the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Variability and Predictability of a reduced-order land atmosphere coupled model
Anupama K. Xavier
Jonathan Demaeyer
Stéphane Vannitsem
Abstract. This study delves into the predictability of atmospheric blocking, zonal, and transition patterns utilizing a simplified coupled model. This model, implemented in Python, emulates midlatitude atmospheric dynamics with a two-layer quasi-geostrophic channel atmosphere on a beta-plane, encompassing simplified land effects. Initially, we comprehensively scrutinize the model's responses to environmental parameters like solar radiation, surface friction, and atmosphere-ground heat exchange. Our findings confirm that the model faithfully replicates real-world Earth-like flow regimes, establishing a robust foundation for further analysis. Subsequently, employing Gaussian mixture clustering, we successfully delineate distinct blocking, zonal, and transition flow regimes, unveiling their dependencies on surface friction. To gauge predictability and persistence, we compute the averaged local Lyapunov exponents for each regime. Our investigation uncovers the presence of zonal, blocking, and transition regimes, particularly under conditions of reduced surface friction. As surface friction increases further, the system transitions to a state characterized by two blocking regimes and a transition regime. Intriguingly, periodic behavior emerges under specific surface friction values, returning to patterns observed under low friction coefficients. Model resolution increase impacts the system in a way that only two regimes are then obtained with the clustering: the transition phase disappears and the predictability drops to roughly 2 days for both of the remaining regimes. In accordance with previous research findings, our study underscores that when all three regimes coexist, zonal patterns exhibit a more extended predictability horizon compared to blocking patterns. Remarkably, transition patterns exhibit reduced predictability when coexisting with the other regimes. In addition, within a specified range of surface friction values where two blocking regimes are found, it is observed that blocked atmospheric situations in the west of the applied topography are marked by instabilities and reduced predictability in contrast to the blockings appearing on the eastern side of the topography.
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Anupama K. Xavier et al.
Status: open (until 24 Dec 2023)
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RC1: 'Comment on egusphere-2023-2257', Anonymous Referee #1, 19 Nov 2023
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This study investigates the predictability of two weather regimes, atmospheric blocking and zonal flows, and their transitions using a simplified coupled atmosphere-land model implemented in Python. The model simulates midlatitude atmospheric dynamics based on a two-layer quasi-geostrophic channel system on a beta-plane, incorporating simplified land effects. The research analyzes the model's responses to environmental parameters and confirms its ability to replicate Earth-like flow regimes.
Through Gaussian mixture clustering, distinct blocking, zonal, and transition flow regimes are identified, revealing their dependence on surface friction. To assess predictability and persistence, the study computes averaged local Lyapunov exponents for each regime. Results indicate the coexistence of zonal, blocking, and transition regimes, with predictability varying based on surface friction conditions. The presence of periodic behavior and the impact of model resolution on predictability are also explored. The study emphasizes that when all three regimes coexist, zonal patterns exhibit longer predictability compared to blocking patterns that are associated with instability, and transition patterns have reduced predictability when coexisting with other regimes. Additionally, specific surface friction values influence the predictability and characteristics of blocking regimes in different geographic locations.
While this study shows promise in enhancing our comprehension of predictability within multiple regime systems, certain crucial issues need to be resolved before considering its publication.
Major comments:
One major concern pertains to the classification of three weather regimes using a machine learning (ML) method and the correlation of each identified regime with stability or instability, determined by averaged local Lyapunov exponents. While Charney and Devore's (1979) model is traditionally used for studying non-chaotic weather regimes, Lorenz's (1963a) model is renowned for illustrating chaotic features. It's crucial to note that Lorenz applied a similar approach in the early 1960s to study chaotic and nonlinear oscillatory solutions in a two-layer quasi-geostrophic system (e.g., Lorenz 1962, 1963b; Shen, Pielke Sr., and Zeng, 2023, https://www.mdpi.com/2073-4433/14/8/1279 ). A brief review of Lorenz's contributions is necessary, and a comparison of the QG-based models should address the variation in the number of Fourier modes concerning chaotic features.
Several issues need attention:
- Gaussian Mixture Clustering (GMC) was employed for classification, assuming each cluster has a Gaussian component. The suitability of this assumption for chaotic regimes should be addressed, especially considering the regular spatial patterns that appear in the classified regimes. Associating different weather regimes with components of the leading Lyapunov vector, particularly in the presence of multiple positive Lyapunov exponents, should be addressed. The challenge is heightened by the time varying components of each Lyapunov vector along the solution orbit, making it difficult to link specific components to zonal or blocking regimes.
- The use of a fixed cluster number (3) in GMC for models with different numbers of positive Lyapunov exponents (LEs) (e.g., 3 positive LEs in Figure 7 and 12 positive LEs in Figure 12) raises concerns. Various clustering values should be explored to illustrate the relationship between the number of weather regimes and the number of positive LEs. For example, can we observe similar weather regimes in the 30 and 165 variable systems? If this is the case, does it imply a consistent number of multiple regimes or equilibrium points across both systems?
- Is it feasible to compute Lyapunov exponents for individual weather regimes? Could the time evolution of each weather regime be graphed for comparative analysis?
- Concerning predictability in typical dynamical systems, characterized by systems of ordinary differential equations (ODEs), a positive Lyapunov exponent (LE) usually signifies temporal chaos (distinct from spatial-temporal chaos). In estimating predictability horizons under different conditions, a higher positive LE, on average, implies a greater averaged growth rate, indicating faster error growth and thus diminished predictability horizons. However, when applying this concept to assess predictability in spatial-temporal systems, it becomes imperative to account for errors related to spatial movement. The analogy of whether more intense hurricanes (with higher growth rates) are less predictable encourages authors to contemplate the influence of spatial movement on error predictions. Therefore, in contrast to a zonal flow, although a blocking regime is linked to instability manifested by a larger LE, the consideration of spatial movement is essential when comparing errors in zonal and blocking cases in order to compare their predictability horizons.
Specific Comments.
Page 5: Please indicate whether and how Eqs. (1) and (2) are coupled with Eqs. (3) and (4).
Page 7: Please indicate the equation(s) that contains Cg.
Page 7, Figure 1c with ACC. Is it possible to identify a time scale of approximately 36 days within the timeframe spanning 20 to 80 days?
Page 7: Can a figure analogous to Figure 1 be generated for each of the categorized regimes?
Page 9: The discussions on the Oseledec method should be expanded to incorporate insights from Lorenz's contributions. (e.g., Lorenz 1965; please see a review by Shen, Pielke Sr, and Zeng, 2023).
Page 11: Please add Figure B3 to include flows for Cg = 400 or kd = 0.12, for periodic flows.
Pages 12 and 13: while lambda_1 and lambda_2 are used for representing the 1st and 2nd LEs, respectively, the symbol lambda indicates heat exchange. Please consider making changes to reduce confusion.
Page 12, line 280. Does the selection of lambda = 0 result in an uncoupled model? How can this be contrasted with the models proposed by Charney and Devore, Lorenz (1962) and/or Lorenz (1963b)?
Pages 12 & 17, (in Figures 7 & 12), please offer perspectives on whether the presence of the plateau suggests the existence of singular eigenvalues with higher multiplicity.
Citation: https://doi.org/10.5194/egusphere-2023-2257-RC1
Anupama K. Xavier et al.
Anupama K. Xavier et al.
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