An investigation into the response of the Langjökull ice cap to future climate change scenarios.Introduction:Understanding the sensitivity of the cryosphere is fundamental when determining the impacts of climate change, due to its dynamic nature whereby ice masses rapidly adjust to changes in climate: temperature and precipitation in particular (Vaughan et al., 2013). Through understanding responses of ice caps, such as Langjökull, to climatic variations, representations can be applied to other maritime ice caps and glaciers in regions around the world (Aoalgeirsdottir et al., 2006). The GRANTISM (Greenland and ANTarctic Ice Sheet Model) model, adapted from Pattyn (2006), has been used to predict the responses of Langjökull ice cap to the future RCP climate change scenarios.  Using temperature, surface elevation and velocity observations, comparisons are made with model outputs to assess the model’s validity and whether it is fit for its required purpose.Study area overview:Langjökull is an ice cap situated in west Iceland; this study focuses an outlet glacier’s response, on the southwest part of the ice cap, has to future climate change (Fig.1). Langjökull has an area of 900km2 and volume of 190km3, covering a 50km-long mountain change (Björnsson and Pálsson, 2008). The ice cap is warm based and therefore dynamic in nature, responding sensitively to climate fluctuations overtime (Björnsson and Pálsson, 2008). Iceland receives a relatively mild and wet climate, with the Irminger ocean current limiting large seasonal fluctuations (Pálsson et al., 2012). Although latitude limits solar altitude, melting is primarily determined by net radiation (2/3) but also influenced by turbulent fluxes (1/3) (Einarsson, 1984; Björnsson and Pálsson, 2008).(a)Elevation (m)Distance along profile (m)N(b)Figure 1: (a) The elevation profile of the flowline from Le Brocq (2018). (b) An overview map to show the location of Langjökull (red box) and the study area (black box).Methods:3.1 GRANTISM set up:The GRANTISM model was modified from Pattyn (2006) to simulate a flowline through the Langjökull ice cap. Conservations of mass and momentum are used to determine the mass balance of the projected glaciers (Pattyn, 2006). Flow (A) and sliding parameters (B) are used to determine to total velocity, comprising of internal deformation and basal sliding velocities (Le Brocq, 2018). Ice thickness is calculated by using conservation of mass laws of accumulation and ablation along the flowline (Le Brocq, 2018). The amount of accumulation is determined using the ice surface elevation, which calculates the annual accumulation as equal to the winter balance, as justified in Flowers et al. (2007). The ablation is determined by the summer temperatures at Hveravellir Met weather station, using a lapse rate for changing temperature at given elevations (Flowers et al., 2007). The standard parameters used for modelling Langjökull accounted for basal sliding, but no isostasy or sea level variations are taken into account. The ice mass is also treated as isotherm, the simplest approach which assumes the temperature is uniform throughout the ice mass (Paterson, 1994). 3.2 Calibration:Equilibrium calibration was undertaken by running the model to its equilibrium state and comparing its surface elevation and length from transient glacier observations in 1997. The results showed equifinality whereby multiple optimum parameters could fit the available observed data by different assessment of the combination of the resulting RMSE of surface elevation and absolute length errors (Kirkby et al., 1987). Le Brocq (2018) selected A = 2×10-16 m2yr-1Pa-3 and B=2.5×10-11m2yr-1Pa-3 as the optimum parameters to represent Langjökull (Table.1 in Le Brocq, 2018). 3.3 Running the model:Future predictions were calculated by running the model glacier to equilibrium with the 1997 climate. This was done to ensure the glacier was responding to the climate scenarios input into the model and not the previous climate. The length and cross sectional areas (CSA) were recorded at 10-year intervals for different RCP scenarios, by altering the temperature and precipitation forcings after each 10-year iteration.Univariate sensitivity analysis was undertaken by running the model to equilibrium for different temperature forcings, whilst keeping other parameters constant (Barnsley, 2007). By comparing Greenland, Antarctica and Langjökull, assessment of the most sensitive ice mass was determined by the percentage of output change for the same change in temperature.Validation of the model was assessed by comparisons of modelled velocity and surface elevation change with observations of the transient glacier.Results:4.1 Future predictions:Fig.2a illustrates the degree to which the different RCP scenarios are predicted to affect glacier length, showing an earlier and greater decline for RCP8.5. RCP2.6 appears to only affect the length by 0.5km in 2077, whereas RCP8.5 initiates a change 20-years earlier, resulting in 2.5km retreat. Although glacier length does not appear to change drastically overtime, Fig.2b shows the CSA appearing to be affected more immediately and to a greater extent. Similarly, RCP2.6 shows the lowest decline in CSA of 1km2 and RCP8.5 impacting CSA most considerably, by 3km2. (a)(b)Figure 2: graphs to show the length (a) and cross sectional area (b) change overtime with different RCP scenarios (Vaughan et al., 2013), from changes in temperature and precipitation forcing. 4.2 Sensitivity:An ice mass with high sensitivity will result in a large change in the model output with only a small change in the model input (Ford, 1999 cited in Barnsley, 2007). Univariate sensitivity analysis of temperature shows Langjökull as the most sensitive ice mass to temperature forcing, shown by the steepest gradient of the trend line (Barnsley, 2007); however precipitation is not considered.Figure 3: a graph to show the sensitivity of Greenland, Antarctica and Langjökull with changes in temperature, with trend lines for each area. 4.3 Calibration:Fig.4 shows observed velocity is considerably lower than the modelled velocities, for the range of parameters given. As velocity is being overestimated, it would not be appropriate to increase the flow parameter so only the sliding parameters have been adjusted. The calibrated parameters determined in Le Brocq (2018) are used as the optimal parameters throughout the analysis due to the lowest combined error values and most accurate modelled values of velocity observations. Figure 4: a graph to show the modelled velocities against observed velocity in 2007 with different sliding (B) parameters and constant flow (A) parameter, run from 1997 equilibrium to 2007 with annual temperature observation forcings.4.4. Uncertainty:Fig.5 indicates a decrease in length and CSA when considering isostasy, with trends following the trends of the original parameters. CSA appears to decline at the same rates however length decreases by a greater amount when considering isostasy. (a)(b)Figure 5: graphs to show the different parameters effect on the length (a) and cross sectional area (b) of the glacier overtime for RCP2.6, comparing the original parameters with isostasy considerations.      Validation:The validity of the model is determined by the suitability to its intended outcomes and comparisons to reality (Barnsley, 2007; Mulligan and Wainwright, 2013). The usefulness of this model is determined by how valid and calibrated a model is (Oerlemans et al., 1998). Fig.4 and 6 both show significant differences between the modelled responses of velocity and elevation change respectively. The modelled mass balance gradient is steeper than the measured mass balance gradient, indicating the model has predicted a higher velocity than the observations of the transient glacier (Fig.4). As velocity was overestimated, it would be expected that elevation change and length would be underestimated as the faster flow would result in less ice lost from the terminus. To counteract this, parameter B was lowered as this would reduce the sliding and therefore velocity of the glacier; the error values of B=2.0×10-11m2yr-1Pa-3 are still low and therefore could be subjectively chosen as the optimal parameter to use. However, Fig.7 shows that a decrease in parameter B resulted in length and CSA increasing, which in glaciological terms is incorrect, suggesting a less accurate calibration or issues with the model numerics. Although no models are perfect representations of reality, this suggests that with the calibrations used, this model is not fit for purpose. This could be due to the model being run to equilibrium in 1997 when the transient glacier was not in an equilibrium state with its climate (Flowers et al., 2007). The lack of validity could also be argued to be a result of the lack of data for predictions to be compared against. Figure 6a: a graph to show the difference between observed surface elevation changes vs. modelled surface elevation changes, using annual temperature observations between 1997 – 2004.Figure 6b: a graph to show the modelled vs. measured 1997 mass balance with trendlines to show the mass balance gradient.      (a)(b)Figure 7: graphs to show modelled lengths (a) and cross-sectional areas (b) for different climate change scenarios, where ’RCP’ represents a change in parameter B to 2.0×10-11 and ’nRCP’ represents the normal parameters used in the original calibration.Discussion:6.1 Future prediction analysis:Future projection trends correlate with corresponding literature, which use more comprehensive 3D models. Björnsson et al. (2006)’s study models two centuries of ice flow showing slow retreat for the next 50-years, accelerating in decline after 100-years before disappearing after 200-years. This correlates with a relatively slow decline is seen within the first 50-years, with no change in length, before an acceleration towards 100-years. Although these trends appear to correlate, the extent of accuracy in the results could be argued as the model is not valid.6.2 Sensitivity:The high sensitivity of Langjökull is likely to be attributed to the low surface elevation whereby large proportions of the ice mass are close to its equilibrium line altitude (Pálsson et al., 2012). The high sensitivity of low lying glaciers such as Langjökull reiterates the importance of accurate predictions with future climate change. 6.3 Calibration:Equilibrium calibration presumes the glacier is in equilibrium with conditions in 1997, however Langjökull was not, therefore the model simulating the glacier from a different mass balance (Flowers et al., 2007). This can be calculated from the negative overall mass balance when the model is first set up, prior to any time-steps, which increases towards zero as the model is run to equilibrium. Oerlemans (1997) claims this is not a good way to assess the performance of a model as there is no assessment of the state of balance. Dynamic equilibrium provides a more accurate calibration where historical observations can be compared to multiple modelled values (Oerlemans, 1997), however there was not sufficient data to do this. 6.4 Uncertainty:As measurement of future parameters are not possible, all predictions carry uncertainty (Bevan, 2009), with forward-uncertainty analysis being prominently evident in this model as decisions such as parameters used are seen to significantly influence the model outputs.6.4.1 HveravellirMet StationPálsson et al. (2012) compares the sensitivity of Langjökull to other large ice caps in Iceland which are situated at high elevations, showing that calculations of mass balance sensitivity can be greatly determined by the locations of local weather stations. This could suggest that Hveravellir Met station is not providing accurate enough climate observations of Langjökull, due to micro-climates that form in these dynamic environments. Whilst temperature is influenced by height above sea level, precipitation varies within short distances, depending on local conditions (Einarsson, 1984). Oerlemans et al. (1999) also shows the development of microclimates in Iceland determined largely by katabatic flows, which occur despite the location of the North Atlantic storm track. GRANTISM model does not consider these variables and also does not take into account seasonal variability, which would disregard changes such as variations in basal melt and therefore sliding, accumulation and ablation.6.4.2 Isostasy and SurgingVillemin (2010) and Árnadóttir et al. (2009) have studied the influence that glacial retreat has had on isostatic uplift. Although studies have focussed on Vatnajökull, Árnadóttir et al. (2009) claims there is a need to model the impacts of smaller ice caps such as Langjökull when considering Iceland’s overall uplift. This indicates that isostasy is a significant factor and should be considered within the model, however this increases the complexity of the model and therefore increases its uncertainty. Suring is another mechanism that can significantly influence the velocity of glaciers, however the periods at which surge cycles occur are much longer than the timeframe of available data (Flowers et al., 2007). This would lead to overestimates of surging and therefore greater modelled glacial retreat.   Future work:The validity of the model was concluded to be a result of inaccurate calibration of model outputs to the observations of the transient glacier. To improve the mass balance gradient of the model and therefore produce more accurate velocity values, alternative lapse rates to Flowers et al. (2007)’s could be used and the model recalibrated. Dynamic calibration could also be undertaken to calibrate the model more accurately, however this would require more observed data.ConclusionIn conclusion, over the next 100-years Langjökull is predicted to retreat at an increasing rate, which supports appropriate literature (Björnsson et al., 2006; Palmer et al., 2009). Although GRANTISM showed these trends, the model outputs appeared to be significantly different to observations between 1997-2007. This could be a result of model numerics, lack of data for calibration and comparison, or inaccurate equilibrium calibration resulting in an inaccurate 1997 mass balance. Other sources of uncertainty within the model were identified as the location of Hveravellir Met station, contribution of isostasy and surging which were not considered within the model. 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