From bc2703fe9936d1cabd0ee464d4eab0bec3b0d1d1 Mon Sep 17 00:00:00 2001 From: HaoyuZhuang Date: Tue, 16 Jan 2024 11:00:32 -0800 Subject: [PATCH 1/2] ENH: Add shear and curvature vorticity calculations --- docs/_templates/overrides/metpy.calc.rst | 2 + src/metpy/calc/kinematics.py | 156 +++++++++++++++++++++++ tests/calc/test_kinematics.py | 16 ++- 3 files changed, 170 insertions(+), 4 deletions(-) diff --git a/docs/_templates/overrides/metpy.calc.rst b/docs/_templates/overrides/metpy.calc.rst index 652f1b02b4..926a82b58f 100644 --- a/docs/_templates/overrides/metpy.calc.rst +++ b/docs/_templates/overrides/metpy.calc.rst @@ -119,6 +119,7 @@ Dynamic/Kinematic advection ageostrophic_wind coriolis_parameter + curvature_vorticity divergence exner_function frontogenesis @@ -129,6 +130,7 @@ Dynamic/Kinematic potential_vorticity_baroclinic potential_vorticity_barotropic q_vector + shear_vorticity shearing_deformation stretching_deformation total_deformation diff --git a/src/metpy/calc/kinematics.py b/src/metpy/calc/kinematics.py index f79d7971d0..21dc753ade 100644 --- a/src/metpy/calc/kinematics.py +++ b/src/metpy/calc/kinematics.py @@ -93,6 +93,162 @@ def vorticity( return dvdx - dudy +@exporter.export +@parse_grid_arguments +@preprocess_and_wrap(wrap_like='u', broadcast=('u', 'v', 'parallel_scale', 'meridional_scale')) +@check_units('[speed]', '[speed]', dx='[length]', dy='[length]') +def shear_vorticity( + u, v, *, dx=None, dy=None, x_dim=-1, y_dim=-2, + parallel_scale=None, meridional_scale=None +): + r"""Calculate the vertical shear vorticity of the horizontal wind. + + Parameters + ---------- + u : (..., M, N) `xarray.DataArray` or `pint.Quantity` + x component of the wind + v : (..., M, N) `xarray.DataArray` or `pint.Quantity` + y component of the wind + + Returns + ------- + (..., M, N) `xarray.DataArray` or `pint.Quantity` + vertical vorticity + + Other Parameters + ---------------- + dx : `pint.Quantity`, optional + The grid spacing(s) in the x-direction. If an array, there should be one item less than + the size of `u` along the applicable axis. Optional if `xarray.DataArray` with + latitude/longitude coordinates used as input. Also optional if one-dimensional + longitude and latitude arguments are given for your data on a non-projected grid. + Keyword-only argument. + dy : `pint.Quantity`, optional + The grid spacing(s) in the y-direction. If an array, there should be one item less than + the size of `u` along the applicable axis. Optional if `xarray.DataArray` with + latitude/longitude coordinates used as input. Also optional if one-dimensional + longitude and latitude arguments are given for your data on a non-projected grid. + Keyword-only argument. + x_dim : int, optional + Axis number of x dimension. Defaults to -1 (implying [..., Y, X] order). Automatically + parsed from input if using `xarray.DataArray`. Keyword-only argument. + y_dim : int, optional + Axis number of y dimension. Defaults to -2 (implying [..., Y, X] order). Automatically + parsed from input if using `xarray.DataArray`. Keyword-only argument. + parallel_scale : `pint.Quantity`, optional + Parallel scale of map projection at data coordinate. Optional if `xarray.DataArray` + with latitude/longitude coordinates and MetPy CRS used as input. Also optional if + longitude, latitude, and crs are given. If otherwise omitted, calculation will be + carried out on a Cartesian, rather than geospatial, grid. Keyword-only argument. + meridional_scale : `pint.Quantity`, optional + Meridional scale of map projection at data coordinate. Optional if `xarray.DataArray` + with latitude/longitude coordinates and MetPy CRS used as input. Also optional if + longitude, latitude, and crs are given. If otherwise omitted, calculation will be + carried out on a Cartesian, rather than geospatial, grid. Keyword-only argument. + + See Also + -------- + divergence, absolute_vorticity, vorticity, curvature_vorticity + + Notes + ----- + This implements a numerical version of the vertical shear vorticity: + + .. math:: \zeta_s = \frac{1}{u^2 + v^2}(v u \frac{\partial u}{\partial x} + + v v \frac{\partial v}{\partial x} - + u u \frac{\partial u}{\partial y} - + u v \frac{\partial v}{\partial y}) + + If sufficient grid projection information is provided, these partial derivatives are + taken from the projection-correct derivative matrix of the vector wind. Otherwise, they + are evaluated as scalar derivatives on a Cartesian grid. + """ + dudx, dudy, dvdx, dvdy = vector_derivative( + u, v, dx=dx, dy=dy, x_dim=x_dim, y_dim=y_dim, parallel_scale=parallel_scale, + meridional_scale=meridional_scale + ) + + return (v * u * dudx + v * v * dvdx - u * u * dudy - u * v * dvdy) / (u ** 2 + v ** 2) + + +@exporter.export +@parse_grid_arguments +@preprocess_and_wrap(wrap_like='u', broadcast=('u', 'v', 'parallel_scale', 'meridional_scale')) +@check_units('[speed]', '[speed]', dx='[length]', dy='[length]') +def curvature_vorticity( + u, v, *, dx=None, dy=None, x_dim=-1, y_dim=-2, + parallel_scale=None, meridional_scale=None +): + r"""Calculate the vertical curvature vorticity of the horizontal wind. + + Parameters + ---------- + u : (..., M, N) `xarray.DataArray` or `pint.Quantity` + x component of the wind + v : (..., M, N) `xarray.DataArray` or `pint.Quantity` + y component of the wind + + Returns + ------- + (..., M, N) `xarray.DataArray` or `pint.Quantity` + vertical vorticity + + Other Parameters + ---------------- + dx : `pint.Quantity`, optional + The grid spacing(s) in the x-direction. If an array, there should be one item less than + the size of `u` along the applicable axis. Optional if `xarray.DataArray` with + latitude/longitude coordinates used as input. Also optional if one-dimensional + longitude and latitude arguments are given for your data on a non-projected grid. + Keyword-only argument. + dy : `pint.Quantity`, optional + The grid spacing(s) in the y-direction. If an array, there should be one item less than + the size of `u` along the applicable axis. Optional if `xarray.DataArray` with + latitude/longitude coordinates used as input. Also optional if one-dimensional + longitude and latitude arguments are given for your data on a non-projected grid. + Keyword-only argument. + x_dim : int, optional + Axis number of x dimension. Defaults to -1 (implying [..., Y, X] order). Automatically + parsed from input if using `xarray.DataArray`. Keyword-only argument. + y_dim : int, optional + Axis number of y dimension. Defaults to -2 (implying [..., Y, X] order). Automatically + parsed from input if using `xarray.DataArray`. Keyword-only argument. + parallel_scale : `pint.Quantity`, optional + Parallel scale of map projection at data coordinate. Optional if `xarray.DataArray` + with latitude/longitude coordinates and MetPy CRS used as input. Also optional if + longitude, latitude, and crs are given. If otherwise omitted, calculation will be + carried out on a Cartesian, rather than geospatial, grid. Keyword-only argument. + meridional_scale : `pint.Quantity`, optional + Meridional scale of map projection at data coordinate. Optional if `xarray.DataArray` + with latitude/longitude coordinates and MetPy CRS used as input. Also optional if + longitude, latitude, and crs are given. If otherwise omitted, calculation will be + carried out on a Cartesian, rather than geospatial, grid. Keyword-only argument. + + See Also + -------- + divergence, absolute_vorticity + + Notes + ----- + This implements a numerical version of the vertical curvature vorticity: + + .. math:: \zeta_c = \frac{1}{u^2 + v^2}(u u \frac{\partial v}{\partial x} - + v v \frac{\partial u}{\partial y} - + v u \frac{\partial u}{\partial x} + + u v \frac{\partial v}{\partial y}) + + If sufficient grid projection information is provided, these partial derivatives are + taken from the projection-correct derivative matrix of the vector wind. Otherwise, they + are evaluated as scalar derivatives on a Cartesian grid. + """ + dudx, dudy, dvdx, dvdy = vector_derivative( + u, v, dx=dx, dy=dy, x_dim=x_dim, y_dim=y_dim, parallel_scale=parallel_scale, + meridional_scale=meridional_scale + ) + + return (u * u * dvdx - v * v * dudy - v * u * dudx + u * v * dvdy) / (u ** 2 + v ** 2) + + @exporter.export @parse_grid_arguments @preprocess_and_wrap(wrap_like='u', broadcast=('u', 'v', 'parallel_scale', 'meridional_scale')) diff --git a/tests/calc/test_kinematics.py b/tests/calc/test_kinematics.py index 71a62069c2..65118f27df 100644 --- a/tests/calc/test_kinematics.py +++ b/tests/calc/test_kinematics.py @@ -8,11 +8,11 @@ import xarray as xr from metpy.calc import (absolute_vorticity, advection, ageostrophic_wind, coriolis_parameter, - divergence, first_derivative, frontogenesis, geospatial_laplacian, - geostrophic_wind, inertial_advective_wind, lat_lon_grid_deltas, - montgomery_streamfunction, potential_temperature, + curvature_vorticity, divergence, first_derivative, frontogenesis, + geospatial_laplacian, geostrophic_wind, inertial_advective_wind, + lat_lon_grid_deltas, montgomery_streamfunction, potential_temperature, potential_vorticity_baroclinic, potential_vorticity_barotropic, - q_vector, shearing_deformation, static_stability, + q_vector, shear_vorticity, shearing_deformation, static_stability, storm_relative_helicity, stretching_deformation, total_deformation, vorticity, wind_components) from metpy.constants import g, Re @@ -151,6 +151,14 @@ def test_vorticity_grid_pole(): assert_array_almost_equal(vort.isel(y=0), vort.isel(y=-1), decimal=9) +def test_sum_shear_curvature(basic_dataset): + """Test the sum of shear and curvature vorticity equals the total vorticity.""" + d = vorticity(basic_dataset.u, basic_dataset.v) + s = shear_vorticity(basic_dataset.u, basic_dataset.v) + c = curvature_vorticity(basic_dataset.u, basic_dataset.v) + assert_array_almost_equal(s + c, d) + + def test_zero_divergence(): """Test divergence calculation when zeros should be returned.""" a = np.arange(3) From 784bec9b7323100b5322271654b9b6a2a043404f Mon Sep 17 00:00:00 2001 From: Ryan May Date: Thu, 6 Feb 2025 14:25:54 -0700 Subject: [PATCH 2/2] DOC: Add reference document for shear/curvature vorticity --- .../Majumdar-2024-curvature-vorticity.pdf | Bin 0 -> 98143 bytes docs/api/references.rst | 3 +++ src/metpy/calc/kinematics.py | 5 +++-- 3 files changed, 6 insertions(+), 2 deletions(-) create mode 100644 docs/_static/Majumdar-2024-curvature-vorticity.pdf diff --git a/docs/_static/Majumdar-2024-curvature-vorticity.pdf b/docs/_static/Majumdar-2024-curvature-vorticity.pdf new file mode 100644 index 0000000000000000000000000000000000000000..16dbc66e25ef7e14c7d3789459d607fe9507c832 GIT binary patch literal 98143 zcma&MW0WOb(=A#yyX;-A>auOywrzLWwr$(CZM#cdwsrb>@tt$V9e3ROXJ@RnA~KMf zD`(`~r1HX|Gz_#%Fr-6AcSq-?_jz+eBQVSWdVrmwB@8z=fKJ-P*38))!18xW5kMzu zVeM?<`1fdS;A|pnVq|A*0^sF^adLJvF|dJg2OiGWXxw6T_1k@=VrOb_HfgsA;JUp1 z$t6p6K2$Lwltr$Rr7S7A97S;Ve2<3&5CFpH-oHz!+@jHDh05|C?AM#%OZBDX^L@|! zx%;iU^47b%!=$Vx)B2&+Q&yvBr1i9@KE0^k^R4dlU2~B-`fA=$QgPlvBPYWoGu#<_ zbaK7JQv7rGQH# z@p`tqqs{H4!s58%GDFI>r>9a;X|=)?Y|MtqO;X0|ytLfny#?&;PXG4F3_=O<>!U?^ zc`5l@jrFLrH%B1df4v++j{BnR?coB;c38@7_RB zzw(JtzAjo>udbKFqjSZcHHFVuwO(%O!rYHLO}@|auU788fRDJS6&3zm1$6X~JUsO^yfl$+%PGr; z9y*=S{_t36mL;X-m~8KNd=$h6-$}Vs@0{Uw?2MMP5y~&JevfAT5_ff^_Rw}xf3@lJ zyB(g{ZRKSd9KCVd+1&4-s<+x*$>o*hq7B2e^9s-q0zv~7cqgrmc*M;yW;G+W6oQM| z2?M;>>$_Ev8MFZpzR#7h!$*%8n4mn%CG{3!zE5?)SBU&a@jRL|JDd_rt5M)s7Cdx@ zgaEu(=mV0^VPhcSbT6O31rpgN5J?3AKioYe`_ppdYVcS2G07*J0nsNoGhMIG{aRBU zeT9IOOL~nvd%C|QuLcrx0fC?AV=126=1cNW!ztD>AgetDk5nHki6DCNmU`=~JKQv7cvWOa@IzI1y+p$CjU!a6qWvKzI=OE}to1~~6g$B9G znntID!7qixj5xi%V_5KBMm=F*+C#djuDCz2Yp;ro&=ieUnU<<3m>DCZG#$)i0}`Dz zme|xnzOrskWB4nv6dJv2+k#&o;Ivy$ZQ@lm?(Vk>z{8iD=tuc+9s56YBG<}UBg~5YypVC~kwW06ZuPW!@4&T9Ep16?I=atGIkf#$jZzc_z_-YavcRVR#Uc0peuO5Vz|)GcbbAb_+OWVX zY(^}=UqIlRa(q30+DP&)Tq=q3E>OT}=eOX8fj}eDvF8~6K$+QrfV2*7SE$(p>uKx&kb?+kd6koe4RD|4cuZt5J;SqR<&_?0IP z#K#~4O#5u+z1mWT&A@=K>1?5r!C=%`hy?<{!Fj>tiy?vXf)O{%NQTB_diW55HVmpl zM37#A`gX)=0djQ}+4k3-0nk01yoFH>H4(r57;t{{SkT5sS zIG*`fR4_0=EGU!UfxLNCyB7l1%s@UoQo&a8ie1-cLP9{vB_5}hS=@DT8i@V(nAZE88M-R#8ip@PTR1m zN0@jUaVeJsK?NggDembaDnl3d0O=4$0)C6L-_DVpo#lCQ|dR{u&uLJF$O0*^1)c&|&dj zW<%a0&yKS0B$rT~j-Mt5LE!gRVw>YhIzjnjD6>PgCKnt%d28Ge!QW!r7LP*t^S;R! za-E4KvRY~Xelj(|-D$Txb>-jF`|e~&9=l`(eFu0R+|Fg9WV*z!>>(dSx%k38G1>U! zR*sI#k$W4x=pp9gn-OaBOrVu$Pc(Zzq^mO{PP$%CkSn_4s(KAk7WDI!yV$mwa3vPi z4UKMP71KFSfum;#>*mEIcYs>7Mm-d3=B2Uf3!h?dP|Q^nN3Hf zkj5CC7cN1e&Wj#Ez~Sn^X&##gs-gruZ~hWOFRn?wuAg_79_E#W5GN=%3mb94l|eiM zy9CAE6JSkmZh3d-fRuHgeE;Vvq{)~DgkbL1? 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[Majumdar2024] Majumdar, Sharan, 2024: `Curvature and Shear Vorticity in Cartesian + Coordinates <../_static/Majumdar-2024-curvature-vorticity.pdf>`_, 2pp. + .. [NOAA1976] National Oceanic and Atmospheric Administration, National Aeronautics and Space Administration, and U. S. Air Force, 1976: `U. S. Standard Atmosphere 1976 `_, diff --git a/src/metpy/calc/kinematics.py b/src/metpy/calc/kinematics.py index 21dc753ade..b22903a8b1 100644 --- a/src/metpy/calc/kinematics.py +++ b/src/metpy/calc/kinematics.py @@ -152,7 +152,7 @@ def shear_vorticity( Notes ----- - This implements a numerical version of the vertical shear vorticity: + This implements a numerical version of the vertical shear vorticity as in [Majumdar2024]_: .. math:: \zeta_s = \frac{1}{u^2 + v^2}(v u \frac{\partial u}{\partial x} + v v \frac{\partial v}{\partial x} - @@ -230,7 +230,8 @@ def curvature_vorticity( Notes ----- - This implements a numerical version of the vertical curvature vorticity: + This implements a numerical version of the vertical curvature vorticity as in + [Majumdar2024]_: .. math:: \zeta_c = \frac{1}{u^2 + v^2}(u u \frac{\partial v}{\partial x} - v v \frac{\partial u}{\partial y} -