Module: NumRu::GPhys::EP_Flux

Extended by:
Misc::EMath
Includes:
Misc::EMath
Defined in:
lib/numru/gphys/ep_flux.rb

Constant Summary collapse

Deriv_methods =

C_p = 1004.0 # specific heat at constant pressure of the earth’s atmosphere [J.K-1.kg-1]

R   = 287.0  # gas constant per unit mass for dry air of the earth [J.K-1.kg-1]

[ 'cderiv', 'threepoint_O2nd_deriv' ]
@@scale_height =

<<< module variable >>>

UNumeric.new(7000,  "m")
@@radius =

radius of the planet

UNumeric.new(6.37E6,"m")
@@rot_period =

rotation period of the planet

UNumeric.new(8.64E4,"s")
@@g_forces = 
UNumeric.new(9.81,"m.s-2")
@@p00 =

gravitational acceleration in the surface

UNumeric.new(1.0E5,"Pa")
@@cp = 
UNumeric.new(1004.0, "J.K-1.kg-1")
@@gas_const =

specific heat at constant pressure

UNumeric.new(287.0, "J.K-1.kg-1")
@@deriv_method =

gas constant per molecular mass

Proc.new{|*args|
  GPhys::Derivative::threepoint_O2nd_deriv(*args)
}

Class Method Summary collapse

Class Method Details

.cp ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 497

def cp
  @@cp
end

.cp=(cp) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 500

def cp=(cp)
  @@cp = cp
  return nil
end

.deriv(*args) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 542

def deriv(*args)
  @@deriv_method.call(*args)
end

.div_sphere(gp_fy, gp_fz, yzdims = [0,1]) ⇒ Object

Raises:

  • (ArgumentError) 


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# File 'lib/numru/gphys/ep_flux.rb', line 628

def div_sphere(gp_fy, gp_fz, yzdims=[0,1])
  raise ArgumentError,"yzdims's size (#{yzdims.size}) must be 2." if yzdims.size != 2
  ## get axis and name
  ax_lat = gp_fy.axis(yzdims[0])    # Axis of latitude
  ax_z   = gp_fy.axis(yzdims[1])    # Axis of vertical
  lat_nm, z_nm = ax_lat.pos.name, ax_z.pos.name
  gp_lat, gp_z = make_gphys(ax_lat, ax_z)
  ## convert
  gp_z =   to_z_if_pressure(gp_z)   # P => z=-H*log(P/P00) (units-based)
  gp_lat = to_rad_if_deg(gp_lat)    # deg => rad (unit convesion)

  ## replace grid (without duplicating data)
  grid = gp_fy.grid_copy
  cp_grid = gp_fy.grid_copy         # saved to use in outputs
  grid.axis(lat_nm).pos = gp_lat.data
  grid.axis(z_nm).pos = gp_z.data
  gp_fy = GPhys.new(grid, gp_fy.data)
  gp_fz = GPhys.new(grid, gp_fz.data)

  ## d_F_phi_dz
  a_cos_lat = @@radius * cos(gp_lat)
  remove_0_at_poles(a_cos_lat)  
  d_gp_fy_d_phi = deriv(gp_fy * cos(gp_lat), lat_nm)
  ## d_F_z_dz
  d_gp_fz_d_z =   deriv(gp_fz, z_nm)
  f_div = ( d_gp_fy_d_phi / a_cos_lat )  + d_gp_fz_d_z

  f_div.data.name = "epflx_div"
  f_div.data.set_att("long_name", "EP Flux divergence")
  ## convert with past grid
  return GPhys.new(cp_grid, f_div.data)
end

.eddy_products(gp_u, gp_v, gp_w, gp_t, dimname) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 754

def eddy_products(gp_u, gp_v, gp_w, gp_t, dimname)
  # get zonal_eddy 
  u_dash = gp_u - gp_u.mean(dimname)
  v_dash = gp_v - gp_v.mean(dimname)
  w_dash = gp_w - gp_w.mean(dimname)
  t_dash = gp_t - gp_t.mean(dimname)

  # get eddy_product 
  uv_dash = u_dash*v_dash  # u'v'
  vt_dash = v_dash*t_dash  # v't'
  uw_dash = u_dash*w_dash  # u'w'

  # set attribute
  uv_dash.data.set_att("long_name", "U'V'")
  vt_dash.data.set_att("long_name", "V'T'")
  uw_dash.data.set_att("long_name", "U'W'")
  uv_dash.data.rename!("uv_dash")
  vt_dash.data.rename!("vt_dash")
  uw_dash.data.rename!("uw_dash")  

  return uv_dash.mean(dimname), vt_dash.mean(dimname), uw_dash.mean(dimname)
end

.ep_full_sphere(gp_u, gp_v, gp_w, gp_t, flag_temp_or_theta = true, xyzdims = [0,1,2]) ⇒ Object

<<< calculation method >>> ———————————————

Raises:

  • (ArgumentError) 


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# File 'lib/numru/gphys/ep_flux.rb', line 547

def ep_full_sphere(gp_u, gp_v, gp_w, gp_t, 
                   flag_temp_or_theta=true, xyzdims=[0,1,2]) ## get axis and name
  raise ArgumentError,"xyzdims's size (#{xyzdims.size}) must be 3." if xyzdims.size != 3 
  ax_lon = gp_u.axis(xyzdims[0]) # Axis of longitude 
  ax_lat = gp_u.axis(xyzdims[1]) # Axis of latitude 
  ax_z =   gp_u.axis(xyzdims[2]) # Axis of vertical 
  lon_nm, lat_nm, z_nm = ax_lon.pos.name, ax_lat.pos.name, ax_z.pos.name
  gp_lon, gp_lat, gp_z = make_gphys(ax_lon, ax_lat, ax_z)
  
  ## convert axes
  gp_z = to_z_if_pressure(gp_z)     # P => z=-H*log(P/P00) (units-based)
  gp_lon = to_rad_if_deg(gp_lon)    # deg => rad (unit convesion)
  gp_lat = to_rad_if_deg(gp_lat)    # deg => rad (unit convesion)
  gp_w = to_w_if_omega(gp_w, gp_z)  # dP/dt => dz/dt (units-based)
  gp_t = to_theta_if_temperature(gp_t, gp_z, flag_temp_or_theta) 
                # temperature => potential temperature (if flag is true)

  ## replace grid (without duplicating data)
  grid = gp_u.grid_copy
  old_grid = gp_u.grid_copy                 # saved to use in outputs
  grid.axis(lon_nm).pos = gp_lon.data       # in radian
  grid.axis(lat_nm).pos = gp_lat.data       # in radian
  grid.axis(z_nm).pos = gp_z.data           # log-p height
  gp_u = GPhys.new(grid, gp_u.data)
  gp_v = GPhys.new(grid, gp_v.data)
  gp_w = GPhys.new(grid, gp_w.data)
  gp_t = GPhys.new(grid, gp_t.data)
  ## get each term
  #  needed in F_y and F_z
  uv_dash, vt_dash, uw_dash = eddy_products(gp_u, gp_v, gp_w, gp_t, lon_nm)
  theta_mean = gp_t.mean(lon_nm)
  dtheta_dz = deriv(theta_mean, z_nm)
  cos_lat = cos(gp_lat)
  a_cos_lat = @@radius * cos_lat
    a_cos_lat.data.rename!('a_cos_lat')
  a_cos_lat.data.set_att('long_name', 'radius * cos_lat')
  remove_0_at_poles(a_cos_lat)
  #  needed in F_y only
  u_mean = gp_u.mean(lon_nm)
  du_dz  = deriv(u_mean, z_nm)
  #  needed in F_z only
  f_cor = 2 * (2 * PI / @@rot_period) * sin(gp_lat) 
    f_cor.data.rename!('f_cor')
  f_cor.data.set_att('long_name', 'Coriolis parameter')
  ducos_dphi = deriv( u_mean * cos_lat, lat_nm)
  avort = (-ducos_dphi/a_cos_lat) + f_cor        # -- absolute vorticity
  avort.data.units = "s-1"
  avort.data.rename!('avort')
  avort.data.set_att('long_name', 'zonal mean absolute vorticity')

  ## F_y, F_z
  sigma = exp(-gp_z/@@scale_height)
  epflx_y = ( - uv_dash + du_dz*vt_dash/dtheta_dz ) * cos_lat * sigma
  epflx_z = ( - uw_dash + avort*vt_dash/dtheta_dz ) * cos_lat * sigma
  epflx_y.data.name = "epflx_y"; epflx_z.data.name = "epflx_z"
  epflx_y.data.set_att("long_name", "EP flux y component")
  epflx_z.data.set_att("long_name", "EP flux z component")

  ## v_rmean, w_rmean
  z_nm = gp_z.data.name    # change z_nm from pressure to z
  v_mean = gp_v.mean(lon_nm); w_mean = gp_w.mean(lon_nm)
  v_rmean = ( v_mean - deriv( (vt_dash/dtheta_dz*sigma), z_nm )/sigma )
  w_rmean = ( w_mean + deriv( (vt_dash/dtheta_dz*cos_lat), lat_nm )/a_cos_lat )
  v_rmean.data.name = "v_rmean"; w_rmean.data.name = "w_rmean"
  v_rmean.data.set_att("long_name", "residual zonal mean V")
  w_rmean.data.set_att("long_name", "residual zonal mean W")

  ## convert with past grid
  gp_ary = [] # grid convertes gphyss into 
  grid_xmean = old_grid.delete_axes(lon_nm)
  [epflx_y, epflx_z, v_rmean, w_rmean, gp_lat, gp_z, u_mean, theta_mean, 
   uv_dash, vt_dash, uw_dash, dtheta_dz].each {|gp|  
    if grid_xmean.shape.size != gp.shape.size
      gp_ary << gp
    else
      gp_ary << GPhys.new(grid_xmean, gp.data) #back to the original grid
    end
  }
  return gp_ary
end

.g_forces ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 483

def g_forces
  @@g_forces
end

.g_forces=(g) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 479

def g_forces=(g)
  @@g_forces = g
  return nil
end

.gas_const ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 504

def gas_const
  @@gas_const
end

.gas_const=(r) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 507

def gas_const=(r)
  @@gas_const = r
  return nil
end

.get_constants ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 521

def get_constants
  return @@scale_height, @@radius, @@rot_period, @@g_forces, 
                                                 @@p00, @@cp, @@gas_const
end

.make_gphys(*ax_ary) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 661

def make_gphys(*ax_ary) 
           # it will be lost when new grid.rb released : to use delete_ax
  gp_ary = []           
  ax_ary.each{|ax|
    if ax.is_a?(Axis)
      ax_data = ax.pos
      ax_grid = Grid.new(ax) 
    elsif ax.is_a?(VArray)
      ax_data = ax
      ax_grid = Grid.new(Axis.new().set_pos(ax))
    end
    gp = GPhys.new(ax_grid, ax_data)
    gp_ary << gp
  }
  return gp_ary
end

.p00 ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 490

def p00
  @@p00
end

.p00=(p00) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 493

def p00=(p00)
  @@p00 = p00
  return nil
end

.preparate_for_vector_on_merdional_section(xax, zax) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 792

def preparate_for_vector_on_merdional_section(xax, zax)
  gp_x, gp_z = make_gphys(xax, zax) # make gphys from axis 
  gp_phi = to_rad_if_deg(gp_x)      # deg => rad (unit convesion)
  gp_aphi = @@radius * gp_phi       # radius * phi
  # check zax units, if proportional to z or p
  if ( gp_z.data.units =~ Units.new('Pa') )
    was_proportional_to_p = true 
  elsif ( gp_z.data.units =~ Units.new('m') )
    was_proportional_to_p = false
  else
    raise ArgumentError,'unit of zax #{gp_z.data.units} must be 
                         compatible to length or pressure.'
  end
  gp_z = to_z_if_pressure(gp_z)   # convert to z if gp_z is pressure
  gp_z[0] = +1E-6 if gp_z.data.val[0] == -0.0
  return gp_aphi.data, gp_z.data, was_proportional_to_p
end

.radius ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 469

def radius
  @@radius
end

.radius=(a) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 472

def radius=(a)
  @@radius = a
  return nil
end

.remove_0_at_poles(a_cos_lat) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 777

def remove_0_at_poles(a_cos_lat)
  eps = 1e-6
  if ( (a_cos_lat.val[0]/@@radius).abs.val < eps )
    a_cos_lat[0] = (a_cos_lat.val[0] + a_cos_lat.val[1])/2
  end
  if ( (a_cos_lat.val[-1]/@@radius).abs.val < eps )
    a_cos_lat[-1] = (a_cos_lat.val[-1] + a_cos_lat.val[-2])/2
  end
  if a_cos_lat.min.val <= 0
    raise "Illegal cos(phi) data. phi must between -pi/2 and +pi/2 " +
          "and aligned in increasing or decreasing order."
  end
  nil
end

.rot_period ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 476

def rot_period
  @@rot_period
end

.rot_period=(rp) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 486

def rot_period=(rp)
  @@rot_period = rp
  return nil
end

.scale_height ⇒ Object

<<< access to constants method >>> ————————————-



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# File 'lib/numru/gphys/ep_flux.rb', line 462

def scale_height 
  @@scale_height 
end

.scale_height=(h) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 465

def scale_height=(h)
  @@scale_height = h 
  return nil
end

.set_constants(scale_height, radius, rot_period, g_forces, p00, cp, gas_const) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 511

def set_constants(scale_height, radius, rot_period, g_forces, p00, cp, gas_const)
  @@scale_height = scale_height
  @@radius       = radius
  @@rot_period   = rot_period
  @@g_forces     = g_forces
  @@p00          = p00
  @@cp           = cp
  @@gas_const    = gas_const
  return nil
end

.set_deriv_method(method_name) ⇒ Object

<<< derivation method >>> ———————————————



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# File 'lib/numru/gphys/ep_flux.rb', line 528

def set_deriv_method( method_name )
  if Deriv_methods.include?( method_name )
    @@deriv_method = eval "    Proc.new{|*args|\n      GPhys::Derivative::\#{method_name}(*args)\n    }\n    EOS\n  else\n    raise ArgumentError, \"Unsupported method: \#{method_name}. \" +\n      \"(Supported are \#{Deriv_methods.inspect}.)\"\n  end\n  nil\nend\n"

.strm_rmean(gp_v, yzdims = [0,1]) ⇒ Object

Raises:

  • (ArgumentError) 


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# File 'lib/numru/gphys/ep_flux.rb', line 810

def strm_rmean(gp_v, yzdims=[0,1])

  raise ArgumentError,"yzdims's size (#{yzdims.size}) must be 2." if yzdims.size != 2
  ## get axis and name
  lat_dim, z_dim = yzdims             # Index of dims
  ax_lat = gp_v.axis(lat_dim)      # Axis of latitude
  ax_z   = gp_v.axis(z_dim)        # Axis of vertical
  lat_nm, z_nm = ax_lat.pos.name, ax_z.pos.name
  gp_lat, gp_z = make_gphys(ax_lat, ax_z)
  ## convert
  gp_lat =   to_rad_if_deg(gp_lat)      # deg. to rad.
  gp_p   =   to_p_if_altitude(gp_z)     # z => p=p00exp(-z/H) (units-based) and "Pa"

  ## copy grid 
  grid =    gp_v.grid_copy

  ## calculate stream function
  na_v  = gp_v.data.val                  # for integration box 
  int_v = gp_v.data.val.dup.fill!(0.0)   # for integration box 
  pres  = gp_p.data.val.dup
  if pres[0] < pres[-1]
    int_v[*([true]*z_dim+[0, false])] = 0.5*(na_v[*([true] + [0, false])])*pres[0]
    1.upto( pres.size-1 ) do |idx|
      dp = (pres[idx] - pres[idx-1])
      int_v[*([true]*z_dim+[idx, false])] = \
   0.5 * (na_v[*([true] + [idx-1, false])] + na_v[*([true] + [idx, false])]) * dp \
 + int_v[*([true] + [idx-1, false])]
    end
  else
    int_v[*([true]*z_dim+[-1, false])] = 0.5*(na_v[*([true] + [-1, false])])*pres[-1]
    ( pres.size-2 ).downto(0) do |idx|
      dp = (pres[idx] - pres[idx+1])
      int_v[*([true]*z_dim+[idx, false])] = \
 0.5 * (na_v[*([true] + [idx+1, false])] + na_v[*([true] + [idx, false])]) * dp \
 + int_v[*([true] + [idx+1, false])]
    end
  end
  int_v = VArray.new( int_v, gp_v.data, gp_v.data.name )
  int_v.units = Units.new("Pa.m.s-1")
  gp_int_v   = GPhys.new(grid, int_v)
  strm_rmean = gp_int_v * cos(gp_lat) * 2 * PI * @@radius / @@g_forces

  ## change attribute
  strm_rmean.name = "strm_rmean"
  strm_rmean.set_att("long_name", "Residual mean mass stream function")

  ## convert with past grid
  return strm_rmean
end

.to_p_if_altitude(gp_z) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 724

def to_p_if_altitude(gp_z) 
                      # number in units is not considerd operater as log.
  if ( gp_z.data.units =~ Units.new('m') )
    h = @@scale_height.convert(gp_z.units)
    gp_z = @@p00*exp(-gp_z/h)
    gp_z.data.set_att('long_name', "p").rename!("p")
  elsif ( gp_z.data.units =~ Units.new('Pa') )
    gp_z = gp_z.convert_units(Units.new("Pa"))
  else
    raise ArgumentError,"units of gp_z (#{gp_z.data.units}) 
                         must be dimention of pressure or length."
  end
  return gp_z
end

.to_rad_if_deg(gp) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 739

def to_rad_if_deg(gp)
  if gp.data.units =~ Units.new("degrees")
    gp = gp.convert_units(Units.new('rad'))
    gp.units = Units[""]   
    gp
  elsif gp.data.units =~ Units.new('rad') 
    gp.data = gp.data.copy
    gp.data.units = Units[""]    
    gp
  else
    raise ArgumentError,"units of gp #{gp.data.units} must be equal to deg or radian."
  end
  return gp
end

.to_theta_if_temperature(gp_t, z, flag_temp_or_theta = true) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 697

def to_theta_if_temperature(gp_t, z, flag_temp_or_theta=true) 
                                         # it is only for z coordinate!!!
  if flag_temp_or_theta
    gp_un = gp_t.data.units
    gp_t = gp_t.convert_units(Units.new("K"))
    gp_t = gp_t*exp((@@gas_const/@@cp)*z/@@scale_height)
    gp_t.data.set_att('long_name', "Potential Temperature")
  end
  return gp_t
end

.to_w_if_omega(gp, z) ⇒ Object

it is only for z coordinate!!!



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# File 'lib/numru/gphys/ep_flux.rb', line 678

def to_w_if_omega(gp, z) # it is only for z coordinate!!!
  gp_units = gp.data.units
  if gp_units =~ Units.new("Pa/s")
    pr = @@p00*exp(-z/@@scale_height)
    gp_un = gp_units
    pr = pr.convert_units(gp_un*Units.new('s'))
    gp = gp*(-@@scale_height/pr)
    gp.data.rename!("wwnd")
    gp.data.set_att('long_name', "log-P vertical wind")
  elsif gp_units =~ Units.new("m/s") 
    gp = gp.convert_units(Units.new('m/s'))
  else
    raise ArgumentError,"units of gp.data (#{gp.data.units}) 
                         must be dimention of pressure/time 
                                           or length/time."
  end
  return gp
end

.to_z_if_pressure(gp_z) ⇒ Object 



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# File 'lib/numru/gphys/ep_flux.rb', line 708

def to_z_if_pressure(gp_z) 
                      # number in units is not considerd operater as log.
  if ( gp_z.data.units =~ Units.new('Pa') )
    p00 = @@p00.convert(gp_z.units)
    gp_z = -@@scale_height*log(gp_z.to_type(NArray::DFLOAT)/p00)
      # it will be change if GPhys is modified for scalor production
    gp_z.data.set_att('long_name', "z").rename!("z")
  elsif ( gp_z.data.units =~ Units.new('m') )
    gp_z = gp_z.convert_units(Units.new("m"))
  else
    raise ArgumentError,"units of gp_z (#{gp_z.data.units}) 
                         must be dimention of pressure or length."
  end
  return gp_z
end