Transports Through Straits

Computing the depth-integrated volume transport through some major straits.

Theory

Formally, mass transports are given by

\[T_x = \rho u\]

\[T_y = \rho v\]

Mass transports are diagnostics that are calculated online by the model:

variable	long name	units	dimensions
tx_trans	T-cell i-mass transport	Sv	(time,st_ocean,xu_ocean,yt_ocean)
ty_trans	T-cell j-mass transport	Sv	(time,st_ocean,xt_ocean,yu_ocean)

Variable tx_trans contains the instantaneous zonal transport multiplied with \(y\)-\(z\) face of the volume of each cell:

tx_trans\(=T_{x}(x, y, z, t)\,\Delta y\,\Delta z\).

Similarly, tx_trans contains

ty_trans\(=T_{y}(x, y, z, t)\,\Delta x\,\Delta z\).

Thus, tx_trans and ty_trans variables come in units of \(\underbrace{kg\,m^{-3}}_{\rm density} \times \underbrace{m\,s^{-1}}_{\rm velocity}\times\underbrace{m^2}_{\rm area} = kg\,s^{-1}\). To get the volume transport (\(m^3\,s^{-1}\)) we have to divide by \(\rho\).

Calculation

import cosima_cookbook as cc
import matplotlib.pyplot as plt

from dask.distributed import Client

Load a dask client.

client = Client()
client

Client Scheduler: tcp://127.0.0.1:43263 Dashboard: /proxy/8787/status

Cluster Workers: 8 Cores: 48 Memory: 202.49 GB

Use default database for this calculation

session = cc.database.create_session()

This dictionary defines a few key choke points that you might be interested in. For the purposes of demonstration we are just using Drake Passage in this example.

straits = { 'DrakePassage': [-69.9, -69.9, -71.6, -51.0],
              'Lombok':     [-244.6+360, -243.9+360, -8.6, -8.6],
              'Ombai' :     [-235.0+360, -235.0+360, -9.2, -8.1],
              'Timor' :     [-235.9+360, -235.9+360, -11.9, -9.9],
              'Bering' :    [-172, -167, 65.8, 65.8],
              'Denmark' :   [-42, -22, 65.8, 65.8],
            }

Here we define a function so that you can specify a given strait, and rely on the function to extract the transport through that strait.

rho = 1036 # kg/m^3, mean density of seawater

def calc_transport(expt, strait):
    """
    Calculate barotropic transport across a given
     line of latitude or longitude.

    Designed for flow through straits.
    """

    xmin, xmax, ymin, ymax = straits[strait]

    if ymax>=65:
        raise ValueError('North of 65N the tripolar grid geometry brings complications and `.sum(''xt_ocean'')` is wrong!')

    print('Calculating {}:{} transport'.format(expt, strait))

    if xmin == xmax:
        tx_trans = cc.querying.getvar(expt,'tx_trans',session)
        transport = tx_trans.sel(xu_ocean=xmin, method='nearest')\
                            .sel(yt_ocean=slice(ymin, ymax))\
                            .sum('st_ocean').sum('yt_ocean')/rho/1e6 #divide by ρ to convert to volume transport, m^3/s, and with 1e6 to convert to Sv.

    elif ymin == ymax:
        ty_trans = cc.querying.getvar(expt,'ty_trans',session)
        transport = ty_trans.sel(yu_ocean=ymin, method='nearest')\
                            .sel(xt_ocean=slice(xmin, xmax))\
                            .sum('st_ocean').sum('xt_ocean')/rho/1e6 #divide by ρ to convert to volume transport, m^3/s, and with 1e6 to convert to Sv.
    else:
        raise ValueError('Transports are computed only along lines of either constant latitude or longitude')

    transport = transport.compute()

    return transport

Now, for a given experiment, calculate the total (barotropic) transport through Drake Passage:

    expt = '025deg_jra55v13_ryf9091_gmredi6'
transport = calc_transport(expt, 'DrakePassage')

Calculating 025deg_jra55v13_ryf9091_gmredi6:DrakePassage transport
CPU times: user 15.5 s, sys: 738 ms, total: 16.3 s
Wall time: 23.2 s

Plot the result

transport.plot(linestyle='-')
plt.title('Drake Passage Transport')
plt.xlabel('Year')
plt.ylabel('Transport (Sv)');

Download python script: Transport_Through_Straits.py

Download Jupyter notebook: Transport_Through_Straits.ipynb