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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.

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 Introduction ...4490 Popular flavors of the EnKF algorithm ...4491 General description...4491 Stochastic and deterministic filters...4492 The stochastic filter...4492 The deterministic filter...4492 Sequential or local filters...4493 Sequential ensemble Kalman filters...4493 The local ensemble transform Kalman filter...4494 Extended state vector...4494 Issues for the development of algorithms...4495 Use of small ensembles ...4495 Monte Carlo methods...4495 Validation of reliability...4497 Use of group filters with no inbreeding...4498 Sampling error due to limited ensemble size: The rank problem...4498 Covariance localization...4499 Localization in the sequential filter...4499 Localization in the LETKF...4499 Issues with localization...4500 Summary...4501 Methods to increase ensemble spread ...4501 Covariance inflation...4501 Additive inflation...4501 Multiplicative inflation...4502 Relaxation to prior ensemble information...4502 Issues with inflation...4503 Diffusion and truncation...4503 Error in physical parameterizations...4504 Physical tendency perturbations...4504 Multimodel, multiphysics, and multiparameter approaches...4505 Future directions...4505 Realism of error sources...4506 Balance and length of the assimilation window ...4506 The need for balancing methods...4506 Time-filtering methods...4506 Toward shorter assimilation windows...4507 Reduction of sources of imbalance...4507 Regional data assimilation ...4508 Boundary conditions and consistency across multiple domains...4509 Initialization of the starting ensemble...4510 Preprocessing steps for radar observations...4510 Use of radar observations for convective-scale analyses...4511 Use of radar observations for tropical cyclone analyses...4511 Other issues with respect to LAM data assimilation...4511 The assimilation of satellite observations ...4512 Covariance localization...4512 Data density...4513 Bias-correction procedures...4513 Impact of covariance cycling...4514 Assumptions regarding observational error...4514 Recommendations regarding satellite observations...4515 Computational aspects ...4515 Parameters with an impact on quality...4515 Overview of current parallel algorithms...4516 Evolution of computer architecture...4516 Practical issues...4517 Approaching the gray zone...4518 Summary...4518 Hybrids with variational and EnKF components ...4519 Hybrid background error covariances...4519 E4DVar with the α control variable...4519 Not using linearized models with 4DEnVar...4520 The hybrid gain algorithm...4521 Open issues and recommendations...4521 Summary and discussion ...4521 Stochastic or deterministic filters...4522 The nature of system error...4522 Going beyond the synoptic scales...4522 Satellite observations...4523 Hybrid systems...4523 Future of the EnKF...4523 APPENDIX A ...4524 Types of Filter Divergence ...4524 Classical filter divergence...4524 Catastrophic filter divergence...4524 APPENDIX B ...4524 Systems Available for Download ...4524 References ...4525

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.

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.

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.

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.

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° 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.

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.

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.

This study explores the spatial and temporal changes in tropical cyclone (TC) thermodynamic and dynamic structures before, near, and during rapid intensification (RI) under different vertical wind shear conditions through four sets of convection-permitting ensemble simulations. A composite analysis of TC structural evolution is performed by matching the RI onset time of each member. Without background flow, the axisymmetric TC undergoes a gradual strengthening of the inner-core vorticity and warm core throughout the simulation. In the presence of moderate environmental shear (5–6 m s −1 ), both the location and magnitude of the asymmetries in boundary layer radial flow, relative humidity, and vertical motion evolve with the tilt vector throughout the simulation. A budget analysis indicates that tilting is crucial to maintaining the midlevel vortex while stretching and vertical advection are responsible for the upper-level vorticity generation before RI when strong asymmetries arise. Two warm anomalies are observed before the RI onset when the vortex column is tilted. When approaching the RI onset, these two warm anomalies gradually merge into one. Overall, the most symmetric vortex structure is found near the RI onset. Moderately sheared TCs experience an adjustment period from a highly asymmetric structure with updrafts concentrated at the down-tilt side before RI to a more axisymmetric structure during RI as the eyewall updrafts develop. This adjustment period near the RI onset, however, is found to be the least active period for deep convection. TC development under a smaller environmental shear (2.5 m s −1 ) condition displays an intermediate evolution between ensemble experiments with no background flow and with moderate shear (5–6 m s −1 ).