scholarly journals On the Predictability of 30-Day Global Mesoscale Simulations of African Easterly Waves during Summer 2006: A View with the Generalized Lorenz Model

Geosciences ◽  
2019 ◽  
Vol 9 (7) ◽  
pp. 281 ◽  
Author(s):  
Shen
Keyword(s):  
Periodic Solutions ◽  
Initial Conditions ◽  
Small Scale ◽  
Stable Steady State ◽  
Lead Times ◽  
African Easterly Waves ◽  
Lorenz Model ◽  
Easterly Waves ◽  
Extended Range ◽  
Hypothetical Mechanism

Recent advances in computational and global modeling technology have provided the potential to improve weather predictions at extended-range scales. In earlier studies by the author and his coauthors, realistic 30-day simulations of multiple African easterly waves (AEWs) and an averaged African easterly jet (AEJ) were obtained. The formation of hurricane Helene (2006) was also realistically simulated from Day 22 to Day 30. In this study, such extended predictability was further analyzed based on recent understandings of chaos and instability within Lorenz models and the generalized Lorenz model. The analysis suggested that a statement of the theoretical predictability of two weeks is not universal. New insight into chaotic and non-chaotic processes revealed by the generalized Lorenz model (GLM) indicated the potential for extending prediction lead times. Two major features within the GLM included: (1) three types of attractors (that also appeared in the original Lorenz model) and (2) two kinds of attractor coexistence. The features suggest a refined view on the nature of weather, as follows: The entirety of weather is a superset that consists of chaotic and non-chaotic processes. Better predictability can be obtained for stable, steady-state solutions and nonlinear periodic solutions that occur at small and large Rayleigh parameters, respectively. By comparison, chaotic solutions appear only at moderate Rayleigh parameters. Errors associated with dissipative small-scale processes do not necessarily contaminate the simulations of large scale processes. Based on the nonlinear periodic solutions (also known as limit cycle solutions), here, we propose a hypothetical mechanism for the recurrence (or periodicity) of successive AEWs. The insensitivity of limit cycles to initial conditions implies that AEW simulations with strong heating and balanced nonlinearity could be more predictable. Based on the hypothetical mechanism, the possibility of extending prediction lead times at extended range scales is discussed. Future work will include refining the model to better examine the validity of the mechanism to explain the recurrence of multiple AEWs.

scholarly journals Is Weather Chaotic? Coexisting Attractors, Multistability, and Predictability

2021 ◽  
Author(s):  
Bo-Wen Shen ◽  
Roger A. Pielke ◽  
Xubin Zeng ◽  
Sara Faghih-Naini ◽  
Jialin Cui ◽  
...  
Keyword(s):  
Real World ◽  
Large Scale ◽  
Initial Conditions ◽  
Single Type ◽  
Small Scale ◽  
Stable Steady State ◽  
Lorenz Model ◽  
Short Article ◽  
Dual Nature ◽  
Limited Scale

Abstract Since Lorenz’s 1963 study and 1972 presentation, the statement “weather is chaotic’’ has been well accepted. Such a view turns our attention from regularity associated with Laplace’s view of determinism to irregularity associated with chaos. In contrast to single type chaotic solutions, recent studies using a generalized Lorenz model (Shen 2019a, b; Shen et al. 2019) have focused on the coexistence of chaotic and regular solutions that appear within the same model, using the same modeling configurations but different initial conditions. The results suggest that the entirety of weather possesses a dual nature of chaos and order with distinct predictability. Furthermore, Shen et al. (2021a, b) illustrated the following two mechanisms that may enable or modulate attractor coexistence: (1) the aggregated negative feedback of small-scale convective processes that enable the appearance of stable, steady-state solutions and their coexistence with chaotic or nonlinear limit cycle solutions; and (2) the modulation of large-scale time varying forcing (heating). Recently, the physical relevance of findings within Lorenz models for real world problems has been reiterated by providing mathematical universality between the Lorenz simple weather and Pedlosky simple ocean models, as well as amongst the non-dissipative Lorenz model, and the Duffing, the Nonlinear Schrodinger, and the Korteweg–de Vries equations (Shen 2020, 2021). We additionally compared the Lorenz 1963 and 1969 models. The former is a limited-scale, nonlinear, chaotic model; while the latter is a closure-based, physically multiscale, mathematically linear model with ill-conditioning. To support and illustrate the revised view, this short article elaborates on additional details of monostability and multistability by applying skiing and kayaking as an analogy, and provides a list of non-chaotic weather systems. We additionally address the influence of the revised view on real-world model predictions and analyses using hurricane track predictions as an illustration, and provide a brief summary on the recent deployment of methods for multiscale analyses and classifications of chaotic and non-chaotic solutions.

scholarly journals What Is the Predictability Limit of Midlatitude Weather?

2019 ◽  
Vol 76 (4) ◽  
pp. 1077-1091 ◽  
Author(s):  
Fuqing Zhang ◽  
Y. Qiang Sun ◽  
Linus Magnusson ◽  
Roberto Buizza ◽  
Shian-Jiann Lin ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Weather Prediction ◽  
Forecast Model ◽  
Small Scale ◽  
Lead Times ◽  
Winter Storms ◽  
Weather Forecasts ◽  
Numerical Weather ◽  
Forecast Lead Time ◽  
Order Of Magnitude

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.

scholarly journals A Recurrence Analysis of Multiple African Easterly Waves during Summer 2006

2020 ◽  
Author(s):  
Tiffany Reyes ◽  
Bo-Wen Shen
Keyword(s):  
Large Scale ◽  
Mesoscale Model ◽  
Recurrence Plot ◽  
Temporal Variations ◽  
Local Analysis ◽  
Lead Times ◽  
African Easterly Waves ◽  
Easterly Waves ◽  
Weather Forecasts

Accurate detection of large-scale atmospheric tropical waves, such as African easterly waves (AEWs), may help extend lead times for predicting tropical cyclone (TC) genesis. Since observed AEWs have comparable but slightly different periods showing spatial and temporal variations, local analysis of frequencies and amplitudes of AEWs is crucial for revealing the role of AEWs in the modulation of TC genesis. To achieve this goal, we investigate the recurrence plot (RP) method. A recurrence is defined when the trajectory of a state returns to the neighborhood of a previously visited state. To verify implementation of the RP method in Python and its capability for revealing a transition between different types of solutions, we apply the RP to analyze several idealized solutions, including periodic, quasiperiodic, chaotic and limit cycle solutions, and various types of solutions within the three- and five-dimensional Lorenz models. We then extend the RP analysis to two datasets from the European Centre for Medium-Range Weather Forecasts global reanalysis and global mesoscale model data in order to reveal the recurrence of multiple AEWs during summer 2006. Our results indicate that the RP analysis effectively displays the major features of time-varying oscillations and the growing or decaying amplitudes of multiple AEWs.

scholarly journals Trains of African Easterly Waves and Their Relationship to Tropical Cyclone Genesis in the Eastern Atlantic

2017 ◽  
Vol 145 (2) ◽  
pp. 599-616 ◽  
Author(s):  
Abdou L. Dieng ◽  
Saidou M. Sall ◽  
Laurence Eymard ◽  
Marion Leduc-Leballeur ◽  
Alban Lazar
Keyword(s):  
West African ◽  
Dynamical Structure ◽  
African Easterly Waves ◽  
The South ◽  
The West ◽  
Easterly Waves ◽  
West African Coast ◽  
African Coast ◽  
Tropical Depressions ◽  
The Relationship

In this study, the relationship between trains of African easterly waves (AEWs) and downstream tropical cyclogenesis is studied. Based on 19 summer seasons (July–September from 1990 to 2008) of ERA-Interim reanalysis fields and brightness temperature from the Cloud User Archive, the signature of AEW troughs and embedded convection are tracked from the West African coast to the central Atlantic. The tracked systems are separated into four groups: (i) systems originating from the north zone of the midtropospheric African easterly jet (AEJ), (ii) those coming from the south part of AEJ, (iii) systems that are associated with a downstream trough located around 2000 km westward (termed DUO systems), and (iv) those that are not associated with such a close downstream trough (termed SOLO systems). By monitoring the embedded 700-hPa-filtered relative vorticity and 850-hPa wind convergence anomaly associated with these families along their trajectories, it is shown that the DUO generally have stronger dynamical structure and statistically have a longer lifetime than the SOLO ones. It is suggested that the differences between them may be due to the presence of the previous intense downstream trough in DUO cases, enhancing the low-level convergence behind them. Moreover, a study of the relationship between system trajectories and tropical depressions occurring between the West African coast and 40°W showed that 90% of tropical depressions are identifiable from the West African coast in tracked systems, mostly in the DUO cases originating from the south zone of the AEJ.

scholarly journals Saturation of Zeldovich stretch–twist–fold map dynamos

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
Amit Seta ◽  
Pallavi Bhat ◽  
Kandaswamy Subramanian
Keyword(s):  
Initial Conditions ◽  
Reynolds Numbers ◽  
Small Scale ◽  
Saturation Properties ◽  
Field Amplification ◽  
Saturated State ◽  
Shape Invariant ◽  
Fold Map ◽  
Scale Fluctuation ◽  
The Magnetic Field

Zeldovich’s stretch–twist–fold (STF) dynamo provided a breakthrough in conceptual understanding of fast dynamos, including the small-scale fluctuation dynamos. We study the evolution and saturation behaviour of two types of generalized Baker’s map dynamos, which have been used to model Zeldovich’s STF dynamo process. Using such maps allows one to analyse dynamos at much higher magnetic Reynolds numbers $\mathit{Re}_{M}$ as compared to direct numerical simulations. In the two-strip map dynamo there is constant constructive folding, while the four-strip map dynamo also allows the possibility of a destructive reversal of the field. Incorporating a diffusive step parametrized by $\mathit{Re}_{M}$ into the map, we find that the magnetic field $B(x)$ is amplified only above a critical $\mathit{Re}_{M}=R_{\mathit{crit}}\sim 4$ for both types of dynamos. The growing $B(x)$ approaches a shape-invariant eigenfunction independent of initial conditions, whose fine structure increases with increasing $\mathit{Re}_{M}$. Its power spectrum $M(k)$ displays sharp peaks reflecting the fractal nature of $B(x)$ above the diffusive scale. We explore the saturation of these dynamos in three ways: via a renormalized reduced effective $\mathit{Re}_{M}$ (case I) or due to a decrease in the efficiency of the field amplification by stretching, without changing the map (case IIa), or changing the map (case IIb), and a combination of both effects (case III). For case I, we show that $B(x)$ in the saturated state, for both types of maps, approaches the marginal eigenfunction, which is obtained for $\mathit{Re}_{M}=R_{\mathit{crit}}$ independent of the initial $\mathit{Re}_{M}=R_{M0}$. On the other hand, in case II, for the two-strip map, we show that $B(x)$ saturates, preserving the structure of the kinematic eigenfunction. Thus the energy is transferred to larger scales in case I but remains at the smallest resistive scales in case II, as can be seen from both $B(x)$ and $M(k)$. For the four-strip map, $B(x)$ oscillates with time, although with a structure similar to the kinematic eigenfunction. Interestingly, the saturated state in case III shows an intermediate behaviour, with $B(x)$ similar to the kinematic eigenfunction at an intermediate $\mathit{Re}_{M}=R_{\mathit{sat}}$, with $R_{M0}>R_{\mathit{sat}}>R_{\mathit{crit}}$. The $R_{\mathit{sat}}$ value is determined by the relative importance of the increased diffusion versus the reduced stretching. These saturation properties are akin to the range of possibilities that have been discussed in the context of fluctuation dynamos.

scholarly journals Evaluating sub-seasonal heatwave reforecasts of the ECMWF over Europe

2021 ◽  
Author(s):  
Natalia Korhonen ◽  
Otto Hyvärinen ◽  
Matti Kämäräinen ◽  
Kirsti Jylhä
Keyword(s):  
Heat Wave ◽  
Heat Waves ◽  
Lead Times ◽  
Weather Forecasts ◽  
Wave Forecast ◽  
Extended Range ◽  
Hot Days ◽  
Medium Range ◽  
Summer Temperatures

<p>Severe heatwaves have harmful impacts on ecosystems and society. Early warning of heat waves help with decreasing their harmful impact. Previous research shows that the Extended Range Forecasts (ERF) of the European Centre for Medium-Range Weather Forecasts (ECMWF) have over Europe a somewhat higher reforecast skill for extreme hot summer temperatures than for long-term mean temperatures. Also it has been shown that the reforecast skill of the ERFs of the ECMWF was strongly increased by the most severe heat waves (the European heatwave 2003 and the Russian heatwave 2010).</p><p>Our aim is to be able to estimate the skill of a heat wave forecast at the time the forecast is given. For that we investigated the spatial and temporal reforecast skill of the ERFs of the ECMWF to forecast hot days (here defined as a day on which the 5 days running mean surface temperature is above its summer 90<sup>th</sup> percentile) in the continental Europe in summers 2000-2019. We used the ECMWF 2-meter temperature reforecasts and verified them against the ERA5 reanalysis. The skill of the hot day reforecasts was estimated by the symmetric extremal dependence index (SEDI) which considers both hit rates and false alarm rates of the hot day forecasts. Further, we investigated the skill of the heatwave reforecasts based on at which time steps of the forecast the hot days were forecasted. We found that on the mesoscale (horizontal scale of ~500 km) the ERFs of the ECMWF were most skillful in predicting the life cycle of a heat wave (lasting up to 25 days) about a week before its start and during its course. That is, on the mesoscale those reforecasts, in which hot day(s) were forecasted to occur during the first 7…11 days, were more skillful on lead times up to 25 days than the rest of the heat wave forecasts. This finding is valuable information, e.g., in the energy and health sectors while preparing for a coming heat wave.</p><p>The work presented here is part of the research project HEATCLIM (Heat and health in the changing climate) funded by the Academy of Finland.</p>

scholarly journals Nonlinear feedback in a six-dimensional Lorenz Model: impact of an additional heating term

2015 ◽  
Vol 2 (2) ◽  
pp. 475-512
Author(s):  
B.-W. Shen
Keyword(s):  
Rayleigh Number ◽  
Numerical Solutions ◽  
Critical Rayleigh Number ◽  
Critical Value ◽  
Small Scale ◽  
Solution Stability ◽  
Nonlinear Feedback ◽  
Lorenz Model ◽  
Additional Heating ◽  
The Impact

Abstract. In this study, a six-dimensional Lorenz model (6DLM) is derived, based on a recent study using a five-dimensional (5-D) Lorenz model (LM), in order to examine the impact of an additional mode and its accompanying heating term on solution stability. The new mode added to improve the representation of the steamfunction is referred to as a secondary streamfunction mode, while the two additional modes, that appear in both the 6DLM and 5DLM but not in the original LM, are referred to as secondary temperature modes. Two energy conservation relationships of the 6DLM are first derived in the dissipationless limit. The impact of three additional modes on solution stability is examined by comparing numerical solutions and ensemble Lyapunov exponents of the 6DLM and 5DLM as well as the original LM. For the onset of chaos, the critical value of the normalized Rayleigh number (rc) is determined to be 41.1. The critical value is larger than that in the 3DLM (rc ~ 24.74), but slightly smaller than the one in the 5DLM (rc ~ 42.9). A stability analysis and numerical experiments obtained using generalized LMs, with or without simplifications, suggest the following: (1) negative nonlinear feedback in association with the secondary temperature modes, as first identified using the 5DLM, plays a dominant role in providing feedback for improving the solution's stability of the 6DLM, (2) the additional heating term in association with the secondary streamfunction mode may destabilize the solution, and (3) overall feedback due to the secondary streamfunction mode is much smaller than the feedback due to the secondary temperature modes; therefore, the critical Rayleigh number of the 6DLM is comparable to that of the 5DLM. The 5DLM and 6DLM collectively suggest different roles for small-scale processes (i.e., stabilization vs. destabilization), consistent with the following statement by Lorenz (1972): If the flap of a butterfly's wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado. The implications of this and previous work, as well as future work, are also discussed.

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