Sea Ice Diagnostics in ACCESS-ESM1.6¶

As far as possible, the default configurations of ACCESS-ESM1.6 output sea ice diagnostics in the format requested for CMIP7 as native output. This page describes the availability and interpretation of these diagnostics available in ACCESS-ESM1.6

Masking over time and space¶

It's import to note that CMIP 6/7 sea ice diagnostics are averaged using two different methods, as described in Notz et al. 2016:

• extensive : for variables proportional to sea ice concentation (area fraction), these are averaged over all time and ocean cells. These are marked with the cell_methods : area: mean where sea time: mean

• intensive : for variables not proportional to sea ice concentration, these are averaged only when there is sea ice in the cell. These are marked with cell_methods: area: time: mean where sea_ice (mask=siconc).

Using siflcondtop as an example, intensive diagnostics are calculated as:

$$ siflcondtop = \frac{\displaystyle\sum_{n=0}^N (aice * fcondtop)}{\displaystyle\sum_{n=0}^N (aice)} $$

where N is the number of timesteps in the averaging interval, aice is the sea ice fraction in the timestep, and fcondtop is the conductive heat flux in that timestep.

Therefore intensive variables should be interpreted as the average over only the proportion of the averaging interval that sea ice was present. It is possible to convert between extensive and intensive variables by multiplying by sea ice conentration averaged at the same frequency, which returns a grid cell average for the variable:

$$ siflcondtop * \frac{siconc}{100} = \frac{\displaystyle\sum_{n=0}^N (aice * fcondtop)}{\displaystyle\sum_{n=0}^N (aice)} * \frac{\displaystyle\sum_{n=0}^N (aice)} {N} = \frac{\displaystyle\sum_{n=0}^N (aice * fcondtop)} {N} $$

The use of intensive variables has the impact that sometimes diagnostics may have the same or similar descriptions but be masked differently.

e.g.

There are seperate ocean and sea ice variables labelled Water Flux into Sea Water Due to Sea Ice Thermodynamics

• siflfwbot is masked only where sea_ice (in time and space)
• fsithem (as an ocean diagnostic) is in all wet cells for all time

both are reported in kg m-2 s-1 but the areas and time they are calculated for are different

Thickness

• sivol is Sea-Ice Volume per Area, calculated using grid cell area
• sithick is a true Sea-Ice Thickness (alternative description would be Sea Ice Volume per Sea Ice Area)

both are repored in m

In the sections below, we provide some general comment and validation of diagnostics, split into groupings by diagnostic purpose

Load Data¶

To demonstrate some concepts, we are going to load some data.

In [1]:

PATH = "/g/data/tm70/as2285/payu/esm1.6/401/401-dev-preindustrial+concentrations/archive/output000/"

import xarray as xr
import cf_xarray
from matplotlib import pyplot as plt

In [2]:

daily_ds = xr.open_mfdataset(f'{PATH}/ice/iceh-1daily-mean_*.nc', decode_times=xr.coders.CFDatetimeCoder(use_cftime=True))

monthly_ds = xr.open_mfdataset(f'{PATH}/ice/iceh-1monthly-mean_*.nc', decode_times=xr.coders.CFDatetimeCoder(use_cftime=True))

ds = monthly_ds.isel(time=0)

In [3]:

# divide hemishperes exactly
NJ = len(ds.nj)
sh = {'slice':slice(0,int(NJ/2)), 'name':'sh', 'title':'Antarctic'}
nh = {'slice':slice(int(NJ/2),None), 'name':'nh', 'title':'Arctic'}

Mass / Concentrations¶

The CICE5 configuration of ACCESS-ESM1.6 uses fixed densities for sea ice, sea water and snow:

In [4]:

rhos      = 330.0  # density of snow (kg/m^3)
rhoi      = 917.0  # density of ice (kg/m^3)
rhow      = 1026.0 # density of seawater (kg/m^3)

You can also check these through the diagnostics, for example, sea ice mass divided by volume shows constant density:

In [5]:

plt.figure(figsize=(5,4))
(ds.simass/ds.sivol).plot(cbar_kwargs={'label':'density of sea-ice, $kg/m^3$'})
plt.title('Sea Ice Mass/Volume')
plt.show()

/g/data/xp65/public/apps/med_conda/envs/analysis3-25.09/lib/python3.11/site-packages/dask/_task_spec.py:764: RuntimeWarning: invalid value encountered in divide
  return self.func(*new_argspec)

Using these densities, mass and volume terms balance :

• $sivol*rhoi = simass$ (sivol and simass are extensive)
• $sisnthick* \frac{siconc}{100}*rhos = sisnmass$. (sisnthick is intensive and sisnmass is extensive)

ACCESS-ESM1.6 uses a fixed salinity for sea ice of 4 g/kg. Therefore:

• $sisalt = simass * 0.004$

Sea ice freeboad, thickness and snow thickness should balance to rounding error following Archimedes principal of buoyancy. On the LHS we have mass of snow and sea ice together. On the RHS we have mass of sea water displaced, calculated as the volume of sea ice below the surface multiplied by density of water

$simass+sisnmass = (sithick-sifb)*rhow$

sithick, sisnthick, sifb are all weighted by ice fraction in time, and presented as $kg/m^2$

In [6]:

plt.figure(figsize=(5,4))
(ds.simass+ds.sisnmass-(ds.sithick-ds.sifb)*ds.siconc/100*rhow).plot()
plt.title('Difference between mass of (sea ice + snow) and mass of water displaced')
plt.show()

Temperatures¶

Heat flux and sea ice surface temperature are calculated within the atmosphere model, and are not prognostic in the sea ice model component. Therefore sea ice surface temperature (sitemptop) and snow-ice interface temperature (sitempsnic) are not available as sea ice diagnostics. There is an sea ice surface temperature in the atmosphere diagnostics (surface_temperature - UM stash code - s00i508). This is an average of the surface temperature of the sea ice portion of the cell only. This is different to the CMIP variable for sitemptop (which should be weighted by sea ice concentration over time as its an intensive variable).

(N.B. s00i508 is the surface temperature over sea ice only, even when sea ice only fill parts of the grid cell. However for open ocean without sea ice, the diagnostic is arbitrarily set to -1.8°C - the approximate freezing point of the ocean. The open ocean and land values for this diagnostic don't have a realistic meaning, and should be masked out for analysis.)

In [7]:

atm_ds = xr.open_mfdataset(f'{PATH}/atmosphere/netCDF/aiihca.pa-*01_mon.nc', decode_times=xr.coders.CFDatetimeCoder(use_cftime=True))

In [8]:

plt.figure(figsize=(4,3))
((atm_ds['fld_s00i508'].where(atm_ds['fld_s00i031']>0))-273.15).plot() #mask where sea ice area fraction is 0
plt.title('Sea ice surface temperature diagnostic')

Out[8]:

Text(0.5, 1.0, 'Sea ice surface temperature diagnostic')

Sea ice bottom temperature (sitempbot) is available and is equal to the freezing point of sea water. The freezing point is calculated as :

$Tf = - sss * depressT$ where depressT is 0.054°/ppt

Heat Fluxes¶

There is no process for penetrating shortwave through sea ice (sifswdbot is zero). The sea ice thermodynamic model is zero-layer, so top and bottom conductive heat flux are equal (siflcondtop = siflcondbot)

There is no heat flux diagnostic for frazil melt potential but there is a diagnostic for Sea-Ice Mass Change Through Growth in Supercooled Open Water (Frazil) (sidmassgrowthwat)

We report surface fluxes as atmospheric diagnostics only:

Var Name	Description	Stash Code
rsds	Surface Downwelling Shortwave Radiation	s01i235
rsus	Surface Upwelling Shortwave Radiation	*
rlds	Surface Downwelling Longwave Radiation	s02i207
rlus	Surface Upwelling Longwave Radiation	*
hfss	Surface Upward Sensible Heat Flux	s03i217
hfls	Surface Upward Latent Heat Flux	s03i234

These are extensive diagnostics on the atmosphere grid, which include the ocean, sea ice and land fraction in the same variable. The intensive form, as requested for SIMIP variables, is not available (i.e. sifllattop, sifllwdtop, sifllwutop, siflsenstop, siflswdtop, siflswutop are not provided). Where marked with * - variables are only available through post-processing.

The heat fluxes siflsensbot, siflcondtop and siflcondbot are available (note they are intensive diagnostics)

Salt / Water Fluxes¶

The sea ice diagnostic siflfwbot (Freshwater Flux from Sea Ice) is intensive, and different from the ocean diagnostic fsitherm (Water Flux into Sea Water Due to Sea Ice Thermodynamics) which is extensive. We attempt to balance sea and ice diagnostics of salt and water fluxes below. They are close but not an exact match.

We use split fsitherm into wfimelt and wfiform for water fluxes associated with melting (of sea ice and snow) and forming sea ice. (i.e. $fsitherm = wfimelt + wfiform$)

Open some ocean diagnostics:

In [9]:

wfimelt = xr.open_mfdataset(f'{PATH}/ocean/ocean-2d-wfimelt-1monthly-mean-ym_*_01.nc', decode_times=xr.coders.CFDatetimeCoder(use_cftime=True), decode_timedelta=True)
wfiform = xr.open_mfdataset(f'{PATH}/ocean/ocean-2d-wfiform-1monthly-mean-ym_*_01.nc', decode_times=xr.coders.CFDatetimeCoder(use_cftime=True), decode_timedelta=True)
ocean_tarea = xr.open_dataset(f'{PATH}/ocean/ocean-2d-area_t.nc', decode_times=xr.coders.CFDatetimeCoder(use_cftime=True))

First we compare ocean and sea ice diganostics for sea ice formation

In [10]:

plt.figure(figsize=(10,4))
for i,hemi in enumerate([sh,nh], start =1):
    plt.subplot(1,2,i)
    ((monthly_ds.sidmassgrowthwat+monthly_ds.sidmassgrowthbot)*monthly_ds.tarea
        ).sel(nj=hemi['slice']).sum(['ni','nj']).plot(label='Sea Ice Growth from Seawater')

    (-1*wfiform.wfiform*ocean_tarea.area_t
        ).isel(yt_ocean=hemi['slice']).sum(['xt_ocean','yt_ocean']).plot(label='Ocean Freshwater Removed')

    plt.legend()
    plt.ylabel('Freshwater change (kg)')
    plt.title(hemi['title'])

plt.show()

And we compare ocean and sea ice diganostics for melt

In [11]:

plt.figure(figsize=(10,4))
for i,hemi in enumerate([sh,nh], start =1):
    plt.subplot(1,2,i)
    ((
     monthly_ds.sisndmassmelt
     + monthly_ds.sidmassmelttop
     + monthly_ds.sidmassmeltbot
     + monthly_ds.sidmassmeltlat
     )*monthly_ds.tarea).sel(nj=hemi['slice']).sum(['ni','nj']).plot(label='Sea Ice Melt Into Ocean')

    (-1*wfimelt.wfimelt*ocean_tarea.area_t
        ).isel(yt_ocean=hemi['slice']).sum(['xt_ocean','yt_ocean']).plot(label='Ocean Diagnostic')

    plt.legend()
    plt.ylabel('Freshwater change (kg)')
    plt.title(hemi['title'])

plt.show()

Salt is only transferred between the ocean and sea ice, there is no salt fluxes into or out of the atmosphere. ACCESS-ESM1.6 uses fixed salinity in sea ice, therefore all mass change in sea ice has a corresponding salt flux in the ocean (even though mass change can occur without a freshwater flux, e.g. if due to sno->ice conversion or evaporation/sublimation).

The sea ice diagnostic sidmassth equals the ocean diagnostic sfc_salt_flux_ice divided by 0.004. This is should be true in all areas - we see differences in the order of $1e-6 kg/m^2$ (~5%) in cells around the outer ice edge, possibly as the sea ice and ocean diagnostics will be offset by one model timestep from each other.

In [12]:

salt = xr.open_mfdataset(f'{PATH}/ocean/ocean-2d-sfc_salt_flux_ice-1monthly-mean-ym_*_01.nc', decode_times=xr.coders.CFDatetimeCoder(use_cftime=True), decode_timedelta=True)

In [13]:

plt.pcolor((monthly_ds.sidmassth.isel(time=0).values+(salt.sfc_salt_flux_ice/0.004).isel(time=0).values))
plt.colorbar()

Out[13]:

<matplotlib.colorbar.Colorbar at 0x146cb928fcd0>

In [14]:

plt.figure(figsize=(10,4))
for i,hemi in enumerate([sh,nh], start=1):
    plt.subplot(1,2,i)
    (monthly_ds.sidmassth*monthly_ds.tarea).sel(nj=hemi['slice']).sum(['ni','nj']).plot(label='Sea Ice Mass Change from Thermodynamics')

    (-1*salt.sfc_salt_flux_ice/0.004*ocean_tarea.area_t).isel(yt_ocean=hemi['slice']).sum(['xt_ocean','yt_ocean']).plot(label='Salt Flux / 0.004')

    plt.legend()
    plt.ylabel('Sea ice mass change (kg)')
    plt.title(hemi['title'])

plt.show()

Dynamics¶

By convention, diagnostics follow the same spatial discretisation as prognostic calculations within the model. CICE5 uses a generalised orthogonal B-grid as described in Murray 1996 or Smith, Korta and Meltz 1995. The ice and snow area, volume and energy are given at the centre of the cell, whilst velocity is defined at the corners. For diagnostics which combined quantities at cell centres and corners, e.g. mass transport, these are reported at the centre of the cell.

At cell centers:

Var Name	Description
sidmassdyn	Sea-Ice Mass Change from Dynamics
sidmasstranx	X-Component of Sea-Ice Mass Transport
sidmasstrany	Y-Component of Sea-Ice Mass Transport

sidmassdyn is the change in mass in a cell due to dynamics. Sea ice mass transport (sidmasstran) is calculated as a rate of transport through the right (positive x) and top (positive y) edge of the cell. The sidmasstran terms are calculated as $velocity * celledgelength*rhoi$, where velocity is a mean of the velocity in the relevant corners of the cell to reflect an average velocity across the edge.

These quantities are all reported on the corner points :

Var Name	Description
sicompstren	Compressive Sea Ice Strength
sistrxdtop	X-Component of Atmospheric Stress on Sea Ice
sistrxubot	X-Component of Ocean Stress on Sea Ice
sistrydtop	Y-Component of Atmospheric Stress on Sea Ice
sistryubot	Y-Component of Ocean Stress on Sea Ice

Sea ice mass change from dynamics sums to zero (with rounding error) for each hemisphere as sea ice mass is conserved during sea ice dynamics processes.

In [15]:

plt.figure(figsize=(5,4))
for hemi in [sh,nh]:
    (monthly_ds.sidmassdyn*monthly_ds.tarea).isel(nj=hemi['slice']).sum(['ni','nj']).plot(label = hemi['title']+' Sea Ice Mass Change')
plt.ylabel('Change in Mass, kg')
plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.title('Mass change from sea ice dynamics')
plt.show()

Snow is not conserved during sea ice dynamics

In [16]:

for hemi in [sh,nh]:
    (monthly_ds.sisndmassdyn*monthly_ds.tarea).isel(nj=hemi['slice']).sum(['ni','nj']).plot(label = hemi['title']+' Snow Mass Change')

plt.ylabel('Change in Mass, kg')
plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))
plt.title('Snow Mass change from sea ice dynamics')
plt.show()

Thermodynamics¶

The diagnostic for evaporation and sublimation can be positive in some model cells (i.e. mass gain) whilst as the sum for each hemisphere is negative (mass loss). This is for two reasons, firstly (sidmassevapsubl) can include condensation and deposition (desublimation). In addition, the evaporation flux is calculated within the atmosphere model, on the atmosphere grid, and conservatively regridded to the sea ice grid. Conservative regridding can lead to sign changes in some cells.

Diagnostics for Sea ice mass change are extensive

Var Name	Description
sidmassth	Sea-Ice Mass Change from Thermodynamics

is the sum of

Var Name	Description
sidmassgrowthbot	Sea-Ice Mass Change Through Basal Growth
sidmassgrowthsi	Sea-Ice Mass Change Through Snow-to-Ice Conversion
sidmassgrowthwat	Sea-Ice Mass Change Through Growth in Supercooled Open Water (Frazil)
sidmassmeltbot	Sea-Ice Mass Change Through Bottom Melting
sidmassmeltlat	Sea-Ice Mass Change Through Lateral Melting
sidmassmelttop	Sea-Ice Mass Change Through Surface Melting
sidmassevapsubl	Sea-Ice Mass Change Through Evaporation and Sublimation

In [17]:

plt.figure(figsize=(5,4))
for hemi in [sh,nh]:
    ((   monthly_ds.sidmassgrowthwat
     + monthly_ds.sidmassgrowthbot
     + monthly_ds.sidmassgrowthsi
     + monthly_ds.sidmassevapsubl
     + monthly_ds.sidmassmelttop
     + monthly_ds.sidmassmeltbot
     + monthly_ds.sidmassmeltlat
    )*monthly_ds.tarea).isel(nj=hemi['slice']).sum(['ni','nj']).plot(label = hemi['title']+' Sum')
    (monthly_ds.sidmassth*monthly_ds.tarea).isel(nj=hemi['slice']).sum(['ni','nj']).plot(
        label = hemi['title']+' sidmasstherm', linestyle='--')

plt.title('Change in mass due to thermodynamics')
plt.ylabel('sea ice mass change, $kg/m^2$')
plt.legend()
plt.show()

Similarly, siflfwbot should balance with the relevant sidmass terms. This is not an exact match, so maybe the sidmass terms are missing snow into the ocean due to ridging and rain on sea-ice which do get included into siflfwbot. Rain passes straight through the sea ice and into the ocean, so sipr is not provided, however siflfwbot includes rain passing through the sea-ice.

In [18]:

plt.figure(figsize=(10,4))
for i,hemi in enumerate([sh,nh], start=1):
    plt.subplot(1,2,i)

    ((   monthly_ds.sidmassgrowthwat
     + monthly_ds.sidmassgrowthbot
     + monthly_ds.sidmassmelttop
     + monthly_ds.sidmassmeltbot
     + monthly_ds.sidmassmeltlat
     + monthly_ds.sisndmassmelt
    )*monthly_ds.tarea).isel(nj=hemi['slice']).sum(['ni','nj']).plot(label = hemi['title']+' Sum')
    (-1*monthly_ds.siflfwbot*monthly_ds.siconc/100*monthly_ds.tarea).isel(nj=hemi['slice']).sum(['ni','nj']).plot(label = hemi['title']+' siflfwbot')

    plt.ylabel('mass change, $kg/m^2$')
    plt.legend()

plt.suptitle('Change in mass due to siflfwbot')
plt.show()

Snow¶

We do not provide snow area fraction (sisnconc) or snow thickness (sisnthick) as they are prognostic only in the atmosphere model.

There is no process for blown snow on sea ice, so sisndmasswind (Snow Mass Rate of Change Through Wind Drift of Snow) is not reported. There are no melt ponds.

Variables for snow are generally masked for when there is sea ice (i.e. intensive)

There is no overall CMIP diagnostic for snow mass rate of change, however the sum of the following diagnostics should be the rate of snow accumulation for each hemisphere.

Var Name	Description
sisndmassmelt	Snow Mass Rate of Change Through Melt
sisndmasssi	Snow Mass Rate of Change Through Snow-to-Ice Conversion
sisndmasssnf	Snow Mass Change Through Snowfall
sisndmasssubl	Snow Mass Rate of Change Through Evaporation or Sublimation

In [19]:

plt.figure(figsize=(10,4))
for i,hemi in enumerate([sh,nh], start=1):
    plt.subplot(1,2,i)

    (( + monthly_ds.sisndmassmelt
      + monthly_ds.sisndmasssi
      + monthly_ds.sisndmasssnf
      + monthly_ds.sisndmasssubl
     )*monthly_ds.tarea).isel(nj=hemi['slice']).sum(['ni','nj']).plot(label = 'Snow diags sum (kg)')
    ((monthly_ds.dvsdtt/86400*rhos/100)*monthly_ds.tarea).isel(nj=hemi['slice']).sum(['ni','nj']).plot(
        label = 'dvsdtt * density (kg)', linestyle='--')
    plt.legend()
    plt.title(hemi['title'])
plt.show()

In CICE, Snow-to-Ice conversion only occurs when the weight of the snow pushes the sea ice below the water level (i.e. freeboard is negative) and the mass of snow is directly converted to a mass of sea ice. The process is adiabiatic, there is no energy exchanged in the process. However sidmassgrowthsi is not equal to sisndmasssi as sidmassgrowthsi is extensive and sisndmasssi is intensive.

Hemispheric Scalars¶

Diagnostics which do not have a spatial coordinate are only available via post-processings:

Var Name	Description
siareaacrossline	Sea-Ice Area Flux Through Straits
simassacrossline	Sea-Ice Mass Flux Through Straits
siarean	Sea-Ice Area North
siareas	Sea-Ice Area South
siextentn	Sea-Ice Extent North
siextents	Sea-Ice Extent South
sisnmassn	Snow Mass on Sea Ice North
sisnmasss	Snow Mass on Sea Ice South
sivoln	Sea-Ice Volume North
sivols	Sea-Ice Volume South