2.3. Tracers

The basic conservation equations for ice area fraction \(a_{in}\), ice volume \(v_{in}\), and snow volume \(v_{sn}\) for each thickness category \(n\) are

(1)\[{\frac{\partial}{\partial t}} (a_{in}) + \nabla \cdot (a_{in} {\bf u}) = 0,\]

(2)\[\frac{\partial v_{in}}{\partial t} + \nabla \cdot (v_{in} {\bf u}) = 0,\]

(3)\[\frac{\partial v_{sn}}{\partial t} + \nabla \cdot (v_{sn} {\bf u}) = 0.\]

The ice and snow volumes can be written equivalently in terms of tracers, ice thickness \(h_{in}\) and snow depth \(h_{sn}\):

(4)\[\frac{\partial h_{in}a_{in}}{\partial t} + \nabla \cdot (h_{in}a_{in} {\bf u}) = 0,\]

(5)\[\frac{\partial h_{sn}a_{in}}{\partial t} + \nabla \cdot (h_{sn}a_{in} {\bf u}) = 0.\]

Although we maintain ice and snow volume instead of the thicknesses as state variables in CICE, the tracer form is used for volume transport (section Horizontal Transport). There are many other tracers available, whose values are contained in the trcrn array. Their transport equations typically have one of the following three forms

(6)\[\frac{\partial \left(a_{in} T_n\right)}{\partial t} + \nabla \cdot (a_{in} T_n {\bf u}) = 0,\]

(7)\[\frac{\partial \left(v_{in} T_n\right)}{\partial t} + \nabla \cdot (v_{in} T_n {\bf u}) = 0,\]

(8)\[\frac{\partial \left(v_{sn} T_n\right)}{\partial t} + \nabla \cdot (v_{sn} T_n {\bf u}) = 0.\]

Equation (6) describes the transport of surface temperature, whereas Equation (7) and Equation (8) describe the transport of ice and snow enthalpy, salt, and passive tracers such as volume-weighted ice age and snow age. Each tracer field is given an integer index, trcr_depend, which has the value 0, 1, or 2 depending on whether the appropriate conservation equation is Equation (6), Equation (7), or Equation (8), respectively. The total number of tracers is \(N_{tr}\ge 1\). Table Tracers provides an overview of available tracers, including the namelist flags that turn them on and off, and their indices in the tracer arrays. If any of the three explicit pond schemes is on, then tr_pond is true. Biogeochemistry tracers can be defined in the skeletal layer, dependent on the ice area fraction, or through the full depth of snow and ice, in which case they utilize the bio grid and can depend on the brine fraction or the ice volume, if the brine fraction is not in use.

Tracer flags and indices

flag	num tracers	dependency	index (CICE grid)	index (bio grid)
default	1	aice	nt_Tsfc=1
default	1	vice	nt_qice
default	1	vsno	nt_qsno
default	1	vice	nt_sice
tr_iage	1	vice	nt_iage
tr_FY	1	aice	nt_FY
tr_lvl	2	aice	nt_alvl
		vice	nt_vlvl
tr_pond_cesm	2	aice	nt_apnd
		apnd	nt_vpnd
tr_pond_lvl	3	aice	nt_apnd
		apnd	nt_vpnd
		apnd	nt_ipnd
tr_pond_topo	3	aice	nt_apnd
		apnd	nt_vpnd
		apnd	nt_ipnd
tr_aero	n_aero	vice, vsno	nt_aero
tr_brine		vice	nt_fbri
solve_zsal	n_trzs	fbri or (a,v)ice	nt_bgc_S
tr_bgc_N	n_algae	fbri or (a,v)ice	nt_bgc_N	nlt_bgc_N
tr_bgc_Nit		fbri or (a,v)ice	nt_bgc_Nit	nlt_bgc_Nit
tr_bgc_C	n_doc	fbri or (a,v)ice	nt_bgc_DOC	nlt_bgc_DOC
	n_dic	fbri or (a,v)ice	nt_bgc_DIC	nlt_bgc_DIC
tr_bgc_chl	n_algae	fbri or (a,v)ice	nt_bgc_chl	nlt_bgc_chl
tr_bgc_Am		fbri or (a,v)ice	nt_bgc_Am	nlt_bgc_Am
tr_bgc_Sil		fbri or (a,v)ice	nt_bgc_Sil	nlt_bgc_Sil
tr_bgc_DMS		fbri or (a,v)ice	nt_bgc_DMSPp	nlt_bgc_DMSPd
		fbri or (a,v)ice	nt_bgc_DMSPd	nlt_bgc_DMSPd
		fbri or (a,v)ice	nt_bgc_DMS	nlt_bgc_DMS
tr_bgc_PON		fbri or (a,v)ice	nt_bgc_PON	nlt_bgc_PON
tr_bgc_DON		fbri or (a,v)ice	nt_bgc_DON	nlt_bgc_DON
tr_bgc_Fe	n_fed	fbri or (a,v)ice	nt_bgc_Fed	nlt_bgc_Fed
	n_fep	fbri or (a,v)ice	nt_bgc_Fep	nlt_bgc_Fep
tr_bgc_hum		fbri or (a,v)ice	nt_bgc_hum	nlt_bgc_hum
tr_zaero	n_zaero	fbri or (a,v)ice	nt_zaero	nlt_zaero
	1	fbri	nt_zbgc_frac

Users may add any number of additional tracers that are transported conservatively, provided that the dependency trcr_depend is defined appropriately. See Section Adding Tracers for guidance on adding tracers.

Please see the Icepack documentation for additional information about tracers that depend on other tracers, age of the ice, aerosols, brine height, and the sea ice ecosystem.