Air Sea Exchange¶

import xarray as xr
from matplotlib import pyplot as plt
import numpy as np
import gsw
import pooch
import cartopy.crs as ccrs
import hvplot.xarray
import hvplot.pandas
import re

%matplotlib inline
%config InlineBackend.figure_format = 'retina'
plt.rcParams['figure.figsize'] = (15,9)
plt.rcParams['font.size'] = 16
#plt.rcParams['lines.linewidth'] = 3
from IPython.display import SVG, display, Image, display_svg, YouTubeVideo

opts = dict(geo=True, frame_width=800, frame_height=420, projection=ccrs.Robinson(), coastline=True, legend=False ,features={'land': '110m'})

As anyone who has been to sea knows, the interface between ocean and atmosphere can be an incredibly violent place. Within a hurricane, for example, it is in fact impossible to draw a clear boundary between ocean and atmosphere; the extreme winds whip up a continuous emulsion of air and water. Nevertheless, outside of such extreme cases, there exist robust and relatively simple equations for describing the exchange of heat, freshwater, and momentum between atmosphere and ocean.

display(YouTubeVideo("BhduxaGtNJ8", width=640, height=480))

Atmospheric Circulation¶

Although this is an oceanography class, this topic requires us to know a bit about the atmosphere. We must have some grasp of the patterns of global atmospheric circulation in order to interpret the patterns of cloud, precipitation, and evaporation which influence air-sea interaction.

Hadley Circulation¶

The large-scale atmospheric circulation is shown in this figure:

Kaidor, CC BY-SA 3.0 https://creativecommons.org/licenses/by-sa/3.0, via Wikimedia Commons

Major important feature of the global circulation include:

Two overturning ciruclation cells (Hadley Cells) centered around the equator:
- Strong ascent near the equator (Intertropical Convergence Zone; ITCZ), which drives precipitation and cloud cover.
- Strong descent in the extratropics. The descending air comes from high in the atmosphere and is thus very dry. As a result, there is little rain and atmospheric moisture at these latitudes. This is why we have deserts.
Strong westerly winds in midlatitudes
Strong synoptic-scale storms in midlatitudes. These storms bring heavy wind gusts and precipitation to higher latitudes.

Heat Exchange¶

The heat content of the mixed layer (per unit area) is given by.

\[\mathcal{H} = h \rho c_p^0 \Theta \]

If the mixed layer is isolated from the interior, the first law of thermodynamics can be written as

\[ \frac{d \mathcal{H}}{dt} = Q \]

where \(Q\) is the air-to-sea heat flux.

Because density \(\rho\) only changes by a about 0.1% during air-sea interaction, it is reasonable to approximate \(\rho \simeq \rho_0\). If we further assume that the mixed layer depth \(h\) doesn’t change, we can write the heat equation as

\[ \frac{d \Theta}{d t} = \frac{Q}{h \rho_0 c_p^0} \]

Components of the Heat Flux¶

We divide the heat flux \(Q\) into four separate components associated with different physical processes.

\[ Q = \underbrace{Q_{sw}}_\text{shortwave radiation} + \underbrace{Q_{lw}}_\text{longwave radiation} + \underbrace{Q_{sh}}_\text{sensible heat flux} + \underbrace{Q_{lh}}_\text{latent heat flux} \]

registry = {
    "hfns11a.nc.Z": None,
    "hfls11a.nc.Z": None,
    "hfss11a.nc.Z": None,
    "rss11a.nc.Z": None,
    "rls11a.nc.Z": None
}
POOCH = pooch.create(
    path=pooch.os_cache("Grist_Josey_2003"),
    base_url="ftp://ftp.noc.soton.ac.uk/pub/sxj/clim/netcdf/",
    registry=registry
)

fnames = {fname: POOCH.fetch(fname) for fname in registry}

import unlzw3
def uncompress(input_fname):
    assert input_fname[-2:] == '.Z'
    output_fname = input_fname[:-2]
    with open(input_fname, "rb") as fp:
        uncompressed_data = unlzw3.unlzw(fp.read())
    with open(output_fname, "wb") as fp:
        fp.write(uncompressed_data)
    return output_fname

fnames_uncompressed = [uncompress(f) for f in fnames.values()]

noca = xr.open_mfdataset(fnames_uncompressed, combine='by_coords')
noca = noca.assign_coords({'month': noca.time.dt.month}).swap_dims({'time': 'month'})
noca

/srv/conda/envs/notebook/lib/python3.8/site-packages/xarray/coding/times.py:119: SerializationWarning: Ambiguous reference date string: 2-1-1 0. The first value is assumed to be the year hence will be padded with zeros to remove the ambiguity (the padded reference date string is: 0002-1-1 0). To remove this message, remove the ambiguity by padding your reference date strings with zeros.
  warnings.warn(warning_msg, SerializationWarning)
/srv/conda/envs/notebook/lib/python3.8/site-packages/xarray/coding/times.py:527: SerializationWarning: Unable to decode time axis into full numpy.datetime64 objects, continuing using cftime.datetime objects instead, reason: dates out of range
  dtype = _decode_cf_datetime_dtype(data, units, calendar, self.use_cftime)
/srv/conda/envs/notebook/lib/python3.8/site-packages/xarray/core/indexing.py:572: SerializationWarning: Unable to decode time axis into full numpy.datetime64 objects, continuing using cftime.datetime objects instead, reason: dates out of range
  return np.asarray(array[self.key], dtype=None)

<xarray.Dataset>
Dimensions:    (latitude: 170, longitude: 360, month: 12)
Coordinates:
    time       (month) object 0002-01-01 00:00:00 ... 0002-12-01 00:00:00
  * longitude  (longitude) float64 -179.5 -178.5 -177.5 ... 177.5 178.5 179.5
  * latitude   (latitude) float64 -84.5 -83.5 -82.5 -81.5 ... 82.5 83.5 84.5
  * month      (month) int64 1 2 3 4 5 6 7 8 9 10 11 12
Data variables:
    hfls11a    (month, latitude, longitude) float32 dask.array<chunksize=(12, 170, 360), meta=np.ndarray>
    hfns11a    (month, latitude, longitude) float32 dask.array<chunksize=(12, 170, 360), meta=np.ndarray>
    hfss11a    (month, latitude, longitude) float32 dask.array<chunksize=(12, 170, 360), meta=np.ndarray>
    rls11a     (month, latitude, longitude) float32 dask.array<chunksize=(12, 170, 360), meta=np.ndarray>
    rss11a     (month, latitude, longitude) float32 dask.array<chunksize=(12, 170, 360), meta=np.ndarray>
Attributes:
    Conventions:  COARDS
    calendar:     standard
    comments:     Climatological estimate based on ship meteorological report...
    model:        
    center:       National Oceanography Centre, Southampton, UK

xarray.Dataset

Dimensions:
- latitude: 170
- longitude: 360
- month: 12

Coordinates: (4)

time

(month)

object

0002-01-01 00:00:00 ... 0002-12-...

array([cftime.DatetimeGregorian(2, 1, 1, 0, 0, 0, 0, has_year_zero=False),
       cftime.DatetimeGregorian(2, 2, 1, 0, 0, 0, 0, has_year_zero=False),
       cftime.DatetimeGregorian(2, 3, 1, 0, 0, 0, 0, has_year_zero=False),
       cftime.DatetimeGregorian(2, 4, 1, 0, 0, 0, 0, has_year_zero=False),
       cftime.DatetimeGregorian(2, 5, 1, 0, 0, 0, 0, has_year_zero=False),
       cftime.DatetimeGregorian(2, 6, 1, 0, 0, 0, 0, has_year_zero=False),
       cftime.DatetimeGregorian(2, 7, 1, 0, 0, 0, 0, has_year_zero=False),
       cftime.DatetimeGregorian(2, 8, 1, 0, 0, 0, 0, has_year_zero=False),
       cftime.DatetimeGregorian(2, 9, 1, 0, 0, 0, 0, has_year_zero=False),
       cftime.DatetimeGregorian(2, 10, 1, 0, 0, 0, 0, has_year_zero=False),
       cftime.DatetimeGregorian(2, 11, 1, 0, 0, 0, 0, has_year_zero=False),
       cftime.DatetimeGregorian(2, 12, 1, 0, 0, 0, 0, has_year_zero=False)],
      dtype=object)

longitude
(longitude)
float64
-179.5 -178.5 ... 178.5 179.5
units :
degrees_east
long_name :
Longitude
```
array([-179.5, -178.5, -177.5, ...,  177.5,  178.5,  179.5])
```

latitude

(latitude)

float64

-84.5 -83.5 -82.5 ... 83.5 84.5

units :: degrees_north
long_name :: Latitude

array([-84.5, -83.5, -82.5, -81.5, -80.5, -79.5, -78.5, -77.5, -76.5, -75.5,
       -74.5, -73.5, -72.5, -71.5, -70.5, -69.5, -68.5, -67.5, -66.5, -65.5,
       -64.5, -63.5, -62.5, -61.5, -60.5, -59.5, -58.5, -57.5, -56.5, -55.5,
       -54.5, -53.5, -52.5, -51.5, -50.5, -49.5, -48.5, -47.5, -46.5, -45.5,
       -44.5, -43.5, -42.5, -41.5, -40.5, -39.5, -38.5, -37.5, -36.5, -35.5,
       -34.5, -33.5, -32.5, -31.5, -30.5, -29.5, -28.5, -27.5, -26.5, -25.5,
       -24.5, -23.5, -22.5, -21.5, -20.5, -19.5, -18.5, -17.5, -16.5, -15.5,
       -14.5, -13.5, -12.5, -11.5, -10.5,  -9.5,  -8.5,  -7.5,  -6.5,  -5.5,
        -4.5,  -3.5,  -2.5,  -1.5,  -0.5,   0.5,   1.5,   2.5,   3.5,   4.5,
         5.5,   6.5,   7.5,   8.5,   9.5,  10.5,  11.5,  12.5,  13.5,  14.5,
        15.5,  16.5,  17.5,  18.5,  19.5,  20.5,  21.5,  22.5,  23.5,  24.5,
        25.5,  26.5,  27.5,  28.5,  29.5,  30.5,  31.5,  32.5,  33.5,  34.5,
        35.5,  36.5,  37.5,  38.5,  39.5,  40.5,  41.5,  42.5,  43.5,  44.5,
        45.5,  46.5,  47.5,  48.5,  49.5,  50.5,  51.5,  52.5,  53.5,  54.5,
        55.5,  56.5,  57.5,  58.5,  59.5,  60.5,  61.5,  62.5,  63.5,  64.5,
        65.5,  66.5,  67.5,  68.5,  69.5,  70.5,  71.5,  72.5,  73.5,  74.5,
        75.5,  76.5,  77.5,  78.5,  79.5,  80.5,  81.5,  82.5,  83.5,  84.5])

month

(month)

int64

1 2 3 4 5 6 7 8 9 10 11 12

array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12])

Data variables: (5)

hfls11a

(month, latitude, longitude)

float32