Analysis of Veros output

In this tutorial, we will use xarray and matplotlib to load, analyze, and plot the model output. We will also use the cmocean colormaps. You can run these commands in IPython or a Jupyter Notebook. Just make sure to install the dependencies first:

$ pip install xarray matplotlib netcdf4 cmocean

The analysis below is performed for 100 yr integration of the global_4deg setup from the setup gallery.

If you want to run this analysis yourself, you can download the data here. We access the files through the dictionary OUTPUT_FILES, which contains the paths to the 4 different files:

In [1]: OUTPUT_FILES = {
   ...:     "snapshot": "4deg.snapshot.nc",
   ...:     "averages": "4deg.averages.nc",
   ...:     "overturning": "4deg.overturning.nc",
   ...:     "energy": "4deg.energy.nc",
   ...: }
   ...: 

Let’s start by importing some packages:

In [2]: import xarray as xr

In [3]: import numpy as np

In [4]: import cmocean

Most of the heavy lifting will be done by xarray, which provides a data structure and API for working with labeled N-dimensional arrays. xarray datasets automatically keep track how the values of the underlying arrays map to locations in space and time, which makes them immensely useful for analyzing model output.

Load and manipulate averages

In order to load our first output file and display its content execute the following two commands:

In [5]: ds_avg = xr.open_dataset(OUTPUT_FILES["averages"])

In [6]: ds_avg
Out[6]: 
<xarray.Dataset>
Dimensions:       (Time: 10, isle: 6, nmonths: 12, yu: 40, xu: 90, zt: 15,
                   yt: 40, xt: 90, tensor1: 2, tensor2: 2, zw: 15)
Coordinates:
  * Time          (Time) timedelta64[ns] 32760 days 33120 days ... 36000 days
  * isle          (isle) float64 0.0 1.0 2.0 3.0 4.0 5.0
  * nmonths       (nmonths) float64 0.0 1.0 2.0 3.0 4.0 ... 8.0 9.0 10.0 11.0
  * tensor1       (tensor1) float64 0.0 1.0
  * tensor2       (tensor2) float64 0.0 1.0
  * xt            (xt) float64 2.0 6.0 10.0 14.0 ... 346.0 350.0 354.0 358.0
  * xu            (xu) float64 4.0 8.0 12.0 16.0 ... 348.0 352.0 356.0 360.0
  * yt            (yt) float64 -78.0 -74.0 -70.0 -66.0 ... 66.0 70.0 74.0 78.0
  * yu            (yu) float64 -76.0 -72.0 -68.0 -64.0 ... 68.0 72.0 76.0 80.0
  * zt            (zt) float64 -4.855e+03 -4.165e+03 -3.575e+03 ... -65.0 -35.0
  * zw            (zw) float64 -4.51e+03 -3.87e+03 -3.28e+03 ... -50.0 0.0
Data variables:
    psi           (Time, yu, xu) float64 ...
    salt          (Time, zt, yt, xt) float64 ...
    surface_taux  (Time, yt, xu) float64 ...
    surface_tauy  (Time, yu, xt) float64 ...
    temp          (Time, zt, yt, xt) float64 ...
    u             (Time, zt, yt, xu) float64 ...
    v             (Time, zt, yu, xt) float64 ...
    w             (Time, zw, yt, xt) float64 ...
Attributes:
    date_created:      2021-10-26T12:02:31.193084
    veros_version:     1.4.2
    setup_identifier:  4deg
    history:           Thu Oct 28 16:05:51 2021: ncks -d Time,90,99 4deg.aver...
    NCO:               netCDF Operators version 4.8.0 (Homepage = http://nco....

We can easily access/modify individual data variables and their attributes. To demonstrate this let’s convert the units of the barotropic stream function from \(\frac{m^{3}}{s}\) to \(Sv\):

In [7]: ds_avg["psi"] = ds_avg.psi / 1e6

In [8]: ds_avg["psi"].attrs["units"] = "Sv"

Now, we select the last time slice of psi and plot it:

In [9]: ds_avg["psi"].isel(Time=-1).plot.contourf(levels=50, cmap="cmo.balance")
Out[9]: <matplotlib.contour.QuadContourSet at 0x7f1fb9059340>
../_images/psi.png

In order to compute the decadal mean (of the last 10yrs) of zonal-mean ocean salinity use the following command:

In [10]: (
   ....:     ds_avg["salt"]
   ....:     .isel(Time=slice(-10,None))
   ....:     .mean(dim=("Time", "xt"))
   ....:     .plot.contourf(levels=50, cmap="cmo.haline")
   ....: )
   ....: 
Out[10]: <matplotlib.contour.QuadContourSet at 0x7f1fb6e6a2e0>
../_images/salt.png

One can also compute meridional mean temperature. Since the model output is defined on a regular latitude / longitude grid, the grid cell area decreases towards the pole. To get an accurate mean value, we need to weight each cell by its area:

In [11]: ds_snap = xr.open_dataset(OUTPUT_FILES["snapshot"])

# use cell area as weights, replace missing values (land) with 0
In [12]: weights = ds_snap["area_t"].fillna(0)

Now, we can calculate the meridional mean temperature (via xarray’s .weighted method) and plot it:

In [13]: temp_weighted = (
   ....:     ds_avg["temp"]
   ....:     .isel(Time=-1)
   ....:     .weighted(weights)
   ....:     .mean(dim="yt")
   ....:     .plot.contourf(vmin=-2, vmax=22, levels=25, cmap="cmo.thermal")
   ....: )
   ....: 
../_images/temp.png

Explore overturning circulation

In [14]: ds_ovr = xr.open_dataset(OUTPUT_FILES["overturning"])

In [15]: ds_ovr
Out[15]: 
<xarray.Dataset>
Dimensions:      (Time: 100, zw: 15, yu: 40, isle: 6, nmonths: 12, sigma: 60,
                  tensor1: 2, tensor2: 2, xt: 90, xu: 90, yt: 40, zt: 15)
Coordinates:
  * Time         (Time) timedelta64[ns] 360 days 720 days ... 36000 days
  * isle         (isle) float64 0.0 1.0 2.0 3.0 4.0 5.0
  * nmonths      (nmonths) float64 0.0 1.0 2.0 3.0 4.0 ... 7.0 8.0 9.0 10.0 11.0
  * sigma        (sigma) float64 5.804 5.934 6.064 6.195 ... 13.23 13.36 13.49
  * tensor1      (tensor1) float64 0.0 1.0
  * tensor2      (tensor2) float64 0.0 1.0
  * xt           (xt) float64 2.0 6.0 10.0 14.0 18.0 ... 346.0 350.0 354.0 358.0
  * xu           (xu) float64 4.0 8.0 12.0 16.0 20.0 ... 348.0 352.0 356.0 360.0
  * yt           (yt) float64 -78.0 -74.0 -70.0 -66.0 ... 66.0 70.0 74.0 78.0
  * yu           (yu) float64 -76.0 -72.0 -68.0 -64.0 ... 68.0 72.0 76.0 80.0
  * zt           (zt) float64 -4.855e+03 -4.165e+03 -3.575e+03 ... -65.0 -35.0
  * zw           (zw) float64 -4.51e+03 -3.87e+03 -3.28e+03 ... -120.0 -50.0 0.0
Data variables:
    bolus_depth  (Time, zw, yu) float64 ...
    bolus_iso    (Time, zw, yu) float64 ...
    trans        (Time, sigma, yu) float64 ...
    vsf_depth    (Time, zw, yu) float64 ...
    vsf_iso      (Time, zw, yu) float64 ...
    zarea        (Time, zt, yu) float64 ...
Attributes:
    date_created:      2021-10-26T12:02:33.542479
    veros_version:     1.4.2
    setup_identifier:  4deg

Let”s convert the units of meridional overturning circulation (MOC) from \(\frac{m^{3}}{s}\) to \(Sv\) and plot it:

In [16]: ds_ovr["vsf_depth"] = ds_ovr.vsf_depth / 1e6

In [17]: ds_ovr.vsf_depth.attrs["long_name"] = "MOC"

In [18]: ds_ovr.vsf_depth.attrs["units"] = "Sv"

In [19]: ds_ovr.vsf_depth.isel(Time=-1).plot.contourf(levels=50, cmap="cmo.balance")
Out[19]: <matplotlib.contour.QuadContourSet at 0x7f1fb6b5e940>
../_images/vsf_depth_2d.png

Plot time series

Let’s have a look at the Time coordinate of the dataset:

In [20]: ds_ovr["Time"].isel(Time=slice(10,))
Out[20]: 
<xarray.DataArray 'Time' (Time: 10)>
array([ 31104000000000000,  62208000000000000,  93312000000000000,
       124416000000000000, 155520000000000000, 186624000000000000,
       217728000000000000, 248832000000000000, 279936000000000000,
       311040000000000000], dtype='timedelta64[ns]')
Coordinates:
  * Time     (Time) timedelta64[ns] 360 days 720 days ... 3240 days 3600 days
Attributes:
    long_name:    Time
    time_origin:  01-JAN-1900 00:00:00

We can see that it has the type np.timedelta64, which by default has a resolution of nanoseconds. In order to have a more meaningful x-axis in our figures, we add another coordinate “years” by dividing Time by the length of a year (360 days in Veros):

In [21]: years = ds_ovr["Time"] / np.timedelta64(360, "D")

In [22]: ds_ovr = ds_ovr.assign_coords(years=("Time", years.data))

Let’s select values of array by labels instead of index location and plot a time series of the overturning minimum between 40°N and 60°N and 550-1800m depth, with years on the x-axis:

In [23]: (
   ....:     ds_ovr.vsf_depth
   ....:     .sel(zw=slice(-1810., -550.), yu=slice(40., 60.))
   ....:     .min(dim=("yu", "zw"))
   ....:     .plot(x="years")
   ....: )
   ....: 
Out[23]: [<matplotlib.lines.Line2D at 0x7f1fb69f63a0>]
../_images/vsf_depth_min.png