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Dynamical analysis of sea breeze hodograph rotation in Sardinia : [supplementary material] Moisseeva, Nadejda 2014

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Extracting Horizontal Momentum TendencyTerms from WRF 3.4.1Nadya MoisseevaNovember 2013This document is intended to summarize the steps for extracting in-dividual tendency terms of the horizontal momentum equations from theWRF model for real case simulations. For full description of the modeldynamics please refer to the WRF Technical Manual (Skamarock et al.,2008). For a detailed description of a similar procedure for an idealizedLES simulation in WRF see Lehner (2012).This work was completed as part of a masters thesis project, availableat https://circle.ubc.ca/handle/2429/46069 (Moisseeva, 2014).Please note that modified WRF code files are included asembedded content in this PDF document. Instructions on usingthe modified modules are provided at the end of the summary.Modifications of the Dynamical SolverThe horizontal momentum equations in WRF are formulated using terrain-following dry-hydrostatic pressure as a vertical coordinate ?, defined as:? = (ph ? pht)/? (1)where ? = phs ? pht, and ph, pht, phs correspond to hydrostatic componentof pressure, pressure at the top and surface boundaries for a dry atmosphere,respectively. Since ? represents the mass of a dry air column per unit area,flux-form velocity can be written asV = ?v = (U, V,?), (2)where v = (u, v, ?) are the covariant velocities in horizontal and vertical direc-tions and ? = ???, with ?? = ???t . Using the above definition, flux-form horizontalmomentum equations can be written as follows:?tU + (? ?Vu) + ???xp+??d??p?x? = FU (3)1?tV + (? ?Vv) + ???yp+??d??p?y? = FV (4)where subscripts t, x and y correspond to derivatives with respect to time andhorizontal coordinates, p denotes pressure, ? = gz is the geopotential and ?and ?d are the specific volume of moist air and specific volume of dry air,respectively. The right hand side terms FU and FV represent the sum of theforcing terms arising from map projections, earth rotation, advection, physics,turbulent mixing, and boundary layer parameterizations.Standard WRF configuration allows a user to easily output the total mass-coupled horizontal momentum tendencies ru tend and rv tend (first terms inEquations (3) and (4)), which are accumulated over each user-defined largetime-step. However, additional variables must be introduced within the dynam-ical solver to output individual forcing terms, making up the RHS of Equa-tions (3) and (4). These variables must be appropriately staggered, mass-coupled and passed on to the %grid structure, which in turn makes them avail-able for history output.Advection and pressure gradient tendencies are expressed explicitly on theLHS of Equations (3) and (4) (terms 2, 3 and 4). These can be extracted fromthe rk tendency subroutine in module em.F module by tracking the change intotal accumulated momentum tendency prior to and after the terms are re-calculated. Curvature forcing, arising from map projections, Coriolis, turbulentmixing and physics parameterizations are contained in the RHS of the equations.Similarly to advection and pressure gradient, these are extracted by introducingadditional variables in rk tendency prior to and after the calls to the respectiveroutines.WRF offers a number of formulations for spatial dissipation including dif-fusion along coordinate surfaces, diffusion in physical space and sixth-orderdiffusion applied on horizontal coordinate surfaces, as well as several options forcalculating eddy viscosities. Similarly to the forcings described above, horizontaldiffusion tendencies are calculated on a staggered grid as part of rk tendencysubroutine, and can be deduced by tracking the change in the accumulated hor-izontal tendency terms. If a PBL parameterization scheme is enabled verticaldiffusion is handled independently and stored as a physics tendency term. Cou-pled PBL momentum tendency terms from PBL scheme are already available inthe Registry.EM COMMON, however, as the physics in the model are calculatedon mass points (unstaggered Arakawa-A grid), these would subsequently needto be interpolated to produce balanced equations with the rest of non-physicstendencies. As there are no other interactions with momentum tendencies inthe physics driver it is more efficient to extract these tendencies as total mo-mentum forcing due to physics ru tendf and rv tendf. These are present inthe Registry as i1 variables and hence cannot be output directly. Once again,new variables can be introduced in the main solver to extract them prior tothe call to rk addtend dry in solve em.F, which sums physics and dynamicstendencies.WRF advances the horizontal momentum Equations (3) and (4) on a user-2defined time step ?t using a third-order RK integration scheme in three sub-steps. Within each substep acoustic modes are integrated using time-split inte-gration with a smaller time step ?? , which varies among the three RK substeps.A correction term is then introduced to adjust the pressure-gradient tendency.This code adaptation was tested for a mesoscale simulation, where the acous-tic correction was found to be insignificant and remained less 1 % of the totalpressure-gradient term throughout the domain, except near mountain peaks andhence was not extracted from the model. However, the procedure is summarizedin detail by Lehner (2012) for an idealized Large Eddy Simulation (LES).Instructions for Using Modified Code? save the files attached to this PDF document into a temporary location(ensure your viewer can display embedded content, e.g. Adobe Reader)[Registry.EM COMMON, module em.F, solve em.F]? switch to your WRF directory and clean your previous build using./clean -a? locate and backup the original versions of the following files:./dyn em/module em.F./dyn em/solve em.F./Registry/Registry.EM COMMON? copy the enclosed modified versions of the files to their correspondinglocations? edit the Registry.EM COMMON to suit the needs of your simulation (theenclosed version only makes dynamical and velocity terms available foroutput)? run ./configure and ./compile em realSuccessful build should produce real.exe and wrf.exe in the ./main direc-tory. After completion of each model run, ensure that the momentumequations are balanced within the desired accuracy:ru tend ? ru tend adv + ru tend pgf +ru tend cor + ru tend curv + ru tend hdiff + ru tend physrv tend ? rv tend adv + rv tend pgf +rv tend cor + rv tend curv + rv tend hdiff + rv tend physUnsatisfactory balance likely indicates that the acoustic correction is re-quired.3ReferencesLehner, M. (2012), Observations and large-eddy simulations of the thermallydriven cross-basin circulation in a small, closed basin, Ph.D. thesis, Universityof Utah.Moisseeva, M. (2014), Dynamical analysis of sea breeze hodograph rotation insardinia, Master?s thesis, University of British Columbia, https://circle.ubc.ca/handle/2429/46069.Skamarock, W., J. Klemp, J. Dudhia, D. Gill, D. Barker, W. Wang, and J. Pow-ers (2008), A description of the advanced research WRF version 3, Tech. rep.4


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