Eddy Length Scale Response to Static Stability Change in an Idealized Dry Atmosphere: A Linear Response Function Approach*

2021 ◽  
Author(s):  
Pak Wah Chan ◽  
Pedram Hassanzadeh ◽  
Zhiming Kuang
Keyword(s):  
Response Function ◽  
Zonal Wind ◽  
Linear Response ◽  
Static Stability ◽  
Length Scale ◽  
Controlled Experiments ◽  
Mean Flow ◽  
Near Surface ◽  
Zonal Scale ◽  
Linear Response Function

AbstractThe response of mid-latitude equilibrated eddy length scale to static stability has long been questioned but not investigated in well-controlled experiments with unchanged mean zonal wind and meridional temperature gradient. With iterative use of the linear response function of an idealized dry atmosphere, we obtain a time-invariant and zonally-uniform forcing to decrease the near-surface temperature by over 2 K while keeping the change in zonal wind negligible (within 0.2m s−1). In such experiments of increased static stability, energy-containing zonal scale decreases by 3–4%, which matches with Rhines scale decrease near the jet core. Changes in Rossby radius (+2%), maximum baroclinic growth scale (-1%) and Kuo scale (0%) fail to match this change in zonal scale. These findings and well-controlled experiments help with better understanding of eddy–mean flow interactions and hence the mid-latitude circulation and its response to climate change.

Macroturbulence Response to Vertical Stratification Change Using Linear Response Function of an Idealized Dry Atmosphere

2020 ◽  
Author(s):  
Pak-Wah Chan ◽  
Pedram Hassanzadeh ◽  
Zhiming Kuang
Keyword(s):  
Response Function ◽  
Linear Response ◽  
Momentum Flux ◽  
Pearson Correlation ◽  
Vertical Stratification ◽  
Near Surface ◽  
Zonal Scale ◽  
Linear Response Function ◽  
Zonal Wavenumber ◽  
Scaling Arguments

<p>Rossby radius and Rhines scale are two popular scaling arguments for eddy length scale. They have not been tested in a well-controlled experiment with increased vertical stratification and unchanged jet. This is done using the linear response function of an idealized dry atmosphere calculated by Hassanzadeh and Kuang (2016). The resulting change in zonal wind is mostly less than 0.2m/s when temperature near surface is cooled by more than 2K. In such experiment, energy-containing zonal scale decreases, which is against the prediction of Rossby radius but consistent with the prediction of Rhines scale. Eddy kinetic energy decreases for all wavenumbers and latitudes, but eddy momentum flux strengthens locally around zonal wavenumber 8 and 40°S. This local strengthening is associated with a stronger Pearson correlation between u and v.</p>

scholarly journals The Linear Response Function of an Idealized Atmosphere. Part I: Construction Using Green’s Functions and Applications

2016 ◽  
Vol 73 (9) ◽  
pp. 3423-3439 ◽  
Author(s):  
Pedram Hassanzadeh ◽  
Zhiming Kuang
Keyword(s):  
Response Function ◽  
Linear Response ◽  
Mean Flow ◽  
Turbulent Eddies ◽  
Fluctuation Dissipation ◽  
Linear Response Function ◽  
Potential Applications ◽  
Neutral Vector ◽  
The Mean ◽  
Flow Changes

Abstract A linear response function (LRF) determines the mean response of a nonlinear climate system to weak imposed forcings, and an eddy flux matrix (EFM) determines the eddy momentum and heat flux responses to mean-flow changes. Neither LRF nor EFM can be calculated from first principles owing to the lack of a complete theory for turbulent eddies. Here the LRF and EFM for an idealized dry atmosphere are computed by applying numerous localized weak forcings, one at a time, to a GCM with Held–Suarez physics and calculating the mean responses. The LRF and EFM for zonally averaged responses are then constructed using these forcings and responses through matrix inversion. Tests demonstrate that LRF and EFM are fairly accurate. Spectral analysis of the LRF shows that the most excitable dynamical mode, the neutral vector, strongly resembles the model’s annular mode. The framework described here can be employed to compute the LRF and EFM for zonally asymmetric responses and more complex GCMs. The potential applications of the LRF and EFM constructed here are (i) forcing a specified mean flow for hypothesis testing, (ii) isolating/quantifying the eddy feedbacks in complex eddy–mean flow interaction problems, and (iii) evaluating/improving more generally applicable methods currently used to construct LRFs or diagnose eddy feedbacks in comprehensive GCMs or observations. As an example for (iii), in Part II, the LRF is also computed using the fluctuation–dissipation theorem (FDT), and the previously calculated LRF is exploited to investigate why FDT performs poorly in some cases. It is shown that dimension reduction using leading EOFs, which is commonly used to construct LRFs from the FDT, can significantly degrade the accuracy owing to the nonnormality of the operator.

scholarly journals The Linear Response Function of an Idealized Atmosphere. Part II: Implications for the Practical Use of the Fluctuation–Dissipation Theorem and the Role of Operator’s Nonnormality

2016 ◽  
Vol 73 (9) ◽  
pp. 3441-3452 ◽  
Author(s):  
Pedram Hassanzadeh ◽  
Zhiming Kuang
Keyword(s):  
Dimension Reduction ◽  
Response Function ◽  
Linear Response ◽  
Poor Performance ◽  
Mean Flow ◽  
Dynamical Core ◽  
Fluctuation Dissipation ◽  
The Poor ◽  
Fluctuation Dissipation Theorem ◽  
Linear Response Function

Abstract A linear response function (LRF) relates the mean response of a nonlinear system to weak external forcings and vice versa. Even for simple models of the general circulation, such as the dry dynamical core, the LRF cannot be calculated from first principles owing to the lack of a complete theory for eddy–mean flow feedbacks. According to the fluctuation–dissipation theorem (FDT), the LRF can be calculated using only the covariance and lag-covariance matrices of the unforced system. However, efforts in calculating the LRFs for GCMs using FDT have produced mixed results, and the reason(s) behind the poor performance of the FDT remain(s) unclear. In Part I of this study, the LRF of an idealized GCM, the dry dynamical core with Held–Suarez physics, is accurately calculated using Green’s functions. In this paper (Part II), the LRF of the same model is computed using FDT, which is found to perform poorly for some of the test cases. The accurate LRF of Part I is used with a linear stochastic equation to show that dimension reduction by projecting the data onto the leading EOFs, which is commonly used for FDT, can alone be a significant source of error. Simplified equations and examples of 2 × 2 matrices are then used to demonstrate that this error arises because of the nonnormality of the operator. These results suggest that errors caused by dimension reduction are a major, if not the main, contributor to the poor performance of the LRF calculated using FDT and that further investigations of dimension-reduction strategies with a focus on nonnormality are needed.

Unified linear response function for zonal flows with full finite orbit effects

2007 ◽  
Vol 14 (11) ◽  
pp. 112512 ◽  
Author(s):  
T. Watari ◽  
Y. Hamada ◽  
A. Nishizawa ◽  
J. Todoroki
Keyword(s):  
Response Function ◽  
Linear Response ◽  
Zonal Flows ◽  
Linear Response Function
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