Brief Communication : Upper air relaxation in RACMO 2 significantly improves modelled interannual surface mass balance variability in Antarctica

The regional climate model (RCM) RACMO2 has been a powerful tool for improving surface mass balance (SMB) estimates from GCMs or reanalyses. However, new yearly SMB observations for West Antarctica show that the modelled interannual variability in SMB is poorly simulated by RACMO2, in contrast to ERA-Interim, which resolves this variability well. In an attempt to remedy RACMO2 performance, we included additional upper air relaxation (UAR) in 5 RACMO2. With UAR, the correlation to observations is similar for RACMO2 and ERA-Interim. The spatial SMB patterns and ice sheet integrated SMB modelled using UAR remain very similar to the estimates of RACMO2 without UAR. We only observe an upstream smoothing of precipitation in regions with very steep topography like the Antarctic Peninsula. We conclude that UAR is a useful improvement for RCM simulations, although results in regions with steep topography should be 10 treated with care.


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.Shepherd et al. (2012) and Velicogna et al. (2014), 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 (Favier et al., 2013;Van Wessem et al., 2014a), 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 (Medley et al., 2013(Medley et al., , 2014)).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.Van de Berg et al., 2006;Lenaerts et al., 2012).Here, we use model data from the Regional Atmospheric Climate Model (RACMO2), version 2.3 (Van Wessem et al., 2014a).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.

Published by Copernicus Publications on behalf of the European Geosciences Union.
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.Pohl and Crétat, 2014;Omrani et al., 2015) 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.

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 Van Wessem et al. (2014a, b).We compare the simulation presented by Van Wessem et al. (2014a) with ERA-Interim (Dee et al., 2011) 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 ( ) at location (x = {x, y, σ }) is adjusted to the driving fields using where (x) R and (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. (1).
A relaxation timescale (τ ) of 6 h is applied, so for a model time step (t R ) of 600 s, λ τ , defined as is 0.027.The vertical relaxation coefficient λ σ (σ ) is defined with (2) Figure 1 shows the values of σ and λ σ as a function of the pressure and elevation for a site at sea level, 2000 m a.s.l, and 4000 m a.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. 2).The data and retrieval method are discussed in detail in Medley et al. (2013).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.

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 3 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 Gt a −1 (4 %) to 1979 Gt a −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. 4  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. 4 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. 5.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.2), 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.

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.

Figure 2 .
Figure2.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(Scambos et al., 2007).

Figure 3 .
Figure 3. 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.

Figure 5 .
Figure 5. Relative difference (%) in precipitation between the UAR simulation and the reference RACMO2 simulation over the Antarctic Peninsula.

Table 1 .
Statistics of modelled SMB for Thwaites Glacier catchment, West Antarctica.The mean 1980-2009 SMB derived by snow radar is 457 mm w.e. a −1 .
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 www.the-cryosphere.net/10/459/2016/The Cryosphere, 10, 459-463, 2016