Climate variability from annual to multi-decadal timescales in a two-layer stochastic energy balance model: analytic solutions and implications for general circulation models

Sergei Soldatenko; Robert Colman

doi:10.1080/16000870.2018.1554421

Climate variability from annual to multi-decadal timescales in a two-layer stochastic energy balance model: analytic solutions and implications for general circulation models

Tellus

Volume 71 (2019): Issue 1

By: Sergei Soldatenko and Robert Colman

Open Access

|Jan 2019

Figures & Tables

Table 1.

Maximum, minimum and multi-model mean values of radiative feedback parameter $λ$ and climate system inertia parameters C, C_D and $γ$ obtained from analysis of the CMIP5 models (Geoffroy et al., 2013a) and the corresponding values for σ_s from this study.

ParameterMin. valueMax. valueMulti-model mean

λ

(W m⁻² K⁻¹)0.611.701.13

γ

(W m⁻² K⁻¹)0.501.160.73C (W yr m⁻² K⁻¹)4.78.67.3C_D (W yr m⁻² K⁻¹)53145106

σ_{s}

(W m⁻²)0.300.600.46

Table 2.

Maximum, minimum and multi-model mean values of model parameters used in calculations.

ParameterMin valueMax valueBase value

f

0.10.80.64

γ

(W m⁻² K⁻¹)0.11.31.13C (W yr m⁻² K⁻¹)4407.5/20/30C_D (W yr m⁻² K⁻¹)50250100

σ_{s}

(W m⁻²)0.10.80.46

[i] Shown values for the parameter C correspond, respectively, to inter-annual, decadal and multi-decadal timescale variability.

Surface temperature variance as a function of (a) upper layer effective heat capacity C, (b) feedback parameter f, (c) parameter γ and (d) lower layer effective heat capacity *C_D*. The bold line indicates the range of parameter values obtained from analysis of the CMIP5 models (Geoffroy et al.,2013a).

Surface temperature variance as a function of parameter $σ_{s}$ . The bold line here is the calculated range from the CMIP5 models listed in Geoffroy et al., (2013a).

Table 3.

Calculated surface temperature variance $δ T^{2}〉$ for various values of the upper layer effective heat capacity C and the inter-annual, decadal and multi-decadal surface temperature variances obtained from the CMIP5 models.

C (W yr m^-2 K^-1)57.5101520253040Calculated variances

δ T^{2}〉 (K^{2})

Base parameter values0.01170.00790.00590.00400.00300.00240.00210.0016Base values except

γ = 0.9

0.01060.00710.00540.00370.00280.00230.00190.0015Base values except

γ = 0.9

and C_D=2000.01050.00710.00530.00360.00270.00220.00180.0014Base values except

γ = 0.9

, C_D=200 and

σ_{S} = 0.4

0.00800.00530.00400.00270.00200.00160.00140.0011Variances

δ T^{2}〉 (K^{2})

from CMIP5 modelsInter-annualDecadalMulti-decadal0.007010.002120.00071

Sensitivity of surface temperature variance to (a) upper layer effective heat capacity C, (b) feedback parameter f, (c) parameter γ and (d) lower layer effective heat capacity *C_D*. The bold line indicates the range of parameter values obtained from analysis of the CMIP5 models (Geoffroy et al.,2013a).

Sensitivity of the surface temperature variance to parameter $σ_{s}$ . The bold line here is the calculated range from the CMIP5 models listed in Geoffroy et al., (2013a).

Table 4.

Changes in the absolute value of surface temperature variance $Δ δ T^{2}〉|$ caused by variations in model parameters whose absolute values $δ p_{i}|$ deviate 5% from the base values $p_{i}^{*}$ .

Parameter

C

(W yr m⁻² K⁻¹)

f

γ

(W m⁻² K⁻¹)

C_{D}

(W yr m⁻² K⁻¹)

σ_{s}

(W m⁻²)Variation in absolute value of parameter

δ p_{i}|

0.37500.03200.035050.0230Change in

Δ δ T^{2}〉|

3.87 × 10⁻⁴4.50 × 10⁻⁴1.40 × 10⁻⁴6.54 × 10⁻⁶7.86 × 10⁻⁴

Relative sensitivity of surface temperature variance to (a) upper layer effective heat capacity C, (b) feedback parameter f, (c) parameter γ and (d) lower layer effective heat capacity *C_D*. The bold line indicates the range of parameter values obtained from analysis of the CMIP5 models (Geoffroy et al.,2013a).

Table 5.

Relative sensitivity coefficients calculated for annual, decadal and multi-decadal surface temperature variability.

ParameterCC_Dfγσ_SAnnual variability
C = 7.5 W yr m⁻² K⁻¹−0.97−0.021.14−0.362.00Decadal variability
C = 20 W yr m⁻² K⁻¹−0.94−0.041.21−0.322.00Multi-decadal variability
C = 30 W yr m⁻² K⁻¹−0.91−0.051.26−0.292.00Multi-decadal variability
C = 40 W yr m⁻² K⁻¹−0.89−0.071.30−0.272.00

Table 6.

Surface temperature variances $δ T^{2}〉 (K^{2})$ calculated for maximum and minimum values of model parameters.

ParameterFor max. parameter valueFor min. parameter valueDifference (absolute value)C (W yr m⁻² K⁻¹)0.00690.01250.0056

γ

(W m⁻² K⁻¹)0.00640.00880.0024

λ

(W m⁻² K⁻¹)0.00590.01120.0053C_D (W yr m⁻² K⁻¹)0.00780.00800.0002σ_s (W m⁻²)0.01340.00330.0101

[i] The values for C, $γ$ , $λ$ and C_D are obtained from analysis of the CMIP5 models (Geoffroy et al., 2013a), and the values for $σ_{s}$ are from this study.

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DOI: https://doi.org/10.1080/16000870.2018.1554421 | Journal eISSN: 3035-9554

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Language: English

Page range: 1554421 - 1554421

Accepted on: Nov 26, 2018

Published on: Jan 1, 2019

Published by: Stockholm University Press

In partnership with: Paradigm Publishing Services

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© 2019 Sergei Soldatenko, Robert Colman, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 71 (2019): Issue 1

Climate variability from annual to multi-decadal timescales in a two-layer stochastic energy balance model: analytic solutions and implications for general circulation models

Figures & Tables

Table 1.

Table 2.

Fig. 1.

Fig. 2.

Table 3.

Fig. 3.

Fig. 4.

Table 4.

Fig. 5.

Table 5.

Table 6.

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