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Robert G. Nystrom
and
Falko Judt

Abstract

In addition to initial conditions, uncertainty in model physics can also influence the practical predictability of tropical cyclones. In this study, the influence that various magnitudes of uncertainty in the surface exchange coefficients of momentum (Cd ) and enthalpy (Ck ) can have on an otherwise highly predictable major hurricane (Hurricane Patricia) is compared with that resulting from climatological environmental initial condition uncertainty and the intrinsic limit for this case. As the systematic uncertainty in Cd and Ck is reduced from 40% to 1%, the simulated uncertainty in the intensity and structure is substantially reduced and approaches the intrinsic limit when uncertainty is reduced to 1%. In addition, the forecasted intensity and structure uncertainty only becomes less than that resulting from climatological environmental initial condition uncertainty once the systematic uncertainty in Cd and Ck is reduced to ∼10%, highlighting the strong influence of model error in limiting TC predictability. If Cd and Ck are perturbed stochastically, instead of systematically, it is shown that the influence on the simulated intensity and structure is negligible and nearly identical to the intrinsic limit, regardless of the magnitude of the stochastic Cd and Ck perturbations. While the magnitude of the stochastic Cd and Ck perturbations are comparable to the systematic perturbations, the stochastic perturbations are shown to not substantially perturb the time-integrated inner-core fluxes of momentum or enthalpy that predominantly determine simulated tropical cyclone intensity. Last, it is shown that the kinetic energy error growth behavior varies with the radius, azimuthal wavenumber, and ensemble design.

Significance Statement

The air–sea energy exchange beneath hurricanes is highly uncertain but strongly influences intensity. In this study, the influences of different magnitudes of surface-exchange coefficient uncertainty on the simulated intensity of an intense hurricane is compared with that resulting from environmental initial condition uncertainty and the intrinsic predictability limit. The main takeaway is that current surface-exchange coefficient uncertainties result in larger intensity uncertainty than environmental initial condition uncertainty, and substantial improvements in predictions are possible if current surface-exchange coefficient uncertainties are reduced. Furthermore, it is shown that randomly perturbing the surface-exchange coefficients at each point in space and time is not the best approach to account for the influences of this uncertain physical process on hurricane prediction because it has minimal influence on the simulated intensity.

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J. B. Klemp
and
W. C. Skamarock

Abstract

For the numerical simulation of atmospheric flows that extend as high as the thermosphere, it is more appropriate to represent the upper boundary of the model domain as a material surface at constant pressure rather than one characterized by a rigid lid. Consequently, in adapting the Model for Prediction Across Scales (MPAS) for geospace applications, a modification of the height-based vertical coordinate is presented that permits the coordinate surfaces at upper levels to transition toward a constant pressure surface at the model’s upper boundary. This modification is conceptually similar to a terrain-following coordinate at low levels, but now modifies the coordinate surfaces at upper levels to conform to a constant pressure surface at the model top. Since this surface is evolving in time, the height of the upper boundary is adaptively adjusted to follow a designated constant pressure upper surface. This is accomplished by applying the hydrostatic equation to estimate the change in height along the boundary that is consistent with the vertical pressure gradient at the model top. This alteration in the vertical coordinate requires only minor modifications and little additional computational expense to the original height-based time-invariant terrain-following vertical coordinate employed in MPAS. The viability of this modified vertical coordinate formulation has been verified in a 2D prototype of MPAS for an idealized case of upper-level diurnal heating.

Significance Statement

Most atmospheric numerical models that use a height-based vertical coordinate employ a rigid lid at the top of the model domain. While a rigid lid works well for applications in the troposphere and stratosphere, it is not well suited for applications extending into the thermosphere where significant vertical expansion/contraction occurs due to deep heating/cooling of the atmosphere. This paper develops and tests a simple modification to the height-based coordinate formulation that allows the height of the upper boundary to adaptively follow a constant pressure surface. This added flexibility in the treatment of the upper domain boundary for height-based models may be particularly beneficial in facilitating their transition to a deep atmosphere configuration without significant retooling of the model numerics.

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Yueya Wang
,
Xiaoming Shi
,
Lili Lei
, and
Jimmy Chi-Hung Fung

Abstract

Remote sensing data play a critical role in improving numerical weather prediction (NWP). However, the physical principles of radiation dictate that data voids frequently exist in physical space (e.g., subcloud area for satellite infrared radiance or no-precipitation region for radar reflectivity). Such data gaps impair the accuracy of initial conditions derived from data assimilation (DA), which has a negative impact on NWP. We use the barotropic vorticity equation to demonstrate the potential of deep learning augmented data assimilation (DDA), which involves reconstructing spatially complete pseudo-observation fields from incomplete observations and using them for DA. By training a convolutional autoencoder (CAE) with a long simulation at a coarse “forecast” resolution (T63), we obtained a deep learning approximation of the “reconstruction operator,” which maps spatially incomplete observations to a model state with full spatial coverage and resolution. The CAE was applied to an incomplete streamfunction observation (∼30% missing) from a high-resolution benchmark simulation and demonstrated satisfactory reconstruction performance, even when only very sparse (1/16 of T63 grid density) observations were used as input. When only spatially incomplete observations are used, the analysis fields obtained from ensemble square root filter (EnSRF) assimilation exhibit significant error. However, in DDA, when EnSRF takes in the combined data from the incomplete observations and CAE reconstruction, analysis error reduces significantly. Such gains are more pronounced with sparse observation and small ensemble size because the DDA analysis is much less sensitive to observation density and ensemble size than the conventional DA analysis, which is based solely on incomplete observations.

Significance Statement

Data assimilation plays a critical role in improving the skills of modern numerical weather prediction by establishing accurate initial conditions. However, unobservable regions are common in observation data, particularly those derived from remote sensing. The nonlinear relationship between data from observable regions and the physical state of unobservable regions may impede DA efficiency. As a result, we propose that deep learning be used to improve data assimilation in such cases by reconstructing a spatially complete first guess of the physical state with deep learning and then applying data assimilation to the reconstructed field. Such deep learning augmentation is found effective in improving the accuracy of data assimilation, especially for sparse observation and small ensemble size.

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Rong Kong
,
Ming Xue
,
Chengsi Liu
,
Alexandre O. Fierro
, and
Edward R. Mansell

Abstract

In a prior study, GOES-R Geostationary Lightning Mapper (GLM) flash extent density (FED) data were assimilated using ensemble Kalman filter into a convection-allowing model for a mesoscale convective system (MCS) and a supercell storm. The FED observation operator based on a linear relation with column graupel mass was tuned by multiplying a factor to avoid large FED forecast bias. In this study, new observation operators are developed by fitting a third-order polynomial to GLM FED observations and the corresponding FED forecasts of graupel mass of the MCS and/or supercell cases. The new operators are used to assimilate the FED data for both cases, in three sets of experiments called MCSFit, SupercellFit, and CombinedFit, and their performances are compared with the prior results using the linear operator and with a reference simulation assimilating no FED data. The new nonlinear operators reduce the frequency biases (root-mean-square innovations) in the 0–4-h forecasts of the FED (radar reflectivity) relative to the results using the linear operator for both storm cases. The operator obtained by fitting data from the same case performs slightly better than fitting to data from the other case, while the operator obtained by fitting forecasts of both cases produce intermediate but still very similar results, and the latter is considered more general. In practice, a more general operator can be developed by fitting data from more cases.

Significance Statement

Prior studies found that assimilation of satellite lightning observation can benefit storm forecasts for up to 4 h. A linear lightning observation operator originally developed for assimilating pseudo-satellite lightning observations was tuned earlier through sensitivity experiments when assimilating real lightning data. However, the linear relation does not fit the model and observational data well and significant bias can exist. This study develops new lightning observation operators by fitting a high-order polynomial to satellite lightning observations and model-predicted quantities that directly relate to lightning. The new operator was found to reduce the frequency biases and root-mean-square innovations for lightning and radar reflectivity forecasts, respectively, up to several hours relative to the linear operator. The methodology can be applied to larger data samples to obtain a more general operator for use in operational data assimilation systems.

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Quinton A. Lawton
,
Sharanya J. Majumdar
,
Krista Dotterer
,
Christopher Thorncroft
, and
Carl J. Schreck III

Abstract

While considerable attention has been given to how convectively coupled Kelvin waves (CCKWs) influence the genesis of tropical cyclones (TCs) in the Atlantic Ocean, less attention has been given to their direct influence on African easterly waves (AEWs). This study builds a climatology of AEW and CCKW passages from 1981 to 2019 using an AEW-following framework. Vertical and horizontal composites of these passages are developed and divided into categories based on AEW position and CCKW strength. Many of the relationships that have previously been found for TC genesis also hold true for non-developing AEWs. This includes an increase in convective coverage surrounding the AEW center in phase with the convectively enhanced (“active”) CCKW crest, as well as a buildup of relative vorticity from the lower to upper troposphere following this active crest. Additionally, a new finding is that CCKWs induce specific humidity anomalies around AEWs that are qualitatively similar to those of relative vorticity. These modifications to specific humidity are more pronounced when AEWs are at lower latitudes and interacting with stronger CCKWs. While the influence of CCKWs on AEWs is mostly transient and short lived, CCKWs do modify the AEW propagation speed and westward-filtered relative vorticity, indicating that they may have some longer-term influences on the AEW life cycle. Overall, this analysis provides a more comprehensive view of the AEW–CCKW relationship than has previously been established, and supports assertions by previous studies that CCKW-associated convection, specific humidity, and vorticity may modify the favorability of AEWs to TC genesis over the Atlantic.

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Jinhui Xie
,
Pang-Chi Hsu
,
Pallav Ray
,
Kuiping Li
, and
Weidong Yu

Abstract

As rainfed agriculture remains India’s critical source of livelihood, improving our understanding of rainy season onset timing in the region is of great importance for a better prediction. Using a new gridded dataset of rainy season characteristics, we found a clear phase relationship between the Madden–Julian oscillation (MJO) and the onset timing of the rainy season over the Indian subcontinent. A significantly high probability of rainy season onset is observed when the MJO convection stays over the western-central Indian Ocean. On the other hand, the rainy season onset is infrequent when the MJO is over the Maritime Continent and western Pacific. The MJO-associated convective instability with anomalous warm and moist air in the lower troposphere appears and grows during the period 10 days prior to the onset of rainy season, and drops substantially after the start of rainy season, suggesting its role as a trigger of rainy season onset. In contrast, the low-frequency background state (LFBS) with a period > 90 days favors a convectively unstable stratification even after the onset of the rainy season, supporting the succeeding precipitation during the entire rainy season. Based on the scale-decomposed moisture budget diagnosis, we further found that the key processes inducing the abrupt transition from a dry to a wet condition come mainly from two processes: 1) convergence of LFBS moisture by MJO-related circulation perturbations and 2) advection of MJO moisture anomalies by the background cross-equatorial flow toward the Indian subcontinent. The results may help provide a better and longer lead-time prediction of the rainy season onset over the Indian subcontinent.

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Ching-Yuang Huang
,
Sheng-Hao Sha
, and
Hung-Chi Kuo

Abstract

The global model FV3GFS is used to simulate Typhoon Lekima (2019), which exhibited track deflection when approaching west-northwestward toward Taiwan. The model successfully simulates the observed northward deflection and the track deflection is produced by topographically induced wavenumber-1 flow with a pair of vorticity gyres around the typhoon center. The gyres tend to rotate counterclockwise about the typhoon center and thus induce an earlier northward and then westward movement. Azimuthal-mean kinetic energy budget of the typhoon indicates that the effect of Taiwan terrain modifies the correlation between the recirculating flow and pressure gradient force east of Taiwan, leading to a slight weakening of the typhoon during the later track deflection. The northward cyclonic deflection in general will be induced for a cyclone to move toward the central to northern terrain such as Lekima. The curvature of the northward cyclonic deflection, however, is large (small) for a northwestbound (nearly westbound) vortex depending on the track-topography-impinging angle. The curvature difference can be explained with the concept of recirculating flow, which is the flow splitting due to topography and rejoins the vortex to produce the wavenumber-1 asymmetry. The cyclonic track curvature of the northwestbound Lekima is larger than that of the westbound Maria (2018) in the FV3GFS simulations. This adds robustness to the conclusion that minor to moderate terrain-related track deflections can be well simulated by the FV3GFS global model near Taiwan.

Open access
Joël Stein
and
Fabien Stoop

Abstract

The neighborhood-based ensemble evaluation using the continuous ranked probability score is based on the pooling of the cumulative density function (CDF) for all the points inside a neighborhood. This methodology can be applied to the forecast CDF for measuring the predictive input of neighboring points in the center of the neighborhood. It can also be applied at the same time to forecast CDF and observed CDF so as to quantify the quality of the pooled ensemble forecast at the scale of the neighborhood. Fair versions of these two neighborhood scores are also defined in order to reduce their dependencies on the size of ensemble forecasts. The borderline case of deterministic forecasts is also explored so as to be able to compare them with ensemble forecasts. The information of these new scores is analyzed on idealized and real cases of rain accumulated during 3 h and of 2-m temperature forecast by four deterministic and probabilistic forecasting systems operational at Météo-France.

Open access
Andrea Zonato
,
Alberto Martilli
,
Pedro A. Jimenez
,
Jimy Dudhia
,
Dino Zardi
, and
Lorenzo Giovannini

Abstract

A new one-dimensional 1.5-order planetary boundary layer (PBL) scheme, based on the K–ε turbulence closure applied to the Reynolds-averaged Navier–Stokes (RANS) equations, is developed and implemented within the Weather Research and Forecasting (WRF) Model. The new scheme includes an analytic solution of the coupled equations for turbulent kinetic energy and dissipation rate. Different versions of the PBL scheme are proposed, with increasing levels of complexity, including a model for the calculation of the Prandtl number, a correction to the dissipation rate equation, and a prognostic equation for the temperature variance. Five different idealized cases are tested: four of them explore convective conditions, and they differ in initial thermal stratification and terrain complexity, while one simulates the very stable boundary layer case known as GABLS. For each case study, an ensemble of different large-eddy simulations (LES) is taken as reference for the comparison with the novel PBL schemes and other state-of-the-art 1- and 1.5-order turbulence closures. Results show that the new PBL K–ε scheme brings improvements in all the cases tested in this study. Specifically, the more significant are obtained with the turbulence closure including a prognostic equation for the temperature variance. Moreover, the largest benefits are obtained for the idealized cases simulating a typical thermal circulation within a two-dimensional valley. This suggests that the use of prognostic equations for dissipation rate and temperature variance, which take into account their transport and history, is particularly important with the increasing complexity of PBL dynamics.

Open access
Yanqiu Zhu
,
Ricardo Todling
, and
Nathan Arnold

Abstract

In this study, we have assessed the effectiveness of the use of existing observing systems in the lower troposphere in the GEOS hybrid–4DEnVar data assimilation system through a set of observing system experiments. The results show that microwave radiances have a large impact in the Southern Hemisphere and tropical ocean, but the large influence is mostly observed above 925 hPa and dissipates relatively quickly with longer forecast lead times. Conventional data information holds better in the forecast ranging from the surface to 100 hPa, depending on the field evaluated, in the Northern Hemisphere and lowest model levels in the tropics. Infrared radiances collectively have much less impact in the lower troposphere. Removing surface observations has small but persistent impact on specific humidity in the upper atmosphere, but small or negligible impact on planetary boundary layer (PBL) height and temperature. The model responses to the incremental analysis update (IAU) forcing are also analyzed. In the IAU assimilation window, the physics responds strongly to the IAU forcing in the lower troposphere, and the changes of physics tendency in the lower troposphere and hydrodynamics tendency in the mid- and upper troposphere are viewed as beneficial to the reduction of state error covariance. In the subsequent forecast, the model tendencies continue to deviate further from the original free forecast with forecast lead times around 300–400 hPa, but physics tendency has showed signs of returning to its original free forecast mechanisms at 1-day forecast in the lower troposphere.

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