[Paper Review] Quantifying the eddy-jet feedback strength of the annular mode in an idealized GCM and reanalysis data

Ding Ma, Hassanzadeh, Pedram+1 more|arXiv (Cornell University)|Aug 14, 2016

Fluid Dynamics and Turbulent Flows3 citations

TL;DR

This study introduces a linear response function (LRF) to quantify the eddy-jet feedback strength in the annular mode, demonstrating a positive feedback of 0.137 day⁻¹ in an idealized GCM and 0.121 day⁻¹ in reanalysis data. It proposes a low-pass filtering method that converges to LRF results at timescales >200 days, improving accuracy over prior statistical methods by accounting for the quasi-oscillatory nature of eddy forcing.

ABSTRACT

A linear response function (LRF) that relates the temporal tendency of zonal mean temperature and zonal wind to their anomalies and external forcing is used to accurately quantify the strength of the eddy-jet feedback associated with the annular mode in an idealized GCM. Following a simple feedback model, the results confirm the presence of a positive eddy-jet feedback in the annular mode dynamics, with a feedback strength of 0.137 day$^{-1}$ in the idealized GCM. Statistical methods proposed by earlier studies to quantify the feedback strength are evaluated against results from the LRF. It is argued that the mean-state-independent eddy forcing reduces the accuracy of these statistical methods because of the quasi-oscillatory nature of the eddy forcing. A new method is proposed to approximate the feedback strength as the regression coefficient of low-pass filtered eddy forcing onto low-pass filtered annular mode index, which converges to the value produced by the LRF when timescales longer than 200 days are used for the low-pass filtering. Applying the new low-pass filtering method to the reanalysis data, the feedback strength in the Southern annular mode is found to be 0.121 day$^{-1}$, which is presented as an improvement over previous estimates. This work also highlights the importance of using sub-daily data in the analysis by showing the significant contribution of medium-scale waves of periods less than 2 days to the annular mode dynamics, which was under-appreciated in most of previous research. The present study provides a framework to quantify the eddy-jet feedback strength in models and reanalysis data.

Motivation & Objective

• To accurately quantify the strength of the eddy-jet feedback in the annular mode, a key mechanism for jet persistence.
• To evaluate the limitations of existing statistical methods in estimating feedback strength due to the quasi-oscillatory nature of eddy forcing.
• To develop and validate a new low-pass filtering method that better isolates the feedback signal from noise and mean-state-independent eddy forcing.
• To assess the role of sub-daily and medium-scale waves (periods <2 days) in annular mode dynamics, previously underappreciated in prior studies.
• To provide a benchmark using a linear response function (LRF) in an idealized GCM to validate statistical methods before applying them to reanalysis data.

Proposed method

• Uses a linear response function (LRF) to isolate mean-state-dependent eddy forcing in response to annular mode anomalies, providing a 'ground truth' for feedback strength in an idealized GCM.
• Applies a simple feedback model where the zonal wind tendency is proportional to the product of the feedback strength and the annular mode index, with the feedback strength derived from the LRF.
• Proposes a new method to estimate feedback strength as the regression coefficient between low-pass filtered eddy forcing and low-pass filtered annular mode index.
• Employs low-pass filtering with timescales longer than 200 days to converge the new method’s estimate to the LRF value, minimizing influence from high-frequency oscillations.
• Validates statistical methods using synthetic time series and model outputs before applying them to reanalysis data, ensuring robustness.
• Conducts spectral analysis on long model simulations (CTL) to estimate the effective timescale τₑ of the mean-state-independent eddy forcing, which constrains the difference between feedback strength and inverse timescale.

Experimental results

Research questions

• RQ1 What is the true strength of the eddy-jet feedback in the annular mode, and how does it compare between an idealized GCM and reanalysis data?
• RQ2 Why do traditional statistical methods overestimate or misestimate feedback strength, and how does the quasi-oscillatory nature of eddy forcing affect their accuracy?
• RQ3 Can a low-pass filtering approach improve the estimation of feedback strength by isolating low-frequency components of eddy forcing and zonal index?
• RQ4 What is the contribution of sub-daily and medium-scale waves (periods <2 days) to the annular mode dynamics, and why has this been overlooked in prior research?
• RQ5 How does the difference between the feedback strength (b) and the inverse timescale (1/τ) arise, and what physical processes determine this difference?

Key findings

• The eddy-jet feedback strength in the idealized GCM is quantified as 0.137 day⁻¹ using the linear response function (LRF), providing a benchmark for model validation.
• The new low-pass filtering method converges to the LRF-estimated feedback strength (0.137 day⁻¹) when filtering timescales exceed 200 days, confirming its accuracy.
• In reanalysis data, the feedback strength is estimated at 0.121 day⁻¹ using the same low-pass filtering method, representing an improvement over previous estimates.
• Statistical methods based on lagged correlations (e.g., LH01 and S13) are shown to be inaccurate due to the influence of mean-state-independent eddy forcing and the quasi-oscillatory nature of eddy forcing.
• The effective timescale τₑ of the mean-state-independent eddy forcing is estimated at 91 days, with a small difference (≤0.011 day⁻¹) between the feedback strength b and the inverse timescale 1/τ.
• Sub-daily and medium-scale waves (periods <2 days) make a significant contribution to annular mode dynamics, a factor previously underappreciated in most studies.