The Lorenz energy cycle: trends and the impact of modes of climate variability

Qiyun Ma; Valerio Lembo; Christian L.E. Franzke

doi:10.1080/16000870.2021.1900033

The Lorenz energy cycle: trends and the impact of modes of climate variability

Tellus

Volume 73 (2021): Issue 1

By: Qiyun Ma, Valerio Lembo and Christian L.E. Franzke

Open Access

|Jan 2021

Figures & Tables

Variations of eddy available potential energy (*P_E* ) and eddy kinetic energy (*K_E* ) for JRA-55 data. Solid black lines are averages over 1958–1979 and 1979–2019, respectively. Unit is $10^{5} {Jm}^{- 2} .$

The Lorenz energy cycle diagram from JRA-55 reanalysis dataset during 1979–2019. The uncertain range of the time-mean values stand for the standard deviations of the time series of the energy components. Units are $10^{5} {Jm}^{- 2}$ for energy and $W m^{- 2}$ for the conversion rate, generation, and dissipation terms. The arrows indicate the direction that corresponds to positive values. Negative values imply the opposite direction.

Time series of the globally averaged atmospheric energies. (a) The mean available potential energy *P_M* . (b) The eddy available potential energy *P_E* . (c) The total available potential energy $P_{M} + P_{E} .$ (d) The mean kinetic energy K _M. (e) The eddy kinetic energy *K_E* . (f) The total kinetic energy $K_{M} + K_{E} .$

Table 1.

Trends in the global energies.

GlobalTrendSig.Unit

P_{M}

344.09

J m^{- 2}

per year

P_{E}

390.48**

J m^{- 2}

per year

P_{M} + P_{E}

543.75

J m^{- 2}

per year

K_{M}

188.06

J m^{- 2}

per year

K_{E}

121.06

J m^{- 2}

per year

K_{M} + K_{E}

214.42

J m^{- 2}

per year

C (P_{M}, P_{E})

0.00

10^{- 3} W m^{- 2}

per year

C (P_{E}, K_{E})

1.08*

10^{- 3} W m^{- 2}

per year

C (K_{E}, K_{M})

0.38

10^{- 3} W m^{- 2}

per year

C (P_{M}, K_{M})

–0.32*

10^{- 3} W m^{- 2}

per year

G (P_{M})

0.53

10^{- 3} W m^{- 2}

per year

G (P_{E})

0.00

10^{- 3} W m^{- 2}

per year

D (K_{M})

1.45*

10^{- 3} W m^{- 2}

per year

D (K_{E})

–0.44

10^{- 3} W m^{- 2}

per year

+ at at 90% level.

* at 95% level.

** at 99% level.

*** at 99.9% level.

Time series of the conversion rate between the eddy available potential energy and the eddy kinetic energy $C (P_{E}, K_{E}) .$

The dissipation rate of the mean kinetic energy $D (K_{M}) .$

Decomposed globally averaged generation and dissipation rates. (a) The generation rate of the stationary eddy available potential energy $G (P_{S E});$ (b) The generation rate of the transient eddy available potential energy $G (P_{T E});$ (c) The dissipation rate of the stationary eddy kinetic energy $D (K_{S E}) .$ (d) The dissipation rate of the transient eddy kinetic energy $D (K_{T E}) .$

Decomposed globally averaged conversion rates. (a) The conversion rate between the transient eddy kinetic energy and mean kinetic energy $C (K_{T E}, K_{M});$ (b) The conversion rate between the transient eddy kinetic energy and transient eddy kinetic energy $C (P_{T E}, K_{T E}) .$

Table 2.

Decomposition of global energies into eddies.

GlobalTrendSig.Unit

G (P_{SE})

–0.32

10^{- 3} W m^{- 2}

per year

G (P_{TE})

0.48

10^{- 3} W m^{- 2}

per year

D (K_{SE})

–0.45

10^{- 3} W m^{- 2}

per year

D (K_{TE})

0.00

10^{- 3} W m^{- 2}

per year

C (P_{M}, P_{SE})

0.00

10^{- 3} W m^{- 2}

per year

C (P_{M}, P_{TE})

0.00

10^{- 3} W m^{- 2}

per year

C (P_{SE}, P_{TE})

0.00

10^{- 3} W m^{- 2}

per year

C (K_{TE}, K_{M})

0.94*

10^{- 3} W m^{- 2}

per year

C (K_{SE}, K_{M})

0.00

10^{- 3} W m^{- 2}

per year

C (K_{TE}, K_{SE})

0.00

10^{- 3} W m^{- 2}

per year

C (P_{TE}, K_{TE})

0.73+

10^{- 3} W m^{- 2}

per year

C (P_{SE}, K_{SE})

–0.35

10^{- 3} W m^{- 2}

per year

Decomposed the globally averaged eddy available potential energy and kinetic energy. (a) The stationary eddy available potential energy *P_SE* ; (b) The transient eddy available potential energy *P_TE* ; (c) The stationary eddy kinetic energy *K_TE* ; (d) The transient eddy kinetic energy *K_TE* .

Table 3.

Decomposition of potential and kinetic energy ( $J m^{- 2}$ per year).

GlobalNHSHTrendSig.TrendSig.TrendSig.

P_{E}

P_{TE}

315.14**132.24539.17***

P_{SE}

61.90100.00–20.00

K_{E}

K_{TE}

54.77–106.11242.58

K_{SE}

–1.3583.3337.72

Table 4.

The climatological eddy available potential and kinetic energy on different wave-number domain during 1979–2019 ( $J m^{- 2}$ per year).

GroupGLONHSHGroupGLONHSH

P_{SE}

PW0.660.630.69

K_{SE}

PW0.470.460.49SW0.250.240.25SW0.230.280.18MW0.020.020.02MW0.020.020.02SUM0.920.890.96SUM0.710.750.68Percent82.57%74.11%92.24%Percent81.11%76.40%86.93%

P_{TE}

PW1.041.280.80

K_{TE}

PW0.921.020.82SW1.861.871.84SW3.382.983.79MW0.260.290.24MW0.720.750.69SUM3.163.442.88SUM5.024.755.29Percent77.59%75.96%79.63%Percent80.50%79.26%81.64%

Decomposed the stationary and transient eddy energies into wave-number domain. (a) Energies in Planetary-scale Waves group for the stationary eddy available potential energy $P_{S E}_P W;$ (b) Energies in Synoptic-scale Waves group for the transient eddy available potential energy $P_{T E}_S W;$ (c) Energies in Planetary-scale Waves group for the stationary eddy kinetic energy $K_{S E}_P W;$ (d) Energies in Synoptic-scale Waves group for the transient eddy kinetic energy $K_{T E}_S W .$

Table 5.

Decomposition of mechanical energy into wave number domain ( $J m^{- 2}$ per year).

GlobalNHSHTrendSig.TrendSig.TrendSig.

P_{SE}

PW–3.5757.19–51.92SW–23.75–44.10+8.01MW–0.00*0.00–5.00***SUM–32.29–55.14–53.49

P_{TE}

PW88.2310.43177.37+SW176.47***146.86*225.66***MW12.50*1.3516.67*SUM279.40***78.24448.81***

K_{SE}

PW–6.9324.17–40.00SW–0.00–50.8133.81MW–2.94***0.00+–3.28**SUM–50.55–67.42–14.64

K_{TE}

PW–100.00+–120.61–62.35SW210.17**93.52276.03**MW–0.00–29.8626.79SUM103.85–34.72252.66+

Table 6.

Correlations between climate indices and different global Lorenz energy cycle components.

P_{M} + P_{E}

K_{M} + K_{E}

P_M P_E K_M K_E

C (P_{M}, P_{E})

A O

–0.31*–0.21–0.32*0.16–0.29+0.35*0.01

NAO

–0.19–0.19–0.210.22–0.31+0.46**–0.07

NINO 3.4

0.54***0.47**0.53***–0.200.41**–0.040.05

PNA

0.30+0.61***0.30+–0.170.56***–0.150.26+

SAM

0.26+0.240.27+–0.190.33*–0.38*0.31*

QBO

–0.080.09–0.04–0.230.060.070.17

PDO

0.44**0.56***0.43**–0.100.47**–0.030.26+

AMO

0.200.29*0.23–0.28+0.38*–0.43**0.13

GMST

0.47**0.68***0.52***–0.49**0.69***–0.39*0.18

Δ T_{N H}

–0.07–0.01–0.070.01–0.040.090.18

Δ T_{S H}

0.32*0.210.36*–0.39*0.35*–0.52***0.46**

C (P_{E}, K_{E})

C (K_{E}, K_{M})

C (P_{M}, K_{M})

G_PM G_PE D_KM D_KE

A O

0.35*0.190.000.010.49**0.170.21

NAO

0.130.040.02–0.080.27+0.030.12

NINO 3.4

–0.17–0.130.020.04–0.30+–0.12–0.05

PNA

0.070.080.090.20–0.160.05–0.02

SAM

0.35*0.41**–0.220.38*0.190.41**–0.09

QBO

0.090.26+–0.090.19–0.040.25–0.24

PDO

–0.08–0.050.130.18–0.37*–0.08–0.03

AMO

0.050.130.000.12–0.060.11–0.10

GMST

0.070.21–0.100.21–0.080.21–0.20

Δ T_{N H}

0.39*0.260.100.120.38*0.200.17

Δ T_{S H}

0.4*0.46**–0.030.43**0.110.41**–0.10

Table 7.

Correlations between climate indices and different eddies Lorenz energy cycle components at different scales.

GlobalNHSHP _SE P_TE K_SE K_TE P_SE P_TE K_SE K_TE P_SE P_TE K_SE K_TE AO0.200.030.27+0.130.23–0.000.40**0.100.080.040.020.08NAO0.31*0.000.42**0.090.40**0.010.47**0.200.08–0.010.22–0.03NINO3.4–0.29+–0.00–0.36*0.39*–0.33*–0.22–0.33*–0.00–0.120.22–0.27+0.46**PNA0.09–0.31*–0.12–0.040.08–0.41**–0.05–0.200.060.01–0.170.10SAM–0.11–0.15–0.26+–0.18–0.090.23–0.28+0.28+–0.09–0.43**–0.16–0.40**QBO–0.07–0.21–0.050.16–0.07–0.44**0.07–0.04–0.040.17–0.170.21PDO0.06–0.19–0.170.180.01–0.25–0.170.080.080.01–0.120.15AMO–0.17–0.21–0.35*–0.12–0.17–0.11–0.33*0.04–0.10–0.16–0.27+–0.17GMST–0.33*–0.34*–0.50***0.12–0.32*–0.35*–0.39*0.09–0.21–0.09–0.46**0.08

Δ T_{N H}

0.000.010.010.120.00–0.050.160.010.000.07–0.160.13

Δ T_{S H}

–0.20–0.33*–0.32*–0.28+–0.100.18–0.36*0.18–0.23–0.60***–0.17–0.45**

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DOI: https://doi.org/10.1080/16000870.2021.1900033 | Journal eISSN: 3035-9554

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Language: English

Page range: 1900033 - 1900033

Published on: Jan 1, 2021

Published by: Stockholm University Press

In partnership with: Paradigm Publishing Services

Keywords:

Lorenz energy cycle,

climate variability,

trends

© 2021 Qiyun Ma, Valerio Lembo, Christian L.E. Franzke, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 73 (2021): Issue 1

The Lorenz energy cycle: trends and the impact of modes of climate variability

Figures & Tables

Fig. 1.

Fig. 2.

Fig. 3.

Table 1.

Fig. 4.

Fig. 5.

Fig. 6.

Fig. 7.

Table 2.

Fig. 8.

Table 3.

Table 4.

Fig. 9.

Table 5.

Table 6.

Table 7.

Paradigm

My account