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Dynamical analysis of sea breeze hodograph rotation in Sardinia Moisseeva, Nadejda 2014

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DYNAMICAL ANALYSIS OF SEA BREEZE HODOGRAPH ROTATION IN SARDINIAbyNadejda MoisseevaB.Sc, The University of British Columbia, 2010A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Atmospheric Science)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)February 2014c? Nadejda Moisseeva, 2014AbstractThis study investigates the diurnal evolution of sea-breeze rotation over an island in the mid-latitudes. Earlier research on sea-breezes in Sardinia shows that the onshore winds around variouscoasts of the island exhibit both the theoretically predicted clockwise rotation as well as seeminglyanomalous anti-clockwise rotation. A non-hydrostatic fully compressible numerical model (WRF)is used to simulate wind fields on and around the island on previously-studied sea-breeze days andis shown to accurately capture the circulation on all coasts. Diurnal rotation of wind is examinedand patterns of clockwise and anti-clockwise rotation are identified. A dynamical analysis is per-formed by extracting individual forcing terms from the horizontal momentum equations. Analysisof several regions around the island shows that the direction of rotation is a result of a complexinteraction between near-surface and synoptic pressure gradient, Coriolis and advection forcings.An idealized simulation is performed over an artificial island with dramatically simplified topog-raphy, yet similar dimensions and latitude to Sardinia. Dynamical analysis of the idealized runsreveals a rather different pattern of hodograph rotation to the real Sardinia, yet similar underlyingdynamics. The research provides new insights into the dynamics underlying sea-breeze hodographrotation, especially in coastal zones with complex topography and/or coastline.iiPrefaceThis thesis contains the details of the original research and analysis undertaken primarily by theauthor N. Moisseeva, under the guidance of supervisor Douw Steyn.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Sea Breeze Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Numerical Modelling of Sea Breezes . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Hodographs and Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.4 Case Study - Sardinia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Proposed Research and Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1 Weather Research and Forecasting Model . . . . . . . . . . . . . . . . . . . . . . . . 9iv2.1.1 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.2 Extracting Dynamics from Weather Research and Forecasting Model (WRF)code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Numerical Simulation of a Real Case . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.1 Observational Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2.2 Data and Model Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.3 Model Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 Idealized Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Analysis and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.1 Model Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2 Dynamical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2.1 Rotation of the Horizontal Wind . . . . . . . . . . . . . . . . . . . . . . . . . 233.2.2 Regional Patterns of Hodograph Rotation . . . . . . . . . . . . . . . . . . . . 243.2.3 Components of the Horizontal Wind Rotation . . . . . . . . . . . . . . . . . . 263.2.4 Relative Importance of Tendency Terms . . . . . . . . . . . . . . . . . . . . . 273.3 Comparison with Earlier Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4 Dynamics of Idealized Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.1 Research Questions Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434.2 Future Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46A WRF Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49B WPS Namelist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51C WRF Namelist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53vD Evaluation of Sea breeze (SB) Episodes . . . . . . . . . . . . . . . . . . . . . . . . . 56viList of Tables2.1 Agrometeorologico Regionale per la Sardengna (SAR) Coastal Station Metadata . . 143.1 Region 1: Daytime Evolution of Rotation Tendency Terms . . . . . . . . . . . . . . . 283.2 Region 2: Daytime Evolution of Rotation Tendency Terms . . . . . . . . . . . . . . . 293.3 Region 3: Daytime Evolution of Rotation Tendency Terms . . . . . . . . . . . . . . . 303.4 Region 4: Daytime Evolution of Rotation Tendency Terms . . . . . . . . . . . . . . . 303.5 Region 1: Daytime Evolution of Rotation Tendency Terms - Idealized Case . . . . . 393.6 Region 2: Daytime Evolution of Rotation Tendency Terms - Idealized Case . . . . . 39viiList of Figures1.1 Sea-breeze system (Sea breeze circulation (SBC)) (Miller et al., 2003). . . . . . . . . . . 21.2 Topographic map of Sardinia with 12 coastal stations and SB hodographs. The island isapproximately 270 km long and 140 km wide.(Furberg et al., 2002) . . . . . . . . . . . . . 62.1 Nest domain for real case simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 Idealized domain with an elliptical island and a bell-shaped topography . . . . . . . . . . 183.1 Modelled and observed wind hodographs on June 21, 1998 . . . . . . . . . . . . . . . . . 203.2 Diurnal evolution of onshore wind at 10m on June 21, 1998 . . . . . . . . . . . . . . . . . 223.3 Regional pattern of hodograph rotation for June 20, 1998. . . . . . . . . . . . . . . . . . 253.4 Evolution of dominant dynamic forcings for Region 1, June 20, 1998. . . . . . . . . . . . . 313.5 Evolution of dominant dynamic forcings for Region 2, June 20, 1998. . . . . . . . . . . . . 323.6 Evolution of dominant dynamic forcings for Region 3, June 20, 1998. . . . . . . . . . . . . 323.7 Evolution of dominant dynamic forcings for Region 4, June 20, 1998. . . . . . . . . . . . . 333.8 Map of Attic Peninsula and regions of Anti-clockwise rotation (ACR) and Clockwise rotation(CR). (Steyn and Kallos, 1992) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.9 Map of Adriatic Coast. (Prtenjak et al., 2008) . . . . . . . . . . . . . . . . . . . . . . . . 363.10 Regional pattern of hodograph rotation for idealized simulation. . . . . . . . . . . . . . . 383.11 Evolution of dominant dynamic forcings for Region 1, idealized case. . . . . . . . . . . . . 403.12 Evolution of dominant dynamic forcings for Region 2, idealized case. . . . . . . . . . . . . 41viiiA.1 Horizontal and vertical grids of WRF-Advanced Research WRF (ARW) (Skamarock et al.,2008) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50D.1 Modelled and observed hodographs, May 17, 1997. . . . . . . . . . . . . . . . . . . . . . 57D.2 Modelled and observed onshore wind, May 17, 1997. . . . . . . . . . . . . . . . . . . . . 57D.3 Modelled and observed hodographs, August 15, 1997. . . . . . . . . . . . . . . . . . . . . 58D.4 Modelled and observed onshore wind, August 15, 1997. . . . . . . . . . . . . . . . . . . . 58D.5 Modelled and observed hodographs, May 20, 1998. . . . . . . . . . . . . . . . . . . . . . 59D.6 Modelled and observed onshore wind, May 20, 1998. . . . . . . . . . . . . . . . . . . . . 59D.7 Modelled and observed hodographs, May 30, 1998. . . . . . . . . . . . . . . . . . . . . . 60D.8 Modelled and observed onshore wind, May 30, 1998. . . . . . . . . . . . . . . . . . . . . 60D.9 Modelled and observed hodographs, June 21, 1998. . . . . . . . . . . . . . . . . . . . . . 61D.10 Modelled and observed onshore wind, June 21, 1998. . . . . . . . . . . . . . . . . . . . . 61D.11 Modelled and observed hodographs, June 29, 1998. . . . . . . . . . . . . . . . . . . . . . 62D.12 Modelled and observed onshore wind, June 29, 1998. . . . . . . . . . . . . . . . . . . . . 62ixList of AcronymsNotation DescriptionACR Anti-clockwise rotationARW Advanced Research WRFCFSR Climate Forecast System ReanalysisCIBL Convective internal boundary layerCR Clockwise rotationKHB Kelvin-Helmholtz billowsLES Large eddy simulationMODIS Moderate-Resolution Imaging Spectroradiome-terMRF Medium Range ForecastNCEP National Centers for Environmental PredictionPBL Planetary boundary layerxNotation DescriptionPGF Pressure gradient forceRAMS Regional Atmospheric Modelling SystemRK3 3rd-order Runge-KuttaRMSE Root-mean squared errorSAR Agrometeorologico Regionale per la SardengnaSB Sea breezeSBC Sea breeze circulationSBF Sea breeze frontSBG Sea breeze gravity currentSBH Sea breeze headSSib Simplified Simple Biosphere modelWPS WRF Preprocessing SystemWRF Weather Research and Forecasting ModelYSU Yonsei University scheme for PBLxiList of SymbolsNotation Description? local rate of horizontal wind rotationFU sum of forcing terms arising from map projec-tions, earth rotation, physics and other param-eterizations in x-direction in WRFFV sum of forcing terms arising from map projec-tions, earth rotation, physics and other param-eterizations in y-direction in WRF? mass of a dry air column per unit area? terrain-following dry-hydrostatic pressure verti-cal coordinate?? contravariant ?vertical? velocity or coordinatevelocity? flux-form vertical coordinate velocityxiiNotation Descriptionp pressureph hydrostatic component of pressurephs hydrostatic component of pressure at the surfacepht hydrostatic component of pressure at the top ofthe atmosphere? geopotentialt time?t full model time step?? acoustic time stepV three dimensional coupled vector velocityv three dimensional velocity vectorVadv flux-form horizontal velocity vector due to ad-vectionVcor flux-form horizontal velocity vector due to Cori-olisVh total horizontal flux-form velocity vectorVhdif flux-form horizontal velocity vector due to hor-izontal diffusionVpg flux-form horizontal velocity vector due to pres-sure gradient forceVsurf flux-form horizontal velocity vector due to sur-face gradientVsyn flux-form horizontal velocity vector due to syn-optic gradientxiiiNotation DescriptionVvdif flux-form horizontal velocity vector due to ver-tical diffusionxivAcknowledgementsKnowing Douw Steyn as my teacher, supervisor and mentor for nearly seven years has been anincredible privilege. I feel deeply indebted to him for his guidance, patience, and ability to gofar beyond his duties as a supervisor. Douw?s continual enthusiasm, knowledge and talent forconnecting people have been truly inspiring and motivating. The opportunities he has given me aretoo many to list, and I am sincerely thankful to Douw for all his kindness and encouragement.I would like to express my gratitude to my graduate committee members Phil Austin and SusanAllen for their guidance, invaluable advice, and willingness to help even when on leave. Specialthank you to Phil for his incredible generosity with time and ongoing technical support.I would like to thank Peter Jackson (UNBC) for his invaluable insights, which saved hours ofproduction runs and computational power. Thank you to Jim Dudhia (UCAR) and Anthony Toigo(Cornell) for their remote assistance with WRF. I would like to acknowledge Maria Furberg forkindly sharing her original thesis work and Kate Le Soeuf for her "blushing" Latex template.I gratefully acknowledge National Centers for Environmental Prediction (NCEP) and Com-putational and Information Systems Laboratory (CISL) for providing Climate Forecast SystemReanalysis (Climate Forecast System Reanalysis (CFSR)) reanalysis data (http://rda.ucar.edu/datasets/ds093.0) as well as Agrometeorologico Regionale per la Sardengna (SAR) and person-ally Alessandro M. S. Delitala and Marina Baldi for assisting me with meteorological data fromSardinia.Financial support for this work was provided by the NSERC CREATE Integrating AtmosphericChemistry And Physics From Earth To Space (IACPES) program and NSERC Discovery grants toD.G. Steyn.Special thanks to Annie, Niamh and Vlad for both the profound and the preposterous discus-sions and great company over the last two years.Deepest gratitude to my family for their unfailing love and support.xvChapter 1IntroductionHaving been studied as far back as 2500 years ago (Miller et al., 2003), sea-breeze circulation (SBC)has received particular attention of researchers since 1950. A considerable body of literature hasaccumulated, which illuminates the basic properties and dynamics of the sea-breeze phenomenon.As coastal regions are expected to accommodate as much as 75% of world population by 2030,the importance of issues associated with coastal air quality and inevitably sea-breezes has beenstrongly emphasized (Crosman and J., 2010). This study will focus on understanding the dynamicsof the sea-breeze and its rotation particularly, using observations as well as a fully compressiblenon-hydrostatic numerical model.1.1 Sea Breeze CirculationSBC is a mesoscale phenomenon driven by a mesoscale, horizontal pressure gradient resulting fromthe differential heating of land and water. Miller (2003) defines it as ?a vertically rotating mesoscalecell, with shoreward flow near Earth?s surface, rising air currents inland, diffuse sinking currentsseveral kilometers out to sea, and (usually) seaward return flow near 900 Pa.? As seen on theschematic diagram in Figure 1.1, cooler air from the water moves towards land as a gravity current,eventually getting lifted vertically at the sea-breeze front and in most cases forming a return flow1Figure 1.1: Sea-breeze system (SBC) (Miller et al., 2003).Also identified: sea-breeze front (Sea breeze front (SBF)), sea-breeze head (Sea breeze head (SBH)),Kelvin-Helmholtz billows (Kelvin-Helmholtz billows (KHB)s), convective internal boundary layer(Convective internal boundary layer (CIBL)), sea-breeze gravity current (Sea breeze gravity current(SBG)) and the pressure gradient force (Pressure gradient force (PGF)).2aloft. The diffuse region of descending currents closes the circuit. Basic understanding of thesedynamics dates far back into history, but the true complexity of the phenomenon has only beenfully understood in the last few decades.A vast amount of current work on SBC is dedicated to understanding the link between geo-physical variables (such as heat flux, atmospheric moisture, Coriolis parameter, surface roughness,slope and topography) and the specific local dynamics. Much of this understanding has come fromthe application of atmospheric numerical models. Crosman and Horel (2010) have conducted athorough review of the existing literature on numerical studies of SBs to summarize the currentstate of knowledge of the dependence of SB on the geophysical variables. Despite the large numbersof scientific studies devoted to the subject, Crosman and Horel have identified several gaps in un-derstanding of SBC. Among them is the ambiguity associated with SB dependence on topographyand anti-clockwise hodograph rotation. The primary purpose of this investigation is to addressthese identified knowledge gaps using numerical modelling.1.2 Numerical Modelling of Sea BreezesWith the growing computational power and resulting improved modeling capabilities numericalsimulations of SBC have gained attention since the 1960?s. Much of the earlier numerical workwas performed using two-dimensional hydrostatic models with coarse grid spacing (?10km). Whilethese contributed greatly to our understanding of the mechanics and structure of the SBC theynever the less remained highly idealized. Recently, with the availability of fully compressible three-dimensional non-hydrostatic numerical models allowing for <1km resolution, there has been atremendous improvement in our understanding of the complex nature of SB and the associatednon-linear interactions on several scales, from meso-? to micro-scale (Miller et al., 2003). Due tothis complexity, numerical models present the only tool for studying the dynamics of SBC overreal domains with complex topography and anti-clockwise hodograph rotation. As shown by Zhang(2005), Ramis and Romero (1995), Steyn and Kallos (1992), Mahrer and Segal (1985) and Walsh(1974) the general structure and diurnal cycle of the SBC can be well reproduced by a numerical3model and agrees closely with the aspects developed by theoretical studies. Numerical simulations,therefore, provide a powerful tool for tackling the knowledge gaps identified by Crosman and Horel(2010) and determining the governing factors in SB dynamics over complex terrain and coastlines.1.3 Hodographs and RotationThe diurnal rotation of SBC is commonly displayed using a wind vector hodograph, which is notonly a useful analytical tool for understanding planetary boundary layer (Planetary boundary layer(PBL)) flow but also has applications to diffusion of pollutants and their possible recirculation(Kusuda and Alpert , 1983), (Steyn et al., 2014). The end point of a wind vector typically tracesa closed ellipse with a clockwise (anticyclonic) rotation in the Northern Hemisphere (Simpson,1996). The mechanism behind the SB rotation was first explained by Haurwitz (1947), as aneffect of the Coriolis force. One can therefore expect all SBs in the Northern hemisphere and theircorresponding hodographs to rotate clockwise. However, a number of cases have been identifiedwhere an apparently anomalous anti-clockwise hodograph rotation (ACR) was observed. Neumann(1977) showed, using a two-dimensional sea and land-breeze model, that the rate of turning ofthe direction of sea and land-breezes is far from uniform over the diurnal cycle. Simpson (1996)expanded on the analysis proposed by Neumann and concluded that in general the Coriolis force,which is the primary factor driving typical clockwise hodograph rotation (CR) in the NorthernHemisphere, is not always the most important term in the equations of motion. Kusuda and Alpert(1983) considered the issue analytically and described hodographs in terms of phase shifts. Usinga linear model they showed that ACR hodograph rotation can be generated by including an ACRthermal force. The switch to ACR occurs at a critical value, which is a function of friction andlatitude. They also employed a simple two-dimensional model with artificial topography and foundthat the dominant term inducing the rotation was a combination of pressure and surface gradient.In contrast to primarily analytical and idealized work, Steyn and Kallos (1992) used a three-dimensional numerical mesoscale model to study the issue in the Attic Peninsula, Greece. Theirfindings were in agreement with Kusuda and Alpert (1983) as well as local observations. The paper4demonstrated that a balance of pressure and terrain gradient forcing is dominant, and can resultin either CR or ACR. A more recent paper by Prtenjak et al (2008) investigated the distributionof clockwise and anti-clockwise rotating SB along the Adriatic Coast using a rotary-componentmethod on wind fields simulated using a three-dimensional non-hydrostatic model. Their findingsshowed that topographic height has a considerable influence on the shape of the wind hodographsas well as their sense of rotation. While the studies described above present extremely valuableinsight into the diurnal evolution of the SB, overall hodograph rotation has been largely neglectedsince the original study by Haurwitz (1947), according to Crosman and Horel (2010) who suggestsimulating the hodograph rotation under a wide array of geophysical variables is a topic for futureexploration.1.4 Case Study - SardiniaThe island of Sardinia, located in the Western Mediterranean Sea, provides an ideal platformfor investigation of SB dynamics in the mid-latitudes. SBC are known to be fairly frequent in theMediterranean region and rich meteorological datasets are readily available from fifty meteorologicalstations on the island (described further in Section 2.2.1), of which twelve coastal locations are shownon Figure 1.2. Sardinia has a complex topography with three mountain ranges situated slightlycloser to the eastern side of the island. The island is approximately elliptical in shape, with lengthand width 270km and 140km, respectively.Several studies have previously examined SB in Sardinia. Melas et al (2000) employed a three-dimensional simulation of SBC on the island, and demonstrated that a SB system develops at everycoastline under weak synoptic forcing and clear skies during the summer. Through hodographanalysis they also showed the onshore-offshore nature of the SBC, as well as its response to localcoastline and interaction with topographically induced flows. Their model results are shown to agreefairly well with observations from several sites located on the west coast of the island. An earliernumerical simulation by Dalu and Cima (1983) also examined airflow over Sardinia and found thatsea-breezes on the island are typically advected eastward by the prevailing winds. A more recent5Figure 1.2: Topographic map of Sardinia with 12 coastal stations and SB hodographs. The island isapproximately 270 km long and 140 km wide.(Furberg et al., 2002)6study by Furberg (2002) focused on devising a statistical climatology of SB in Sardinia based ondata collected over approximately 16-26 months using a network of 12 coastal stations shown inFigure 1.2. The paper examines diurnal hodograph rotation and also shows that under appropriateconditions SB can develop simultaneously on all coasts of Sardinia, which is in close agreement withthe finding of Melas et al (2000). As seen from averaged wind hodographs in Figure 1.2, both CRand ACR are known to occur along the coast.Another important aspect of Furberg?s work, which is of particular interest to this study, is thatseven SB episodes occurring during warmer months of 1997-1998 are identified (described furtherin Section 2.2.1). It is shown that the sense of rotation of wind hodographs varies around the coastof Sardinia during the identified episodes. These findings provide an extremely useful starting pointfor numerical modeling of the SBC and hodograph rotation in Sardinia.1.5 Proposed Research and QuestionsGiven the rich background knowledge available on SB of Sardinia the island provides an idealplatform for tackling the knowledge gap in our understanding of anti-clockwise hodograph rotationidentified by Crosman and Horel (2010). The Weather Research and Forecast Model (WRF),discussed in detail in Section 2.1.1, is used to simulate SB episodes in Sardinia, where SBs areknown to develop on all coasts and have been shown to exhibit both clockwise and anti-clockwisehodograph rotation. The aim of this study is to combine numerical modeling and observational datato examine the effects of complex terrain on wind hodograph rotation though dynamical analysisof horizontal momentum equations. To guide this study, the following research questions have beenformulated:? Can the WRF Model reproduce the SB conditions in Sardinia?? What patterns of hodograph rotation are observed?? What are the dynamical mechanisms responsible for the observed patterns of hodographrotation?7? Can these findings be extrapolated to other islands of similar size/location?8Chapter 2Methods2.1 Weather Research and Forecasting Model2.1.1 Model DescriptionNumerical simulations for the study were performed using Weather Research and Forecasting model(WRF). Advanced Research WRF dynamical solver (WRF-ARW version 3.4) is described in detailin the WRF-ARW Technical Note (Skamarock et al., 2008). The model solves fully compressiblenon-hydrostatic flux-form Euler equations using a 3rd-order Runge-Kutta (3rd-order Runge-Kutta(RK3)) scheme time-split integration, with smaller time steps for acoustic and gravity-wave modes.Meteorologically significant (low-frequency) modes are integrating using a RK3 time integrationscheme, while acoustic modes (high-frequency) are integrated over smaller time steps to improvenumerical stability.The equations are formulated using terrain-following dry-hydrostatic pressure as a vertical co-ordinate ?, defined as:? = (ph ? pht)/? (2.1)where ? = phs? pht, and ph, pht, phs correspond to hydrostatic component of pressure, pressure atthe top and surface boundaries for a dry atmosphere, respectively. Since ? represents the mass of9a dry air column per unit area, flux-form velocity can be written asV = ?v = (U, V,?), (2.2)where v = (u, v, ?) are the covariant velocities in horizontal and vertical directions and ? = ???,with ?? = ???t . Using the above definition, flux-form horizontal momentum equations can be writtenas follows:?tU + (? ?Vu) + ???xp+??d??p?x? = FU (2.3)?tV + (? ?Vv) + ???yp+??d??p?y? = FV (2.4)where subscripts t, x and y correspond to derivatives with respect to time and horizontal coordi-nates, p denotes pressure, ? = gz is the geopotential and ? and ?d are the specific volume of moistair and specific volume of dry air, respectively. The right hand side terms FU and FV represent thesum of the forcing terms arising from map projections, earth rotation, advection, physics, turbulentmixing, and boundary layer parameterizations. The equations are then recast with variables ?, ?,and p defined as perturbations from the hydrostatically balanced base state to reduce truncationerrors. They are further transformed by redefining the momentum variables to include map scalefactors due to projections and subsequently solved in ARW.Horizontal discretization is performed using Arakawa-C grid (refer to Appendix A). Initializationwith three-dimensional data and specified boundary conditions are available for real-case simula-tions. For idealized runs one-, two- and three-dimensional initializations are possible and periodic,open and symmetric boundary condition options are available. Model top is defined as a constantpressure surface.2.1.2 Extracting Dynamics from WRF codeWhile WRF-ARW offers great operational forecasting capabilities, effectively no options for dy-namical analysis are available. The basic dynamical equations are embedded deeply in the solver10and remain inaccessible to the user. This presents a serious limitation to those using WRF forresearch: while the model demonstrates excellent performance and accuracy it does not allow oneto investigate the dynamics driving the modelled phenomena.In order to overcome this limitation the model code was adjusted to allow for the extraction ofthe individual tendency terms of the horizontal momentum equations. Standard WRF configurationallows a user to easily output the total mass-coupled horizontal momentum tendencies (first terms inEquations (2.3) and (2.4)), which are accumulated over each user-defined large time-step. However,additional variables must be introduced within the dynamical solver to output individual forcingterms, making up the RHS of Equations (2.3) and (2.4). These variables must be appropriatelystaggered, mass-coupled and passed on to the grid structure, which in turn makes them availablefor history output. Descriptions of individual forcing terms and their treatment in WRF as well asnecessary adjustments to the code are summarized below.Advection and pressure gradient tendencies are expressed explicitly on the LHS of Equations (2.3)and (2.4) (terms 2, 3 and 4). These can be extracted from the rk_tendency subroutine inmodule_em.F module by tracking the change in total accumulated momentum tendency prior toand after the terms are recalculated. As mentioned earlier, curvature forcing, arising from mapprojections, Coriolis, turbulent mixing and physics parameterizations are contained in the RHS ofthe equations. Due to the relatively modest spatial scale of this study, the curvature term was notfound to contribute significantly to the balance of the horizontal momentum equations and wassubsequently excluded from the dynamical analysis. Similarly to advection and pressure gradient,the curvature, Coriolis and horizontal diffusion tendencies are extracted by introducing additionalvariables in rk_tendency and tracking the changes in the accumulated terms prior to and after thecalls to the respective routines. Physics-related processes are treated separately in WRF and aredescribed in further detail later in this section.WRF offers a number of formulations for spatial dissipation including diffusion along coordi-nate surfaces, diffusion in physical space and sixth-order diffusion applied on horizontal coordinatesurfaces, as well as several options for calculating eddy viscosities. If the PBL parameterizationscheme is enabled vertical diffusion is handled independently and stored as a physics tendency11term. For this study, a simple horizontal diffusion scheme on coordinate surfaces was used witheddy coefficient K diagnosed from horizontal deformation using a Smagorinsky first-order closureapproach. Similarly to the forcings described above, horizontal diffusion tendencies are calculatedon a staggered grid as part of rk_tendency subroutine, and can be deduced by tracking the changein the accumulated horizontal tendency terms.Yonsei University (Yonsei University scheme for PBL (YSU)) scheme selected for PBL parame-terization is described in detail by Hong (2006). YSU PBL is a revised vertical diffusion algorithmwith nonlocal turbulent mixing coefficients and explicit treatment of the entrainment processes.It is the next generation of the Medium Range Forecast PBL (Medium Range Forecast (MRF)),based on the ?nonlocal-K? and counter-gradient approaches, but shown to produce a more realisticstructure of the PBL and its development (Nolan et al., 2009). Coupled PBL momentum tendencyterms from YSU scheme are already available in the Registry.EM_COMMON, however, as the physicsin the model are calculated on mass points (unstaggered Arakawa-A grid), these would subsequentlyneed to be interpolated to produce balanced equations with the rest of non-physics tendencies. Asthere are no other interactions with momentum tendencies in the physics driver (apart from theCumulus scheme, which is not relevant in clear sky conditions prevalent during SB episodes), it ismore efficient to extract these tendencies as total momentum forcing due to physics ru_tendf andrv_tendf. These are present in the Registry as i1 variables and hence cannot be output directly.Once again, new variables must be introduced in the main solver to extract them prior to the callto rk_addtend_dry in solve_em.F, which sums physics and dynamics tendencies.WRF model advances the horizontal momentum Equations (2.3) and (2.4) on a user-definedtime step ?t using a third-order RK integration scheme in three substeps. Within each substepacoustic modes are integrated using time-split integration with a smaller time step ?? , which variesamong the three RK substeps. A correction term is then introduced to adjust the pressure-gradienttendency. For the purpose of this analysis the acoustic correction was found to be insignificant andremained less 1 % of the total pressure-gradient term throughout the domain, except near mountainpeaks and hence was not extracted from the model. However, the procedure is summarized in detailby Lehner (2012) for an idealized Large Eddy Simulation (Large eddy simulation (LES)).12The hourly dynamical tendency terms were summed to ensure that the individual extractedtendencies indeed capture the dynamics of the model and produce balanced horizontal momentumequations described in the previous section.2.2 Numerical Simulation of a Real Case2.2.1 Observational DataFurburg?s (2000) climatological study of Sardinia identifies seven SB episodes occurring over years1997-1998. The knowledge that these days had favorable atmospheric conditions for the formation ofSB on the island provides an extremely useful starting point for the numerical simulation. Identifiedprimarily on the basis of diurnal reversal of surface wind direction, first suggested by Steyn andFaulkner (1986) the following days were considered SB days:? May 17, 1997? August 15, 1997? May 20, 1998? May 30, 1998? June 20, 1998? June 21, 1998? June 29, 1998For her analysis Furberg uses observational data from 12 coastal stations in Sardinia shown inFigure 1.2, operated by the Servizio Agrometeorologico Regionale per la Sardengna (SAR), whomanage a network of 50 stations over the island. The details of the select coastal stations aresummarized in Table 2.1.13Table 2.1: SAR Coastal Station MetadataStation NameLatitude(deg)Longitude(deg)Nearestshore (km)Elevation(m)Aglientu 41.104 9.076 2.75 110Arzachena 41.064 9.389 6.27 20Domus de Maria 38.963 8.863 6.46 133Jerzu 39.793 9.606 5.58 46Masainas 39.058 8.627 5.20 90Muravra 39.419 9.599 2.06 4Putifigari 40.547 8.460 9.47 423San Teodoro 40.793 9.646 2.17 13Siniscola 40.596 9.730 2.07 14Sorso 40.831 8.610 1.97 57Stintino 40.871 8.231 0.94 35Valledoria 40.940 8.832 1.09 5The data used by Furberg (2002) was obtained for the identified SB days and subsequently usedfor model evaluation (described in detail in Section 3.1).2.2.2 Data and Model InitializationStatic DataReal cases in WRF are initialized using WRF Preprocessing System (WRF Preprocessing System(WPS)) software. Standard static input data for WPS includes Regional Atmospheric ModellingSystem (RAMS) as well as various modelled landuse data (such as Simplified Simple Biospheremodel (SSib)). Terrestrial and landuse fields available in 30?, 2?, 5?, and 10? resolutions are interpo-lated to produce a domain of desired size and resolution using WPS. Identical domain configurationwas used for all of the SB episode days. The simulation was set up on a two-way nested domaincentered on the island of Sardinia (the nest is shown in Figure 2.1). The parent and nest domain14Figure 2.1: Nest domain for real case simulations.grid spacing was set to 9km and 3km respectively. Selection of such horizontal spacing was largelybased on earlier studies by Steyn and Ainslie (2013), which concluded that at this resolution thesubgrid-scale effects in WRF have no significant influence on the overall dynamics of the SB. Asample namelist.wps file used for for domain setup can be found in Appendix B.Meteorological DataThe model was initialized using Climate Forecast System Reanalysis (CFSR) data completed over31-year period from 1979-2009 by the National Centers for Environmental Prediction (NCEP),15available from CISL Research Data Archive. The reanalysis product is a global, high resolution,coupled atmosphere-ocean-land surface-sea ice system designed to provide the best estimate of thestate of these coupled domains (Wang et al., 2011). For the select episode days identified in Sec-tion 2.2.1, high resolution pressure-level (0.5 degrees latitude/longitude) and surface and radiativeflux (0.3 degree gaussian grid) 6-hour forecasts were obtained for 0000, 0600, 1200, and 1800 UTC.2.2.3 Model ConfigurationEach of the SB days identified by Furberg (2000) was simulated over 30 hours to account for a 6hour spin-up, beginning at 1800UTC of the previous day. As we are primarily interested in day-time dynamics, the analysis was performed starting 0900 UTC, i.e. 15 hours after the beginning ofeach simulation. RK time-step ?t was set to 54 seconds, as recommended 6??x(km) (Skamarocket al., 2008). Since WRF allows for output of instantaneous fields only, the history interval was setto 10 minutes. Wind and dynamical tendency fields were hence output six times each hour, andsubsequently averaged to produce an estimate of hourly averages.Through the analysis of various production runs it was determined that 50 vertical eta-levelsprovided sufficient vertical resolution within the boundary layer, and hence this configuration wasadopted for all runs. Model pressure top was set to 5000 Pa. A complete namelist.input used formodel initialization can be found in Appendix C.2.3 Idealized CaseIt is important to highlight that the idealized case referred to herein is not to be confused with anideal-case WRF simulations, which introduce severe simplification into the model?s operation. Thestandard idealized test cases included in WRF-ARW do not allow for nesting, typically excludesome dynamical and physics routines or have been reduced to 2D and only allow for initializationwith a single sounding. The results of such idealized simulation would not be fit for comparisonwith our real-case simulation.16Hence, for our idealized simulation the full features of a real-case WRF simulation were retained(including all surface, boundary layer and physics routines, as well as real earth features such ascurvature and Coriolis). The term idealized in this case is meant to indicate that the shape,coastline and topography of the island were generalized to such an extent that they no longerrepresent the particular characteristics of Sardinia, but rather of any elliptical island with a bell-shaped topography in the mid-latitudes.Using the standard WPS software to create a domain, the idealized case study was set up withthe same parameters and nesting options as the real case. The topography was then manually editedto create a perfectly elliptical island in the center of the domain with 40 grid point north-southradius and 18 grid point south-west radius, which approximately matches the size of Sardinia. Theremaining grid points of the nest and parent domains were masked as water. All other standardfields such as land use, soil moisture and type, temperature and pressure were also adjusted. Asseen in Figure 2.2 the topography height was edited to create a bell-shaped mountain with 800mpeak in the center of the island using a 2D Hanning window.Meteorological data from June 20, 1998 was used to create initial fields with WPS. These wereagain manually altered to fit the modified domain. Combined domain (including both static andmeteorological fields) and boundary files generated by WRF had to be further adjusted to removeany inconsistencies arising due to interpolation. The rest of the simulation was performed usingsettings identical to the real cases.17Figure 2.2: Idealized domain with an elliptical island and a bell-shaped topography18Chapter 3Analysis and Discussion3.1 Model EvaluationThe model was evaluated using the observational data available for the twelve meteorological sta-tions described in Section 2.2.1. The primary goal was to demonstrate that the model capturesthe SBC and hodograph rotation on all coasts, and hence we focused on comparing the wind fieldsand the associated diurnal evolution of wind hodographs at each of the station locations. For thepurpose of the analysis, twelve individual modelled grid points were selected on the island whichmost closely represented the location of the meteorological stations based on latitude and longitude.The first step was to determine the direction of the onshore wind vector for both modelled andobservational data. The u and v wind components at 10m were converted into polar coordinatesand plotted as a hodograph for both observed and modelled winds. Figure 3.1 shows the resultsfrom a single simulated SB episode on June 21, 1998. A range of angles was tested for each data setand the onshore wind vector was defined to be the one that produced the least root-mean squarederror (Root-mean squared error (RMSE)), and hence corresponding to the primary direction of airflow.Note that the modelled and observed onshore directions were defined separately for the observedand modelled winds and allowed to differ for each individual day. While these directions were19Figure 3.1: Modelled and observed wind hodographs on June 21, 1998Simulated and observed hodographs are shown in red and blue, respectively. Onshore direction formodelled (purple) and observed (black) winds is shown in dashed lines. Station data is missing forSiniscola.20generally found to be in close agreement, several stations showed a considerable discrepancy betweenmodel and observations (e.g. Valledoria, Jerzu). Introduction of this flexibility is a particularlyimportant aspect of the proposed evaluation methodology. While it may seem that this assumptionmakes the evaluation criteria less stringent, it, in fact, acts as a filter to isolate the subgrid-scaleeffects that are inevitably present in observational data, and entirely absent from the model output.As the hourly winds are subsequently projected onto the identified onshore direction, a slightdifference in the definition of the onshore axis due to inclusion/exclusion of the subgrid-scale effectscan easily mask the model?s overall good performance. The advantage of this approach is that itallows us to compare and evaluate the larger scale kinematics and their diurnal evolution, ratherthen the local effects due to subgrid-scale phenomena.Overall, individual (non-averaged) daily hodographs present one of the most stringent criteriafor model evaluation, as instantaneous wind data is inevitably highly variable. However, as seen inFigure 3.1, there is good agreement between modelled and observed winds. While no observationalrecord is present for Siniscola station for the modelled day, there appears to be a greater discrep-ancy between simulated and observed data on the eastern coast. This can likely be explained bysteep topography in close proximity to the east coast. Simulated winds at Jerzu station, locatedbeneath the highest peak in Gennargentu Ranges (1834m) (Figure 1.2), are consistently inferior tosimulations at other stations on all simulation days. While the terrain-following coordinate systemgreatly simplifies the imposition of lower boundary conditions, the nonorthogonal grid lines areknown to introduce significant truncation errors when attempting to calculate horizontal gradients,leading to computational inaccuracy of advection, diffusion and pressure gradient terms (Yamazakiand Satomura, 2010).The simulated and observed wind fields were then projected onto the corresponding identifiedonshore direction for each station and compared. The results of this evaluation for the episodedescribed above can be seen in Figure 3.2. Overall, the model evaluation demonstrates excellentagreement between model and observations, both due to exceptional model performance and suc-cessful evaluation strategy. Note that the stations where the onshore directions determined byRMSE differed considerably between model and observations still show strong agreement in the21Figure 3.2: Diurnal evolution of onshore wind at 10m on June 21, 1998Scatter points and continuous lines correspond to observed and modelled values respectively.22development and shape of the onshore wind component, suggesting that the overall structure ofthe SB at that location is well represented. WRF clearly captures the kinematics of the SBC, andhence can be used for further dynamical analysis of the SB structure. The evaluation results of theremaining six episodes can be found in Appendix D.3.2 Dynamical Analysis3.2.1 Rotation of the Horizontal WindThe horizontal momentum Equations (2.3) and (2.4) solved in WRF can be represented in simplifiedvector form as?Vh?t=?Vpg?t+?Vadv?t+?Vcor?t+?Vhdif?t+?Vvdif?t(3.1)where Vh is total horizontal velocity vector, V = (U, V ) and subscripts pg, adv, cor, hdif , and vdifcorrespond to forcing due to pressure gradient, advection, Coriolis, horizontal and vertical diffusion.Taking the 850 mb pressure level to be representative of overlying synoptic weather conditions, thepressure gradient term Vpg can be further separated into synoptic (syn) and surface (surf) forcingby assuming thatVsyn = Vpg(850mb) (3.2)The remaining pressure gradient forcing is then assumed to be due to surface effects, i.e.Vsurf = Vpg ? Vsyn (3.3)It is important to note that the formulation of the model does not allow us to further separate thepressure gradient forcing into components to isolate the effects of topography, coastline curvatureand aspect, land/sea temperature contrast, roughness and other local features.Full horizontal momentum equations considered for dynamical analysis (excluding the effects of23curvature and acoustic modes, as discussed in Section 2.1.2 then become?Vh?t=?Vsurf?t+?Vsyn?t+?Vadv?t+?Vcor?t+?Vhdif?t+?Vvdif?t(3.4)Following Neumann (1977), change of horizontal wind direction can be expressed as???t=1V2hk ? (Vh ??Vh?t) (3.5)where ? is the angle of local wind relative to the positive x-axis, Vh is the horizontal wind vector,and k is a vertical unit vector. Positive and negative values of ???t correspond to ACR and CRrespectively. Expanding the cross product in Equations (3.5) using the components of the totalwind vector in Equation (3.4) it is possible to compare the magnitudes of the terms contributingmost strongly to the rotation.3.2.2 Regional Patterns of Hodograph RotationUsing the definition of ? in Equation (3.5) it is possible to create contour maps of regions of CRand ACR for the simulated real domain. June 20, 1998 was selected as a test case, as it has shownstrong agreement between model and observed hodographs based on the results of model evaluation.Hourly contours produce extremely complex patterns. As we are primarily interested in identifyingpossible invariant features of the circulation daytime hourly ???t values were averaged between 0900to 1700 UTC to produce ??day?t . Figure 3.3 shows daytime regional patterns of CR (??day?t < 0)and ACR (??day?t > 0) for the real case simulation. The southwestern region of the nested domainis dominated by strong clockwise rotation. The CR pattern continues around the northern part ofSardinia. The SBC on the eastern coast of the island is largely ACR. The southern tip of Sardiniashows a switch between CR and ACR likely due to the presence of the second mountain range - theSulcis Mountains (Figure 1.2). Overall the rotation pattern appears to respond to the local featuresof the terrain. The island of Corsica to the north of Sardinia exhibits a very complex pattern withseveral extremely sharp gradients in rate of change of direction. This can likely be explained by24Figure 3.3: Regional pattern of hodograph rotation for June 20, 1998.Total ???t values are averaged over daytime hours. Also shown: elevation contours starting at 100m abovesea level with 100m contour interval and subregions identified for further dynamical analysis.25Corsica?s much steeper topography and slopes and proximity to the boundary of the nested domain.Also identified in Figure 3.3 are four subregions off the southwestern, northwestern, southeasternand southwestern coasts of the island exhibiting either CR or ACR. Each subregion is a square of8x8 grid points covering an area of 576 km2. These regions were selected for further dynamicalanalysis in an attempt to understand the underlying processes most strongly influencing the senseof wind rotation.3.2.3 Components of the Horizontal Wind RotationExpanding the cross product in Equations (3.5) using the components of the total wind vector inEquation (3.4) the total rate of rotation can be broken into individual forcing terms as follows:??tot?t=??surf?t+??syn?t+??cor?t+??adv?t+??hdif?t+??vdif?t(3.6)where the subscripts correspond the various tendency components, consistent with terms in Equa-tion (3.4).As described earlier, the Coriolis term always induces CR in the Northern Hemisphere. How-ever, the remaining rotation tendency components have much more complex underlying physics,and are discussed individually below.Surface Pressure GradientThe surface pressure gradient is predominantly driven by the temperature contrast between landand water, and it?s influence on the sense of rotation depends largely on the location and shape ofthe landmass. More subtle, local effects of the sea surface temperature inhomogeneity may furtheralter the turning direction of the surface wind. Moreover, uneven surface heating due to topographyand irregular coastline of Sardinia are likely to introduce further complexity into surface pressuredistribution, as previously suggested by Kusuda and Alpert (1983).Synoptic Pressure Gradient26While the synoptic component of the pressure gradient force generally acts in opposition to thesurface gradient under SB conditions due to the formation of the SB return flow (Miller et al.,2003), it also responds to the local topography. Cyclonic and anti-cyclonic rotation may be induceddepending on the direction of the local wind and shape of the topography. As SBs are known to de-velop on all coasts of Sardinia and have variable inland penetration the direction of dominant windflowing over the primary mountain range on the island is unclear and is likely to vary throughoutthe day.AdvectionAdvection of the horizontal momentum may similarly result in the formation of both CR and ACR.The importance of the term depends largely on the presence of velocity gradients at a given loca-tion. Since the regions selected for our analysis are located away from the coast, we can expect therotational effects of the advection to be of secondary importance.Horizontal and Vertical DiffusionThe horizontal and vertical diffusion are friction driven effects, and hence always act to opposethe local wind. Varying surface roughness due to the spatial distribution of land use, cover andtopography may introduce shear and rotation into wind flow. As our analysis is performed forlocations away from the coast, these remain largely negligible.3.2.4 Relative Importance of Tendency TermsTo apply the term-by-term analysis (Equation 3.6) to each region identified in Figure 3.3, the hourlytendency values for the selected grid points was extracted. This was subsequently normalized bythe Coriolis parameter f to produce non-dimensional values, and also spatially averaged amongstthe 64 grid-points for each hour. Table 3.1 summarizes the daily evolution of the individual forcingsfor Region 1 (Southwest).27Table 3.1: Region 1: Daytime Evolution of Rotation Tendency TermsTime ??tot?tSurfacegradientSynopticgradientCoriolis AdvectionHorizontalDiffusionVerticalDiffusion0900 -0.18 0.60 0.02 -1.01 0.21 0.00 0.001000 -0.47 0.29 0.22 -1.01 0.04 0.00 -0.011100 -0.93 -0.27 0.55 -1.02 -0.18 0.00 -0.021200 -1.36 -0.90 0.90 -1.03 -0.30 0.00 -0.031300 -1.72 -1.34 1.02 -1.02 -0.34 0.00 -0.031400 -2.00 -1.65 1.14 -0.99 -0.47 0.00 -0.031500 -2.52 -1.85 1.05 -0.95 -0.74 0.00 -0.031600 -2.27 -1.20 0.70 -0.93 -0.81 0.00 -0.02One can see that the total clockwise rotation rate increases throughout the day reaching apeak around 1500 UTC, as may be explained by the growth of the land-sea temperature contrast.As expected, the Coriolis component is one of the leading terms inducing CR, and remaininggenerally constant. The surface gradient becomes increasingly important through the day, initiallycontributing slightly to ACR but subsequently turning strongly CR. Note that the surface gradientterm includes the combined effects of surface slope, roughness, temperature and pressure gradientand hence is non-zero even though the sub-domain is located over water. The synoptic gradientacts largely in opposition to the surface gradients, likely due to the formation of SB return flownear 850mb level. As expected this forcing is strongest mid-day, around 1400. Advection effect isalways clockwise, but is of secondary importance in this dynamical balance. Horizontal and verticaldiffusion terms are largely insignificant in this and the remaining cases, as the regions selected werelocated off the coast where friction is much less important. As SBs are mesoscale phenomena, theirscale is not restricted to the immediate coastal region. Hence the analysis can be performed awayfrom the regions of sharp gradients in topography, roughness, and temperature and still capturethe dynamics of the phenomenon. Overall, the balance appears to be dominated by surface and28synoptic pressure gradients and Coriolis.Table 3.2: Region 2: Daytime Evolution of Rotation Tendency TermsTime ??tot?tSurfacegradientSynopticgradientCoriolis AdvectionHorizontalDiffusionVerticalDiffusion0900 0.62 2.02 -0.19 -0.93 -0.31 0.00 0.041000 0.38 1.37 0.08 -0.96 -0.13 0.00 0.031100 0.32 1.02 0.33 -0.98 -0.06 0.00 0.011200 0.41 0.94 0.48 -0.99 -0.02 0.00 0.001300 0.73 0.98 0.84 -1.00 -0.09 0.00 -0.011400 0.91 0.93 1.16 -1.00 -0.17 0.00 0.001500 0.94 0.50 1.59 -1.00 -0.16 0.00 0.011600 0.80 -0.29 2.20 -1.01 -0.10 0.00 0.00Table 3.2 shows the individual hourly tendency components for Region 2 (Southeast). Whilethe Coriolis term remains one of the largest in magnitude acting clockwise, the combined effects ofsurface and synoptic pressure gradients outweigh its influence and induce ACR. Similarly to Region1, a relatively small clockwise advection term is present.The dynamics of the remaining northern regions 3 and 4 are summarized in Tables 3.3 and 3.4below. While clockwise Coriolis forcing remains the largest term throughout the course of the daythe combined anti-clockwise effects of all remaining terms induce ACR in Region 3. A particularfeature of the dynamics of this region is that the advection term is relatively important, and withoutit the ACR would not be possible. Region 4 exhibits largely CR, dominated by the combined effectof Coriolis and pressure gradient terms. Advection and synoptic act to induce ACR, but remainsecondary.29Table 3.3: Region 3: Daytime Evolution of Rotation Tendency TermsTime ??tot?tSurfacegradientSynopticgradientCoriolis AdvectionHorizontalDiffusionVerticalDiffusion0900 0.61 -0.01 1.43 -1.03 0.23 0.00 -0.021000 0.62 0.11 1.31 -1.03 0.24 0.00 -0.021100 0.72 0.45 1.04 -1.04 0.28 0.00 -0.011200 0.68 0.71 0.68 -1.04 0.34 0.00 -0.011300 0.53 0.54 0.60 -1.04 0.43 0.00 -0.001400 0.38 0.33 0.61 -1.04 0.49 0.00 -0.001500 0.46 0.32 0.69 -1.04 0.50 0.00 -0.011600 0.31 0.19 0.70 -1.04 0.48 0.00 -0.01Table 3.4: Region 4: Daytime Evolution of Rotation Tendency TermsTime ??tot?tSurfacegradientSynopticgradientCoriolis AdvectionHorizontalDiffusionVerticalDiffusion0900 -0.75 0.10 -0.15 -1.01 0.15 0.00 0.151000 -0.82 -0.17 0.20 -1.00 0.03 0.00 0.111100 -1.08 -0.68 0.52 -0.99 -0.01 0.00 0.081200 -0.87 -0.77 0.86 -0.98 -0.02 0.00 0.041300 -0.69 -0.75 0.98 -0.98 0.05 0.00 0.011400 -0.59 -0.76 1.08 -0.99 0.08 0.00 0.001500 -0.40 -0.39 0.93 -0.99 0.06 0.00 -0.011600 -0.48 -0.31 0.75 -0.99 0.07 0.00 -0.01It can, hence, be concluded that the sense of rotation is predominantly a result of local balanceof Coriolis, surface and synoptic pressure gradients and advection. While Coriolis forcing generallyremains nearly constant throughout the day, the remaining tendencies each have a unique diurnalpattern. Surface pressure gradient rotation tendency appears to respond faster to the increase in30Figure 3.4: Evolution of dominant dynamic forcings for Region 1, June 20, 1998.the land-sea temperature contrast, generally peaking in magnitude around noon. The forcing dueto the synoptic pressure gradient appears to peak later in the day, which may be explained by theformation of the SB return flow, generally forming with a slight delay in response to the surface SBgravity wave (Miller et al., 2003). The advection term is largest around 1500 UTC and can act toinduce both clockwise and anti-clockwise rotation.To assess the confidence of the above findings the variability of the hourly ???t components wasexamined. Figures 3.4, 3.5, 3.6 and 3.7 show the diurnal evolution of the individual terms as wellas their spatial standard deviation. Note that the shape of the curve of ??tot?t closely resembles theshape of the ??surf?t . This suggests that the evolution of SB rotation is largely dependent on thetopographic and coastal features of the domain.31Figure 3.5: Evolution of dominant dynamic forcings for Region 2, June 20, 1998.Figure 3.6: Evolution of dominant dynamic forcings for Region 3, June 20, 1998.32Figure 3.7: Evolution of dominant dynamic forcings for Region 4, June 20, 1998.3.3 Comparison with Earlier WorkSteyn and Kallos (1992) performed similar analysis to examine the dynamics of SB rotation in AtticPeninsula. It is particularly important to note that the Attic Peninsula shares many similaritieswith Sardinia. Being approximately the same in size and shape, with slightly less steep terrain onecould expect that the dynamics of SB rotation would be very similar to those in Sardinia. Steynand Kallos show that the balance of pressure gradient and terrain-gradient (equivalent to synopticand surface pressure gradients in this study, respectively) forcing is dominant, and that this balancemay result in either CR or ACR. Moreover, they discovered an invariant "tongue" of CR in a broadregion of ACR (Figure 3.8) linked to topography of the peninsula.However, as demonstrated in the previous section (Section 3.2.4), the dynamical balance of termscontributing to SB rotation in Sardinia appears to be much more complicated than that proposedby Steyn in Kallos (1992) for the Attic Peninsula. The rotation tendencies due to pressure gradientswere not typically found to be the largest magnitude terms. Moreover, depending on the specificregion of the domain these terms could be acting in the same or opposite directions. This work has33Figure 3.8: Map of Attic Peninsula and regions of ACR and CR. (Steyn and Kallos, 1992)The stippled boundary between regions of ACR and CR indicates the position occupied by the individual(often quite convoluted) hourly boundaries between ACR and CR.34shown that rather than being the result of a simple balance of the synoptic and surface pressuregradients, the sense of direction is determined by whether the combined effects of surface, synopticand advection tendencies outweigh the Coriolis effect.The spatial pattern has also proved to be much more complex. Since it was suggested bySteyn and Kallos that the shape of the CR region is linked closely to topography, the differencemay be attributed to the presence of multiple mountain ranges in Sardinia. In contrast, the AtticPeninsula has a single smooth bell-shaped hill. One can speculate that the rotation patterns foundaround Corsica, which while having a significantly steeper topography closely resembles "single-hill" structure of the Attic Peninsula, show a similar "CR tongue" formation near the easterncoast. However, the accuracy of the simulation was not evaluated in that region, and the proximityto the boundaries of the nest domain do not allow us to draw such conclusions with certainty.The complexity of the spatial patterns of SB rotation in Sardinia may also be explained by theincreased ability of newer numerical models to capture detail. While Steyn and Kallos performedtheir simulation using an early version of hydrostatic Regional Atmospheric Modelling System(RAMS) (Pielke et al., 1992), a more recent study of CR and ACR of SB on Adriatic Coast byPrtenjak (2008) produced their fields using non-hydrostatic MEMO6. Increased resolution andmore computationally demanding dynamical schemes may have introduced real-world complexityinto the simulations that the earlier models were unable to capture. Figure 3.9 below shows afour-day average of spatial patterns of hodograph rotation over Adriatic Coast. Note that even theaveraging did not reduce the complexity of CR and ACR distribution.35Figure 3.9: Map of Adriatic Coast. (Prtenjak et al., 2008)Regions of CR and ACR are shown in blue and red respectively.363.4 Dynamics of Idealized CaseThe idealized simulation was set up (Section 2.3) to determine whether the complexity of hodographrotation patterns in Sardinia is associated with the specific topographic features of the island orthe improved numerical modelling abilities. It was therefore, extremely important to retain thefull real-case features of WRF. Since WRF was not designed to introduce idealized topographyinto a real-case simulation, the results presented in this section cannot be considered conclusive.The complexity of the WRF model makes tracking potential inconsistencies of these modificationsextremely difficult. The hourly patterns of hodograph rotation of the idealized simulation showeddistributions nearly as complex as the real-case simulation. Attempts to increase the size of bothparent and nest domains did not resolve the issue. The diurnal average shown in Figure 3.10, doesexhibit a much simpler pattern than that of a real case. Interestingly, regions of CR and ACRare arranged on opposite coasts to that of the real Sardinia, and similarly to Corsica from the realsimulation and the Attic Peninsula from Steyn and Kallos (1992).Overall the structure appears to be vortex-like, centering around the peak of the mountain. Onecan speculate that the region of CR on the eastern coast of the island is the equivalent of the "CRtongue" feature of Attic Peninsula. Again, further model evaluation would be necessary to confirmthis finding.The term-by-term dynamical analysis for the idealized simulation is also much less conclusivethat of the real simulation. The west-coast ACR region shows consistent but relatively weak totalrotation forcing, as seen in Table 3.5. Early morning values appear to be unrealistically large. Thismay be an indication of a model response to the morning switch in the direction of surface heatflux, which in some cases produces a spike in model fields. As likely inconsistencies in the domainset-up due to modification of the standard preprocessing routine may reduce the numerical stabilityof the model, the increased values caused by a spike may persist for long periods of time.37Figure 3.10: Regional pattern of hodograph rotation for idealized simulation.Total ???t values are averaged over daytime hours. Also shown: elevation contours starting at 100m with150m contour interval and subregions identified for further dynamical analysis.38Table 3.5: Region 1: Daytime Evolution of Rotation Tendency Terms - Idealized CaseTime ??tot?tSurfacegradientSynopticgradientCoriolis AdvectionHorizontalDiffusionVerticalDiffusion900 3.37 2.35 1.21 -1.01 0.55 0.00 0.261000 2.68 2.90 0.12 -1.03 0.60 0.00 0.091100 1.26 1.60 0.28 -1.03 0.40 0.00 0.001200 0.14 0.31 0.65 -1.02 0.20 0.00 0.001300 0.07 -0.03 0.93 -1.02 0.19 0.00 0.001400 0.55 0.57 0.52 -1.00 0.46 0.00 0.001500 0.53 0.82 0.15 -1.00 0.56 0.00 0.001600 -0.07 0.63 0.18 -1.01 0.12 0.00 0.00Table 3.6: Region 2: Daytime Evolution of Rotation Tendency Terms - Idealized CaseTime ??tot?tSurfacegradientSynopticgradientCoriolis AdvectionHorizontalDiffusionVerticalDiffusion900 -0.55 -0.49 1.01 -0.94 -0.21 0.00 0.081000 -1.85 -1.34 0.31 -0.94 -0.02 0.00 0.131100 -1.37 -1.20 0.16 -0.98 0.53 0.00 0.131200 -1.61 -1.40 -0.19 -1.02 0.92 0.00 0.081300 -2.19 -1.52 -0.86 -1.09 1.33 0.00 -0.051400 -2.10 -0.51 -1.68 -1.12 1.44 0.00 -0.241500 -1.84 0.19 -1.52 -1.11 0.97 0.00 -0.361600 -2.13 0.40 -1.16 -1.12 0.22 0.00 -0.48Overall the dynamics of the ACR region mimic those of Region 3 in the real case simulation,with all significant terms acting to counterbalance Coriolis forcing. Since idealized Region 1 remainsaway from the coast the diffusion terms are again insignificant. Unlike the real case simulation theafternoon surface, synoptic pressure gradients and advection are all of approximately the same39Figure 3.11: Evolution of dominant dynamic forcings for Region 1, idealized case.magnitude.The CR region on the eastern coast of the idealized island shows much stronger rotationaltendency (Table 3.6). The signs of surface and synoptic pressure gradient vary throughout the day.Similarly to Region 1, pressure gradient and advection terms have like magnitudes. As this regionpartially covers land grid points vertical diffusion term can no longer be ignored. Friction effectscontribute to the total balance inducing both clockwise and anti-clockwise rotation depending onthe time of the day.Similarly to the real case, the overall shape of the total diurnal rotation curve appears to bestrongly influenced by that of the surface pressure gradient (Figures 3.11 and 3.12). Though region1 of the idealized simulation has a similar spatial variability to that of the real case simulation,larger standard deviation values were observed for the second region.While these results generally appear to be in agreement with the previous studies further eval-uation is necessary to deem the findings conclusive. The patterns of clockwise and anti-clockwisehodograph rotation are notably simpler than that of a real-case simulation, as anticipated. Whilethe distribution of CR and ACR regions shares little resemblance with that of real Sardinia, the40Figure 3.12: Evolution of dominant dynamic forcings for Region 2, idealized case.underlying dynamics appear similar.41Chapter 4Summary and ConclusionThis study examined the dynamics of SB over an island of Sardinia, Italy. SBC in the regionhas been shown to have a complex structure in earlier, predominantly observational work. WhileSBC formed on all coasts of the island hodographs exhibited both theoretically expected CR aswell as "anomalous" counter-Coriolis ACR. Due to the complex, non-linear nature of SBs, numer-ical modeling presents the only possible opportunity to understand the underlying dynamics ofthis mesoscale phenomenon. A numerical simulation was performed using WRF Model and subse-quently evaluated for accuracy using local observations. Observed and simulated daily hodographswere compared and an evaluation methodology was devised to asses WRF?s ability to capture SBkinematics. The diurnal evolution of modelled and observed onshore winds was shown to be instrong agreement.While the model demonstrated excellent performance in capturing the kinematics of SB inSardinia, WRF offered no options for examining the underlying dynamics of the phenomenon.To overcome this serious limitation, the original WRF-ARW code was adjusted to allow for theextraction of the individual components of the horizontal momentum equations from the solver.Terms found to have significant contribution to the total momentum balance over the domainincluded pressure gradient (subsequently separated into surface and synoptic components), Cori-olis, advection, and horizontal and vertical diffusion. The rate of rotation of the total horizontal42momentum tendency was plotted for the entire domain. Four regions (two CR and two ACR)around the island were selected for term-by-term dynamical analysis. Following Kusuda and Alpert(1983), the strength of rotation due to each component of the horizontal momentum equations wasdetermined for the selected regions. The direction of rotation was found to be a result of a complexinteraction between surface and synoptic pressure gradients, Coriolis and advection.Lastly, an idealized simulation was attempted using a similar domain configuration as thatof a real case, but introducing a completely artificial simplified topography. An elliptical islandwith a single bell-shaped mountain was placed approximately in the same latitude as that of realSardinia. The dynamical analysis was repeated for the simulated fields. Contour maps of regionsof CR and ACR showed the formation of a vortex-like region of ACR around most of the island,with a single protruding "tongue" of CR region in the middle of the East coast. The dynamicalanalysis of regions of CR and ACR showed that the balance of forces resembled those of the realsimulation. However, higher variability as well as unlikely individual term magnitudes suggest thatthe simulation requires further improvements to be considered conclusive.4.1 Research Questions RevisitedCan the WRF Model reproduce the SB conditions in Sardinia?The simulated wind fields produced by WRF for seven SB days showed good agreement with obser-vational data from SAR. Consistent with earlier studies (Melas et al., 2000), the model performancewas more accurate on the west coast of the island. The eastern coast wind fields seemed to be af-fected by the presence of steep topography closer to the shoreline. The overall dynamics of theonshore winds were well captured by WRF.What patterns of hodograph rotation are observed?The real case simulation showed a complex pattern of CR and ACR regions around the island. Thewestern and northern coasts appear to be dominated by ACR, while the southeastern coast formed43a region of CR. The southern coast showed an alternating pattern of CR and ACR - a complexitythat can likely be attributed to the presence of a separate mountain range on that part of the island.What are the dynamical mechanisms responsible for the observed patterns of hodograph rotation?The sense of rotation appears to be a result of a complex interaction between surface and synopticpressure gradients, Coriolis and advection terms. Four regions (two CR and two ACR) selected foranalysis all demonstrated different force balance for achieving their sense of rotation. Overall, theanalysis has shown that the balance is not always dominated by the pressure gradient terms, assuggested by earlier studies.Can these findings be extrapolated to other islands of similar size/location?An idealized simulation was constructed in an attempt to generalize the findings to any approxi-mately elliptical island with non-flat topography in the mid-latitudes. While the patterns differeddramatically from those observed for Sardinia, they did appear to resemble the features identifiedby earlier studies. The underlying dynamics responsible for the rotation showed to be similar tothose identified for the real case simulation.4.2 Future StudyAn interesting alternative to the real case simulation presented in the work would be to focus theinvestigation on Corsica rather than Sardinia. Due to its single-mountain topography it is likely toproduce much simpler patterns of SB rotation, as was suggested by this work. The original choiceof the island was based on the availability of model evaluation data. However, given the exceptionalmodel performance observed for Sardinia, it can likely be assumed that similar agreement can easilybe achieved for Corsica.Further evaluation of the idealized case is necessary. Tracking quality and agreement between theartificial topography and real meteorological fields used for model initialization must be considered.44Reducing topography elevation and broadening the shape of the mountain is also likely to improvestability. A test simulation with a completely flat elliptical island could also yield revealing results.One particularly important consideration for future research, a topic left largely untouched bythis work, is the examination of the vertical structure of the hodograph rotation patterns. Whilethe analysis presented in this work focused entirely on the horizontal distributions of near-surfacerotation, the vertical fields were found to be far from uniform. A full 3D analysis of the boundarylayer would certainly help improve our understanding of the range of influence of topography onthe dynamics of SB rotation.45ReferencesCrosman, E., and H. J. (2010), Sea and lake breezes: A review of numerical studies, Boundary-LayerMeteorology, 137 (1), 1?29.Dalu, G., and A. Cima (1983), Three-dimensional airflow over Sardinia, Il Nuovo Cimento, 6 (5),453?472.Furberg, M. (2000), Sea breezes on Sardinia, Master?s thesis, Uppsala University.Furberg, M., D. Steyn, and M. Baldi (2002), The climatology of sea breezes on Sardinia, Interna-tional Journal of Climatology, 22, 917?932.Haurwitz, B. (1947), Comments on the sea-breeze circulation, Journal of Meteorology, 4 (1), 1?8.Hong, S., Y. Noh, and J. Dudhia (2006), A new vertical diffusion package with an explicit treatmentof entrainment processes, Monthly Weather Review, 134 (9), 2318?2341.Kusuda, M., and P. Alpert (1983), Anti-clockwise rotation of the wind hodograph. Part I: Theo-retical study, Journal of the Atmospheric Sciences, 40 (2), 487?499.Lehner, M. (2012), Observations and large-eddy simulations of the thermally driven cross-basincirculation in a small, closed basin, Ph.D. thesis, University of Utah.Mahrer, Y., and M. Segal (1985), On the effects of islands? geometry and size on inducing sea breezecirculation, Monthly Weather Review, 113 (1), 170?174.46Melas, D., A. Lavagnini, and A. Sempreviva (2000), An investigation of the boundary layer dynamicsof Sardinia island under sea-breeze conditions, Journal of Applied Meteorology, 39 (4), 516?524.Miller, S., B. Keim, R. Talbot, and H. Mao (2003), Sea breeze: Structure, forecasting, and impacts,Reviews of Geophysics, 41 (3).Neumann, J. (1977), On the rotation rate of the direction of sea and land breezes, Journal of theAtmospheric Sciences, 34 (12), 1913?1917.Nolan, D., D. Stern, and J. Zhang (2009), Evaluation of planetary boundary layer parameteriza-tions in tropical cyclones by comparison of in situ observations and high-resolution simulationsof hurricane isabel (2003). Part II: Inner-core boundary layer and eyewall structure, MonthlyWeather Review, 137 (11), 3675?3698.Pielke, R., et al. (1992), A comprehensive meteorological modeling system?RAMS, Meteorologyand Atmospheric Physics, 49 (1-4), 69?91.Prtenjak, M., Z. Pasari?, M. Orli?, and B. Grisogono (2008), Rotation of sea/land breezes alongthe northeastern Adriatic coast, Annales Geophysicae, 26 (7), 1711?1724.Ramis, C., and R. Romero (1995), A first numerical simulation of the development and structureof the sea breeze on the Island of Mallorca, Annales Geophysicae, 13 (9), 981?994.Simpson, J. (1996), Diurnal changes in sea-breeze direction, Journal of Applied Meteorology, 35 (7),1166?1169.Skamarock, W., J. Klemp, J. Dudhia, D. Gill, D. Barker, W. Wang, and J. Powers (2008), Adescription of the advanced research WRF version 3, Tech. rep.Steyn, D., and D. Faulkner (1986), The climatology of sea-breezes in the Lower Fraser Valley, B.C.,Climatological Bulletin, 20 (3), 21?39.Steyn, D., and G. Kallos (1992), A study of the dynamics of hodograph rotation in the sea breezesof Attica, Greece, Boundary-Layer Meteorology, 58 (3), 215?228.47Steyn, D., B. Ainslie, C. Reuten, and P. Jackson (2013), A retrospective analysis of ozone formationin the Lower Fraser Valley, British Columbia, Canada. Part I: Dynamical model evaluation,Atmosphere-Ocean, 51 (2), 153?169.Steyn, D., P. Builtjes, R. Timmermans, A. Seagram, and B. Ainslie (2014), Air Pollution Modelingand its Application XXII, chap. Modelled Recirculation of Pollutants During Ozone Episodes inthe Lower Fraser Valley, B. C., pp. 291?295, Springer Netherlands.Walsh, J. (1974), Sea breeze theory and applications, Journal of the Atmospheric Sciences, 31 (8),2012?2026.Wang, W., P. Xie, S. Yoo, Y. Xue, A. Kumar, and X. Wu (2011), An assessment of the surfaceclimate in the NCEP climate forecast system reanalysis, Climate Dynamics, 37, 1601?1620.Yamazaki, H., and T. Satomura (2010), Nonhydrostatic atmospheric modeling using a combinedcartesian grid, Monthly Weather Review, 138 (10), 3932?3945.Zhang, Y., Y. Chen, T. Schroeder, and K. Kodama (2005), Numerical simulations of sea-breezecirculations over Northwest Hawaii, Weather and Forecasting, 20 (6), 827?846.48Appendix AWRF Grid49Figure A.1: Horizontal and vertical grids of WRF-ARW (Skamarock et al., 2008)50Appendix BWPS Namelist==========================================================namelist.wps==========================================================&share wrf_core = ?ARW?,max_dom = 2,start_date = ?1998-06-19_18:00:00?,?1998-06-19_18:00:00?,end_date = ?1998-06-21_00:00:00?,?1998-06-21_00:00:00?,interval_seconds = 21600,io_form_geogrid = 2,/&geogridparent_id = 1, 1,parent_grid_ratio = 1, 3,i_parent_start = 1, 34,j_parent_start = 1, 30,e_we = 100, 100,e_sn = 100, 175,geog_data_res = ?2m?,?30s?,dx = 9000,dy = 9000,map_proj = ?lambert?,ref_lat = 40.0,ref_lon = 9.0,truelat1 = 40.0,truelat2 = 40.0,stand_lon = 9.0,geog_data_path = ?/mnt/data/nmoissee/data/input/geog/?/&ungribout_format = ?WPS?,prefix = ?PRES?,/&metgridfg_name = ?SFC?,?PRES?,51io_form_metgrid = 2,/52Appendix CWRF Namelist==========================================================namelist.input==========================================================&time_controlrun_days = 0,run_hours = 30run_minutes = 0,run_seconds = 0,start_year = 1998,1998,start_month = 06, 06,start_day = 19, 19,start_hour = 18, 18,start_minute = 00, 00,start_second = 00, 00,end_year = 1998, 1998,end_month = 06, 06,end_day = 21, 21,end_hour = 00, 00,end_minute = 00, 00,end_second = 00, 00,interval_seconds = 21600input_from_file = .true.,.true.,history_interval = 180, 60,frames_per_outfile = 1000, 1000,restart = .false.,restart_interval = 5000,io_form_history = 2,io_form_restart = 2,io_form_input = 2,io_form_boundary = 2,debug_level = 0,/&domains time_step = 54,max_dom = 2,53e_we = 100, 100,e_sn = 100, 175,e_vert = 50, 50,p_top_requested = 5000,num_metgrid_levels = 38,num_metgrid_soil_levels = 4,dx = 9000, 3000,dy = 9000, 3000,grid_id = 1, 2,parent_id = 0, 1,i_parent_start = 1, 34,j_parent_start = 1, 30,parent_grid_ratio = 1, 3,parent_time_step_ratio = 1, 3,feedback = 1,smooth_option = 1/&physicsmp_physics = 6, 6,ra_lw_physics = 1, 1,ra_sw_physics = 1, 1,radt = 9, 9,sf_sfclay_physics = 1, 1,sf_surface_physics = 2, 2,bl_pbl_physics = 1, 1,bldt = 0, 0,cu_physics = 1, 1,cudt = 5, 5,isfflx = 1,ifsnow = 0,icloud = 1,surface_input_source = 1,num_soil_layers = 4,sf_urban_physics = 0, 0,topo_wind = 1,/&fdda/&dynamicsw_damping = 0,diff_opt = 1,km_opt = 4,diff_6th_opt = 0, 0,diff_6th_factor = 0.12, 0.12,base_temp = 290.damp_opt = 0,zdamp = 5000., 5000.,dampcoef = 0.2, 0.2,khdif = 0, 0,kvdif = 0, 0,non_hydrostatic = .true., .true.,moist_adv_opt = 1, 1,54scalar_adv_opt = 1, 1,/&bdy_control spec_bdy_width = 5,spec_zone = 1,relax_zone = 4,specified = .true., .false.,nested = .false., .true.,/&grib2/&namelist_quiltnio_tasks_per_group = 0,nio_groups = 1,/55Appendix DEvaluation of SB Episodes56Figure D.1: Modelled and observed hodographs, May 17, 1997.Figure D.2: Modelled and observed onshore wind, May 17, 1997.57Figure D.3: Modelled and observed hodographs, August 15, 1997.Figure D.4: Modelled and observed onshore wind, August 15, 1997.58Figure D.5: Modelled and observed hodographs, May 20, 1998.Figure D.6: Modelled and observed onshore wind, May 20, 1998.59Figure D.7: Modelled and observed hodographs, May 30, 1998.Figure D.8: Modelled and observed onshore wind, May 30, 1998.60Figure D.9: Modelled and observed hodographs, June 21, 1998.Figure D.10: Modelled and observed onshore wind, June 21, 1998.61Figure D.11: Modelled and observed hodographs, June 29, 1998.Figure D.12: Modelled and observed onshore wind, June 29, 1998.62

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