Masters Thesis

Distributed modelling of the energy and mass-balance at the surface of Langenferner, Ortles-Cevedale Group/Italy

Diploma Thesis

submitted to the Faculty of Geo- and Atmospheric Science University of Innsbruck

presented by: Stephan Peter Galos

supervised by: Priv.-Doz. Dr. Thomas Mölg

Innsbruck, September 2010

für Peter...

Abstract

In order to study the spatial distribution of surface mass balance and the related surface energy fluxes of an alpine glacier, a physically based 2D-model was applied to Langenferner, Ortles-Cevedale Group/Northern Italy for the period 2004-2008. The model was driven by meteorological data from six permanent automatic weather stations in the vicinity of the glacier. Meteorological data from the stations which are maintained by the Hydrographic Office of the Autonomous Province of Bolzano were extrapolated to the glacier surface using simple transfer functions. The energy and mass balance model was optimized using data from an automatic weather station which was temporarily installed nearby the glacier. To validate the results, the model output was compared to stake measurements and snow probing data from the glacier. Modelled annual mean specific mass balance showed a sufficient accordance to the measurements at Langenferner except for the hydrological year 2007/2008. The considerable underestimation of melt ablation in this year could be attributed to deficiencies in the employed albedo parameterization. Model results revealed that the spatial distribution of surface mass balance at Langenferner is strongly dependent on shortwave net radiation while other surface energy fluxes showed less influence on the spatial pattern. In order to test the sensitivity of the model to changes in selected model parameters as well as the meteorological input data, a series of sensitivity tests were performed. The model sensitivity to changes in air temperature shows that an increase of 1°C causes a change in the mean specific mass balance of -1338 mm w.e., which is similar to the result of a 20 % decrease in precipitation. Neglecting topographic shading due to surrounding peaks, in turn, would only lead to a change of -76 mm w.e. in the mean specific mass balance for 2004/05. Finally, some suggestions for further model improvements and perspectives for future work are presented.

vii

Zusammenfassung

Ziel der vorliegenden Arbeit war es, die räumliche und zeitliche Variabilität der Massen- bilanz, sowie der Energieflüsse an der Oberfläche eines alpinen Gletschers mit relativ komplexer Topographie zu studieren. Zu diesem Zweck wurde für den Zeitraum 2004- 2008 ein prozessbasiertes, zweidimensionales Energie- und Massenbilanzmodell auf den Langenferner in der norditalienischen Ortlergruppe angewandt. Als Input für das Modell wurden meteorologische Daten von sechs automatischen Wetterstationen des Lawinen- warndienstes Südtirol im weiteren Umfeld des Gletschers herangezogen. Die Daten dieser Stationen wurden mit Hilfe von einfachen Transferfunktionen auf die Oberfläche des Gletschers extrapoliert. Zur Optimierung des Energie- und Massenbilanzmodells wurde auf die Daten einer automatischen Wetterstation zurückgegriffen, die im Frühjahr 2010 im Rahmen dieser Studie in unmittelbarer Nähe des Gletschers aufgestellt wurde. Daten von Ablationspegeln und Schneesondierungen auf dem Gletscher dienten sowohl zur Optimierung des Modells, als auch zur Validierung der Ergebnisse. Die Übereinstim- mung der modellierten mittleren spezifischen Massenbilanzen mit den Beobachtungen am Langenferner ist im Allgemeinen zufriedenstellend, mit Ausnahme des hydrolog- ischen Jahres 2007/08. Für dieses Jahr wurde die Schmelzablation vom Modell deutlich unterschätzt, was einer Schwäche in der verwendeten Albedoparametrisierung zuge- ordnet werden konnte. Die Modellergebnisse zeigen, dass die räumliche Verteilung der Massenbilanz am Langenferner stark vom Budget der kurzwelligen Strahlung abhängt, während andere Energieflüsse das räumliche Bilanzmuster weniger stark beeinflussen. Um die Empfindlichkeit des Modells auf Änderungen ausgewählter Modellparameter einerseits, und auf Änderungen in den meteorologischen Inputdaten andererseits, zu testen, wurde eine Reihe von Empfindlichkeitsläufen durchgeführt. Diese zeigten, dass die modellierte Bilanz überaus sensibel auf eine Erhöhung der Lufttemperatur um 1°C reagiert (-1338 mm w.e.). Diese Änderung entspricht in etwa einer Änderung des Niederschlags um -20 %. Das Vernachlässigen der Beschattung durch umgebende Gipfel führt hingegen nur zu einer Änderung der mittleren spezifischen Bilanz um -76 mm w.e. Abschließend werden einige Vorschläge zur Weiterentwicklung des Modells sowie mögliche zukünftige Forschungsinhalte präsentiert.

Contents

Abstract vii

Zusammenfassung ix

List of Abbreviations1

1 Introduction and Study Aim3 1.1 Background...... 3 1.2 Methods and Objective...... 3 1.3 Structure of the Thesis...... 5

2 Investigation Area7 2.1 Geographical Setting...... 7 2.2 Climate...... 8 2.3 Historical Aspects...... 9

3 Data 13 3.1 Meteorological Data...... 13 3.1.1 Weather Stations...... 13 3.1.2 Sulden Madritsch...... 14 3.1.3 AWS Felsköpﬂ...... 15 3.1.4 Quality of Meteorological Data...... 16 3.1.5 Temperature...... 17 3.1.6 Global Radiation...... 17 3.1.7 Relative Humidity...... 18 3.1.8 Wind Speed...... 19 3.1.9 Precipitation...... 19 3.1.10 Air Pressure...... 20 3.2 Glaciological Data...... 24 3.3 Topographic Data...... 25

4 The Energy and Mass-Balance Model 27 4.1 Development and Application of the EMB-model...... 27 4.2 Energy and Mass Balance of a Glacier Surface...... 27

xi xii Contents

4.3 Shortwave Radiation...... 30 4.3.1 Direct Shortwave Radiation...... 30 4.3.2 Diﬀuse Shortwave Radiation...... 31 4.3.3 Eﬀective Cloud Cover Fraction and Cloud Impact...... 33 4.3.4 Topographic Shading at the Measurement Site...... 33 4.3.5 Topographic Shading in the EMB-Model...... 35 4.3.6 Surface Albedo...... 35 4.4 Longwave Radiation...... 36 4.4.1 Incoming Longwave Radiation...... 36 4.4.2 Outgoing Longwave Radiation...... 37 4.5 Turbulent Fluxes...... 37 4.5.1 Sensible Heat...... 37 4.5.2 Latent Heat...... 38 4.5.3 Stability Correction...... 38 4.5.4 Roughness Lengths...... 39 4.6 Surface Temperature and Ground Energy Flux...... 40 4.7 Surface Accumulation...... 41

5 Working with the EMB-Model 43 5.1 Model Options and Settings - The mbminﬁle...... 43 5.2 Meteorological Input - The Input File...... 43 5.3 Topographic Model Input...... 44 5.3.1 Glacier Mask...... 44 5.3.2 Elevation...... 44 5.3.3 Slope and Aspect...... 44 5.3.4 Sky View Factor...... 44 5.4 Running the Model...... 46 5.5 Analysing the Model Output...... 46

6 Model Optimization on Felsköpﬂ Data 47 6.1 Incoming Shortwave Radiation...... 47 6.2 Incoming Longwave Radiation...... 48 6.3 Air Temperature...... 49 6.4 Wind Speed...... 50

7 Results 53 7.1 The 0D-Model - Stake Balance...... 53 7.2 The 2D-Model - The Mass Balance of Langenferner...... 55 7.2.1 Vertical Mass Balance Proﬁles...... 56 7.2.2 The Role of Sublimation...... 58 7.2.3 The 2008-Problem...... 58 Contents xiii

7.2.4 The 2006-Problem...... 60 7.3 Surface Energy Fluxes...... 61 7.4 Model Sensitivity...... 69 7.4.1 Topographic Shading...... 70 7.4.2 Model Sensitivity - a Summary...... 71

8 Conclusion 73 8.1 General Aspects...... 73 8.2 Discussion and Outlook...... 74

Bibliography 77

List of Figures 81

List of Tables 83

Appendix A - The mbminﬁle 85

Appendix B - Output Analysis & Analytools 89

Danksagung 91

Curriculum Vitae 93

List of Abbreviations

0D zero dimensional 2D two dimensional AWS automated weather station DEM digital elevation model D-GPS diﬀerential global positioning system EMB energy- and mass balance GPS global positioning system HOB Hydrographic Oﬃce of the Autonomous Province of Bolzano LIA Little Ice Age m meter m a.s.l. meter above sea level mm w.e. millimeter water equivalent m w.e. meter water equivalent NCAR National Center for Atmospheric Research NCEP National Center for Environmental Prediction REA re-analysis RMSE root mean square error SEB surface energy balance SVF sky view factor

Symbols used in the Text

LWin incoming longwave radiation LWnet net longwave radiation LWout outgoing longwave radiation QG ground heat flux QL turbulent flux of latent heat QM melt energy flux QS turbulent flux of sensible heat SWin incoming shortwave radiation SWnet net shortwave radiation SWout outgoing shortwave radiation

1 Introduction and Study Aim

1.1 Background

In the last few decades, retreating glaciers around the world have received much attention. They are often regarded as a clear and unequivocal sign of global climate change (Oerlemans et al., 2009). However, climate change is often focused on changes in temperature while other important atmospheric variables such as humidity, cloudiness, precipitation, solar irradiance and related feedbacks receive much less attention and are often neglected. In fact, climate is the synthesis of all meteorological parameters over a long period of time (at least 30 years). Retreating glaciers therefore are not solely a response to a warming atmosphere but also to changes in precipitation, humidity, solar radiation or cloudiness (Francou et al., 2003; Hastenrath, 2001; Mölg et al., 2003) The surface mass balance of a glacier represents the most direct link between the behaviour of a glacier and the underlying climatic forcing (Mölg et al., 2008). To properly assess and better understand the driving factors behind glacier change in a certain region, it is therefore necessary to study the mass balance processes of the respective glaciers.

1.2 Methods and Objective

A wide range of different models have been developed to simulate glacier mass balance and to study the link between climate change and glacier fluctuations. The complexity of such models is various and ranges from simple regressions of mean summer air temperature and snowfall on mass balance (Greuell, 1992), over degree-day ablation models (Kuhn, 1993; Hock, 1999), to sophisticated physically-based 2D glacier mass balance models (Klok and Oerlemans, 2002; Mölg et al., 2009b) which calculate the sum of accumulation and ablation on a glacier for one or more years on the basis of the surface energy balance (SEB). To better understand and correctly interpret the diverse behaviour of glaciers in the context of a changing climate, it is necessary that a model resolves the governing physical processes on the glacier surface (Oerlemans, 2010) and also their spatial distribution. Examples of studies applying zero dimensional (0D) process based models exist for a variety of locations in the whole world. Bintanja and Van den Broeke(1995) and Hoffman et al.(2008) simulated the SEB of Antarctic glaciers, Greuell and Smeets

3 4 1 Introduction and Study Aim

(2001) and Brock et al.(2000) did the same for mid-latitude glaciers, while Wagnon et al.(2003) and Mölg and Hardy(2004) modelled the mass balance of tropical glaciers. All these models calculate the glacier mass balance or the SEB at one or more points of the respective glacier. One of the first process based two dimensional (2D) mass balance models was the one presented by Klok and Oerlemans(2002). Meanwhile several studies on the spatial distribution of SEB and mass balance of glaciers have been carried out, see e.g. Oerlemans and Klok(2004), Hock and Holmgreen(2005), Reijmer and Hock(2008), Mölg et al.(2009b) or Konya and Matsumoto(2010). Most of these studies are based on meteorological data from weather stations located on a glacier for both driving the model and the validation of model results. Some of the studies use data from off-glacier weather stations as model input but still benefit from weather stations on the glacier to optimize/validate the model output. The aim of the study in hand is to simulate the spatial distribution of the surface energy and mass fluxes on a mid latitude glacier without using meteorological data from the glacier surface. Several permanent weather stations in the vicinity of Langenferner provided data to drive a high resolution 2D energy and mass balance model (Mölg et al., 2009b) (EMB-model hereafter) for the five year period 2004 to 2008. The EMB-model developed by Thomas Mölg (University of Innsbruck) has already been used in several studies on mass balance and the associated climatic drivers of tropical glaciers, e.g. Mölg and Hardy(2004), Mölg et al.(2008), Mölg et al.(2009b) and Winkler et al.(2009). In the course of this thesis work, the model was tested and optimized for the application to a typical alpine glacier. To optimize some of the model parameterizations, especially the scheme for incoming longwave radiation, a one month dataset from a temporarily installed automatic weather station near the glacier was used. Glaciological data from a well distributed ablation stake network on the glacier as well as data of mean specific seasonal mass balances obtained by the direct glaciological method (Kaser et al., 2003), were used to validate the model results. One of the main challenges of this work was to deal with an imperfect set of meteorological data. Even if the time series of input data had been free of gaps, records from at least four different stations would have been needed to provide all of the six required meteorological input variables to the EMB-model. The distance between Langenferner and the station furthest away is 22km, the vertical displacement is up to 1800 m. Due to this fact, methods to transfer data from the weather station sites to the glacier had to be applied. As the weather stations are not located on a glacier and therefore sample boundary layer conditions which strongly differ from that measured on a glacier surface, the transfer of meteorological variables (discussed repeatedly within this work) is even more challenging. 1.3 Structure of the Thesis 5

1.3 Structure of the Thesis

After a short introduction of the study site in chapter2, a detailed description of the data used in this thesis study follows in chapter3. Chapter4 provides information on the EMB-model in general as well as an introduction to the parameterizations of the governing physical processes concerning energy and mass balance in the model. Additionally some site-speciﬁc model adjustments are presented. Chapter5 provides relevant information on both the preparation of model input (meteorological as well as topographic) and on the analysis of the model output. An optimization of the radiation scheme is presented in chapter6. The results of this study are summarized and discussed in chapter7, while chapter8 provides a short conclusion and presents an outlook for possible future work.

2 Investigation Area

2.1 Geographical Setting

Langenferner is a relatively small valley glacier in the eastern Alps, located at the head of Martell-Valley, in the Ortles-Cevedale Group in the Autonomous Province of Bolzano, northern Italy (46.28° north / 10.60° west). The glacier surface area is 1.8 km2 and it extends from 3380 down to 2690 m a.s.l. (2009). Langenferner is one of several glaciers ﬂowing down from the Cevedale-massive. Its upper section is mainly exposed to the north, while the tongue is ﬂowing eastwards. Langenferner is part of the Plima-river catchment which comprises an area of ≈ 162 km2 and contributes to Etsch-river discharge, the main water resource for the extensive agriculture in the Vinschgau-Valley.

Figure 2.1: The study site: Langenferner’s tongue (left) with Königsspitze, 3859 m in the background and the glacier’s upper section (right) with Zufallspitze and Cevedale seen from a ridge near Eisseespitze.

7 8 2 Investigation Area

Figure 2.2: Map of Tirol (Austrian province) and the Autonomous Province of Bolzano (Northern Italy) showing the location of Langenferner (red dot) and the weather stations providing data for this study: 1) Sulden Madritsch, 2) Schöntauf- spitze, 3) Lake Zufritt, 4) Felssporn 5) Rossbänke and 6) Glurns.

2.2 Climate

Similar to the neighbouring Ötztal Alps in the north and the Bernina Group in the west, the Ortles-Cevedale Group is a relatively dry mountain area in the eastern Alps (Fliri, 1975). Yearly mean precipitation (1971-2000) at lake Zufritt (1851 m) is 786 mm while values for Vinschgau are even lower (≈ 500 mm). Most of the precipitation in this area falls in summer due to convective events which lead to an increased precipitation frequency compared to the rest of the year. Synoptic patterns are dominated by southwesterly airﬂow and are often related to cyclones over the Mediterrannean Sea, which occur with increased frequency from September to December. Thus the most substantial precipitation events can be expected at this time of the year. As a consequence of the relatively dry climate, the amount of solar radiation (and thus air temperature) is high compared to similar altitudes in the pre-alps or at the 2.3 Historical Aspects 9 northern alpine ridges. More information on climatic and meteorological conditions at the study site can be found in chapter 3.1.

2.3 Historical Aspects

The glaciers of the Martell-Valley attracted the attention of early glaciologists and hydrologists because the retreating glaciers formed ice dammed glacial lakes which resulted in a number of outburst floods during the late 19th century (Finsterwalder, 1890). In the years 1888, 1889 and 1891 such floods caused considerable damage in the Martell-Valley. In order to constrain the harmful impact of the glacier outbursts for the valley and its inhabitants, an artificial dam was built in 1893. This was one of the largest artificial dams in the Alps at that time and it can still be seen today about 1 km south of Zufall-Hut.

Figure 2.3: A historic map by Sebastian Finsterwalder(1890) showing the supraglacial lake on the tongue of Langenferner (red arrow) the outbursts of which caused severe damage in the Martell Valley. Note also the small dotted line (blue arrow) marking the maximum LIA-extent of the glaciers.

Like many east alpine glaciers, Langenferner reached its Little Ice Age (LIA) maximum-extent in the first half of the 19th century, with little change in mass until the 1850s. At this time the three glaciers Fürkeleferner, Zufallferner and Langen- 10 2 Investigation Area ferner were confluent, with a common terminus at about 2300 m (see 2.3). Fürkeleferner separated around 1870, while Langenferner and Zufallferner probably stayed connected until the early 1890s (Simony, 1865; Finsterwalder, 1890). Compared to its maximum LIA-extent, the terminus of Langenferner retreated approximately 3 km, which is quite uncommon for an alpine glacier of this relatively small size and which is more than the retreat of Fürkeleferner and Zufallferner in the same time. This contrast can be partly explained by the former shape, orientation and area-altitude distribution of the three glaciers. During World War I (1914 to 1918) the Ortler-mountains, including Langenferner, were part of the frontline where Austrian and Italian troops fought against each other at the "Gebirgsfront". A cable lift was installed up to the glacier to sustain the military positions around the glacier. Many relicts of that time, such as parts of weapons and ruins, can still be found on Langenferners surface and on the rocks and summits surrounding it. Toponyms like "Tre Cannoni" or "Hallsche Hütte" illustrate the military history of several places around the glacier. In the late 1950s two ski-lifts were built from Casati Hut up to the uppermost part of Langenferner. In the following years summer-skiing was possible on the slopes of the upper glacier area. Due to weak infrastructure (people had to walk up far from pizzini hut) this business was soon unprofitable and the skiing area was closed. Lift masts and steel ropes remained on the glacier and are still there today.

Figure 2.4: Photograph showing the common terminus of Zufallferner (left) and Langenferner (right) in the late 19th century. (Finsterwalder, 1890) 2.3 Historical Aspects 11

Figure 2.5: A historic postcard showing Zufallferner and a small portion of Langen- ferner (bottom right corner), probably around 1900.

Figure 2.6: A drawing by Friedrich Simony, (1855) showing the terminus of Fürkele- ferner. Langenferner and Zufallferner in the background.

3 Data

Three diﬀerent sorts of data were used in course of this thesis study. Meteorological data for the period January 1st 2004 to December 31st 2008, obtained from six synoptic weather stations in the vicinity of Langenferner, were used as input to the EMB-model. Data from an additional station, installed near the glacier were used to optimize the model. Glaciological data from mass balance measurements were used for both optimzation of the EMB-model and validation of the results. Topographic data of the study site, derived from a digital elevation model (DEM) was also employed as model input.

3.1 Meteorological Data

In the European Alps data from numerous weather stations, maintained by different institutions (Avalanche surveys, national meteorological or hydrological institutions etc.) are available while data from glacier stations is still scarce, and if present, then often only for relatively short time periods. A good glacier mass balance model should be capable to relate meteorological data from synoptic or other off-glacier weather stations to the mass balance of a certain glacier (Klok and Oerlemans, 2002). Therefore data from automated weather stations in the vicinity of Langenferner were used to drive the EMB-model. An advantage in using off-glacier data is that the measurement site in most cases hardly changes with time, whereas automated weather stations on glaciers always suffer from changes in location (glacier flow dynamics), vertical displacement (surface melt) or other site specific problems. Furthermore the usage of data from synoptic weather stations enables to simulate mass balances over longer time periods as long term data series often are available from such stations which can be a great benefit for investigating the climate signal behind glacier fluctuations .

3.1.1 Weather Stations Six permanent weather stations provided meteorological data for this study. Five of them are maintained by the Hydrographic Oﬃce of the Autonomous Province of Bolzano (HOB), while the station at the dam wall of Lake Zufritt is operated by the local energy company, SEL AG (since 2008). Data from Lake Zufritt was used

13 14 3 Data

for assessing the precipitation on the glacier. The two most important stations are Sulden Madritsch and Schöntaufspitze as these are closest to the glacier. These two stations provided model input data of temperature, relative humidity, global radiation, and wind speed over the whole investigation period (2004-2008). All meteorological data series (except precipitation data) from the permanent weather stations were provided as ten-minutes means which were later averaged to hourly means for the use as EMB-model input. Figure 3.1 and Table 3.1 summarise the weather stations, their locations and the measured variables. The station Sulden Madtrisch is described in more detail.

Figure 3.1: Sattelite image showing the locations of Langenferner and the weather stations (except Glurns) that provided meteorological data for this study.

3.1.2 Sulden Madritsch Since the station is located closest to Langenferner, Sulden Madritsch was chosen as the "reference-station". This means, that whenever possible, data from this station is used as input to the EMB-model calculations. For the whole investigation period (2004-2008) direct measurents of air temperature, relative humidity and global radiation were available. Other parameters were taken from the remaining weather stations and were in some way extrapolated or related to the location of Sulden Madritsch (see below). The station is located at an altitude of 2825 m in a high alpine rock cirque, surrounded 3.1 Meteorological Data 15

station name altitude distance T RH G WS P PR Sulden Madritsch 2825 m 2.3 km x x x Schöntaufspitze 3325 m 3.5 km x x x Lake Zufritt 1851 m 9 km x Felssporn 3175 m 12 km x x x Rossbänke 2250 m 14 km x x x Glurns 917 m 22 km x x x x x x

Table 3.1: Description of the weather stations providing meteorological data for this study where "distance" means the distance of the respective station from Langenferner, T is temperature, RH is relative humidity, G is global radiation, WS is wind speed, P is atmospheric air pressure and PR is precipitation. An "x" means that the parameter was measured over the whole period (2004-2008) at the respective site. by several peaks, so the atmospheric surface boundary layer, sampled by this station diﬀers signiﬁcantly from that found on a glacier surface

3.1.3 AWS Felsköpfl As part of this study an automatic weather station (AWS) was installed temporarily on "Felsköpfl" in spring 2010 (see figure 3.2). The station was located on a distinct rock hill at an altitude of approximately 2970 m, 20 m away from the glacier. The variables measured were temperature and relative humidity (Campbell-Scientific HMP45A), incoming and outgoing components of longwave and shortwave radiation (Campbell- Scientific CNR4), wind speed and direction (Young-M05103), air pressure (Campbell- Scientific CS100) and snow height (Campbell-Scientific SR50). Data from this station were logged as halfhourly means on a Campell-Scientific CR1000 datalogger. They were used to calibrate and validate several model parameterizations such as incoming shortwave and longwave radiation, as well as the extrapolation methods for different input variables. An installation of the AWS on the glacier surface was not possible due to the thick spring snowpack and the lack of a proper fixation system (mast and/or tripod) for the instruments. AWS-Felsköpfl operated from May, 18th to June, 18th 2010. The measurements of this one month data record are free of gaps and therefore needed no processing. Only longwave radiation required a correction concerning the real resistance of the PT-100 thermistor. This correction was done as follows. First the true resistance (= 101.33 Ω) of the PT-100 thermistor was determined by comparing a measured (using the PT-100) temperature with the temperature measured by a reference thermometer. Then the following formula was applied to calculate the real instrument resistance for the single time steps:

Ri = 100 · (1 + c · Trec) (3.1) 16 3 Data

where Ri is the temperature dependent resistance at the respective timestep, c is a −3 − constant ( 3.85 · 10 °C 1) and Trec is the logged (wrong) instrument temperature (in °C). From the resultant resistance the true instrument temerature (Tinst, in Kelvin) was computed as follows.

( Ri − 1) T = R0 + 273.15 (3.2) inst c

Incoming longwave radiation (LWin) was then calculated by correcting the data record (LWrec) with the help of equation 3.3:

4 LWin = LWrec − σ · Tinst, (3.3)

where σ is the Stefan-Boltzman constant.

Figure 3.2: The weather station at Felsköpﬂ which ran from May 18th to June 18th 2010 (left) and its location close to Langenferner, indicated by the red spot (right).

3.1.4 Quality of Meteorological Data The series of meteorological data from the permanent weather stations were not free of gaps or erroneous values. The quality control of the data was done manually with the help of some simple MATLAB-functions. Most of the data gaps were relatively short (some hours or shorter), and these were often closed by linear interpolation. Gaps where no data was recorded for several weeks, which typically occured two to four times during the investigation period for each parameter, were ﬁlled using data from one of the neighboring stations, applying transfer functions as detailed below. Air pressure data 3.1 Meteorological Data 17 was only available from Glurns station. Hence gaps in the air pressure series were ﬁlled with NCEP/NCAR - Reanalysis data (Kalnay et al., 1996) from the nearest surface grid point. Due to a substantial lack of data for several parameters in the year 2003, the energy and mass balance calculations could not be performed for the time before January 1st 2004. All in all, it must be stated that data quality is relatively poor considering the fact that most of the stations are easily accessible. Information on data treatment will be given in the following descriptions for the single meteorological parameters.

3.1.5 Temperature Ten-minute mean air temperature (°C) was provided by the Sulden Madritsch station. Data gaps were ﬁlled with data from the nearest station recording air temperature data at the respective time. For this a constant temperature gradient of -0.0065 Km−1 (which was also used in the EMB-model) was used to extrapolate data from other stations to the altitude of Sulden Madritsch.

3.1.6 Global Radiation Global radiation (Wm−2), provided by Sulden Madritsch station, was needed to calculate the effective cloud cover fraction (detailed description follows in chapter4). Here a site specific problem occured in that especially in wintertime, topographic shading affects the measurements of direct solar radiation. In December the sensor is shaded for almost half of the day. In the absence of a better station, close enough to the glacier, solely data for points in time when direct insolation was possible were considered, see section 4.3.4. If possible, gaps were filled with data from Rossbänke station (which suffered from the same shading problem). For the few days when both stations showed data gaps, data from Glurns was used to approximate the global radiation at Sulden Madritsch.

parameter station name missing fraction max-gap temperature Sulden Madritsch 3.22 % 16 relative humidity Sulden Madritsch 5.10 % 17 global radiation Sulden Madritsch 3.04 % 16 wind speed Schöntaufspitze 12.50 % 48 air pressure Glurns 9.53 % 77 precipitation Lake Zufritt 0.00 % 0

Table 3.2: The measured meteorological parameters, measurement location, fraction of erroneous or missing values and the duration of the longest data gap (in days). 18 3 Data

Figure 3.3: Global radiation for days in December (left) and June (right). Days with (exceptional) strong cloud cover in grey and clear sky days in blue. Note the asymmetric shape of the clear sky curve in winter which is due to topographic shading of the measurement site in the ﬁrst half of the day. In June, topographic shading is restricted to early morning and late evening, visible at the steep edges of the clear sky curve.

3.1.7 Relative Humidity Like temperature, data of relative humidity was recorded at all the mountain stations. Gaps of the Sulden-Madritsch record were filled by using the data from the nearest station with data for the respective date and time. Even after extensive comparison of the different records of relative humidity, no systematic differences between the data series could be detected. Thus no reduction or correction was applied for data originating from other stations. Values for relative humidity were corrected for temperatures below freezing point as follows. In a first step water vapor pressure was calculated from relative humidity: RH · e e = s (3.4) 100 where e is the actual water vapor pressure, RH is relative humidity (in percent) and es the respective saturation vapor pressure (in Pa) calculated applying equation 3.5:

Lv 1 1 es(T ) = 611 · exp · ( − ) (3.5) Rv T0 Tm 3.1 Meteorological Data 19

6 −1 Where Lv is the latent heat of vaporisation (2.5·10 Jkg ), Rv is the individual gas −1 −1 constant for water vapor (462 J kg K ), T0 is a reference temperature (273.15 K) and Tm is the temperature at Sulden-Madritsch. Subsequently equation 3.5 was reapplied but this time the latent heat of sublimation Ls was used for temperatures below freezing point instead of Lv. Finally, RH was recalculated from the new es as follows: e RH = · 100 (3.6) es RH-values greater than 100 were reset to 100.

3.1.8 Wind Speed Wind speed data (ms−1) was recorded at Schöntaufspitze. This station is located at the summit of Schöntaufspitze, a free standing mountain about five kilometers north of Langenferner. No disturbance of wind from surrounding terrain can be expected at this location. The main disadvantage in using wind data from a summit station is that this wind record reflects free atmosphere conditions rather than the airflow in a glacial boundary layer, which may differ significantly (Van den Broeke, 1997; Oerlemans and Grisogono, 2002). Whenever possible, data gaps were filled with data from Felssporn station, which had the strongest correlation with the data from Schöntaufspitze station. A correction factor for wind speed was determined by calculating the ratio of the five year-means of the two records. To transfer Felssporn data to Sulden Madritsch the following formula was applied:

meanST WSST = WSFS · (3.7) meanFS where WSST is the wind speed at Schöntaufspitze, WSFS is wind speed at Felssporn, meanST is the mean wind speed at Schöntaufspitze for the period 2004 to 2008 and meanFS is the mean for Felssporn for the same period. A comparison of Schöntaufspitze-data with other records shows that wind speeds at Schöntaufspitze are substantially higher than at the other stations. Due to this fact a correction factor (0.67), calculated by equation 3.7, was applied to the Schöntauf data record to obtain more realistic values for the glacier surface. Since Spring 2009 wind speed data for Sulden Madrisch is also available. These data support the assumption that using wind speed data from Schöntaufspitze would probably result in too high wind speeds for the glacier surface.

3.1.9 Precipitation Lake Zufritt is the only station where precipitation data was recorded during the investigation period. The data is available as daily sums of precipitation which are 20 3 Data

recorded by an observer every morning (08:00) from the rain gauge at the dam of the lake. In the EMB-model the daily sums of precipitation were assigned to the time between two gauge readings, and in the absence of high temporal resolution data, the precipitation rate was assumed to be constant. That means that daily precipitation sums were divided by the number of model timesteps per day so that every timestep between the two readings gets the same amount of precipitation. Wind, and the related redistribution of snow, play a decisive role for accumulation on the glacier. Hence, the assessment of the snow accumulation is based on relating accumulation measurements (winter mass balance) at Langenferner to winter precipitation data from Lake Zufritt. See chapter4 for further details. Assuming a constant temperature gradient of 0.0065 Km−1 and a threshold of 0.5°C to distinguish between solid/liquid precipitation, 61% of the precipitation (2004-2008) was falling as snow at the lowest part of Langenferner (stake 4, 2725 m), while at the upper part (stake 22, 3275 m) 82% of the precipitation during the investigation period was solid.

3.1.10 Air Pressure Air pressure data is recorded at Glurns. This station is the furthest away from Langenferner, and the vertical displacement to the glacier (more then 1800 m) is also the greatest. Nevertheless usage of this data seems appropriate as air pressure shows a relatively low spatial variability and the model is relatively insensitive to this variable (Mölg, 2009) (see section 7.4). Synoptic patterns are expected to be well represented by the Glurns-record. Daily variations of air pressure, which are certainly diﬀerent at Glurns and on Langenferner, are of a minor importance for the modelling. Data gaps were ﬁlled using NCEP/NCAR-Reanalysis (REA) data from the nearest surface gridpoint (47.5°N/10°W, 1107m) because no other air pressure record could be provided by the HOB. As REA-data is solely available in a six hourly resolution, a simple linear interpolation was applied to obtain hourly values. For the transfer of Glurns data and REA data to the altitude of Sulden Madritsch the barometric height formula was applied: 0,034159·∆z ∆z TG−a· 2 PM = PG · e (3.8)

where PM is the air pressure at Sulden-Madritsch (in hPa), PG is the air pressure at Glurns (also in hPa), ∆z the diﬀerence in altitude between the two stations and a is a vertical temperature gradient (here 0.0065 Km−1). Surface air pressure from NCEP/NCAR-REA data was treated the same way. Since December 2008 air pressure data from Sulden Madritsch is available. A one month time series of which was used for validation of the applied transfer method. For 3.1 Meteorological Data 21 this period the RMSE of the diﬀerent series of air pressure data is less than 2.5 hPa (See Figure 3.4).

Figure 3.4: Validation of the air pressure reduction method for December 2008: The blue curve shows measured air pressure at Sulden Madritsch while the green curve symbolizes air pressure data measured at Glurns, 917 m, reduced to the station height of Sulden Madrisch, 2825 m. Red dots refer to 6-hourly NCEP/NCAR-REA data for the nearest NCEP/NCAR surface grid point (47.5°N/10°W, 1107 m) reduced to the station height of Sulden Madritsch. 22 3 Data

Figure 3.5: Overview of meteorological variables during the investigation period at Sulden Madritsch. Daily means in grey, monthly means in red and yearly means in blue. 3.1 Meteorological Data 23

Figure 3.6: Overview of meteorological variables measured at Sulden Madritsch, Schöntaufspitze and Lake Zufritt. Same color scheme as Figure 3.5 except for snow height: blue curve shows measured snow height (in cm) at Sulden Madritsch, while grey bars indicate solid precipitation (in mm w.e). The latter is computed from precipitation at Lake Zufritt (no gradient applied) and temperature at Sulden Madritsch (threshold solid/liquid = 0.5°C). 24 3 Data

3.2 Glaciological Data

Since the hydrological year 2003/2004 mass balance studies have been carried out on Langenferner (since 2009 coordinated by the author of this study). Measurements are made by the University of Innsbruck in collaboration with the HOB. The fixed date direct glaciological method is applied to determine the mean specific surface mass balance of Langenferner. The studies comprise measurements of the spatial distribution of snow height and density at the end of the accumulation season to assess the winter balance and a relatively dense network of 33 stakes (2009) is used to measure ice ablation and its spatial distribution. For a better temporal assessment of ice ablation the stakes are read several times in summer, typically four to six times depending on the location of the respective stake. At the end of the hydrological year the annual mass balance is calculated as the sum of winter balance and summer balance (figure 3.8). Ablation data from stakes, distributed over the whole glacier, as well as the timeseries of mean specific mass balance are used to validate the 2D-EMB-model.

Figure 3.7: Stake network (black dots) and spatial distribution of surface mass balance at Langenferner in the hydrological year 2008/2009. 3.3 Topographic Data 25

Figure 3.8: Seasonal mean speciﬁc mass balance b (mm w.e.) at Langenferner since the start of the mass balance survey in 2003/2004

3.3 Topographic Data

The EMB-Model requires topographic information for the investigation area. This topographic input contains matrizes of elevation, slope, aspect and the sky view factor of each grid cell as well as a glacier mask. Corresponding data is derived from a digital elevation model (DEM). The Oﬃce for Spatial Planning of the Autonomous Province of Bolzano provides a DEM which is derived from data originating from a laserscan air survey in 2006. Horizontal resolution of the DEM is 2.5 m. Vertical accuracy for altitudes above 2000 m is 0.55 m. DEM data can be freely downloaded from http://www.provinz.bz.it/raumordnung/kartografie. All the input data matrices (see chapter5) were derived using ESRI-ArcGis and/or MATLAB and were saved as ASCII-ﬁles using the MATLAB-function dlmwrite.

4 The Energy and Mass-Balance Model

4.1 Development and Application of the EMB-model

The energy and mass-balance model used in this study was developed by Thomas Mölg, University of Innsbruck. The model in its current configuration is based on a surface energy balance model of Mölg and Hardy (Mölg and Hardy, 2004) which later has been extended to a full mass balance model (Mölg et al., 2008). It is intended for application to small or medium size glaciers where vertical rather than horizontal gradients dominate meteorological patterns. As the model is based on both ablation associated with the surface energy balance and accumulation by precipitation, it is not applicable to glaciers where mechanical processes (calving, avalanches) play a major role for mass balance (Mölg, 2009). The EMB-model has been used in different studies on energy and mass balance of tropical glaciers, for instance on the summit ice fields of Kilimanjaro (Tanzania) e.g. (Mölg and Hardy, 2004; Mölg et al., 2009b), Glaciar Artesonraju (Cordillera Blanca, Perú) (Mölg et al., 2009a; Winkler et al., 2009) and in course of an ongoing Study on Lewis Glacier, Mt.Kenya (Kenya). The model in different configurations was also tested on extratropical glaciers like Morteratschgletscher (Switzerland), parts of the Greenland Ice Shield or Brewster Glacier (New Zealand). The study in hand represents the first extensive application of the EMB-model in its 2D-configuration to a typical alpine glacier. For further information on the EMB-model see: Mölg and Hardy(2004), Mölg et al.(2008), Mölg et al.(2009b) and Mölg(2009).

4.2 Energy and Mass Balance of a Glacier Surface

−2 The specific mass balance b(P ) (kg m or mm w.e.) of one point on the glacier surface is defined as the sum of accumulation c(P ) (positive) and ablation a(P ) (negative) at the same point over a specified time span, generally the hydrological year (European Alps: October 1st to September 30th). The latter accounts roughly for the period between one mass minimum (end of ablation period) and the next (Kaser et al., 2003; Paterson, 1994).

b(P ) = c(P ) + a(P ) (4.1)

27 28 4 The Energy and Mass-Balance Model

Accumulation comprises all processes leading to a mass gain for the glacier: solid precipitation, liquid precipitation freezing in the snowpack or at the ice surface, deposition, avalanches etc. Ablation accounts for all processes of mass loss like melt, sublimation or calving (Kuhn, 1981). Redistribution of snow due to wind, a very important process on mid latitude glaciers, can lead to both mass gain or mass loss for a glacier. On alpine valley glaciers wind redistribution is commonly associated with signiﬁcant mass gain (Kuhn, 2003). Another important term is the total mass balance B of a glacier (kg or m3) which can be understood as the spatially integrated sum of b(P ): Z B = b(P ) · ds (4.2) S The most commonly used measure regarding glacier mass balance is the mean speciﬁc mass balance b (kg m−2 or mm w.e.) which is the total mass balance B divided by the surface area SG of the glacier: B 1 Z b = = · b(P ) · ds (4.3) SG SG S The mass balance of a glacier surface and the related physical processes provide the basis for modern glacier mass balance modelling. In the physically based EMB-Model, accumulation is determined by solid precipitation (csp), deposition of frost or dew (cdep) and englacial accumulation (cen), while ablation is represented by the terms of surface melt (msfc) and sublimation (ssfc). Therefore mass balance by the EMB-model is computed as follows (Mölg et al., 2009b):

QM QL b = csp + + + cen + cdep (4.4) LM LS

−2 −2 QM (Wm ) symbolizes the latent energy flux of melting, QL (Wm ) is the turbulent latent heat flux of water vapor and LM /LS are the latent heats of melt/sublimation (Jkg−1). Note that all fluxes are defined as positive (negative) when transporting energy to (away from) the surface. With the exception of accumulation by solid precipitation, all terms of the above equation are assessed by solving the surface energy balance (SEB) which is determined by the exchange of energy between the atmosphere and the glacier surface. The SEB for a "skin-layer" (without heat capacity) can be expressed as follows:

SWnet + LWnet + QS + QL + QG + QP = F (4.5) 4.2 Energy and Mass Balance of a Glacier Surface 29

Where SWnet symbolizes net shortwave radiation, LWnet is net longwave radiation, QS and QL are the turbulent fluxes of sensible and latent heat respectively, QG is the ground energy flux, QP symbolizes the energy supplied by precipitation and F accounts for the resulting energy flux, which equals the energy available for melt if the surface temperature is at the melting point (273.15 K). Budgets of shortwave and longwave radiation can further be split into:

SW = SWin + SWout = SWin · (1 − α) (4.6) and

LW = LWin + LWout (4.7)

Here the subscripts "in" and "out" refer to incoming and outgoing radiation, respectively, while α stands for the (spectrally integrated) surface albedo. The single terms of the SEB (all in Wm−2) and their parameterizations in the EMB-Model are described in detail in the subsequent sections.

Figure 4.1: Daily cycle of surface energy ﬂuxes over a glacier on a hot clear sky day in summer. (Melt energy Qm is depicted as positive for a better graphic illustration) 30 4 The Energy and Mass-Balance Model

4.3 Shortwave Radiation

On many alpine glaciers incoming shortwave radiation (SWin) provides the primary energy source (Hoinkes, 1971; Oerlemans, 2010). As a consequence, the spatial distribution of the SEB is strongly tied to the latter. A proper assessment of the shorwave radiation budget and its spatial distribution is therefore crucial for process based mass balance modelling. This chapter provides insight to the EMB-models shortwave radiation scheme, the related parameterizations, the involved constants and the underlying assumptions and procedures. The EMB-Models shortwave radiation scheme is governed by the equation below:

SWin = (Scs + Dcs) · (1 − k · neff ) (4.8)

Where SWin stands for the incoming shortwave radiation at each single model grid cell, Scs is the direct component of solar radiation at clear sky conditions, Dcs is the diﬀuse part of clear sky solar radiation, k is a constant governing the impact of clouds on incoming shortwave radiation and neff is the eﬀective cloud cover fraction (Mölg et al., 2009a). The single terms of equation 4.8 will be described explicitly in the subsections below.

4.3.1 Direct Shortwave Radiation

The EMB-model computes direct incoming shortwave radiation (Scs) by the following equation:

Scs = S0 · E0 · cosζ · τcs (4.9)

−2 Here S0 is the top of atmosphere "solar constant" (1367 Wm ), E0 is the correction factor for the earth’s eccentricity, ζ is the zenith angle of the sun with respect to an arbitrarily oriented and inclined plane (Mölg, 2009). See Iqbal(1983) for a detailed description on the calculation of ζ. τcs accounts for the (broad-band) clear sky transmission of the atmosphere, which is computed as the product of four diﬀerent atmospheric processes:

τcs = τr · τg · τw · τa, (4.10) where τr is the atmospheric transmission due to Rayleigh scattering, τg accounts for gas absorption, τw is the transmission after water vapor and τa accounts for aerosol attenuation (Klok and Oerlemans, 2002). The single transmission coeﬃcients are calculated from the meteorological model input with help of the equations below. See 4.3 Shortwave Radiation 31

Mölg(2009), as well as Iqbal(1983) and Meyers and Dale(1983):

   p !0.84 p p !1.01 τr = exp −0.09030 · m · 1.0 + · m − · m  , (4.11) p0 p0 p0

h 0.26i τg = exp −0.0127 · m , (4.12)

1 − 2.4959 · m · 46.5 · (e/T ) τ = , (4.13) w 1 + 79.0340.68 · 46.5 · (e/T ) + 6.4 · m · 46.5 · (e/T )

m τa = (β + γ · alt) , (4.14) where p is the actual air pressure (hPa), p0 is a reference air pressure (1013.25 hPa), m is the optical air mass of the atmosphere (see below), Ta is the near surface air temperature (K), e is the actual near surface water vapor pressure (hPa), β and γ are constants (0.8776 and 2.4845 · 10−5) and alt is the altitude (m) of the respective grid cell. Equation 4.14 accounts for the altitude dependence of χ in the equation m τa = (χ) presented by Klok and Oerlemans(2002). The atmospheric optical air mass m is calculated using an expression from Meyers and Dale(1983): 35 m = √ . (4.15) 1224 · cos2ζ + 1

4.3.2 Diﬀuse Shortwave Radiation

−2 Diﬀuse shortwave radiation at clear skies Dcs (W m ) is computed by applying the subsequent formula (Mölg et al., 2009a), derived from the expressions of Iqbal(1983):

Kdif · S0 · E0 · sinh · τg · τw · τaa · (1 − τrτa/τaa) Dcs = 1.02 (4.16) 1 − p/p0 · m + (p/p0 · m) with

p p 1.06 τaa = 1 − (1 − αss) · (1 − · m + ( · m) ) · (1 − τa). (4.17) p0 p0

Here h stands for the elevation angle of the sun, τaa is the transmissivity due to the absorption of solar radiation by aerosols, p is the local air pressure (hPa), and p0 is 32 4 The Energy and Mass-Balance Model

mean sea level air pressure (1013.25 hPa) and αss is the single scattering albedo (here 0.9). Kdif is a constant which in this study incorporates both forward scatterance due to Rayleigh- and aerosol scattering as well as site specific influences of the sourrounding terrain such as reflections from nearby slopes. In order to find the appropriate Kdif , the modelled SWin for clear sky conditions was fitted to measured clear sky solar radiation at the site of Sulden Madritsch. For this purpose, a sample of 152 clear sky days had been established. The selection of clear sky days was made manually as the application of objective criteria for an automatised procedure proved to be difficult. Anyway, the criteria defined in Mölg et al.(2009a) for Kilimanjaro were not applicable for this site due to both higher temporal variability (seasonal and day to day) of the meteorological parameters and significant topographic shading (especially in winter) at the measurement site. At typical alpine sites, diffuse shortwave radiation consists to a large degree of reflected radiation from slopes surrounding the respective site (Greuell et al., 1997; Niemelä et al., 2001). This fraction is even larger when these slopes are covered with snow. With respect to this fact the sample of clear sky days was divided in two parts: one part consisting of days with snow cover and the other one consisting of days without snow cover. The distinction of these could be easily made using the snow height data of the Sulden Madritsch station. For this a snow height threshold of 25 cm was applied. Minimizing the difference between measured and modelled clear sky solar radiation for the two samples leads to two Kdif : 0.51 for days without and 0.66 for days with snow cover.

Figure 4.2: Modelled (blue) and measured (green) global radiation as well as the modelled diﬀuse portion (for Kdif = 0.66, red curve) for a clear sky day in late spring at the site of Sulden Madritsch. 4.3 Shortwave Radiation 33

4.3.3 Eﬀective Cloud Cover Fraction and Cloud Impact

The effective cloud cover fraction neff is one of the six input variables of the distributed EMB-model. It is used to extrapolate incoming shortwave radiation from the measurement site to the whole glacier surface (equation 4.8) as well as to calculate incoming longwave radiation (see section 4.4.1). Therefore neff is assumed to be spatially invariant which is not the fact in reality but can be considered an appropriate assumption on alpine and tropical glaciers because of their relatively small size. In order to calculate neff , equation 4.8 was applied. Measured global radiation (Gmeas) was inserted for SWin and the two modelled components of direct and diffuse clear sky radiation Scs and Dcs were inserted on the right hand side of the equation. The constant k was determined with the help of the following criteria: Total cloudiness (neff = 1) was assumed for those five percent of all days with the lowest proportion of Gmeas . Fitting modelled SW to measured global radiation for all timesteps (Scs+Dcs) in fullfilling this "total cloud cover requirement" leads to a k of 0.76. This means that for all timesteps with n = 1, SWin is reduced to 24 percent (1 − k) of the clear sky insolation. Even if the percentile approach above seems quite arbitrary, the calculation of a k with an other method supports the result: Cloud cover was also computed with a formula suggested by Greuell et al.(1997):

Gmeas 2 Tcl = = 1.000 − 0.233 · n − 0.415 · n (4.18) (Scs + Dcs) where Tcl is the sky’s transmissivity associated with clouds and n is the fractional cloud cover. n was computed out of equation 4.18 (resetting all n > 1 to 1 and all n < 0 to 0). The resultant series of n was then inserted (for neff ) in equation 4.8. The computation of a mean k for all timesteps (2004-2008) leads to a value of 0.77 which supports the result of the "percentile approach". Finally the model input timeseries of neff was calculated by inserting Gmeas from Sulden Madritsch at the left hand side and modelled Scs and Dcs as well as a k (0.76) on the right hand side of equation 4.8.

4.3.4 Topographic Shading at the Measurement Site Topographic shading at the station of Sulden Madritsch (see figure 3.3) exerts a considerable influence on several calculations related to the shortwave radiation scheme. Especially in winter time the weather station experiences shading due to the high ridges southeast of the station. For the calculations of radiation constants Kdif and k as well as the effective cloud cover fraction neff , solely these timesteps were considered, when direct insolation at the site of Sulden Madritsch was possible. With respect to this circumstance, time intervals for each month of the year were defined to exclude all 34 4 The Energy and Mass-Balance Model

Figure 4.3: Mean measured global radiation GCS at Sulden Madritsch for eight selected clear sky days respectively as well as the 95- and 5-percentiles , G95 and G5, of global radiation for all days of one month (n = 155 in December, on the left; n = 150 for June, on the right)

Figure 4.4: Comparison of measured and modelled global radiation for two selected days with "extreme" radiation conditions. The applied parameterization of SWin overestimates radiation on days with very strong cloud cover while insolation for days with higher than clear sky SWin (due to diffuse multiple reflections) is underestimated. timesteps with topographic shading. All the precalculations concerning solar radiation were carried out in timesteps of ten minutes (144 timesteps per day) to ensure a maximal benefit from the meteorological records. For instance in June the daily timesteps 39 to 114 could be used, while in December calculations were restricted to the timesteps 74 to 95. For the assessment of neff during the timesteps without direct insolation, a linear interpolation in time was applied between the last value before sunset and the first after sunrise. All in all, topographic shading at the measurement site clearly affects the optimization of the radiation model (Klok and Oerlemans, 2002). Nevertheless, in summer, when almost all of the glacier mass ablation occurs, the performance of the radiation scheme is satisfactory (see chapter6). 4.3 Shortwave Radiation 35

4.3.5 Topographic Shading in the EMB-Model The model offers two different treatments of topographic grid cell shading. Mode 1 solely accounts for self shading of the respective grid cell related to the angle of incidence of the solar beam, while mode 2 calculates SWin with respect to self- and topographic shading caused by the the surrounding terrain. For that reason, it is important to use an appropriate DEM-scene which captures the main features of topography responsible for shading. To asses the effect of topographic shading on the spatial distribution of energy and mass balance on a glacier surface, the model calculations are carried out with both model options.

4.3.6 Surface Albedo The albedo scheme of the EMB-model is based on the method of Oerlemans and Knap (1998). It calculates the (broadband) surface albedo of each grid cell as a function of snow depth and the time since the last snowfall event. First the snow albedo of each glacier grid cell is calculated: s − t α = α + (α − α ) · exp (4.19) snow firn fsn firn t∗ where αsnow is the albedo of snow, αfirn is the albedo of ﬁrn (0.50), αfsn is the albedo of fresh fallen snow (0.9), s is the time (in days) since the last snowfall event, t is the actual time (also in days) and t∗ is a timescale (Klok and Oerlemans, 2002). Subsequently the albedo of the glacier surface is assessed by the following formulation:

d ! α = α + (α − α ) · exp (4.20) snow ice snow d∗ where α symolizes the resultant albedo of the glaciers surface, αice is the albedo of ice (0.20), d is the snow depth (mm w.e.) and d∗ is the characteristic scale for snow depth (11 mm w.e.). For further information on the albedo parameterization scheme see Oerlemans and Knap(1998). An albedo value for ice of 0.20 seems a bit low but was necessary to simulate ice ablation in a realistic matter. Unfortunately no measurements of albedo are available for Langenferner. The fact that the glacier showed a series of years with very negative mass balances (b ≈ −1600 mm w.e.) and the related accumulation of dust on the glacier surface justiﬁes such a low albedo value (Oerlemans et al., 2009). 36 4 The Energy and Mass-Balance Model

4.4 Longwave Radiation

The budget of net longwave radiation on alpine glaciers is generally a heat sink for the surface, e.g. Greuell and Smeets(2001) or Oerlemans(2010). Nevertheless longwave radiation is of major importance for mass balance modelling as the incoming part is usually the largest source of melt energy for the glacier surface (Sedlar and Hock, 2009).

4.4.1 Incoming Longwave Radiation For the current study an additional parameterization for the incoming longwave radiation was implemented in the EMB-model. The existing model options had been developed for conditions on tropical glaciers (Kilimanjaro, Glaciar Artesonraju etc.) and are therefore not appropriate for midlatitude glaciers. The parameterization employed here has also been used by Klok and Oerlemans(2002) for their investigations on energy and mass balance at Morteratschgletscher, Switzerland. It is based on relating the incoming longwave radiation to air temperature, water vapor pressure and cloud cover:

4 LWin = ε · σ · Ta , (4.21)

where LWin is the incoming longwave radiation, ε is the emissivity of the sky, σ is −8 −2 −4 the Stefan-Boltzmann constant (5.67 · 10 Wm K ) and Ta is the near-surface air temperature (K) above the glacier. As the emissivity of the sky is a function of cloud cover, it is calculated following a parameterization presented by Konzelmann et al. (1994):

p p ε = εcs · (1 − neff ) + εcl · neff (4.22)

εcs stands for the clear sky emissivity, neff is the eﬀective cloud cover fraction, p is an exponent presented by Greuell et al.(1997) (here 2) and εcl accounts for emissivity of clouds. The clear sky emissivity εcs varies with water vapor pressure, air temperature and the concentration of greenhouse gases. It is calculated as follows:

1/8 ea εcs = 0.23 + b · , (4.23) Ta

where ea is the water vapor pressure (Pa) and b is a constant incorporating site-specific effects on incoming longwave radiation, such as radiation emitted by surrounding terrain (Greuell et al., 1997). In this study, values of 0.51 for b and 0.976 for εcl are used. Note that these are fitted values (see section6) for the usage of neff instead of n . 4.5 Turbulent Fluxes 37

4.4.2 Outgoing Longwave Radiation

Outgoing longwave radiation (LWout) is computed by inserting surface temperature of the glacier into the Stefan-Boltzmann law:

4 LWout = σ · Ts (4.24)

Where σ is again the Stefan-Boltzmann constant and Ts is the glacier surface temperature. Emissivity of snow and ice is assumed to be 1.

4.5 Turbulent Fluxes

Turbulent fluxes of sensible and latent heat are functions of surface micro topography (aerodynamic roughness) and even more of the micrometeorological surface layer conditions. The wind over a glacier surface in most cases - especially in the melting season - can be described as a special sort of slope wind, which is driven by the generation of negative buoyancy close to the surface (Oerlemans and Grisogono, 2002; Kuhn, 1978). The typical depth of such a katabatic wind layer above an alpine valley glacier is about 10 to 50 m (Van den Broeke, 1997). The stratification of the boundary layer over a melting glacier surface is often very stable. Near surface air temperature gradients can be of several degrees per meter. The glacier wind therefore acts as an energy pump by generating turbulence which enables the transport of heat to the surface. Regarding the SEB-equation of a glacier surface (see equation 4.1), the above mentioned process is represented by the terms of the turbulent fluxes of sensible and latent heat (QS and QL). Many ways to parameterize the turbulent fluxes can be found in the literature. A commonly used parameterization in modern energy and mass balance modelling, also used in this study, is the bulk aerodynamic method.

4.5.1 Sensible Heat

The turbulent sensible heat ﬂux QS is mostly dependent on wind speed and air temperature at a certain height above the surface. In mid latitudes, QS is the most important energy source for a melting glacier surface besides the net radiation budget (Oerlemans, 2010; Braithwaite, 1995). The EMB-model calculates QS as follows.

p k2 · u · (T − T ) Q = c · ρ · · a s , (4.25) S p 0 z z p0 ln m · ln h z0m z0h

−1 −1 where cp (Jkg K ) is the speciﬁc heat capacity of air, ρ0 is the density of air (1.29 −3 kgm ) at mean sea level pressure p0 (1013.25 hPa), p is the actual air pressure (hPa), 38 4 The Energy and Mass-Balance Model

−1 k is the von Kármán constant (0.4), u is the actual wind speed (ms ), Ta is the near surface air temperature (K), Ts is the temperature of the glaciers surface (K), zm is the measurement height of wind (m) , z0m is the surface roughness length for momentum (m), zh is the measurement height of temperature and z0h is the surface roughness length for temperature (both in m).

4.5.2 Latent Heat

Similar to the sensible heat flux, the turbulent flux of latent heat (QL) is mainly a function of wind speed. The other driving factor is the difference in humidity between the surface and the air above. QL is calculated as follows: 1 k2 · u · (e − E ) Q = 0.623 · L · ρ · · a s , (4.26) L v 0 z z p0 ln m · ln v z0m z0v

6 −1 where Lv is the latent heat for vaporisation (2.5 · 10 Jkg ), which is replaced by the 6 −1 latent heat of sublimation (2.83 · 10 Jkg ) if Ts (K) is below freezing point, ea is water vapor pressure (hPa) of the air at measurement height, Es is the water vapor pressure (hPa) at the surface (assumed to be saturated), zv is the measurement height of humidity (m) and z0v (also m) is the surface roughness length for water vapor. A positive QL is associated with deposition of dew or frost at the glacier surface while a negative ﬂux means vaporisation/sublimation.

4.5.3 Stability Correction The equations above for sensible and latent heat fluxes are based on the assumption of a logarithmic near surface wind profile. This assumption is only strictly valid for conditions of neutral stratification of the atmospheric surface layer. As mentioned above, the stratification of the near surface glacier boundary layer is not neutral for most of the real cases. Especially in the melting period, very stable conditions are the rule rather than the exception. During the PASTEX-Experiment (Greuell et al., 1997; Oerlemans and Grisogono, 2002), stable conditions occurred throughout 85 % of the observation period (melting season, June to August). But even in winter a stable stratification of the surface layer is very common. In order to correctly calculate turbulent heat fluxes for stable conditions, but also for the relatively few unstable cases, "Phi-functions" were applied, see Mölg and Hardy(2004) or Wagnon et al.(2003). For this procedure the bulk Richardson number (Rib) as a measure of near surface atmospheric stability was computed as follows (Garrat, 1992):

zm − z0m Rib = 9.81 · (Ta − Ts) · 2 (4.27) Ta · u 4.5 Turbulent Fluxes 39

The two phi-functions for stable (Rib > 0) and unstable (Rib < 0) stratiﬁcations then read:

2 Φstable = (1 − 5 · Rib) (4.28) and

3/4 Φunstable = (1 − 16 · Rib) (4.29)

For all cases with Rib > 0.2 a laminar ﬂow is assumed, while all Rib < −0.2 are associated with a state of local free convection. Both cases supress turbulent heat exchange and are therefore regarded as the boundaries for turbulent ﬂux computation.

Figure 4.5: Plot of the two phi-functions for stable and unstable conditions.

4.5.4 Roughness Lengths The surface rougness length of momentum (temperature and humidity) is defined as the very small height above the surface where wind speed is zero (temperature and humidity are the same as at the surface), e.g. Braithwaite(1995). As neither detailed profile measurements nor eddy-covariance data were available for Langenferner, the exact surface roughness lengths could not be determined. For this study a model option with variable (in space and time) surface roughness lengths was applied. The EMB-model therefore makes use of three different roughness lengths for fresh snow, old snow and ice-surfaces, respectively (Mölg et al., 2009b). For the surface roughness length of momentum, z0m, values of 1 mm for fresh snow, 4 mm for old snow or firn and 2 mm for bare ice were used. These are typical values mentioned 40 4 The Energy and Mass-Balance Model in literature, e.g. Brock et al.(2006), or Van den Broeke(1997). Roughness lengths for scalars (temperature and humidity) were assumed to be one order of magnitude smaller than those for momentum (Hock and Holmgreen, 2005). It is well known that in nature a significant variability of roughness lengths even within these cases (e.g. for bare ice) can be observed. But the parameterization above represents at least an approximation of the temporal roughness variability of a mid latitude glacier surface.

4.6 Surface Temperature and Ground Energy Flux

Surface temperature (TS) is a key variable for the SEB (Mölg et al., 2008). For the EMB model TS represents the link between the meteorological conditions above the glacier surface and the ground energy flux, which is determined by the EMB-models subsurface module. This module consists of a multi-layer grid stretching down into the glacier. The current model configuration makes use of 16 subsurface layers (plus the surface layer), the deepest of which is at a depth of 11 meters. This is more than the penetration depth of the winter coldwave (Paterson, 1994) and definitely exceeds the minimum depth of the bottom layer, which must be greater than the maximum snow depth expected. The spacing between the layers increases with increasing depth in order to maximize computational efficiency and maintain numerical stability. Ice temperature at the bottom model layer is fixed at 273.15 K as Langenferner is assumed to be a temperate glacier. Heat transport into the subsurface of a glacier can be due to conductive processes or meltwater/liquid precipitation seeping down the snow and freezing in the snowpack or at the snow-ice interface. Penetrating shortwave radiation (existing model option) is not taken into account for this study due to the lack of corresponding measurements for mid latitude glaciers. The subsurface module numerically solves the thermodynamic energy equation on the multi-layer grid described above. This leads to a vertical profile of subsurface temperatures which can be used to compute the conductive heat flux (QC ). For details and values of thermal diffusivity and conductivity see Mölg et al.(2008). Surface temperature is computed following the procedure presented by Klok and Oerlemans(2002). There TS is calculated by converting the net energy flux F (see equation 4.1) of the previous time step into a temperature change over a defined surface layer thickness dsfl which is defined as the depth at which the amplitude of the diurnal temperature wave has reduced to 5 percent of its amplitude at the surface (Mölg et al., 2009b). 4.7 Surface Accumulation 41

4.7 Surface Accumulation

Surface accumulation in the EMB-model is determined by solid precipitation. To distinguish snowfall from liquid precipitation a threshold temperature of 0.5°C was assumed. This threshold is lower than the one presented by (Klok and Oerlemans, 2002), but considering observations, which show that significant snow accumulation does hardly occur at air temperatures higher than freezing point, the lower threshold seems to be justified. In order to account for the high (compared to precipitation data) accumulation amounts at Langenferner, which can be explained by redistribution of snow due to wind ,the modelled winter balance was fitted to the observations for the respective year. Applying this procedure, "winterly" (October to early May) ablation processes were also considered and an accumulation factor (AF) for each year was determined by fitting measured precipitation at Lake Zufritt to the corresponding accumulation data of measured mean specific winter mass balance at the glacier. Density of fresh snow was assumed to be 250 kg/m3. Except for the summer months (June-September), the precipitation rates, derived from Lake Zufritt data, were multiplied with the respective AF in order to assess accumulation on the glacier. For the investigation period of this study, the AFs are in the order of 2.7 to 4.5, where years with less precipitation at Lake Zufritt tend to have greater AFs at Langenferner. For the summer months a constant precipitation factor of 1.2 was applied. The underlying assumptions are that (i) wind-redistribution of snow does not play a significant role in summer and (ii) the precipitation scheme in summer, when a main part of precipitation is due to convective processes, is not comparable to the winterly precipitation scheme. An analysis of precipitation records at Sulden Madritsch and Lake Zufritt for the year 2009 supports the above assumption. The main insufficiency of the presented method is that enhanced accumulation due to redistribution of snow is just represented as a mean over the whole glacier area. A simulation of the large spatial variability of snow depth, which often can be observed in nature, is very difficult and goes beyond the scope of this study.

5 Working with the EMB-Model

5.1 Model Options and Settings - The mbminﬁle

All the used model options, settings and constants must be specified in the mbminfile which consists of seven sections detailing information on (1) topography, (2) geographic features of the study site, (3) the main model options, (4) solar radiation (5) the surface module, (6) the subsurface module and (7) the albedo module. A careful preparation of the mbminfile, together with the meteorological input data series, is a precondition for a successful model run. For this study the EMB-model was applied in a horizontal resolution of 50 meters and a temporal resolution of 60 minutes. Higher model resolutions were difficult to operate as the computational resources were limited. Anyway, the model results would probably not change substantially using higher model resolutions (Arnold and Rees, 2009). The reader can find the mbminfile with the specifications used in this study in the appendix of this thesis. Additionally Mölg(2009), p. 231-236, provides helpful information for EMB-model users.

5.2 Meteorological Input - The Input File

The EMB-input file must be provided as a ASCII-file which consists of the meteorological records (free of gaps) and the associated time reference, which is represented by the first four columns (year, month of year, day of year, hour of day). "Hour of day" is the end of the respective timestep in hours. For instance if hourly means are used as model input and the first timestep represents the first hour of the day (00:00-01:00 hours), then the respective value in the input file is 1. If the model is driven with 10-minute means then the first value is 1/6 = 0.1667 The other columns of the input file contain mean values (sums for precipitation) of the required meteorological input parameters over the respective timestep. Meteorological input variables are: air temperature, relative humidity, wind speed, effective cloud cover fraction (see section 4.3.3), air pressure and precipitation. Note that all the meteorological data should originate from the same location. If this is not the case transfer-functions must be applied to consider the spatial variability of the respective variables (see chapter3). The Input file for the study in hand was prepared in MATLAB

43 44 5 Working with the EMB-Model

and stored using the function dlmwrite. The filename as well as the path to the input file must be specified in the mbminfile.

5.3 Topographic Model Input

5.3.1 Glacier Mask As a ﬁrst step the glacier mask was calculated. The mask can be understood as a matrix with the value 1 for all glacierized grid points and the value 0 for non glacierized grid points. This matrix was determined using the existing glacier outline of the year 2006 which had been derived using orthophotos and data from a D-GPS survey in the year 2005. Due to diﬀerent spatial referencing of the DEM and the glacier outline, a horizontal shift error occured. As this error was small (≤ 1.8 m) due to the very high horizontal resolution of the original DEM, a correction of the spatial referencing was not necessary.

5.3.2 Elevation The ESRI-ArcGis operation resample was applied to the original DEM to derive the input matrix of grid cell elevation. Within this procedure the horizontal resolution of the original DEM was reduced from 2.5 m to 50 m.

5.3.3 Slope and Aspect The two matrices for slope and aspect of each grid cell were calculated by applying ESRI-ArcGis spatial analyst functions Slope and Aspect to the original DEM. The reduction of resolution from 2.5 m to 50 m was also done by using these functions. Slope and Aspect could also have been calculated using MATLAB by applying the function gradientm. For further information on topographic model input see e.g. Manzl (2010).

5.3.4 Sky View Factor The sky view factor (SVF) can be understood as the fraction of the upper hemisphere above one point which represents the non-obstructed part of the sky. At high alpine sites this fraction is commonly reduced by surrounding mountains or ridges. The SVF aﬀects incoming shortwave radiation (shading, reﬂections from surrounding slopes) and incoming longwave radiation (emissions from surrounding terrain). In this study the SVF was calculated using the function compsvf, which is part of the analysis tools of the EMB-model. 5.3 Topographic Model Input 45

Important for the calculation of the SVF is a DEM which captures all relevant sky- obstructing obstacles surrounding the glacier. Since the DEM used was delimited by the border between the Autonomous Province of Bolzano and the Province of Trentino, the summit of Monte Cevedale, to the south of the glacier, was not captured by the employed DEM which leads to a slight underestimation of the SVF in some of the upper glacier areas but does not aﬀect direct incoming shortwave radiation as there is no shading from Monte Cevedale.

Figure 5.1: Topographic MEB-model input for altitude (m a.s.l.) slope (degrees) and aspect (degrees from north) and the sky view factor. 46 5 Working with the EMB-Model

5.4 Running the Model

The EMB-model consists of several modules and the mbminfile which are linked through the main control file, named mbm2dtm1p6.m in the current version 1.6. The model is started by entering the name of the control file in the command window in the code1p6 folder or simply by starting the control file.

5.5 Analysing the Model Output

For storage of the EMB-model output a path must be specified in the mbminfile. The output is then automatically saved to disc as cdf -files. For each month up to three cdf-files are stored following the naming convention VariableTypeyYearmMonth.cdf. VariableType can be sfc (surface variables), subsfc (subsurface variables), metvar (meteorological variables) or tergrids (topographic variables). For instance all the surface variables for June 2008 are stored in the file sfcy2008m6.cdf. A list of all variable names is provided by Mölg(2009). If the model in its 2D-configuration is run for a time span longer than one year, then the file shad1yr.cdf is also saved to disc. This file contains information on topografic shading at each time step for each model grid cell and is calculated only once. For all following model runs with the same temporal and spatial resolution this file can be used again. In this case the user must set the mbminfile-variable shadflg == 3. For the analysis of the EMB-model output the code1p6 folder contains a subfolder named analytools in which the user can find three useful functions simplifying the data analysis. To load a cdf -file, the basic MATLAB command is cdfread. To bring a variable from a cdf file to matlab workspace use the function extmbfield. Note that the variable is now still in a spatially decomposed form if the model output originates from a 2D-model run. To assign the columns to their correct spatial position, continue with the function spatialass. Third, the function altprof offers a fast possibility to create a vertical profile of the required variable. More information on the usage of the analytool-functions can be found in the appendix of the thesis. 6 Model Optimization on Felsköpfl Data

In order to calibrate the EMB-model’s radiation scheme, the model output was compared and fitted to the one month meteorological data record from Felsköpfl. While the parameterization of the incoming shortwave radiation seemed to be satisfying, the longwave radiation scheme needed a revision. As the parameterization of incoming longwave radiation (see section 4.4.1 for a detailed description) was developed for usage with the cloud factor n, the method had to be fitted with respect to the effective cloud cover fraction neff as proposed by Mölg et al.(2009a).

6.1 Incoming Shortwave Radiation

An examination of shortwave radiation by comparing modelled (using meteorological input from Sulden Madritsch station) SWin and measured SWin at Felsköpfl shows a quite satisfying result. RMSE for the half hourly means is 134 Wm−2 with a correlation coefficient of 0.92 (n=1392 ). Mean difference (measured - modelled) is 6.7 Wm−2, see Figure 6.1. The assumption of a spatially invariant neff therefore seems to be justified and no further corrections were applied to the parameterization scheme of incoming shortwave radiation.

Figure 6.1: Left: curves for measured and modelled incoming shortwave radiation. The last thirteen days in May 2010 were chosen because a large variability of SWin occured through this period. Right: scatterplot of measured against modelled incoming shortwave radiation for the whole measurement period (29 days).

47 48 6 Model Optimization on Felsköpﬂ Data

6.2 Incoming Longwave Radiation

After the correction of measured LWin (see section 3.1.3) the comparison of modelled and measured longwave incoming radiation showed that LWin was underestimated by the model by the order of about 20 Wm−2. The reason for this underestimation is the parameterization of incoming longwave radiation (see section 4.4.1) which was developed for usage with the cloud cover fraction n proposed by Greuell et al.(1997). The usage of neff , which is in general somewhat lower than n, leads to a lower incoming longwave radiation. Fitting modelled LWin to measured LWin at Felsköpﬂ station by tuning the constant b (see section 3.1.3) and emissivity of clouds εcl leads to a higher modelled LWin and clearly reduces RMSE between modelled and measured LWin (Greuell et al., 1997; Klok and Oerlemans, 2002). The ﬁtting procedure leads to b = 0.51 and εcl = 0.976 while the initial values were 0.433 and 0.984 respectively.

Figure 6.2: Temporal variability of measured and modelled incoming longwave radiation at Felsköpﬂ station. The unﬁtted case in the upper plot and the optimized case in the lower plot. 6.3 Air Temperature 49

Figure 6.3: Scatter plots of measured versus modelled incoming longwave radiation at Felsköpfl for the unfitted (left) and the fitted (right) model. n=1392

6.3 Air Temperature

The comparison of transferred (using Sulden Madritsch data) and measured temperature at Felsköpfl (2976 m) shows that mean measured temperature at Felsköpfl is 0.8°C lower than the transferred series from Sulden Madritsch. An explanation for this may be the fact that the station of Sulden Madritsch was already snow free during almost the whole measurement period, while Felsköpfl is strongly influenced by the glacial katabatic air flow which brings cool air from the glacier and from the snow-covered surrounding slopes. No further corrections on temperature were applied, as the dataseries from Felsköpfl is too short to properly determine temperature differences within different seasons which would be the basis of an improved transfer function.

Figure 6.4: Measured and modelled air temperature at Felsköpfl (2976m). Mean air temperature at Sulden Madritsch transferred to Felsköpfl (using a gradient of -0.0065 Km−1) is 0.8 K higher than the measurement. 50 6 Model Optimization on Felsköpfl Data

6.4 Wind Speed

The comparison of wind speed at Schöntaufspitze and Felsköpfl (see Figures 6.5 and 6.6) shows that wind speeds at Schöntaufspitze are in most cases substantially higher than those recorded at Felsköpfl. This finding supports the transfer method described in section 3.1.8. Mean wind speed at Felsköpfl is 61% of the mean wind speed at Schöntaufspitze. Nevertheless the transfer factor of 0.67, introduced in section 3.1.8, was applied due to the fact that (i) the measurement period at Felsköpfl is very short and (ii) higher wind speeds (compared to Felsköpfl) can be expected at the upper glacier areas as these are less influenced by surrounding topography.

Figure 6.5: Wind speeds at Felsköpﬂ (in blue) and Schöntaufspitze (in red). Original values for Schöntaufspitze are depicted in the upper plot while the bottom plot shows transferred wind speed values. For the data extrapolation, a transfer factor of 0.67 was aplied (see section 3.1.8) 6.4 Wind Speed 51

Figure 6.6: Scatter plots of original (left) and transferred wind speeds at Schöntauf- spitze versus measured wind speed at Felsköpﬂ.

7 Results

7.1 The 0D-Model - Stake Balance

The first model runs were performed for two point locations using the EMB-models zero-dimensional (0-D) mode. As the computations are made for one grid point only, the 0D-model offers a fast method to efficiently test the model for different sites on the

Figure 7.1: Modelled and observed surface change at stake 4, 2725 m (top) and at stake 22, 3275 m (bottom). Blue curves represent the modelled surface change while red markers show stake readings. The ﬁrst marker for measured ablation in the lower plot is an estimate by R. Prinz, 2005 (unpublished data). Note the diﬀerent vertical scales.

53 54 7 Results

glacier as the resulting surface change can easily be compared to stake measurements or snow probing data which simplifies a precise model validation. For a first evaluation of the model performance two stakes with long data series were chosen: stake 4, located at the glacier tongue at approximately 2725 m and stake 22 in the upper glacier part at 3275 m. Stake 4 was redrilled several times during the investigation period as it is located in an area with an annual ice ablation of up to six meters. The position was always corrected for an estimated dynamical ice flow, so a homogeneous data series is available for this stake. Stake 22 was drilled in 2005. There is no data available for this site until then. The original stake 22 is still (August 2010) in operation and will probably need to be redrilled in 2011. Annual ice ablation at this site is of the order of a few centimeters to about one meter per year and is strongly tied to redistribution of snow due to wind, which cannot be simulated by the EMB-model. Therefore, it is very difficult to simulate mass balance at this location and in the upper regions of Langenferner in general while the model results for stake 4 (at the glacier tongue) match the observations quite well (see Figure 7.1). Figures 7.2 and 7.3 show the temporal variability of the modelled surface energy fluxes at stake 4 on the daily and on the annual scale respectively.

Figure 7.2: Temporal variability (daily means) of the SEB components at stake 4, 2725 m. Net shortwave radiation (red), net longwave radiation (blue), turbulent sensible heat flux (black), turbulent flux of latent heat (orange) and ground heat flux (green). 7.2 The 2D-Model - The Mass Balance of Langenferner 55

Figure 7.3: Annual means of the SEB components at stake 4, 2725m. Net shortwave radiation (red), net longwave radiation (blue), turbulent sensible heat flux (black), turbulent flux of latent heat (orange), ground heat flux (green) and melt energy flux (yellow).

7.2 The 2D-Model - The Mass Balance of Langenferner

The central aim of this work was to simulate temporal and spatial variability of the surface mass balance on Langenferner during the ﬁve year period 2004-2008. In this section the main results of the thesis are presented and discussed. Table 7.1 shows the measured and modelled annual mean speciﬁc mass balances during the investigation period. Generally the measured annual mass balance of Langenferner shows a small variability. Considering this fact, the EMB-model results match the observations quite well. The main patterns of the spatial distribution of Langenferners mass balance (see Figure 7.5) are also well captured by the model with some exceptions, especially in the uppermost glacier part, where the model calculates positive mass balances for all years. In reality, as this area is particularly exposed to wind, a notable part of the snow accumulated here is lost to wind ablation, which is a process not included in the EMB-model. Stake measurements in this area show a negative mass balance in most years. The modelled mass balance for the hydrological year 2007/08 is greatly overestimated by the model. The reason for this overestimation is discussed in section 7.2.3. 56 7 Results

Year bmeas. bmod. bmeas. − bmod. 2003/04 -1524 mm w.e. -1590 mm w.e. 66 mm w.e. 2004/05 -1233 mm w.e. -1399 mm w.e. 166 mm w.e. 2005/06 -1560 mm w.e. -1910 mm w.e. 350 mm w.e. 2006/07 -1616 mm w.e. -1225 mm w.e. -391 mm w.e. 2007/08 -1637 mm w.e. -594 mm w.e. -1043 mm w.e.

Table 7.1: Measured and modelled mean speciﬁc mass balance at Langenferner.

7.2.1 Vertical Mass Balance Profiles Figure 7.4 shows a comparison of measured and modelled vertical mass balances profiles at Langenferner. In order to properly interpret the differences between measured and modelled balance profiles, it is important to know that the profiles of measured balance are derived by "manual" extrapolations of point measurements (stake readings, snow pits and probings). The uncertainties of this method occur especially in the upper glacier regions where the stake density is relatively low. The measured mass balance gradient is largest in the lower glacier parts where the melt rates are high and it generally decreases in the upper glacier regions. In some years this behavior is not well reflected by the model. This can be explained to a large part by wind redistribution of snow which is not resolved in the model. The most significant difference between model result and observation occurs again for the year 2007/08 (see section 7.2.3).

Figure 7.4: Vertical proﬁles of modelled (red) and measured (black) mass balance at Langenferner. 7.2 The 2D-Model - The Mass Balance of Langenferner 57

Figure 7.5: Spatial distribution of modelled annual speciﬁc surface mass balance at Langenferner and the accumulated surface mass balance for the investigation period in mm w.e. The black line indicates the equlibrium line. 58 7 Results

7.2.2 The Role of Sublimation Ablation on midlatitude glaciers is mostly due to melt, while sublimation plays a minor role. On Langenferner approximately one percent of the modelled ablation occurs due to sublimation. Figure 7.6 shows daily sums of modelled sublimation and deposition at stake 4, 2725 m. The rates of sublimation are in agreement with the ﬁndings of Kaser (1982). A considerable part of sublimation (mainly during day time) is compensated by deposition (mainly during the night). Accumulated modelled sublimation at stake 4 during the investigation period was 460 mm w.e., while net sublimation (sublimation - deposition) for the same time was 120 mm w.e. The dominance of sublimation at Langenferner increases with altitude (see Figure 7.14). Even if the processes of sublimation and deposition do not play an important role in terms of mass exchange, they are still relevant for the SEB as the related (latent) energy ﬂuxes are of considerable magnitude.

Figure 7.6: Modelled sums of daily sublimation and deposition at Langenferner’s stake 4, 2725 m.

7.2.3 The 2008-Problem The most remarkable difference between modelled and measured surface mass balance on Langenferner occurs for the year 2008 (Table 7.1). The measured mean specific mass balance for this year is -1637 mm w.e. while the model calculates a much less negative value of -594 mm.w.e. Initially snow accumulation and its redistribution due to wind were belived to play an imortant role in this discrepancy. Therefore an input matrix for the measured snowcover distribution (on the basis of the winter balance) in May 2008 was created. Then the model was run again from the date of the winter balance (May 09th 2008) to the end of the hydrological year 2008. Surprisingly this procedure lead to hardly any change in the modelled mean specific mass balance. A comparison of modelled snow depth and the snow depth measured at Sulden Madritsch showed that the modelled snow pack in late spring/early summer 2008 melts significantly slower 7.2 The 2D-Model - The Mass Balance of Langenferner 59

Figure 7.7: Modelled and observed snow melt in late spring/early summer 2008. Due to a unrealistic high snow albedo the model underestimates melt. The feedback between albedo and melt in the model leads to a significant underestimation of melt ablation in 2008. than the observed snowpack at Sulden Madritsch (see figure 7.7) which leads to an modelled overestimation of the snow pack throughout the summer 2008 (Figure 7.8). This was found to be related to an overestimation of the snow albedo by the employed albedo parameterization. The timescale of 21.9 days (see section 4.3.6) introduced by Klok and Oerlemans(2002) seems to be inappropriate, especially during periods in late spring with frequent substantial snow falls, which was the case especially in 2008. Snow depth at this time of the year is still substantial but surface albedo changes very fast due to high insolation and relatively high temperatures. The timescale means that the surface albedo after a snowfall changes within 21.9 days from fresh-snow albedo (0.9) to the albedo of firn (0.50), which is definitely happening much faster in summer, while in winter snow albedo is probably higher than 0.50 even after more than 21.9 days. A time scale of 9.5 days would lead to a modelled mean specific mass balance which fits to the observations for 2008. But employing this value for the other years would result in unrealistic modelled mass balances. For further applications of the EMB-model to alpine glaciers, the albedo parameterization should be further developed, or the use of a different scheme should be considered. In order to test the effect of the modelled 2008-albedo feedback issue discussed above, a 60 7 Results test run was carried out for 2008, setting the precipitation between May 17th and June 9th (177 mm w.e.) to zero. This procedure results in a change of the mean specific mass balance of -948 mm w.e. Even if the precipitation between May 17th and June 9th is assumed to be solid on the whole glacier (not true in reality), then still 771 mm w.e of this 948 mm w.e. change in the mean specific mass balance can be attributed to the feedback between surface albedo and ablation by melt.

Figure 7.8: Modelled and observed snow cover on Langenferner in summer 2008. White areas symbolize snow covered grid cells while blue areas represent bare ice. The red circle indicates the location of the area shown in the last photo

7.2.4 The 2006-Problem For the hydrological year 2005/2006 the EMB-model overestimates summer mass loss at Langenferner by 350 mm w.e. (Table 7.1) which is not much compared to the discrepacy for 2007/08 but is still a considerable difference. Summer 2006 was characterised by an extremely hot July, which was by far the warmest month at Sulden Madritsch during the investigation period (see Figure 3.5). For this month the model calculates melt rates which are higher than indicated by observations for this period. This circumstance seems to be related to the fact that the model input originates from off-glacier stations, where the meteorological data capture a surface boundary layer not influenced by the glacier surface. Temperature at the site of Sulden Madritsch, which was used as a model input (see section 3.1.2), is influenced by an alpine rock surface which can heat up to 35°C or more on hot days with high insolation. Due to this effect, which is definitely influencing the measured near surface air temperature, 7.3 Surface Energy Fluxes 61 the difference between temperature at Sulden Madritsch and the temperature over a nearby glacier surface of the same altitude is therefore greatest for such days. The higher ablation rates in the anomalously hot July 2006 can probably be attributed to an "overestimation" of the temperature input during this period.

7.3 Surface Energy Fluxes

A further aim of this study was to investigate the spatial distribution of the surface energy fluxes on a typical alpine glacier in relatively complex terrain. The hydrological year 2004/05 was chosen for those plots because the model results matched the observations quite well for this year and no significant anomalies concerning meteorological conditions occured in this year. To correctly interpret the distribution of the surface energy fluxes, it is important to note that some features which influence the spatial variability in reality are not captured by the model. Incoming longwave radiation for instance is strongly dependent on radiation emitted by surrounding terrain (Greuell et al., 1997) which shows a considerable spatial variation. The same is true for the shortwave radiation budget which is dependent on reflected radiation from slopes arround the glacier and even from multiple reflections between ground and atmosphere (Klok and Oerlemans, 2002; Greuell et al., 1997). These variations are not explicitly resolved by the EMB-model. Turbulent fluxes are mostly dependent on wind speed, which in this study is assumed to be the same over the whole glacier. Due to a lack of measurements, no vertical wind speed gradient was applied in the model. Anyway, to realistically simulate the distribution of turbulent fluxes it would be necessary to resolve variations of the wind field over the glacier. Nevertheless the subsequent figures illustrate at least the basic features of the spatial variations of the surface energy fluxes well. Figure 7.9 shows the surface energy fluxes for January 2005 and Langenferners topography (bottom right corner) while important surface variables as well as a plot of the mean phi-function values (see section 4.5) for January 2005 are shown in (Figure 7.10). The winter budget of shortwave radiation is mainly determined by topographic features (such as slope, aspect and shading) as the whole glacier is covered with snow and the albedo differences therefore are small (Figure 7.10). Longwave radiation in winter shows more or less the distribution of the shortwave budget (inverted sign) indicating that most of the absorbed shortwave part is emitted by LWout while LWin is mostly dependent on air temperature and moisture which in the model solely depend on altitude. Turbulent fluxes in winter show a similar distribution, which can be explained by their dependence on the temperature difference between surface and and the overlying air, which in turn is also a function of the radiation budget. Surface roughness lengths show no significant variations in this month (Figure 7.10) and spatial variations of the wind field are, as discussed before, not treated by the model. Modelled 62 7 Results

ground heat flux is mainly a function of altitude. It is greatest in the uppermost part of the glacier, where the surface temperature is lowest. The remaining variations of ground heat flux are determined by the the sum of the other surface fluxes at the respective grid cell as melt energy (not shown) is zero throughout the month. Spatial distribution of the modelled surface energy fluxes during July 2005 is shown in Figure 7.11, while Figure 7.12 shows the spatial variability of relevant surface variables and the phi-function. The distribution of shortwave radiation in summer is characterised by a sharp transition of values higher than 180 Wm−2 to values lower than 80 Wm−2 which marks the transition from bare ice (low surface albedo) to snow covered areas (Figure 7.12). The budget of longwave radiation is much less negative compared to winter, while its distribution is mainly a function of altitude (air temperature) as the outgoing part is determined by surface temperature, which is at melting point or slightly below (and therefore does not show a great variability, Figure 7.12) and the incoming part mostly depends on air temperature and vapor pressure, which in turn are functions of altitude. The turbulent fluxes of sensible and latent heat both show a maximum at the glacier tongue and a secondary one in the mid part of the glacier. High values at the lower parts can be explained by the large gradients in near surface temperature and water vapor pressure while the minimum arround 3000 m can be attributed to a smaller temperature gradient related to higher mean surface temperature due to enhanced insolation in this steep, east exposed part of the glacier (Figure 7.9). Note that the mean modelled latent heat flux for July 2005 is negative (⇒ sublimation) in the upper parts of Langenferner. Mean modelled ground heat flux, which is determined by the temperature difference between the surface and the model’s first subsurface layer is negative in the lower glacier part and postive in the upper areas. The distribution of the melt energy flux mainly reflects the variability of shortwave net radiation which once more illustrates the importance of net shortwave radiation for the spatial distribution of a glacier’s mass balance. Snow depth (Figure 7.12) in July 2005 ranges from zero (all areas below an altitude of about 3000 m) to more than 2 m in the uppermost glacier part. Surface albedo is mainly dependent on the presence/absence of snow cover and therefore shows a sharp transition at around 3000 m which is also reflected by surface temperature. As the wind is assumed to be spatially invariant, phi-function values mainly reflect the stability of the near surface boundary layer, which in the model is determined by the difference between the temperature at the glacier surface and the air at measurement height. The distribution of surface roughness lengths resembles the picture for surface albedo as they are also dependent on the presence/absence of snow and the age of snow. Figure 7.13 shows the spatial distribution of the surface energy fluxes averaged over the whole hydrological year 2004/05 while Figure 7.14 shows the according vertical profiles. Net shortwave radiation decreases with altitude as the mean albedo increases. The increase in SWnet between 2800 and 2900 m (Fig.7.14) is due to the relatively steep, east exposed surface topography in this region, which leads to enhanced insolation 7.3 Surface Energy Fluxes 63

Figure 7.9: Spatial distribution of modelled surface energy fluxes averaged over January 2005 and Langenferners topography indicated by 10 m-contours (dashed) and 50 m-contours (thick). Note that melt energy flux (no figure) was zero for all grid cells throughout the whole month. 64 7 Results

Figure 7.10: Spatial distribution of important surface variables in winter. z0m is surface roughness length for momentum while z0s is surface roughness length for scalars. Means for January 2005 7.3 Surface Energy Fluxes 65 in the morning hours. The minimum around 3150 m is the result of steep north exposed slopes (see Figure 7.5, bottom-right corner). Net longwave radiation also decreases with altitude and is negative for all glacier regions. Turbulent heat fluxes show similar distributions but in contrast to the sensible heat flux, mean latent heat flux is negative for the whole glacier. Mean ground energy flux is slightly positive and increases with altitude because of the greater temperature difference between the EMB-model’s deepest subsurface layer and the surface. The resultant melt energy flux mainly reflects shortwave net radiation. 66 7 Results

Figure 7.11: Spatial distribution of modelled surface energy ﬂuxes averaged over July 2005. 7.3 Surface Energy Fluxes 67

Figure 7.12: Spatial distribution of important surface variables in summer. z0m is surface roughness length for momentum while z0s is surface roughness length for scalars. Means for July 2005 68 7 Results

Figure 7.13: Spatial distribution of modelled surface energy ﬂuxes averaged over the hydrological year 2004/2005. 7.4 Model Sensitivity 69

Figure 7.14: Vertical profiles of modelled surface energy fluxes averaged over the hydrological year 2004/2005. For a better graphical illustration the melt energy flux QM (negative) is shown as positive.

7.4 Model Sensitivity

Many parameters and constants are involved in the EMB-model calculations. Some of them were fitted to measurements at Felsköpfl or other stations (b, εcl, k, Kdif ) while others were taken from the literature ( z0m, z0hv, αfsn), or estimated by fitting the model output to observations (αice, αfirn). In order to test the sensitivity of the EMB-model to changes in these parameters, more than 40 sensitivity model runs were carried out. Table 7.2 shows the impact of the parameter changes on Langenferners modelled mean specific mass balance for the hydrological year 2004/05. A variation of b (constant governing LWin, see section 4.4.1) by +(-) 0.02 leads to a change in mass balance of -267 (+240) mm w.e while a change of the clear sky emissiviy by +(-) 0.008 results in a balance change of -53 (+52) mm w.e. Changes in the ice albedo of +(-) 0.05 bring a decrease (increase) in ablation of 114 (116) mm w.e. A change of the firn albedo by +(-) 0.04 affects mass balance sligthly stronger: +133 (-130) mm w.e. As the albedo scheme is one of the weak points in this study, the albedo time scale was also varied. A lowering of the time scale by five days which leads to a faster albedo decrease after a snow fall event results in a mass balance change of -329 mm w.e. while a five day rise of the time scale changes the mass balance by 211 mm w.e. dif1, a constant determining the fraction of the diffuse part in incoming shortwave radiation was altered by +(-)0.04 which lead to balance change of -112 (+108) mm w.e. Changing the shortwave radiation constant k (governing the impact of clouds) by +(-)0.04 shows a similar result. An increased k enhances the impact of clouds to incoming shortwave radiation and leads to a 103 mm w.e increase in mean specific mass balence while a decrease in k decreases the balance by 107 mm w.e. Surface roughness lengths show a minor impact on mass balance (see table 7.2) which can 70 7 Results

partly be explained by the (most of the time) different sign of the two turbulent fluxes (Figure 7.2). To investigate the effect of a changing climate on Langenferners modelled mass balance, its sensitivity was also tested for changes in the meteorological variables. Another aim of the sensitivity tests was also to estimate the effect of uncertainties in the meteorological input (e.g. neff ). The most important meteorological variable seems to be air temperature. A 1°C increase in air temperature leads to a change in mean specific mass balance of -1338 mm w.e. which is surprisingly high, as similar studies for other glaciers show lower sensitivities to air temperature (Greuell and Böhm, 1998; Klok and Oerlemans, 2002). A lowering of summer precipitation by 20 % has a much larger impact (-641 mm w.e) than an increase of the same magnitude (+124 mm w.e.) which is probably due to the non linear effect of precipitation amount and snowdepth on surface albdeo. Altering relative humidity by +/-10 % leads to a similar result (-445/+250 mm w.e.) as a +/-20 % change in wind speed (-436/+427 mm w.e). Both variables affect mainly the turbulent fluxes, while relative humidity also influences incoming longwave radiation as the skies emissivity is a function of water vapor pressure. Effective cloud cover fraction neff seems to be of minor relevance for the modelled mean specific mass balance. A 20 % decrease of neff hardly affects mass balance as the resultant increase in incoming shortwave radiation is compensated by a decreasing longwave incoming part. A 20 % increase of neff leads to 50 mm w.e. more ablation. Klok and Oerlemans(2002) explain this asymmetry by the non linear effect of cloud cover on incoming shortwave radiation.

7.4.1 Topographic Shading The sensitivity of the modelled glacier surface mass balance was also tested for topographic shading by surrounding peaks and ridges. The eﬀect of topographic shading was smaller than expected. Mean speciﬁc mass balance for the hydrological year 2004/05 solely considering self shading of the grid cells is -1475 mm w.e. compared to -1399 mm w.e. in the reference run. The distribution of mass balance does also not change very much. The importance of topographic shading is slightly greater for (i) years with more negative mass balances or (ii) for years in which a main portion of melt occurs late in the ablation season. The reason for this is (i) the greater portion of absorbed SWin at low albedo conditions and (ii) the decreasing elevation angles of sun with progressing summer which enhance relative importance of shading as shaded areas enlarge. 7.4 Model Sensitivity 71

7.4.2 Model Sensitivity - a Summary The sensitivity tests showed that the EMB-model is most sensitive to changes in air temperature and precipitation. An increased air temperature by 1°C is almost equivalent to a change in precipitation of -20 %, while a 20 % increase in precipitation shows a smaller effect (+540 mm w.e.) than a 1°C temperature decrease (+912 mm w.e.). Note that an interpretation of an all year precipitation change is difficult as winter precipitation rates are fitted to the measured winter balance for the respective years (see section 4.7). Changing summer precipitation leads to a smaller effect. Several parameters show an interesting non-linearity when comparing the results of an increase and a decrease of the respective variable. The largest non-linearity was shown by the density of fresh snow (in the model 250 kgm−3) where a density of 350 kgm−3 lead to a decrease in annual mass balance of 1036 mm w.e., while a lower density (150 kgm−3) lead to hardly any change (4 mm w.e.). Air pressure was shown to be relatively unimportant which justifies the use of NCEP/NCAR-REA-data as model input. A change in surface roughness lengths was also found to be of minor relevance which can be explained by the (most of the time) different sign of the two turbulent heat fluxes (see Figure 7.2) 72 7 Results

Parameter change explanation ∆b

b +0.02 increased LWin (see sect. 6.2) -267 b -0.02 decreased LWin (see sect. 6.2) 240 εcs +0.008 increased LWin (see sect. 6.2) -53 εcs -0.008 decreased LWin (see sect. 6.2) 52 αice +0.05 lower SWnet 114 αice -0.05 increased SWnet -116 αfirn +0.04 lower SWnet 133 αfirn -0.04 increased SWnet -130 t∗ +5 days slower albedo decrease (sect. 7.2.3) 211 t∗ -5 days faster albedo decrease (sect. 7.2.3) -329 dif1 +4% increased portion of dif. SW in -112 dif1 -4% portion of dif. SWin decreased 108 k +0.04 increased cloud impact (sect. 4.3.3) 103 k -0.04 decreased cloud impact(sect. 4.3.3) -107 3 rhofsn +100kg/m higher density of fresh snow -1036 3 rhofsn -100kg/m lower density of fresh snow 4 z0m -1mm, z0hv -0.1mm higher roughness lengths for ice -15 z0m -1mm, z0hv -0.1mm lower roughness lengths for ice 20 z0max +1mm, z0hvmax +0.1mm higher roughness lengths for old snow 25 z0max -1mm, z0hvmax -0.1mm lower roughness lengths for old snow -24 air temperature +1K higher air temperature -1338 air temperature -1K lower air temperature 912 temp. gradient +0.0010K/m increased T.-change with altidude 251 temp. gradient -0.0010K/m decreased T.-change with altidude -351 precipitation +20% more precipitation 540 precipitation -20% less precipitation -1304 prec.-gradient +0.03%/m precipitation increase with altitude 226 prec.-gradient -0.03%/m precipitation decrease with altitude -528 summer precipitation +20% more precipitation (May-Sept.) 124 summer precipitation -20% less precipitation (May-Sept.) -641 neff +20% more cloudcover, less SWin, moreLWin -50 neff -20% les cloudcover, more SWin, lessLWin 9 rel. humidity +10% higher humidity,→ turb. fluxes, LWin -445 rel. humidity -10% lower humidity→ turb. fluxes, LWin 250 wind speed +20% higher w.s.→ turb. fluxes -436 wind speed -20% lower w.s.→ turb. fluxes 427 wind sp. gradient +0.002s−1 increasing wind sp. with altitude -336 wind sp. Gradient -0.002s−1 decreasing wind sp. with altitude 216 air pressure +20hPa higher air pressure -20 air pressure -20hPa lower air pressure 19

Table 7.2: Sensitivity of modelled mean speciﬁc mass balance [ mm w.e. ] to changes in the meteorological input and to changes of selected model constants. 8 Conclusion

8.1 General Aspects

The aim of this thesis was to simulate the temporal and spatial variability of the surface mass balance of an alpine glacier in relatively complex topography for the five year period 2004 to 2008. Therefore a spatially distributed, physically based energy and mass balance model, developed by Thomas Mölg/University of Innsbruck was applied. The model, which until now was mainly used for studies on tropical sites, was tested and optimized for use on Langenferner, Ortles-Cevedale Group/Northern Italy. Data from several permanent automatic weather stations located in the vicinity of Langenferner and maintained by the Hydrographic Office of the Autonomous Province of Bolzano were used as model input while glaciological field data such as stake readings and snow probings served to optimize the model and to validate the results. In order to properly extrapolate the meteorological input data to the glacier surface, transfer functions (statistical corrections) were applied. In the course of this study, an automatic weather station was temporarily installed at Felsköpfl, a distinct rock hill next to the glacier. Taking advantage of the resultant one-month meteorological data-set, some of the model parameterizations (especially the longwave radiation scheme) could be optimized for the conditions at the study site. Meteorological data from the glacier surface boundary layer was not available for this work. The spatial distribution of Langenferner’s mass balance was computed as the sum of accumulation and ablation. Winter accumulation was derived by fitting modelled to observed winter balance using daily precipitation sums measured at Lake Zufritt as model input. This procedure was applied in order to consider high winter accumulation rates at the glacier which can be explained by snow redistribution due to wind rather than by a vertical precipitation gradient. Ablation was simulated on the basis of the energy balance of the glacier surface, converting the net surface energy flux to an ablation rate. A comparison of modelled mass balances at Langenferner to stake measurements showed a generally sufficient model performance for most of the years. A major discrepancy between modelled and observed mass balance for the hydrological year 2007/2008 could be attributed to an insufficiency in the albedo parameterization, while some of the remaining disaccordances were assigned to difficulties in extrapolating meteorological

73 74 8 Conclusion

data from the measurement sites to the glacier. The distributions of the surface mass balance as well as of the related surface energy fluxes were discussed in detail. Finally, a series of model sensitivity tests were carried out in order to test the influence of changes in selected model parameters as well as in the meteoroloical input data on the modelled mean specific mass balance of Langenferner. These tests lead to the result that the model is most sensitive to changes in air temperature and precipitation. All in all, driving a high resolution, physically based mass balance model with off-glacier data seems to be reasonable even if a minimum data set from the glacier surface is still needed to optimize the model for the respective site. Nevertheless meteorological data from the glacier is substantial for an upcoming further developpment of some of the existing model parameterizations.

8.2 Discussion and Outlook

Another scope of this research was to show potential difficulties in the application of the EMB-model to alpine glaciers. In the following, some problematic aspects are discussed and an outlook for possible future work is presented. The spatial variability of incoming shortwave radiation is well captured by the model as slope, aspect and altitude of each grid cell are considered and topographic shading is taken into account. Nevertheless the the spatial variability of the diffuse portion of shortwave radiation in the model might be improved. Especially reflections from (snow-covered) surrounding slopes can considerably influence the amount of SWin. Similar is true for incoming longwave radiation, which in the model solely varies with altitude due to the altitude dependence of near surface air temperature and water vapor pressure. Spatial variation of radiation emitted from slopes nearby the glacier is neglected as the constant b is the same for the whole glacier area. The albedo scheme is a major question in this study as the assumption of a temporal constant albedo timescale t∗ seems to be not justified. An improvement of the albedo scheme is necessary for further studies on the mass balance of midlatitude glaciers. To simulate the distribution of turbulent heat fluxes more realistically, a better estimate of variable (in space and time) roughness lengths is needed. Eddy correlation measurements would provide a great help to further develop the parameterization of turbulent fluxes (Cullen et al., 2007). An even more important, but difficult, improvement of the model would be a wind module which accounts for the spatial variability of the near surface glacier wind field. A realistical simulation of the glacier wind field would also be needed to properly assess the redistribution of snow due to wind, which is not captured by the model. Redistribution of snow plays an important role on the spatial patterns of the surface mass balance of midlatitude glaciers. On Langenferner especially the uppermost areas are influenced by wind ablation which leads to an overestimation of the modelled mass 8.2 Discussion and Outlook 75 balance in this area. The precondition for all these possible improvements would be meteorological data from the study site, recorded by at least one automatic weather station on the surface of Langenferner. The measurements on Felsköpfl showed the relevance of data from the study site for optimizing and improving the model even if a desirable goal is still a realistic simulation of a glacier’s mass balance using off-glacier data and maybe a minimum set of on-glacier measurements.

Bibliography

Arnold, N. and G. Rees, 2009: Eﬀects of digital elevation model spatial resolution on distributed calculations of solar radiation loading on a high arctic glacier. Journal of Glaciology, 55 (194), 973–984.

Bintanja, R. and M. Van den Broeke, 1995: The surface energy balance of Antarctic snow and blue ice. Journal of applied Meteorology, 34, 902–926.

Braithwaite, R., 1995: Aerodynamic stability and turbulent sensible heat ﬂux over a melting ice surface, the Greenland Ice Sheet. Journal of Glaciology, 41 (139), 562–571.

Brock, B., I. Willis, and M. Sharp, 2006: Measurement and parameterization of aerodynamic roughness length variations at Haut Glacier d’Arolla, Switzerland. Journal of Glaciology, 52 (177), 281–297.

Brock, B., I. Willis, M. Sharp, and N. Arnold, 2000: Modelling seasonal and spatial variations in the surface energy balance of Haut Glacier d’Arolla, Switzerland. Annals of Glaciology, (31), 53–62.

Cullen, N., T. Mölg, D. Hardy, K. Steﬀen, and G. Kaser, 2007: Energy balance model validation on the top of Kilimanjaro using eddy correlation data. Annals of Glaciology, 46, 292–302.

Finsterwalder, 1890: Die Gletscherausbrüche des Martell-Thales. Mitteilungen des Deutsch- Österreichischen Alpenvereines, 20, 21–34.

Fliri, F., 1975: Das Klima der Alpen im Raume von Tirol. Universitätsverlag Wagner, 454 pp.

Francou, B., M. Vuille, P. Wagnon, J. Mendoza, and J. Sicart, 2003: Tropical climate change recorded by a glacier in the central Andes during the last decades of the twentieth century: Chacaltaya, Bolivia, 16°S. Journal of Geophysical Research, 108, 4154–4165.

Garrat, J., 1992: The Atmospheric Boundary Layer. Cambridge University Press, 316 pp.

Greuell, W., 1992: Hintereisferner, Austria: mass balance reconstruction and numerical modelling of the length variations. Journal of Glaciology, 38 (129), 233–244.

Greuell, W. and R. Böhm, 1998: 2 m temperatures along melting midlatidtude glaciers, and implications for the sensitivity of the mass balance to variations in temperature. Journal of Glaciology, 44 (146), 9–20.

77 78 Bibliography

Greuell, W., W. Knap, and P. Smeets, 1997: Elevational changes in meteorological variables along a midlatitude glacier during summer. Journal of Geophysical Research, 102 (D22), 25,941–25,954.

Greuell, W. and P. Smeets, 2001: Variations with elevation in the surface energy balance on Pasterze (Austria). Journal of Geophysical Research, 106, 31,717–31,727.

Hastenrath, S., 2001: Variations of East African climate during the past two centuries. Climatic Change, 50, 209–217.

Hock, R., 1999: Temperature index melt modelling in mountain areas. Journal of Hydrology, 282, 104–115.

Hock, R. and B. Holmgreen, 2005: A distributed surface energy-balance model for complex topography and its application to Storglaciären . Journal of Glaciology, 51 (172), 25–36.

Hoﬀman, M., A. Fountain, and G. Liston, 2008: Surface energy balance and melt thresh- olds over 11 years at Taylor Glacier, Antarctica. Journal of Geophysical Research, 113 (F04014).

Hoinkes, H., 1971: Methoden und Möglichkeiten von Massenhaushaltsstudien auf Gletschern. Zeitschrift für Gletscherkunde und Glazialgeologie, 6 (1-2), 37–90.

Iqbal, M., 1983: An Introduction to Solar Radiation. International Geophysic Series, 649 pp.

Kalnay, E., M. Kanamitsu, R. Kistler, W. Collins, D. Deaven, L. Gandin, and M. Iredell, 1996: The NCEP/NCAR 40 year reanalysis project. Bulletin of the American Meteorological Society, 77 (3), 437–471.

Kaser, G., 1982: Measurements of evaporation from snow. Archiv für Met.Geoph.Biokl., B30, 333–340.

Kaser, G., A. Fountain, and P. Jansson, 2003: A manual for monitoring the mass balance of glaciers. Technical Documents in Hydrology, 59, 107.

Klok, E. and J. Oerlemans, 2002: Spatial distribution of mass and energybalance of Morter- atschgletscher, Switzerland. Journal of Glaciology, 48 (132), 1349–1369.

Konya, K. and T. Matsumoto, 2010: Inﬂuence of weather conditions and spatial variability on glacier surface melt in Chilean Patagonia. Theoretical and Applied Climatology, 102 (1-2), 139–149.

Konzelmann, T., R. Van de Wal, J. W. Greuell, R. Bintanja, E. Henneken, and A. Abe-Ouchi, 1994: Parameterization of global and longwave incoming radiation for the Greenland Ice Sheet. Global and Planetary Change, 9, 143–164. Bibliography 79

Kuhn, M., 1978: Die Höhe des Geschwindigkeitsmaximums im Gletscherwind als Param- eter des Wärmehaushalts. Arbeiten aus der Zentralanstalt für Meteorologie und Geody- namik,Wien, (31), 69/1–69/8.

Kuhn, M., 1981: Climate and glaciers. Sea level, ice and climatic change., (Proceedings of the Canberra Symposium, Dec. 1979) IAHS publ. no. 131, 3–20.

Kuhn, M., 1993: Methods of assessing the eﬀects of climatic changes on snow and glacier hydrology. Snow and glacier hydrology., (218), 135–144.

Kuhn, M., 2003: Redistribution of snow and glacier mass balance from a hydrometeorological model. Journal of Hydrology, (282), 95–103.

Manzl, R., 2010: Neuberechnung bzw. Verbesserung des Energiebilanzmodells von Hoﬁnger und Kuhn. M.S. thesis, Universität Innsbruck.

Meyers, T. and R. Dale, 1983: Predicting daily insolation with hourly cloud height and coverage. Journal of Climate and applied Meteorology, 22, 537–546.

Mölg, T., 2009: Climate change in the tropics derived from glacier atmosphere interactions. habilitation thesis, Universität Innsbruck.

Mölg, T., N. Cullen, D. Hardy, G. Kaser, and E. Klok, 2008: Mass balance of a slope glacier on Kilimanjaro and its sensitivity to climate. International Journal of Climatology, 28 (7), 881–892.

Mölg, T., N. Cullen, D. Hardy, M. Winkler, and G. Kaser, 2009b: Quantifying climate change in the tropical midtroposphere over East Africa from glacier shrinkage on Kilimanjaro. Journal of Climate, 22, 4162–4181.

Mölg, T., N. Cullen, and G. Kaser, 2009a: Solar radiation, cloudiness and longwave radiation over low-latitude glaciers: implications for mass-balance modelling. Journal of Glaciology, 55, 292–302.

Mölg, T. and D. Hardy, 2004: Ablation and associated energy balance of a horizontal glacier surface on Kilimanjaro. Journal of Geophysical Research, 109 (D16104).

Mölg, T., D. Hardy, and G. Kaser, 2003: Solar-radiation-maintained glacier recession on Kilimanjaro drawn from combined ice-radiation geometry modeling. Journal of Geophysical Research, 108 (D23), 4731.

Niemelä, S., P. Räisänen, and H. Savijärvi, 2001: Comparison of surface radiative ﬂux parameterizations, part II. shortwave radiation. Atmospheric Research, 58, 141–154.

Oerlemans, J., 2010: The Microclimate of Valley Glaciers. Utrecht Publishing and Archiving Services, Universiteitbibliotheek Utrecht, 138 pp. 80 Bibliography

Oerlemans, J., R. Giesen, and K. Van den Broeke, 2009: Retreating alpine Glaciers: increased melt rates due to accumulation of dust (Vadret da Morteratsch, Switzerland). Journal of Glaciology, 55 (192), 729–736.

Oerlemans, J. and B. Grisogono, 2002: Glacier wind and parameterization of the related surface heat ﬂux. Tellus, 122, 440–452.

Oerlemans, J. and E. Klok, 2004: Modeled climate sensitivity of the mass balance of Morteratschgletscher and its dependence on albedo parameterization. International Journal of Climatology, 24, 231–245.

Oerlemans, J. and W. Knap, 1998: A one-year record of global radiation and albedo in the ablation zone of the Morteratschgletscher, Switzerland. Journal of Glaziology, 44 (147), 231–238.

Paterson, W., 1994: The Physics of Glaciers. Elsevier, 481 pp.

Reijmer, C. and R. Hock, 2008: Internal accumulation on Storglaciären, Sweden, in a multi- layer snow model coupled to a distributed energy- and mass balance model. Journal of Glaciology, 54 (184), 61–72.

Sedlar, J. and R. Hock, 2009: Testing longwave radiation parameterizations under clear and overcast skies at Storglaciären, Sweden. The Cryosphere, 3, 75–84.

Simony, 1865: Der Suldener und Marteller Ferner im Jahre 1855. Jahrbuch des Österreichis- chen Alpenvereines, 1.

Van den Broeke, M., 1997: Momentum, heat and moisture budgets of the katabatic wind layer over a mid-latitude glacier in summer. Journal of Applied Meteorology, 36, 763–774.

Wagnon, P., J. Sicard, E. Berthier, and J. Chazarin, 2003: Wintertime high-altitude surface energy balance of a Bolivian glacier, Illimani, 6340 m above sea level. Journal of Geophysical Research, 108 (D6), 4177.

Winkler, M., I. Juen, T. Mölg, P. Wagnon, J. Gómez, and G. Kaser, 2009: Measured and modelled sublimation on the tropical Glaciar Artesonraju, Perú. The Cryosphere, 3, 21–30. List of Figures

2.1 The study site: Langenferner...... 7 2.2 Location of the study site...... 8 2.3 Historic Map of Langenferner...... 9 2.4 Historic photograph of Langenferners terminus...... 10 2.5 Historic postcard...... 11 2.6 The terminus of Fürkeleferner 1855...... 11

3.1 Location of the weather stations...... 14 3.2 AWS Felsköpﬂ...... 16 3.3 Measured and modelled global radiation...... 18 3.4 Validation of air pressure transfer...... 21 3.5 Meteorological conditions at the weather stations I...... 22 3.6 Meteorological conditions at the weather stations II...... 23 3.7 Mass balance and stake network...... 24 3.8 Seasonal mass balances at Langenferner...... 25

4.1 Surface energy ﬂuxes on Langenferner on a warm summer day..... 29 4.2 Modelled and measured incoming shortwave radiation at Sulden Madritsch 32 4.3 Incoming shortwave radiation for clear and obstructed skies...... 34 4.4 Modelled and observed SWin for "extreme" conditions...... 34 4.5 Phi-functions for stable and unstable conditions...... 39

5.1 Topographic model input...... 45

6.1 Validation of incoming shortwave radiation...... 47 6.2 Optimization of incoming longwave radiation (I)...... 48 6.3 Optimization of incoming longwave radiation (II)...... 49 6.4 Measured and transferred air temperature at Felsköpﬂ...... 49 6.5 Transfer of wind speed data from Schöntaufspitze to the glacier (I)... 50 6.6 Transfer of wind speed data from Schöntaufspitze to the glacier (II)... 51

7.1 Suface change at stake 4...... 53 7.4 Vertical mass balance proﬁles...... 56 7.6 Modelled sublimation and deposition on Langenferner...... 58

81 82 List of Figures

7.7 Measured and modelled snow melt in summer 2008...... 59 7.8 Measured and modelled snow cover in summer 2008...... 60 7.9 Spatial variability of surface energy fluxes in winter...... 63 7.10 Spatial variability of relevant surface variables in winter...... 64 7.11 Spatial variability of surface energy fluxes in summer...... 66 7.12 Spatial variability of relevant surface variables in summer...... 67 7.13 Spatial distribution of all year mean energy fluxes...... 68 7.14 Vertical profile of mean surface energy fluxes...... 69 List of Tables

3.1 Weather stations and measured variables...... 15 3.2 Quality of meteorological data...... 17

7.1 Mean speciﬁc mass balances at Langenferner...... 56 7.2 Model sensitivity...... 72

Appendix A - The mbminﬁle

%input file of 2D-EMB-model...LANGENFERNER VERSION,l.m.:stephan galos 2010_09_08 %author: Thomas Mölg, 2007 (based on EB model, 2003-2006) %version 1.6: Apr 2010 %new since 1.4: heat flux from precipitation, initialization with variable %snow depth and density, stability function limits for very stable and %unstable conditions (laminar, free convection)

%***********METEOROLOGICAL INPUT***************** %provide the following in an ascii, tab-delimited file specified by 'theinfile' %and define in which column the respective variable is located %make sure all columns have the same length! theinfile = 'respective storage_loction'; %path to input file ip_colyear = 1; %year ip_colmon = 2; %month ip_coljday = 3; %day number of year (1=1 Jan; 365=31 Dec) ip_colhour = 4; %hour (e.g., 1=average between 0 and 1 LT) ip_colswin = [ ]; %incoming SW radiation, if available; otherwise say [ ] ip_colalb = [ ]; %albedo, if available; otherwise say [ ] ip_collwin = [ ]; %incoming LW radiation, if available; otherwise say [ ] ip_colt = 5; %air temp. in °C ip_colrh = 6; %relative humidity in 1/100 ip_colcld = 7; %cloud factor 0-1; can be [ ] if 0D-run and solar rad. measured input ip_colv = 8; %wind speed in m/s ip_colp = 9; %air pressure in hPa ip_colaccrat = 10; %precipitation sum (solid+liquid phase) per timestep (cm or mm WE: specify below) PRCUNTFLG=1; %unit of precip. input: 0=actual cm; 1=mm WE; tpertu=0; %temperature perturbation for standard sensitivity runs (K) ppertu=0; %precipitation perturbation for standard sensitivity runs (%)

%*********TOPOGRAPHY INPUT********* %define paths to, and limits of, topography grids (if run is two-dimensional) latra=[46.492891 46.440265]; %[north- south-boundary] in degrees lonra=[10.590973 10.660625]; %[west- east-boundary] in degrees locgridelv = 'respective storage_loction';% grid input: elevation (m asl) locgridslo = 'respective storage_loction';% grid input: slope (deg) locgridasp = 'respective storage_loction';% grid input: aspect (deg from N) locgridglac = 'respective storage_loction';% grid input: glacier mask %1 if grid point is glacier, 0 if grid point is glacier-free locgridsvf = 'respective storage_loction';% grid input: sky view factor (0-1) %if not available or not necessary (e.g., a flat and open site), make line above inactive "%"

%*********GEOGRAPHIC CHARACTERISTICS AND VERTICAL GRADIENTS********* lat = 46.4666; %mean latitude in degrees, southern hemisphere negative altref = 2825; %reference altitude (m asl): altitude where input data are recorded dtdz = -0.0065; %air temp. gradient (°C per m) dPdz = 0.00; %precipitation gradient (percent per m) dvdz = 0.000; %wind speed gradient (m/s per m) dalphdz = 0.0000; %if ALBPARFLG==0: albedo gradient (per m) wphastrh = 0.5; %air temp. threshold (°C) between liquid-solid precipitation pointterr = [ ];%only if SPATFLG==0: elevation, slope, aspect, and sky view factor of point

85 %***********MODEL OPTIONS***************** SPATFLG = 2; %spatial dimensions: 0=point; 2=2D SINPARFLG = 1; %SW_in: 0=measured, 1=parameterized (see "sol.rad. module" below) SHADFLG = 3; %shading: 0=self-shading of cell, 1=self- and relief shading (possible if 2D), %3=relief shading - look-up table exists from previous run (must be "shad1yr.cdf") LWINPARFLG = 4; %LW_in: 0=measured, 1=parameterized (Mölg/Hardy, 2004), 2=from vp, T, and clouds %Mölg et al. (2009, J. Glac); 3=quadr.fit (Mölg et al, 2008, IJC) %4= from vp, T, and clouds for mid latitudes (Klok & Oerlemans, 2002) TSPARFLG = 2; %surface temp. scheme: 1=iterative, 2=from residual flux, 3=extrapolation from subsurface TSdummy = 264; %if TSPARFLG==1: surf. temp. to initialize iterative scheme; TSt1 = 265; %if TSPARFLG==2 or 3; surf. temp. of first time step to initialize scheme repsfcl = 0.22; %if TSPARFLG==2; representative surface layer thickness (m) (Klok & Oerlemans, 2002) repsfclisr = 1.0; %ice/snow ratio of that thickness (>1: smaller in snow; 1: no difference) TSminpar2 = 240; %if TSPARFLG==2; minimum TS allowed (K), to avoid unstability in scheme ts3fac = 1.0; %if TSPARFLG==3; multiplication factor controlling surf.temp. amplitude QSTFLG = 0; %energy storage in surface layer: 0=no, 1=yes (Garratt, 1992), 2=yes (empirically) dqstamp = 1; %if QSTFLG==1; amplitude of energy storage in percent/100 (standard: 1) ALBPARFLG = 1; %albedo: 0=measured, 1=parameterized, 2=spat.dist. measurement (not working yet) ALBMODMOD=1; %albedo model: 1=const. ice albedo, 2=ice albedo as f(dew point), % 3=albedo as f(dewpoint, melt rate) ALBMODMOD2=1; %ratio snowdepth/depscale in albedo parameterization: 1=actual height, 2=WE values TCONDFLG = 0; %thermal conductivity: 0=f(kappa, density), 1=defined in tci and tcs below REFRFLG = 1; %refreezing of surface melt water in snowpack: 0=no, 1=yes CKFLG = 1; %if REFRFLG==1; 0=constant CK (section "subsurface"), 1=CK weighted by terrain slope QPSFLG = 0; %penetrating SW radiation: 0=no, 1=yes QPRCFLG = 2; %heat flux from precipitation: 0=no, 1=yes (only from rain), 2=yes (from rain and solid prec.) ROUGHFLG=1; %surface roughness length: 0=constant, 1=variable PSCALFLG = 1; %correct precipitation height as function of terrain slope: 0=no, 1=yes sloref = 0; %slope at reference grid cell, only if PSCALFLG == 1 METSTORFLG = 1; %write spatial grids of met. input data to output files: 0=no, 1=yes SUBWRTFLG = 0; %subsurface field; write penetrating SW radiation: 0=no, 1=yes SOLPOSFLG = 0; %output sun position data: 0=no, 1=yes (returns array sunpos: illum. dir, elev., TOA rad.) storpath = 'respective storage_loction'; %storage location of output (CDF files) SUSEDICHFLG = 0; %surface-T/RH/wind sensor distance: 0=const., 1=variable ip_colsfcch = [ ]; %if SUSEDICHFLG==1 --> column of surface distance change values (in m, relative to starting point), %this must be a cumulative time series (surface increase is positive, lowering negative); otherwise [ ]; dtstep = 3600; %time step in seconds

%*********SOLAR RADIATION MODULE********* %define constants (see Mölg et al., 2009, J. Glac.) S0 = 1367; %solar "constant" difra = 0.66; %diffuse radiation constant (K_dif in Mölg et al.) dif1 = 13; %diffuse rad. as percentage of potenial clear-sky GR at cld = 0 Cf = 0.76; %constant that governs cloud impact (k in Mölg et al.) aesc1 = 0.87764; %transmissivity due to aerosols at sea level aesc2 = 2.4845e-5; %increase of aerosol transmissivity per meter altitude dirovc = 0; %direct solar radiation at overcast conditions %(as fraction of clear-sky direct solar radiation; e.g., 10%=0.1) tcart = 0; %station time correction in hour angle units (1=4min), max. ~1/4 of time step

%*********SURFACE MODULE********* %define constants z0m = 0.002; %m, roughness length momentum (if ROUGHFLG==0) or %roughness length (mom.) of ice (if ROUGHFLG==1) z0h = 0.0002; %m, roughness length scalars (if ROUGHFLG==0) or %roughness length (scal.) of ice (if ROUGHFLG==1) z0mhfs=1e-3; %m, roughness length of fresh snow, only if ROUGHFLG==1 z0mmax=4e-3; %m, roughness length (mom.) of aged snow, only if ROUGHFLG==1 z0hmax=4e-4; %m, roughness length (scal.) of aged snow, only if ROUGHFLG==1 z0mpet=4e-3; %m, roughness length (mom.) of penitentes, only if ROUGHFLG==1

86 z0hpet=4e-3; %%m, roughness length (scal.) of penitentes snow, only if ROUGHFLG==1 zm = 3.5; %m, initial wind speed sensor height zh = 3.0; %m, initial T/RH sensor height emice = 1; %glacier surface emissivity tci = 2.2; %W/m/K (standard: 2.2), if TCONDFLG==1 tcs = 0.5; %W/m/K (standard: 0.5), if TCONDFLG==1 rohsfd=250; %density of precipitation during daytime (kg/m3) rohsfn=250; %density of precipitation during night (kg/m3) daybeg=10; %begin of daytime (e.g., 9 = 9LT minus timestep) dayend=19; %end of daytime (e.g., 20 = 20LT) SND0FLG=1; %2D-run: initial snow depth treatment: 0=constant in space,1=variable (grid input needed!) locgridsnd0 = 'respective storage_loction'; %grid input: initial snow depth in cm (only if SND0FLG==1) ROH0FLG=1; %2D-run: initial snow density treatment: 0=constant in space, 1=variable (grid input needed!) locgridroh0 = 'respective storage_loction'; %grid input: initial snow density in kg/m3 (only if ROH0FLG==1) sndeppre=00; %snow depth at beginning of first time step (cm) if SND0FLG==0; rohspre=400; %bulk density of settled snow (kg/m3) at t0 (relevant if there is snow and ROH0FLG==0) rohbus=500; %mean (all-time) bulk density of settled snow (kg/m3), only relevant if ALBMODMOD2==2 rohi = 900; %ice density (kg/m3)

%*********SUBSURFACE MODULE********* %thermal diffusivity (m2 s-1) kappai = 1.3e-6; %ice; standard: 1.3e-6 kappas = 0.5e-6; %snow; standard: 0.5e-6 CK = 1; %actual refr. as fraction of max. refreezing amount per time step; only relevant if REFRFLG==1 & CKFLG==0 suifra=0.3; %fraction (0-1) of refreezing mass that forms superimposed ice; only relevant if REFRFLG==1

%define constants for QPSFLG==1 (Bintanja & Van den Broeke, 1995) zetai = 0.71; %portion of Snet absorbed at ice surface (near-infrared) zetas = 1; %portion of Snet absorbed at snow surface (near-infrared) pentrh = 0; %snow depth in cm above which zetas gets active (standard is 0) betai = 2.5; %m-1, extinction coefficient ice; standard: 2.5 betas = 17.1; %m-1, extinction coefficient snow; standard: 17.1

%specify layer structure layers = [0 0.1 0.2 0.3 0.4 0.5 0.7 0.9 1.3 1.7 2.3 3 4 5 7 9 11 ]';%number of layers %and depth in meters (1st must be zero, i.e., surface), %either [surface:increment:bottom]' or [0 depth_layer1 depth_layer2 ...]' %deepest layer must be > than max. snowdepth if REFRFLG==1!

%specify inital temp. profile (constant or variable), surf. temp., and constant bottom temp. SUBTINITFLG = 0; %is initial profile known? 0=no, 1=yes (for point location only) subtinitfig = 269.8; %single value, if SUBTINITFLG == 0 subtinitfigvar = [1:1:29]'; %if SUBTINITFLG == 1, must be vertical array of length (number of layers-2), %describing the initial temperature profile bottomtfig = 273.15; %single value for bottom temperature (kept const.)

%*********ALBEDO MODULE********* %define control parameters alphice = .20; %ice albedo, only relevant if ALBMODMOD==1 alphfir = .50;%firn albedo or (tropics) old snow albedo alphfrsnow = .9;%fresh snow albedo tscale = 21.9;%t* (days), Oerlemans and Knap (1998)21.9 tsccoef = 1.5;%constant, only relevant if ALBMODMOD==3 (yet in test phase!) depscale = 3.7;%d* (cm), Oerlemans and Knap (1998) apaci1=0.013;%constant if ALBMODMOD==2 (Mölg et al., 2008) apaci2=0.65;%constant if ALBMODMOD==2 (Mölg et al., 2008) evday1diff = 0; %when was last event before series starts (e.g., 5 days ago = -5; %if not known use zero) sfeth = 1; %daily treshhold (cm) to define a "snowfall event"

%END of user input

Appendix B - Output Analysis & Analytools

To analyse the model output, which is saved to disc as cdf-files, use the three functions extmbfield, spatialass and altprof as speciefied below: To extract for instance the accumulated surface mass balance for every single grid cell over the whole investigation period (2004 to 2008) the syntax is as follows:

>>glaciergridID = cdfread(’tergrids.cdf’,’variables’,’gridglac’); >>glaciergrid = glaciergridID{1}(:,:);

These commands extract the glaciergrid to workspace which is needed for the spatial assignment of the decomposed variables (see below). To load the required variable to MATLAB-workspace now type:

>> all_MB = extmbﬁeld(’sfc’, ’totalmbacc’,2004,2008,1,12); where sfc is the variable type (surface), totalmbacc is the variable name (accumulated mass balance), 2004 and 2008 are the start and end years, 1 is the start month (Jan- uary) and 12 is the end month (December) for the period of interest. If the model is used in its spatial distributed conﬁguration, then the following command must be typed:

>> sp_MB = spatialass(glaciergrid,all_MB,25,48); where 25 and 48 are the timestep numbers marking the beginning and the end of the period the user is interested in. To calculate a mean vertical proﬁle of one variable use the function altprof. For instance if a mean vertical mass balance proﬁle is required, then type:

>>profile = altprof(2700,3400,50,gridelv(glaciergrid==1),sp_MB(glaciergrid==1)); where 2700 is the lower boundary of the mass balance profile (m), 3400 is the upper boundary (m), 50 is the vertical extent (m) of the elevation bands and gridelv is the grid cell elevation which must be extracted for this calculation. More information is provided by the file mbm2d_1.6.pdf which can be found (in the actual version) in the code1p6 folder or as a reprint of an older version in (Mölg, 2009). Note that the analy-functions must be stored in the same folder as the output cdf-files!

Danksagung

Ohne die Unterstützung einer Reihe von Personen und vielen Freunden wäre es mir nicht möglich gewesen, mein Studium erfolgreich abzuschließen. Deswegen möchte ich mich besonders bedanken bei: • Priv.-Doz. Dr. Thomas Mölg, der mich bei dieser Arbeit mit viel Einsatz exzellent betreut hat. • Prof. Dr. Michael Kuhn für wertvolle Kommentare zur Arbeit, sowie für die schöne Studienzeit am Institut für Meteorologie und Geophysik, für die Prof. Kuhn als Institutsleiter mitverantwortlich war. • Prof. Dr. Georg Kaser, der mir den Einstieg in seine Arbeitsgruppe ermöglicht, und mir die Leitung der Massenbilanzmessungen am Langenferner anvertraut hat. • Allen anderen Mitgliedern und Freunden der Innsbruck Tropical Glaciology Group: Irmi Juen, Lindsey Nicholson, Marlis Hofer, Susanna Hoinkes, Alex Jarosch, Ben Marzeion, Daniel Maurer, Martin Großhauser, Michael Winkler, Rainer Prinz und Nicolas J. Cullen. Sie alle wurden für mich schnell viel mehr als nur Kollegen! • Dr. Ing. Roberto Dinale und vor allem Dr. Daniel Schrott vom Hydrographischen Amt Bozen für das Bereitstellen der meteorologischen Daten. Ein Dankeschön gebührt auch meinen Freunden und Verwandten, die mich während des Studiums unterstützt haben. Im Besonderen: • Veronika Stadler für viele idiotische Aktionen und vor allem für die große Unterstützung in jedweder Form, • Alexander Klee für gemeinsame Bergtouren und für viele lustige Momente, • meiner Mutter Inge für das Ermöglichen des Studiums, • meiner Schwester Christine und ihrer Familie, wo ich immer willkommen bin, • meiner Taufpatin Annemarie für den positiven Einﬂuss auf meine Entwicklung, • meinen Freunden Barbara Pﬂanzner, Christoph Erath, Johanna Pöcheim, Yasmin Markl, Daniel Maier, Florian Wachter, Stefan Schauer, Sigi Fink, Thomas Gärtner, Tobias Reisch und allen die ich vergessen habe. Zu guterletzt noch ein großes Danke an meine Freundin Anna, die sich in den letzten Monaten oft mein Gejammer anhören musste, es aber stets verstanden hat, mich wieder aufzubauen.

Curriculum Vitae

Stephan Peter Galos Riedstraße 15 6820 Nenzing Vorarlberg/Austria

Born: November 26th, 1982 in Feldkirch, Austria

EDUCATION:

1989-1993 Primary school in Frastanz, Austria. 1993-2002 Grammar school in Feldkirch, Austria. MATURA. 2003-2010 Diploma study "Meteorology and Geophysics" at the University of Innsbruck. 2008-2010 Diploma Thesis under the guidance of Priv.-Doz. Dr. Thomas Mölg and Prof. Dr. Michael Kuhn at the Center of Climate and Cryosphere/University of Innsbruck: "Distributed modelling of the energy and mass-balance at the surface of Langenferner, Ortles-Cevedale Group/Italy".

METEOROLOGICAL TRAINING COURSES:

2010: "Monsoon Variability and Impacts on Mid- to Low Latitude Glaciers" summerschool, Obergurgl/Austria.

FIELDWORK:

since 2009: Responsible for the mass balance measurements at Langenferner (direct glaciological method).

OTHER:

2006: Instructor for high alpine mountain tours (Austrian Alpine Club). 2008: Instructor for ski-tours and avalanche security (Austrian Alpine Club). my personal answer to the question why we should study snow and ice...