What Glaciers Are Telling Us About Earth's Changing Climate

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This discussion paper is/has been under review for the journal The Cryosphere (TC). What glaciers are Please refer to the corresponding ﬁnal paper in TC if available. telling us about Earth’s changing What glaciers are telling us about Earth’s climate changing climate W. Tangborn and M. Mosteller

W. Tangborn1 and M. Mosteller2

1HyMet Inc., Vashon Island, WA, USA Title Page 2 Vashon IT, Vashon Island, WA, USA Abstract Introduction

Received: 12 June 2014 – Accepted: 24 June 2014 – Published: 1 July 2014 Conclusions References Correspondence to: W. Tangborn ([email protected]) and Tables Figures M. Mosteller ([email protected])

Published by Copernicus Publications on behalf of the European Geosciences Union. J I

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3475 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Abstract TCD A glacier monitoring system has been developed to systematically observe and docu- ment changes in the size and extent of a representative selection of the world’s 160 000 8, 3475–3491, 2014 mountain glaciers (entitled the PTAAGMB Project). Its purpose is to assess the impact 5 of climate change on human societies by applying an established relationship between What glaciers are glacier ablation and global temperatures. Two sub-systems were developed to accom- telling us about plish this goal: (1) a mass balance model that produces daily and annual glacier bal- Earth’s changing ances using routine meteorological observations, (2) a program that uses Google Maps climate to display satellite images of glaciers and the graphical results produced by the glacier 10 balance model. The recently developed PTAA glacier balance model is described and W. Tangborn and applied to eight glaciers to produce detailed mass balance reports. Comparing annual M. Mosteller balances produced by the model to traditional manual measurements for 50–60 years yields R2 values of 0.50–0.60. The model also reveals an unusual but statistically significant relationship between the average ablation of Wrangell Range glaciers and global Title Page 15 temperatures that have been derived from temperature data at 7000 stations in the Abstract Introduction Northern Hemisphere. This glacier ablation/global temperature relationship provides the means to use worldwide ablation results to anticipate problems caused by climate Conclusions References change. Tables Figures

1 Introduction J I J I 20 Glaciers are extraordinarily sensitive to climate variations, making relatively large changes in size and extent (a measure of mass balance) in response to a small change Back Close

in the climate. A substantial change in the climate, such as has occurred during the Full Screen / Esc past several decades, is causing many of them to disappear entirely. Measuring the

mass balance (the diﬀerence between snow accumulation and snow and ice ablation) Printer-friendly Version 25 of a glacier is labor intensive and expensive – only a few dozen of the world’s approximately 160 000 glaciers are measured consistently (Meier and Bahr, 1996). A glacier Interactive Discussion 3476 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion monitoring system is developed and will be applied to a representative selection of forty glaciers. A recently developed mass balance model is applied that produces daily TCD balances for each glacier at each altitude interval using routine precipitation and tem- 8, 3475–3491, 2014 perature observations collected at one or two weather stations in the region. The PTAA 5 model (precipitation-temperature-area-altitude) has been tested for glaciers in Alaska, Washington, Austria and Nepal. Comparison of measured annual balances with those What glaciers are produced by the model yields R2 values for linear regressions that range from 0.20 to telling us about 0.67. The main advantages of this model are that it is inexpensive to apply, it produces Earth’s changing daily and annual mass balances (for the net, ablation and accumulation components) climate 10 and its approximate accuracy is known. In addition, the balance as a function of elevation is calculated for each component. It resembles a degree-day model only in its W. Tangborn and weather data requirements but does not require manual balances for calibration. M. Mosteller

2 Mass balance measurements (background) Title Page

Conventional methods for measuring mass balance have been well developed since Abstract Introduction 15 the pioneering work of Swedish glaciologists (Williams et al., 2012; Holmlund and Jans- Conclusions References son, 1999; Ahlmann, 1953). The original field manuals for making mass balance measurements on a glacier (Ostrem and Stanley, 1966), were updated by Ostrem and Brug- Tables Figures man (1991). Early work by Hoinkes and others measuring the mass balance of glaciers in the Austrian Alps laid the foundation for manual measurement techniques (Hoinkes, J I 20 1955). Recent advancements in reporting and documenting glacier fluctuations have J I been made by the World Glacier Monitoring Service (2011), based on research by Haberli (2007, 2011) and Zemp (2009). Recent analyses of mass balance measure- Back Close ments have been made for the 1945–2003 period by Dyurgerov et al. (2005). Satellite Full Screen / Esc photogrammetry and airborne lidar permits differencing between digital-elevation mod- 25 els (DEMs) to calculate mass balance from volume changes between mappings (the Printer-friendly Version geodetic balance method) (Bauder et al., 2006; Haakensen, 1986). The mass balance Interactive Discussion of the Greenland and Antarctic ice sheets is of great concern because continuous 3477 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion negative balances will result in a rise in global sea level (Rignot and Thomas, 2002). Negative glacier balances and the disappearance of glaciers also create problems for TCD millions of people who rely on glaciers to store water during wet periods and release it 8, 3475–3491, 2014 when the weather is hot and dry.

What glaciers are 5 3 The PTAA mass balance model telling us about Earth’s changing 3.1 Model description climate The PTAA model (Precipitation-Temperature-Area-Altitude) is dependent on the cli- W. Tangborn and mate history that is embedded in the glacier’s surface conﬁguration (its area-altitude M. Mosteller distribution) and relies on the internal consistency of mass balance variables, for ex- 10 ample the relationship between snowline elevation and glacier balance. Detailed ex-

planations of the model and how it functions are provided in Tangborn (1997, 1999, Title Page 2013), and Tangborn and Rana, (2000). In the PTAA model, snow and ice ablation is calculated at each elevation interval Abstract Introduction

from the observed daily mean temperature and the diurnal temperature range, based Conclusions References 15 on the temperature lapse rate that is also calculated from temperature observations. Snow accumulation is calculated at each elevation interval from observed precipitation Tables Figures at a regional weather station, times a multiplier that is determined from the observed ◦ temperature and the lapse rate. If temperature is less than 0 C, precipitation occurs as J I snow; if the temperature is greater than 0 ◦C it occurs as rain. (See simulation model J I 20 structure in Tangborn, 1999.) Each calculated value of precipitation and temperature is multiplied by the fraction Back Close

of total glacier area at each elevation interval (the sum of all fractions = 1.0). The area- Full Screen / Esc altitude distribution of a glacier is a critical aspect of the PTAA model that controls how

weather observations are converted to accumulation, ablation and mass balance. Printer-friendly Version

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3478 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 3.2 Model calibration TCD Coeﬃcients that convert precipitation and temperature observations to snow accumulation and snow and ice ablation are calculated by minimizing the calibration error that 8, 3475–3491, 2014 is produced by regressing multiple combinations of simulated balance parameters. Fig- 5 ure 1 shows the mean annual balance for the 1951–2012 period for each iteration of What glaciers are the simplex optimizing system, which is a numeric method for solving problems in lin- telling us about ear programming (Nelder and Mead, 1965). Figure 2 shows the relationship between Earth’s changing mean annual balance and calibration error. climate

3.3 Monte Carlo similarity W. Tangborn and M. Mosteller 10 The PTAA model resembles Monte Carlo simulation in that it uses repeated random sampling of calculated coeﬃcients to optimize numerical results. Output from the model are daily snow accumulation (Bc) and ablation (Ba) for each altitude interval, which is Title Page converted to mass balance by Bn = Bc − Ba. The daily balance is calculated by summing the balance at each area-altitude interval times the fraction of the total glacier Abstract Introduction 15 area at that altitude. The calculated coeﬃcients are derived from the area-altitude val- Conclusions References ues for each interval but are subject to uncertainties when observed precipitation and temperature are converted to accumulation and ablation. As many as 300 iterations of Tables Figures the simplex (a linear programming technique for solving numerical problems) calculating the daily balance at each altitude interval for 60 years are required to calibrate one J I 20 glacier. The line plot in Fig. 1 demonstrates the calibration process. J I The PTAA model was initially developed and tested for South Cascade Glacier in Washington State (Tangborn, 1999). Back Close Full Screen / Esc 3.4 Model applications

Printer-friendly Version The PTAA model has been applied to calculate the mass balance for eight glaciers in 25 Alaska, Washington, Austria and Nepal. Calculated annual balances are compared Interactive Discussion

3479 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion with measured balances for approximately 60 years for each of five glaciers (see www.ptaagmb.com). Linear regressions of model vs. measured annual balances yields TCD R2 values of 0.20 to 0.70 (Table 1). Application of the model to Bering Glacier in Alaska 8, 3475–3491, 2014 demonstrated a close agreement with ice volume loss for the 1972–2003 period mea- 5 sured with the geodetic method (Tangborn, 2013). The first application of the model was for the rapidly retreating Columbia Glacier in Alaska (Tangborn, 1997). However, What glaciers are manual balance field measurements of Columbia Glacier have not been made, mak- telling us about ing comparison of model and measured balances impossible. Determining the mass Earth’s changing balance and runoff of the partially debris-covered Langtang Glacier in Nepal demon- climate 10 strates an application of this model to a glacier in the Himalayan Range (Tangborn and Rana, 2000). Simulated ablation for the Langtang Glacier agrees with manual ablation W. Tangborn and measurements on the nearby Lirung Glacier at the same altitude and on the same day. M. Mosteller Application to the glaciers in the Wrangell Range in Alaska revealed a significant correlation (r = +0.78 for a 60 year period) between annual ablation of these glaciers and Title Page 15 global temperatures observed at 7000 weather stations in the Northern Hemisphere. These results indicate that glaciers are more sensitive to the global climate than are in- Abstract Introduction dividual temperature stations, which do not show similar correlations (Tangborn, 2012). Conclusions References The physical relationship between glacier ablation and global temperatures suggests that glaciers can be used to anticipate future climate changes. Annual anomalies of Tables Figures 20 both glacier ablation and global temperatures are shown in Fig. 3. Balances determined for the Hintereisferner, Vernagtferner and Kesselwandferner J I in the Austrian Alps for the 1942–2012 period are based on weather observations collected at Innsbruck, Austria, which is approximately 100 km from these glaciers. J I The relationship between glacier balance and the recent climate change has been Back Close 25 developed for these glaciers (Weber et al., 2014). Full Screen / Esc Comparison of annual balances calculated with the PTAA model and balances determined with a geodetic method for Wrangell Range glaciers show poor agreement for Printer-friendly Version both the 1957–2000 and 2000–2007 periods (Das et al., 2014). The model balances are an order of magnitude more negative than the geodetic balances for both periods. Interactive Discussion

3480 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion The cause for such a large disparity is unknown but both methods likely contribute to the diﬀerence. By regressing Wrangell glacier vs. Gulkana glacier balances calculated TCD by the model, and measured Gulkana balances vs. simulated Wrangell balances it may 8, 3475–3491, 2014 be possible to determine the relative error for each method.

What glaciers are 5 4 Glacier ablation and global temperatures telling us about Annual ablation for an average of thirty glaciers in the Wrangell Range is calculated Earth’s changing by the PTAA model using daily temperature and precipitation observations collected climate at McKinley Park and Big Delta located approximately 300 km from these glaciers. W. Tangborn and The mass balance (accumulation, ablation and net) is determined independently by M. Mosteller 10 minimizing the calibration error as described in Tangborn (1999). Annual temperature anomalies averaged for observations at 7000 stations in the Northern Hemisphere by the Hadley Climate Center are correlated with annual ablation for the 1951–2012 Title Page period. Both temperature and ablation are referenced to the 1961–1990 mean. There is a striking similarity in the glacier ablation and global temperature patterns Abstract Introduction 15 shown as line plots in Fig. 3 that suggests a common cause; the most obvious is vari- Conclusions References ability in the concentration of atmospheric carbon dioxide, which aﬀects both ablation and temperature, but a cause and eﬀect mechanism is not apparent. The dependency Tables Figures of ablation anomalies on global temperature is shown in Fig. 4. J I

5 Displaying graphical results J I Back Close 20 The main goal of the PTAAGMB project is to analyze glacier mass balance results to understand and predict climate change. Each of the 200 glaciers planned for the study Full Screen / Esc will respond diﬀerently to the global climate and provide useful information for planners who want to mitigate the eﬀects of climate change on human societies. (Forty glaciers Printer-friendly Version

are currently in the study and just six have complete reports.) The value of having Interactive Discussion 25 a graphical display of a large number of glaciers for monitoring is that each glacier 3481 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion will contribute to a slightly different understanding of how the climate is changing. All of them taken together will provide a unique tool for looking at climate variations. A glacier TCD located in the high Himalayas will respond to a global climate perturbation differently 8, 3475–3491, 2014 than one located at a low-elevation on Alaska’s coast, but together will reveal meteoro- 5 logical subtleties not demonstrated by meteorological instruments or climate models. For example, a change in the global temperature lapse-rate would be apparent from What glaciers are simultaneous analysis of Himalayan and Alaskan glacier mass balances. telling us about The correlation between average ablation of the thirty glaciers in the Wrangell Range Earth’s changing and temperature averaged for 7000 weather stations in the Northern Hemisphere pro- climate 10 vides another example of the value of analyzing a large number of glaciers and temperature stations simultaneously that is easily accomplished by using the graphical display W. Tangborn and shown on the GMB website. M. Mosteller The information produced each day on the PTAAGMB Project website (www. ptaagmb.com) would be essential to a scientific study analyzing changes in the mass Title Page 15 balance of glaciers over a wide geographic range. The website is designed to make glacier research more straightforward and prolific for nearly any region of the earth. Abstract Introduction Another goal is to make the research accessible to both the scientific community and Conclusions References the general public. The general public can be distanced from science and often unin- terested, so we wanted to make glaciers personally relevant. We did this by including Tables Figures 20 lots of visuals, especially interactive maps and satellite images of glaciers. People can find a glacier perhaps near where they live or have visited, where they have friends or J I family, or perhaps near a region in which they have other interests. The website is contained and rendered dynamically in a Content Management Sys- J I tem (CMS), to make it relatively easy to post new articles as they develop as more Back Close 25 glaciers are added to the GMB website. The CMS system automatically generates Full Screen / Esc new pages, links and menu items as glaciers are added. Content and chart graphics are placed into a report form in the CMS, to enforce Printer-friendly Version standardized reporting and maintain consistency with the goals of the project. Having a flexible CMS has helped in developing a report structure that accommodates the Interactive Discussion

3482 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion many variations of glaciers being studied, and the different notable findings in each report, depending on the glacier’s type and location. TCD The display of satellite images on the website is accomplished with the Google Maps 8, 3475–3491, 2014 JavaScript API. Through that interface, the maps are set to a satellite view, zoomed in 5 to an appropriate level for the size and shape of the area or individual glacier and centered to give the best view in the image area contained at the top of each page. What glaciers are A marker is then automatically generated on each glacier that shows exactly where telling us about the glacier in question is located. Maps are generated for the world, continents, coun- Earth’s changing tries, states/regions and each glacier. Each glacier marker is clickable from any map climate 10 and will pop up a supplemental marker window showing the glacier’s name, region and country, and these links are each clickable to navigate to pages showing the area W. Tangborn and chosen and the glaciers located there. M. Mosteller Navigation through the glacier/map system can be done completely through the images at the top, starting from the home page, or the regional breakdown on the right- Title Page 15 hand side, or through “The Glaciers” page. “The Glaciers” page lists all the glaciers contained in the website in alphabetical order, with a complete list on the first page or Abstract Introduction a subset when a continent, country or state/region is selected. Conclusions References The country and state/region maps use a street map view to increase personal asso- ciations and to better show details like the names of countries, states, cities and roads. Tables Figures 20 At some point, most people will have discovered that there is in fact a glacier being studied in an area of some personal interest to them, and in some cases, the roads to J I get there. When an individual glacier marker is selected, the top image view changes to a satel- J I lite image, which shows the glacier in its natural state. This image is also convertible to Back Close 25 a map view and can be zoomed in or out to show more or less detail. Full Screen / Esc More information about Google Maps API can be found at https://developers.google. com/maps/web/. Printer-friendly Version Information about the CMS used can be found at http://umbraco.com/. Interactive Discussion

3483 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 6 Conclusions TCD The world’s glaciers provide a unique and reliable gauge of climate variations because they are unusually sensitive to minute changes in temperature, precipitation and other 8, 3475–3491, 2014 meteorological parameters. Currently temperature is the main concern, but as the cli- 5 mate continues to change, other weather factors may become equally important, there- What glaciers are fore continued monitoring is essential. telling us about Earth’s changing Acknowledgements. Many thanks to Andrew Tangborn for his wise guidance, to Indrani Das for calculating the area-altitude distributions of the Wrangell Range glaciers, and to Andrea Lewis climate for editing. Funding for the project was provided by HyMet Inc. and Vashon IT. W. Tangborn and M. Mosteller

10 References

Ahlmann, H. W.: Glacier Variations and Climatic Fluctuations, American Geographical Society, Title Page Bowman Memorial Lectures, Series 3, New York, 1953. Mass balance determination using photogrammetric methods and numerical flow modeling, Abstract Introduction EOS, Transactions, AGU, 81(48), F437–F438, Fall Meet. Suppl., Abstract H62D-12, 2006. Conclusions References 15 Das, I., Hock, R., Berthier, E., and Lingle, C.: 21st century increase in glacier mass loss in Wrangell Mountains, Alaska, USA, from airborne laser altimetry and satellite stereo im- Tables Figures agery, J. Glaciol., 60, 283–293, 2014. Dyurgerov, M.: Glacier mass balance and regime measurements and analysis, 1945–2003, edited by: Meier, M. and Armstrong, R., Institute of Arctic Alpine Research, University of J I 20 Colorado, Distributed by National Snow and Ice Data Center, Boulder, CO, 2005. J I Haakensen, N.: Glacier mapping to confirm results from mass-balance measurements, Ann. Glaciol., 8, 73–77, 1986. Back Close Haeberli, W.: Changing views of changing glaciers, in: Darkening Peaks – Glacial Retreat, Full Screen / Esc Science and Society, edited by: Orlove, B., Wiegandt, E., and Luckman, B. H., University of 25 California Press, Berkeley, CA, 23–32, 2007. Haeberli, W.: Glacier mass balance, in: Encyclopedia of Snow, Ice and Glaciers, edited by: Printer-friendly Version Singh, V. P., Singh, P., and Haritashia, U., Encyclopedia of Earth Sciences Series, Springer, Interactive Discussion 399–408, 2011. 3484 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Haeberli, W. and Herren, E. (Eds.): Glacier Mass Balance Bulletin no. 1: World Glacier Moni- toring Service, ETH Zürich, IAHS(ICSI)/UNEP/UNESCO, Zurich, 1991. TCD Hoinkes, H. C.: Measurements of ablation and heat balance on alpine glaciers, J. Glaciol., 2, 497–501, 1955. 8, 3475–3491, 2014 5 Holmlund, P. and Jansson, P.: The Tarfala mass balance programme, Geogr. Ann. A, 81, 621– 631, 1999. Meier, M. F. and Bahr, D. B.: Counting glaciers – use of scaling methods to estimate the number What glaciers are and size distribution of glaciers of the world: Glaciers, Ice Sheets and Volcanos – A tribute telling us about 15 to Mark Meier, edited by: Colbeck, S. C., Special Report 96–27, Cold Regions Research Earth’s changing 10 and Engineering Laboratory, Hanover, NH, US Army Corps of Engineers, 89–94, 1996. climate Nelder, J. A. and Mead, R.: A simplex method for function minimization, Comput. J., 7, 308–312, 1965. W. Tangborn and Ostrem, G. and Brugman, M.: Glacier Mass Balance Measurements, a Manual for Field and M. Mosteller Office Work, National Hydrology Research Institute (NHRI), Saskatoon, Saskatchewan, and 15 Norwegian Water Resources and Energy Administration, Oslo, NHIR, Science Report No 4, 224 p., 1991. Title Page Ostrem, G. and Stanley, A. D.: Glacier Mass Balance Measurements, a Manual for Field Work, a guide to field officers and assistants with limited background in glaciology, Department of Abstract Introduction Energy, Mines and Resources, Glaciology Section, Ottawa, Ontario, 81 p., 1966. Conclusions References 20 Rignot, E. and Thomas, R. H.: Mass balance of polar ice sheets, Science, 297, 1502–1506, 2002. Tables Figures Tangborn, W. V.: Using low-altitude meteorological observations to calculate the mass balance of Alaska’s Columbia Glacier and relate it to calving and speed: Byrd Polar Research Center Report No. 15, Calving Glaciers Report of a Workshop, available at: http://www.hymet.com/ J I 25 docs/columbiaglacier.pdf (last access: 2014), 1997. Tangborn, W. V.: A mass balance model that uses low-altitude meteorological observations and J I the area-altitude distribution of a glacier, Geogr. Ann. A, 81, 753–765, 1999. Back Close Tangborn, W. V.: Winter warming indicated by recent temperature and precipitation anomalies, Polar Geogr., 4, 320–338, 2003. Full Screen / Esc 30 Tangborn, W. V.: Mass Balance of the Wrangell Range Glaciers: Mountain Views Newslet- ter, Vol 6, No. 2, November (page 28), available at: http://www.fs.fed.us/psw/cirmount/ Printer-friendly Version publications/pdf/Mtn_Views_nov_12.pdf (last access: 2014), 2012. Interactive Discussion

3485 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Tangborn, W. V.: Mass balance, runoﬀ and surges of Bering Glacier, Alaska, The Cryosphere, 7, 867–875, doi:10.5194/tc-7-867-2013, 2013. TCD Tangborn, W. V. and Rana, B.: Mass balance and runoﬀ of the partially debris-covered Langtang Glacier, Nepal, IAHS Publication no. 264 (Debris Covered Glaciers), available at: http://www. 8, 3475–3491, 2014 5 hymet.com/docs/langtang.pdf (last access: 2014), 2000. Weber, M., Braun, L., Kuhn, M., and Tangborn, W.: Impact of topography on the climate-glacier- relationship of 3 neighboring glaciers in the Eastern Alps, Zeitschrift für Gletscherkunde und What glaciers are Glazialgeologie, in preparation, 2014. telling us about Williams, R. S., Jr. and Ferrigno, J. G. (Eds.): State of the Earth’s Cryosphere at the Beginning of Earth’s changing 10 the 21st Century, Glaciers, Global Snow Cover, Floating Ice, and Permafrost and Periglacial climate Environments, Professional Paper 1386-A, US Geological Survey, Denver, CO, 2012. Zemp, M., Hoelzle, M., and Haeberli, W.: Six decades of glacier mass balance observations – W. Tangborn and a review of the worldwide monitoring network, Ann. Glaciol., 50, 101–111, 2009. M. Mosteller

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2 W. Tangborn and Table 1. Comparisons of measured vs. PTAA annual balance (R ). (Period 1965–2012 used for Alaska glaciers; period 1953–2011 used for Austria glaciers.) M. Mosteller

Glacier name NET ABL ACC Title Page Gulkana 0.51 0.58 0.01 Wolverine 0.57 0.18 0.44 Abstract Introduction Lemon Creek 0.20 n/a n/a Hintereisferner 0.47 n/a n/a Conclusions References Kesselwandferner 0.37 n/a n/a Tables Figures Vernagtferner 0.67 0.54 0.25

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3487 82 annual balance for the 1951-2012 period for each iteration of the simplex optimizing system, 83 which is a numeric method for solving problems in linear programming (Nelder and Mead, 84 1965). Figure 2 shows the relationship between mean annual balance and calibration | Paper error. Discussion | Paper Discussion | Paper Discussion | Paper Discussion 85 86 TCD 8, 3475–3491, 2014

What glaciers are telling us about Earth’s changing climate

W. Tangborn and M. Mosteller

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87 J I Figure 1. Mean annual balance for the 1951–2012 period for south-facing glaciers of the 88 Fig. 1. Mean annual balance for the 1951-2012 period for south-facing glaciers of the Back Close Wrangell Range, Alaska vs. iteration number. The first fifteen balances are calculated from 89 Wrangell Range, Alaska versus iteration number. The first fifteen balances are pre-set coefficients, the remaining 250 are determined by the simplex by minimizing the cali- 90 calculated from pre-set coefficients, the remaining 250 are determined by the simplex Full Screen / Esc bration error. 91 by minimizing the calibration error. Printer-friendly Version

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W. Tangborn and M. Mosteller

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93 FigureFig. 2. Mean 2. Mean annual annual balance balance of of the the south-facing south-facingglaciers glaciers ofof thethe Wrangell Range versus vs. calibra- Back Close 94 tion error.calibration The calibration error. The error calibration is a minimum error is a (about minimum 43 %) (about when 43 the%) when mean the annual mean balance is Full Screen / Esc 95 approximatelyannual balance−0.6 m is w.e. approximately -0.6 mwe.

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97 3.3 Monte Carlo similarity Interactive Discussion

98 The PTAA model resembles Monte Carlo simulation3489 in that it uses repeated random sampling of 99 calculated coefficients to optimize numerical results. Output from the model are daily snow 100 accumulation (Bc) and ablation (Ba) for each altitude interval, which is converted to mass balance 101 by Bn = Bc – Ba. The daily balance is calculated by summing the balance at each area-altitude 102 interval times the fraction of the total glacier area at that altitude. The calculated coefficients are 103 derived from the area-altitude values for each interval but are subject to uncertainties when 104 observed precipitation and temperature are converted to accumulation and ablation. As many as 105 300 iterations of the simplex (a linear programming technique for solving numerical problems) 106 calculating the daily balance at each altitude interval for 60 years are required to calibrate one 107 glacier. The line plot in Figure 1 demonstrates the calibration process. 108 The PTAA model was initially developed and tested for South Cascade Glacier in 109 Washington State (Tangborn, 1999).

What glaciers are telling us about Earth’s changing climate

W. Tangborn and M. Mosteller

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J I 178 179 J I Figure180 Fig. 3. Annual 3. Annual ablation ablation anomalies anomalies for thefor Wrangellthe Wrangell Range Range glaciers glaciers and and annual annual temperature temperature 2 Back Close anomalies181 anomalies derived derived from 7000 from weather7000 weather stations stations in the in Northernthe Northern Hemisphere. Hemisphere. The TheR Rfor2 for a re-a gression ﬁt of these variables is 0.61 (see Fig. 2). The similar patterns of each variable and 182 regression fit of these variables is 0.61 (see Figure 2). The similar patterns of each variable and Full Screen / Esc ﬁtted183 trendfitted lines trend suggest lines suggest that both that globalboth global temperatures temperatures and and glacier glacier ablation ablation are are controlled controlled by by a a184 common common forcing forcing mechanism, mechanism, which which likely likely is the is risingthe rising concentration concentration of atmospheric of atmospheric carbon carbon Printer-friendly Version dioxide185 dioxide but a direct but a cause direct iscause unknown. is unknown. 186 Interactive Discussion

What glaciers are telling us about Earth’s changing climate

W. Tangborn and M. Mosteller

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J I 187 J I Figure188 Fig. 4. Annual 4. Annual ablation ablation of Wrangellof Wrangell Range Range glaciers glaciers in in Alaska Alaska vs.versus global global maximum maximum tempera- Back Close ture189 anomaliestemperature (the anomalies same data (the as same shown data in as Fig. shown 3). Glacier in Figure ablation 1). Glacier is dependent ablation is on dependent global tem- on perature190 global anomalies temperature by: DAanomalies= 0.6(DT) by: +DA0.17, = 0.6 where (DT) DA+ 0.17,= ablation where DA anomaly, = ablation DT =anomaly,temperature DT = Full Screen / Esc anomaly.191 temperature The correlation anomaly. coe Theﬃcient correlation is +0.78. coefficient is +0.78.0 192 Printer-friendly Version 193 5 Displaying graphical results 194 Interactive Discussion 195 The main goal of the PTAAGMB project is to analyze glacier mass balance results to understand 196 and predict climate change. Each of the 2003491 glaciers planned for the study will respond 197 differently to the global climate and provide useful information for planners who want to 198 mitigate the effects of climate change on human societies. (Forty glaciers are currently in the 199 study and just six have complete reports.) The value of having a graphical display of a large 200 number of glaciers for monitoring is that each glacier will contribute to a slightly different 201 understanding of how the climate is changing. All of them taken together will provide a unique 202 tool for looking at climate variations. A glacier located in the high Himalayas will respond to a 203 global climate perturbation differently than one located at a low-elevation on Alaska’s coast, but 204 together will reveal meteorological subtleties not demonstrated by meteorological instruments or 205 climate models. For example, a change in the global temperature lapse-rate would be apparent 206 from simultaneous analysis of Himalayan and Alaskan glacier mass balances. 207 The correlation between average ablation of the thirty glaciers in the Wrangell Range and 208 temperature averaged for 7000 weather stations in the Northern Hemisphere provides another 209 example of the value of analyzing a large number of glaciers and temperature stations 210 simultaneously that is easily accomplished by using the graphical display shown on the GMB 211 website.