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On unravelling mechanism of interplay between cloud and large scale circulation: a grey area in climate science

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Abstract

The interaction between cloud and large scale circulation is much less explored area in climate science. Unfolding the mechanism of coupling between these two parameters is imperative for improved simulation of Indian summer monsoon (ISM) and to reduce imprecision in climate sensitivity of global climate model. This work has made an effort to explore this mechanism with CFSv2 climate model experiments whose cloud has been modified by changing the critical relative humidity (CRH) profile of model during ISM. Study reveals that the variable CRH in CFSv2 has improved the nonlinear interactions between high and low frequency oscillations in wind field (revealed as internal dynamics of monsoon) and modulates realistically the spatial distribution of interactions over Indian landmass during the contrasting monsoon season compared to the existing CRH profile of CFSv2. The lower tropospheric wind error energy in the variable CRH simulation of CFSv2 appears to be minimum due to the reduced nonlinear convergence of error to the planetary scale range from long and synoptic scales (another facet of internal dynamics) compared to as observed from other CRH experiments in normal and deficient monsoons. Hence, the interplay between cloud and large scale circulation through CRH may be manifested as a change in internal dynamics of ISM revealed from scale interactive quasi-linear and nonlinear kinetic energy exchanges in frequency as well as in wavenumber domain during the monsoon period that eventually modify the internal variance of CFSv2 model. Conversely, the reduced wind bias and proper modulation of spatial distribution of scale interaction between the synoptic and low frequency oscillations improve the eastward and northward extent of water vapour flux over Indian landmass that in turn give feedback to the realistic simulation of cloud condensates attributing improved ISM rainfall in CFSv2.

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Acknowledgements

Authors are thankful to Director; IITM for providing constant encouragement to carry out the research work. High Power Computing System (HPCS), Prithvi facility is highly acknowledged. Thanks are due to ERA, CFSR for the free data availability. Authors are also thankful to Brian Doty, COLA for the use of GrADS software. Anonymous reviewers’ comments are also gratefully acknowledged. The model output data for different experiments of CFSv2 are in the archive of national monsoon mission project, Ministry of Earth Science, Govt. of India and may be disseminated after taking permission from appropriate authority.

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  1. Indian Institute of Tropical Meteorology, Dr. Homi Bhabha Road, Pashan, Pune, Maharastra, 411 008, India

    S. De, N. K. Agarwal, Anupam Hazra, Hemantkumar S. Chaudhari & A. K. Sahai

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Appendix

Appendix

Mathematical equation for error energy growth rate budget:

$$\begin{aligned} &\mathop { \sum }\limits_{n} \left[ {\frac{\partial }{{\partial t}}\left( {\frac{1}{2}{u_e}C_{n}^{2}} \right)+\frac{\partial }{{\partial t}}\left( {\frac{1}{2}{u_e}S_{n}^{2}} \right)+\frac{\partial }{{\partial t}}\left( {\frac{1}{2}{v_e}C_{n}^{2}} \right)+\frac{\partial }{{\partial t}}\left( {\frac{1}{2}{v_e}S_{n}^{2}} \right)} \right]= - \frac{1}{2}\left( {\mathop \sum \limits_{{n=r+s}}^{{}} +\mathop \sum \limits_{{n=r - s}} +\mathop \sum \limits_{{n=s - r}} } \right), \\ & \quad \times \left\{ {\begin{array}{*{20}{c}} {{u_m}{C_n} \cdot {u_e}{C_r}\frac{{\partial {u_e}{C_s}}}{{\partial x}}+{u_m}{C_n} \cdot {v_e}{C_r}\frac{{\partial {v_e}{C_s}}}{{\partial x}}+\frac{1}{2}\frac{{\partial {u_m}{C_n}}}{{\partial x}}{u_e}{C_r} \cdot {u_e}{C_s}+\frac{1}{2}\frac{{\partial {u_m}{C_n}}}{{\partial x}}{v_e}{C_r} \cdot {v_e}{C_s}} \\ {+{v_m}{C_n} \cdot {u_e}{C_r}\frac{{\partial {u_e}{C_s}}}{{\partial y}}+{v_m}{C_n} \cdot {v_e}{C_r}\frac{{\partial {v_e}{C_s}}}{{\partial y}}+\frac{1}{2}\frac{{\partial {v_m}{C_n}}}{{\partial y}}{u_e}{C_r} \cdot {u_e}{C_s}+\frac{1}{2}\frac{{\partial {v_m}{C_n}}}{{\partial y}}{v_e}{C_r} \cdot {v_e}{C_s}} \end{array}} \right\}F, \\ & \quad - \frac{1}{2}\left( { - \mathop \sum \limits_{{n=r+s}} +\mathop \sum \limits_{{n=r - s}} +\mathop \sum \limits_{{n=s - r}} } \right)\left\{ {\begin{array}{*{20}{c}} {{u_m}{C_n} \cdot {u_e}{S_r}\frac{{\partial {u_e}{S_s}}}{{\partial x}}+{u_m}{C_n} \cdot {v_e}{S_r}\frac{{\partial {v_e}{S_s}}}{{\partial x}}+\frac{1}{2}\frac{{\partial {u_m}{C_n}}}{{\partial x}}{u_e}{S_r} \cdot {u_e}{S_s}} \\ {+\frac{1}{2}\frac{{\partial {u_m}{C_n}}}{{\partial x}}{v_e}{S_r} \cdot {v_e}{S_s}+{v_m}{C_n} \cdot {u_e}{S_r}\frac{{\partial {u_e}{S_s}}}{{\partial y}}+{v_m}{C_n} \cdot {v_e}{S_r}\frac{{\partial {v_e}{S_s}}}{{\partial y}}} \\ {+\frac{1}{2}\frac{{\partial {v_m}{C_n}}}{{\partial y}}{u_e}{S_r} \cdot {u_e}{S_s}+\frac{1}{2}\frac{{\partial {v_m}{C_n}}}{{\partial y}}{v_e}{S_r} \cdot {v_e}{S_s}} \end{array}} \right\}L, \\ & \quad - \frac{1}{2}\left( {\mathop \sum \limits_{{n=r+s}} - \mathop \sum \limits_{{n=r - s}} +\mathop \sum \limits_{{n=s - r}} } \right)\left\{ {\begin{array}{*{20}{c}} {{u_m}{S_n} \cdot {u_e}{C_r}\frac{{\partial {u_e}{S_s}}}{{\partial x}}+{u_m}{S_n} \cdot {v_e}{C_r}\frac{{\partial {v_e}{S_s}}}{{\partial x}}+\frac{1}{2}\frac{{\partial {u_m}{S_n}}}{{\partial x}}{u_e}{C_r} \cdot {u_e}{S_s}} \\ {+\frac{1}{2}\frac{{\partial {u_m}{S_n}}}{{\partial x}}{v_e}{C_r} \cdot {v_e}{S_s}+{v_m}{S_n} \cdot {u_e}{C_r}\frac{{\partial {u_e}{S_s}}}{{\partial y}}+{v_m}{S_n} \cdot {v_e}{C_r}\frac{{\partial {v_e}{S_s}}}{{\partial y}}} \\ {+\frac{1}{2}\frac{{\partial {v_m}{S_n}}}{{\partial y}}{u_e}{C_r} \cdot {u_e}{S_s}+\frac{1}{2}\frac{{\partial {v_m}{S_n}}}{{\partial y}}{v_e}{C_r} \cdot {v_e}{S_s}} \end{array}} \right\}U, \\ & \quad - \frac{1}{2}\left( {\mathop \sum \limits_{{n=r+s}} +\mathop \sum \limits_{{n=r - s}} - \mathop \sum \limits_{{n=s - r}} } \right)\left\{ {\begin{array}{*{20}{c}} {{u_m}{S_n} \cdot {u_e}{S_r}\frac{{\partial {u_e}{C_s}}}{{\partial x}}+{u_m}{S_n} \cdot {v_e}{S_r}\frac{{\partial {v_e}{C_s}}}{{\partial x}}+\frac{1}{2}\frac{{\partial {u_m}{S_n}}}{{\partial x}}{u_e}{S_r} \cdot {u_e}{C_s}} \\ {+\frac{1}{2}\frac{{\partial {u_m}{S_n}}}{{\partial x}}{v_e}{S_r} \cdot {v_e}{C_s}+{v_m}{S_n} \cdot {u_e}{S_r}\frac{{\partial {u_e}{C_s}}}{{\partial y}}+{v_m}{S_n} \cdot {v_e}{S_r}\frac{{\partial {v_e}{C_s}}}{{\partial y}}} \\ {+\frac{1}{2}\frac{{\partial {v_m}{S_n}}}{{\partial y}}{u_e}{S_r} \cdot {u_e}{C_s}+\frac{1}{2}\frac{{\partial {v_m}{S_n}}}{{\partial y}}{v_e}{S_r} \cdot {v_e}{C_s}} \end{array}} \right\}X, \\ & \quad - \frac{1}{2}\left( {\mathop \sum \limits_{{n=r+s}} +\mathop \sum \limits_{{n=r - s}} +\mathop \sum \limits_{{n=s - r}} } \right)\left\{ {\begin{array}{*{20}{c}} {\frac{{\partial {u_a}{C_n}}}{{\partial x}}{u_e}{C_r} \cdot {u_e}{C_s}+\frac{{\partial {u_a}{C_n}}}{{\partial y}}{u_e}{C_r} \cdot {v_e}{C_s}+\frac{{\partial {v_a}{C_n}}}{{\partial x}}{u_e}{C_r} \cdot {v_e}{C_s}} \\ {+\frac{{\partial {v_a}{C_n}}}{{\partial y}}{v_e}{C_r} \cdot {v_e}{C_s}} \end{array}} \right\}GE, \\ & \quad - \frac{1}{2}\left( { - \mathop \sum \limits_{{n=r+s}} +\mathop \sum \limits_{{n=r - s}} +\mathop \sum \limits_{{n=s - r}} } \right)\left\{ {\begin{array}{*{20}{c}} {\frac{{\partial {u_a}{C_n}}}{{\partial x}}{u_e}{S_r} \cdot {u_e}{S_s}+\frac{{\partial {u_a}{C_n}}}{{\partial y}}{u_e}{S_r} \cdot {v_e}{S_s}+\frac{{\partial {v_a}{C_n}}}{{\partial x}}{u_e}{S_r} \cdot {v_e}{S_s}} \\ {+\frac{{\partial {v_a}{c_n}}}{{\partial y}}{v_e}{S_r} \cdot {v_e}{S_s}} \end{array}} \right\}NE, \\ & \quad - \frac{1}{2}\left( {\mathop \sum \limits_{{n=r+s}} - \mathop \sum \limits_{{n=r - s}} +\mathop \sum \limits_{{n=s - r}} } \right)\left\{ {\begin{array}{*{20}{c}} {\frac{{\partial {u_a}{S_n}}}{{\partial x}}{u_e}{C_r} \cdot {u_e}{S_s}+\frac{{\partial {u_a}{S_n}}}{{\partial y}}{u_e}{C_r} \cdot {v_e}{S_s}+\frac{{\partial {v_a}{S_n}}}{{\partial x}}{u_e}{C_r} \cdot {v_e}{S_s}} \\ {+\frac{{\partial {v_a}{S_n}}}{{\partial y}}{v_e}{C_r} \cdot {v_e}{S_s}} \end{array}} \right\}RA, \\ & \quad - \frac{1}{2}\left( {\mathop \sum \limits_{{n=r+s}} +\mathop \sum \limits_{{n=r - s}} - \mathop \sum \limits_{{n=s - r}} } \right)\left\{ {\begin{array}{*{20}{c}} {\frac{{\partial {u_a}{S_n}}}{{\partial x}}{u_e}{S_r} \cdot {u_e}{C_s}+\frac{{\partial {u_a}{S_n}}}{{\partial y}}{u_e}{S_r} \cdot {v_e}{C_s}+\frac{{\partial {v_a}{S_n}}}{{\partial x}}{u_e}{S_r} \cdot {v_e}{C_s}} \\ {+\frac{{\partial {v_a}{S_n}}}{{\partial y}}{v_e}{S_r} \cdot {v_e}{C_s}} \end{array}} \right\}TION, \\ & \quad +{\text{ }}{V_e} \cdot R{\text{ }}\left( {RESIDUAL} \right). \\ \end{aligned}$$
(5)

In the above equation, umC, vmC and umS, vmS are the cosine and sine component of zonal and meridional wind field of model output, respectively. Similarly, uaC, vaC and uaS, vaS are the cosine and sine component of zonal and meridional analysis/observed wind field, respectively. The subscript n, r and s represent three wavenumber of participating waves in triad interactions. The left hand side of the equation evaluates the spectral error growth rate term. The extent of flux, generation and residual term are shown by indicating outside the second bracket in the right hand side of above equation.

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De, S., Agarwal, N.K., Hazra, A. et al. On unravelling mechanism of interplay between cloud and large scale circulation: a grey area in climate science. Clim Dyn 52, 1547–1568 (2019). https://doi.org/10.1007/s00382-018-4211-6

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