RID diagnostics explained

The RID provides various data divided into three components:

Component	Label
Zonal-mean data on pressure levels	zonal
Horizontal slices of selected pressure levels	single-level
Zonal slices of selected latitudes *under development	longitude-pressure
Surface variables *under development	surface

Zonal

The zonal-mean component of the dataset is composed of the following subcomponents:

Label	Description
core	Core set of zonal-mean variables
fluxes	Eddy covariance terms based on zonal anomalies
dt	Temporal derivatives
mom	Diagnostics based on the momentum equation
tem-qg	Transformed Eulerian mean diagnostics based on quasi-geostrophic equations
tem-pr	Transformed Eulerian mean diagnostics based on primitive equations
tem-thermo	Thermodynamic diagnostics based on Transformed Eulerian mean primitive equations
moist	Diagnostics involving specific humidity
diab	Diabatic heating diagnostics *under development

Notation: Overbars ($\overline{x}$) denote zonal averages and primes ($’$) departures therefrom.

Zonal diagnostics are provided on the following pressure levels:

core: zonal mean of core variables

Symbol	Description	NetCDF name	Units
$\overline{u}$	Zonal-mean zonal wind	u	$m\,s^{-1}$
$\overline{v}$	Zonal-mean meridional wind	v	$m\,s^{-1}$
$\overline{\omega}$	Zonal-mean pressure velocity	w	$Pa\,s^{-1}$
$\overline{T}$	Temperature	t	$K$
$\overline{Z}$	Geopotential height	z	$m$

fluxes: eddy covariance terms based on zonal anomalies

Symbol	Description	NetCDF name	Units
$\overline{u’^2}$	Zonal wind variance	uu	$m^2\,s^{-2}$
$\overline{v’^2}$	Meridional wind variance	vv	$m^2\,s^{-2}$
EKE	Eddy kinetic energy	obtained by adding uu and vv	$m^2\,s^{-2}$
$\overline{Z’^2}$	Variance of geopotential height	zz	$m^2$
$\overline{T’^2}$	Temperature variance	tt	$K^2$
$\overline{u’v’}$	Covariance of zonal and meridional wind anomalies, or meridional mementum flux	vu	$m^2\,s^{-2}$
$\overline{u’\omega’}$	Covariance of zonal wind anomalies and pressure-velocity wind anomalies, or meridional momentum flux	wu	$m\,Pa\,s^{-2}$
$\overline{v’T’}$	Covariance of meridional wind anomalies and temperature anomalies, or meridional heat flux	vt	$m\,K\,s^{-1}$
$\overline{\omega’T’}$	Covariance of pressure velocity anomalies and temperature anomalies, or vertical heat flux	wt	$Pa\,K\,s^{-1}$

dt: temporal derivatives

Symbol	Description	NetCDF name	Units
$\partial{}\overline{T}/\partial{}t$	Time derivative of temperature	t_dt	$K\, s^{-1}$
$\partial{}\overline{u}/\partial{}t$	Time derivative of zonal wind	u_dt	$m\,s^{-2}$

mom: diagnostics of the momentum equation

Symbol	Description	NetCDF name	Units
$f\overline{v}$	Acceleration by Coriolis torque	coriolis_torque	$m\,s^{-2}$
$ – \overline{v}\frac{1}{a\cos\phi}\frac{\partial{}(\overline{u}\cos\phi)}{\partial\phi}$	Acceleration by meridional advection of momentum	u_adv_by_v	$m\,s^{-2}$
$- \overline{\omega}\frac{\partial\overline{u}}{\partial{}p} $	Acceleration by vertical advection of momentum	u_adv_by_w	$m\,s^{-2}$
$-\frac{\partial{}(\overline{\omega’u’})}{\partial{}p}$	Acceleration by vertical momentum flux convergence	u_accel_by_wu_flux	$m\,s^{-2}$
$- \frac{1}{a\cos^2\phi}\frac{\partial(\overline{u’v’}\cos^2\phi)}{\partial\phi}$	Acceleration by meridional momentum flux convergence	u_accel_by_vu_flux	$m\,s^{-2}$

In the zonal mean, the momentum equation is written:

$$\frac{\partial\overline{u}}{\partial{}t} = \overbrace{f\overline{v}}^{\text{coriolis_torque}} \underbrace{- \overline{v}\frac{1}{a\cos\phi}\frac{\partial{}(\overline{u}\cos\phi)}{\partial\phi}}_{\text{u_adv_by_v}} \overbrace{-\overline{\omega}\frac{\partial\overline{u}}{\partial{}p}}^{\text{u_adv_by_w}} \underbrace{- \frac{1}{a\cos^2\phi}\frac{\partial(\overline{u’v’}\cos^2\phi)}{\partial\phi}}_{\text{u_accel_by_vu_flux}}\overbrace{-\frac{\partial{}(\overline{\omega’u’})}{\partial{}p}}^{\text{u_accel_by_wu_flux}} $$

tem-qg and tem-pr: diagnostics of Eliassen-Palm flux and transformed Eulerian mean

Symbol	Description	NetCDF name	Units
$\phi$	latitude	lat
$p$	pressure	pre
$a$	Earth radius, 6371000 m		$m$
$\overline{v}^*$	Meridional component of residual circulation	vres	$m\,s^{-1}$
$\overline{\omega}^*$	Vertical component of residual circulation	wres	$Pa\,s^{-1}$
$f\overline{v}^*$	Coriolis torque	coriolis_torque_tem	$m\,s^{-2}$
$- \overline{v}^*\frac{1}{a\cos\phi}\frac{\partial{}(\overline{u}\cos\phi)}{\partial{}\phi}$	Momentum advection by meridional residual circulation	u_adv_by_vres$^{1}$	$m\,s^{-2}$
$- \overline{\omega}^*\frac{\partial\overline{u}}{\partial{}p}$	Momentum advection by vertical residual circulation	u_adv_by_wres$^{1}$	$m\,s^{-2}$
$F_p$	vertical component of EP-flux	EPF_pre_[qg,pr]	$Pa\,m^{2}\,s^{-2}$
$F_\phi$	meridional component of EP-flux	EPF_lat_[qg,pr]	$m^{3}\,s^{-2}$
$\frac{(\nabla\cdot\mathbf{F})_p}{a\cos\phi}$	EP-flux divergence impact on zonal wind acceleration, vertical component	EPFD_pre_[qg,pr]$^{2}$	$m\,s^{-2}$
$\frac{(\nabla\cdot\mathbf{F})_\phi}{a\cos\phi}$	EP-flux divergence impact on zonal wind acceleration, meridional component	EPFD_lat_[qg,pr]$^{2}$	$m\,s^{-2}$
$\frac{\nabla\cdot\mathbf{F}}{a\cos\phi}$	EP-flux divergence impact on zonal wind acceleration	obtained by adding EPFD_pre_[qg,pr] and EPFD_lat_[qg,pr]	$m\,s^{-2}$

In the transformed Eulerian mean, the momentum equation is written

$$\frac{\partial{}\overline{u}}{\partial{t}} = \overbrace{f\overline{v}^*}^{\text{coriolis_torque_tem}} \underbrace{- \overline{v}^*\frac{1}{a\cos\phi}\frac{\partial{}(\overline{u}\cos\phi)}{\partial{}\phi}}_{\text{u_adv_by_vres}} \overbrace{- \overline{\omega}^*\frac{\partial\overline{u}}{\partial{}p}}^{\text{u_adv_by_wres}} + \frac{\nabla\cdot\mathbf{F}}{a\cos\phi}$$

where the residual circulation is defined as

$$\overbrace{\overline{v}^*}^{\text{vres}}=\overline{v}-\frac{\partial}{\partial{}p}\left[\frac{\overline{v’\theta’}}{\partial{}\overline{\theta}/\partial{}p}\right]$$

$$\overbrace{\overline{\omega}^*}^{\text{wres}}= \overline{\omega}+\frac{1}{a\cos\phi}\frac{\partial}{\partial\phi}\left[\frac{\overline{v’\theta’}\cos\phi}{\partial\overline{\theta}/\partial{}p}\right]$$

The equation of the EP-flux divergence is:

$$\nabla\cdot\mathbf{F}=\underbrace{ \frac{1}{a\cos{}\phi} \frac{\partial{}(\overbrace{F_\phi}^{\text{EPF_lat_[qg,pr]}}\cos\phi)}{\partial{}\phi}}_{(\nabla\cdot\mathbf{F})_\phi}+\underbrace{\frac{\partial{}\overbrace{F_p}^{\text{EPF_pre_[qg,pr]}}}{\partial{}p}}_{(\nabla\cdot\mathbf{F})_p}$$

In the dataset, the EP-flux divergence is provided in the form of its impact on zonal wind acceleration. It is therefore scaled by $\frac{1}{a\cos\phi}$:

$$\overbrace{\frac{(\nabla\cdot\mathbf{F})_p}{a\cos\phi}}^{\text{EPFD_pre_[qg,pr]}}= \frac{1}{a\cos\phi}\frac{\partial{}\overbrace{F_p}^{\text{EPF_pre_[qg,pr]}}}{\partial{}p}$$

$$\overbrace{\frac{(\nabla\cdot\mathbf{F})_\phi}{a\cos\phi}}^{\text{EPFD_lat_[qg,pr]}}= \frac{1}{(a\cos{}\phi)^2} \frac{\partial{}(\overbrace{F_\phi}^{\text{EPF_lat_[qg,pr]}}\cos\phi)}{\partial{}\phi}$$

EP-flux is defined as follows (terms only included in the primitive-equation version are indicated with “pr”)

$$\{F_{\phi},\,F_p\} = a\cos\phi\left\{\overbrace{\frac{\overline{v’\theta’}}{\partial\overline{\theta}/\partial{}p}\frac{\partial\overline{u}}{\partial{p}}}^{\text{pr}}-\overline{u’v’} , \, -\overbrace{\frac{\overline{v’\theta’}}{\partial\overline{\theta}/\partial{}p}\frac{1}{a\cos\phi}\frac{\partial{}(\overline{u}\cos\phi)}{\partial\phi}}^{\text{pr}}+\frac{\overline{v’\theta’}}{\partial{}\overline{\theta}/\partial{}p}f-\overbrace{\overline{\omega’u’} }^{\text{pr}}\right\} $$

For a reference with these equations, although in a slightly different form, refer to Martineau, P., Wright, J. S., Zhu, N. and Fujiwara, M.: Zonal-mean data set of global atmospheric reanalyses on pressure levels, Earth Syst. Sci. Data, 10(4), 1925–1941, doi:10.5194/essd-10-1925-2018, 2018.

Wavenumber decompositions are provided for EP-flux in the NetCDF files in the following order: full field, wavenumber 1, wavenumber 2

tem-thermo: thermodynamic equation from the transformed Eulerian mean

Symbol	Description	NetCDF name	Units
$-\overline{v}^*\frac{1}{a}\frac{\partial\overline{\theta}}{\partial{}\phi}$	Advection of potential temperature by the meridional residual circulation	theta_adv_by_vres	$K \,s^{-1}$
$ – \overline{\omega}^*\frac{\partial\overline{\theta}}{\partial{}p}$	Advection of potential temperature by the vertical residual circulation	theta_adv_by_wres	$K \,s^{-1}$
$-\frac{\partial}{\partial{}p}\left(\frac{\overline{v’\theta’}\frac{\partial\overline{\theta}}{\partial\phi}}{a\frac{\partial\overline{\theta}}{\partial{}p}}+\overline{\omega’\theta’}\right)$	Potential temperature tendency due to eddy fluxes	flux_term	$K \,s^{-1}$

In the transformed Eulerian mean, the thermodynamic equation takes the following form:

$$\frac{\partial\overline{\theta}}{\partial{}t} = \overbrace{-\overline{v}^*\frac{1}{a}\frac{\partial\overline{\theta}}{\partial{}\phi}}^{\text{theta_adv_by_vres}} \underbrace{- \overline{\omega}^*\frac{\partial\overline{\theta}}{\partial{}p}}_{\text{theta_adv_by_wres}}\overbrace{-\frac{\partial}{\partial{}p}\left(\frac{\overline{v’\theta’}\frac{\partial\overline{\theta}}{\partial\phi}}{a\frac{\partial\overline{\theta}}{\partial{}p}}+\overline{\omega’\theta’}\right)}^{\text{flux_term}}+Q$$

moist: diagnostics involving specific humidity

Symbol	Description	NetCDF name	Units
$\overline{q}$	Specific humidity	q	$kg\, kg^{-1}$
$\overline{v’q’}$	Meridional flux of specific humidity / meridional moisture flux	vq	$m\,s^{-1}\,kg\,kg^{-1}$
$\overline{\omega’q’}$	Vertical flux of specific humidity / vertical moisture flux	wq	$Pa\,s^{-1}\,kg\,kg^{-1}$

diab: diagnostics involving diabatic processes

Under development

Variable	Description	NetCDF name
Longwave heating	Diabatic heating by longwave radiation	ttlwhr
Shortwave heating	Diabatic heating by shorwave radiation	ttswhr
Diabatic heating	Diabatic heating	ttdiab

Single-level

Variable	Description	Levels (hPa)
$T$	Temperature	850
$q$	Specific humidity	850
$Z$	Geopotential height	500, 10
$u$	Eastward wind / zonal wind	850

Longitude-pressure

This component is under development, some files are available on our server.

Variable	Description	Latitudes
$T$	Temperature	0
$u$	Eastward wind / zonal wind	0
$v$	Northward wind / meridional wind	0

Surface

Under development