Interaction of Sea Breeze and Deep Convection over the Northeastern Adriatic Coast: An Analysis of Sensitivity Experiments Using a High-Resolution Mesoscale Model

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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References

  1. Acs, F., Gyöngyösi, A. Z., Breuer, H., Horváth, A., Mona, T., & Rajkai, K. (2014). Sensitivity of WRF-simulated planetary boundary layer height to land cover and soil changes. Meteorologische Zeitschrift, 23, 279–293.

    Article  Google Scholar 

  2. Andrejczuk, M., Moszkowicz, S., Haman, K. E., & Szoplik, T. (2003). Radar-echo tracking by use of invariant moments. Applied Optics, 42, 5891–5896.

    Article  Google Scholar 

  3. Arakawa, A., & Jung, J.-H. (2011). Multiscale modeling of the moist-convective atmosphere—A review. Atmospheric Research, 102, 263–285.

    Article  Google Scholar 

  4. Babić, K., Mikuš, P., & Prtenjak, M. T. (2012). The relationship between shallow thermal circulation regimes and cumulonimbus clouds along the northeastern Adriatic coast. Geofizika, 29, 103–120.

    Google Scholar 

  5. Barthlott, C., & Kirshbaum, D. J. (2013). Sensitivity of deep convection to terrain forcing over Mediterranean islands. Quarterly Journal of the Royal Meteorological Society, 139, 1762–1779.

    Article  Google Scholar 

  6. Beaver, S., Tanrikulu, S., Palazoglu, A., Singh, A., Soong, S. T., Jia, Y., et al. (2010). Pattern-based evaluation of coupled meteorological and air quality models. Journal of Applied Meteorology and Climatology, 49, 2077–2091.

    Article  Google Scholar 

  7. Bellerby, T. J. (2004). A feature-based approach to satellite precipitation monitoring using geostationary IR imagery. Journal of Hydrometeorology, 5, 910–921.

    Article  Google Scholar 

  8. Bougeault, P., & Lacarrère, P. (1989). Parameterization of orography-induced turbulence in a mesobeta-scale model. Monthly Weather Review, 17, 1872–1890.

    Article  Google Scholar 

  9. Brooks, H. E., Lee, J. W., & Craven, J. P. (2003). The spatial distribution of severe thunderstorm and tornado environments from global reanalysis data. Atmospheric Research, 67–68, 73–94.

    Article  Google Scholar 

  10. Challa, V. S., Indracanti, J., Rabarison, M. K., Patrick, C., Baham, J. M., Young, J., et al. (2009). A simulation study of mesoscale coastal circulations in Mississippi Gulf coast. Atmospheric Research, 91, 9–25.

    Article  Google Scholar 

  11. Chen, S.-H., & Sun, W.-Y. (2002). A one-dimensional time-dependent cloud model. Journal of the Meteorological Society of Japan, 80, 99–118.

    Article  Google Scholar 

  12. Clark, A. J., Gallus, W. A., Jr., & Weisman, M. L. (2010a). Neighborhood-based verification of precipitation forecasts from convection-allowing NCAR WRF model simulations and the operational NAM. Weather and Forecasting, 25, 1495–1509.

    Article  Google Scholar 

  13. Clark, A. J., Gallus, W. A., Jr., Xue, M., & Kong, F. (2010b). Growth of spread in convection-allowing and convection-parameterizing ensembles. Weather and Forecasting, 25, 594–612.

    Article  Google Scholar 

  14. Cohen, A. E., Cavallo, S. M., Coniglio, M. C., & Brooks, H. E. (2015). A review of planetary boundary layer parameterization schemes and their sensitivity in simulating southeastern U.S. cold season severe weather environments. Journal of Applied Meteorology and Climatology, 30, 591–612.

    Google Scholar 

  15. Crook, N. A. (1996). Sensitivity of moist convection forced by boundary layer processes to low-level thermodynamic fields. Monthly Weather Review, 129, 1550–1563.

    Article  Google Scholar 

  16. Crook, N. A. (2001). Understanding Hector: The dynamics of island thunderstorms. Monthly Weather Review, 124, 1767–1785.

    Article  Google Scholar 

  17. Crosman, E. T., & Horel, J. D. (2010). Sea and lake breezes: A review of numerical studies. Boundary-Layer Meteorology, 137, 1–29.

    Article  Google Scholar 

  18. Demoli, N., Mrčela, I., & Šariri, K. (2013). Correlation and image moment approaches to analyze the Glagolitic script carved in stone tablets. Optik, 124, 1424–1430.

    Article  Google Scholar 

  19. Dudhia, J. (1989). Numerical study of convection observed during the winter monsoon experiment using a mesoscale two-dimensional model. Journal of the Atmospheric Sciences, 46, 3077–3107.

    Article  Google Scholar 

  20. Dudhia, J. (1996). A multi-layer soil temperature model for MM5. The Sixth PSU/NCAR Mesoscale Model Users’ Workshop, pp. 22–24.

  21. Feudale, L., & Manzato, A. (2014). Cloud-to-ground lightning distribution and its relationship with orography and anthropogenic emissions in the Po Valley. Journal of Applied Meteorology and Climatology, 53, 2651–2670.

    Article  Google Scholar 

  22. Feudale, L., Manzato, A., & Micheletti, S. (2013). A cloud-to-ground lightning climatology for north-eastern Italy. Advances in Science and Research, 10, 77–84.

    Article  Google Scholar 

  23. Franchito, S. H., Rao, V. B., Stech, J. L., & Lorenzzetti, J. A. (1998). The effect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil: A numerical experiment. Annales Geophysicae, 16, 866–881.

    Article  Google Scholar 

  24. Franchito, S. H., Toda, T. O., Rao, V. B., & Kayano, M. T. (2008). Interaction between coastal upwelling and local winds at Cabo Frio, Brazil: An observational study. Journal of Applied Meteorology and Climatology, 47, 1590–1598.

    Article  Google Scholar 

  25. Gilland, E. K., & Rowe, C. M. (2012). A comparison of cumulus parameterization schemes in the WRF model. 2012 AMS annual meeting, P2.16. https://ams.confex.com/ams/pdfpapers/120591.pdf. Accessed December 2, 2016.

  26. Givati, A., Lynn, B., Liu, Y., & Rimmer, A. (2012). Using the WRF model in an operational stream forecast system for the Jordan River. Journal of Applied Meteorology and Climatology, 51, 285–299.

    Article  Google Scholar 

  27. Gómez-Navarro, J. J., Raible, C. C., & Dierer, S. (2015). Sensitivity of the WRF model to PBL parametrisations and nesting techniques: Evaluation of wind storms over complex terrain. Geoscientific Model Development, 8, 3349–3363.

    Article  Google Scholar 

  28. Güttler, I., Stepanov, I., Branković, Č., Nikulin, G., & Jones, C. (2015). Impact of horizontal resolution on precipitation in complex orography simulated by the regional climate model RCA3. Monthly Weather Review, 143, 3610–3627.

    Article  Google Scholar 

  29. Hong, S. Y., & Lim, J. O. (2006). The WRF single-moment 6-class microphysics scheme (WSM6). Journal of the Korean Meteorological Society, 42, 129–151.

    Google Scholar 

  30. Hong, S. Y., Noh, Y., & Dudhia, J. (2006). A new vertical diffusion package with an explicit treatment of entrainment processes. Monthly Weather Review, 134, 2318–2341.

    Article  Google Scholar 

  31. Horvath, K., & Vilibić, I. (2014). Atmospheric mesoscale conditions during the Boothbay meteotsunami: a numerical sensitivity study using a high-resolution mesoscale model. Natural Hazards, 74, 55–74.

    Article  Google Scholar 

  32. Janjić, Z. I. (1994). The step-mountain eta coordinate model: Further developments of the convection, viscous sublayer, and turbulence closure schemes. Monthly Weather Review, 122, 927–945.

    Article  Google Scholar 

  33. Jury, M. R., & Chiao, S. (2013). Leeside boundary layer confluence and afternoon thunderstorms over Mayaguez, Puerto Rico. Journal of Applied Meteorology and Climatology, 52, 439–454.

    Article  Google Scholar 

  34. Kessler, E. (1995). On the continuity and distribution of water substance in atmospheric circulations. Atmospheric Research, 38, 109–145.

    Article  Google Scholar 

  35. Kleczek, M. A., Steeneveld, G.-J., & Holtslag, A. A. M. (2014). Evaluation of the weather research and forecasting mesoscale model for GABLS3: Impact of boundary-layer schemes, boundary conditions and spin-up. Boundary-Layer Meteorology, 152, 213–243.

    Article  Google Scholar 

  36. Lin, Y.-L., Richard, D. F., & Harold, D. O. (1983). Bulk parameterization of the snow field in a cloud model. Journal of Applied Meteorology and Climatology, 22, 1065–1092.

    Article  Google Scholar 

  37. Mayor, Y. G., & Mesquita, M. D. S. (2015). Numerical simulations of the 1 May 2012 deep convection event over Cuba: Sensitivity to cumulus and microphysical schemes in a high-resolution model. Advances in Meteorology, 2015. doi:10.1155/2015/973151.

  38. Menendez, M., Garcia-Diez, M., Fita, L., Fernandez, J., Mendez, F. J., & Gutierrez, F. J. (2014). High-resolution sea wind hindcasts over the Mediterranean area. Climate Dynamics, 42, 1857–1872.

    Article  Google Scholar 

  39. Meteorological Office. (1962). Weather in the Mediterranean (Vol. 1). London: General Meteorology, Her Majesty’s Stationery Office.

    Google Scholar 

  40. Miao, J. F., Wyser, K., Chen, D., & Ritchie, H. (2009). Impacts of boundary layer turbulence and land surface process parameterizations on simulated sea breeze characteristics. Annales Geophysicae, 27, 2303–2320.

    Article  Google Scholar 

  41. Miglietta, M. M., Moscatello, A., Conte, D., Mannarini, G., Lacorata, G., & Rotunno, R. (2011). Numerical analysis of a Mediterranean ‘Hurricane’ over south-eastern Italy: Sensitivity experiments to sea surface temperature. Atmospheric Research, 101, 412–426.

    Article  Google Scholar 

  42. Mikuš, P., Prtenjak, M. T., & Strelec-Mahović, N. (2012). Analysis of the convective activity and its synoptic background over Croatia. Atmospheric Research, 104–105, 139–153.

    Google Scholar 

  43. Milovac, J., Warrach-Sagi, K., Behrendt, A., Späth, F., Ingwersen, J., & Wulfmeyer, V. (2016). Investigation of PBL schemes combining the WRF model simulations with scanning water vapor differential absorption lidar measurements. Journal of Geophysical Research, 121, 624–649 (2016). doi:10.1002/2015JD023927.

    Google Scholar 

  44. Mlawer, E. J., Taubmanm, S. J., Brown, P. D., Iacono, M. J., & Clough, S. A. (1997). Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. Journal of Geophysical Research, 102, 16663–16682.

    Article  Google Scholar 

  45. Mohan, M., & Bhati S., (2011). Analysis of WRF model performance over subtropical region of Delhi, India. Advances in Meteorology, 2011. doi:10.1155/2011/621235.

  46. Penzar, B., Penzar, I., & Orlić, M. (2001). Vrijeme i klima hrvatskog Jadrana. Zagreb: Nakladna kuća Dr. Feletar.

    Google Scholar 

  47. Petrova, S., Mitzeva, R., & Kotroni, V. (2014). Summer-time lightning activity and its relation with precipitation: Diurnal variation over maritime, coastal and continental areas. Atmospheric Research, 135–136, 388–396.

    Article  Google Scholar 

  48. Pielke, R. A. (2002). Mesoscale meteorological modeling. New York: Academic Press.

    Google Scholar 

  49. Poljak, G., Prtenjak, M. T., Kvakić, M., Strelec-Mahović, N., & Babić, K. (2014). Wind patterns associated with the development of daytime thunderstorms over Istria. Annales Geophysicae, 32, 401–420.

    Article  Google Scholar 

  50. Prein, A. F., Gobiet, A., Truhetz, H., Keuler, K., Goergen, K., Teichmann, C., et al. (2016). Precipitation in the EURO-CORDEX 0.11° and 0.44° simulations: High resolution, high benefits? Climate Dynamics, 46, 383–412.

    Article  Google Scholar 

  51. Prtenjak, M. T. (2003). Main characteristics of sea/land breezes along the eastern coast of the northern Adriatic. Geofizika, 20, 75–92.

    Google Scholar 

  52. Prtenjak, M. T., Grisogono, B., & Nitis, T. (2006). Shallow mesoscale flows at the north-eastern Adriatic coast. Quarterly Journal of the Royal Meteorological Society, 132, 2191–2216.

    Article  Google Scholar 

  53. Prtenjak, M. T., Horvat, I., Tomažić, I., Kvakić, M., Viher, M., & Grisogono, B. (2015). Impact of mesoscale meteorological processes on anomalous radar propagation conditions over the northern Adriatic area. Journal of Geophysical Research, 120, 8759–8782.

    Google Scholar 

  54. Prtenjak, M. T., Pasarić, Z., Orlić, M., & Grisogono, B. (2008). Rotation of sea/land breezes along the northeastern Adriatic coast. Annales Geophysicae, 26, 1711–1724.

    Article  Google Scholar 

  55. Segal, M., & Pielke, R. A. (1985). On the effect of water temperature and synoptic flows on the development of surface flows over narrow elongated water bodies. Journal of Geophysical Research, 90, 4907–4910.

    Article  Google Scholar 

  56. Skamarock, W. C., & Klemp, J. B. (2008). A time-split nonhydrostatic atmospheric model for weather research and forecasting applications. Journal of Computational Physics, 227, 3465–3485.

    Article  Google Scholar 

  57. Skamarock, W. C., Klemp, J. B., Dudhia, J., Gill, D. O., Barker, D. M., Duda, M. G., et al. (2008). A description of the advanced research WRF version 3, NCAR/TN-475+STR. Boulder: NCAR.

    Google Scholar 

  58. Sović, I., Šariri, K., & Živčić, M. (2013). High frequency microseismic noise as possible earthquake precursor. Research in Geophysics, 3, 8–12.

    Google Scholar 

  59. Stanešić, A., & Brewster, K. A. (2015). Impact of radar data assimilation on the numerical simulation of a severe storm in Croatia. Meteorologische Zeitschrift, 25, 37–53.

    Google Scholar 

  60. Sweeney, J. K., Chagnon, J. M., & Gray, S. L. (2014). A case study of sea breeze blocking regulated by sea surface temperature along the English south coast. Atmospheric Chemistry and Physics, 14, 4409–4418.

    Article  Google Scholar 

  61. Tang, Y. (2012). The effect of variable sea surface temperature on forecasting sea fog and sea breezes: A case study. Journal of the Atmospheric Sciences, 51(986–990), 2012.

    Google Scholar 

  62. Teague, M. R. (1980). Image analysis via the general theory of moments. Journal of the Optical Society of America, 70, 920–930.

    Article  Google Scholar 

  63. Teixeira, J. C., Carvalho, A. C., Carvalho, M. J., Luna, T., & Rocha, A. (2014). Sensitivity of the WRF model to the lower boundary in an extreme precipitation event—Madeira island case study. Natural Hazards and Earth System Sciences, 14, 2009–2025.

    Article  Google Scholar 

  64. Thunis, P., & Bornstein, R. (1996). Hierarchy of mesoscale flow assumptions and equations. Journal of the Atmospheric Sciences, 53, 380–397.

    Article  Google Scholar 

  65. van Delden, A. (2001). The synoptic setting of thunderstorms in western Europe. Atmospheric Research, 56, 89–110.

    Article  Google Scholar 

  66. Večenaj, Ž., Belušić, D., Grubišić, V., & Grisogono, B. (2012). Along-coast features of the bora related turbulence. Boundary-Layer Meteorology, 143, 527–545.

    Article  Google Scholar 

  67. Wang, D., Miao, J., & Tan, Z. (2013). Impacts of topography and land cover change on thunderstorm over the Huangshan (Yellow Mountain) area of China. Natural Hazards, 67, 675–699.

    Article  Google Scholar 

  68. Wee, C.-Y., & Paramesran, R. (2007). On the computational aspects of Zernike moments. Image and Vision Computing, 25, 967–980.

    Article  Google Scholar 

  69. Weisman, M. L., Christopher, D., Wang, W., Manning, K. W., & Klemp, J. B. (2008). Experiences with 0–36-h explicit convective forecasts with the WRF-ARW model. Weather and Forecasting, 23, 407–437.

    Article  Google Scholar 

  70. Žabkar, R., Koračin, D., & Rakovec, J. (2013). A WRF/Chem sensitivity study using ensemble modelling for a high ozone episode in Slovenia and the northern Adriatic area. Atmospheric Environment, 77, 990–1004.

    Article  Google Scholar 

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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.

$$z(x,y) = \frac{(\cos (x \cdot \pi /50) + 1)(\cos (y \cdot \pi /50) + 1)}{4};\quad x,y \in \left[ { - 50,50} \right]$$
(1)
Fig. 14
figure14

A comparison between initial (black) and modified (blue) topography over one arbitrary chosen vertical cross-section A1A2 shown by dashed line in 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.

$${\text{filter}}_{\text{original}} (x,y) = (1 - 0.1 \cdot z)^{100}$$
(2)

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.

$${\text{filter}}_{\text{rescaled}} (x,y) = 0.9 + 0.1 \times \frac{{({\text{filter}}_{\text{original}} - \hbox{min} \,({\text{filter}}_{\text{original}} ))}}{{(\hbox{max} \,({\text{filter}}_{\text{original}} ) - \hbox{min} \,({\text{filter}}_{\text{original}} ))}}\,$$
(3)

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:

$${\text{filter}}_{30\% } (x,y) = ({\text{filter}}_{\text{rescaled}} )^{12} .$$
(4)

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:

$$A_{pq} = \frac{p + 1}{\pi }\iint {Z_{pq} (r,\theta )f(x,y){\text{d}}x{\text{d}}y},$$
(5)

where x = r·cos θ and y = 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

$$R_{pq} (r) = \sum\limits_{k = 0}^{(p - \left| q \right|)/2} {\frac{{( - 1)^{k} (p - k)!}}{{k!\left( {\frac{p + \left| q \right|}{2} - k} \right){\kern 1pt} {\kern 1pt} !\left( {\frac{p - \left| q \right|}{2} - k} \right){\kern 1pt} {\kern 1pt} !}}\,} r^{p - 2k}$$
(6)

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:

$${\text{ED}}_{ij} = \sum\limits_{p,q = 0}^{7} {\left| {(A_{pq} )_{i} - (A_{pq} )_{j} } \right|}$$
(7)

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