User:Haisbrwe/sandbox

= Cloud Parameterization = Cloud Parameterization is the concept of how the formation and dissolving of clouds is represented in climate and weather models. Many cloud related processes occur on too small scales to be solve by these models with resolutions around 10-200 km. Cloud parameterization at minimum provides the determination of the horizontal cloud fraction and the amount of condensed cloud water inside the grid boxes. A distinction is drawn between diagnostic and prognostic parameterization schemes which vary in clompexity and performance. Main uncertainities occur due to the determination of cloud water that is strongly affected by convection which also needs to be parameterized in large scale models as well as the microphysics.

Usage
The representation of clouds in weather and climate models is a crucial factor for their accuracy. They influence processes like turbulence, circulation and radiation. . Especially the close interaction of clouds and radiation plays a significant role in short term and long term predictions. ?) While cloud fraction and their water content directly influence the radiative budget, radiation on the other hands has an effect on formating and dissolving clouds. Cloud feedback is one of the main uncertainties in climate models. Although model resolutions continuously increase neither cloud microphysics that determine cloud formation nor most cloud types itselt can be resolved in current large scale models. To resolve all physical process that affect weather or climate gridlength of models would need to be at millimeter scale. The required computing power will not be provided in near future for global models. Therefore several subgrid scale processes need to be simplified to take them into account in large scale models. Cloud parameterization is one example for it. Instead of calculating every single cloud models parameterize clouds by other determined properties of the grid cells. The cloud parameterization is used to estimate cloud properties like the cloud fraction as well as phase and amount of condensated water. They are used in models possesing a lower resolution than LES models with meshgrid sizes around 100m. The main parameterization schemes in large scale models besides cloud parameterization are boundary layer turbulence parameterization, cumulus convective parameterization and radiative transport parameterization. Cloud parameterization can be seen as an interface between the convective and radiation scheme. The convection scheme includes processes like condesation which serve as input parameters for the cloud parameterization whereas the cloud parameterization returns parameters like the cloudiness needed for the radiation scheme.

Cloud parameterization schemes
Depending on gridsize and available computing power cloud parameterizations differ in complexity. They vary from simple RH schemes to way more sophisticated prognostic schemes which can be combined with complex consideration of the cloud microphysics.

RH schemes
The simplest way to implement a cloud parameterization is by estimating the cloud fraction $$ a_c $$ by the mean relative humidity $$  RH $$ inside the grid box. If humidity would be equally distributed over the grid box one could simply assume the formation of clouds when $$ RH =100 \% $$ for the whole grid box. As this is not the case and humidity is usually distributed inhomogeneuos it is estimated that cloud form as soon as a critical relative humidity $$ RH_{crit} $$ is reached. Often the cloud fraction is then calculated by:

$$ RH > RH_{crit}: \qquad a_c = 1-\sqrt\frac{1-RH}{1-RH_{crit}}$$

$$ RH < RH_{crit}: \qquad a_c = 0$$

$$ RH_{crit} $$ itself can depend on multiple other grid properties like the height, the mean vertical velocity or the mean grid condensate.

Statistical schemes
In a statistical cloud parameterization scheme the humidity e.g. by the total total specific humidity $$ q_t $$ is expressed as a probability density function (PDF) around the mean value for every grid cell. The areas where $$ q_t $$ exceeds the saturation value $$ q_s $$ are considered as clouds. The type of the PDF determines how the sub grid variability of the humidity is estimated e.g. by a Gaussian form.

Process based cloud schemes
The main reason for an unequally distribution of moisture is vertical mixing due to turbulence and convection. Processes which often take place on a subgrid scale. A diagnostic estimation of the variance of $$ q_t $$ can be determined by a balance of its production and dissipation:

$$ \overline{ q_t'^2 } = -\frac{1}{c_q} \tau \overline{w'q'_t}\partial_z \overline{q_t} $$

with a production  of humidity variance generated by a turbulent flux $$ \overline{w'q'_t} $$ times the vertical humidity gradient. The coefficent $$ c_q $$ and the dissipation timescale $$ \tau $$ parameterize the dissipation term. Further the turbulent flux is also parameterized. In the boundary layer parameterization  an eddy diffusivity can be optainend to simplify the boundary layer turbulence flux whereas the cumulus convection paramterization often uses convective mass flux approximation. A disadvantage of the diagnostic approach is that a variance in humidity can just occur due to turbulence and convection. This can lead to a large underestimation of clouds in condition without convection like at nighttime. The so called lack of memory means that the system 'forgets' the variability of humidity inside the gridbox when turbulence and convection are not present.

Prognostic cloud schemes
To apply a memory effect into the cloud parameterization a prognostic variable can be included in the scheme. One choice can be the aforementioned variance of total water specific humidity $$ \overline{ q_t'^2 } $$ which would also provide information about the water vapor content in cloud free conditions and can be easily combined with turbulence and convection schemes. The amount of liquid water is estimated by the exceeding of the saturation value. An assumption that is valid for warm clouds. Whereas a main reason for the condensed water amount $$ q_c $$ as the prognostic variable is the more realistic consideration of the microphysics. This applies especially in mixed phased clouds where liquid cloud droplets and ice particles coexist. Here conditions with high supersaturation must be taken into account. A prognostic equation for the condensed water content can be established as following:

$$ (\partial_t \overline{ q_c })_{sub-grid} = - \frac{1}{\rho}\partial_z \rho \overline{w'q'_c} + (c-e) -G $$

The first term considers moistenting due to convection. Condensation $$ c $$ and evaporation $$ e $$ as well as the conversion from cloud water to precipitation represented by the autoconversion term $$ G $$ affect the change in cloud water content and are provided by a microphysics parameterization scheme.

Limits
As mentionend before the cloud parameterizations relies on other parameterization schemes and can therefore just be as accurate as the convection, turbulence and microphysics schemes are that provide the input values for the cloud parameterization.

Further in weather and climate models not just the horizontal resolution needs to be considers but also the vertical. The cloud parameterization can just estimate the cloud fraction for every vertical level but not the exact position of the clouds and thereby the cloud fraction overlapping. According to the assumption of the horizontal positioning in the grid cells the total cloud cover can vary strongly with the number of vertical grid points. The maximum overlapping assumptions considers just the maximum cloud fractions in the vertical column of grid boxes as the total cloud cover. The random overlap assumptions takes a random overlapping of the cloud fraction between adjacent levels into account. The most realistic total cloud fractions are assumed to lie in between this two methods. That's why most models use the random overlap assumption which considers the maximum overlapping approach for adjacent levels with cloud covers larger than zero and the random overlapping approach for bundles of levels which are separated by levels with no cloud cover.

Another source of error is inhomogeneous distribution of liquid cloud water. Realistically the amount of liquid water is not equally distributed in clouds. Assuming a homogeneous distribution the cloud albedo tends to be overestimated as it depends on the liquid water path and therefore on the liquid water distribution. An simple approach to reduce this error is by lowering the cloud optical depth.