Van de Wal R S W and J Oerlemans (1995): Response of valley glaciers to climate change and kinematic waves: a study with a numerical ice-flow model. J. of Glaciology., 41, No. 137, 142-152.
Abstract. In this paper kinematic
waves are studied with a simple numerical flow model that couples mass
divergence directly to basal shear stress as the only driving force. The
kinematic waves that result from a perturbation of the ice thickness or
mass balance are compared with the linear kinematic wave theory of Nye/Weertman.
The wave velocity is calculated as a function of the wavelength and amplitude
of a perturbation. The modelled wave velocity is typically 6-8 times the
vertically averaged velocity in the flow direction whereas linear theory
predicts 5 times the velocity.
An increasing wave velocity in the ablation zone can be explained by the increasing velocity gradient in the ablation zone. In model glacier experiments the increase in the wave velocity due to an increasing velocity gradient in the ablation zone is larger than the decrease in the wave velocity resulting from diffusion.
An experiment in connection with the Hintereisferner demonstrated, that the increase in the local ice velocity during a kinematic wave is about 10%, but varies slightly depending on the position along the glacier and the magnitude of the kinematic wave. This means that it is difficult to observe kinematic waves at a small glacier.
Since the response time of a glacier to a kinematic wave is the same as its response to mass balance perturbations, one can conclude that simple ice flow models are accurate enough to be used for glacier-climate studies.
Van de Wal R S W, R Bintanja, W Boot, M R van den Broeke, L A Conrads, P G Duynkerke, J P F Fortuin, E A C Henneken, W H Knap, M J Portanger, H F Vugts, J Oerlemans (1996): Mass balance measurements in the Søndre Strømfjord area in the period 1990-1994. Z. Gletscherk. Glazialgeol. , 31, 57-63
Abstract. Results are described from four years of mass balance measurements near the ice margin of the Greenland ice sheet in the period 1990-1994. The profiles of the specific balance indicate that a simple linear regression between elevation and specific balance is not valid. Meteorological measurements carried out during the first two summers, enable an explanation of the observed specific balance. The gradient in the absorbed shortwave radiation just below the equilibrium-line is higher than on the lower parts of the ice sheet. This results in a stronger mass balance gradient just below the equilibrium-line than near the ice margin.
Van de Wal RS W (1996): Mass balance modelling of the Greenland ice sheet: A comparison of energy balance and degree-day models. Annals of Glaciology, 23, 36-45.
Abstract. A degree-day model and
an energy balance model for the Greenland ice sheet are compared. The two
models are compared at a grid with 20 km spacing. Input for both models
is elevation, latitude and accumulation. The models calculate the annual
ablation over the entire ice sheet. Although on the whole the two models
yield similar results depending, on the tuning of the models, regional
discrepancies of up to 45% occur, especially for Northern Greenland. The
performance of the two types of models is evaluated by comparing the model
results with the sparsely available (long-term) mass balance measurements.
Results show that the energy balance model tends to predict a more accurate
mass balance gradient with elevation than does the degree-day model.
Since so little is known about the present day climate of the ice sheet, it is more useful to consider the sensitivity of the ablation to various climate elements than to consider the actual present day ablation. Results show that for a 1K temperature perturbation, sea level rise is 0.31 mm per year for the energy balance model and 0.34 mm per year for the degree-day model. After tuning the degree-day model to a value of the ablation, equivalent to the ablation calculated by the energy balance model, sensitivity of the degree-day model increases to 0.37 mm sea level change per year. This means that the sensitivity of the degree-day model for a 1K temperature perturbation is about 20% higher than the sensitivity of the energy balance model. Another set of experiments shows that the sensitivity of the ablation is dependent on the magnitude of the temperature perturbation for the two models. Both models show an increasing sensitivity per degree for larger perturbations. The increase in the sensitivity is larger for the degree-day model than for the energy balance model. The differences in the sensitivity are mainly concentrated in the Southern parts of the ice sheet. Experiments for the Bellagio temperature scenario, 0.3ûC increase in temperature per decade, leads to sea level rise of 4.4 cm over a period of 100 years for the energy balance model. The degree-day model predicts for the same forcing a 5.8 cm rise which is about 32% higher than the result of the energy balance model.
Van de Wal R S W, and S Ekholm (1996): On elevation models as input for mass balance calculations of the Greenland ice sheet. Annals of Glaciology, 23, 181-186.
Abstract. In this paper the elevation
model for the Greenland ice sheet based upon radio-echo sounding flights
of the Technical University of Denmark (TUD) Letréguilly et al (1991)
is compared with the satellite altimetry model (Tscherning et al. 1993)
improved with airborne laser and radar altimetry (IA-model). Although the
general hypsometry of both data sets is rather similar, differences seem
to be large at individual points along the ice margin. Over the entire
ice sheet the difference between the IA-model and the TUD-model is 33 metres
with a root mean squared error of 112 metres. Differential GPS measurements
collected in the ice marginal zone near Søndre Strømfjord
show that the IA-model is more accurate than the TUD-model. The latter
data set underestimates the elevation by approximately 150 metre in the
ice marginal zone near Søndre Strømfjord.
Calculation of the ablation with an energy balance model and with a degree-day model points to a 20% decrease in the ablation if the IA-model is used. Not only does this show the sensitivity of ablation calculations to the orographic input, but it also indicates that the ablation calculated by the models used nowadays is relatively overestimated.
Van de Wal R S W, and J Oerlemans (1997): Modelling the short-term response of the Greenland ice sheet to global warming. Climate Dynamics, 13, 733-744.
Abstract. A two-dimensional vertically-integrated
ice flow model has been developed to test the importance of various processes
and concepts used for the prediction of the contribution of the Greenland
ice sheet to sea-level rise over the next 350 years (short-term response).
The mass balance is modelled by the degree-day method and the energy-balance
method. The lithosphere is considered to respond isostatic to a point load
and the time evolution of the bedrock follows from a viscous asthenosphere.
According to the IPCC -IS92a scenario (with constant aerosols after 1990) the Greenland ice sheet is likely to cause a global sea level rise of 10.4 cm by 2100 AD. It is shown, however, that the result is sensitive to precise model formulations and that simplifications as used in the sea-level projection in the IPCC-96 report yield less accurate results. Our model results indicate that, on a time scale of hundred years, including the dynamic response of the ice sheet yields more mass loss than the fixed response in which changes in geometry are not incorporated. It turns out to be important to consider sliding, as well as the fact that climate sensitivity increases for larger perturbations.
Variations in predicted sea-level change on a time scale of hundred years depend mostly on the initial state of the ice sheet. On a time scale of a few hundred years, however, the variability in the predicted melt is dominated by the variability in the climate scenarios.
Wallinga J and R S W van de Wal (1998): Sensitivity of the Rhone glacier to climate change: experiments with a one-dimensional flow-line model. Journal of Glaciology, 44(147), 383-393.
Abstract. A one-dimensional time-dependent
flow-line model of the Rhône Glacier has been used to test the glacier's
response to climatic warming. Mass balance variations over the last hundred
years are obtained from observations of the equilibrium line altitude (ELA)
and a reconstruction of the ELA based on a statistical correlation between
temperature and ELA. For the period prior to 1882 AD, for which no reliable
climate data exist, we chose equilibrium line altitudes that enabled us
to simulate accurately the glacier length from 1602 AD.
The model simulates the historical glacier length nearly perfectly and glacier geometry very well. It underestimates glacier surface velocities by 1-18%. Following these reference experiments, we investigated the response of the Rhône Glacier to a number of climate change scenarios for the period 1990 to 2100 AD. For a constant climate equal to the 1961-1990 mean, the model predicts a 6% decrease in glacier volume by 2100 AD. The Rhône Glacier will retreat by almost 1 kilometre over the next hundred years at this scenario. At a warming rate of 0.04 K per year, only 4% of the glacier volume will be left by 2100 AD.
Van de Wal R S W (1999): The importance of thermodynamics for modelling the volume of the Greenland ice sheet. Journal of Geophysical Research, 104(D4), 3887-3898.
Abstract. Two different kinds of ice flow models, one two-dimensional (2-D) and the other three-dimensional (3-D), have been used to test the importance of the thermodynamic response of the Greenland ice sheet. The basic difference between the two models is that the thermodynamics are neglected in the two-dimensional model, whereas these are incorporated in the three-dimensional model. The 2-D and 3-D models are compared in terms of volume response time and total volume of the ice sheet. Results indicate that the sawtooth character of the ice volume on glacial-interglacial timescales is, among other possible reasons, a result of the thermodynamic coupling. The changes in elevation over the last 130,000 years calculated with the three-dimensional version are 230 m for the Summit drill site and 190 m for the N-GRIP site. The standard deviation of the changes in elevation is 55 m for the Summit site and 43 m for the N-GRIP site. The present-day imbalance is merely a result of the rather constant climate over the last 10 kyr and is not determined by the thermodynamics. Consequently, Pleistocene temperatures do still exist in the ice sheet but are not important for volume calculations of the present-day ice sheet. For short-term perturbation experiments in the future, the pronounced sensitivity of the mass balance will determine the response of the Greenland ice sheet, whereas thermodynamics will play only a minor role.
Van de Wal R S W (1999): Processes of buildup and retreat of the Greenland ice sheet. Journal of Geophysical Research, 104(D4), 3899-3906.
Abstract. Sensitivity experiments
were conducted to study the influence of several physical processes on
the evolution of the Greenland ice sheet over the last 250,000 years. The
experiments were carried out by means of a three-dimensional thermodynamical
model. The mass balance is modeled by a surface energy balance model..
This means that variations in orbital parameters following from the astronomical
(Milankovitch) theory can be incorporated in the ablation calculations.
It is shown that with regard to the Greenland ice sheet, variations in
shortwave radiation are only of minor importance for the changes in volume
over time. Calculations of the various components of the energy balance
under glacial and interglacial conditions show that the changes in absorbed
shortwave radiation resulting from changes in orbital parameters are considerably
smaller than the variations in the sensible heat flux caused by temperature
variations. Thermodynamics are only of importance for the volume changes
of the ice sheet if the climate, is on average, stable over a long period.
In between 110 kyr B.P. and 20 kyr B.P. the ice volume increased slowly
due to the cooling of the ice, which resulted in a higher effective viscosity
and thus a thicker ice sheet. The long response time of the thermodynamics
means that the thermodynamics cannot play a crucial role during transition
from a glacial to a deglacial period which occur typically within several
thousands of years. The mass balance height feedback has an important function
in the buildup of the ice sheet after a warm period like the Eemian. Without
isostatic bedrock compensation the ablation will remain very high in some
marginal parts, yielding a considerably smaller ice sheet volume for the
last glacial period.
Karlöf L, J-G Winther, E Isaksson, J Kohler, J F Pinglot, F Wilhelms, M Hansson, P Holmlund, M Nyman, R Petterson, M Stenberg, M P A Thomassen, C van der Veen, R S W van de Wal: A 1500 years record of accumulation at Amundsenisen Western Dronning Maud Land, Antarctica, derived from electrical and radioactive measurements on a 120 m ice core. Journal of Geophysical Research.
Abstract. During the Nordic EPICA
pre-site survey in Dronning Maud Land in 1997/98 a 120 m long ice core
was retrieved (76 S 08 W, 2400 m a.s.l.). The whole core has been measured
using the Electric Conductivity Measurement (ECM) and Di-Electric Profiling
(DEP) techniques, and the core chronology has been established by detecting
major volcanic eruptions. In a nearby snow-pit high-resolution density
profile have revealed a annual accumulation record and in a nearby shallow
core radioactive traces from nuclear tests conducted during the 50's and
60's have been identified. Altogether, 15 ECM and DEP peaks in the long
core are identified as originating from specific volcanic eruptions as
well as two peaks of increased Total -activity in the short core. Accumulation
is calculated as averages over the time periods between these dated events.
Accumulation rate is 62 mm w eq/y. for the last 181 years (1816-present),
and 61 mm w eq./y. for the last 1457 years (540-present). Our record shows
a 9% decrease in accumulation, between 1452-1641 AD, (i.e. part of the
little ice age), compared to the long term mean. Counting low density layers
in the snow pit gives an average accumulation rate of 73 mm w eq./y ( 23
mm). for the period 1989-97 AD.