• MSFD is the abbreviation for Mixed Spectral Finite Deference. It is a numerical model for atmospheric boundary-layer flow over complex terrain. Initially it was a linear model with relatively simple turbulence closure schemes for neutrally stratified atmospheric surface flows. In recent years, the model has been extended along lines of planetary boundary-layer, non-linearity, stable stratification and more sophisticated turbulence closure schemes.
• Methodologically, a spectral technique in the horizontal and a finite deference scheme in the vertical are adapted. In addition, a terrain-following coordinate system, staggered grids and a logarithmic coordinate transformation are used in the vertical.

• Beljaars, Walmsley and Taylor (1987) developed a linear MSFD model. The model had three turbulence closure schemes built in, namely mixing length, E-epsilon and E-epsilon-tau. The model was confined to neutrally stratified atmospheric surface layer flows.
• Karpik (1988) replaced the shooting method used in the initial MSFD model with a block LU factorization algorithm.
• Walmsley and Padro (1990) made cerrections to coefficients in the shear stress equations.
• Padro and Walmsley (1991) implemented the model with pollutant concentration and flux variables.
• Xu and Taylor (1991) added two missing terms in the turbulent kinetic energy and dissipation rate equations.
• Xu and Taylor (1992) developed a non-linear version of MSFD.
• Xu, Ayotte and Taylor (1992) upgraded the non-linear MSFD model with a second-order turbulence closure, q2l.
• Ayotte, Xu and Taylor (1993) incorporated three more turbulence closures, kz, E-kz and q2l, to the MSFD model. Of the three, q2l is a second order turbulence closure.
• Li, Xu and Taylor (1994) applied the non-linear MSFD model to air over water waves.
• Ayotte (1994) added one more second order closure, LRR, to the MSFD model.
• Xu, Ayotte and Taylor (1994) refined the non-linear MSFD model and included LRR scheme in the model.
• Xu and Taylor (1995) modified the constant set used in the E- epsilon-tau closure.
• Xu and Taylor (1995) applied the non-linear MSFD model to parameterization of drag over small scale topography.
• Xu and Taylor (1995) reviewed the recent developments.
• Karpik, Walmsley and Weng (1995) discussed and solved the problems associated with the top boundary conditions of the linear MSFD model.
• Ayotte and Taylor (1995) developed a planetary boundary-layer version of the MSFD model.
• Li (1995) did more work on air over water waves with the non-linear MSFD model.
• Weng, Chan and Taylor (1997) developed an MSFD model for stably stratified flow, MSFD-STAB.
• Weng (1997) compared the MSFD-STAB model results with field data.
• Li (1999) developed a more efficient method to calculate the values of the non-linear terms in the non-inear MSFD model.

1. Linearity
   • L = linear (default)
   • NL = nonlinear
2. Closure (no default)
   • MIX = Mixing Length
   • K-Z = kappa-Z
   • EKZ = E-kappa-Z
   • TKE = Turbulent Kinetic Energy
   • E-E = E-epsilon
   • EET = E-epsilon-tau
   • Q2L = q-squared-L
   • LRR = Launder-Reece-Rodi
3. Dimension
   • 2D
   • 3D (default)
4. Regime
   • SFC = Surface Layer (default)
   • PBL = Planetary Boundary Layer
5. Pollutants
   • NONE (default)
   • CONC = Concentration and Flux
6. Stratification
   • NEUT = Neutral (default)
   • STAB = Stable
7. Researchers and Primary Models (refer to PIs for initials)
   • DX, PT, PL => NLMSFD-LRR
   • KA, PT => MSFD-LRR-PBL
   • JW, SK,WW => MSFD-EET
   • JP, JW => MSFD-EET-CONC
   • SK, WW, PT => MSFD-EET-STAB

Developments to Date

• MSFD-PC, a commercial package, for more details go to MSFD-PC.
• NLMSFD, 2D and 3D, with turbulence closures including E-kz, E-epsilon, E-epsilon-tau, q2l and LRR, interested contact Dapeng Xu.
• PBL version of the MSFD with LRR turbulence closure for neutral stratification is available from Keith Ayotte.
• MSFD for stably stratified atmosphere is under development, for more infomation contact Wensong Weng.

Model Validation and Applications

• The MSFD model has been validated against wind tunnel measurements (Taylor et al. 1994) and field observations (Walmsley et al. 1994 and Weng et al. 1995)
• The model has been applied to flow over water waves (Li et al. 1994).
• As an application we have used the model to parameterize drag over small scale topography (Xu and Taylor, 1995).
• The MSFD-STAB model results have been compared with field observations (Weng, 1997)

MSFD-PC

MSFD-PC is a numerical model for estimating wind speed variations in complex terrain. It is a new generation model (Mixed Spectral Finite-Difference, Personal Computer version) that retains many of the advantages of its parent, MS-Micro/3.

Latest Release: Version 3.21

Main features:

• Three-dimensional steady-state surface boundary-layer flow
• Spatial variations in terrain height and/or surface roughness
• Results at any height or heights above ground
• High spatial resolution
• Computation is much faster than a 3D Finite-Difference Model, but about 20 times slower than MS-Micro/3. Unlike MS-Micro/3, however, computation time is independent of the number of output levels.
• Neutral thermal stratification; stable stratification version under development. A pollutant concentration & flux extension is also being developed.
• Turbulence closure: mixing length, E-epsilon, or E-epsilon-tau
• Horizontal scales of order 100 m to 10 km
• Terrain slopes less than 0.3 to 0.5
• Amplitude of roughness-length variations of order 0.001 to 1000

Principal uses:

• Wind-energy site selection, wind resource and turbulence estimates, wind-loading estimates, local climatological studies, evaluation of representativeness of measured wind data. Whereas MS-Micro/3 is a practical model for applications, MSFD is primarily a research model. The higher-order turbulence closure options, however, provide information on turbulence and turbulent kinetic energy that is not available in MS-Micro/3.

Computer Configuration:

• Minimum desired: IBM-compatible 386 (or, preferably 486), 8 M RAM (preferably 16 M) with memory manager, MS-DOS 5.0, math coprocessor, hard disk, 1.44 M (3.5 inch) floppy disk drive, EGA/VGA colour monitor, printer. The hard disk must have about 3 MB available for the executable programs and the test case data. Another 10 M free space will be required to run the test case. Even larger amounts of free space are needed for typical applications.
• Optional but useful: Virtual disk, digitizer (or access to a scanner, plus appropriate raster-to-vector software), plotter.

Compiler:

• The Lahey F77L-EM/32 Version 5.2 Compiler was used to generate the executable code. Some extensions to the FORTRAN-77 Standard were used in the source code, but these exceptions are in the new FORTRAN-90 Standard. The Lahey compiler is available from:

            Lahey Computer Systems, Inc.
            P.O. Box 6091
            Incline Village, NV 89450-6091
            USA
            Phone: 1-702-831-2500
            Fax:   1-702-831-8123
  

Libraries:

• MSFD-PC makes use of the Lahey F77L-EM/32 Version 5.2 GRAPH3 library and the Spindrift Laboratories API Library for Fortran Version 3.0 SPINEM32 library. The latter is available from Lahey or from: Spindrift Laboratories Ltd. 116 South Harvard Avenue Arlington Heights, IL 60005-1644 USA Phone: 1-708-255-6909 Fax: 1-708-255-6101

Supplied Software:

• Executable code, about 2.5 MB. (Source code, about 800 KB, may be supplied by special arrangement.) Routines for use with Calcomp 2000, 2300 or 9100 digitizers (for preparing topographic and roughness input files) and an EGA/VGA monitor (for quality-control and display). Plotting routines may require a graphics monitor and/or plotter and the separate purchase of commercial software - see below.

Raster-to-Vector Software:

• Not supplied. We have successfully used the Cadix Research & Development PixelTrak software together with a special program, AESCONV (also available from Cadix) for converting the PixelTrak output (DXF file) to the format (TCN or RBS) required by the MSFD-PC grid generation programs, MSMT and MSMR. PixelTrak accepts raster input (e.g., RLE format from a scanner) and produces vector output. PixelTrak and AESCONV are available from:

            Cadix Research & Development (Canada) Corp.
            3600 Erindale Station Road
            Mississauga, Ontario L5C 2T1
            Canada
            Phone: 1-905-270-7050
            Fax:   1-905-270-4606
  

Plotting Options:

• The purchaser may supply a graphics package to plot files that are written in standard SURFER output - see below.
• The purchaser may obtain the SURFER graphics software from Golden Software Inc., P. O. Box 281, Golden CO 80402, USA (Telephone: 1-303- 279-1021). Cost estimate is about US$ 500.

References:

• Beljaars et al., 1987: Boundary-Layer Meteorol. 38, 273-303.
• Karpik, 1988: Boundary-Layer Meteorol. 43, 273-286.
• Walmsley and Padro 1990: Boundary-Layer Meteorol. 51, 169-177.
• Karpik, S.R., Walmsley, J.L. and Weng, W., 1995: The Mixed Spectral Finite Difference (MSFD) Model: Improved Upper Boundary Conditions. Boundary-Layer Meteorol., 75, 353-380.

Prices & Ordering:

• A price list and ordering information for MSFD-PC and other software may be obtained by contacting:

            Zephyr North
            (Attention Dr. J.R. Salmon)
            4034 Mainway
            Burlington, Ontario  L7M 4B9
            Canada
            Phone: 1-905-335-9670
            Fax:   1-905-335-0119
  
            E-mail: zephyr.north@sympatico.ca
  
  

References

Ayotte, K.W., Xu, D. and Taylor, P.A., 1994, 'The impact of
     different turbulence closures on predictions of the mixed
     spectral finite difference model for flow over topography',
     Boundary-Layer Meteorol., 68:1-33.

Ayotte K.W. and Taylor (1995)
     A mixed finite spectral finite difference 3D model of neutral planetary
     boundary layer flow over topography. 
     Journal of the Atmospheric Sciences, Vol. 52, No. 20, 3523-3537

Ayotte K.W. (1995)
     Source code gernation for linear and non-linear numerical models
     using Maple. Maple Tech, Vol. 2, No. 1, 39-48

Beljaars, A.C.M., Walmsley, J.L. and Taylor, P.A., 1987, 'A mixed
     spectral finite difference model for neutrally stratified
     boundary layer flow over roughness changes and topography',
     Boundary-Layer Meteorol., 38:273-303.

Gong, W., Taylor, P.A. and Dornbrack, A., 1994, 'Turbulent boundary
     layer flow over fixed aerodynamically rough 2D sinusoidal
     waves (wind tunnel and LES model studies), J. Fluid Mech., in press.

Jackson, P.S. and Hunt, J.C.R., 1975, 'Turbulent wind flow over a
     hill', Q. J. R. Meteorol. Soc., 101:925-955.

Karpik, S.R., 1988, 'An improved method for integrating the mixed
     spectral finite difference (MSFD) model equations', Boundary-
     Lyaer Meteorol., 43:273-286.

Karpik, S.R., Walmsley, J.L. and Weng, W., 1995, 'The mixed spectral
     finite difference (MSFD) model: improved upper boundary conditions.'
     Boundary-Layer Meteorol., 75:353-380.

Launder, B.E., Reece, G.J. and Rodi, W., 1975, 'Progress in the
     development of a Reynolds stress turbulence closure', J.Fluid
     Mech., 68:537-566.

Li, P.Y., 1999. 'An improved method for evaluating the non-linear terms
     in the NLMSFD model.' Boundary-Layer Meteorol., 93:163-168.

Li, P.Y., Xu, D. and Taylor, P.A., 1996, 'A non-linear model of the
     air flow above water waves', Proc. of International Symposium
     on Air-Sea Interface, M. Donelan (ed.) University of Miami Press,
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Mason, P.J., 1994, 'Large-eddy simulation: A critical review of the
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Newley, T.M.J., 1985, 'Turbulent air flow over hills', Ph.D thesis,
     University of Cambridge.

Taylor, P.A. and Gent, P.R., 1974, 'A model of atmospheric boundary
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     7:349-362.

Taylor, P.A., Xu, D., Gong, W. and Ayotte, K.W., 1996, 'Modelling
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     Donelan (ed.) Proc. Internat. Symposium on the Air-Sea
     Interface, University of Toronto press, in press.
 
Walmsley, J.L., Weng, W., Karpik, S.R. Xu, D. and Taylor, P.A.,
     1994, 'Applications of Mixed spectral finite difference (MSFD)
     model and its nonlinear extension (NLMSFD) to wind flow over
     Blashval hill', In S.E. Gryning and M.M. Millan (eds.), Air Pollution 
     Modelling and its Application', Plenum Press, New York, pp.263-271.

Weng, W., Walmsley, J.L, Karpik, S.R., Xu, D., Taylor, P.A.,
     Ayotte, K.W. and Salmon, J.R., 1995, Applications of the MSFD
     and NLMSFD models to air flow over Askervein hill', In 
     J.L. Tsipouridis (ed.) 5th European Wind Energy Association 
     Conference, 10-14 October 1994, Thessaloniki, Greece, 3:79-84.

Xu, D., Ayotte, K.W, and Taylor, P.A., 1992, 'Simulations of
     turbulent flow over a hill by a q2l level 4 closure model',
     Tenth Symposium on Turbulence and Diffusion, Sep. 1992,
     Portland, Oregan, USA.

Xu, D., Ayotte, K.W. and Taylor, P.A., 1994, 'Development of a
     non-linear mixed spectral finite difference model for
     turbulent boundary layer flow over topography', Boundary-Layer
     Meteorol., 70:341-367. 

Xu, D. and Taylor, P.A., 1992, 'A non-linear extension of the mixed
     spectral finite difference model for neutrally stratified
     turbulent flow over topography', Boundary-Layer Meteorol.,
     59:177-186.

Xu, D. and Taylor, P.A., 1995, 'Boundary Layer parameterization of
     drag over small scale topography', Q. J. R. Meteorol. Soc., 121:
     433-443.

Weng, W. Chan, L. and Taylor, P.A., 1997, `Modelling stably stratified
     boundary-layer flow over low hills', Q. J. R. Meteorol. Soc. 123,
     1841-1866.

Weng, W., 1997, `Stably stratified boundary-layer flow over
     low hills: A comparison of model results and field data', Boundary-Layer
     Meteorol., 85, 223-241.

Weng, W., 1998, "Reply to comments by Wood, Hewer and Belcher on `Stably
     stratified boundary-layer flow over low hills: A comparison of model
     results and field data' (1997)", Boundary-Layer Meteorol., 88, 330-340.