# Spin-up Drivers

New to the Glimmer source code and important to the development of CISM are the spin-up drivers to aid in the initialization of the Antarctica and Greenland ice sheets.

Included in the spin-up drivers are a simple forcing scheme, similar to the EISMINT type forcing, and a more complex forcing as outlined further below. These drivers deal with mass balance, temperature and sea level forcing.

## Temperature Forcing

Modern temperature and precipitation fields provide a basis for paleo-climate. These fields are altered according to temperature forcing from ice core records which provide the temperature anomoly ($\Delta T$), and according to latitude and elevation lapse rates.

### Antarctica

For Antarctica these equations are:

$TMA = 34.46 + {\gamma}_{a} H_{sur} - 0.68775{\phi} + {\Delta} T$

$TMS = 16.81 + {\gamma}_{s} H_{sur} - 0.27937{\phi} + {\Delta} T$

$T_{monthly} = TMA - (TMS - TMA) \cos\left(\frac{2{\pi}t}{A}\right).$

TMA is the mean annual temperature, TMS, the summer temperature and $T_{monthly}$ is the mean monthly temperature. All are given in $^\circ$C. ${\phi}$ is the latitude. ${\gamma}$ is the lapse rate and varies based on the 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

### Greenland

For Greenland temperature forcing equations are:

$TMA = 41.83 - 6.309H_{sur} - 0.7189{\phi} + 0.0672{\lambda} + {\Delta}T$

$TMS = 14.70 - 5.426H_{sur} - 0.1585{\phi} + 0.0518{\lambda} + {\Delta}T$

where $H_{sur}$ is the surface elevation(m), $\phi$ is the geographical latitude in positive $^\circ$ in both hemispheres, $\lambda$ is the temperature dependence on longitude, TMA is the mean annual temperature, TMS is the summer temperature (Fausto et al. 2009). TMA is the same calculation as is present in the Greenland data set for present day surface temperature. From the Fausto paper this uses the equations with land stations and using longitudinal dependence.

## Precipitation

### Antarctica

Precipitation scheme for Antarctica:

$P_{A}\left[T_{I}\left(t\right)\right] = P_{A}\left[T_{I}\left(p\right)\right]exp\left[22.47\left(\frac{T_{0}}{T_{I}\left(pres\right)} - \frac{T_{0}}{T_{I}(t)}\right)\right] \times \left[\frac{T_{I}\left(p\right)}{T_{I}\left(t\right)}\right]^{2}\left[1 + {\beta}\left(T_{I}(t) - T_{I}(0)\right)\right]$

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. $T_{I}$ is further related to $T_{S}$, the mean annual surface temperature by:

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

### Greenland

The precipitation scheme for Greenland is as follows:

$P_{G}(x,y,t) = P_{G}(x,y,0)exp\left[f\left({\delta}^{18}O(t) + 34.83 + \frac{{\Delta}T_{E}(x,y,t) - {\Delta}T_{SC}(t)}{d}\right)\right]$

where $P_G(0)$ is the precipitation for the present Greenland ice sheet, $P_G(t)$ is the precipitation adjusted over time, ${\Delta}T_{E}$(x,y,t) is a spatially dependent temperature change resulting from local elevation changes anywhere on Greenland, d is the ${\delta}_{18}$0 conversion factor of $2.4^{\circ}C/\frac{0}{00}$, ${\Delta}T_{SC}$ is a correction term for the change of altitude of the central dome during the Greenland ice sheet's evolution. It is equal to the summit elevation changes in the reference experiment, multiplied by the observed atmospheric lapse rate of 0.00792. In this case f = 0.169 and corresponds to a 7.3% change of precipitation rate for every $^{\circ}$ C of temperature change.

## PDD

The spin-up mass balance driver uses the above equations to find precipitation and this result is then used in the Annual Positive Degree Day scheme in CISM. More about PDD can be found in the Glimmer documentation.

## Configuration File Settings

The spin-up drivers can be used by making reference in the configuration file. For example, to run Antarctica without simple forcing, the following would be added to the configuration file.

[SPIN MB]
model_type = 0
use_simple = 0

[SPIN Temperature]
model_type = 0
use_simple = 0
temp_file = temperature_forcing_over_time.data

[SPIN SLC]
slc_file = sea_level_forcing_over_time.data


The default values for both model_type and use_simple are 0. Using a value of 1 for both would use simple forcing equations for the Greenland ice sheet. One other difference to note is that the Greenland ice sheet has an additional mass balance input file option:

[SPIN MB]
oxygen_isotope_file = delO18_change_over_time.data


From the equations above, precipitation change for Greenland is dependant on the isotope record rather than temperature.

## References

• Huybrechts, P.(1998). Report of the Third EISMINT Workshop on Model Intercomparison. European Science Foundation (Strasbourg), 120 p.
• Huybrechts, P., and J. de Wolde (1999). The dynamic response of the Greenland and Antarctic ice sheets to multiple-century climatic warming. Journal of Climate, 12(8), 2169-2188.
• Huybrechts, P. (2002). Sea-level changes at the LGM from ice-dynamic reconstructions of the Greenland and Antarctic ice sheets during the glacial cycles. Quaternary Science Reviews, 21, 1-3, 203-231.
• Huybrechts, P., O. Rybak, F. Pattyn, U. Ruth, and D. Steinhage (2007): Ice thinning, upstream advection, and non-climatic biases for the upper 89% of the EDML ice core from a nested model of the Antarctic ice sheet, Climate of the Past, 3, 577-589.
• Janssens, I., and P. Huybrechts (2000). The treatment of meltwater retention in mass-balance parameterisations of the Greenland ice sheet. Annals of Glaciology 31, 133-140.