Mixed layer module

Summary

This module updates the sea surface temperature (SST) noted as \(T_s\) below.

SST boundary condition options

The SST options are:

• prescribe SST from an input file (do_sc_sst namelist option).

• prescribe SST to follow an AquaPlanet Experiment protocol (APE) analytic form (do_ape_sst namelist option).

• calculate SST based on the surface fluxes and mixed layer depth of a slab ocean, with the option of including a Q-flux (either analytic or read from a file).

Note that only the final case will generate a closed surface energy budget. Each of these options are discussed below, followed by an outline of the implicit time-stepping process used when SST is not prescribed.

Input SST file

Set do_sc_sst to True if you want to specify the SST field. The SST field will be read in from a NetCDF file with a file name specified by the sst_file variable. Using an input SST field is useful, for example, when you want to add a temperature anomaly. The file is read in during the initialisation (i.e. within the call to mixed_layer_init from within idealized_moist_phys). The input file can be time independent (i.e. no diurnal or seasonal cycle or any changes in the SST from one time step to another) or vary with time. More information can be found in the Diagnostics section below.

APE aquaplanet (analytic SST)

The prescribed SST for the APE aquaplanet protocol is given by:

\[T_s = 27 \left( 1 - \sin^2\left( \frac{3}{2} \lambda \right) \right),\]

between 60N-60S, equation 1 of Neele and Hoskins 2004 [NealeHoskins2004], and 0 deg C poleward of 60N/S.

Slab ocean

To allow the SST to evolve based on the surface fluxes, the atmosphere can be coupled to a slab ocean, whose depth is specified by the namelist parameter depth. This also allows a closed surface energy budget, useful for e.g. simulations with increased greenhouse gases.

In this case, during the initialisation, if there is no restart file to open, the surface temperature is set to the prescribed initial distribution (prescribe_initial_dist = True):

\[T_s = T_{surf} -\frac{1}{3} dT \left(3\sin(\lambda)^2-1\right),\]

where the default values we use in the trip test for the Frierson test case (exp/test_cases/frierson/frierson_test_case.py) are: \(T_{surf} = 285 K\) and \(dT = 40 K\).

This form of \(T_{surf}\) is similar to a 2nd legendre polynomial, it is a parabola that maximises at the equator.

Implicit timestepping procedure

The mixed layer module calculates the evolution of surface temperature using an implicit timestep. Whereas an explicit method uses the current state of the system to calculate the state of the system at the next timestep, an implicit method uses the inferred state of the system at the next timestep.

The net flux into the surface is given by:

net_surf_sw_down + surf_lw_down - flux_r - SH - LH + ocean_qflux

where net_surf_sw_down is the net shortwave radiation into the surface, surf_lw_down the downwelling longwave radiation into the surface, and flux_r the upwelling longwave radiation at the surface. The sensible heat (SH) is the sum of the surface sensible heat flux and the temperature diffusion flux. The latent heat (LH) is the sum of the surface latent heat and the moisture diffusion flux (only included if evaporation is true). The ocean_flux is an optional term and is zero if the Q-flux is not used.

If do_calc_eff_heat_cap is True, the land_sea_heat_capacity is used at each timestep to compute the surface temperature using the following equation:

land_sea_heat_capacity * dTs/dt = - corrected_flux - t_surf_dependence * dTs

The change in surface temperature in this timestep (dTs/dt) times the heat capacity of the surface is equal to the net flux into the surface at the given timestep (- corrected_flux) plus the change in the net flux into the surface caused by the change in surface temperature (- t_surf_dependence * dTs).

This is simplified by defining eff_heat_capacity as land_sea_heat_capacity + t_surf_dependence * dt, and then Ts is updated using:

eff_heat_capacity * dTs/dt = - corrected_flux

Optional Q-flux

The slab ocean model only communicates between grid-boxes in the vertical (i.e. air-sea exchange) but does not represent any horizontal transport (i.e. no north-south or east-west communications between grid cells). An idealised horizontal transport can be included using an ocean heat flux (Q-flux). Atmospheric heat transport is more realistic with an ocean heat transport.

Isca is able to calculate an analytic Q-flux, appropriate to an aquaplanet, following Merlis et al 2013 [MerlisEtAl2013] if do_qflux is True. Additionally, an analytic warmpool can be added by setting do_warmpool. The warmpool structure is set in Isca/src/atmos_param/qflux/qflux.f90. Alternatively an arbitrary Q-flux may be read from a file if load_qflux is True.

In the case where both a specific SST distribution (e.g. AMIP climatology) and closed surface energy budget are desired, a Q-flux input file can be generated by running a control experiment with the prescribed SST, creating a NetCDF Q-flux file offline and then passing this file to the model via the python interface run script.

1. Run a prescribed experiment (i.e. a control) using either observations, AMIP or similar.

2. Using the prescribed SST field and the surface fluxes from step 1, create the Q-flux file. This is an offline script that is run independently of the model. An example script is shown in: src/extra/python/scripts/calculate_qflux/calculate_qflux.py but you can create your own script to do this depending on your application.

3. Add the Q-Flux file to the inputfiles in the python run script (same as you would for ozone, land etc). Then in the mixed_layer_nml namelist in the python run script set load_qflux to True, qflux_file_name to the name of the input file (don’t include the .nc extension) and qflux_field_name is the Q-flux variable name in the file.

See Q-flux options below for namelist options. Note that the Q-flux is only relevant for slab ocean experiments (not fixed or prescribed SST runs). Also note that if the MiMA radiation code is used then the Q-flux is implemented following Merlis et al 2013 [MerlisEtAl2013]

More information on the method for Q-flux can be found in Russel et al 1985 [RusselEtAl1985]

Namelist options

Option	Summary	Default
evaporation	Switch for surface evaporation.	True
depth	Mixed layer depth.	40.0

Q-flux options

If do_qflux is True, use qflux_amp and qflux_width to calculate a time-independent surface Q-flux.

Option	Summary	Default
do_qflux	Switch to calculate time-independent Q-flux.	False
qflux_amp	Amplitude of time-independent Q-flux if do_qflux is True.	0.0
qflux_width	Width of time-independent Q-flux if do_qflux is True.	16.0

If load_qflux is True, use input file to load in a time-independent or time-dependent Q-flux.

Option	Summary	Default
load_qflux	Switch to use input file to get Q-flux.	False
qflux_file_name	Name of file among input files, from which to get Q-flux.	ocean_qflux
qflux_field_name	Name of field name in Q-flux file name, from which to get Q-flux. This is only used when time_varying_qflux is False. Otherwise the code assumes field_name = file_name.	ocean_qflux
time_varying_qflux	Flag that determines whether input Q-flux file is time dependent.	False

Initialize surface temperature

Option	Summary	Default
prescribe_initial_dist	Switch to turn on setting the initial surface temperature distribution.	305.0
tconst	Initial surface temperature following formula in Slab ocean section.	305.0
delta_T	Initial surface temperature gradient following formula in Slab ocean section.	40.0
do_read_sst	Flag to use fixed SSTs, prescribed from input file (sst_file).	False
sst_file	Name of file containing fixed SSTs.	False
do_sc_sst	Flag to use fixed SSTs, prescribed from input file (sst_file).	False
specify_sst_over_ocean_only	Flag to specify SSTs only over ocean, only works if do_sc_sst is True.	False
do_ape_sst	Flag to set prescribed SST according to the APE aquaplanet analytic form	False
add_latent_heat_flux_anom	Flag to add an anomalous latent heat flux	False
do_warmpool	Flag to call warmpool module, which returns ocean_qflux.	False

Surface albedo options

There are 5 options for setting the surface albedo, determined by the value of albedo_choice.

• 1: Surface albedo is a constant (albedo_value).

• 2: Glacier with higher albedo in one hemisphere only. If lat_glacier >0, albedo = higher_albedo North of lat_glacier. If lat_glacier <0, albedo = higher_albedo South of lat_glacier.

• 3: Glacier with higher albedo in both hemispheres. Albedo = higher_albedo where latitude > |lat_glacier|.

• 4: Albedo set by albedo_value + (higher_albedo - albedo_value) (lat/90) ^ albedo_exp.

• 5: Tanh increase around albedo_cntr with albedo_wdth:

  albedo(lat) = albedo_value + (higher_albedo-albedo_value)* 0.5 *(1+tanh((lat-albedo_cntr)/albedo_wdth)).
  

Option	Summary	Default
albedo_choice	Switch to choose surface albedo option described above.	1
albedo_value	Parameter that sets surface albedo depending on albedo choice.	0.06
higher_albedo	Parameter that sets surface albedo depending on albedo choice.	0.10
lat_glacier	Parameter that sets the glacier latitude for albedo choices 2 and 3.	60.0
albedo_exp	Parameter that sets surface albedo latitude dependence for albedo choice 4.	2.
albedo_cntr	Parameter that sets surface albedo for albedo choice 5.	45.0
albedo_wdth	Parameter that sets surface albedo for albedo choice 5.	10

Land options

There are 4 options for setting up the land, determined by the value of land_option.

• none: No land.

• input: Use input file to determine land mask.

• zsurf: The surface heat capacity is set to land_capacity where the surface geopotential is greater than 10.

• lonlat: The surface heat capacity is set to land_capacity in the longitude / latitude boxes set by [slandlon(k), elandlon(k)] and [slandlat(k), elandlat(k)] for all k’s.

Option	Summary	Default
land_option	Switch to choose land option as described above.	none
land_depth	Value of land mixed layer depth.	-1
slandlon	Vector determining lower bounds of longitudes for land masses.	0
slandlat	Vector determining lower bounds of latitudes for land masses.	0
elandlon	Vector determining higher bounds of longitudes for land masses.	-1
elandlat	Vector determining higher bounds of latitudes for land masses.	-1
land_h_capacity_prefactor	Factor by which to multiply ocean heat capacity to get land heat capacity if input option is used.	1.0
land_albedo_prefactor	Factor by which to multiply ocean albedo to get land albedo if input option is used.	1.0

Ice options

Option	Summary	Default
update_albedo_from_ice	Flag to set the surface albedo to ice_albedo_value where there is ice as specified by ice_file_name	False
ice_albedo_value	Value for ice albedo when update_albedo_from_ice is True.	0.7
ice_file_name	Name of file containing sea ice concentration.	siconc_clim_amip
ice_concentration_threshold	Value of sea ice concentration above which albedo should be set to ice_albedo_value.	0.5
ice_file_name	Name of file containing sea ice concentration.	siconc_clim_amip

Diagnostics

Name	Description	Units
t_surf	Surface temperature	K
delta_t_surf	Surface temperature change	K
flux_t	Surface sensible heat flux	\(\text{W}\,\text{m}^{-2}\)
flux_lhe	Surface latent heat flux	\(\text{W}\,\text{m}^{-2}\)
flux_oceanq	Ocean heat flux	\(\text{W}\,\text{m}^{-2}\)
ice_conc	Sea ice concentration	0-1
albedo	Surface albedo	0-1
land_sea_heat_capacity	Heat capacity of land and sea	\(\text{J}\,\text{m}^{-2},\text{K}^{-1}\)

Relevant modules and subroutines

The mixed layer code is located in: src/atmos_spectral/driver/solo/mixed_layer.F90. The name of this file reflects the fact that the code determines the properties of the single layer (either a slab ocean model or prescribed SST) below the air-sea interface.

The mixed layer ocean is initialised and called by: src/atmos_spectral/driver/solo/idealized_moist_phys.F90.

Relevant routines which are called by the mixed layer ocean:

• The SST input file is read in using the interpolator module found here: src/atmos_shared/interpolator/interpolator.F90.

• The Q-flux and warmpool components use the Q-flux module: src/atmos_param/qflux/qflux.f90.

References

[Vallis2017] [NealeHoskins2004] [MerlisEtAl2013] [RusselEtAl1985]

Authors

This documentation was written by Matthew Henry and Penelope Maher, peer reviewed by Stephen Thomson, and quality controlled by Ruth Geen.