The University of Miami Wave Model (UMWM) Version 1.0.1
Contents
1. explim Exponent limiter This parameter limits the exponential growth of wave energy Should be set between 0 6 and 0 9 for most simulations Larger values allow longer time steps but may lead to numerical instability and model failure sin_fac Wave growth factor from following winds See A in 2 1 and 2 2 sin_diss1 Dissipation factor from opposing wind input See A in 2 1 and 2 2 sin_diss2 Dissipation factor from swell overrunning wind See A in 2 1 and 2 2 sds_fac Dissipation factor from deep water breaking waves spilling See A in 2 3 sds_power Exponent power index of the saturation spectrum equation 2 3 mss_fac Sum square slope adjustment to Sys See Ag in 2 3 17 snl_fac Wave energy downshifting factor See As in 2 6 sdt_fac Dissipation factor due to turbulence in the wave boundary layer ocean top See A4 in 2 4 sbf_fac Bottom friction coefficient i See Gf in 2 7 Typically with values between 0 001 and s 0 01m s depends on bed roughness m ee sbp_fac Bottom percolation coefficient Typically with values between 0 0006 See Gp in 2 s and 0 01m s depends on sand grain size 6 3 3 GRID namelist gridFromFile A boolean parameter that determines whether grid cell size Ax and Ay are going to be computed from longitude and la2. FALSE the model will be initiated from a calm state If set to TRUE a valid restart file umwmrst_YYYY MM DD_hh mm ss nc must be present at run time in the restart direc tory A valid restart file must have mm nm om pm fmin fmax same as the current simulation setup For more information about restarting UMWM from a file see section 8 1 6 3 2 PHYSICS namelist The PHYSICS namelist contains parameters that govern the physical processes relevant to wave energy evolution mM g Gravitational acceleration 3 s 2 nu_air Kinematic viscosity of air s 2 nu_water Kinematic viscosity of water s N sfct Water surface tension m kappa Von Karman constant z Height of the input wind speed m gustiness Addition of a stochastic component to x and y wind speed components The value of this parameter is a maximum fraction of the wind speed to be added or substracted For example setting gustiness to 0 2 will allow wind speed components to be randomly modulated by up to 20 This option may be used to introduce wind fluctuations when available wind forcing files are on coarse temporal and spatial resolutions Must be positive and should not be larger than 0 2 dmin Depth limiter m Must be larger than 0 All sea points shallower than dmin will be set to this value Values of a few meters or fractions of a meter are allowed but may lead to a shorter time step and longer model integration time
3. eds Plenum New York pp 347 372 30
4. A boolean that controls the calculation and output of Stokes drift If set to TRUE the STOKES namelist see next section will be read 6 3 7 STOKES namelist If the parameter stokes in the OUTPUT namelist is set to TRUE this namelist will be read by the model It contains only one entry depths which is an array of depths at which the Stokes drift will be computed Depth values are defined as positive numbers e g amp STOKES depths 0 1 2 3 4 5 10 15 20 25 30 35 40 50 60 70 80 90 100 The number of levels at which Stokes drift velocities are to be computed is arbitrary and can be chosen by the user 6 4 Input files For a typical regional scale simulation UMWM requires a grid and topography file umwm gridtopo and input forcing files in the form of umwmin_YYYY MM DD_hh mm ss nc Both grid and topography file and forcing files must be written in NetCDF standard format and must be present in the input directory The umwm gridtopo must contain 2 dimensional fields of longitude latitude and terrain elevation under names lon lat and z respectively Longitude and latitude fields are used internally to calculate grid cell size fields Ar and Ay Terrain elevation field z is defined as positive upward from mean sea level A forcing file may contain some or all of the following 2 dimensional fields 20 uw z component of wind Used if the winds switch in the OUTPUT namelist is set to TRUE vw y component
5. Grid size in y North dlon 0 04 Grid increment in degrees longitude dlat 0 04 Grid increment in degrees latitude lon0 162 Longitude of SW corner point range is 180 180 latO 10 Latitude of SW corner point exclusive range is 90 90 Once all the parameters in the namelist have been set up the program can be run from the tools directory by typing umwm_gridgen This will generate a UMWM grid file umwm grid This file can then be used as input to the wave model itself or to umwm_topogen for bathymetry field generation 7 2 umwm_topogen Once a UMWM grid file umwm grid has been generated program topogen may be used to generate the bathymetry field for input to the wave model The namelist file that needs to be editted is tools namelists topogen nml amp topogen umwmInputFile umwm grid topoInputFile ETOPO1_Ice_c_gmt4 grd useSeamask Sons topogen takes two files as input First is a target grid file for which a bathymetry field is desired in this case UMWM grid file umwm grid and the second is the raw topography file to be read There are several requirements about the format of input files Both need to be in netCDF format with spatial dimensions defined as x and y umwmInputFile must have 2 dimensional longitude and latitude fields defined as lon and lat respectively topoInputFile must have 1 dimensional longitude and latitude fields defined as lon and lat respectively and a 2 dimensi
6. The directory tree in the parent umwm directory is clean A script that cleans all output files from the output directory config Directory which contains compilation setup files COPYING Licensing input Directory where model input files need to be placed INSTALL Short installation instructions Makefile Compilation rules namelists Directory which contains namelist input files for the model output Directory where all model output will be written restart Directory in which all model restart files are being read and written 13 src Directory which contains the source code of the model tools Auxiliary pre processing programs The next section describes the steps necessary to compile the model source code 6 2 Compiling the source code Before doing a simulation the model code needs to be compiled The source code is located in the src directory The user must set up compiler and NetCDF library variables This is done in the config directory For example configuration files intel and intel mpi contain configuration settings for the Intel Fortran Compiler for serial and parallel execution respectively The appropriate configuration file should be then copied or linked to a file named umwm config in the same directory This is the file that is being read at compile time for both the model and the auxiliary tools If you have successfully compiled and run UMWM on a platform that was not provided originally in the
7. field are related by the phase speed E Mc 3 1 The form drag components of the wind on the waves Ty and Ty are calculated from the wind input source function T Kinti Ty pog I Sin cos 6k dk do 3 2 T mas a pug Sin sin dk dk d 3 3 The form drag coefficient Cdy is then calculated ASET Cd 3 4 paU where U is the wind speed at the measured or modeled height z The form drag is in the wave direction The skin drag coefficient Cds in the absence of waves is in the wind direction 4 and is computed from Von Karman s relationship 2 k2 Oy j where u is the friction velocity U z is wind speed at height z and is the Von Karman s constant The roughness length zo is determined by the scale of the molecular sublayer for smooth flow zo 0 13222 3 6 Ux where Va is the kinematic viscosity of air In the presence of waves Cd is reduced due to the sheltering of the surface in the lee of steep waves The degree of sheltering of the skin is taken to be proportional to the ratio of total drag to skin drag and may be as large as 50 corresponding to full sheltering of the lee face of each wave The algorithm is as follows Cdol4 Cdol4 New S 1 2 Ss s i 3 Cadel a a In order to obtain the correct form stress magnitude the high frequency limit should be equal to or greather than 2 Hz A power law wind speed dependent tail is appended to the spectrum beyond the high
8. frequency limit This additional form stress component T tail is in the wind direction as is the skin stress T skin These form stress on the resolved waves form stress on the spectral tail and skin stress are the stress components of the wind on the surface They are the mechanical couplers with the atmospheric model Both skin and form stress components as well as total drag coefficient Cd are part of the standard gridded output of UMWM 3 2 Momentum flux into ocean Similarly as momentum flux from wind we can integrate source dissipation functions over the spectrum to obtain momentum fluxes into ocean top and bottom T pias Gi S Say a l EEE T EEE EA 3 8 T min c T kmar _ TOT pug J Pas Pat TN A Ty tail Ty skin 3 9 r kia e T phmoz Sy Sy 7OB pos J MP cos pk dk do 3 10 T min c T phmos Sho Sp m pos EP sin pk dk dd 3 11 7 kohin e All momentum fluxes are defined as positive downward i e breaking of waves in x direction would yield a positive value of momentum flux in that direction These fluxes are part of UMWM standard gridded output 4 Numerical approaches 4 1 Spatial discretization The time evolution of the variance spectrum due to advection in Cartesian projection is given by OE _ 0Ol egcos u E _ Ol egsin v E SE 4 1 at Ox dy 09 l where u and v are ocean current components in x and y respectively and db is the rotatio
9. given as pair of integers each that belong in enclosed seas that are to be filled It is sufficient to specify one point coordinates per enclosed sea One line must contain only one pair of grid indices For example namelists exclude nml containing lines 2 2 105 226 will instruct the model to fill lakes that contain grid cells at 2 2 and 105 226 24 9 Reading model output data As mentioned in the previous section the output files will appear in the output directory The user can open and read output files with any program in a language that has NetCDF libraries provided Fortran MATLAB Python C C Java etc In addition convenience NetCDF viewing programs exist e g Neview http meteora ucsd edu pierce ncview_home_page html 9 1 Grid definition file A grid definition file is generated at the beginning of every simulation and is written in output umwmout grid It contains grid information that may be used for quantitative analysis of wave model results This file may also be used as an input grid file to umwm_topogen see section 7 2 The fields that are written in umwmout grid are lon 2 dimensional longitude field degE lat 2 dimensional latitude field degN dlon Grid cell increment in longitude deg dlat Grid cell increment in latitude deg dx Grid cell increment in x m dy Grid cell increment in y m area Grid cell area m depth Bathymetry m after processing
10. k 2 5 where v is the kinematic viscosity of the liquid It is negligible in clean water for all but the shortest waves A lt 20 cm 2 5 The non linear wave wave interaction function Sn A quantity proportional to the energy dissipated in spilling is passed to longer waves in the next two lower wavenumber bins The amount transferred decays exponentially with the square of the relative frequency separation Snilk o As bi Ssy k i Ak o baSsy k a 2Ak TA Ssolk 2 6 A A where As 5 b exp 16 Da ba exp1604 2 and b and bz are normalized such that by bp 1 Ss is the wave breaking dissipation function due to spilling only Sse Sas coth kd 2 6 The bottom friction function Syp The bottom friction function is related to orbital velocity at the bottom and the roughness of the bed Komen et al 1994 give the following form for a sandy bed k yp Gr hd E k 2 7 where the roughness factor Gy varies from 0 001 to 0 01 m s depending on bed roughness 2 7 The bottom percolation function Sbp On a porous bed the percolation of flow through the bed induces wave energy dissipation The dissipation rate due to percolation is given by Shemdin et al 1978 k Sop Gp cosh kd E k 6 2 8 where the permeability factor Gp varies from 0 0006 to 0 01 m s depending on sand grain size 3 Stress calculation 3 1 Momentum flux from wind Energy E and momentum M in the wave
11. third and fourth terms on the left hand side are the advection terms in geographical wavenumber and directional space respectively Advection in wavenumber space is non zero only in case of changing ocean currents or moving bottom Here currents are considered to be quasi stationary on the time scale of wave growth decay Thus this term is neglected Advection in directional space refraction is non zero in case of variable water n depth and or inhomogeneous currents 5 S are the source sink functions that act to grow decay i 1 the waves locally pw is the liquid density and g is acceleration due to gravity The energy spectrum and the variance spectrum are related by E x k pugE x k 1 2 For convenience the variance spectrum is the predicted quantity 2 Source functions The source functions S are parametric descriptions of the various phenomena that increase decrease or interchange among wavenumbers the energy in the wavenumber spectrum The wavenumber spectrum is evaluated in separable magnitude and direction bins The phenomena relevant to the prediction of storm waves in water of arbitrary depth are 1 Input of energy and momentum from the wind and export of wave energy and momentum to the wind when the waves overrun or run against the wind ii Dissipation of wave energy at and near the surface due to viscosity ambient turbulence and breaking iii Enhanced dissipation at and near the top and bottom int
12. 29 23 NDBC42035 19 88 80 30 09 NDBC42007 The first line of the file must contain either XY or LL This 2 character string describes whether the coordinates of spectrum output location are given in model grid indices or in longitude and latitude respectively In case of XY spectrum at exact specified grid cell will be output In case Of LL spectrum at grid cell nearest to specified location will be output The following lines each contain 3 elements x and y coordinate or longitude and latitude and location identi fier character string up to 40 characters no spaces A spectrum output file in the form of umwmspc_ID_YYYY MM DD_hh mm ss nc will appear in the output directory where ID is the lo cation identifier specified in namelists spectrum nml and YYYY MM DD_hh mm ss nc is the initial time of the simulation and has the same value as startTimeStr All output times during the simulation are stored in the same file Each requested spectrum location is stored in a separate file outrst Restart output interval hours Allowed values are 0 1 2 3 4 6 8 12 and 24 If outrst is larger than 0 restart files in the form of umwmrst_YYYY MM DD_hh mm ss will appear in the restart directory These files can be used later to re start a simulation in case of interruption or abnormal termination of the model see section 8 1 xpl Grid cell index in x for stdout screen ypl Grid cell index in y for stdout screen stokes
13. Change log Contributed by Added Stokes drift calculation and output Mean square slope algorithm improved in UMWM_physics F90 1 0 1 2012 09 05 Grid spacing now computed from lat lon input UM RSMAS fields Fixed filling of isolated seas lakes Source code clean up Minor bug fixes 1 0 0 2012 04 01 First public release UM RSMAS 29 11 References Donelan M A and W J Plant 2009 A threshold for wind wave growth J Geophys Res 114 C07012 doi 10 1029 2008JC005238 Donelan M A M Curcic S S Chen and A K Magnusson 2012 Modeling waves and wind stress J Geophys Res 117 C00J23 doi 10 1029 2011JC007787 Jeffreys H 1924 On the formation of waves by wind Proc Roy Soc A 107 pp 189 206 Jeffreys H 1925 On the formation of waves by wind II Proc Roy Soc A 110 pp 341 347 Komen G J L Cavaleri M Donelan K Hasselmann S Hasselmann and P A E M Janssen 1994 Dynamics and Modelling of Ocean Waves Cambridge University Press 532 pp Pierson W L and L Moskowitz 1964 A proposed spectral form for fully developed wind seas based on the similarity theory of S A Kitaigorodskii J Geophys Res 69 pp 5181 5190 Shemdin O H K Hasselmann S V Hsiao and K Herterich 1978 Non linear and linear bottom interaction effects in shallow water Turbulent flures through the sea surface wave dynamics and prediction A Favre and K Hasselmann
14. The University of Miami Wave Model UMWM Version 1 0 1 Description and User s Manual M A Donelan and M Curcic September 2012 Rosenstiel School of Marine and Atmospheric Science University of Miami Contents Wave breaking dissipation function Sds lt lt o s0 s e e a e e a a FORCING CONSTANT namelist aa a ee 1 Model description 2 Source functions 2 1 Wind input function Sin 22 2 3 Dissipation by turbulence function Sg 2 4 Dissipation by viscosity function Sq 2 5 The non linear wave wave interaction function So 2 6 The bottom friction function Sh 2 7 The bottom percolation function Sp 3_ Stress calculation 3 1 Momentum flux from wind 3 2 Momentum flux into ocean 4 Numerical approaches 4 1 Spatial discretization ooo ee 4 2 Time discretization 5 Software implementation 6 Installation and setup 6 1 Obtaining the software package 6 2 Compiling the source code 2 ee 6 3 Setting up the simulation 6 3 1 DOMAIN namelist 6 3 2 PHYSICS namelist 6 3 3 GRID namelist 6 3 4 FORCING namelist 6 3 5 6 3 6 OUTPUT namelist 6 3 7 STOKES namelist 6 4 Input files 7 Pre proc
15. an 90 programming language and takes advantage of Unidata s NetCDF standard library for I O required and parallel processing through the Message Passing Interface MPI optional It is written in readable and transparent form i e free of low level instructions and is well documented The model may be defined on any structured curvilinear grid Most common applications are on a Cartesian and spherical latitude longitude grid More general and un structured grids are planned to be implemented in future versions of the model A choice is available between limited area regional and global simulation In the latter case a periodic boundary condition in x direction is applied automatically and no additional action is required by the user In case of parallel processing model s partitioning scheme tile distribution is designed in such a way that any number of processors is allowed for running the model This may prove to be useful when a very limited number of processors is available or in the case of coupled modeling where fine tuning the work load distribution between model components can be beneficial for computational efficiency The user is encouraged to look into the code for information that is not provided in this docu ment The model is open source and is licensed under a GPL General Public License Version 3 http www gnu org copyleft gpl html 12 6 Installation and setup In order to successfully convey a numerical
16. by the wave model This field is positive below the mean sea level and has the values effective after the depth limiter has been applied see section 6 3 2 seamask Integer field that masks sea points with a value of 1 and land points with a value of 0 nproc Integer field that marks tiles of the domain covered by each processor in MPI mode 9 2 Gridded output The integrated spectrum quantities that describe the wave field as well as forcing fields are being output in the file of the form umwmout_YYYY MM DD_hh mm ss nc where YYYY MM DD_hh mm ss represent the exact simulation time of the output The output fields are listed below frequency Frequency range Hz theta Angles of directional bins rad defined using mathematical convention lon 2 dimensional longitude field deg lat 2 dimensional latitude field deg seamask Integer field with values of 1 over ocean grid cells and 0 over land depth Water depth after processing at initialization time downward is positive 25 wspd Wind speed forcing m al s wdir Wind direction rad defined using mathematical convention m uc x component of ocean surface currents s m vc y component of ocean surface currents s k rhoa Air density pal m k rhow Water density 2 m N taux_form x component of form drag from wind 5 See section 3 1 for more details on this and m the following 3 fields tauy_form y
17. component of form drag from wind 3 m N taux_skin x component of skin drag from wind 3 m P N tauy_skin y component of skin drag from wind 5 m eos T N taux_ocn x component of momentum flux from wave dissipation into ocean top e m oe ga N tauy_ocn y component of momentum flux from wave dissipation into ocean top 5 m 2 taux_bot x component of momentum flux from wave dissipation into ocean bottom 5 tauy_bot y component of momentum flux from wave dissipation into ocean bottom 5 cd Atmospheric drag coefficient nondimensional Calculated as described in 3 1 swh Significant wave height m Equals the average of the highest third of all waves Calculated in the model as the integral over the whole spectrum H fff E k d kdkdd 9 1 mwp Mean wave period s Calculated in the model as T E k 9 kdkd NV TJ PEC 9 kdkdo 9 2 26 mwl Mean wave length m ff Elk 9 kdkd AN T E k kdkd 9 3 mwd Mean wave direction rad mathematical convention dwp Dominant wave period s corresponding to the discrete peak of the spectrum dw1 Dominant wave length m corresponding to the discrete peak of the spectrum dwd Dominant wave direction rad corresponding to the discrete peak of the spectrum u_stokes Three dimensional field of z component of Stokes drift Lagrangian mean of wave induced fluid motion 2 The extent of the thi
18. config directory please send an e mail to milan orca rsmas miami edu and we will include the configuration file for that platform in the next release Once the umwm config file has been set up from the main UMWM directory type make umwm to build the model code make tools to build auxiliary pre processing programs see section 7 or just type make to build both the model and auxiliary programs The model executable umwm will appear in the main directory and auxiliary programs executables will appear in the tools directory 6 3 Setting up the simulation Once the executable umwm has been generated the user should set up a desired experiment The first step is to edit the main UMWM namelist that defines model parameters The namelist is located in namelists main nml An example main nml file is shown below amp DOMAIN isGlobal F Global T or regional F mm 399 Domain size in x nm 359 Domain size in y om 37 Number of frequency bins pm 36 Number of directions fmin 0 0313 Lowest frequency bin Hz fmax 2 0 Highest frequency bin Hz fprog 0 5 Highest prognostic frequency bin Hz startTimeStr 2008 09 08_00 00 00 Simulation start time 14 stopTimeStr dtg restart PHYSICS g nu_air nu_water s ct kappa z gustiness dmin explim sin_fac sin_diss1 sin_diss2 sds_fac sds_power mss_fac snl_fac sdt_fac sbf_fac sbp_fac amp GRID gridFromFil
19. e delx dely topoFromFile dpt fillEstuaries fillLakes amp FORCING winds currents air_density water_density amp FORCING_CONSTANT wspd0 wdir0 uco vco rhoa0 rhow0 3600 ES 9 80665 1 56E 5 0 9E 6 0 07 0 4 10 0 0 10 mam 4 25 1 2 1025 2008 09 13_00 00 00 Simulation end time Global 1 0 time step s Restart from file Gravitational acceleration m s 2 Kinematic viscosity of air m 2 s Kinematic viscosity of water m 2 s Surface tension N m Von Karman constant Height of the input wind speed m Random wind gustiness factor should be between 0 and 0 2 Depth limiter m Exponent limiter 0 69 100 growth Input factor from following winds Damping factor from opposing winds Damping factor from swell overrunning wind Breaking dissipation factor Saturation spectrum power Mean square slope adjustment to Sds Wave energy downshifting factor Dissipation due to turbulence factor Bottom friction coefficient m s Bottom percolation coefficient m s Set to T if lon lat fields are input from file Grid spacing in x m if gridFromFile F Grid spacing in y m if gridFromFile F Set to T to input bathymetry from file Constant water depth m if topoFromFile F Set to T to fill cells with 3 land neighbours Set to T to fill user chosen seas lakes Wind input from file Currents input from file Air density input from file Water density inpu
20. ed if currents FALSE S k rhoa0 Surface air density i Used if air_density FALSE m k rhow0 Surface water density 2 Used if water_density FALSE m 6 3 6 OUTPUT namelist Parameters in this namelist control the model output gridded spectrum and restart Gridded output contains integrated 2 dimensional quantities of the spectrum Fields from the whole domain are stored in gridded output files Spectrum output is defined at individual geographical locations in the domain one file per location and contain full wavenumber directional spectrum and source functions Sin Sas and Sai Restart output files contain snapshots of the wave spectrum from the whole domain They are used for continuing a model simulation at a later time see section 8 1 outgrid Gridded output interval hours Allowed values are 0 1 2 3 4 6 8 12 and 24 If outgrid is larger than 0 gridded output files in the form of umwmout_YYYY MM DD_hh mm ss nc will appear in the output directory where YYYY MM DD_hh mm ss denotes model time of the output outspec Spectrum output interval hours Allowed values are 0 1 2 3 4 6 8 12 and 24 If outspec is larger than 0 another input file namelists spectrum nml will be read Although technically not a Fortran namelist file it works in a similar way An example spectrum input file may look like this LL 89 66 25 89 NDBC42001 93 67 25 79 NDBC42002 96 66 25 96 NDBC42020 94 41
21. en to be 20 m in the field 0 11 if U r 2c080 gt c ucos vsing wind sea A 40 01 if0 lt U y2cos lt c ucos vsing swell with wind 2 2 0 1 if cos lt 0 swell against wind 2 2 Wave breaking dissipation function Sj The wave breaking dissipation source function is strongly nonlinear in the saturation spectrum B k k E k In addition the dissipation is enhanced by the straining due to the velocity field of all longer waves and increased by coth kd due to the plunging breakers that occur for small values of kd wavenumber times depth Sas k Ag coth kd 1 Asx2 k o Blk o ERD 2 3 where x k is the sum squared slope in direction of all waves longer than k Coefficients A and A3 have values 42 and 120 respectively 2 3 Dissipation by turbulence function Su Turbulence mixing in the wave boundary layer attenuates waves The wave dissipation due to ambient turbulence is Sat Agua KE k o 2 4 where Us is the friction velocity in the water near the surface and A 0 01 2 4 Dissipation by viscosity function Sw Some wave energy is converted directly to heat through the action of the viscosity of the liquid Viscous dissipation in the surface sublayer prevents the growth of waves until a threshold wind speed is exceeded The theoretical viscous dissipation rate 4vk has been verified in the laboratory for a range of viscosities y Donelan and Plant 2009 Say 4vk E
22. erfaces due to shoaling iv Movement of energy to lower wavenumbers down shifting due to nonlinear interactions includ ing breaking v Enhanced dissipation due to straining by longer waves The theoretical and experimental justifications for the source functions corresponding to these phe nomena are given in Donelan et al 2012 Here the source functions are simply listed 2 1 Wind input function Sin Jeffreys 1924 1925 sheltering hypothesis leads to Sia of the form kw pa Sin As Uyy2 0080 c ucos vsin Ux 2 cos c ucos vsing e k o 2 1 w where 0 is the angle between wind direction 4 and waves of wavenumber k and direction Aj is the sheltering coefficient Sin is positive energy and momentum transferred from wind to waves when Uy 2cos gt c ucos vsin p and negative energy and momentum transferred from waves swell to wind when 0 lt Uy 2 cos 8 lt c ucos vsin or when the waves swell propagate against the wind cos 9 lt 0 As waves approach full development Sin goes to zero i e the direct wind forcing vanishes The sheltering coefficient which describes the strength of the source sink function is different depending on whether Sin is positive wind sea or negative when the waves run before the wind or against it swell The wind velocity is that at one half wavelength above the surface up to the top of the logarithmic layer which is usually tak
23. essing tools 7 1 umwm gridgen 7 2 umwm _topogenl 7 3 wrf2umwmgrid 7 4 wrf2umwmin 8 Running the model 8 1 Restarting the model 8 2 Excluding enclosed seag 9 Reading model output data 9 1 Grid definition file 9 2 Gridded output DD O MONO A w I 22 22 22 23 23 9 3 Spectriim Output s se ace a AA A a ia 27 9 4 Restart output evi a Ga Re a a 28 10 Revision history 29 11 References 30 1 Model description The University of Miami Wave Model UMWM is a prediction model for wave energy and wind stress on the interface between a liquid and a gas It proceeds through a numerical solution of the wave energy balance equation on a horizontal 2 dimensional grid The wave energy is a positive definite quantity in logarithmically spaced frequency f bins and uniformly spaced directional bins The energy spectrum is carried as the wavenumber directional surface elevation variance spectrum and every frequency at each location is identified with the theoretical wavenumber Thus wave energy is a 5 dimensional quantity y k t Time t evolution is done by integrating in time the energy balance equation OE O kE O kE OE abaya 1 1 t Ox Ok where E x k t is the energy spectrum and x c u where c is the group velocity and u is the current in the wave boundary layer The second
24. ilable in the form of E P erp E sia 4 12 i 1 10 The time increment At is dynamically computed so that the variance spectrum E can only grow by a pre determined finite factor gn l n Ban emp Y SAt lt r 4 13 i l where r is usually set between 1 5 and 2 Lower values of r will draw E closer to the solution attractor Then a time splitting approach is used to achieve a more stable integration _ EE ED 2 E 4 14 E is used to compute the advection and refraction terms described in the previous section Finally their contribution is evaluated by simple forward Euler differencing O c cos u E Ox A cg sing v E A dE Oy Od Be EH At 4 15 The above approach is applied to the prognostic part of the spectrum A cut off frequency fe which separates the prognostic and diagnostic parts is proportional to the peak frequency of the fully developed Pierson Moskowitz spectrum Pierson and Moskowitz 1964 0 53g Uxo fe 4fpm 4 16 For all bins higher than fe the waves are assumed to be in equilibrium with the wind traveling centered on the wind direction and their spectral densities are established from a balance of wind input and dissipation This approach is justified by the presumption that the quasi equilibrium range is wider in higher wind conditions 11 5 Software implementation UMWM source code is written in standard Fortr
25. m the boundaries if provided by the user In the case of global domain simulation periodic boundary conditions are applied at East and West domain edges The rotation rate db in the refraction term is evaluated as csing v O ccosp u Ox Oy b 4 8 The change due to refraction is then computed using 4 2 4 5 with replaced by Positive and negative values of correspond to counter clockwise and clockwise rotation of energy respectively The stability constraint for the refraction term is the same as for one dimensional advection _ At For most domain cells the allowed refraction time step is larger than the advective step given in 4 7 In case that condition 4 9 is violated which can occur on sharp bathymetric or current gradients the rotation at these points is limited so that y 1 This affects the solution insignificantly while maintaining computational efficiency Because the domain is periodic in directional space there is no need for boundary conditions 4 2 Time discretization Once all the source terms in 1 1 have been evaluated E k is integrated forward in time We evaluate the contribution from source and advection terms separately a a ew The contribution from source terms can be written as 5 gt y se 4 11 s i 1 where S is just S E Then by integrating 4 11 over a finite time interval At a solution is ava
26. n rate Both geographical propagation and refraction terms are discretized using first order upstream differencing This scheme is positive definite quantity conserving implicitly diffusive and computationally effi cient A certain amount of diffusion is desirable in order to avoid swell separation between discrete directional and frequency bins A spatial differencing operator is then discretized as OE Piyija Pi_ 1 2 w 5 Ox Ax 4 2 where is a discrete index along dimension x Fluxes at cell edges 41 2 and _1 2 are defined as Ti 1 2 Ti 1 21 2 Deis jot ti 17 2 Diy1 2 L 5 AS Ej 1 4 3 ti 1 2 Ei 1 2 ti 1 2 ti 1 2l 1 2 2 Ej 1 E 4 4 and Li T Lit Ti 1 2 gt 4 5 The above treatment of flux differencing ensures upstream definiteness For propagation in two dimensional space the stability of the scheme is ensured for At Z 1 min Az Ay y2 jie 4 6 where y is the Courant number Depending on the choice of number of directional bins the stability criterion is more permissive At T Ad Pte mag G ou where Ag is the directional bin size To ensure that 4 7 holds the number of directions must be divisible by 8 For ocean grid cells next to the land an open boundary condition is applied energy can freely propagate into land Same is applied for domain edges except that there can be incoming wave energy fro
27. nal space rad s 27 Sdt One dimensional wave dissipation due to turbulence in the wave boundary layer in wavenumber 7 directional space rad s m4 rad3s Sbf One dimensional wave dissipation bottom friction and bottom percolation total in wavenumber 4 Sdv One dimensional wave dissipation due to viscosity in wavenumber directional space directional space p bada ma Snl Non linear wave wave interaction source sink function in wavenumber directional space Bel rad3s 9 4 Restart output If enabled using the outrst switch in the OUTPUT namelist see section 6 3 6 UMWM restart files will be written at desired intervals in the restart directory These files contain full domain snapshots of the wave spectrum and can be used to restart the simulation at a later time see section 8 1 The spectrum data is written in an unstructured 1 dimensional array however 1 dimensional latitude and longitude arrays are stored as well so these files can also be used for analysis post processing when spectrum data from the whole domain is desired 28 10 Revision history Below is the summary of changes made to the UMWM source code since origination It documents the UMWM version number date of release brief summary of changes made and the author of the changes The revision history can be also found in the header of the main UMWM program source file src umwm F90 Version Date
28. of wind Used if the winds switch in the OUTPUT namelist is set to TRUE S 5 m uc x component of ocean surface currents Used if the currents switch in the OUTPUT namelist s is set to TRUE m vc y component of ocean surface currents Used if the currents switch in the OUTPUT namelist s is set to TRUE k ee rhoa Air density 2 Used if the air_density switch in the OUTPUT namelist is set to TRUE m k Rahs rhow Water density ap Used if the water_density switch in the OUTPUT namelist is set to m TRUE The forcing files required during model run time must be present in the input directory 21 7 Pre processing tools Several pre processing tools are available to the user for generation of input grid and bathymetry files for UMWM as well as input forcing files from WRF Weather Research and Forecasting atmospheric model output files The program source files are located in the tools src directory After successful compilation the program executable files will be located in the tools directory Individual pre processing tools for UMWM are described in the following sections 7 1 umwm_gridgen Program umwm_gridgen may be used for a quick generation of a UMWM grid file umwm grid in a regular spherical lat lon projection Before running the program a tools namelists gridgen nml namelist file must be configured amp gridgen idm 400 Grid size in x East jdm 300
29. onal topography field positive up negative down defined as z This format is compatible with e g ETOPO 22 1 minute topography in netCDF format by NOAA National Geophysical Data Center topography data can be downloaded from http www ngdc noaa gov mgg global global htm1 The third parameter in the namelist useSeamask may be used only if there is a seamask field defined in umwmInputFile e g if the grid file was generated by wrf2umwmgrid or added by user If set to TRUE the bathymetry field will be modified at points where its values and seamask do not match This may be useful when coupling UMWM with an atmosphere or ocean model and identical seamasks are desired 7 3 wrf2umwmgrid vr 2umwmgrid is a convenience program for extraction of 2 dimensional longitude latitude and seamask fields from a WRF output file The program takes a WRF file name path as a command line argument e g wrf2umwmgrid wrfout_d01_2008 09 06_00 00 00 This will generate a UMWM grid file umwm grid This file can then be used as input to the wave model itself or to umwm_topogen for bathymetry field generation vr 2umwmgrid will operate on any wrfout wrfrst or wrfinput file 7 4 wrf2umwmin Similarly to wrf2umwmgrid this program can be used to convert a WRF output file to a UMWM input forcing file Since WRF output does not contain any ocean fields only wind components and air density may be computed using these files The program
30. rd dimension z depth levels is specified by the user see s 6 3 7 v_stokes Three dimensional field of y component of Stokes drift Lagrangian mean of wave induced fluid motion eas The extent of the third dimension z depth levels is specified by the user see s 6 3 7 9 3 Spectrum output Spectrum output at any geographical point in the domain may be optionally enabled through the switch in the OUTPUT namelist For instructions on how to enable spectrum point output see section 6 3 6 The list of fields currently being output in a UMWM spectrum file follows Frequency One dimensional frequency array Hz a rad Wavenumber One dimensional wavenumber array m Direction One dimensional array of directional bins mathematical convention rad Longitude Longitude degE of the point output Available only if topoFromFile is set to TRUE Latitude Latitude degN of the point output Available only if topoFromFile is set to TRUE m wspd One dimensional array of wind speed as function of time at the location of point output s wdir One dimensional array of wind direction rad mathematical convention as function of time at the location of point output 4 F Surface elevation variance spectrum in wavenumber directional space aE ra 4 Sin Wind input source in wavenumber directional space FE rads mnt Sds Wave dissipation sink in wavenumber directio
31. ropagation properties fmin Minimum frequency Hz Determines the longest wave resolved by the model Domain and application specific A value between 0 03 Hz and 0 05 Hz is commonly used for real case larger scale basins fmax Maximum frequency Hz Determines the shortest wave resolved by the model Domain and application specific Typical values for regional or global wave forecasting is 0 5 Hz or larger 2 0 Hz or larger is required for accurate stress estimation fprog Highest frequency Hz in the prognostic range of the spectrum Can be used to limit the prognostic range if the cutoff frequency determined by local wind speed see section 4 2 for more information is too high resulting in short time steps If this is not desired set to the value of fmax startTimeStr A character string in the form of YYYY MM DD_hh mm ss that determines the start time of the simulation See restart below stopTimeStr A character string in the form of YYYY MM DD_hh mm ss that determines the stop time of the simulation 16 dtg An integer that determines global time step of the wave model in seconds If forcing data is to be input from files see forcing options below dtg corresponds to the input time step dtg is the shortest time interval at which output to file can be made see output options below restart A boolean that determines if the model is to be initiated from initial conditions written in a restart file If set to
32. simulation with UMWM a procedure is usually as follows 1 Obtaining the software package 2 Compiling the source code 3 Setting up the simulation 4 Running the model 5 Reading model output data In general steps 1 and 2 need to be done only once A working Fortran compiler and NetCDF library must be provided by the user Re compiling the source code step 2 is necessary only if change has been made to any of the source files Naturally step 3 needs to be repeated if the setup of the experiment is to be changed If only input forcing files are changed one needs only to re run the model step 4 Description of the output data files is provided in section 9 6 1 Obtaining the software package The current version of UMWM can be downloaded from this URL http rsmas miami edu groups umwm download html On a UNIX like system Linux Mac OS X or other UNIX unpack the downloaded file by typing tar xzf umwm 1 x x tar gz 1 x x should be replaced with the appropriate version number This will create the directory umwm In addition UMWM requires NetCDF Fortran libraries for input and output NetCDF libraries and installation instructions can be downloaded from http ww unidata ucar edu downloads netcdf index jsp Also a common build tool make or gmake is recommended for easier compilation make is included by default in most UNIX Linux distributions but may need to be installed separately on a Microsoft Windows system
33. t from file Wind speed m s Wind direction rad x component ocean current m s y component ocean current m s Air density kg m 3 Water density kg m 3 15 amp OUTPUT outgrid 1 Gridded output interval hours outspec O Spectrum output interval hours outrst 0 Restart output interval hours xpl 160 Grid cell in x for stdout screen ypl 160 Grid cell in y for stdout screen stokes T Output Stokes drift velocity fields amp STOKES depths 0123 45 10 15 20 25 30 35 40 50 60 70 80 90 100 All simulation parameters in namelists main nml are summarized below 6 3 1 DOMAIN namelist The DOMAIN namelist contains main parameters that define a wave model simulation In particular these include domain grid size in geographical and frequency directional space and time limits of the simulation Full list of DOMAIN nameslist parameters follow isGlobal A boolean value describing whether the simulation is global or regional If set to TRUE the domain will be periodic in a mm Domain size in z nm Domain size in y om Total number of discrete frequency bins See fmin and fmax below pm Total number of discrete directional bins For small to medium size real case basins e g Mediterranean Gulf of Mexico at least 24 is recommended For larger basins oceans or global simulations set to at least 32 Must be divisible by 4 A value of pm divisible by 8 is recommended for optimal p
34. takes a WRF file name path as a command line argument e g wrf2umwmin wrfout_d01_2008 09 06_00 00 00 This will generate a UMWM input forcing file umwmin_d01_2008 09 06_00 00 00 nc The air density field is calculated using the ideal gas law for moist air wrf2umwmin will operate on any wrfout wrfrst or wrfinput file 23 8 Running the model Once namelists have been configured and input files are provided the user can start the simulation by executing umwm If the model was compiled in the MPI mode refer to the documentation of the MPI implementation about executing programs in parallel On a UNIX Linux system with a common modern MPI implementation e g MPICH2 or OpenMPI one would type mpiexec n 16 umwm This command would execute umwm on 16 parallel processes 8 1 Restarting the model If restart is set to TRUE in namelists main nml the model will read initial conditions from a restart file startTimeStr must match the time string in the restart file name For example if a user specifies 2008 09 08_18 00 00 as startTimeStr umwmrst_2008 09 08_18 00 00 nc file must be present in the restart directory 8 2 Excluding enclosed seas It is possible to mask out lakes or enclosed seas in the domain if they are not desired at model run time If the switch fillLakes in the GRID namelist is set to TRUE UMWM will read the input file namelists exclude nml at run time This file should contain a list of grid coordinates
35. the switches is set to FALSE a FORCING_CONSTANT namelist will be read If any of the switches is set to TRUE input forcing file s will be read winds Wind speed 2 input from file switch If set to FALSE parameters wspd0 and wdir0 in s the FORCING_CONSTANT namelist will provide the values for constant wind speed and wind direction mathematical convention respectively m currents Ocean surface currents input from file switch If set to FALSE parameters ucO and vc0 in the FORCING_CONSTANT namelist will provide the values for constant x and y components of ocean surface currents respectively 18 k air_density Surface air density pas input from file switch If set to FALSE parameter rhoa0 in the FORCING_CONSTANT namelist will provide the value for constant surface air density field k water_density Surface water density 2 input from file switch If set to FALSE parameter rhow0 in the FORCING_CONSTANT namelist will provide the value for constant surface water density field 6 3 5 FORCING CONSTANT namelist Parameters in this namelist are used only in the case where any of the forcing fields are not provided in the input files m wspd0 Wind speed Used if winds FALSE s wdir0 Wind direction rad mathematical convention Used if winds FALSE m uc0 Ocean surface current z component Used if currents FALSE s m vc0 Ocean surface current y component Us
36. titude fields in input umwm gridtopo If set to FALSE Az and Ay are constant and they are input as delx and dely below delx Grid spacing in x m if gridFromFile is set to FALSE Must be larger than 0 dely Grid spacing in y m if gridFromFile is set to FALSE Must be larger than 0 topoFromFile When set to TRUE bathymetry field is to be input from file input umwm gridtopo netCDF variable z If set to FALSE bathymetry is constant and has the value specified by namelist variable dpt below dpt Constant water depth m if topoFromFile is set to FALSE Must be larger than 0 fillEstuaries lf set to TRUE all sea points that have 3 land neighbors will be masked iteratively as land Use to reduce computational time if wave simulation in narrow channels or estuaries is not desired Do not use if running a coupled atmosphere wave simulation where atmosphere and wave model have identical sea land mask fields fillLakes If set to TRUE enclosed seas lakes marked by the user will be filled with land mask Do not use if running a coupled atmosphere wave simulation where atmosphere and wave model have identical sea land mask fields For more information about how to specify and fill enclosed seas that are not desired in the wave simulation see section 8 21 6 3 4 FORCING namelist The FORCING namelist contains switches that control input of forcing fields from file There is one switch for each forcing field If any of
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