On the spread of changes in marine low cloud cover in climate model simulations of the 21st century

Abstract

In 36 climate change simulations associated with phases 3 and 5 of the Coupled Model Intercomparison Project (CMIP3 and CMIP5), changes in marine low cloud cover (LCC) exhibit a large spread, and may be either positive or negative. Here we develop a heuristic model to understand the source of the spread. The model’s premise is that simulated LCC changes can be interpreted as a linear combination of contributions from factors shaping the clouds’ large-scale environment. We focus primarily on two factors—the strength of the inversion capping the atmospheric boundary layer (measured by the estimated inversion strength, EIS) and sea surface temperature (SST). For a given global model, the respective contributions of EIS and SST are computed. This is done by multiplying (1) the current-climate’s sensitivity of LCC to EIS or SST variations, by (2) the climate-change signal in EIS or SST. The remaining LCC changes are then attributed to changes in greenhouse gas and aerosol concentrations, and other environmental factors. The heuristic model is remarkably skillful. Its SST term dominates, accounting for nearly two-thirds of the intermodel variance of LCC changes in CMIP3 models, and about half in CMIP5 models. Of the two factors governing the SST term (the SST increase and the sensitivity of LCC to SST perturbations), the SST sensitivity drives the spread in the SST term and hence the spread in the overall LCC changes. This sensitivity varies a great deal from model to model and is strongly linked to the types of cloud and boundary layer parameterizations used in the models. EIS and SST sensitivities are also estimated using observational cloud and meteorological data. The observed sensitivities are generally consistent with the majority of models as well as expectations from prior research. Based on the observed sensitivities and the relative magnitudes of simulated EIS and SST changes (which we argue are also physically reasonable), the heuristic model predicts LCC will decrease over the 21st-century. However, to place a strong constraint, for example on the magnitude of the LCC decrease, will require longer observational records and a careful assessment of other environmental factors producing LCC changes. Meanwhile, addressing biases in simulated EIS and SST sensitivities will clearly be an important step towards reducing intermodel spread in simulated LCC changes.

Appendices

Appendix 1: Calculating EIS and SST slopes

EIS slope is calculated based on detrended time series of LCC, EIS and SST in 20th-century ($LCC^{\prime}, EIS^{\prime}, SST^{\prime}$) as follows. First, we regress $EIS^{\prime}$ onto $SST^{\prime}$ ($EIS^{\prime}\approx\alpha_{1}\cdot SST^{\prime}+\alpha_{\rm o}$). Then we tease out the component of $EIS^{\prime}$ uncorrelated with $SST^{\prime}, EIS^{\prime}_{clean}$ ($= EIS^{\prime}-\alpha_{1}\cdot SST^{\prime}$). Third, we regress $LCC^{\prime}$ onto $SST^{\prime}$ ($LCC^{\prime}\approx\beta_{1}\cdot SST^{\prime}+\beta_{\rm o}$), and tease out the component of $LCC^{\prime}$ uncorrelated with $SST^{\prime}, LCC^{\prime}_{clean}$ ($= LCC^{\prime}-\beta_{1}\cdot SST^{\prime}$). Finally, we regress $LCC_{clean}^{\prime}$ onto $EIS_{clean}^{\prime}$ ($LCC_{clean}^{\prime}\approx\gamma_{1}\cdot EIS_{clean}^{\prime}+\gamma_{\rm o}$). EIS slope assumes the value of γ ₁.

Likewise, to calculate SST slope, we first regress $SST^{\prime}$ onto $EIS^{\prime}$ ($SST^{\prime}\approx\alpha_{1}\cdot EIS^{\prime}+\alpha_{\rm o}$). Then we tease out the component of $SST^{\prime}$ uncorrelated with $EIS^{\prime},$ $SST_{clean}^{\prime}$ = ($SST^{\prime}-\alpha_{1}\cdot EIS^{\prime}$). Third, we regress $LCC^{\prime}$ onto $EIS^{\prime}$ ($LCC^{\prime}\approx\beta_{1}\cdot EIS^{\prime}+\beta_{\rm o}$), and tease out the component of $LCC^{\prime}$ uncorrelated with $EIS^{\prime}, LCC^{\prime}_{clean}$ = ($LCC^{\prime}-\beta_{1}\cdot EIS^{\prime}$). Finally, we regress $LCC_{clean}^{\prime}$ onto $SST_{clean}^{\prime}$ ($LCC_{clean}^{\prime}\approx\gamma_{1}\cdot SST_{clean}^{\prime}+\gamma_{\rm o}$). SST slope assumes the value of γ ₁.

Using the methodology described above, we also estimate EIS and SST slopes in pre-industrial control simulations and 21st-century simulations (scenario A1B for CMIP3 models and RCP 8.5 for CMIP5 models) with 18 CMIP3 and 18 CMIP5 models (The long-term trends in LCC, EIS and SST in the 21st-century simulations were removed before calculating EIS and SST slopes.). Figure 15a scatters the EIS slope in the historical simulations against the EIS slope in their corresponding pre-industrial control simulations, and Fig. 15b scatters the EIS slope in the historical simulations against the EIS slope in their corresponding 21st-century simulations. The EIS slope exhibits a high degree of correspondence among differ simulations of each CMIP3 or CMIP5 model. Figure 15c scatters the SST slope in the historical simulations against the SST slope in their corresponding pre-industrial control simulations, and Fig. 15d scatters the SST slope in the historical simulations against the SST slope in their corresponding 21st-century simulations. The SST slope also exhibits a high degree of correspondence among different simulations of each CMIP3 or CMIP5 model, though some discrepancy in this quantity between the historical and 21st-century simulations is visible.

Fig. 15

a Scatterplot of the EIS slope in the historical simulations versus the EIS slope in the respective pre-industrial control simulations in 36 models. b Scatterplot of the EIS slope in the historical simulations versus the EIS slope in the respective 21st-century simulations in 36 models. c As in (a) but for the SST slope. d As in (b) but for the SST slope. In each model, the EIS or SST slope is first calculated for each region and then averaged over the 5 regions. CMIP3 models are color-coded in blue and CMIP5 models in red. Solid line in each diagram represents the line y = x. Note that the pre-industrial control simulation with model F has no cloud data, so it is not shown in panels (a) and (c)

Appendix 2: An analytical expression for EIS change

Based on the definition of LTS, we rewrite Eq. (1) as follows

$$EIS = T_{700}\cdot\left(\frac{1000}{700}\right)^{Ra/c_{p}} - T_{s}\cdot\left(\frac{1000}{p_{s}}\right)^{Ra/c_{p}} - \Upgamma_{m}^{850}\cdot(z_{700}-LCL)$$

(4)

where Ra (=287 J K⁻¹ kg⁻¹) is gas constant for air, c _p (=1,004 J K⁻¹ kg⁻¹) is specific heat of air at constant pressure, and p _s is surface pressure, typically, 1,020 hPa. Treating z700 and LCL as constants, we obtain an expression for EIS change

$$\Updelta EIS = 1.11\cdot \Updelta T_{700} - 0.99\cdot \Updelta T_{s} - \frac{d\Upgamma_{m}^{850}}{dT_{850}}\cdot \Updelta T_{850}\cdot(z_{700}-LCL)$$

(5)

Consistent with Wood and Bretherton (2006), we approximate T ₈₅₀ by the mean of T _s and T ₇₀₀. So, $\Updelta T_{850}=\frac{1}{2}\cdot(\Updelta T_{s}+\Updelta T_{700})$. Based on the formula for $\Upgamma_{m}^{850}$ in Wood and Bretherton (2006) and assuming some typical values for T _s , T ₇₀₀ and surface relative humidity (respectively: 295, 280 K and 80 %), we obtain $d\Upgamma_{m}^{850}/dT_{850}=1\times10^{-4}\, \hbox{m}^{-1}, z700=3250$ m and LCL = 430 m. With these estimates, we arrive at an analytical expression for EIS change.

$$\Updelta EIS \approx 0.97\cdot \Updelta T_{700} - 1.14\cdot \Updelta T_{s}$$

(6)

Appendix 3: PBL parameterization

The three categories of PBL schemes are described in order of increasing complexity:

Category 1, the “K(Ri)” scheme. In 15 of the 36 models (models A, C, D, E, M, N, O, P, R, c, d, l, m, n and q), K is parameterized as a decreasing function of the local Richardson number Ri, with unstable situations (Ri < 0) associated with a larger K than stable situations (Ri > 0).

Category 2, the “K profile” scheme. In 13 of the 36 models (models B, G, H, I, Q, a, b, f, g, h, j, k and r), a fixed vertical profile of K is assumed when boundary layers are unstable (Ri < 0): K peaks somewhere inside the PBL and decreases towards both the surface and PBL top where it vanishes. When boundary layers are stable (Ri > 0), the K is parameterized as a decreasing function of Ri as in the “K(Ri)” scheme.

Category 3, the “K(TKE)” scheme. In 8 of the 36 models (models F, J, K, L, e, i, o and p), K is parameterized as a function of turbulent kinetic energy (TKE). TKE is predicted with a prognostic equation including terms corresponding to generation by wind shear and buoyancy, a vertical transport term, and a dissipation term.

Appendix 4: Cloud cover parameterization

The four categories of cloud schemes are described in order of increasing complexity:

Category 1, the “Diag (RH)” scheme. In 3 of the 31 diagnostic models (models L, P and p), cloud cover is a simple function of relative humidity.

Category 2, the “Diag (RH, stability)” scheme. In 14 of the remaining diagnostic models (models B, C, D, G, J, K, M, Q, a, b, d, e, i and r), cloud cover is parameterized through relative humidity with some consideration of thermal stability effects.

Category 3, the “Diag (PDF)” scheme. In the final 14 of the diagnostic models (models A, E, F, N, O, R, c, j, k, l, m, n, o and q), cloud cover is determined by accounting for the sub-grid scale variability in both total water content and temperature. This variability often assumes some simple probability density functions (PDFs).

Category 4, the “Prog” scheme. A prognostic scheme developed by Tiedtke (1993) is implemented in five models (models H, I, f, g and h). In this scheme, cloud cover is determined by a prognostic equation that accounts for various cloud formation and dissipation processes.