Assimilation

Strongly coupled data assimilation emulates the real-world pairing of the atmosphere and ocean by solving the assimilation problem in terms of a single combined atmosphere–ocean state. A significant challenge in strongly coupled variational atmosphere–ocean data assimilation is a priori specification of the cross covariances between the errors in the atmosphere and ocean model forecasts. These covariances must capture the correct physical structure of interactions across the air–sea interface as well as the different scales of evolution in the atmosphere and ocean; if prescribed correctly, they will allow observations in one medium to improve the analysis in the other. Here, the nature and structure of atmosphere–ocean forecast error cross correlations are investigated using an idealized strongly coupled single-column atmosphere–ocean 4D-Var assimilation system. Results are presented from a set of identical twin–type experiments that use an ensemble of coupled 4D-Var assimilations to derive estimates of the atmosphere–ocean error cross correlations. The results show significant variation in the strength and structure of cross correlations in the atmosphere–ocean boundary layer between summer and winter and between day and night. These differences provide a valuable insight into the nature of coupled atmosphere–ocean correlations for different seasons and points in the diurnal cycle.

Impact of GPS-RO Data Assimilation in 3DVAR System on the Typhoon Event

Impact of GPS-RO Data Assimilation in 3DVAR System on the Typhoon Event

Application of Physical Filter Initialization in 4DVar

Abstract Generally, the results of data assimilation are not well balanced dynamically due to errors in background, observations, or the model itself. So, initialization methods have been introduced to remove spurious gravity waves from the analysis. One of the initialization methods is digital filter initialization (DFI), which has been used in operational forecast systems, though its physical meaning is not well understood. Other methods eliminate high-frequency noise in optimized initial conditions by introducing physical constraints, such as the model constraint scheme, which minimizes the time tendency of model variables. In this study, a physical filter initialization (PFI) scheme, based on the model constraint scheme, is implemented in the four-dimensional variational data assimilation (4DVar) system of the Weather Research and Forecasting (WRF) Model. The impacts of the PFI scheme are examined by both single-observation and real-data experiments. The results indicate that the PFI scheme can eliminate high-frequency noise effectively, obtain flow-dependent analysis increments, and shorten forecast spinup time. Consequently, the precipitation forecast is improved to a certain extent, especially during the first few hours thanks to the shorter spinup time.

Observing System Experiments in a 3DVAR Data Assimilation System at CPTEC/INPE

Abstract The Center for Weather Forecast and Climate Studies [Centro de Previsão e Tempo e Estudos Climáticos (CPTEC)] at the Brazilian National Institute for Space Research [Instituto Nacional de Pesquisas Espaciais (INPE)] has recently operationally implemented a three-dimensional variational data assimilation (3DVAR) scheme based on the Gridpoint Statistical Interpolation analysis system (GSI). Implementation of the GSI system within the atmospheric global circulation model from CPTEC/INPE (AGCM-CPTEC/INPE) is hereafter referred to as the Global 3DVAR (G3DVAR) system. The results of an observing system experiment (OSE) measuring the impacts of radiosonde, satellite radiance, and GPS radio occultation (RO) data on the new G3DVAR system are presented here. The observational impact of each of these platforms was evaluated by measuring the degradation of the geopotential height anomaly correlation and the amplification of the RMSE of the wind. Losing the radiosonde, GPS RO, and satellite radiance data in the OSE resulted in negative impacts on the geopotential height anomaly correlations globally. Nevertheless, the strongest impacts were found over the Southern Hemisphere and South America when satellite radiance data were withheld from the data assimilation system.

Assessing the Impact of Surface and Wind Profiler Data on Fog Forecasting Using WRF 3DVAR: An OSSE Study on a Dense Fog Event over North China

AbstractBecause fog is a high-impact weather phenomenon, there has been increased demand for its accurate prediction. Both surface data and wind profiler data possess great potential for improved fog prediction. This study aimed to quantitatively assess the impact of surface and wind profiler data on fog prediction in terms of their spatial resolutions and distributions and also to assess the relative effect of these two types of observations. A dense fog event in northern China that occurred on 20 February 2007 was studied using the Weather Research and Forecasting (WRF) Model’s three-dimensional variational data assimilation (3DVAR) system with observing system simulation experiments (OSSE). The results indicated that the incorporation of surface data has an obvious positive impact on fog forecasts, especially with respect to effective assimilation of automated weather station data. Dense planetary boundary layer (PBL) wind profilers are more beneficial for fog forecasting than troposphere wind profilers, and an even spatial distribution over a large region is superior to a localized distribution. Surface data show greater benefit for fog forecasting than wind profiler data, with a 6.6% increase of skill score as a result of the improvement of near-surface thermal stratification. Moreover, combining both types of data greatly enhances fog predictive skill, with a 13.6% increase in skill score relative to the experiment assimilating only surface data, as a result of better dynamically balanced fields of thermodynamic and kinematic variables within the PBL with the assimilation of PBL wind profiler data.

A 4D-Var inversion system based on the icosahedral grid model (NICAM-TM 4D-Var v1.0) – Part 1: Offline forward and adjoint transport models

Abstract. A four-dimensional variational (4D-Var) method is a popular algorithm for inverting atmospheric greenhouse gas (GHG) measurements. In order to meet the computationally intense 4D-Var iterative calculation, offline forward and adjoint transport models are developed based on the Nonhydrostatic ICosahedral Atmospheric Model (NICAM). By introducing flexibility into the temporal resolution of the input meteorological data, the forward model developed in this study is not only computationally efficient, it is also found to nearly match the transport performance of the online model. In a transport simulation of atmospheric carbon dioxide (CO2), the data-thinning error (error resulting from reduction in the time resolution of the meteorological data used to drive the offline transport model) is minimized by employing high temporal resolution data of the vertical diffusion coefficient; with a low 6-hourly temporal resolution, significant concentration biases near the surface are introduced. The new adjoint model can be run in discrete or continuous adjoint mode for the advection process. The discrete adjoint is characterized by perfect adjoint relationship with the forward model that switches off the flux limiter, while the continuous adjoint is characterized by an imperfect but reasonable adjoint relationship with its corresponding forward model. In the latter case, both the forward and adjoint models use the flux limiter to ensure the monotonicity of tracer concentrations and sensitivities. Trajectory analysis for high CO2 concentration events are performed to test adjoint sensitivities. We also demonstrate the potential usefulness of our adjoint model for diagnosing tracer transport. Both the offline forward and adjoint models have computational efficiency about 10 times higher than the online model. A description of our new 4D-Var system that includes an optimization method, along with its application in an atmospheric CO2 inversion and the effects of using either the discrete or continuous adjoint method, is presented in an accompanying paper Niwa et al.(2016).

Background error covariances for a BlendVar assimilation system

We propose a new climatological background error covariance matrix suitable for the so-called BlendVar scheme, which deals with a problem on how to best preserve large-scale information of the global coupling system in the high-resolution limited area model (LAM) analysis. The BlendVar scheme is composed from a Digital Filter (DF) Blending step, treating the inclusion of the global model analysis, and from high resolution 3D-Var. The new background error covariance matrix forces 3D-Var to act mainly at smaller scales. We created a LAM assimilation ensemble forecasting system, where the DF Blending step is present, to sample the new matrix. To build and demonstrate properties of such a background error covariance matrix, we use the high-resolution model ALADIN coupled to the global model ARPEGE. The DF Blending step is taking advantage of ARPEGE 4D-Var assimilation system while 3D-Var is improving the small-scale part of ALADIN analysis. We assess the impact of using the new background error covariances in the BlendVar scheme with the full data assimilation cycle over the period of one month. We also compare performance of the new BlendVar set-up with respect to DF Blending and 3D-Var used alone. Objective scores with respect to radiosonde and aircraft observations favour the BlendVar scheme with the newly specified background error statistics.

Improvements of storm surge forecasting in the Gulf of Venice exploiting the potential of satellite data: the ESA DUE eSurge-Venice project

ABSTRACTThe northern Adriatic Sea is affected by storm surges, which often cause the flooding in Venice and the surrounding areas. We present the results of the eSurge-Venice project, funded by the European Space Agency (ESA) in the framework of its Data User Element programme: the project was aimed to demonstrate the potential of satellite data in improving storm surge forecasting, with focus on the Gulf of Venice. The satellite data used were scatterometer wind and altimeter sea level height. Hindcast experiments were conducted to assess the sensitivity of a storm surge model to a model wind forcing modified with scatterometer data and to altimeter retrievals assimilated with a dual 4D-Var system. The modified model wind forcing alone was responsible for a reduction of the mean difference between modelled and observed maximum surge peaks from −15.1 to −8.2 cm, while combining together scatterometer and altimeter data the mean difference further reduced to −6.0 cm. In terms of percent, the improvements in the reduction on the mean differences between modelled and observed surge peaks reaches 46% using only the scatterometer data, and 60% using both scatterometer and altimeter data.

Impact of 3D Var GSI-ENKF hybrid data assimilation system

The hybrid two-way coupled 3DEnsVar assimilation system was tested with the NCMRWF global data assimilation forecasting system. At present, this system consists of T574L64 deterministic model and the grid-point statistical interpolation analysis scheme. In this experiment, the analysis system is modified with a two-way coupling with an 80 member Ensemble Kalman Filter of T254L64 resolution and runs are carried out in parallel to the operational system for the Indian summer monsoon season (June–September) for the year 2015 to study its impact. Both the assimilation systems are based on NCEP GFS system. It is found that hybrid assimilation marginally improved the quality of the forecasts of all variables over the deterministic 3D Var system, in terms of statistical skill scores and also in terms of circulation features. The impact of the hybrid system in prediction of extreme rainfall and cyclone track is discussed.

Towards the assimilation of all-sky microwave radiances from the SAPHIR humidity sounder in a limited area NWP model over tropical regions

Microwave radiances from the humidity sounder SAPHIR at 183GHz onboard the MEGHA-TROPIQUES satellite are simulated in cloudy and rainy conditions (all-sky radiances) using short-range forecasts from the operational limited area model ALADIN-Réunion over the Indian Ocean. The simulation of SAPHIR radiances uses cloud and precipitation profiles from the moist physical parameterizations of ALADIN-Réunion describing deep convection and large-scale precipitation, that are coupled to the fast radiative transfer model RTTOV-SCATT accounting for scattering by hydrometeors. Sensitivity studies show that within cloud systems the SAPHIR sounder is particularly sensitive to solid precipitating hydrometeors. An optimal choice of scattering properties for snow particles is undertaken by a systematic comparison of simulated and observed SAPHIR radiances over a 1-month period in February 2012. This choice has required defining a criterion for rain occurrence from SAPHIR radiances that has been calibrated with the TMPA 3B40RT surface precipitation rate product. Finally, a retrieval technique based on Bayesian inversion is proposed to derive atmospheric profiles within clouds to be assimilated in the ALADIN 3D-Var system in a forthcoming study. The retrieved profiles are evaluated through the simulation of radiances from the microwave imager MADRAS that also flew on MEGHA-TROPIQUES.

Atmosphere data assimilation system for the Siberian region with the WRF-ARW model and three-dimensional variational analysis WRF 3D-Var

The system of the cyclic assimilation of data on atmospheric conditions used in the West Siberian Administration for Hydrometeorology and Environmental Monitoring is described. It is based on the WRF-ARW mesoscale atmospheric model and on the WRF 3D-Var system of the three-dimensional variational analysis of data. The system is verified when the first approximation data (6-hour forecast) and WRF-ARW forecasts with the lead time up to 24 hours are compared with the observational data. The problems of assimilation of observations from the AMSU-A and AIRS satellite instruments are considered. The effect of using AMSU-A and AIRS for the analysis in the Novosibirsk region is estimated. The experiments demonstrated that the cyclic data assimilation system operates successfully. The AMSU-A observations improve the quality of analyses and forecasts in winter. In summer the impact of satellite observations on the forecast skill scores is ambiguous. Good short-term forecasts are provided by the initial conditions obtained using the system of detailing of the NCEP large-scale analysis.

Exploiting the Potential of Satellite Microwave Remote Sensing to Hindcast the Storm Surge in the Gulf of Venice

The potential of active microwave satellite observations of sea surface height (radar altimetry) and of sea surface wind (radar scatterometry) has been exploited for storm surge modeling purposes. The altimetry observations were assimilated into a storm surge model (SSM) with a dual 4D-Var system, in order to obtain the best possible surge level field as initial condition to reforecast runs. The scatterometer wind data were instead used to improve the accuracy of the wind fields of a global atmospheric model used as forcing to the SSM through a procedure that has been proved to be able to reduce the differences between the model winds and the scatterometer observations. Hindcast experiments were performed to test the sensitivity of the SSM to the altimetry data assimilation and to the modified wind forcing. Remarkable improvements of the storm surge level hindcast have been obtained for what concerns the modified model wind forcing, while encouraging results have been obtained with the altimeter data assimilation.

Assimilation of Flash Extent Data in the Variational Framework at Convection-Allowing Scales: Proof-of-Concept and Evaluation for the Short-Term Forecast of the 24 May 2011 Tornado Outbreak

AbstractThis work evaluates the performance of the assimilation of total lightning data within a three-dimensional variational (3DVAR) framework for the analysis and short-term forecast of the 24 May 2011 tornado outbreak using the Weather Research and Forecasting (WRF) Model at convection-allowing scales. Between the lifted condensation level and a fixed upper height, pseudo-observations for water vapor mass first are created based on either the flash extent densities derived from Oklahoma Lightning Mapping Array data or the lightning source densities derived from the Earth Networks pulse data, and then assimilated by the 3DVAR system. Assimilation of radar data with 3DVAR and a cloud analysis algorithm (RAD) also are performed as a baseline for comparison and in tandem with lightning to evaluate the added value of this lightning data assimilation (LDA) method.Given a scenario wherein the control experiment without radar or lightning data assimilation fails to accurately initiate and forecast the observed storms, the LDA and RAD yield comparable short-term forecast improvements. The RAD alone produces storms of similar strength to the observations during the first 30 min of forecast more rapidly than the LDA alone; however, the LDA is able to better depict individual supercellular features at 1-h forecast. When both the lightning and radar data are assimilated, the 30-min forecast showed noteworthy improvements over RAD in terms of the model’s ability to better resolve individual supercell structures and still maintained a 1-h forecast similar to that from the LDA. The results chiefly illustrate the potential value of assimilating total lightning data along with radar data.

Design Strategies of an Hourly Update 3DVAR Data Assimilation System for Improved Convective Forecasting

Abstract This study examines two strategies for improving the analysis of an hourly update three-dimensional variational data assimilation (3DVAR) system and the subsequent quantitative precipitation forecast (QPF). The first strategy is to assimilate synoptic and radar observations in different steps. This strategy aims to extract both large-scale and convective-scale information from observations typically representing different scales. The second strategy is to add a divergence constraint to the momentum variables in the 3DVAR system. This technique aims at improving the dynamic balance and suppressing noise introduced during the assimilation process. A detailed analysis on how the new techniques impact convective-scale QPF was conducted using a severe storm case over Colorado and Kansas during 8 and 9 August 2008. First, it is demonstrated that, without the new strategies, the QPF initialized with an hourly update analysis performs worse than its 3-hourly counterpart. The implementation of the two-step assimilation and divergence constraint in the hourly update system results in improved QPF throughout most of the 12-h forecast period. The diagnoses of the analysis fields show that the two-step assimilation is able to preserve key convective-scale as well as large-scale structures that are consistent with the development of the real weather system. The divergence constraint is effective in improving the balance between the momentum control variables in the analysis, which leads to less spurious convection and improved QPF scores. The improvements of the new techniques were further verified by eight convective cases in 2014 and shown to be statistically significant.

Mesoscale Hybrid Data Assimilation System based on JMA Nonhydrostatic Model

This paper discusses the benefits of using a hybrid ensemble Kalman filter and four-dimensional variational (4D-Var) data assimilation (DA) system rather than a 4D-Var system employing the National Meteorological Center (NMC, now known as NCEP) method (4D-Var-Bnmc) to predict severe weather events. An adjoint-based 4D-Var system was employed with a background error covariance matrix [Formula: see text] constructed from the NMC method and perturbations in a local ensemble transform Kalman filter system. The DA systems are based on the Japan Meteorological Agency’s nonhydrostatic model. To reduce the sampling noise, three types of implementation (the spatial localization, spectral localization, and neighboring ensemble approaches) were tested. The assimilation of a pseudosingle observation of sea level pressure located at a tropical cyclone (TC) center yielded analysis increments physically consistent with what is expected of a mature TC in the hybrid systems at the beginning of the assimilation window, whereas analogous experiments performed using the 4D-Var-Bnmc system did not. At the end, the structures of the 4D-Var-based increments became similar to one another, while the analysis increment by the 4D-Var-Bnmc system was broad in the horizontal direction. Realistic DA experiments showed that all of the hybrid systems provided initial conditions that yielded more accurate TC track and intensity forecasts than those achievable by the 4D-Var-Bnmc system. The hybrid systems also yielded some statistically significant improvements in forecasting local heavy rainfall events in terms of fraction skill scores when a 160 km × 160 km window size was used. The overall skills of the hybrid systems were relatively independent of the choice of implementation.

A Lightning Parameterization for the ECMWF Integrated Forecasting System

A new parameterization able to diagnose lightning flash densities is proposed for the ECMWF Integrated Forecasting System, including its tangent-linear and adjoint versions. Total lightning densities are expressed as a function of hydrometeors contents, convective available potential energy, and cloud-base height output by the convective parameterization. Potential future applications range from the computation of NOx emissions by lightning in atmospheric chemistry models, severe convection forecasting, and data assimilation. In this study, a decade-long experiment is used to calibrate the simulated global annual mean flash density against the LIS/Optical Transient Detector (OTD) climatological value. On the seasonal and continental scales, the new parameterization is shown to agree well with the LIS/OTD observations. In forecast mode, output lightning densities are found to be almost independent of the horizontal resolution used in the model. Decade-long experiments also show that the new parameterization gives better results overall than the main existing lightning parameterizations designed for global models. Sensitivity experiments using its adjoint version are also performed to assess its potential for the future assimilation of lightning observations in the ECMWF 4D-Var system.

Comparison of Hybrid Four-Dimensional Data Assimilation Methods with and without the Tangent Linear and Adjoint Models for Predicting the Life Cycle of Hurricane Karl (2010)

AbstractTwo four-dimensional hybrid data assimilation systems based on the Weather Research and Forecasting (WRF) Model are applied over the life cycle of Hurricane Karl (2010). One method uses a mix of ensemble- and climate-based background error covariance in a four-dimensional variational data assimilation (4DVar) system that uses an adjoint model to assimilate observations over a time window (denoted E4DVar). The second method approximates the function of linearized models in 4DVar with perturbations generated from an ensemble forecast using the full nonlinear model (denoted 4DEnVar). Ensemble perturbations in 4DEnVar provide a four-dimensional covariance, which is combined with a static climate-based covariance for performing the data assimilation. In cycling data assimilation experiments, analyses produced by both methods provide more accurate intensity forecasts than E3DVar, owing mostly to a better representation of moisture near the developing storm. Despite providing a computationally efficient alternative to E4DVar, predictions made from 4DEnVar analyses are less accurate than E4DVar for the tested case study. Numerical experiments using identical background error statistics in both schemes reveal differences in the mesoscale structure of the developing storm, which are suspected to be responsible for this result. In particular, 4DEnVar analyses contain a less intense inner-core circulation and lower column relative humidity than E4DVar at analysis times closest to Karl’s genesis, which lead to a persistent slow bias in intensifying the storm. These results suggest errors introduced in the linearization of the model for E4DVar may be less severe than errors introduced by the localization of time covariances. This study provides the first comparison of hybrid E4DVar and 4DEnVar for a tropical cyclone application.

A three-dimensional variational data assimilation system for the South China Sea: preliminary results from observing system simulation experiments

A three-dimensional variational data assimilation (3DVAR) system based on the Regional Ocean Modeling System (ROMS) is established for the South China Sea (SCS). A set of Observing System Simulation Experiments (OSSEs) are performed to evaluate the performance of this data assimilation system and investigate the impacts of different types of observations on representation of three-dimensional large-scale circulations and meso-scale eddies in the SCS. The pseudo-observations that are examined include sea surface temperatures (SSTs), sea surface heights (SSHs), sparse temperature/salinity (T/S) profiles, sea surface velocities (SSVs), and sea surface salinities (SSSs). The results show that SSHs can extend their impacts into the subsurface or even the deep ocean while other surface observations only have impacts within surface mixed layer. SSVs have similar impacts though confined to their spatial coverage, suggesting that SSVs could be a substitute of SSHs nearshore where SSHs are of poor quality. Despite their sparseness, the T/S profiles improve the representation of the temperature and salinity structures below the mixed layer, and a combination of T/S profiles with surface observations leads to a better representation of the meso-scale eddies. Based on the OSSE results, an affordable observing network for the SCS in the near future is proposed.

Analyses and forecasts of a tornadic supercell outbreak using a 3DVAR system ensemble

As part of NOAA’s “Warn-On-Forecast” initiative, a convective-scale data assimilation and prediction system was developed using the WRF-ARW model and ARPS 3DVAR data assimilation technique. The system was then evaluated using retrospective short-range ensemble analyses and probabilistic forecasts of the tornadic supercell outbreak event that occurred on 24 May 2011 in Oklahoma, USA. A 36-member multi-physics ensemble system provided the initial and boundary conditions for a 3-km convective-scale ensemble system. Radial velocity and reflectivity observations from four WSR-88Ds were assimilated into the ensemble using the ARPS 3DVAR technique. Five data assimilation and forecast experiments were conducted to evaluate the sensitivity of the system to data assimilation frequencies, in-cloud temperature adjustment schemes, and fixed- and mixed-microphysics ensembles. The results indicated that the experiment with 5-min assimilation frequency quickly built up the storm and produced a more accurate analysis compared with the 10-min assimilation frequency experiment. The predicted vertical vorticity from the moist-adiabatic in-cloud temperature adjustment scheme was larger in magnitude than that from the latent heat scheme. Cycled data assimilation yielded good forecasts, where the ensemble probability of high vertical vorticity matched reasonably well with the observed tornado damage path. Overall, the results of the study suggest that the 3DVAR analysis and forecast system can provide reasonable forecasts of tornadic supercell storms.

The Implementation of the Ice-Phase Microphysical Process into a Four-Dimensional Variational Doppler Radar Analysis System (VDRAS) and Its Impact on Parameter Retrieval and Quantitative Precipitation Nowcasting

Abstract The microphysical process of a cloud-scale model used by a four-dimensional Variational Doppler Radar Analysis System (VDRAS) is extended from its original warm rain parameterization scheme to a cold rain process containing ice and snow. The development of the adjoint equations for the additional control variables related to ice physics is accomplished by utilizing the existing four-dimensional variational (4DVar) minimization framework employed by VDRAS. Experiments are conducted to examine the accuracy of the new 4DVar system with the ice physics scheme implemented and to explore the impact of the ice-phase process on numerical simulations, parameter retrievals, and the model’s quantitative precipitation nowcasting (QPN) capability. It is shown that the ice-phase microphysical process can significantly alter the kinematic and thermodynamic structure of deep convection and provide a better description of the contents of the hydrometeors. During the 4DVar minimization, using the VDRAS-predicted freezing level after the previous assimilation cycle to replace the true but unknown 0°C line is found to be a feasible approach for separating the rain and snow and, at the same time, allowing the 4DVar minimization algorithm to converge to an optimal solution. A real case study from intensive observation period 8 of the 2008 Southwest Monsoon Experiment shows that, with the added ice-phase process, VDRAS is more capable of capturing the actual evolution of the reflectivity field than the original scheme. The model’s QPN skill is also improved significantly. Thus, the benefits of adding the ice-phase process into a 4DVar radar data assimilation system on the convective-scale weather analysis and forecast are demonstrated.