Robustness, uncertainties, and emergent constraints in the radiative responses of stratocumulus cloud regimes to future warming

Abstract

Future responses of cloud regimes are analyzed for five CMIP5 models forced with observed SSTs and subject to a patterned SST perturbation. Correlations between cloud properties in the control climate and changes in the warmer climate are investigated for each of a set of cloud regimes defined using a clustering methodology. The only significant (negative) correlation found is in the in-regime net cloud radiative effect for the stratocumulus regime. All models overestimate the in-regime albedo of the stratocumulus regime. Reasons for this bias and its relevance to the future response are investigated. A detailed evaluation of the models’ daily-mean contributions to the albedo from stratocumulus clouds with different cloud cover fractions reveals that all models systematically underestimate the relative occurrence of overcast cases but overestimate those of broken clouds. In the warmer climate the relative occurrence of overcast cases tends to decrease while that of broken clouds increases. This suggests a decrease in the climatological in-regime albedo with increasing temperature (a positive feedback); this is opposite to the feedback suggested by the analysis of the bulk in-regime albedo. Furthermore we find that the inter-model difference in the sign of the in-cloud albedo feedback is consistent with the difference in sign of the in-cloud liquid water path response, and there is a strong positive correlation between the in-regime liquid water path in the control climate and its response to warming. We therefore conclude that further breakdown of the in-regime properties into cloud cover and in-cloud properties is necessary to better understand the behavior of the stratocumulus regime. Since cloud water is a physical property and is independent of a model’s radiative assumptions, it could potentially provide a useful emergent constraint on cloud feedback.

Appendices

Appendix 1: Breakdown of net CRE into contributions from cloud regimes

$$netCRE = \sum\limits_{i = 1}^{R} {netCRE_{i} }$$

(1)

Net CRE can be broken down into contributions of different cloud regimes.

R is the total number of the regimes, netCRE _i is the mean contribution of regime i to the net CRE.

netCRE _i is broken down into the relative frequency of occurrence of regime i (RFO _i ) and the in-regime net CRE (netCREO _i ),

$$netCRE_{i} = RFO_{i} \cdot netCREO_{i}$$

(2)

The future response of net CRE from each cloud regime (ΔnetCRE _i ) is from contributions from changes in the RFO and changes in the in-regime net CRE, based on the following equation.

$$\Delta netCRE_{i} =\Delta RFO_{i} \cdot netCREO_{i} + RFO_{i} \cdot\Delta netCREO_{i} +\Delta RFO_{i} \cdot\Delta netCREO_{i}$$

(3)

The definitions of RFO _i and netCREO _i are as follows.

$$RFO_{i} = \frac{{\sum\nolimits_{j = 1}^{n\left( i \right)} {w\left( j \right)} }}{{\sum\nolimits_{j = 1}^{N} {w\left( j \right)} }},$$

(4)

here n(i) is the number of points which are assigned to the cloud regime i and N is the total number of points.

$$N = \sum\limits_{i = 1}^{R} {n\left( i \right)}$$

(5)

$$netCREO_{i} = \frac{{\sum\nolimits_{j = 1}^{n\left( i \right)} {w(j) \cdot netCRE\left( j \right)} }}{{\sum\nolimits_{j = 1}^{n\left( i \right)} {w(j)} }}.$$

(6)

w(j) is the area weight of the point normalized by the total area of interest.

Appendix 2: Decomposition of sw CRE into the solar insolation and the albedo

The SW CRE (swCRE) contribution from regime i is swCRE _i and the in-regime SW CRE (swCREO _i ) is defined as follows,

$$swCREO_{i} = \frac{{\sum\nolimits_{j = 1}^{n\left( i \right)} {w(j) \cdot swCRE\left( j \right)} }}{{\sum\nolimits_{j = 1}^{n\left( i \right)} {w(j)} }}$$

(7)

n(i) is the number of points which are assigned to the cloud regime i, and w(j) is an area weight of the point normalized by the total area of the interest. As defined in Eq. 5, N is the total number of data points.

swCRE(j) is affected by the solar insolation S ₀(j) and the cloud albedo effect CAE(j).

$$swCRE\left( j \right) = S_{0} \left( j \right) \cdot CAE\left( j \right)$$

(8)

CAE is defined as the difference of the all-sky albedo (A _total ) from the clear sky albedo (A _clr ) at the TOA.

$$CAE\left( j \right) = A_{clr} \left( j \right) - A_{total} \left( j \right)$$

(9)

Further, CAE can be expressed in terms of cloud cover (c) and in-cloud TOA albedo (A _ic ).

$$\begin{aligned} CAE\left( j \right) &= A_{clr} \left( j \right) - \left\{ {\left( {1 - c\left( j \right)} \right) \cdot A_{clr} \left( j \right) + c\left( j \right) \cdot A_{ic} \left( j \right)} \right\} \hfill \\ &= - c\left( j \right) \cdot \left( A_{ic} \left( j \right) - {A_{clr} \left( j \right) } \right) \hfill \\ \end{aligned}$$

(10)

An in-regime CAE of regime i (CAEO _i ) is defined as follows.

$$CAEO_{i} = \frac{{ - \sum\nolimits_{j = 1}^{n\left( i \right)} {w(j) \cdot c\left( j \right) \cdot \left( {A_{ic} \left( j \right) - A_{clr} \left( j \right)} \right)} }}{{\sum\nolimits_{j = 1}^{n\left( i \right)} {w(j)} }}$$

(11)

For the stratocumulus regime, scatter plots of the in-regime SW CRE for the stratocumulus regime in amip run and their feedback in amipFuture for stratocumulus regime for the tropics (20°S, 20°N) is similar to that of in-regime CAE. This suggests that the inter-model difference in the swCREO is dominated by the difference in CAEO for the stratocumlus regime.

On the other hand, a regime’s average in-regime albedo (A _i ) is expressed by the average cloud cover (c _i ) and the average in-cloud albedo (A _ic,i ) as follows.

$$c_{i} = \frac{{\sum\nolimits_{j = 1}^{n\left( i \right)} {w\left( j \right) \cdot c\left( j \right)} }}{{\sum\nolimits_{j = 1}^{n\left( i \right)} {w\left( j \right)} }}$$

(12)

$$A_{ic,i} = \frac{{\sum\nolimits_{j = 1}^{n\left( i \right)} {w\left( j \right) \cdot c\left( j \right) \cdot A_{ic} \left( j \right)} }}{{\sum\nolimits_{j = 1}^{n\left( i \right)} {w\left( j \right) \cdot c\left( j \right)} }}$$

(13)

$$A_{i} = \frac{{\sum\nolimits_{j = 1}^{n\left( i \right)} {w\left( j \right) \cdot c\left( j \right) \cdot A_{ic} \left( j \right)} }}{{\sum\nolimits_{j = 1}^{n\left( i \right)} {w\left( j \right)} }}$$

(14)

By definition, the in-regime albedo is a product of the c _i and A _ic,i .

$$A_{i} = c_{i} \cdot A_{ic,i}$$

(15)

Appendix 3: Basic physical equations relating in-cloud LWP to in-cloud albedo

In a plane-parallel cloud, in-cloud LWP (W) and in-cloud optical thickness (τ) can be related to cloud effective radius (R_e) (Stephens 1978).

$$\tau = \frac{2}{3}\frac{W}{{R_{e} }}$$

(16)

Also, in-regime LWP (cW, c is cloud cover) can be expressed in terms of R_e, number of cloud condensation nuclei (N·z) and a scaling parameter k.

$$c \cdot W = \frac{4}{3}k \cdot \pi \cdot N \cdot z \cdot R_{e}^{3}$$

(17)

The number of cloud condensation nuclei is strongly related to aerosol number concentration, which in turn is strongly related to aerosol emissions. In the amip and amipFuture experiments the aerosol emissions are fixed to be the same. The aerosol number concentrations and also the Nz are assumed to remain the same in amip and amipFuture experiments, under the current circumstance that the daily-mean data for these variables were not requested in CMIP5. We also assume that k is the same in cloud water from large-scale processes and cloud water from convective processes because LWP data from large-scale processes and convective processes were not separately requested and only combined data are available in CMIP5. The conversion from the optical thickness to albedo is based on the ISCCP-simulator. Using each model’s in-cloud LWP data and in-cloud albedo data in the control climate simulation, each model’s R_e are estimated. Using the R_e, kNz can be estimated. Then R_e in the future experiment is estimated with each model’s kNz and the in-cloud LWP data. Finally, the future in-cloud albedo expected from the in-cloud LWP is estimated.

Appendix 4: Formulations to constrain the net CRE feedback using observations and models

Here we describe formulations to estimate a possible change in a cloud regime’s contribution to net CRE feedback if models could simulate the regime in a manner consistent with the observations.

Errors in modeled cloud regimes could affect the regime’s contribution to cloud radiative feedback in two ways. Firstly, an error in netCREO _i or RFO _i in the control climate could intensify or weaken the contribution of the responses ΔRFO _i or ΔnetCREO _i to ΔnetCRE _i by weighting the first or the second terms in Eq. 3 in a different way from the observations. This error in the ΔnetCRE _i can be removed by replacing the netCREO _i and RFO _i in the Eq. 3 to the observational values i.e. $netCREO_{{_{i} }}^{obs}$ and $RFO_{{_{i} }}^{obs}$, respectively.

$$\Delta netCRE_{i}^{ctl\_obs\_} =\Delta RFO_{i} \cdot netCREO_{i}^{obs} + RFO_{{_{i} }}^{obs} \cdot\Delta netCREO_{i} +\Delta RFO_{i} \cdot\Delta netCREO_{i}$$

(18)

A second possible error in the estimated feedback is that the magnitude of a cloud regime property (e.g. RFO or in-regime net CRE) in the current climate could be related to the amplitude of the response in climate change. We can estimate an ‘observationally-based’ cloud property feedback of the regime by putting the observational value in the equation of the regression line by assuming that a strong correlation found in a cloud regime is based on a mechanism which operates in reality. If a correlation is found either in RFO or in-regime netCRE, the estimated changes from the regression line are $\Delta RFO_{i}^{robs}$, $\Delta netCREO_{i}^{robs}$, respectively. This error in the $\Delta netCRE_{i}$ can be removed by replacing $\Delta netCREO_{i}$ to $\Delta netCREO_{i}^{robs}$ or ΔRFO _i to $\Delta RFO_{i}^{robs}$ in the Eq. 18, e.g.

$$\Delta netCRE_{i}^{ctl\_obs,\Delta netCREO_{i}^{robs}} =\Delta RFO_{i} \cdot netCREO_{i}^{obs} + RFO^{obs} \cdot\Delta netCREO_{i}^{robs} +\Delta RFO_{i} \cdot\Delta netCREO_{i}^{robs}$$

(19)

For this case, a change in net CRE feedback is the difference of $\Delta netCRE_{i}^{ctl\_obs,\Delta netCREO_{i}^{robs}}$ from $\Delta netCRE_{i}$.