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- Author or Editor: Y. Qiang Sun x
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Abstract
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.
Abstract
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.
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.
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.
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
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
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
Strong tropical cyclones often undergo eyewall replacement cycles that are accompanied by concentric eyewalls and/or rapid intensity changes while the secondary eyewall contracts radially inward and eventually replaces the inner eyewall. To the best of our knowledge, the only documented partial/incomplete tertiary eyewall has been mostly inferred from two-dimensional satellite images or one-dimensional aircraft flight-level measurements that can be regarded as indirect and tangential. This study presents the first high spatial and temporal resolution Doppler radar observations of a tertiary eyewall formation event in Typhoon Usagi (2013) over a 14-h time period before it makes landfall. The primary (tangential) and secondary (radial) circulations of Usagi deduced from the Ground-Based Velocity Track Display (GBVTD) methodology clearly portrayed three distinct axisymmetric maxima of radar reflectivity, tangential wind, vertical velocity, and vertical vorticity. Usagi’s central pressure steadily deepened during the contraction of the secondary and tertiary eyewalls until the tertiary eyewall hit the coast of southeast China, which erminated the intensification of the storm.
Abstract
Strong tropical cyclones often undergo eyewall replacement cycles that are accompanied by concentric eyewalls and/or rapid intensity changes while the secondary eyewall contracts radially inward and eventually replaces the inner eyewall. To the best of our knowledge, the only documented partial/incomplete tertiary eyewall has been mostly inferred from two-dimensional satellite images or one-dimensional aircraft flight-level measurements that can be regarded as indirect and tangential. This study presents the first high spatial and temporal resolution Doppler radar observations of a tertiary eyewall formation event in Typhoon Usagi (2013) over a 14-h time period before it makes landfall. The primary (tangential) and secondary (radial) circulations of Usagi deduced from the Ground-Based Velocity Track Display (GBVTD) methodology clearly portrayed three distinct axisymmetric maxima of radar reflectivity, tangential wind, vertical velocity, and vertical vorticity. Usagi’s central pressure steadily deepened during the contraction of the secondary and tertiary eyewalls until the tertiary eyewall hit the coast of southeast China, which erminated the intensification of the storm.
Abstract
The sensitivity of the secondary eyewall formation (SEF) of Hurricane Edouard (2014) to the diurnal solar insolation cycle is examined with convection-permitting simulations. A control run with a real diurnal radiation cycle and a sensitivity experiment without solar insolation are conducted. In the control run, there is an area of relatively weak convection between the outer rainbands and the primary eyewall, that is, a moat region. This area is highly sensitive to solar shortwave radiative heating, mostly in the mid- to upper levels in the daytime, which leads to a net stabilization effect and suppresses convective development. Moreover, the heated surface air weakens the wind-induced surface heat exchange (WISHE) feedback between the surface fluxes (that promote convection) and convective heating (that feeds into the secondary circulation and then the tangential wind). Consequently, a typical SEF with a clear moat follows. In the sensitivity experiment, in contrast, net radiative cooling leads to persistent active inner rainbands between the primary eyewall and outer rainbands, and these, along with the absence of the rapid filamentation zone, are detrimental to moat formation and thus to SEF. Sawyer–Eliassen diagnoses further suggest that the radiation-induced difference in diabatic heating is more important than the vortex wind structure for moat formation and SEF. These results suggest that the SEF is highly sensitive to solar insolation.
Abstract
The sensitivity of the secondary eyewall formation (SEF) of Hurricane Edouard (2014) to the diurnal solar insolation cycle is examined with convection-permitting simulations. A control run with a real diurnal radiation cycle and a sensitivity experiment without solar insolation are conducted. In the control run, there is an area of relatively weak convection between the outer rainbands and the primary eyewall, that is, a moat region. This area is highly sensitive to solar shortwave radiative heating, mostly in the mid- to upper levels in the daytime, which leads to a net stabilization effect and suppresses convective development. Moreover, the heated surface air weakens the wind-induced surface heat exchange (WISHE) feedback between the surface fluxes (that promote convection) and convective heating (that feeds into the secondary circulation and then the tangential wind). Consequently, a typical SEF with a clear moat follows. In the sensitivity experiment, in contrast, net radiative cooling leads to persistent active inner rainbands between the primary eyewall and outer rainbands, and these, along with the absence of the rapid filamentation zone, are detrimental to moat formation and thus to SEF. Sawyer–Eliassen diagnoses further suggest that the radiation-induced difference in diabatic heating is more important than the vortex wind structure for moat formation and SEF. These results suggest that the SEF is highly sensitive to solar insolation.
Abstract
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
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
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.
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.
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
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
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.
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.
