This paper reviews the development of the ensemble Kalman filter (EnKF) for atmospheric data assimilation. Particular attention is devoted to recent advances and current challenges. The ...distinguishing properties of three well-established variations of the EnKF algorithm are first discussed. Given the limited size of the ensemble and the unavoidable existence of errors whose origin is unknown (i.e., system error), various approaches to localizing the impact of observations and to accounting for these errors have been proposed. However, challenges remain; for example, with regard to localization of multiscale phenomena (both in time and space). For the EnKF in general, but higher-resolution applications in particular, it is desirable to use a short assimilation window. This motivates a focus on approaches for maintaining balance during the EnKF update. Also discussed are limited-area EnKF systems, in particular with regard to the assimilation of radar data and applications to tracking severe storms and tropical cyclones. It seems that relatively less attention has been paid to optimizing EnKF assimilation of satellite radiance observations, the growing volume of which has been instrumental in improving global weather predictions. There is also a tendency at various centers to investigate and implement hybrid systems that take advantage of both the ensemble and the variational data assimilation approaches; this poses additional challenges and it is not clear how it will evolve. It is concluded that, despite more than 10 years of operational experience, there are still many unresolved issues that could benefit from further research. Contents 1. 1. Introduction...4490 2. 2. Popular flavors of the EnKF algorithm...4491 1. a. General description...4491 2. b. Stochastic and deterministic filters...4492 1. The stochastic filter...4492 2. The deterministic filter...4492 3. c. Sequential or local filters...4493 1. Sequential ensemble Kalman filters...4493 2. The local ensemble transform Kalman filter...4494 4. d. Extended state vector...4494 5. e. Issues for the development of algorithms...4495 3. 3. Use of small ensembles...4495 1. a. Monte Carlo methods...4495 2. b. Validation of reliability...4497 3. c. Use of group filters with no inbreeding...4498 4. d. Sampling error due to limited ensemble size: The rank problem...4498 5. e. Covariance localization...4499 1. Localization in the sequential filter...4499 2. Localization in the LETKF...4499 3. Issues with localization...4500 6. f. Summary...4501 4. 4. Methods to increase ensemble spread...4501 1. a. Covariance inflation...4501 1. Additive inflation...4501 2. Multiplicative inflation...4502 3. Relaxation to prior ensemble information...4502 4. Issues with inflation...4503 2. b. Diffusion and truncation...4503 3. c. Error in physical parameterizations...4504 1. Physical tendency perturbations...4504 2. Multimodel, multiphysics, and multiparameter approaches...4505 3. Future directions...4505 4. d. Realism of error sources...4506 5. 5. Balance and length of the assimilation window...4506 1. a. The need for balancing methods...4506 2. b. Time-filtering methods...4506 3. c. Toward shorter assimilation windows...4507 4. d. Reduction of sources of imbalance...4507 6. 6. Regional data assimilation...4508 1. a. Boundary conditions and consistency across multiple domains...4509 2. b. Initialization of the starting ensemble...4510 3. c. Preprocessing steps for radar observations...4510 4. d. Use of radar observations for convective-scale analyses...4511 5. e. Use of radar observations for tropical cyclone analyses...4511 6. f. Other issues with respect to LAM data assimilation...4511 7. 7. The assimilation of satellite observations...4512 1. a. Covariance localization...4512 2. b. Data density...4513 3. c. Bias-correction procedures...4513 4. d. Impact of covariance cycling...4514 5. e. Assumptions regarding observational error...4514 6. f. Recommendations regarding satellite observations...4515 8. 8. Computational aspects...4515 1. a. Parameters with an impact on quality...4515 2. b. Overview of current parallel algorithms...4516 3. c. Evolution of computer architecture...4516 4. d. Practical issues...4517 5. e. Approaching the gray zone...4518 6. f. Summary...4518 9. 9. Hybrids with variational and EnKF components...4519 1. a. Hybrid background error covariances...4519 2. b. E4DVar with the alpha control variable...4519 3. c. Not using linearized models with 4DEnVar...4520 4. d. The hybrid gain algorithm...4521 5. e. Open issues and recommendations...4521 10. 10. Summary and discussion...4521 1. a. Stochastic or deterministic filters...4522 2. b. The nature of system error...4522 3. c. Going beyond the synoptic scales...4522 4. d. Satellite observations...4523 5. e. Hybrid systems...4523 6. f. Future of the EnKF...4523 APPENDIX A...4524 Types of Filter Divergence...4524 1. a. Classical filter divergence...4524 2. b. Catastrophic filter divergence...4524 APPENDIX B...4524 Systems Available for Download...4524 References...4525
The NCEP–NCAR reanalysis, NCEP Climate Forecast System Reanalysis (CFSR), 40-yr ECMWF Re-Analysis (ERA-40), and interim ECMWF Re-Analysis (ERA-Interim) products are evaluated with sounding ...observations froman enhanced radiosonde network available every 6 h during the Tibetan Plateau Experiment (TIPEX) conducted from 10 May to 9 August 1998. This study uses more than 3000 high-quality, independent rawinsondes at 11 stations (which were not assimilated in any of the reanalyses), which represents the first time that such a comprehensive evaluation is performed to assess the quality of these four most widely used reanalysis products over this region, which is highest in the world and crucial to the global climate and weather.
Averaging over the entire three-month period, it is found that each reanalysis dataset produces mean values of temperature and horizontal winds consistent with the verifying soundings (indicating relatively small mean bias); however, there are considerable differences (biases) in the mean relative humidity. Onaverage, except for temperature at higher levels, both newer-generation reanalyses (CFSR and ERA-Interim) have smaller root-mean-square (RMS) error and bias than their predecessors (NCEP–NCAR and ERA-40). With some exceptions, the RMS errors of all variables for both CFSR and ERA-Interim (verifying with soundings) are similar in magnitude to the RMS difference between these two reanalyses, all of which are approximately twice as large as the corresponding observation errors. It is also found that there are strong diurnal variations in both RMS error and mean bias that differ greatly among different reanalyses and at different pressure levels.
Abstract
The skill of tropical cyclone intensity forecasts has improved slowly since such forecasts became routine, even though track forecast skill has increased markedly over the same period. In ...deciding whether or how best to improve intensity forecasts, it is useful to estimate fundamental predictability limits as well as sources of intensity error. Toward that end, the authors estimate rates of error growth in a “perfect model” framework in which the same model is used to explore the sensitivities of tropical cyclone intensity to perturbations in the initial storm intensity and large-scale environment. These are compared to estimates made in previous studies and to intensity error growth in real-time forecasts made using the same model, in which model error also plays an important role. The authors find that error growth over approximately the first few days in the perfect model framework is dominated by errors in initial intensity, after which errors in forecasting the track and large-scale kinematic environment become more pronounced. Errors owing solely to misgauging initial intensity are particularly large for storms about to undergo rapid intensification and are systematically larger when initial intensity is underestimated compared to overestimating initial intensity by the same amount. There remains an appreciable gap between actual and realistically achievable forecast skill, which this study suggests can best be closed by improved models, better observations, and superior data assimilation techniques.
Abstract
This study explores the impacts of assimilating all-sky infrared satellite radiances from Himawari-8, a new-generation geostationary satellite that shares similar remote sensing technology ...with the U.S. geostationary satellite GOES-16, for convection-permitting initialization and prediction of tropical cyclones with an ensemble Kalman filter (EnKF). This case studies the rapid intensification stages of Supertyphoon Soudelor (2015), one of the most intense tropical cyclones ever observed by Himawari-8. It is found that hourly cycling assimilation of the infrared radiance improves not only the estimate of the initial intensity, but also the spatial distribution of essential convective activity associated with the incipient tropical cyclone vortex. Deterministic convection-permitting forecasts initialized from the EnKF analyses are capable of simulating the early development of Soudelor, which demonstrates encouraging prospects for future improvement in tropical cyclone prediction through assimilating all-sky radiances from geostationary satellites such as Himawari-8 and GOES-16. A series of forecast sensitivity experiments are designed to systematically explore the impacts of moisture updates in the data assimilation cycles on the development and prediction of Soudelor. It is found that the assimilation of the brightness temperatures contributes not only to better constraining moist convection within the inner-core region, but also to developing a more resilient initial vortex, both of which are necessary to properly capture the rapid intensification process of tropical cyclones.
An empirical flow-dependent adaptive observation error inflation (AOEI) method is proposed for assimilating all-sky satellite brightness temperatures through observing system simulation experiments ...with an ensemble Kalman filter. The AOEI method adaptively inflates the observation error when the absolute difference (innovation) between the observed and simulated brightness temperatures is greater than the square root of the combined variance of the uninflated observational error variance and ensemble-estimated background error variance. This adaptive method is designed to limit erroneous analysis increments where there are large representativeness errors, as is often the case for cloudy-affected radiances, even if the forecast model and the observation operator (the radiative transfer model) are perfect. The promising performance of this newly proposed AOEI method is demonstrated through observing system simulation experiments assimilating all-sky brightness temperatures from GOES-R (now GOES-16) in comparison with experiments using an alternative empirical observation error inflation method proposed by Geer and Bauer. It is found that both inflation methods perform similarly in the accuracy of the analysis and in the containment of potential representativeness errors; both outperform experiments using a constant observation error without inflation. Besides being easier to implement, the empirical AOEI method proposed here also shows some advantage over the Geer–Bauer method in better updating variables at large scales. Large representative errors are likely to be compounded by unavoidable uncertainties in the forecast system and/or nonlinear observation operator (as for the radiative transfer model), in particular in the areas of moist processes, as will be the case for real-data cloudy radiances, which will be further investigated in future studies.
Through cloud-resolving simulations, this study examines the effect of vertical wind shear and system-scale flow asymmetry on the predictability of tropical cyclone (TC) intensity during different ...stages of the TC life cycle. A series of ensemble experiments is performed with varying magnitudes of vertical wind shear, each initialized with an idealized weak TC-like vortex, with small-scale, small-amplitude random perturbations added to the initial conditions. It is found that the environmental shear can significantly affect the intrinsic predictability of tropical cyclones, especially during the formation and rapid intensification stage. The larger the vertical wind shear, the larger the uncertainty in the intensity forecast, primarily owing to the difference in the timing of rapid intensification. In the presence of environmental shear, initial random noise may result in changes in the timing of rapid intensification by as much as 1-2 days through the randomness (and chaotic nature) of moist convection. Upscale error growth from differences in moist convection first alters the tilt amplitude and angle of the incipient tropical storms, which leads to significant differences in the timing of precession and vortex alignment. During the precession process, both the vertical tilt of the storm and the effective (local) vertical wind shear are considerably decreased after the tilt angle reaches 90 degree to the left of the environmental shear. The tropical cyclone intensifies immediately after the tilt and the effective local shear reach their minima. In some instances, small-scale, small-amplitude random noise may also limit the intensity predictability through altering the timing and strength of the eyewall replacement cycle.
Abstract
Errors in tropical cyclone intensity forecasts are dominated by initial-condition errors out to at least a few days. Initialization errors are usually thought of in terms of position and ...intensity, but here it is shown that growth of intensity error is at least as sensitive to the specification of inner-core moisture as to that of the wind field. Implications of this finding for tropical cyclone observational strategies and for overall predictability of storm intensity are discussed.
Abstract
Convection-permitting numerical experiments using the Weather Research and Forecasting (WRF) Model are performed to examine the diurnal cycles of land and sea breeze and its related ...precipitation over the south China coastal region during the mei-yu season. The focus of the analyses is a 10-day simulation initialized with the average of the 0000 UTC gridded global analyses during the 2007–09 mei-yu seasons (11 May–24 June) with diurnally varying cyclic lateral boundary conditions. Despite differences in the rainfall intensity and locations, the simulation verified well against averages of 3-yr ground-based radar, surface, and CMORPH observations and successfully simulated the diurnal variation and propagation of rainfall associated with the land and sea breeze over the south China coastal region. The nocturnal offshore rainfall in this region is found to be induced by the convergence line between the prevailing low-level monsoonal wind and the land breeze. Inhomogeneity of rainfall intensity can be found along the coastline, with heavier rainfall occurring in the region with coastal orography. In the night, the mountain–plain solenoid produced by the coastal terrain can combine with the land breeze to enhance offshore convergence. In the daytime, rainfall propagates inland with the inland penetration of the sea breeze, which can be slowed by the coastal mountains. The cold pool dynamics also plays an essential role in the inland penetration of precipitation and the sea breeze. Dynamic lifting produced by the sea-breeze front is strong enough to produce precipitation, while the intensity of precipitation can be dramatically increased with the latent heating effect.
Abstract
This study explores both the practical and intrinsic predictability of severe convective weather at the mesoscales using convection-permitting ensemble simulations of a squall line and bow ...echo event during the Bow Echo and Mesoscale Convective Vortex (MCV) Experiment (BAMEX) on 9–10 June 2003. Although most ensemble members—initialized with realistic initial condition uncertainties smaller than the NCEP Global Forecast System Final Analysis (GFS FNL) using an ensemble Kalman filter—forecast broad areas of severe convection, there is a large variability of forecast performance among different members, highlighting the limit of practical predictability. In general, the best-performing members tend to have a stronger upper-level trough and associated surface low, producing a more conducive environment for strong long-lived squall lines and bow echoes, once triggered. The divergence in development is a combination of a dislocation of the upper-level trough, surface low with corresponding marginal environmental differences between developing and nondeveloping members, and cold pool evolution by deep convection prior to squall line formation. To further explore the intrinsic predictability of the storm, a sequence of sensitivity experiments was performed with the initial condition differences decreased to nearly an order of magnitude smaller than typical analysis and observation errors. The ensemble forecast and additional sensitivity experiments demonstrate that this storm has a limited practical predictability, which may be further improved with more accurate initial conditions. However, it is possible that the true storm could be near the point of bifurcation, where predictability is intrinsically limited. The limits of both practical and intrinsic predictability highlight the need for probabilistic and ensemble forecasts for severe weather prediction.
An adaptive background error inflation (ABEI) method is proposed for assimilating all‐sky satellite brightness temperatures with an ensemble Kalman filter. This empirical cloud‐scene‐dependent ...covariance inflation method is designed to mitigate the model's difficulties in initiating convection in the observed cloudy regions where the background prior estimated from the ensemble mean incorrectly simulates clear‐sky conditions. This new approach calculates a spatially varying, flow‐dependent, multiplicative ensemble covariance inflation factor based on error statistics produced by a well‐constructed, off‐line observing system simulation experiment (OSSE) that assimilates similar all‐sky radiance observations but were generated by the model, in which case the truth is known for all the state variables and the assimilated radiances. The adaptive inflation factor is a linear function of a cloud parameter which is only applied to the observed cloudy regions where there are less or no cloud in the prior ensemble mean estimates. The performance of ABEI is evaluated through assimilating synthetic and real‐data all‐sky radiance experiments from the Advanced Baseline Imager on board GOES‐16 for Hurricanes Karl of 2010 and Harvey of 2017. Assimilation experiments with ABEI allow adaptive inflation of the ensemble covariance in the model‐simulated clear‐sky regions when there are observed clouds while avoiding unnecessarily large ensemble spread in other cloud scenarios. This new approach alleviates the difficulty in estimating the appropriate inflation factors in the model state space using the innovation statistics in the observation space (radiance) with a highly nonlinear observation operator. It serves as an alternative to existing methods using spatially varying adaptive inflations; their relative performance and potential combinations are to be further assessed in the future.
An adaptive background error inflation (ABEI) method is proposed to calculate a cloud‐scene‐dependent multiplicative covariance inflation factor, which is fully flow‐dependent and spatio‐temporally varying. ABEI is designed to alleviate the difficulty in estimating the inflation factors in the model state space using the innovation statistic in the observation space with a highly nonlinear observation operator. ABEI is found to help initiating convection from the incorrectly estimated clear‐sky conditions, in all‐sky satellite radiance assimilation with an ensemble Kalman filter.
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