Abstract
Understanding the predictability limit of day-to-day weather phenomena such as midlatitude winter storms and summer monsoonal rainstorms is crucial to numerical weather prediction (NWP). ...This predictability limit is studied using unprecedented high-resolution global models with ensemble experiments of the European Centre for Medium-Range Weather Forecasts (ECMWF; 9-km operational model) and identical-twin experiments of the U.S. Next-Generation Global Prediction System (NGGPS; 3 km). Results suggest that the predictability limit for midlatitude weather may indeed exist and is intrinsic to the underlying dynamical system and instabilities even if the forecast model and the initial conditions are nearly perfect. Currently, a skillful forecast lead time of midlatitude instantaneous weather is around 10 days, which serves as the practical predictability limit. Reducing the current-day initial-condition uncertainty by an order of magnitude extends the deterministic forecast lead times of day-to-day weather by up to 5 days, with much less scope for improving prediction of small-scale phenomena like thunderstorms. Achieving this additional predictability limit can have enormous socioeconomic benefits but requires coordinated efforts by the entire community to design better numerical weather models, to improve observations, and to make better use of observations with advanced data assimilation and computing techniques.
Limits of intrinsic versus practical predictability are studied through examining multiscale error growth dynamics in idealized baroclinic waves with varying degrees of convective instabilities. In ...the dry experiment free of moist convection, error growth is controlled primarily by baroclinic instability under which forecast accuracy is inversely proportional to the amplitude of the baroclinically unstable initial-condition error (thus the prediction can be continuously improved without limit through reducing the initial error). Under the moist environment with strong convective instability, rapid upscale growth from moist convection leads to the forecast error being increasingly less sensitive to the scale and amplitude of the initial perturbations when the initial-error amplitude is getting smaller; these diminishing returns may ultimately impose a finite-time barrier to the forecast accuracy (limit of intrinsic predictability and the so-called "butterfly effect"). However, if the initial perturbation is sufficiently large in scale and amplitude (as for most current-day operational models), the baroclinic growth of large-scale finite-amplitude initial error will control the forecast accuracy for both dry and moist baroclinic waves; forecast accuracy can be improved (thus the limit of practical predictability can be extended) through the reduction of initial-condition errors, especially those at larger scales. Regardless of the initial-perturbation scales and amplitude, the error spectrum will adjust toward the slope of the background flow. Inclusion of strong moist convection changes the mesoscale kinetic energy spectrum slope from -3 to ~-5/3. This change further highlights the importance of convection and the relevance of the butterfly effect to both the intrinsic and practical limits of atmospheric predictability, especially at meso- and convective scales.
This study investigates the October and November MJO events observed during the Cooperative Indian Ocean Experiment on Intraseasonal Variability in the Year 2011 (CINDY)/Dynamics of the MJO (DYNAMO) ...field campaign through cloud-permitting numerical simulations. The simulations are compared to multiple observational datasets. The control simulation at 9-km horizontal grid spacing captures the slow eastward progression of both the October and November MJO events in surface precipitation, outgoing longwave radiation, zonal wind, humidity, and large-scale vertical motion. The vertical motion shows weak ascent in the leading edge of the MJO envelope, followed by deep ascent during the peak precipitation stage and trailed by a broad second baroclinic mode structure with ascent in the upper troposphere and descent in the lower troposphere. Both the simulation and the observations also show slow northward propagation components and tropical cyclone–like vortices after the passage of the MJO active phase. Comparison with synthesized observations from the northern sounding array shows that the model simulates the passage of the two MJO events over the sounding array region well. Sensitivity experiments to SST indicate that daily SST plays an important role for the November MJO event, but much less so for the October event.
Analysis of the moist static energy (MSE) budget shows that both advection and diabatic processes (i.e., surface fluxes and radiation) contribute to the development of the positive MSE anomaly in the active phase, but their contributions differ by how much they lead the precipitation peak. In comparison to the observational datasets used here, the model simulation may have a stronger surface flux feedback and a weaker radiative feedback. The normalized gross moist stability in the simulations shows an increase from near-zero values to ∼0.8 during the active phase, similar to what is found in the observational datasets.
Abstract
With high-resolution mesoscale model simulations, the authors have confirmed a recent study demonstrating that convective systems, triggered in a horizontally homogeneous environment, are ...able to generate a background mesoscale kinetic energy spectrum with a slope close to −5/3, which is the observed value for the kinetic energy spectrum at mesoscales. This shallow slope can be identified at almost all height levels from the lower troposphere to the lower stratosphere in the simulations, implying a strong connection between different vertical levels. The present study also computes the spectral kinetic energy budget for these simulations to further analyze the processes associated with the creation of the spectrum. The buoyancy production generated by moist convection, while mainly injecting energy in the upper troposphere at small scales, could also contribute at larger scales, possibly as a result of the organization of convective cells into mesoscale convective systems. This latter injected energy is then transported by energy fluxes (due to gravity waves and/or convection) both upward and downward. Nonlinear interactions, associated with the velocity advection term, finally help build the approximate −5/3 slope through upscale and/or downscale propagation at all levels.
Abstract
Through successful convection-permitting simulations of Typhoon Sinlaku (2008) using a high-resolution nonhydrostatic model, this study examines the role of peripheral convection in the ...storm's secondary eyewall formation (SEF) and its eyewall replacement cycle (ERC). The study demonstrates that before SEF the simulated storm intensifies via an expansion of the tangential winds and an increase in the boundary layer inflow, which are accompanied by peripheral convective cells outside the primary eyewall. These convective cells, which initially formed in the outer rainbands under favorable environmental conditions and move in an inward spiral, play a crucial role in the formation of the secondary eyewall. It is hypothesized that SEF and ERC ultimately arise from the convective heating released from the inward-moving rainbands, the balanced response in the transverse circulation, and the unbalanced dynamics in the atmospheric boundary layer, along with the positive feedback between these processes.
Abstract Here we present a new theoretical framework that connects the error growth behavior in numerical weather prediction (NWP) with the atmospheric kinetic energy spectrum. Building on previous ...studies, our newly proposed framework applies to the canonical observed atmospheric spectrum that has a −3 slope at synoptic scales and a −5/3 slope at smaller scales. Based on this realistic hybrid energy spectrum, our new experiment using hybrid numerical models provides reasonable estimations for the finite predictable ranges at different scales. We further derive an analytical equation that helps understand the error growth behavior. Despite its simplicity, this new analytical error growth equation is capable of capturing the results of previous comprehensive theoretical and observational studies of atmospheric predictability. The success of this new theoretical framework highlights the combined effects of quasi-two-dimensional dynamics at synoptic scales (−3 slope) and three-dimensional turbulence-like small-scale chaotic flows (−5/3 slope) in dictating the error growth. It is proposed that this new framework could serve as a guide for understanding and estimating the predictability limit in the real world.
With the development of advanced data assimilation and computing techniques, many modern global reanalysis datasets aim to resolve the atmospheric mesoscale spectrum. However, large uncertainties ...remain with respect to the representation of mesoscale motions in these reanalysis datasets, for which a clear understanding is lacking. The aforementioned challenges have served as a strong motivation to reveal and quantify their mesoscale differences. This study presents the first comprehensive global intercomparison of the tropospheric and stratospheric mesoscale kinetic energy and its spectra over two selected periods of summer and winter events among six leading high‐resolution atmospheric reanalysis products: European Centre for Medium‐Range Weather Forecasts (ECMWF) Reanalysis v5 (ERA5), China Meteorological Administration Reanalysis, Modern‐Era Retrospective Analysis for Research and Applications version 2, National Centers for Environmental Prediction's Climate Forecast System version 2 (CFSv2), Japanese 55‐year Reanalysis, and ECMWF Reanalysis‐Interim. A state‐of‐the‐art global operational model is adopted as a supplementary reference. Although all reanalysis datasets can reproduce broad distribution characteristics that are grossly consistent with the 9 km model, there are substantial discrepancies among them in magnitudes. The ability to capture mesoscale signals is closely linked to their resolutions, but it is also impacted by other factors, including, but not limited to, the selected types of energy, seasons, altitudes, latitudes, model diffusions, parametrization schemes, moist condition, assimilation methods, and observation inputs. Moreover, all datasets illustrate conclusive behaviors for the prevalence of the rotational component in the troposphere, whereas only very few products fail to exhibit the dominance of the divergent component in the stratosphere. Overall, stratospheric ERA5 and CFSv2 outperform the other reanalysis datasets, and only these two can reproduce the feature of the canonical kinetic energy spectrum with a distinct shift from a steeper slope (approximately −3) at lower wave numbers to a shallower slope (approximately −5/3) at higher wave numbers. In addition, the relative disparities among datasets increase dramatically with height, and they are more pronounced in the divergent component. It is also found that the correlations among these datasets are much weaker in the Tropics.
The ability of reanalysis datasets to capture mesoscale signals is strongly influenced by resolution, and it is also related to other factors. Only ERA5, CFSv2, and the model simulations by the 9‐km ECMWF Integrated Forecast System (IFS‐9) can reproduce the observed kinetic energy spectrum with a transition from k−3 to k−5/3 in the stratosphere. The differences of mesoscale kinetic energy among datasets increase with height, and they are more pronounced in the divergent component.
Abstract
Based on 20-day control forecasts by the 9-km Integrated Forecasting System (IFS) at the European Centre for Medium-Range Weather Forecasts (ECMWF) for selected periods of summer and winter ...events, this study investigates global distributions of gravity wave momentum fluxes resolved by the highest-resolution-ever global operational numerical weather prediction model. Two supplementary datasets, including 18-km ECMWF IFS experiments and the 30-km ERA5, are included for comparison. In the stratosphere, there is a clear dominance of westward momentum fluxes over the winter extratropics with strong baroclinic instability, while eastward momentum fluxes are found in the summer tropics. However, meridional momentum fluxes, locally as important as the above zonal counterpart, show different behaviors of global distribution characteristics, with northward and southward momentum fluxes alternating with each other especially at lower altitudes. Both events illustrate conclusive evidence that stronger stratospheric fluxes are found in the ECMWF forecast with finer resolution, and that ERA5 datasets have the weakest signals in general, regardless of whether regridding is applied. In the troposphere, probability distributions of vertical motion perturbations are highly asymmetric with more strong positive signals especially over latitudes covering heavy rainfall, likely caused by convective forcing. With the aid of precipitation accumulation, a simple filtering method is proposed in an attempt to eliminate those tropospheric asymmetries by convective forcing, before calculating tropospheric wave-induced fluxes. Furthermore, this research demonstrates promising findings that the proposed filtering method could help in reducing the potential uncertainties with respect to estimating tropospheric wave-induced fluxes. Finally, absolute momentum flux distributions with proposed approaches are presented, for further assessment in the future.
Abstract
In their comment, Žagar and Szunyogh raised concerns about a recent study by Zhang et al. that examined the predictability limit of midlatitude weather using two up-to-date global models. ...Zhang et al. showed that deterministic weather forecast may, at best, be extended by 5 days, assuming we could achieve minimal initial-condition uncertainty (e.g., 10% of current operational value) with a nearly perfect model. Žagar and Szunyogh questioned the methodology and the experiments of Zhang et al. Specifically, Žagar and Szunyogh raised issues regarding the effects of model error on the growth of the forecast uncertainty. They also suggested that estimates of the predictability limit could be obtained using a simple parametric model. This reply clarifies the misunderstandings in Žagar and Szunyogh and demonstrates that experiments conducted by Zhang et al. are reasonable. In our view, the model error concern in Žagar and Szunyogh does not apply to the intrinsic predictability limit, which is the key focus of Zhang et al. and the simple parametric model described in Žagar and Szunyogh does not serve the purpose of Zhang et al.
Atmospheric gravity waves (GWs) span a broad range of length scales. As a result, the un‐resolved and under‐resolved GWs have to be represented using a sub‐grid scale (SGS) parameterization in ...general circulation models (GCMs). In recent years, machine learning (ML) techniques have emerged as novel methods for SGS modeling of climate processes. In the widely used approach of supervised (offline) learning, the true representation of the SGS terms have to be properly extracted from high‐fidelity data (e.g., GW‐resolving simulations). However, this is a non‐trivial task, and the quality of the ML‐based parameterization significantly hinges on the quality of these SGS terms. Here, we compare three methods to extract 3D GW fluxes and the resulting drag (Gravity Wave Drag GWD) from high‐resolution simulations: Helmholtz decomposition, and spatial filtering to compute the Reynolds stress and the full SGS stress. In addition to previous studies that focused only on vertical fluxes by GWs, we also quantify the SGS GWD due to lateral momentum fluxes. We build and utilize a library of tropical high‐resolution (Δx = 3 km) simulations using weather research and forecasting model. Results show that the SGS lateral momentum fluxes could have a significant contribution to the total GWD. Moreover, when estimating GWD due to lateral effects, interactions between the SGS and the resolved large‐scale flow need to be considered. The sensitivity of the results to different filter type and length scale (dependent on GCM resolution) is also explored to inform the scale‐awareness in the development of data‐driven parameterizations.
Plain Language Summary
Gravity waves (GWs) present a challenge to climate prediction: waves on scales of O(1)–O(100) km can neither be systematically measured with conventional observational systems, nor properly represented (resolved) in operational climate models, which have a typical grid spacing on the order of 100 km. Therefore, in these climate models, small‐scale GWs must be parameterized, or estimated, based on the resolved (large‐scale) flow. The primary effects of these small‐scale waves on the resolved flow is the so‐called sub‐grid scale drag (Gravity Wave Drag GWD), resulting from the propagation and breaking of these waves. Existing GW parameterizations in general circulation models are all highly simplified; for example, they only account for vertical propagation of GWs. With growing computing power, a promising alternative approach is to use machine learning to develop data‐driven parameterizations. However, this requires to first generate reliable high‐resolution computer simulations and then extract GWD from these simulations. This study follows these steps, compares different extraction methods, and describes some challenges and pathways to make advances. Furthermore, our results suggest that the horizontal propagation of GWs should be included in parameterizations too, however, extra care is needed in order to extract the resulting GWD from high‐resolution data.
Key Points
In a library of weather research and forecasting model simulations, we compare methods for estimating 3D gravity wave drag force that are un‐ and under‐resolved by general circulation models
For drag associated with vertical fluxes, different methods agree on time‐ and zonal‐mean but not on instantaneous spatiotemporal patterns
Drag associated with horizontal fluxes is significant but is very sensitive to the estimation methodology
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