Synthetic cloud generators

RELATED INFORMATION
 

As clouds have a complex structure with variability at all scales making it is difficult to measure and model them well. Due to the large variability we would have to measure the full 3D field of the cloud properties of interest at high resolutions, which we are not able to do. As a consequence, 3-dimensional cloud fields are often simulated by physical cloud models. However, it would be dangerous to rely on model clouds alone. Models have to parameterize the cloud physics and chemistry, have a limited resolution and are often forced with too simple boundary conditions. Thus an independent alternative to model clouds would be valuable.

That is why many scientists work with synthetic cloud fields to study problems related to clouds. At the moment many people are working on developing better algorithms to generate such clouds. This page will introduce some of these methods, focusing on the newer methods, but also including some tradional methods. Below you will find the methods sorted into categories. The clickable methods link to a short description, links and references, which are found in an alphabetic list further below. If you would like to have your algorithm mentioned here, please send me a short description, and some links or references, Victor.Venema@uni-bonn.de.

Are the cloud fields self-similar?

Yes
Bounded Cascade
tdMAP
P-model multifractals

Normally, but not necessarily
Standard Fourier
Fourier ice clouds

No, intentionally not
Iterative surrogate clouds
Constrained surrogate clouds
SITCOM
Cumulus clouds by Frank Evans

Does it use the Fourier transform?

Yes
Iterative surrogate clouds
Cumulus clouds by Frank Evans
Standard Fourier
SITCOM
Fourier ice clouds

No
Bounded Cascade
tdMAP
Constrained surrogate clouds
P-model multifractals

Can you use an arbitrary PDF?

Yes, any PDF you would like
Constrained surrogate clouds
Iterative surrogate clouds
tdMAP (indirectly)
Cumulus clouds by Frank Evans

No, the algorithm determines it
Bounded Cascade
Standard Fourier
SITCOM
Fourier ice clouds
P-model multifractals

Bounded Cascade method

The bounded cascade (BC) method is a simple and fast method to make self-similar time series and 2-dimensional fields. The BC clouds have a PDF that is similar to a log-normal distribution; it is always positive and on a logarithmic scale its PDF is symmetric. The structure has discontinuous jumps at all scales. The BC time series can be used to validate (multi-)fractal processing (Davis et al., 1996) and its 2D fields have often been used to simulate stratocumulus clouds, and study the accuracy of various simplifications about cloud structure and radiative transfer. The custodian of the model is Robert Cahalan, who has made a clear page explaining the algorithm.
My advice to users of this method, is to also use another method next to it, to verify whether your results may depend on specific details of the structures. Good additional methods would be Fourier clouds, which are just as simple, but have a more continuous structure, or iterative surrogate clouds, which can be made to have the same PDF.

Links

References

Cahalan, R.F., Bounded cascade clouds: albedo and effective thickness, Nonlinear Proc. Geophys., 1, 156-176, 1994.

Davis, Anthony, Alexander Marshak, Warren Wiscombe, and Robert Cahalan. Multifractal characterizations of intermittency in nonstationary geophysical signals and fields. In Current topics in nonstationary analysis, ed. G. Trevino, J. Hardin, B. Douglas, and E. Andreas, pp. 97-158, World Scientific, Singapore, 1996.

Cumulus clouds by Frank Evans

Evans and Wiscombe have developed an advanced method to generate 3-dimensional cloud fields, based on 2-dimensional cloud measurements (made with radar). As input a 2D Liquid Water Content (LWC) measurement is used, i.e. measured LWC-height-profiles as a function of time. This measurement is described in terms of its LWC PDF as a function of height and the power spectrum of the cloud mask. Their algorithm is able to make a 3D LWC field that has these same statistical properties.

Links

Reference

Evans, K.F., and W.J. Wiscombe, An algorithm for generating stochastic cloud fields from radar profile statistics, accepted by Atmospheric Research special issue on Clouds and Radiation, 2004.

Constrained surrogate clouds

Constrained surrogate clouds can have any (statistical) property one in interested in. These fields are created by searching for a cloud field that has the required properties using a robust global search algorithm. We use an evolutionary search algorithm. One can make such a search in finite time, by first searching for the right cloud at low resolution, before gradually increasing the resolution. Still, the method is computationally heavy.

This method can probably best be seen as a benchmark method to investigate which cloud properties are important for radiative transfer. Thus taking advantage of the very flexible cost function, where in principle any cloud property can be used. As calculating the cost function takes most of the time, it is important, however, that it is easy to calculate the cloud properties. One of the main advantages over my iterative method is that the autocorrelation function can be used instead of the Fourier transform. Thus, one does not have to require periodic boundary conditions. Periodic boundary conditions are troublesome given the nonstationary structure of clouds. Additionally, one could describe cloud boundary their generalized dimensions, which is much more powerful than, e.g. a power spectrum of cloud top height, as it can handle situations with no cloud boundary (gaps) and more than one cloud boundary (thus, also heterogeneous mixing).

Links

My page on constrained surrogate clouds, which are created using an evolutionary search algorithm.

Fourier ice clouds by Robin Hogan

Robin Hogan and Sarah Kew developed a beautiful Fourier method to generate 3-dimensional ice clouds which can have anisotropic comma-shaped fall streak structures due to wind shear. Furthermore, the exponent of the power law power spectrum (slope of the spectrum) is a function of height, as was measured with radar. The basis of these fields of Ice Water Content (IWC) is a 3D field made using the standard Fourier method. In the next step, working in 2D, for every height level the magnitudes of the 2D-Fourier coefficients are adapted to reflect the height depend slope of the spectrum. Furthermore, the phases of the 2D-Fourier coefficients are modified to make the fall streaks drift away horizontally.

This cloud model was used to show that for the radiative properties of ice clouds, the wind shear is also an important parameter, next to the IWC distribution and its power spectrum.

Links

Reference

Hogan, R. J., and S. F. Kew, 2005: A 3D stochastic cloud model for investigating the radiative properties of inhomogeneous cirrus clouds. Q. J. R. Meteorol. Soc., in press.

Kew, S., Development of a 3D fractal cirrus model and its use in investigating the impact of cirrus inhomogeneity on radiation. MSc. Dissertation, Department of Mathematics, University of Reading, Aug. 2003.

IAAFT algorithm

The Iterative Amplitude Adapted Fourier Transform (IAAFT) algorithm is one of the methods I am working on to make surrogate cloud fields. With this Fourier method, you can create cloud fields with a specific power spectrum and PDF (as a function of height). This makes the method very suited to make cloud fields using a specific measurement, which will not have one of the fixed shapes required by many algorithms. We have made 3D Liquid Water Content (LWC) fields from 2D time-height LWC-profile retrievals by assuming that the structure is isotropic. The power spectrum and the PDF(z) together provide a very accurate description of cloud structure for use in radiative transfer studies. A validation made by comparing LES clouds with their IAAFT surrogates showed that such pairs have almost the same radiative properties.

Links

P-Model multifractals (with fractional integration)

The p-model is used to generate time series and fields with a fractal structure. These time series can be made more smooth by fractional integration. Such time series are occasionally used to model fractal cloud time series. I haven't used this model myself for cloud studies, but worte a page that illustrates the range of time series that can be made with this model, and gives a Matlab code to generated 1D time series.
The first reference is the paper I used to program it, the second is (one of) the first that presented the model.

Links

Reference

Davis, A., A. Marshak, R. Cahalan, and W. Wiscombe, The landsat scale break in stratocumulus as a three-dimensional radiative transfer effect: implications for cloud remote sensing. J. Atmos. Sci., 54, no. 2, 1997.

Wilson, J., S. Lovejoy, D. Schertzer, 1991: Continuous multiplicative cascade models of rain and clouds. Scaling, fractals and non-linear variability in geophysics, D. Schertzer, S. Lovejoy eds.,185-208, Kluwer.

SITCOM

Spectral Idealised Thermodynamically COnsistent Model (SITCOM) is an advanced Fourier method to generate cloud fields with a mean Liquid Water Content (LWC) height profile and a profile of the LWC standard deviation. Both profiles derive from an analytic cloud physics model. For these 3-dimensional cloud fields, one 2D (!) Fourier field is created, that is scaled at each height level to obtain the wanted profiles. Thus, the method assumes maximum cloud overlap. Gaps in the cloud are created by allowing negative LWC values and setting them to zero at the end. The method could be used together with power law power spectra, but it their paper the developers (Francesca Di Giuseppe and Adrian Tompkins) chose to use a Gamma function power spectra, so that they can systematically change the dominant scale.

Links and reference

Standard Fourier method

Arguably the easiest way to make cloud time series and fields is the use of the Fourier transform. The standard Fourier method uses Fourier coefficients with follow a power law, typically with a -5/3 exponent. These complex Fourier coefficients are given random phases to generate various cloud fields. The PDF of such cloud fields is on average Gaussian.
The method is much used in various applications. An important advantage of this method is the large body of literature on the Fourier transform. There are those, who do not see these standard Fourier clouds as fractal clouds as the algorithm is not iterative. It is true that many fractal algorithms are iterative, but the crucial point is the self-similarity of the time series. You could also construct an iterative method to generate ‘Fourier’ clouds that sums sinuses with increasing frequencies, decreasing amplitudes and random phases. However, another important advantage of the Fourier method is the computationally efficient Fast Fourier Transform (FFT) that allows one to generate large fields at little cost.

Links

Reference

The potential of spaceborne dual-wavelength radar to make global measurements of cirrus clouds. Hogan, R. J., and A. J. Illingworth, J. Atmos. Oceanic Tech., 16(5), 518-531, 1999.

tdMAP

tdMap stands for Tree Drive, Mass Accumulation Process. The method generates a tree with nodes in analogy to the wavelet transform. Every height level of the tree represents one spatial scale, which increasing height the number of nodes increases. Every node describes a spatial function (e.g. a 2D Gaussian bell), with a certain amplitude and position. Free parameters are the shape of the spatial function, the number of branches growing from one node, the probability that nodes are removed, the standard deviation of stochastic node position changes, and the amplitudes of the spatial function. All of these parameters can be set as a function of the height in tree to be able to make fractal structures. With this method it is possible to make 2D stratocumulus and cumulus cloud fields, that look reasonably realistic.

Links

References

Albert Benassi, Frédéric Szczap, Anthony Davis, Matthieu Masbou, Céline Cornet and Pascal Bleuyard, Thermal Radiative Fluxes through Inhomogeneous Cloud Fields: A Sensitivity Study using a New Stochastic Cloud Generator. Submitted to Atmospheric Research, 2004.

Benassi, A., F. Szczap, A. B. Davis, C. Celine, P. Bleuyard, and B. Guillemet, 2004: Large averaging thermal radiative fluxes through inhomogeneous cloud fields: A sensitivity study using the tdMAP cloud generator. In: Proceedings of the 2004 CGU, AGU, and SEG Joint Assembly, Montreal, Canada (May 17-21, 2004), U21A-11.

   
Victor.Venema@uni-bonn.de
Last update: April 2006
URL: http://www2.meteo.uni-bonn.de/victor/themes/surrogates/cloud_generators.html