A modo de breve reseña histórico contextual

The coefficients found here allow us to create, using the rhs of relation 4.25, pseudo water vapour images that can be compared with the images captured by satellite. The proce- dure used in the previous sections and in particular the normalization of the coefficients αc ensures that each pixel of these images represents a weighted mean of the vertical

water vapour profile, so that its unit of measurement is g kg−1.

However, the model and the satellite have different resolutions, and it is thus necessary to degrade the resolution of both in order to allow for a comparison. One would wonder why we upscale a high resolution model output from 0.03◦to 0.25◦, and what is the reason of running a high-resolution model, with increased computation times, if the output will be upscaled to such a coarse resolution. The answer is as follows: a high resolution in the model is essential for a better description of the atmospheric fields, including small scale features that grow during the evolution, but once the output has been computed, in addition to find a common resolution with satellite images, another effect has to be faced, i.e. it is the double penalty effect.

Fighting the double penalty effect

be somewhat misplaced. This misplacing could lead to dramatic results when a high- resolution model is verified with common verification measures, because the timing and space errors will result in a much larger RMSE7 _{than for a lower resolution model com-}

petitor. Double penalty effect thus causes a reduction in the model skill because a high resolution model can lead to an event that is correctly simulated, but it is misplaced with respect to the original position, so that a high resolution forecast is penalized twice for not getting the event at the correct location (miss) and forecasting the event at the wrong location (false alarm). Some solutions have been found to fight against this effect, as the spatial matching technique (Ebert and McBride, 2000), which applies a spatial translation and matching of the high resolution forecast pattern with the observed field, or the neighbourhood methods, also called “fuzzy” verification, whose key point is the use of a spatial window or neighbourhood surrounding the forecast and/or observations through averaging (upscaling), thresholding or generation of a pdf8.

The most widely used neighbourhood verification technique is upscaling (e.g., Zepeda- Arce et al., 2000; Cherubini et al., 2002; Yates et al., 2006) In this work the new upscaled fields will be computed by averaging at a spatial scale of 0.25◦, that is close to the relative peak in performance (0.3◦) that Rossa et al. (2008) found in the case of the heavier rain rates.

6.2 µm PWV maps

Once the upscaled fields have been computed through the creation of a regular grid at 0.25◦ resolution and by assigning to every grid point the average of the values that fall into a square centered in that point, it is possible to proceed to the creation of the 6.2 µm PWV9 map.

Since the coefficients for this channel (figure 4.7), take very low values at levels below 500 hPa, for faster calculations we only consider levels above this threshold by performing a new renormalization of the coefficients. The PWV map is thus computed using a specific adjustement of rel. 4.25 where the summation extremes are 200 and 500 hPa.

An example of the resulting fields concerning the phase that preceded the November 2011 medicane is shown in figure 4.8 a. In this situation the equivalent water vapour content in the upper atmosphere ¯q200−500ranges from some hundredth to few tenth grams

per kilogram and we can easily see: a dry tongue that from the African coast goes right in the Tyrrhenian Sea through a semicircular path, and high water vapour content areas over Sardinia, over the coast of Tuscany and north of the Balearic Islands.

The second picture represents the spectral radiance at the nominal wavelength that is

7_{Root Mean Square Error} 8_{probability density function} 9_{pseudo water vapour}

computed from brightness temperature using equation 4.4 for the Meteosat 9 WV 6.2µm channel. This image, computed through the same averaging techinique at the same resolution of 0.25◦ of the model one, was selected among the other satellite maps with the criterion of the maximum correlation (in absolute value) with the WRF pseudomap (see later). The main characteristics represented by the model are well represented here, and despite the approximations used in the derivation of the relations, satellite acquisition errors and model errors, the linear correlation coefficient between these two maps is -0.78.

7.3 µm and 6.2 µm PWV maps

Applying the same procedure followed for the 6.2µm PWV maps, we can now build the corresponding maps at 7.3µm, with the differences that the weighting functions and the emissivity profiles are computed for this wavelength, and the summation extremes are 200 hPa and 600 hPa, due to the vertical structure of the coefficients.

The example in figure 4.9 concerns the same meteorological situation of figure 4.8. The different penetration of this wavelength through the atmosphere implies that the higher response is at a lower altitude approximately in middle troposphere where the water vapour content is generally higher with respect to the 6.2µm map. The radiance is higher too, because this wavelength is closer to the blackbody emission peak. The linear correlation coefficient between these two maps is -0.77 that is consistent with the coefficient between the 6.2µm images.

For the 2003 case, Meteosat Second Generation images are not available because Meteosat 9 became operational in 2006, and the analysis must be carried out using MVIRI data acquired at 6.4µm. Nothing changes in the process and the result are similarly acceptable.

On the comparison between PWV and WV maps

The different measurement units of the satellite and of the model derived maps suggest us to find a dimensional proportionality coefficient and an offset in order to turn the proportionality relation expressed in 4.25 into a linear equation that could be reversed to obtain for a given satellite map and in the absence of an atmospheric model a pseudo water vapour field representative of some tropospheric layers. This process is basic to move from a qualitative view of higher troposphere dynamics through an animation of satellite maps to a quantitative analysis of the estimated water vapour field, and it will be displayed in the next subsection.