Quantitative evaluation of the seasonal variations in climate model cloud regimes

Abstract

An extended cloud-clustering method to assess the seasonal variation of clouds is applied to five CMIP5 models. The seasonal variation of the total cloud radiative effect (CRE) is dominated by variations in the relative frequency of occurrence of the different cloud regimes. Seasonal variations of the CRE within the individual regimes contribute much less. This is the case for both observations, models and model errors. The error in the seasonal variation of cloud regimes, and its breakdown into mean amplitude and time varying components, are quantified with a new metric. The seasonal variation of the CRE of the cloud regimes is relatively well simulated by the models in the tropics, but less well in the extra-tropics. The stratocumulus regime has the largest seasonal variation of shortwave CRE in the tropics, despite having a small magnitude in the climatological mean. Most of the models capture the temporal variation of the CRE reasonably well, with the main differences between models coming from the variation in amplitude. In the extra-tropics, most models fail to correctly represent both the amplitude and time variation of the CRE of congestus, frontal and stratocumulus regimes. The annual mean climatology of the CRE and its amplitude in the seasonal variation are both underestimated for the anvil regime in the tropics, the cirrus regime and the congestus regime in the extra-tropics. The models in this study that best capture the seasonal variation of the cloud regimes tend to have higher climate sensitivities.

Appendices

Appendix 1: Cloud regime error metrics for the present day annual mean climatology

According to WW09, cloud regime error metric of the present-day annual mean climatology

$$ CREMpd = \sqrt {\frac{{\sum\nolimits_{r = 1}^{nregimes} {CREMpd_{r}^{2} } }}{nregimes}} $$

(8)

$$ CREMpd_{r} = aw\sqrt {\left( {RFO_{r}^{\prime} NCRE_{obsr} } \right)^{2} + \left( {NCRE_{r}^{\prime} RFO_{obsr} } \right)^{2} } $$

(9)

where $NCRE_{r}^{\prime}$ and $RFO_{r}^{\prime}$ are regime mean differences between the model and ISCCP observations, RFO _obsr and NCRE _obsr are the ISCCP observed regime mean values which are used to weight the regimes, and aw is the respective area weight for the region.

Appendix 2: Amplitude of seasonal variation

x _n is defined to be a climatological monthly mean of variable x of a regime in a region for month n, and $\overline{x}$ is the climatological annual mean. The standard deviations (σ) of $x_{n} \left( {n = 1, \ldots ,N} \right)$ is as follows.

$$ \sigma^{2} = \frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {x_{n} - \overline{x} } \right)}^{2} $$

(10)

$$ \overline{x} = \frac{{\sum\nolimits_{n = 1}^{N} {x_{n} } }}{N} $$

(11)

For the seasonal variation of NSCRE and longwave cloud radiative effect (LCRE) of each cloud regime, the amplitude is obtained by using monthly climatological means of NSCRE and LCRE of the regime as $x_{n} \left( {n = 1, \ldots ,N} \right)$ and N is the total number of climatological month n (N =12).

Appendix 3: RMS error in the seasonal variation

Superscript o and m indicates the value from the observation and a model.

The standard deviations of observational and model variable x; σ _x,o , σ _x,m are

$$ \sigma_{x,o}^{2} = \frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {x_{n}^{o} - \overline{{x^{o} }} } \right)}^{2} $$

(12)

$$ \sigma_{x,m}^{2} = \frac{1}{N}\sum\limits_{n = 1}^{N} {\left( {x_{n}^{m} - \overline{{x^{m} }} } \right)}^{2} $$

(13)

In centred RMS error, climatological annual mean is subtracted from the climatological monthly mean for both the observation and the model, and the square of the difference of the anomaly of the model from the anomaly of the observation is averaged over the 12 months as follows.

$$ e_{x}^{\prime2} = \frac{1}{N}\sum\limits_{n = 1}^{N} {\left\{ {\left( {x_{n}^{m} - \overline{{x^{m} }} } \right) - \left( {x_{n}^{o} - \overline{{x^{o} }} } \right)} \right\}}^{2} $$

(14)

A pattern correlation coefficient (R) between $\left( {x_{n}^{m} - \overline{{x^{m} }} } \right)$ and $\left( {x_{n}^{o} - \overline{{x^{o} }} } \right)$ is defined as follows.

$$ R = \frac{{\sum\nolimits_{n = 1}^{N} {\left( {x_{n}^{m} - \overline{{x^{m} }} } \right)\left( {x_{n}^{o} - \overline{{x^{o} }} } \right)} }}{{\sqrt {\left\{ {\sum\nolimits_{n = 1}^{N} {\left( {x_{n}^{m} - \overline{{x^{m} }} } \right)^{2} } } \right\}\left\{ {\sum\nolimits_{n = 1}^{N} {\left( {x_{n}^{o} - \overline{{x^{o} }} } \right)}^{2} } \right\}} }} $$

(15)

The second term of Eq. (3) can be rewritten as follows.

$$ 2\sigma_{x,m} \sigma_{x,o} (1 - R) = \frac{{\sigma_{x,m} }}{{\sigma_{x,o} }}\frac{1}{N}\sum\limits_{n = 1}^{N} {\left\{ {\frac{{\sigma_{x,o} }}{{\sigma_{x,m} }}\left( {x_{n}^{m} - \overline{{x^{m} }} } \right) - \left( {x_{n}^{o} - \overline{{x^{o} }} } \right)} \right\}^{2} } $$

(16)

It consists of $\frac{{\sigma_{x,m} }}{{\sigma_{x,o} }}$ and $\frac{1}{N}\sum\nolimits_{n = 1}^{N} {\left\{ {\frac{{\sigma_{x,o} }}{{\sigma_{x,m} }}\left( {x_{n}^{m} - \overline{{x^{m} }} } \right) - \left( {x_{n}^{o} - \overline{{x^{o} }} } \right)} \right\}^{2} }$, the former is the ratio of the model standard deviation to that observed, while the latter corresponds to the RMS error of a hypothetical model whose standard deviation is normalized to that observed.