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set_depth.m
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set_depth.m
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function [z]=set_depth(Vtransform, Vstretching, ...
theta_s, theta_b, hc, N, ...
igrid, h, zeta, report);
%
% SET_DEPTH: Compute ROMS grid depth from vertical stretched variables
%
% [z]=set_depth(Vtransform, Vstretching, theta_s, theta_b, hc, N, ...
% igrid, h, zeta);
%
% Given a batymetry (h), free-surface (zeta) and terrain-following parameters,
% this function computes the 3D depths for the request C-grid location. If the
% free-surface is not provided, a zero value is assumef resulting in unperturb
% depths. This function can be used when generating initial conditions or
% climatology data for an application. Check the following link for details:
%
% https://www.myroms.org/wiki/index.php/Vertical_S-coordinate
%
% On Input:
%
% Vtransform Vertical transformation equation:
% Vtransform = 1, original transformation
%
% z(x,y,s,t)=Zo(x,y,s)+zeta(x,y,t)*[1+Zo(x,y,s)/h(x,y)]
%
% Zo(x,y,s)=hc*s+[h(x,y)-hc]*C(s)
%
% Vtransform = 2, new transformation
%
% z(x,y,s,t)=zeta(x,y,t)+[zeta(x,y,t)+h(x,y)]*Zo(x,y,s)
%
% Zo(x,y,s)=[hc*s(k)+h(x,y)*C(k)]/[hc+h(x,y)]
% Vstretching Vertical stretching function:
% Vstretching = 1, original (Song and Haidvogel, 1994)
% Vstretching = 2, A. Shchepetkin (UCLA-ROMS, 2005)
% Vstretching = 3, R. Geyer BBL refinement
% Vstretching = 4, A. Shchepetkin (UCLA-ROMS, 2010)
% theta_s S-coordinate surface control parameter (scalar)
% theta_b S-coordinate bottom control parameter (scalar)
% hc Width (m) of surface or bottom boundary layer in which
% higher vertical resolution is required during
% stretching (scalar)
% N Number of vertical levels (scalar)
% igrid Staggered grid C-type (integer):
% igrid=1 => density points
% igrid=2 => streamfunction points
% igrid=3 => u-velocity points
% igrid=4 => v-velocity points
% igrid=5 => w-velocity points
% h Bottom depth, 2D array at RHO-points (m, positive),
% h(1:Lp+1,1:Mp+1).
% zeta Free-surface, 2D array at RHO-points (m), OPTIONAL,
% zeta(1:Lp+1,1:Mp+1).
% report Flag to report detailed information (OPTIONAL):
% report = 0, do not report
% report = 1, report information
%
% On Output:
%
% z Depths (m, negative), 3D array.
%
% svn $Id: set_depth.m 544 2011-04-01 23:51:17Z arango $
%===========================================================================%
% Copyright (c) 2002-2011 The ROMS/TOMS Group %
% Licensed under a MIT/X style license %
% See License_ROMS.txt Hernan G. Arango %
%===========================================================================%
z=[];
%----------------------------------------------------------------------------
% Set several parameters.
%----------------------------------------------------------------------------
if (nargin < 8),
disp(' ');
disp([setstr(7),'*** Error: SET_DEPTH - too few arguments.',setstr(7)]);
disp([setstr(7),' number of supplied arguments: ',...
num2str(nargin),setstr(7)]);
disp([setstr(7),' number of required arguments: 8',...
setstr(7)]);
disp(' ');
return
end,
if (Vtransform < 1 | Vtransform > 2),
disp(' ');
disp([setstr(7),'*** Error: SET_DEPTH - Illegal parameter Vtransform = ' ...
num2str(Vtransfrom), setstr(7)]);
disp(' ');
return
end,
if (Vstretching < 1 | Vstretching > 4),
disp(' ');
disp([setstr(7),'*** Error: SET_DEPTH - Illegal parameter Vstretching = ' ...
num2str(Vstretching), setstr(7)]);
disp(' ');
return
end,
if (hc > min(min(h)) & Vtransform == 1),
disp(' ');
disp([setstr(7),'*** Error: SET_DEPTH - critical depth exceeds minimum' ...
' bathymetry value.',setstr(7)]);
disp([setstr(7),' Vtranform = ', ...
num2str(Vtransform),setstr(7)]);
disp([setstr(7),' hc = ', ...
num2str(hc),setstr(7)]);
disp([setstr(7),' hmax = ', ...
num2str(min(min(h))), setstr(7)]);
disp(' ');
return
end,
if (nargin < 9),
zeta=zeros(size(h));
end,
if (nargin < 10),
report=1;
end,
Np=N+1;
[Lp Mp]=size(h);
L=Lp-1;
M=Mp-1;
hmin=min(min(h));
hmax=max(max(h));
%----------------------------------------------------------------------------
% Compute vertical stretching function, C(k):
%----------------------------------------------------------------------------
if (report),
disp(' ');
if (Vtransform == 1),
disp(['Vtransform = ',num2str(Vtransform), ' original ROMS']);
elseif (Vtransform == 2),
disp(['Vtransform = ',num2str(Vtransform), ' ROMS-UCLA']);
end,
switch ( igrid ),
case 1
disp([' igrid = ',num2str(igrid), ' at horizontal RHO-points']);
case 2
disp([' igrid = ',num2str(igrid), ' at horizontal PSI-points']);
case 3
disp([' igrid = ',num2str(igrid), ' at horizontal U-points']);
case 4
disp([' igrid = ',num2str(igrid), ' at horizontal V-points']);
case 5
disp([' igrid = ',num2str(igrid), ' at horizontal RHO-points']);
end,
end,
if (igrid == 5),
kgrid=1;
else,
kgrid=0;
end,
[s,C]=stretching(Vstretching, theta_s, theta_b, hc, N, kgrid, report);
%----------------------------------------------------------------------------
% Average bathymetry and free-surface at requested C-grid type.
%----------------------------------------------------------------------------
switch ( igrid ),
case 1
hr=h;
zetar=zeta;
case 2
hp=0.25.*(h(1:L,1:M)+h(2:Lp,1:M)+h(1:L,2:Mp)+h(2:Lp,2:Mp));
zetap=0.25.*(zeta(1:L,1:M)+zeta(2:Lp,1:M)+zeta(1:L,2:Mp)+zeta(2:Lp,2:Mp));
case 3
hu=0.5.*(h(1:L,1:Mp)+h(2:Lp,1:Mp));
zetau=0.5.*(zeta(1:L,1:Mp)+zeta(2:Lp,1:Mp));
case 4
hv=0.5.*(h(1:Lp,1:M)+h(1:Lp,2:Mp));
zetav=0.5.*(zeta(1:Lp,1:M)+zeta(1:Lp,2:Mp));
case 5
hr=h;
zetar=zeta;
end,
%----------------------------------------------------------------------------
% Compute depths (m) at requested C-grid location.
%----------------------------------------------------------------------------
if (Vtransform == 1),
switch ( igrid ),
case 1
for k=1:N,
z0=(s(k)-C(k))*hc + C(k).*hr;
z(:,:,k)=z0 + zetar.*(1.0 + z0./hr);
end,
case 2
for k=1:N,
z0=(s(k)-C(k))*hc + C(k).*hp;
z(:,:,k)=z0 + zetap.*(1.0 + z0./hp);
end,
case 3
for k=1:N,
z0=(s(k)-C(k))*hc + C(k).*hu;
z(:,:,k)=z0 + zetau.*(1.0 + z0./hu);
end,
case 4
for k=1:N,
z0=(s(k)-C(k))*hc + C(k).*hv;
z(:,:,k)=z0 + zetav.*(1.0 + z0./hv);
end,
case 5
z(:,:,1)=-hr;
for k=2:Np,
z0=(s(k)-C(k))*hc + C(k).*hr;
z(:,:,k)=z0 + zetar.*(1.0 + z0./hr);
end,
end,
elseif (Vtransform == 2),
switch ( igrid ),
case 1
for k=1:N,
z0=(hc.*s(k)+C(k).*hr)./(hc+hr);
z(:,:,k)=zetar+(zeta+hr).*z0;
end,
case 2
for k=1:N,
z0=(hc.*s(k)+C(k).*hp)./(hc+hp);
z(:,:,k)=zetap+(zetap+hp).*z0;
end,
case 3
for k=1:N,
z0=(hc.*s(k)+C(k).*hu)./(hc+hu);
z(:,:,k)=zetau+(zetau+hu).*z0;
end,
case 4
for k=1:N,
z0=(hc.*s(k)+C(k).*hv)./(hc+hv);
z(:,:,k)=zetav+(zetav+hv).*z0;
end,
case 5
for k=1:Np,
z0=(hc.*s(k)+C(k).*hr)./(hc+hr);
z(:,:,k)=zetar+(zetar+hr).*z0;
end,
end,
end,
return