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Interpolation and IAAFT surrogate cloud fields

The normal IAAFT algorithm generates cloud fields with the same structure as the measurement (Venema et. al., 2006). It can be used to study the relation between the measured cloud microphysical properties and its radiative properties averaged over the modelled field, e.g. the mean transmittance or reflectance or also the histogram of these variables, which we have performed in Schmidt et. al. (2007).

If you want to combine measurements of a cloud field with radiation measurements performed at a specific location, you additionally need the to be clouds at the right positions (or its equivalent for stratiform clouds). For such studies one needs an algorithm that interpolates between the measurements and does so in a way that the full field has the right cloud structure.

Typically such an interpolation method would be used together with ground-based scanning microwave radiometer or radar measurements. A typical scanning measurement would be to rotate the instrument on its azimuth-axis, at a fixed elevation angle, while the clouds drift by on the wind. In this way one would measure Liquid Water Path (LWP) values in a spiral pattern at cloud height, assuming that the cloud thickness is less than the cloud height. Not only are such measurements well suited for interpolation, but such scanning measurements also sample the cloud field much better than typical nonscanning zenith measurements, given that cloud fields are highly correlated; see also article by Pincus et al. (2004). Furthermore, one can estimate the 2D power spectrum from such measurements; one does not need the assumption of an isotropic field, which is necessary for zenith measurements. On this page we will simulate a perfect scanning measurement on a Large Eddy Simulation (LES) stratocumulus and cumulus fields, as a first step to making such surrogates from measurements.

Example of a stratocumulus cloud (top left panel) on which five zenith pointing speudo-measurements are simulated (top right) and the kriged (bottom right) and kriging-based surrogate fields that are produced based on the these speudo-measurements.

Interpolation

Arguably the most powerful interpolation method is kriging. However, like any normal interpolation method it smoothes the cloud field, if only because a normal interpolation method can only produce values between the measured ones and will never generate a more extreme one. In the example to the left, you see a liquid water path field from the top (top left panel) generated by an LES model. The top right panel shows an example of a cloud measurement using 5 zenith pointing microwave radiometers; together with the wind and using the frozen turbulence assumption, this amounts to measuring 5 lines with LWP values. The bottom right panel shows the interpolated speudo-measurements and it clearly more smooth than the original LES field (top left). Consequently, the interpolated field will also have a too high reflectance and a too low transmittance.

To be able to interpolate without smoothing a new version of the IAAFT algorithm has been developed. It includes an additional iterative step that nudges the surrogate fields towards the kriged field. The kriging algorithm also computes the uncertainty in the interpolated values. This information is used by the new IAAFT algorithm to nudge the values stronger towards the kriged fields for those pixels where the uncertainty is smallest. In the bottom left panel such a kriging-based surrogate field is shown, whose structure is clearly more similar to the original LES cloud and more suited for radiative transfer computations. For more details please read this extended abstract.

IAAFT surrogate cloud fields with local forcing

In an older method, described in Venema et. al. (2006), the interpolation was performed by directly forcing the field to have the measured values at the measured locations. This algorithm utilizes an enhanced version of the IAAFT algorithm that also takes the LWP values measured on the spirals as its third input. In an extra iterative step, between the spectral adaptation and the amplitude adaptation, the algorithm forces the LWP values at the measured locations, to correspond with the measurement. Additionally from the LWP values on the spiral, the 2D periodic autocorrelation function is estimated. Using the Fourier transform one then obtains the 2D anisotropic power spectrum. The LWP distribution is also only estimated from the LWP values on the spirals.

In the initial version of this algorithm, the scanning pattern was still somewhat visible. To remove these artifacts the algorithm used here does not utilise white noise as initial field, but a field estimated from the scanning pattern using a kernel estimator. Furthermore, a smoothing filter was applied during the first iterations. At the end this filter was no longer active, thus, the statistics of the cloud fields are not changed by alterations of the algorithm.

Stratocumulus fields

The scanning pattern is plotted on top of the template LWP field. The measured values, which correspond to 16.5 % of all values, were used to calculate the surrogate. This version of the algorithm can be seen as an interpolation algorithm that does not smooth the field, but maintains the structure of the measurement.

Cumulus fields

For cumulus clouds the exact estimation of the power spectrum is very important. In our validation study we have seen that the surrogate from a sparse cumulus cloud was simply a copy of the template. In this case we used the full error-free power spectrum. Using scanning data, however, the estimate of the power spectrum is not good enough. This can be seen in the figures below. The first figure is a sparse cumulus template cloud. The second a surrogate with local forcing that was made like the surrogate stratocumulus above. This surrogate field is much more 'noisy' than its template and will have a higher albedo.

We can make good quality surrogate cumulus fields, if we include a cloud mask. Such a cloud mask could be derived from an imager. The third figure shows a surrogate cumulus fields with local forcing and a cloud mask forcing that is very similar to the original template cloud field.

In future, we want to validate this method, i.e., determine the bias and RMS error of the radiative properties of templates and surrogates. Furthermore, this algorithm, or a version for 3-dimensional fields, should be applied to real cloud measurements. And the radiative properties of such surrogate cloud should be compared with radiation measurements in a radiation closure study.

References

Venema, V.K.C., R. Lindau, T. Varnai, and C. Simmer. Combining surrogate clouds with geostatistics to ease the comparisons of point radiation measurements with cloud measurements. (poster | extended abstract) ISTP2009, 18-23 October, 2009, Delft University of Technology, The Netherlands.

Venema, V.K.C., St. Meyer, S. Gimeno García, A. Kniffka, C. Simmer, S. Crewell, U. Löhnert, Th. Trautmann, and A. Macke. Surrogate cloud fields generated with the iterative amplitude adapted Fourier transform algorithm. (color | black/white) Tellus, 58A, no. 1, pp. 104-120, doi: 10.1111/j.1600-0870.2006.00160.x, 2006.

Schmidt, K.S., V.K.C. Venema, F. di Giuseppe, R. Scheirer, M. Wendisch, and P. Pilewski. Reproducing cloud microphysics and irradiance measurements using three 3D cloud generators. Q.J.R. Meteorol. Soc., 133, doi: 10.1002/qj.53, pp. 765-780, 2007.