Introduction
With an annual mass turnover equivalent to a 6 mm change in
global sea level, the Antarctic Ice Sheet (AIS) plays an important role in
sea-level change. The surface mass balance (SMB) and ice discharge determine
the net mass change of the AIS. Recent satellite mass budget studies,
e.g. and , show a large temporal
variability in the AIS mass balance acting on monthly and decadal timescales.
Although ice discharge can vary strongly on multiyear timescales,
the SMB variability is responsible for most of the interannual variability in
ice-sheet mass balance. Since AIS-integrated SMB can neither be measured remotely
nor derived from in situ observations, the SMB and its variability must be
derived from atmospheric modelling. Evaluation of the mean modelled SMB
fields is possible , but until recently
a direct evaluation of annual SMB has been impossible in the absence of suitable
observations. The newly developed technique of combining airborne radar with
ice core data provides annual SMB estimates on the scale of a glacier
catchment . These data provide new opportunities
for evaluation of modelled SMB evaluation, specifically over the Thwaites
Glacier catchment in West Antarctica.
The SMB can be obtained from reanalysis products like ERA-Interim, but
regional atmospheric climate models driven by reanalyses outperform the
reanalyses in representing the spatial patterns
e.g.. Here, we use model data from the
Regional Atmospheric Climate Model (RACMO2), version 2.3 .
Over Antarctica, where the variability is set by the large-scale circulation,
a regional climate model (RCM) will unlikely improve upon
the reanalysis interannual variability unless data assimilation is applied.
RACMO2 in its default version has neither data assimilation nor relaxation to
large-scale forcing fields in the upper atmosphere. Hence, the free evolution
of the model interior will partly remove the true interannual variability,
deteriorating the correlation with observational time series. Therefore, we
discuss whether relaxation to large-scale forcing fields (nudging) is
beneficial. This relaxation can be implemented by using spectral and
indiscriminate nudging. In the case of indiscriminate nudging, model fields
are adjusted to the large-scale forcing fields without regard to any spatial
scales and structures in the modelled deviations. As a result, modelled
small-scale patterns are partially suppressed because these patterns are
absent in the coarser-resolution forcing fields. Relaxation with spectral
nudging circumvents smoothing of the model state because relaxation is
applied in the spectral space, which allows for adjustment of only the longer
wavelengths to the large-scale forcing fields. Spectral nudging is thus
potentially better than indiscriminate nudging, but it is computationally
more expensive. Although applied at different geographical locations and
under different meteorological conditions, several studies
e.g. have shown that relaxation improves the
representation of the surface climate and precipitation fields. These studies
show that the wind and temperature fields are the most important fields to
constrain by nudging and that spectral and indiscriminate nudging both
improve the representation of the modelled fields.
In this study, we applied upper-air relaxation (UAR), which is indiscriminate
nudging applied to the upper part of the atmosphere only. Indiscriminate
nudging is justifiable because the upper atmosphere only is gently stirred
towards the large-scale forcing fields. In this manner, UAR aims to retain
not only the improved spatial patterns provided by a RCM but also the resolved
interannual variability of ERA-Interim.
Model, methods and observations
RACMO2
RACMO2 has been used for over a decade to estimate the climate and SMB of
Antarctica. RACMO consists of the dynamics of the RCM HIRLAM (High-Resolution
Limited-Area Model), the physics package of the ECMWF IFS (European Centre
for Medium-Range Weather Forecasts Integrated Forecast Systems) and
a multilayer snow model including grain-size-dependent albedo and snow drift.
Here, we use RACMO2 version 2.3, which has been described
and evaluated in detail for Antarctica by .
We compare the simulation presented by with ERA-Interim
and an additional simulation using UAR. Both RACMO2
simulations employ an identical domain and code except for the UAR, and both
were driven by ERA-Interim and run from 1979 to 2013. The simulation domain
has a resolution of 27 km, utilizes 40 vertical levels, and extends
well outside Antarctica.
Upper-air relaxation (UAR)
The default version of RACMO2 is adjusted only at its lateral boundaries to
weather fields from the driving global model. The interior of the domain is
allowed to evolve freely; hence, no nudging is applied to the weather over
Antarctica. This freedom is reduced if indiscriminate UAR is applied. In that
case, the upper part of the modelled atmosphere is weakly relaxed to the
ERA-Interim fields.
This relaxation is implemented in the following manner and is only applied on
temperature and wind fields. Humidity fields are not relaxed because that
would lead to undesired distortions to the modelled clouds and precipitation
fluxes, as already observed in the lateral boundary relaxation zones. The
relaxation uses the scaled, terrain-following σ coordinate which
ranges from 0 (zero air pressure) to 1 (at the earth surface). At every time
step, a model value (Φ) at location (x={x,y,σ}) is
adjusted to the driving fields using
Φ(x)=(1-λτλσ(σ))Φ(x)R+λτλσ(σ)Φ(x)B,
where Φ(x)R and Φ(x)B are the
specific values from RACMO2 and the large-scale forcing, respectively, valid
for that location and time step. If x is located in the boundary
relaxation zone, the boundary relaxation is applied additively on
Eq. ().
A relaxation timescale (τ) of 6 h is applied, so for a model time step
(tR) of 600 s, λτ, defined as
λτ=1-1exp(tR/τ),
is 0.027. The vertical relaxation coefficient
λσ(σ) is defined with
σ≤0.6:λσ(σ)=(1+cos(σπ/0.6))2σ≥0.6:λσ(σ)=0.
Figure shows the values of σ and
λσ as a function of the pressure and elevation for a site
at sea level, 2000 ma.s.l, and 4000 ma.s.l. This function allows
a gradual stronger relaxation with elevation without sharp gradients.
Using the terrain-following coordinate ensures that the
near-surface fields are never relaxed to the driving fields.
Radar observations in West Antarctica
For the evaluation of interannual SMB variability, we use airborne radar
observations made in the Thwaites Glacier catchment
(Fig. ). The data and retrieval method are discussed in
detail in . In brief, the snow radar tracks radar reflection
layers along flight lines that are dated using firn cores drilled at
strategic locations along the flight lines. Using radar wave propagation and
firn compaction modelling, the retrieval time difference between reflection
layers is converted into annual accumulation.
λσ(σ) (solid lines) and σ (dashed lines)
as a function of (a) pressure and (b) elevation for
a location at 0 (black lines), 2000 (red lines) and 4000 (green
lines) ma.s.l., respectively.
Map of the study area, including catchment delineation (white line),
elevation contours (black lines), radar-derived SMB and the location of the
RACMO2 grid points used for comparison (black dots). The background image is the MODIS
Mosaic of Antarctica .
Difference in SMB (%) between the UAR and reference RACMO2
simulation for 1979–2013. Grid points with negative SMB in the reference
simulation are masked grey.
Observed and modelled integrated annual SMB for Thwaites Glacier
catchment, West Antarctica (Fig. ).
Statistics of modelled SMB for Thwaites Glacier catchment, West
Antarctica. The mean 1980–2009 SMB derived by snow radar is
457 mmw.e.a-1.
Model simulation
Correlation (r)
RMSD
Bias
( )
(mmw.e.a-1)
ERA-Interim
0.93
78
-75
Reference run
0.69
48
-17
UAR run
0.91
43
-35
Results
Evaluation of mean SMB and climate
First, the mean 1979–2013 SMB modelled by RACMO2 including UAR is compared
to the reference model version. Figure shows that large-scale
SMB patterns are largely unchanged; the differences are typically
10 % of the reference value. Integrated over the grounded ice sheet, the
mean annual SMB decreases by 80 Gta-1 (4 %) to
1979 Gta-1. Some areas along the coast receive more mass, but in
general precipitation and subsequently SMB decrease. This decrease is related
to a small increase of upper-air temperature without an equivalent increase
of absolute humidity. At the 500 hPa level, temperatures increase above
Antarctica by 0.2 to 0.6 K (not shown), while relative humidities
decrease by 0 to 2 %. All in all, the difference in the modelled mean
climate between the reference and UAR runs is very limited. For example, mean
surface pressures and 2 m temperatures differ only at max 0.7 hPa
and 0.6 K, respectively.
Interannual variability
In Fig. and Table , the integrated annual
SMB derived from observations, ERA-Interim, and the two RACMO2 runs are
displayed. The ERA-Interim SMB, derived from precipitation minus sublimation,
is systematically lower than the observed SMB, due to underestimated
precipitation. The ERA-interim correlation with observed interannual
variability, however, is high. With r=0.93, 87 % of the interannual
variability is explained by the ERA-Interim. The reference RACMO2 simulation
provides a large improvement on the mean SMB: RACMO2 is on average less than
2 % drier than observed, leading to a lower root mean square deviation
(RMSD). However, much of the representation of the interannual variability is
lost: the range is comparable, but the correlation (r=0.69) has
deteriorated. A closer inspection of Fig. shows that model
deviations have an episodic nature. For example, the reference run captures the
annual SMB well for the period 1985–1991 but deviates strongly for the subsequent
3 years. Hence, lateral boundary conditions alone do not
provide enough constraints for RACMO2 to reproduce day-to-day weather
patterns for some years, but for some years they do. This intermittent model
drift is removed in the UAR simulation, which combines the best of both the
reference run and ERA-Interim. The mean SMB remains well modelled although
the dry bias has increased to 5.5 %. This new simulation, however,
reproduces 83 % (r=0.91) of the observed variability, a similar
correlation with observations to the ERA-Interim, and has the lowest RMSD.
Regional patterns
Since ERA-Interim has a native resolution of 0.75∘, UAR dampens
small-scale upper-air structures in the RCM. Mesoscale topographic features
like the Antarctic Peninsula (AP) are much better resolved in RACMO2 than in
ERA-Interim. As a result, for the ERA-Interim fields that are fed into
RACMO2, the topographic effect on the circulation in the free atmosphere
extends over a much larger area than RACMO2, and the maximum elevation of the
mountain ridge is reduced. UAR thus introduces topographic effects at
locations where they are not modelled by RACMO2 and fewer topographic effects
at the mountain ridge. These artefacts affect the precipitation fields
modelled on, for example, the AP as shown in Fig. . In the
adjusted simulation, orographic precipitation is modelled for a much wider
area than the AP alone, leading to a decrease of precipitation on the
mountain range itself. Although temperature and humidity fields also show
small-scale disturbances around the AP, the upper-air wind field is the
driving component. Prescribed orographic divergence of the upper-air flow
enhances upward motion west of the AP, while on the spine of the AP, UAR
reduces the orographically driven vertical motion. An additional test, in
which UAR was applied on the wind fields only, shows a similar dispersion of
precipitation to the normal UAR simulation. A second test, in which only the
stratosphere was constrained, i.e. relaxation for σ≤0.25
(Eq. ), showed no improvement of the patterns over the AP,
while the correlation of modelled SMB with snow radar data for Thwaites
Glacier basin clearly deteriorated. We, therefore, conclude that the
topographic convergence and divergence of wind fields as prescribed by
ERA-Interim affect the precipitation fields over the AP. The limited amount
of SMB observations and the high spatial variability of SMB across the AP
inhibit evaluation of the model results. Nevertheless, we assess that this
dispersion of precipitation is likely a deterioration of the precipitation
fields, since in general RACMO2 has a better representation of spatial
precipitation patterns than ERA-Interim.
Relative difference (%) in precipitation between the UAR
simulation and the reference RACMO2 simulation over the Antarctic Peninsula.
Discussion and conclusions
In this manuscript, we show the
potential of upper-air relaxation to improve the representation of
interannual variability in regional climate models over Antarctica,
specifically, RACMO2. For this study, we used the regional climate model
RACMO2 and the reanalysis ERA-Interim. With this method, the modelled
interannual variability closely resembles the variability of ERA-Interim,
which reproduces the variability in the observations well. RACMO2 still
largely improves the representation of the spatial patterns and total mass
flux as compared to ERA-Interim. Nevertheless, a smoothing of precipitation
fields is observed, mostly over very steep topography. This effect is induced
by the prescribed upper-air winds, leading to extended regions of forced
large-scale precipitation. Upper-air relaxation is thus not an ideal method
for rugged regions. In those regions, spectral nudging, which only adjusts
the larger spatial scales in weather patterns, might be a better approach. We
believe that these conclusions, although not demonstrated with runs using
other reanalyses or GCM boundaries, are
general valid for using UAR.