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 <<-EOS
	  Proc.new{|*args|
	    GPhys::Derivative::#{method_name}(*args)
	  }
    EOS
  else
    raise ArgumentError, "Unsupported method: #{method_name}. " +
	    "(Supported are #{Deriv_methods.inspect}.)"
  end
	nil
end

.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