# Model Initialization

## Ice sheet model initialization

Models that are able to initialize over long periods (approximately a glacial cycle, ~125kyr) can use the following suggestions for model initialization. The method detailed here is used in the CISM Climate Drivers.

### Antarctica

The basis for temperature forcing of Antarctica comes from the Vostok ice core records. The record for Vostok is interpolated over the last 125kyr BP in 100-yr intervals using the standard conversion of the deuterium record to temperature with the relation

$\ 0.166^{\circ}$ C per $\frac{0}{00}{\delta}$ D (Petit et al 1999).

The other necessary forcing fields are found in the Data sets.

Temperature forcing over the Antarctica continent is mean annual ($\ TMA$ and is dependent on elevation ($\ H_{sur}$), latitude (degrees south, counted positive) ($\ {\phi}$) and lapse rate ($\ {\gamma}$) as follows,

$\ TMA = 7.405 - 0.014285 * H_{sur} - 0.180 \phi~~~(H_{sur}$ above 1500 m)
$\ TMA = 36.689 - 0.005102 * H_{sur} - 0.725 \phi~~~ (H_{sur}$ = 200-1500 m)
$\ TMA = 49.642 - 0.943 \phi ~~~ (H_{sur}$ = 0-200 m)

These relations give temperature in $^\circ$C. Fortuin and Oerlemans (Ann. Glaciol. 14, 1990, 78-84)

Please observe that seaRISE previously included the following scheme for computing the TMA:
$TMA = 34.46 + {\gamma}_{a} H_{sur} - 0.68775{\phi} + {\Delta} T$
$TMS = 16.81 + {\gamma}_{s} H_{sur} - 0.27937{\phi} + {\Delta} T$
$T_{monthly} = TMA - (TMS - TMA) \cos\left(\frac{2{\pi}t}{A}\right).$
The lapse rate and varies according to the elevation as follows

 for $H_{sur} <$ 1500 m ${\gamma}_{a}$ = -0.005102 for $H_{sur} {\geq}$ 1500 m ${\gamma}_{a}$= -0.014285 for all $H_{sur}$ ${\gamma}_{s}$ = -0.00692

(Huybrechts and de Wolde 1999)

This method has a flaw due to a 13 degree (!) discontinuity at 1500m. This was noted by Ralf Greve (thanks!),
and the problem corrected by suggesting the above parametrization of Fortuin and Oerlemans (Ann. Glaciol. 14, 1990, 78-84)


Precipitation for Antarctica in the model uses changes in temperature as the main forcing factor, and a $P_{A}\left[T_{I}\left(t\right)\right] = P_{A}\left[T_{I}\left(p\right)\right]exp\left[22.47\left(\frac{T_{0}}{T_{I}\left(pres\right)} - \frac{T_{0}}{T_{I}(t)}\right)\right] \times \left[\frac{T_{I}\left(p\right)}{T_{I}\left(t\right)}\right]^{2}\left[1 + {\beta}\left(T_{I}(t) - T_{I}(0)\right)\right]$

where $T_{0}$ = 273.16 K, $T_{I}$ (in K) is the mean annual temperature above the surface inversion layer and $P_{A}$ (in $myr^{-1}$ of ice equivalent) is a map of the present day precipitation, and $\beta$ is a constant fitting parameter. $\beta$ is intended to account for glacial-interglacial changes of the accumulation pattern. $\beta$ = 0.046 and has been empirically determined by comparing upstream accumulation rates derived from firn cores. Precipitation changes are proportional to the water vapor pressure gradient relative to condensation temperature above the surface inversion layer (Robin et al. 1977,Lorius et al. 1985).$T_{I}$ is further related to $T_{S}$, the mean annual surface temperature by:

$T_{I}(t) = 0.67T_{S}(t) + 88.9.$

### Greenland

The oxygen isotope record (${\delta}^{18}O$) from the GRIP ice core (Dansgaard et al., 1993; Johnsen et al., 1997) is included as NetCDF variable oisotopes_time_series in the present day Greenland data set. That isotope record is used to generate a record of temperature variation from 125kyr BP to the present by the formula

${\Delta}T(t) = d({\delta}^{18}O(t) + 34.83)$

where $d = 2.4^{\circ}C/\frac{0}{00}$ is a standard value for the conversion between oxygen isotope anomaly and temperature; compare (Huybrechts et al. 2002). (Units of $d$ are $^{\circ}$ C per mil.) The variable ${\Delta}T(t)$ is called temp_time_series in the present day Greenland data set. This temperature has an elevation-dependent aspect because the elevation of the GRIP site has varied by as much as hundreds of meters since 125kyr BP (reference?).

The SPECMAP eustatic sea level record, from sea bed coring (Imbrie et al., 1984), is the NetCDF variable sealevel_time_series in the present day Greenland data set.

Note that the Vostok temperature curve is well-behaved as compared to the GRIP ice core used for Greenland. The period before 114kyr in the GRIP record is questionable, which explains the 125kyr BP start date. According to Huybrechts et al. (2002), mass loss in Greenland possibly contributed to the spike in sea level rise between the period of 120kyr to 125kyr, and is seen in the sea level curve. Around 120kyr b.p. is when SPECMAP and the GRIP temperature record are assumed to both return to present day conditions for Greenland.

The spatially-variable mean annual temperature (TMA) and mean summer temperature (TMS) for the present epoch are described by Fausto et al. (2009). With the added temperature offset ${\Delta}T$ from the GRIP core, these parameterizations become a (suggested and default only) time- and location-dependent paleo-temperature parameterization:

$TMA(x,y,t) = 41.83 - 6.309H_{sur}(x,y,t) - 0.7189{\phi} + 0.0672{\lambda} + {\Delta}T(t)$

$TMS(x,y,t) = 14.70 - 5.426H_{sur}(x,y,t) - 0.1585{\phi} + 0.0518{\lambda} + {\Delta}T(t)$

Here $H_{sur}(x,y,t)$ is the modeled surface elevation (m), while $\phi=\phi(x,y)$ is the latitude (positive degrees N) and $\lambda=\lambda(x,y)$ is the longitude (positive degrees W) of the location $(x,y)$ on the model grid.

A calculation of $TMA(x,y,t)$ using ${\Delta}T = 0$ and the present day surface elevation data was used to generate the present day mean annual surface temperature variable presartm in the present day Greenland data set.

(The CF standard name for the $TMA$ result of the Fausto et al. (2009) parameterization is possibly air_temperature or possibly surface_temperature, because the actual meaning is the near-surface air temperature (at 2 m). It could use the proposed name land_ice_surface_temperature, but that name is somewhat ambiguous when the ice is covered by a layer of snow or firn. The proposed CF standard name for the ice temperature at the near-surface level within the ice sheet model, but below the completion of firn processes, is either land_ice_surface_temperature_below_firn or land_ice_temperature_at_firn_base. It is likely that this land_ice quantity is different from, and presumably warmer than, the air temperature $TMA$ from the Fausto et al. (2009) parameterization.)

The (suggested and default only) time- and location-dependent paleo-precipitation for Greenland is as follows:

$P_{G}(x,y,t) = P_{G}(x,y,0)exp\left[\frac{0.169}{d}\left({\Delta}T(t)+ {\Delta}T_{SC}(t)\right)\right]$

where $P_G(x,y,0)$ is the precipitation for the present Greenland ice sheet (van der Veen et al, 2001). It is variable presprcp in the present day Greenland data set. The time dependent precipitation is $P_G(x,y,t)$, d is the ${\delta}_{18}$0 conversion factor of $2.4^{\circ}C/\frac{0}{00}$, and ${\Delta}T_{SC}$ is a correction term for the change of altitude of the central dome during the Greenland ice sheet's evolution. The coefficient "$0.169/d$" corresponds to a 7.3% change of precipitation rate for every $1^{\circ}C$ of temperature change (Huybrechts et al. 2002).

One possible scheme for ${\Delta}T_{SC}(t)$ is to take it to be zero, which regards the height correction as belonging to the set of uncertainties related to the conversion between isotopic and temperature signals.

Alternatively, following Huybrechts et al. (2002), the temperature correction ${\Delta}T_{SC}(t)$ can be computed by multiplying the lapse rate of 0.00792 by the Summit elevation anomaly at each time step taken from an initial model run. In this case, and for consistency, the temperature correction should also be used for the temperature forcing. For an estimate of the magnitude of the temperature correction, see figure 8 of Huybrechts et al. (2002), http://homepages.vub.ac.be/~phuybrec/pdf/QSR.2002.pdf. In their simulation, the correction range is (-1.5, 0.5) degrees C, and the effect of this correction is regarded as small (compare their simulations G0 and G4 and see discussion in subsection 5.4.3.)

The units of $P_{G}(x,y,0)$ and $P_{G}(x,y,t)$ in the present day Greenland data set are "meters/year", and this means liquid water equivalent. The CF standard name is lwe_precipitation_rate.

## Higher Order- Shorter Initialization

Due to the computation demands of first order and higher models, long term spin ups done by the reduced order models are rarely used. Instead, the participating higher order models obtained their starting configuration for the SeaRISE experiments using a variety of techniques that assimilate present day observations.