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On this page you will find:
1. Meridional structures of the Hough functions for the realistic background state of the mean zonal wind and for the background state at rest,
2. Horizontal structures of the Hough harmonics (Kelvin wave, mixed Rossby-gravity wave, Rossby and inertia-gravity waves) for different equivalent depths.
    (1) Kelvin Waves
    (2) Mixed Rossby-gravity Waves
    (3) Eastward-propagating Inertia-gravity Waves
    (4) Rossby Waves
    (5) Westward-propagating Inertia-gravity Waves

The Effect of the Background Flow on the Meridional Structure of the Hough Functions


Meridional structures of the Hough functions for the zonal wavenumber k=1 and equivalent depth 10 km. The comparison is between the case of the background state at rest and the background flow derived from ERA5 reanalysis data for level 500 hPa and MAM season.
These results reproduce ones from Kasahara, A., 1981: Corrigendum, J. Atmos. Sci. 38, 2284-2285. The original article is Kasahara, A., 1980: Effect of Zonal Flows on the Free Oscillations of a Barotropic Atmosphere, J. Atmos. Sci. 37, 917-929.
background_flow_500hPa_MAM
merid_prof_bg_nobg_EIG_k1_m1_n0 merid_prof_bg_nobg_EIG_k1_m1_n1 merid_prof_bg_nobg_EIG_k1_m1_n2
merid_prof_bg_nobg_EIG_k1_m1_n3 merid_prof_bg_nobg_EIG_k1_m1_n4 merid_prof_bg_nobg_EIG_k1_m1_n5
merid_prof_bg_nobg_WIG_k1_m1_n0 merid_prof_bg_nobg_WIG_k1_m1_n1 merid_prof_bg_nobg_WIG_k1_m1_n2
merid_prof_bg_nobg_WIG_k1_m1_n3 merid_prof_bg_nobg_WIG_k1_m1_n4 merid_prof_bg_nobg_WIG_k1_m1_n5
merid_prof_bg_nobg_Rossby_k1_m1_n0 merid_prof_bg_nobg_Rossby_k1_m1_n1 merid_prof_bg_nobg_Rossby_k1_m1_n2
merid_prof_bg_nobg_Rossby_k1_m1_n3 merid_prof_bg_nobg_Rossby_k1_m1_n4 merid_prof_bg_nobg_Rossby_k1_m1_n5


Hough Harmonics


These and further Hough harmonics are available for two projections:
https://modes.cen.uni-hamburg.de/ebla/MODES/Robinson and
https://modes.cen.uni-hamburg.de/ebla/MODES/EquidistantCylindrical
Feel free to use them. Please acknowledge the MODES project webpage.

Kelvin Waves

HoughHarmonic_Kelvin_k1_D10km HoughHarmonic_Kelvin_k1_D6905m
HoughHarmonic_Kelvin_k1_D1536m HoughHarmonic_Kelvin_k1_D576m
HoughHarmonic_Kelvin_k1_D313m HoughHarmonic_Kelvin_k1_D203m
HoughHarmonic_Kelvin_k1_D152m HoughHarmonic_Kelvin_k1_D110m
HoughHarmonic_Kelvin_k1_D53m HoughHarmonic_Kelvin_k1_D27m

Mixed Rossby-gravity Waves

HoughHarmonic_MRG_k1_D10km HoughHarmonic_MRG_k1_D6905m
HoughHarmonic_MRG_k1_D1536m HoughHarmonic_MRG_k1_D576m
HoughHarmonic_MRG_k1_D313m HoughHarmonic_MRG_k1_D203m
HoughHarmonic_MRG_k1_D152m HoughHarmonic_MRG_k1_D110m
HoughHarmonic_MRG_k1_D53m HoughHarmonic_MRG_k1_D27m

Eastward-propagating Inertia-gravity Waves

HoughHarmonic_eig_k1_n1_D10km HoughHarmonic_eig_k1_n1_D6905m
HoughHarmonic_eig_k1_n1_D1536m HoughHarmonic_eig_k1_n1_D576m
HoughHarmonic_eig_k1_n1_D313m HoughHarmonic_eig_k1_n1_D203m
HoughHarmonic_eig_k1_n1_D152m HoughHarmonic_eig_k1_n1_D110m
HoughHarmonic_eig_k1_n1_D53m HoughHarmonic_eig_k1_n1_D27m
HoughHarmonic_eig_k1_n2_D10km HoughHarmonic_eig_k1_n2_D6905m
HoughHarmonic_eig_k1_n2_D1536m HoughHarmonic_eig_k1_n2_D576m
HoughHarmonic_eig_k1_n2_D313m HoughHarmonic_eig_k1_n2_D203m
HoughHarmonic_eig_k1_n2_D152m HoughHarmonic_eig_k1_n2_D110m
HoughHarmonic_eig_k1_n2_D53m HoughHarmonic_eig_k1_n2_D27m
HoughHarmonic_eig_k1_n3_D10km HoughHarmonic_eig_k1_n3_D6905m
HoughHarmonic_eig_k1_n3_D1536m HoughHarmonic_eig_k1_n3_D576m
HoughHarmonic_eig_k1_n3_D313m HoughHarmonic_eig_k1_n3_D203m
HoughHarmonic_eig_k1_n3_D152m HoughHarmonic_eig_k1_n3_D110m
HoughHarmonic_eig_k1_n3_D53m HoughHarmonic_eig_k1_n3_D27m
HoughHarmonic_eig_k1_n4_D10km HoughHarmonic_eig_k1_n4_D6905m
HoughHarmonic_eig_k1_n4_D1536m HoughHarmonic_eig_k1_n4_D576m
HoughHarmonic_eig_k1_n4_D313m HoughHarmonic_eig_k1_n4_D203m
HoughHarmonic_eig_k1_n4_D152m HoughHarmonic_eig_k1_n4_D110m
HoughHarmonic_eig_k1_n4_D53m HoughHarmonic_eig_k1_n4_D27m

Rossby Waves

HoughHarmonic_rot_k1_n1_D10km HoughHarmonic_rot_k1_n1_D6905m
HoughHarmonic_rot_k1_n1_D1536m HoughHarmonic_rot_k1_n1_D576m
HoughHarmonic_rot_k1_n1_D313m HoughHarmonic_rot_k1_n1_D203m
HoughHarmonic_rot_k1_n1_D152m HoughHarmonic_rot_k1_n1_D110m
HoughHarmonic_rot_k1_n1_D53m HoughHarmonic_rot_k1_n1_D27m
HoughHarmonic_rot_k1_n2_D10km HoughHarmonic_rot_k1_n2_D6905m
HoughHarmonic_rot_k1_n2_D1536m HoughHarmonic_rot_k1_n2_D576m
HoughHarmonic_rot_k1_n2_D313m HoughHarmonic_rot_k1_n2_D203m
HoughHarmonic_rot_k1_n2_D152m HoughHarmonic_rot_k1_n2_D110m
HoughHarmonic_rot_k1_n2_D53m HoughHarmonic_rot_k1_n2_D27m
HoughHarmonic_rot_k1_n3_D10km HoughHarmonic_rot_k1_n3_D6905m
HoughHarmonic_rot_k1_n3_D1536m HoughHarmonic_rot_k1_n3_D576m
HoughHarmonic_rot_k1_n3_D313m HoughHarmonic_rot_k1_n3_D203m
HoughHarmonic_rot_k1_n3_D152m HoughHarmonic_rot_k1_n3_D110m
HoughHarmonic_rot_k1_n3_D53m HoughHarmonic_rot_k1_n3_D27m
HoughHarmonic_rot_k1_n4_D10km HoughHarmonic_rot_k1_n4_D6905m
HoughHarmonic_rot_k1_n4_D1536m HoughHarmonic_rot_k1_n4_D576m
HoughHarmonic_rot_k1_n4_D313m HoughHarmonic_rot_k1_n4_D203m
HoughHarmonic_rot_k1_n4_D152m HoughHarmonic_rot_k1_n4_D110m
HoughHarmonic_rot_k1_n4_D53m HoughHarmonic_rot_k1_n4_D27m
HoughHarmonic_rot_k1_n5_D10km HoughHarmonic_rot_k1_n5_D6905m
HoughHarmonic_rot_k1_n5_D1536m HoughHarmonic_rot_k1_n5_D576m
HoughHarmonic_rot_k1_n5_D313m HoughHarmonic_rot_k1_n5_D203m
HoughHarmonic_rot_k1_n5_D152m HoughHarmonic_rot_k1_n5_D110m
HoughHarmonic_rot_k1_n5_D53m HoughHarmonic_rot_k1_n5_D27m
HoughHarmonic_rot_k1_n6_D10km HoughHarmonic_rot_k1_n6_D6905m
HoughHarmonic_rot_k1_n6_D1536m HoughHarmonic_rot_k1_n6_D576m
HoughHarmonic_rot_k1_n6_D313m HoughHarmonic_rot_k1_n6_D203m
HoughHarmonic_rot_k1_n6_D152m HoughHarmonic_rot_k1_n6_D110m
HoughHarmonic_rot_k1_n6_D53m HoughHarmonic_rot_k1_n6_D27m

Westward-propagating Inertia-gravity Waves

HoughHarmonic_wig_k1_n0_D10km HoughHarmonic_wig_k1_n0_D6905m
HoughHarmonic_wig_k1_n0_D1536m HoughHarmonic_wig_k1_n0_D576m
HoughHarmonic_wig_k1_n0_D313m HoughHarmonic_wig_k1_n0_D203m
HoughHarmonic_wig_k1_n0_D152m HoughHarmonic_wig_k1_n0_D110m
HoughHarmonic_wig_k1_n0_D53m HoughHarmonic_wig_k1_n0_D27m
HoughHarmonic_wig_k1_n1_D10km HoughHarmonic_wig_k1_n1_D6905m
HoughHarmonic_wig_k1_n1_D1536m HoughHarmonic_wig_k1_n1_D576m
HoughHarmonic_wig_k1_n1_D313m HoughHarmonic_wig_k1_n1_D203m
HoughHarmonic_wig_k1_n1_D152m HoughHarmonic_wig_k1_n1_D110m
HoughHarmonic_wig_k1_n1_D53m HoughHarmonic_wig_k1_n1_D27m
HoughHarmonic_wig_k1_n2_D10km HoughHarmonic_wig_k1_n2_D6905m
HoughHarmonic_wig_k1_n2_D1536m HoughHarmonic_wig_k1_n2_D576m
HoughHarmonic_wig_k1_n2_D313m HoughHarmonic_wig_k1_n2_D203m
HoughHarmonic_wig_k1_n2_D152m HoughHarmonic_wig_k1_n2_D110m
HoughHarmonic_wig_k1_n2_D53m HoughHarmonic_wig_k1_n2_D27m
HoughHarmonic_wig_k1_n3_D10km HoughHarmonic_wig_k1_n3_D6905m
HoughHarmonic_wig_k1_n3_D1536m HoughHarmonic_wig_k1_n3_D576m
HoughHarmonic_wig_k1_n3_D313m HoughHarmonic_wig_k1_n3_D203m
HoughHarmonic_wig_k1_n3_D152m HoughHarmonic_wig_k1_n3_D110m
HoughHarmonic_wig_k1_n3_D53m HoughHarmonic_wig_k1_n3_D27m
HoughHarmonic_wig_k1_n4_D10km HoughHarmonic_wig_k1_n4_D6905m
HoughHarmonic_wig_k1_n4_D1536m HoughHarmonic_wig_k1_n4_D576m
HoughHarmonic_wig_k1_n4_D313m HoughHarmonic_wig_k1_n4_D203m
HoughHarmonic_wig_k1_n4_D152m HoughHarmonic_wig_k1_n4_D110m
HoughHarmonic_wig_k1_n4_D53m HoughHarmonic_wig_k1_n4_D27m
HoughHarmonic_wig_k1_n6_D10km HoughHarmonic_wig_k1_n6_D6905m
HoughHarmonic_wig_k1_n6_D1536m HoughHarmonic_wig_k1_n6_D576m
HoughHarmonic_wig_k1_n6_D313m HoughHarmonic_wig_k1_n6_D203m
HoughHarmonic_wig_k1_n6_D152m HoughHarmonic_wig_k1_n6_D110m
HoughHarmonic_wig_k1_n6_D53m HoughHarmonic_wig_k1_n6_D27m
HoughHarmonic_wig_k1_n8_D10km HoughHarmonic_wig_k1_n8_D6905m
HoughHarmonic_wig_k1_n8_D1536m HoughHarmonic_wig_k1_n8_D576m
HoughHarmonic_wig_k1_n8_D313m HoughHarmonic_wig_k1_n8_D203m
HoughHarmonic_wig_k1_n8_D152m HoughHarmonic_wig_k1_n8_D110m
HoughHarmonic_wig_k1_n8_D53m HoughHarmonic_wig_k1_n8_D27m