por_023.fm 168 Polar Research 26 2007 168 – 174 © 2007 The Authors mussen & J. Kohler Mass balance of three Svalbard glaciers reconstructed back to 1948 L. A. Rasmussen 1 & J. Kohler 2 1 Department of Earth and Space Sciences, University of Washington, Seattle, WA 98195, USA 2 Norwegian Polar Institute, Polar Environmental Centre, NO-9296 Tromsø, Norway Abstract A simple model using upper-air meteorological variables in the NCEP-NCAR Reanalysis database is used to model seasonal components of mass balance of three glaciers in Svalbard. The model was originally developed for glaciers in North America, and has been applied to glaciers in Norway, Sweden and Iceland. Over the period for which mass balance data are available for the three Svalbard glaciers, the model fit yields r 2 values ranging from 0.46 to 0.61 for winter balance B w and from 0.56 to 0.59 for summer balance B s . Sensitivity to + 1 ° C warming was about − 0.36 m yr − 1 water equivalent (w.eq.), caused mainly by increased ablation and secondarily by shift of precipitation from snow to rain. Sensitivity to a 10% increase in precipitation was about + 0.06 m yr − 1 w.eq. The model, calibrated over the period of observations, was used to extend the mass balance series back to 1948. At annual resolution, observed mass balance of the three glaciers correlates poorly with both the North Atlantic Oscillation (NAO) and with glaciers in Norway. Over two multiyear periods, the strongly positive NAO period 1990–1996 and the period afterward, glaciers in both Svalbard and especially Norway showed a pronounced decline in B w . However, B s for Svalbard glaciers was not more strongly negative after 1996, in contrast to glaciers in Norway. Keywords glacier mass balance; Svalbard; upper air model; NCEP-NCAR Re-analysis. Glacier volume changes fundamentally in response to climate change. Glacier volume changes over long time- scales amount to changes in glacier thickness or, equiva- lently, in the surface elevation, and can be studied using comparison of maps or digital elevation models. On shorter timescales, mass balance measurements are used to characterize changes. Glacier mass balance is the quan- tity of snow and ice either lost or gained on a particular glacier, and represents the material flux through the gla- cier surface over an interval of time. Although volume change estimates for glaciers argu- ably go as far back as the 1700s, in the form of front position measurements (Oerlemans 2001), the longest continuous annual mass balance measurements only date back to the 1940s. The latter are for glaciers in Scandina- via; in the Arctic, mass balance time series are even shorter, only going back to the early 1960s. The three glaciers considered in this paper, Austre Brøggerbreen, Midre Lovénbreen and Kongsvegen in western Svalbard (Fig. 1) have some of the longest time series (1967– present, 1968–present and 1987–present, respectively) in the High Arctic. A detailed description of the glaciers can be found in Lefauconnier et al. (1999). Previous workers have sought to extend the mass bal- ance record for these glaciers. Hagen & Leistol (1990) used meteorological measurements at Ny-Ålesund in a positive degree day (PDD) model of summer balance B s at Midre Lovénbreen. Lefauconnier & Hagen (1990) used multivariable linear regression between Ny-Ålesund observations and Austre Brøggerbreen net or annual mass balance B n . DeWoul & Hock (2005) applied a PDD model of ablation, using daily observations of tempera- ture at Ny-Ålesund, and linear regression between pre- cipitation observations there and accumulation for each of the three glaciers. In this paper we extend the mass balance using a sim- ple model driven by upper-air meteorological variables in the NCEP-NCAR Reanalysis database. The database has the advantage that it is global in extent, has 6-h temporal resolution, is free from missing observations and is main- Correspondence L.A. Rasmussen, Department of Earth and Space Sciences, University of Washington, Seattle, WA, 98195, USA. E-mail: LAR@ess.washington.edu. doi:10.1111/j.1751-8369.2007.00023.x L. A. Rasmussen & J. Kohler Three Svalbard glaciers reconstructed back to 1948 Polar Research 26 2007 168 – 174 © 2007 The Authors 169 tained as an integral part of a major scientific enterprise. The model was developed with data from South Cascade Glacier (48.4 ° N, 121.1 ° W): first for winter balance B w (Rasmussen & Conway 2001) and then for B s (Rasmus- sen & Conway 2003). It was successfully applied to glaciers in Alaska (Rasmussen & Conway 2004), Scandi- navia (Rasmussen & Conway 2005) and Iceland (Ras- mussen 2005). Data US National Centers for Environmental Prediction and US National Center for Atmospheric Research (NCEP-NCAR) Reanalysis data (Kalnay et al. 1996; Kistler et al. 2001) give values of meteorological variables at many levels in the atmosphere at 10 512 gridpoints spanning the entire globe, at integral multiples of 2.5 ° in both latitude and longitude. Data for 1948–2005 at the 1000- and 850-hPa levels were downloaded from East Anglia University, UK (http://www.cru.uea.ac.uk/cru/data/ncep). Variation of mean September–May upper-air variables with wind direction at the Reanalysis gridpoint (77.5 ° N, 12.5 ° E; Fig. 1) is shown in Fig. 2. Their seasonal varia- tion is shown in Fig. 3, along with the precipitation flux F and snow flux f (Eqns 1–3) calculated from direction φ ′ = 210 ° . Both figures show that f is strongest when the wind is from the south-west. The glacier mass balance data used are winter, summer and net balances B i , where i = winter, summer and net for the years 1967–2005 (Austre Brøggerbreen), 1968–2005 (Midre Lovénbreen) and 1987–2005 (Kongsvegen) (Hagen et al. 2003; Kohler, unpubl. data). Standard devi- ations of the seasonal balance components are shown in Table 1. The correlations r ns of B n with B s are larger than Fig. 1 Map showing the three study glaciers: Austre Brøggerbreen (A), Midre Lovénbreen (M) and Kongsvegen (K). Upper-air conditions are taken at the NCEP-NCAR Reanalysis gridpoint nearest the glaciers at 77.5 ° N, 12.5 ° E (filled circle). K M A 10º 20º Svalbard 30º 77º 79º 5 km N Fig. 2 Variation with wind direction of mean September–May conditions over the period 1948–2005 at the NCEP-NCAR Reanalysis gridpoint (77.5 ° N, 12.5 ° E): (a) relative humidity RH, (b) temperature T , (c) wind speed and snow flux and (d) frequency distribution of wind direction. RH and wind are at 850 hPa; T and are at 200 m. 90 180 2700 360 Wind direction Relative frequency (d) Wind speed Snow flux 6 8 10 m s -1 (c) -10 -5 C Temperature (b) 70 80 Relative humidityP e rc e n ta g e (a) fw fw http://www.cru.uea.ac.uk/cru/data/ncep 170 Polar Research 26 2007 168 – 174 © 2007 The Authors Three Svalbard glaciers reconstructed back to 1948 L. A. Rasmussen & J. Kohler r nw ( B n with B w ), in rough proportion to the amount by which σ s is larger than σ w , because the correlation r ws between B w and B s is so small (see Eqn 13 of Rasmussen & Conway 2001). The r ws are small, as is the case for glaciers elsewhere in the world (see fig. 6 of Dyurgerov & Meier 1999; and fig. 5 of Braithwaite & Zhang 1999). Glacier to glacier correlation of B s and of B w are both coherent spatially (Table 2). Recent variations Although mass balance at the three Svalbard glaciers correlates poorly with the mass balance at glaciers in northern and maritime Norway (Rasmussen, in press), they do share some longer-term characteristics. Correla- tions of B n and B s between the two regions are positive but small. Correlations of B, and of B 3 between the two regions are positive but small, and those of B w are nega- tive but small. The only exceptions are r ( B n ) = 0.69 between Kongsvegen and Langfjordjøkelen (70.1 ° N, 21.8 ° E) and 0.47 < r ( B s ) < 0.50 for the three glaciers with Engabreen (66.6 ° N, 13.8 ° E). Correlation with three dif- ferent measures of the North Atlantic Oscillation (NAO) that are significant at annual resolution for glaciers in Norway with r ( B n ) > 0 and r ( B w ) > 0 are negligible for all three glaciers in Svalbard. Low correlation with the NAO was also found by Pohjola & Rogers (1997), Nesje et al. (2000) and Washington et al. (2000). There were some similar changes in the two regions, however, over multi- year periods in phase with the NAO regime. At ten gla- ciers in Norway the mean change in the mass balance components δ B i (in units of m w.eq.) obtained from com- paring the strong NAO period 1990–1996 with the fol- lowing period 1997–2004 was δ B n ≈ –1.0, consisting of changes δ B w ≈ –0.4 and δ B s ≈ –0.6 (Andreassen et al. 2005). At the glaciers in Svalbard, changes between 1990–1996 and 1997–2005 were − 0.29 < δ B w < –0.18, all significant at 99%, but changes in summer balance − 0.13 < δ B s < + 0.03 were weaker. Upper-air model Precipitation at the glacier is assumed to be proportional to the precipitation flux F at the 850-hPa level. It is estimated from measurements of wind and humidity by the relation (1)F U U = ≥( ) ( )    RH otherwise 0 0 . Fig. 3 Seasonal variation of mean conditions over the period 1948–2005 at the NCEP-NCAR Reanalysis gridpoint (77.5 ° N, 12.5 ° E). (a) Wind direc- tion at 850 hPa, (b) wind speed at 850 hPa, (c) temperature T interpolated at 200 m, (d) percentage relative humidity RH at 850 hPa and (e) precipita- tion flux F calculated from Eqns (1) and (2) using φ′ = 210° and snow flux f, the part of F when T < +2°C at 200 m. Monthly resolution. Jan Mar May Jul Sep Nov 240 260 280 300 Wind direction D e g re e s (a) 1 2 Wind speed (b) -10 -5 0 Temperature C (c) 72 76 80 Relative humidity P e rc e n ta g e (d) 1 2 3 Precipitation Snow (e) m s -1 m s -1 Table 1 Mean and standard deviation (both in m water equivalent [m w.eq.]) and correlation (percentage r) of seasonal mass balance components over the period of record of observations (n years). All rnw and rns are significant at 99%. Glacier °N °E n σw σs rnw rns rws Austre Brøggerbreen 78.9 11.8 39 0.67 −1.16 0.15 0.30 43 89 −3 Midre Lovénbreen 78.9 12.1 38 0.70 −1.09 0.17 0.29 40 84 −16 Kongsvegen 78.8 13.0 19 0.71 −0.79 0.19 0.28 74 89 36 Bw Bs Table 2 Glacier to glacier correlation (percentage r, significant at 99%) of winter balance Bw (above the diagonal) and summer balance Bs (below the diagonal) over the common period of observations. Values on the diago- nal are for both Bw and Bs. Glacier 1 2 3 1 Austre Brøggerbreen 100 94 76 2 Midre Lovénbreen 96 100 80 3 Kongsvegen 90 84 100 L. A. Rasmussen & J. Kohler Three Svalbard glaciers reconstructed back to 1948 Polar Research 26 2007 168 – 174 © 2007 The Authors 171 Here, 0 ≤ RH ≤ 1 is the relative humidity, and U is the component of the 850-hPa wind in the empirically deter- mined critical direction φ′. That is, (2) in which φ850 is the wind direction and is its speed in ms−1. Although precipitation indeed might occur with the wind in the opposite direction to φ′, empirical results show it correlates most strongly with the U component. Moreover, the simple model described here obtained bet- ter results (Hayes et al. 2002) in a direct comparison with a sophisticated mesoscale precipitation model. Precipitation is assumed to fall as snow if the tempera- ture at elevation z1 = 200 m is less than the critical tem- perature T ′ (3) Here f is termed the snow flux, T(z1) is interpolated between the 1000- and 850-hPa levels in the NCEP- NCAR Reanalysis data, and T ′ = +2°C is the rain–snow discriminator (Oerlemans 1993; Rasmussen et al. 2000; Forland & Hanssen-Bauer 2003; Kohler & Aanes 2004). The physical basis for using +2°C as the discriminator is that precipitation forming at high altitude as snow requires a layer of air with T > 0°C to change to rain; at the average wet adiabatic lapse rate of −6°C km−1, +2°C corresponds to a layer thickness of ≈300 m. The model estimates winter balance by (4) Coefficients αw and βw are obtained by linear regression of observed winter balance Bw and , which is the September–May average of f. Because RH is dimension- less, both F and f have the same units as U (ms−1), so αw has units to convert to m w.eq. The quantity αw corresponds most closely to actual snowfall, but is higher by about a factor of two than the September–May precipitation measured at Ny-Ålesund, which might reflect either higher precipitation on the glaciers caused by orographic lifting or undercatch in the precipitation gage (e.g. Forland & Hanssen-Bauer 2000). U V= − ′( ) r 850 850cos f f , r V850 f F T z T = ( ) ≤ ′( ) ( )    1 0 otherwise . Bw* B* fw w w w= +α β f w f w The model estimates summer balance by (5) in which is the June–August average of temperature interpolated at altitude z2 = 500 m between the 1000- and 850-hPa levels, considering only T ′ > T ″, where T ″ is the degree-day temperature threshold, here taken to equal 0°C. Coefficients αs and βs are obtained by linear regres- sion of the observed summer balance Bs with . Both and are estimated from upper-air condi- tions at the NCEP-NCAR Reanalysis gridpoint 77.5° N, 12.5° E. Mean winter conditions for the period 1948– 2005 are shown in Fig. 2. The only model parameter that was varied experimentally to optimize the model results was the critical direction φ′ (Table 3). All the other param- eters, the altitudes z1 = 200 m and z2 = 500 m, the critical temperatures T′ = +2°C and T″ = 0°C, and the seasons September–May and June–August, were held constant. For each glacier, model parameters α and β were deter- mined by the regressions of Eqns (4) and (5) fitted to the observed B. For all three glaciers βw ≈ 0.05 so that α accounts for almost all of . Model results Model estimates of seasonal components, both of which are identified by the calendar year in which the balance year ends, are illustrated in Fig. 4. As pointed out by von Storch (1999), the variance of regression results is smaller than that of the variable being fitted (unless the regres- sion fits it exactly). Goodness of fit (Bevington 1969) is expressed by the coefficient of determination (6) Here, rms is the root mean square of the differences between the model estimates B* and the measured values B, and σ is the standard deviation of B. Results are shown in Table 3. They are generally much better for Bw and slightly worse for Bs compared with those obtained by deWoul & Hock (2005). Bs* B* T ,s s s= +α β T T B*w B*s f w B*w r 2 2 1= −     rms s . Table 3 Model results (percentage r2 and m water equivalent [m w.eq.], per year rms) over the period of record using critical direction φ′ with upper-air model and and from deWoul & Hock (2005). Models: (1) upper-air model, (2) correlation with Austre Brøggerbreen, (3) average of models (1) and (2). Glacier Model φ′ rmsw rmsn rmss Austre Brøggerbreen 1 210 49 55 56 0.11 0.23 0.20 <15 61 Midre Lovénbreen 1 210 46 52 56 0.12 0.21 0.19 <15 76 Kongsvegen 1 235 61 68 59 0.12 0.22 0.18 67 68 Kongsvegen 2 58 80 80 0.13 0.18 0.13 Kongsvegen 3 67 80 77 0.11 0.17 0.14 r̂w 2 r̂s 2 rw 2 rn 2 rs 2 r̂w 2 r̂s 2 172 Polar Research 26 2007 168 – 174 © 2007 The Authors Three Svalbard glaciers reconstructed back to 1948 L. A. Rasmussen & J. Kohler Hagen & Leistøl (1990) obtained linear relations between Lovénbreen Bs and Ny-Ålesund meteorological observations with r = 0.75 for June–August temperature and r = 0.88 for June–September PDD. Lefauconnier & Hagen (1990) used multivariable linear regression to relate Brøggerbreen Bn to Ny-Ålesund observations, obtaining r 2 = 0.77 with July–August PDD and October– May precipitation, whereas with PDD taken separately for four individual summer periods, r 2 increased to 0.81. Our model results are only weakly sensitive to values of model parameters z1 and z2 as well as to the period of days over which averages are formed. If the period of forming is extended into June, for instance, it will be lower because f decreases in June (Fig. 3); in the regression of Eqn (4), however, the coefficient αw will tend to increase so as to match the observed Bw as well as possible with the smaller . Varying z2 has little effect because appears linearly in Eqn (5) and T(z) is roughly linear, so that αs will be adjusted during the regression by an amount roughly proportional to the product of the lapse rate dT/dz and the difference in z2, so as to match the observed Bs as well as possible. The values for the critical direction φ′ are slightly differ- ent for Kongsvegen and the two smaller glaciers Austre Brøggerbreen and Midre Lovénbreen. This might reflect local topographic effects as the accumulation area of the smaller glaciers is protected from southerly winds by surrounding mountains, whereas snowfall on the more f w f w T exposed Kongsvegen is more susceptible to wind redistri- bution. On the other hand, the differences in critical direction φ′ are relatively small, so this may simply reflect random errors in the data. Sensitivities of calculated Bw and Bs to hypothetical warming ∆T or increased precipitation ∆F are shown in Table 4. Sensitivities to ∆T are less than those found by deWoul & Hock (2005), and sensitivities to ∆F are about the same. A possible explanation of the lower Bs sensitiv- ities compared with those of deWoul & Hock (2005) is that the upper-air model has arbitrarily fixed dates, and might therefore miss some ablation occurring in May or September. Reconstructed mass balance, 1948–2005 For each glacier, coefficients of Eqns (4) and (5) obtained over the period of record (POR) of observations were applied to upper-air data from prior to the POR back to 1948. Cumulative for Brøggerbreen and Lovénbreen is formed from for the years before the POR, and from observed Bn during the POR. For Kongsvegen, however, the model was used for 1948–1966, but for 1967–1987 was taken to be the average of the model estimate and that of the linear correlation with Brøggerbreen. As was the case for all seven glaciers in southern Nor- way, where the record from Storbreen spanned the entire period of model results, the average of the model and the linear correlation with Storbreen was a more accurate estimator than either the model alone or the correlation alone. For Kongsvegen, the rms error for the model was 0.22, and for the correlation with Brøggerbreen the rms error was 0.18. For the average of the model and the correlation it was 0.17. Cumulative balance before 2005 (Fig. 5) is defined by (7) Here, Bj is the value of in year j and B2005 is defined to be zero. Bn* B B Bn w s* * *= + Bn* B Bj j j = − +∑ 1 2004 * . Bn* Table 4 Sensitivity (m water equivalent [m w.eq.]) to +1°C temperature change and to a 10% increase in precipitation flux F, from the upper-air model and from deWoul & Hock (2005). Glacier Upper-air deWoul & Hock dBw/dT dBs/dT dBn/dF dBw/dT dBs/dT dBn/dF Austre Brøggerbreen −0.06 −0.33 +0.06 −0.47 Midre Lovénbreen −0.06 −0.30 +0.07 −0.56 Kongsvegen −0.06 −0.29 +0.07 −0.02 −0.41 +0.05 Fig. 4 Model (line) and observed seasonal mass balance components (�, winter balance [Bw]; �, summer balance [Bs]). (a) Austre Brøgger- breen, (b) Midre Lovénbreen, (c) Kongsvegen. 1960 1980 2000 -1 0 +1 -1 0 +1 -1 0 +1 M a ss b a la n ce (m w .e q .) (a) (b) (c) L. A. Rasmussen & J. Kohler Three Svalbard glaciers reconstructed back to 1948 Polar Research 26 2007 168 – 174 © 2007 The Authors 173 For the years when Bn was measured, uncertainty is taken to be ∆obs = 0.3 m w.eq., and for years when it was not, (8) in which the rmsn values from lines 1, 2 and 5 of Table 3 are used for ∆est. On the assumption that errors in the combined reconstructed–observed series are uncorrelated from year to year, the uncertainty in the cumulative value Bj is (9) The cumulative curves in Fig. 5 are shown with a ±1σ band. If there are systematic errors in the series, how- ever, the true σj will be larger. Between the periods 1948–1967 and 1968–2005, net balance Bn became more negative, as shown by the change of mean slope of the cumulative curves in Fig. 5. This was caused by Bs becoming more negative, whilst Bw was little changed. For Austre Brøggerbreen between these periods, the mean (Eqn 5) increased from 1.19 to 1.64°C, but the mean (Eqn 4) declined only from 2.41 to 2.36 m s−1. Lefauconnier & Hagen (1990) used multivariable linear regression to relate Bn at Brøggerbreen to the July– August temperature and the September temperature at Longyearbyen over the period 1967–1988 with r 2 = 0.52. ∆ ∆ ∆= +obs est ,2 2 s j j j = ∑ ∆2 2004 . Bn* T f w They obtained cumulative changes of −18 m over 1912– 1948 and −9 m over 1948–1967. The 1948–1967 cumula- tive change from the upper-air model (Fig. 5) was −6 m. Linear regression over the period of measurements of Bn at the three glaciers had r = 0.96 between Brøgger- breen and Lovénbreen and 0.90 between Brøggerbreen and Kongsvegen (see also Table 2). When these regres- sion coefficients are applied to the −18 m cumulative change found by Lefauconnier & Hagen (1990), at Brøg- gerbreen, the 1912–1948 changes are −15 m at Lovén- breen and −2 m at Kongsvegen. Combined with the 1948–2005 changes (Fig. 5), the 1912–2005 changes are −42 m at Brøggerbreen, −33 m at Lovénbreen and 0 m at Kongsvegen. Conclusions The upper-air model gives a good fit to the observed balances, is substantially better than another published model for Bw at two glaciers, and is moderately worse for Bs. Its sensitivity of Bs to warming is less than that calcu- lated by the other model, and its sensitivity of Bn to increased precipitation is about the same. The upper-air model has the advantage of using a database maintained as an integral part of an ongoing major scientific enter- prise as its input. Calculations can therefore easily be extended as future mass balance measurements become available. Moreover, the model can also be used to esti- mate mass balance for years in which it is not measured. It could also be easily applied to mass balance records for other glaciers in Svalbard. 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