Module: NumRu::GAnalysis::QG_sphere

Extended by:
QG_common, QG_sphere_common
Defined in:
lib/numru/ganalysis/qg.rb

Overview

QG on sphere with non-divergent but inaccurate geostrophic wind

Class Method Summary collapse

Methods included from QG_common

cut_bottom, div_waf, extend_bottom, gp2gpref, gpd2qzz, gph2gpd_gpref, gph2gpref, gpref2n2

Methods included from QG_sphere_common

f, f_mask0

Class Method Details

.cos_phi(gphys) ⇒ Object

cosine of latitude



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# File 'lib/numru/ganalysis/qg.rb', line 496

def cos_phi(gphys)
  lam, phi, = Planet::get_lambda_phi(gphys)
  phi.cos
end

.div_h(fx, fy) ⇒ Object

horizontal divergence (spherical)



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# File 'lib/numru/ganalysis/qg.rb', line 529

def div_h(fx, fy)
  Planet::div_s(fx, fy)
end

.div_waf(*args) ⇒ Object

divergence of wave activity flux (redirected to ((<div_waf>)))



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# File 'lib/numru/ganalysis/qg.rb', line 538

def self.div_waf(*args)
  super(*args)    # defined in QG_common
end

.gph2psi(gph, gpref) ⇒ Object

geopotential height -> QG stream function



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# File 'lib/numru/ganalysis/qg.rb', line 461

def gph2psi(gph, gpref)
  gpd = gph * Met::g - gpref
  f = f_mask0(gph)
  psi = gpd / f
  psi.name = "psi"
  psi.long_name = "QG stream function"
  psi
end

.gph2psi_gpref(gph) ⇒ Object

geopotential height -> QG stream function and the reference geopotential



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# File 'lib/numru/ganalysis/qg.rb', line 451

def gph2psi_gpref(gph)
  gpd, gpref = gph2gpd_gpref(gph)
  f = f_mask0(gph)
  psi = gpd / f
  psi.name = "psi"
  psi.long_name = "QG stream function"
  [psi, gpref]
end

.gph2q(gph) ⇒ Object

geopotential height to quasi-geostrophic potential vorticity (QGPV)



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# File 'lib/numru/ganalysis/qg.rb', line 430

def gph2q(gph)
  psi, gpref = gph2psi_gpref(gph)
  n2 = gpref2n2(gpref)
  psi2q(psi, n2)
end

.gph2qb(gph) ⇒ Object

same as gph2q, but the QGPV is extended to reflect the lowest-level temperature anomalies



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# File 'lib/numru/ganalysis/qg.rb', line 437

def gph2qb(gph)
  psi, gpref = gph2psi_gpref(gph)
  n2 = gpref2n2(gpref)
  psi2qb(psi, n2)
end

.gph2ug_vg(gph) ⇒ Object

geopotential height -> geostrophic winds



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# File 'lib/numru/ganalysis/qg.rb', line 444

def gph2ug_vg(gph)
  gpx, gpy = Planet::grad_s(gph * Met::g)
  f = f_mask0(gph)
  [ -gpy/f, gpx/f]
end

.grad_h(gphys) ⇒ Object

horizontal gradient (spherical)



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# File 'lib/numru/ganalysis/qg.rb', line 524

def grad_h(gphys)
  Planet::grad_s(gphys)
end

.psi2q(psi, n2, perturbation = false) ⇒ Object

QG stream function -> QGPV



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# File 'lib/numru/ganalysis/qg.rb', line 471

def psi2q(psi, n2, perturbation=false)
  ug, vg = psi2ug_vg(psi)

  if !perturbation
    avor = Planet::absvor_s(ug,vg)
    avor.name = "qgavor"
    avor.long_name = "QG abs vor"
  else
    vor = Planet::vor_s(ug,vg)
    vor.name = "qgvor"
    vor.long_name = "QG vorticity"
    avor = vor
  end

  f = f_mask0(psi)
  qzz = gpd2qzz(psi, n2) * (f*f)

  q = avor + qzz
  q.name = "q"
  q.long_name = "QG PV"

  [q, avor, qzz, ug, vg]
end

.psi2qb(psi, n2, perturbation = false) ⇒ Object

same as psi2q, but the QGPV is extended to reflect the lowest-level temperature anomalies



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# File 'lib/numru/ganalysis/qg.rb', line 503

def psi2qb(psi, n2, perturbation=false)
  psie = extend_bottom(psi, nil)
  n2e = extend_bottom(n2, nil)
  results = psi2q(psie, n2e, perturbation)
  results.collect{|z| cut_bottom(z)}
end

.psi2ug_vg(psi) ⇒ Object

QG stream function -> geostrophic winds



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# File 'lib/numru/ganalysis/qg.rb', line 511

def psi2ug_vg(psi)
  f = f_mask0(psi)
  gpx, gpy = Planet::grad_s(psi)
  vg = gpx
  ug = -gpy
  ug.name = "ug"
  vg.name = "vg"
  ug.long_name = "ug"
  vg.long_name = "vg"
  [ug, vg]
end

.waf_plumb1986_B1(psi, n2) ⇒ Object

Flux of the pseudo-momentum in y direction by Plumb (1986). Specifically, B_1j in Eq.(2.9), but without the factor p. This flux is relative to the mean flow. Averaged over time (if the data is 4D).



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# File 'lib/numru/ganalysis/qg.rb', line 574

def waf_plumb1986_B1(psi, n2)
  psi_x, psi_y = Planet::grad_s(psi)
  psi_z = LogP.pcdata_dz( psi )
  f2 = f_mask0(psi) ** 2
  cosphi = cos_phi(psi)
  fx = -psi_x * psi_y * cosphi
  fy = (psi_x**2 - psi_y**2 + psi_z**2 * f2 / n2) * cosphi / 2.0
  fz = -psi_y * psi_z * (cosphi * f2) / n2
  fx.name = "B_11"
  fy.name = "B_12"
  fz.name = "B_13"
  fx.long_name = "x-comp of Px flux Plumb86"
  fy.long_name = "y-comp of Px flux Plumb86"
  fz.long_name = "z-comp of Px flux Plumb86"
  if psi.rank >= 4
    fx = fx.mean(-1)
    fy = fy.mean(-1)
    fz = fz.mean(-1)
  end
  [fx, fy, fz]
end

.waf_plumb1986_B2(psi, n2) ⇒ Object

Flux of the pseudo-momentum in x direction by Plumb (1986). Specifically, B_2j in Eq.(2.9), but without the factor p. This flux is relative to the mean flow. Averaged over time (if the data is 4D).



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# File 'lib/numru/ganalysis/qg.rb', line 547

def waf_plumb1986_B2(psi, n2)
  psi_x, psi_y = Planet::grad_s(psi)
  psi_z = LogP.pcdata_dz( psi )
  f2 = f_mask0(psi) ** 2
  cosphi = cos_phi(psi)
  fx = (psi_x**2 - psi_y**2 - psi_z**2 * f2 / n2) * cosphi / 2.0
  fy = psi_x * psi_y * cosphi 
  fz = psi_x * psi_z * (cosphi * f2) / n2
  fx.name = "B21"
  fy.name = "B22"
  fz.name = "B23"
  fx.long_name = "WAF B2x"
  fy.long_name = "WAF B2y"
  fz.long_name = "WAF B2z"
  if psi.rank >= 4
    fx = fx.mean(-1)
    fy = fy.mean(-1)
    fz = fz.mean(-1)
  end
  [fx, fy, fz]
end