## Abstract

This study investigates the sensitivity of a high-resolution mesoscale atmospheric model in the model reproduction of thermally induced local wind (i.e., sea breezes, SB) on the development of deep convection (Cb). The three chosen cases are simulated by the Weather and Research Forecasting (WRF-ARW) model at three (nested) model domains, whereas the area of the interest is Istria (peninsula in the northeastern Adriatic). The sensitivity tests are accomplished by modifying (1) the model setup, (2) the model topography and (3) the sea surface temperature (SST) distribution. The first set of simulations (over the three 1.5-day periods during summer) is conducted by modifying the model setup, i.e., microphysics and the boundary layer parameterizations. The same events are simulated with the modified topography where the mountain heights in Istria are reduced to 30% of their initial height. The SST distribution has two representations in the model: a constant SST field from the ECMWF skin temperature analysis and a varying SST field, which is provided by hourly geostationary satellite data. A comprehensive set of numerical experiments is statistically analyzed through several different approaches (i.e., the standard statistical measures, the spectral method and the image moment analysis). The overall model evaluation of each model setup revealed certain advantages of one model setup over the others. The numerical tests with the modified topography showed the influence of reducing the mountains heights on the pre-thunderstorm characteristics due to: (1) decrease of sensible heat flux and mid-tropospheric moisture and (2) change of slope-SB wind system. They consequently affect the evolution and dimensions of SBs and the features of the thunderstorm itself: timing, location and intensity (weaker storm). The implementation of the varying SST field in the model have an impact on the characteristics and dynamics of the SB and finally on the accuracy of Cb evolution, duration and the intensity. SST variations emphasized the importance of the phase matching in both daytime cycles of SB and Cb due to their extremely strong nonlinear relationship.

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## Acknowledgements

We are very grateful to the Meteorological and Hydrological Service of the Republic of Croatia for providing the meteorological data and to the Slovenian Environment Agency for providing radar images. METAR reports are available from website, http://www.wunderground.com. This research was supported by the ECMWF (http://www.ecmwf.int/) data and the SEVIRI data, which are accessible through the EUMETSAT Ocean and Sea Ice Satellite Application Facility (http://www.osi-saf.org). We would like to thank Igor Tomažić for creating the SST fields in the WRF model (freely available at http://www.wrf-model.org/index.php). This work contributes to the VITCLIC project and HyMeX programme. We thank to the Editor and anonymous referees for their in-depth review and valuable suggestions.

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## Appendices

### Appendix 1

### Modification of the Topography (Učka and Ćićarija Mountains)

The impact of the terrain height on the (“pure”) SB characteristics (without convection) over Istria was already estimated in Prtenjak et al. (2006). In that study, one designed test had greatly idealized terrain height (*h*) over Istria and Kvarner Bay where *h* did not exceed 10 m asl. In such circumstances, the main convergence zone over peninsula had very unrealistic lifetime and position in space compared to the “real” case due to significant change in SBs evolutions. Here we wanted to examine only the influence of high mountains and the reduction to approximately 30% corresponds to leveling of mountains with other surrounding terrain without abrupt transitions (Fig. 14). Therefore, topography was modified by a simple cosine weight function (Eq. 1), which is zero at the boundary and one in the center, as defined over a 100 × 100 point square area; Fig. 1.

The cosine weights were then subtracted from 1 according to Eq. (2), producing weights that reduced the terrain height through simple multiplication. A “uniform” height reduction was achieved by raising the subtracted weights to the power of 100. Another sought effect was to avoid producing sharp gradients at the boundary, which would induce errors and instabilities during integration.

The final weight function was then rescaled by Eq. (3) to have a value of 0.9 at its minimum, and 1 at its border.

The weight function that was used on the topography data was constructed by the former function and raised to the power of 12, which would reduce the height to approximately 30% around its center point (Fig. 14) according to:

### Appendix 2

### Moment Invariants (IMA) Approach

The IMA approach is invariant to the translation, rotation and scale of the input image. The initial problem of inputting radar images is a spherically symmetrical issue that is why Zernike moments were chosen for analysis (Teague 1980). These are given as projections of an image function *f* (*x, y*) on a unit circle:

where *x* = *r*·cos *θ* and *y* = *r·*sin *θ* and \(Z_{pq} (r,\theta ) = R_{pq} (r)e^{iq\theta }\)is the Zernike function of order *p* + *q* in polar coordinates (*r* is a radial vector and *θ* is an angle with a positive *x*-axis) and

is the radial polynomial. The advantages of this approach are fast and relatively simple computation and a satisfactory signal-to-noise ratio (e.g., Wee and Paramesran 2007).

All the images that were used (e.g. Fig. 3 but without wind vectors) in this comparison were first represented as real-valued images of size 694 × 694 pixels with 256 gray scale levels (8-bit). The set of measured radar images was used as the reference set (Fig. 3). The procedure to obtain the measure of similarity between two images, namely, *i* from the model set and *j* from the referent set, was as follows:

(1) calculate of the first eight orders of Zernike moments by using Eq. (1) and (2) compare of each moment of the set that was calculated for image *i* with the corresponding moment of the reference image *j* by using the formula for Euclidean distance ED_{
ij
} between images *i* and *j*:

A situation without any radar reflectivity (e.g., Fig. 2a), when only the shoreline contour was present on the input image, was considered a zero-order signal, and the corresponding ED_{
ij
} value was subtracted from all other values. Thus, the final ED_{
ij
} values showed similarity between the model results and the radar images.

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Kehler-Poljak, G., Telišman Prtenjak, M., Kvakić, M. *et al.* Interaction of Sea Breeze and Deep Convection over the Northeastern Adriatic Coast: An Analysis of Sensitivity Experiments Using a High-Resolution Mesoscale Model.
*Pure Appl. Geophys.* **174, **4197–4224 (2017). https://doi.org/10.1007/s00024-017-1607-x

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### Keywords

- Sea breeze
- convection
- SST
- WRF
- the image moments analysis