.. _clim_atm_forcing: Atmospheric forcing ******************* .. |nbsp| unicode:: 0xA0 :trim: Atmospheric forcing consists of the surface temperature and surface mass balance (SMB). Both must be provided for the simulated ice sheet as functions of space and time. .. _atm_eismint: EISMINT ======= For the EISMINT (simplified geometry) domain, the surface temperature and SMB are specified by simple parameterizations. These parameterizations depend either on the horizontal distance from the centre of the domain, :math:`r`, or on the surface elevation, :math:`h`. The distance-dependent parameterizations (parameter ``SURFACE_FORCING = 1``) are those from the original EISMINT set-up by Payne et al. :cite:`payne_etal_2000`. The surface temperature, :math:`T_\mathrm{s}`, is given by .. math:: :label: eq_emt_st_param_1 T_\mathrm{s} = T_\mathrm{min} + S_\mathrm{T}\,r, where :math:`T_\mathrm{min}` is the minimum temperature and :math:`S_\mathrm{T}` the gradient of surface-temperature change with distance. The SMB, :math:`a_\mathrm{s}`, is also made a function of :math:`r`, .. math:: :label: eq_emt_smb_param_1 a_\mathrm{s} = \mathrm{min}[B_\mathrm{max},\,S_\mathrm{b}(R_\mathrm{EL}-r)], where :math:`B_\mathrm{max}` is the maximum SMB, :math:`S_\mathrm{b}` the gradient of SMB change with horizontal distance and :math:`R_\mathrm{EL}` the distance of the equilibrium line from the centre of the domain (:numref:`eismint_smb_param_1`). .. _eismint_smb_param_1: .. figure:: figs/SMB_Parameterization_1.png :width: 270 px :alt: EISMINT SMB parameterization :align: center Parameterization of the SMB, :math:`a_\mathrm{s}`, as a function of the horizontal distance from the domain centre, :math:`r`. The three parameters are the maximum SMB, :math:`B_\mathrm{max}`, the gradient of SMB change with horizontal distance, :math:`S_\mathrm{b}`, and the equilibrium line distance, :math:`R_\mathrm{EL}`. In the run-specs headers, the parameters to be defined are * ``TEMP_MIN`` (:math:`=T_\mathrm{min}`, in degC), * ``S_T`` (:math:`=S_\mathrm{T}`, in K/km), * ``B_MAX`` (:math:`=B_\mathrm{max}`, in m/a), * ``S_B`` (:math:`=S_\mathrm{b}`, in m/(a*km)), * ``ELD`` (:math:`=R_\mathrm{EL}`, in km). The more realistic elevation-dependent parameterizations (``SURFACE_FORCING = 2``) are by Greve and Blatter :cite:`greve_blatter_2009` (their Section 5.7.4). The surface temperature, :math:`T_\mathrm{s}`, follows the linear relationship .. math:: :label: eq_emt_st_param_2 T_\mathrm{s} = T_\mathrm{sl} - \gamma h, where :math:`T_\mathrm{sl}` is the surface temperature at elevation :math:`h=0` ("sea level") and :math:`\gamma` the atmospheric lapse rate. The SMB, :math:`a_\mathrm{s}`, is parameterized by .. math:: :label: eq_emt_smb_param_2 a_\mathrm{s} = \mathrm{min}[S_0,\,m_0(h-h_\mathrm{EL})], where :math:`S_0` is the snowfall rate, :math:`m_0` the melting gradient and :math:`h_\mathrm{EL}` the equilibrium-line altitude (:numref:`eismint_smb_param_2`). .. _eismint_smb_param_2: .. figure:: figs/SMB_Parameterization_2.png :width: 270 px :alt: EISMINT SMB parameterization :align: center Parameterization of the SMB, :math:`a_\mathrm{s}`, as a function of the surface elevation, :math:`h`. The three parameters are the snowfall rate, :math:`S_0`, the melting gradient, :math:`m_0`, and the equilibrium line altitude, :math:`h_\mathrm{EL}`. In the run-specs headers, the parameters to be defined are * ``TEMP_0`` (:math:`=T_\mathrm{sl}`, in degC), * ``GAMMA_T`` (:math:`=\gamma`, in K/km), * ``S_0`` (:math:`=S_0`, in m/a), * ``M_0`` (:math:`=m_0`, in m/(a*km)), * ``ELA`` (:math:`=h_\mathrm{EL}`, in km). Currently, it is not implemented to make the parameters of the above parameterizations time-dependent. (This feature can be added quite easily if need arises.) However, time-dependent anomalies of the surface temperature can be defined via the parameter ``TSURFACE`` and additional parameters, as described in the run-specs headers. .. _atm_ant_grl_etc: Antarctica, Greenland, etc. =========================== For the terrestrial ice sheets and ice caps, the choice of the surface temperature and SMB is controlled by the run-specs-header paramaters ``TSURFACE``, ``ACCSURFACE`` and ``ABLSURFACE``, as well as further, dependent parameters. The following methods are available: * | For ``TSURFACE``, ``ACCSURFACE``, ``ABLSURFACE`` all ``<= 5``, the surface temperature and precipitation are prescribed via a present-day distribution plus time-dependent anomaly approach, while the runoff is parameterized by either the positive-degree-day (PDD) method (version by Calov and Greve :cite:`calov_greve_2005`) or the linear-temperature-index (LTI) method (Ohmura :cite:`ohmura_2001`). | The time dependency results either from a time-dependent surface temperature anomaly :math:`\Delta{}T_\mathrm{s}(t)` (``TSURFACE`` and ``ACCSURFACE < 5``), or from a time-dependent glacial index :math:`g(t)` (``TSURFACE = ACCSURFACE = 5``). * | For ``TSURFACE = ACCSURFACE = ABLSURFACE = 6``, the surface temperature and (net) SMB are prescribed, typically from GCM output. This is the method used for the ISMIP6 future predictions (Goelzer et al. :cite:`goelzer_etal_2020`, Seroussi et al. :cite:`seroussi_etal_2020`) and follow-up studies. It requires present-day distributions plus annual anomalies for the surface temperature and SMB, all to be provided as NetCDF files. * | The setting ``ACCSURFACE = ABLSURFACE = 7`` selects the "implied SMB" by Calov et al. :cite:`calov_etal_2018`. It has a similar effect as the setting ``THK_EVOL = 3`` (topography nudging towards a prescribed target with a constant relaxation time; see Section ":ref:`Ice-thickness evolution `"). For details on the different settings, see the documentation in the run-specs headers. Note that not all options are implemented for all domains. .. _atm_n_s_mars: North and south polar caps of Mars ================================== For the north and south polar caps of Mars, the surface temperature and SMB are provided by a set of parameterizations called the Mars Atmosphere-Ice Coupler MAIC-1.5. It is driven directly by the orbital parameters obliquity, eccentricity and solar longitude of perihelion, to be provided as time-dependent values in an input file specified by the parameter ``INSOL_MA_90N_FILE`` (north polar cap) or ``INSOL_MA_90S_FILE`` (south polar cap). Further required parameter settings are ``TSURFACE = 6`` and ``ACCSURFACE = 3``. The surface temperature is parameterized by the Local Insolation Temperature (LIT) scheme, which uses a daily and latitude-dependent radiation balance and includes a treatment of the seasonal CO\ :sub:`2` cap (Greve et al. :cite:`greve_etal_2010`). The SMB is parameterized by a distance-dependent equilibrium-line approach similar to Eq. |nbsp| :eq:`eq_emt_smb_param_1` (Greve et al. :cite:`greve_etal_2004`, Greve and Mahajan :cite:`greve_mahajan_2005`). For details, see the references and the documentation in the run-specs headers.