Master’s thesis in climate dynamics Erlend Moster Knudsen
April 1, 2011
Himalayan glacier melting on water availability
A study on the sources to the Indus Basin
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UNIVERSITY OF BERGEN
GEOPHYSICAL INSTITUTE
Nepal. Photo by Prakash Mathema/AFP (Blaker, 2010).
The thesis is written in LATEX in report style, 12 point text and two-sided format.
Four strong winds that blow long Seven seas that run high
All these things that won’t change Come what may
Johnny Cash, ”Four Strong Winds”
In a changing environment, the words of Johnny Cash - the king of long days in the reading room - are good to bring along. Unfortunately, the changes that are upon the ice masses in the Himalayas are of the radical kind. Their importance for the innumerable people living downstream makes them in my opinion one of the most severe possible effects of climate changes.
When one of the best lecturers and researchers at my institute gave me the possibility to do research on this topic, I just could not say no. On the basis of his support, help to keep the right focus and by asking the important questions, my supervisor Asgeir Sorteberg is worthy many thanks. All our conversions on skiing have also made advantageously breaks.
I am also very grateful to the Ph.D. fellows Silje Lund Sørland and Marius Opsanger Jonassen who read the proofs of my thesis. I was happy to spend six days in and around New Delhi, India, with Silje where we shared some memorable and unmemorable experiences. Marius also worked as a great head for MATLAB questions.
The IT responsible at the institute, Idar Hessevik, should also be mentioned. He did his best to minimize all network problems and shared my resignation over the IT department.
Finally, my fellow students at the reading room ODD have been very valuable.
Perhaps not regarding scientific contribution on the research topic, but rather when it comes to valuing a good study environment.
At this point I mark the start of the factual part. I hope it will make worthwhile reading and that it also highlights a very important field of research.
i
In this thesis, the mass balance model CROCUS is employed to represent how Himalayan glaciers are influenced by a changing environment. It gives an estimation of the mass balance evolution of the glaciers, in which factors contributing to accumulation (mass gain) and ablation (mass loss) are described. The glacial runoff resulting from ablation has a representation compared to many other glacier and hydrologic models, so that an estimate on the glaciers’ contribution to river water discharges are available.
A sensitivity test of the model is carried out which shows that correct representation of meteorological data and glacier geometry are important both for the glacier’s mass and equilibrium line altitude (ELA). The latter is a measure of the state of the glacier.
A warming of 1 K raises the ELA by 174.5 m, suggesting a significant loss in mass in all climate scenarios, even if a gain in precipitation would contribute to a slight mass increase.
For each subbasin in the Indus Basin, the glaciers are represented by a ”mean”
glacier. Its properties (glacier length, depth, altitude etc.) is found using information from the World Glacier Inventory - Extended Format (WGI-XF) data set. The CROCUS model is then applied to calculate the mass balance and river water contribution from today’s state and the impact of various climate changes. Using the average climate changes from models participating in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4) (+4.4 ◦C and −0.8 % precipitation), the glacier model projects that the glacial runoff contribution to rivers will increase from 6.0 to 10.2 % by the end of the century.
In this scenario, the relative change in the glacial runoff also rises considerably. 74.8
% more runoff is on average drained from the glaciers in the Indus Basin under these conditions. The behavior is an interaction between the additional melt due to warming and the smaller glacier mass prone to melting. As climate scenarios project different warming rates and enhanced or reduced precipitation, the changes in water availability in the region is uncertain.
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1 Introduction 1
1.1 Background . . . 1
1.1.1 The Himalayas . . . 3
1.2 Earlier work . . . 4
1.3 Motivation . . . 6
2 Snow and Ice Physics 9 2.1 Energy balance . . . 9
2.1.1 Shortwave radiation . . . 11
2.1.2 Longwave radiation . . . 12
2.1.3 Net radiation . . . 12
2.1.4 Turbulent heat fluxes . . . 13
2.1.5 Heat flux between the snow and the ground . . . 13
2.1.6 Radiation properties of snow . . . 14
2.2 Snow processes . . . 15
2.2.1 Snowfall . . . 15
2.2.2 General characteristics . . . 16
2.2.3 Snow classification . . . 17
2.2.4 Snow metamorphism . . . 17
2.2.5 Grain size and growth rate . . . 20
2.2.6 Snow compaction . . . 20
2.2.7 Thermal behavior of snow . . . 20
2.2.8 Fluid flow behavior in snow . . . 22
2.3 Ice processes . . . 23
2.3.1 Glacier classification . . . 26
2.3.2 Mass balance principles . . . 27
2.3.3 Climatic impact . . . 29 iii
3 Methods and Tools 32
3.1 Data basis . . . 34
3.1.1 The Dokriani glacier . . . 34
3.1.2 The Indus Basin . . . 36
3.2 Input files . . . 40
3.2.1 The MET file . . . 40
3.2.2 The PROi file . . . 42
3.2.3 The GEO file . . . 43
3.2.4 The PARAM file . . . 43
3.3 The mass balance model . . . 44
3.3.1 Model sensitivity . . . 45
3.3.2 Advantages and disadvantages . . . 46
3.4 Output files . . . 47
3.4.1 The PROo file . . . 47
3.4.2 The QUOT file . . . 48
3.4.3 The TSURF file . . . 48
3.4.4 The FLUX file . . . 48
3.4.5 The TRACROCUS and ERRCROCUS files . . . 49
3.5 The dynamical model . . . 49
3.6 Processing of output data . . . 50
3.6.1 River sources . . . 51
4 Results and Discussion 53 4.1 The Dokriani glacier . . . 53
4.1.1 Altered meteorological inputs . . . 54
4.1.2 Altered glacier geometry . . . 57
4.1.3 Altered dynamical interaction . . . 60
4.1.4 Glacier thickness . . . 61
4.1.5 Specific and volume balance . . . 66
4.1.6 Gain and loss factors . . . 73
4.1.7 Winter and summer seasons . . . 82
4.2 The Indus Basin . . . 82
4.2.1 The Zaskar subbasin . . . 83
4.2.2 The Nubra/Shyok subbasin . . . 84
4.2.3 The Indus 1 subbasin . . . 86
4.2.4 The Gilgit/Hunza subbasin . . . 87
4.2.5 The Astor subbasin . . . 88
4.2.6 The Kabul/Swat/Alingar subbasin . . . 89
4.2.7 The Krishen Ganga subbasin . . . 90
4.2.8 The Jhelum subbasin . . . 91
4.2.9 The Chenab 1 subbasin . . . 93
4.2.10 The Sutlej subbasin . . . 94
4.2.11 Climate scenarios compared to sensitivity tests . . . 95
4.2.12 River sources . . . 96
5 Conclusions 102 5.1 Future model improvements . . . 104
6 Impacts on the Society 106 A Representation of Physical Properties in CROCUS 110 A.1 Heat and conductivity . . . 110
A.2 Solar radiation . . . 111
A.2.1 Optical diameter . . . 111
A.2.2 Spectral albedo . . . 111
A.2.3 Spectral absorption . . . 112
A.2.4 Energy entering . . . 113
A.2.5 Energy absorbation . . . 113
A.3 Heat fluxes . . . 114
A.3.1 Surface turbulent fluxes . . . 114
A.3.2 Bottom flux . . . 114
A.4 Percolation . . . 114
A.5 Settling . . . 115
A.6 Precipitation . . . 115
A.7 Snow metamorphism . . . 116
A.7.1 Dry snow metamorphism . . . 118
A.7.2 Wet snow metamorphism . . . 119
B Additional Tables 120
C Additional Figures 126
References 132
1.1 Observed and modelled temperature trends in Himalaya . . . 3
1.2 Observed and modelled precipitation trends in Himalaya . . . 4
1.3 Properties of the Indus, Ganges and Brahmaputra River . . . 7
3.1 Properties of the subbasins in the Indus Basin . . . 37
3.2 Properties of the glacier representatives in the subbasins of the Indus Basin 37 4.1 Names and properties of model runs representing the Dokriani glacier . . 54
4.2 Sensitivity of glacier size and mass balance due to meteorological input parameter alterations . . . 55
4.3 Sensitivity of glacier size and mass balance due to initial glacier geometry alterations . . . 59
4.4 Sensitivity of glacier size and mass balance due to dynamical interaction alterations . . . 61
4.5 Sensitivity of glacier mass and ELA per unit of alteration . . . 72
4.6 Gain and loss factors of the Dokriani glacier for model runs with meteo- rological input parameter alterations . . . 75
4.7 Gain and loss factors of the Dokriani glacier for model runs with initial glacier geometry alterations . . . 77
4.8 Gain and loss factors of the Dokriani glacier for model runs with dynam- ical interaction alterations . . . 79
4.9 Signification of sensitivity tests on the modelled glacier’s gain and loss factors . . . 81
4.10 Glacier size and mass balance changes in model runs representing glaciers in the Zaskar subbasin in the Indus Basin . . . 83
4.11 Glacier size and mass balance changes in model runs representing glaciers in the Nubra/Shyok subbasin in the Indus Basin . . . 85
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4.12 Glacier size and mass balance changes in model runs representing glaciers in the Indus 1 subbasin in the Indus Basin . . . 87 4.13 Glacier size and mass balance changes in model runs representing glaciers
in the Gilgit/Hunza subbasin in the Indus Basin . . . 88 4.14 Glacier size and mass balance changes in model runs representing glaciers
in the Astor subbasin in the Indus Basin . . . 89 4.15 Glacier size and mass balance changes in model runs representing glaciers
in the Kabul/Swat/Alingar subbasin in the Indus Basin . . . 90 4.16 Glacier size and mass balance changes in model runs representing glaciers
in the Krishen Ganga subbasin in the Indus Basin . . . 91 4.17 Glacier size and mass balance changes in model runs representing glaciers
in the Jhelum subbasin in the Indus Basin . . . 92 4.18 Glacier size and mass balance changes in model runs representing glaciers
in the Chenab 1 subbasin in the Indus Basin . . . 93 4.19 Glacier size and mass balance changes in model runs representing glaciers
in the Sutlej subbasin in the Indus Basin . . . 95 4.20 Modelled sizes and portions of river sources in subbasins of the Indus Basin 97 B.1 Content of the World Glacier Inventory - Extended Format . . . 121 B.2 Gain and loss factors of models runs representing glaciers in the Zaskar
subbasin in the Indus Basin . . . 122 B.3 Gain and loss factors of models runs representing glaciers in the Nubra/Shyok
subbasin in the Indus Basin . . . 122 B.4 Gain and loss factors of models runs representing glaciers in the Indus 1
subbasin in the Indus Basin . . . 122 B.5 Gain and loss factors of models runs representing glaciers in the Gilgit/Hunza
subbasin in the Indus Basin . . . 123 B.6 Gain and loss factors of models runs representing glaciers in the Astor
subbasin in the Indus Basin . . . 123 B.7 Gain and loss factors of models runs representing glaciers in the Kabul/Swat/Alingar
subbasin in the Indus Basin . . . 123 B.8 Gain and loss factors of models runs representing glaciers in the Krishen
Ganga subbasin in the Indus Basin . . . 124 B.9 Gain and loss factors of models runs representing glaciers in the Jhelum
subbasin in the Indus Basin . . . 124 B.10 Gain and loss factors of models runs representing glaciers in the Chenab
1 subbasin in the Indus Basin . . . 124 B.11 Gain and loss factors of models runs representing glaciers in the Sutlej
subbasin in the Indus Basin . . . 125
1.1 Mass balance trends of glaciers and ice caps in large regions . . . 2
1.2 Satellite image of two Himalayan glaciers . . . 5
2.1 Energy balance for an open snowpack . . . 10
2.2 Mass balance for an open snowpack . . . 11
2.3 Snow albedo as a function of wavelength . . . 14
2.4 Snow crystal morphology diagram . . . 16
2.5 Schematic phase diagram of water . . . 17
2.6 Classification schemes of snow types . . . 18
2.7 Metamorphism processes between main snow classes . . . 19
2.8 In-snow temperature profiles . . . 21
2.9 Transformation of snow to ice . . . 24
2.10 Variation in snow zones with altitude . . . 25
2.11 Cross sections of glacier types . . . 26
2.12 Specific net budget as a function of elevation . . . 28
2.13 Albedo and temperature feedback . . . 30
3.1 The model set up . . . 33
3.2 Modelled glacier geometry of the Dokriani glacier in the control run . . . 35
3.3 Climate change projections from the time period 1901-1998 to the period 2001-2098 in the Indus basin . . . 39
3.4 Evolution of meteorological data in a model run . . . 42
3.5 Schematic diagram of the snow layers in the mass balance model CROCUS 45 4.1 Modelled glacier geometry of the Dokriani glacier in scenarios of surface geometry alterations . . . 58
4.2 Modelled glacier geometry of the Dokriani glacier in scenarios of cross section geometry alteration . . . 58
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4.3 Modelled glacier thickness of the Dokriani glacier for model runs with
altered meteorological input parameters . . . 62
4.4 Modelled glacier thickness of the Dokriani glacier for model runs with altered initial glacier geometry . . . 64
4.5 Modelled glacier thickness of the Dokriani glacier for model runs with altered dynamical interaction . . . 65
4.6 Modelled specific and volume balance of the Dokriani glacier for model runs with altered meteorological input parameters . . . 67
4.7 Modelled specific and volume balance of the Dokriani glacier for model runs with altered initial glacier geometry . . . 69
4.8 Modelled specific and volume balance of the Dokriani glacier for model runs with altered dynamical interaction . . . 70
4.9 Variations in modelled ELA of the Dokriani glacier . . . 71
4.10 Modelled accumulation and ablation of the control run for the Dokriani glacier . . . 74
4.11 Modelled precipitation and glacial runoff for the Dokriani glacier in model runs with altered meteorological input parameters . . . 76
4.12 Modelled precipitation and glacial runoff for the Dokriani glacier in model runs with altered initial glacier geometry . . . 78
4.13 Modelled precipitation and glacial runoff for the Dokriani glacier in model runs with altered dynamical interaction . . . 80
4.14 Modelled glacial runoff for the glacier representatives in the Zaskar, Indus 1 and Jhelum subbasins of the Indus Basin . . . 99
4.15 Importance of glacial runoff on river systems in the Indus Basin . . . 101
6.1 Crisis drivers in the Hindu-Kush Himalaya region . . . 109
C.1 Modelled cumulative balance of the Dokriani glacier . . . 127
C.2 Modelled accumulation area ratio of the Dokriani glacier . . . 128
C.3 Modelled glacial runoff for the glacier representatives in the Nubra/Shyok, Gilgit/Hunza and Astor subbasins of the Indus Basin . . . 129
C.4 Modelled glacial runoff for the glacier representatives in the Kabul/Swat/Alingar and Krishen Ganga subbasins of the Indus Basin . . . 130
C.5 Modelled glacial runoff for the glacier representatives in the Chenab 1 and Sutlej subbasins of the Indus Basin . . . 131
Chapter 1
Introduction
According to the Intergovernmental Panel on Climate Change (IPCC) the Earth is warming at a pace higher than ever in modern times1 (Le Treut et al., 2007). The effects on Mother Nature are huge, which of raised sea level height, spreading of deserts and melting of glaciers are some examples. Disregard of natural or anthropogenic causes the glaciers at the Poles are melting. Along with their fellow ice masses other places around the globe, they are among the most visible indications of the result of climate change with a direct link to their surface mass balance (Lemke et al., 2007).
Considering the so called Third Pole, Himalaya, earlier research draws different con- clusions. Whereas Raina (2009) found no link between global warming and glacial retreat, Cruz et al. (2007) operates with a reduction in total glacier area from 500 000 to 100 000 km2. More familiar is the complete allegation by 2035 of the latter authors, but this has later been withdrawn as a poorly substantiated estimate (Carrington, 2010).
Nevertheless, on the Himalaya-Karakoram-Hindu Kush (HKH) mountains as a whole, Rasul et al. (2008) report that snow and ice extent is shrinking at a higher rate than ever. Notwithstanding, it is a hard projection, and the experts are quarrelling.
In this thesis, an analysis of simulated glacier changes will be made which is based upon a simple glacier model, simplified physical laws and the IPCC reanalysis and projection models of weather data from 1980 to 2098. The goal is to derive a model that can reproduce the evolution of the glaciers over the last decades. With this at hand, an estimate of their future in the 21st century may be drawn.
1.1 Background
Glaciers located in Himalaya are typically categorized as temperate glaciers (Hooke, 2005). Due to their temperature close to the melting point throughout their whole ice
1The last 1300 years
1
mass, they strongly react to climate change as a temperature increase would convert the additional energy into melting. They are thus good indicators on global climate (Hooke, 2005), and their climate response time is found to be relatively short.
Since the Little Ice Age, glaciers worldwide have been shrinking dramatically and at an even higher pace in the last two decades. At present more than 90 % of all observed glaciers are retreating. A retreating rate of 10 to 60 m a−1 (meters per year) and a thinning rate of up to 1 m a−1 has been found, and many small glaciers (smaller than 0.2 km2) have already vanished. A projection on the glaciers shorter than 4 km in the Tibetan Plateau leaves no ice left in the near future. Further, the Chinese Academy of Sciences reported a volume shrinkage of 5.5 % of 46 928 glaciers in China has taken place during the last 24 years (similar to a loss of more than 3000 km2 of ice), and rates of about the same size are found in Nepal, India and Bhutan (Bajracharya et al., 2007).
Figure 1.1: Cumulative mean specific mass balances (a) and cumulative total mass balances (b) of glaciers and ice caps in large regions. Definition of terms is given in chapter 2.3.2.
Taken from Dyurgerov & Meier (2005).
The Himalayan glaciers (the black line in figure 1.1) have, together with rest of the glaciers and ice caps around the world, contributed to a 0.33 mm sea-level rise per year between 1961 and 1990 (Kaser et al., 2006). This rate doubled in the period from 1991 to 2004. In comparison, Cruz et al. (2007) reported the current sea-level rise from all sources to be 1−3 mm a−1 in the coastal areas of Asia.
There have been some exceptions, but the ongoing trend predicts a fast or even accelerating glacier shrinkage that may lead to the deglaciation of several mountain
regions before end of the 21st century.
1.1.1 The Himalayas
17 % or about three million hectares of the Himalayas are covered by the about 15 000 glaciers in the region (Cruz et al., 2007). Dyurgerov & Meier (2005) have estimated the ice extent to be about 33 050 km2, containing about 12 000 km3 of water. In comparison, glaciers in the Swiss Alps cover 2.2 % or 0.3 hectares of the surface here.
The observed temperature trend during the last century shows a distinct trend of warming, as seen in table 1.1, with an accelerated warming over the last decades (see for example Kothawale & Kumar (2005)). The warming has been much greater than the global mean of 0.74◦C (Trenberth et al., 2007). Similarly, also the projected mean annual temperature increase for High Asia based on the IPCC scenarios is expected to be well above the global mean, and the range is between 1 to 6 ◦C by the end of the century. The degree of warming seems to increase with elevation as observed in Nepal and Tibet (Xu et al., 2007), suggesting a higher climate sensitivity with elevation.
Table 1.1: Observed and modelled temperature trends in Himalaya from 1961 to 2050. All trends are in ◦C/decade. The10% lowest trend is the outcome of10% of the models that have the lowest trend, and the 10 % highest trend similarly comes from the models with the highest trend. The modelled data comes from 20 IPCC models, where the future values are averages over the emission scenarios Special Report on Emission Scenarios (SRES) A1B, B1 and A2.
T AR = Tibet Autonomous Region. Taken from Sorteberg (2009).
Region
10 % 10 % Time Observed Average lowest highest period trend trend trend trend
TAR 1961-2003 0.31 0.24 0.16 0.32
2001-2050 0.38 0.21 0.54
Nepal 1977-1994 0.59 0.16 -0.11 0.48
2001-2050 0.32 0.20 0.43
India 1971-2001 0.20 0.17 0.03 0.26
2001-2050 0.28 0.17 0.40
In addition to temperature changes, precipitation patterns are also under the influ- ence of a changing climate. This is shown in table 1.2. Most IPCC models project an intensification of the seasons, i.e. less precipitation during the dry season (December to February) and an increase over rest of the year.
The biggest proportion of accumulation and ablation (see chapter 2.3.2 for definition of terms) takes place during the summer for most of the Himalayan regions (Fujita &
Ageta, 2000). Both the magnitude and the length of the two mass balance seasons will change in accordance with a changing climate. As the warming is more pronounced
Table 1.2: Observed and modelled precipitation trends in Himalaya from 1901 to 2050. All trends are in %/decade. The 10 % lowest trend is the outcome of 10 % of the models that have the lowest trend, and the 10 % highest trend similarly comes from the models with the highest trend. The modelled data comes from 20 IPCC models, where the future values are averages over the emission scenarios SRES A1B, B1 and A2. T AR = Tibet Autonomous Region. Taken from Sorteberg (2009).
Region
10 % 10 % Time Observed Average lowest highest period trend trend trend trend
TAR 1961-2001 1.4 0.0 -1.8 1.4
2001-2050 0.7 -0.9 2.5
Nepal 1959-1994 0.0 -1.2 -5.0 4.0
2001-2050 0.8 -2.0 3.4
India 1901-2003 0.1 -0.2 -1.0 0.5
2001-2050 0.5 -1.3 2.6
during winter than in summer in the region, the melt season will extend (Cruz et al., 2007). On the other hand, this may possibly be counteracted by an increase in winter precipitation to a certain degree. By 2100 the likely outcome concerning the glaciers is a decline in the current coverage by 43 to 81 % (B¨ohner & Lehmkuhl, 2005).
1.2 Earlier work
Himalaya homes the largest concentration of glaciers outside the polar ice caps, which gives it the name the Third Pole. Still, relatively little research has been done on the region, partly due to a historical lack of international as well as internal data exchange between the two largest home countries of the mountain chain, China and India (Khadka, 2008).
Nijampurkar & Rao (1993) worked with cosmogenic (32Si), natural (210Pb) and ar- tificial radioisotopes (137Cs, 95Zr) along with stable isotopes (δ18O and δ D) to obtain a reconstruction of Himalayan glaciers for a period of 500 to 2000 years. The emphasis was put on valley glaciers during the two previous decades. Although their area of concern were large, wide assumptions were made and only a few glaciers were examined closely.
Ren et al. (2004) published a paper on the results they obtained from using terminus positions and ice cores to study glacier variations. The areas of investigation were Mount Qomolangma2, Mt. Xxiabangma and Mts. Tanggula, China. In all areas they found a retreat rate between 3.0 and 9.1 m a−1 since the 1960s, whereof a speedier rate was observed the latest years. Here, a finger may naturally be put on the small region of
2The Tibetan name of Mt. Everest
observation along with the asserted relationship between climate change and glacier terminus retreat (see for example Raina (2009) for a counter claim). In fact, increased winter precipitation may give a larger net glacier at the end of the season despite the observed annual warming. The study also outlines this as it states that a temperature increase has come along with a precipitation decrease in the central Himalayas. An important note to make here is that glaciers react to external changes dependent on their response time. In this way, present advance or retreat may be a result of an atmospheric change taking place several decades ago.
Satellite data was used by Kulkarni et al. (2007) to estimate glacial retreat. 466 glaciers in Chenab, Parbati and Baspa Basins in India were examined, and some expe- ditions were also included in the work. The results showed a 21 % overall deglaciation along with a reduction in mean area of glacial extent from 1.4 to 0.32 km2 between 1962 and 2001. However, this resulted in an increase in the number of glaciers. They con- cluded that this was an outcome of climate changes, glacial fragmentation and higher retreat of small glaciers. Limitations here lay in the delimited area in focus and the short time series of data acquisition. The latter comes from the fact that glacial extent may alternate annually. In addition the general drawbacks of the low image resolution, dependence on cloud cover and inability to reproduce the total picture of the glacier’s size features of satellite images play a role.
Figure 1.2: Satellite imagery of glacier number 52H12003 and 52H12004 of LISS-IV sensor showing glacial boundary of 1962 and 2004. Taken from Kulkarni et al. (2007).
These are all examples of some of the research been done on the topic. Hopefully, this thesis will contribute in this environment.
1.3 Motivation
The reproduction of the robust features of the shrinking Himalayan glaciers is anticipated as a result of the study. Attaining an acceptable reproduction of the last decades, the model will be used to predict the future of the ice masses at the Third Pole. In a wider perspective this study can contribute to the ongoing discussion of climate change existence and effects. The consequences of a changing climate in the region may affect the glacier mass, snowfall and runoff. A change in the glacier mass will have regionally as well as globally impacts through the ice-albedo feedback, although the process is small compared to water vapor, cloud and lapse rate feedbacks (Randall et al., 2007).
Ice has a higher albedo than bare ground, so that more solar radiation will be reflected into the atmosphere. If there is a decrease in the snow and ice covered areas, more solar heat will be absorbed, leading to a temperature increase.
Second; a change in the snowfall does not only play a large role for tourism in the mountains, but may lead to more hazards for villages underneath sloping hills and mountains. Avalanches is one thing, flooding or oppositely drought is another, as some regions will experience more snow and others less.
Third; varying runoff may be the one factor causing the biggest effects. Water for drinking, irrigation, electric power, religious acts and use in industry may face a new weekday. In addition, there will be an impact on both the ecosystems and landmasses.
The five major rivers in the Himalayas, the Indus, Ganges, Brahmaputra, Yangtze and Yellow Rivers, together provide water to more than 1.4 billion people, or over 20 % of the global population (Immerzeel et al., 2010). Globally, slight sea level rise, as from the ice on Greenland and in Antarctica, may be notable (Eamer & Prestrud, 2007). These impacts are considered in chapter 6.
The Himalayas are located at a latitude of about 27 to 37◦N, i.e. in the warm and dry subtropical belt. The need for fresh water is thus even higher than in glacial regions at higher latitudes. The glaciers form a unique reservoir which supports perennial rivers such as the Indus, Ganges and Brahmaputra. These, in turn, are the lifeline of millions of people in South Asian countries as they provide water, food and energy. The Gangetic Basin alone homes 500 million people, about 10 % of the total human population in the region (Cruz et al., 2007).
In this thesis the effects on the Indus River are investigated. It is especially interest- ing because it is one of the rivers in the Himalayan region that are heaviest influenced by glacial melt water. Flowing through the land areas of China, India and Pakistan, it plays a big role in the daily life to many Asians. Its regional impact and hydrological role is described in Table 1.3, where also two other major rivers - Brahmaputra and Ganges - are described for comparison.
Current and possible future glacier hazards are strongly affected by three major challenges in the coming decades: climate change, political will and socio-economic development. This thesis does not try to solve the questions related to these fields of
Table 1.3: Characteristics of three of the major Southeast Asia basins - the Indus, Ganges and Brahmaputra River. The data are based on the Gridded Population of the World, version 3 (GPWv3) dataset (SEDAC, 2005) in the case of population (2005), Huffman et al. (2007) concerning precipitation (average from 2001 to 2007), and the Global Land Ice Measurement from Space (GLIMS) project (Raup et al., 2007) has provided the data on glacier areas. The rest of the data are taken from Immerzeel et al. (2010); Cruz et al. (2007); Eamer & Prestrud (2007); Edwards et al. (2010); Qin (2002).
River Indus Ganges Brahmaputra
Basin [km2] 1 005 786 990 316 525 797
Upstream area [%] 40 14 68
Water discharge [109 m3 yr−1] 175 590 626
Population [103] 209 619 477 937 62 421
Population density [people km−2] 208 483 119
Large cities (>100 000 people) 11 11 6
Water supply per person [m3 yr−1] 830 1 700−4 000 1 700−4 000
Dams (>60 m) under construction 0 5 3
Climate zone Semi-arid Tropical Tropical
Annual basin precipitation [mm] 423 1 035 1 071
Net irrigation water demand [mm] 908 716 480
Annual upstream precipitation [%] 36 11 40
Annual downstream precipitation [%] 64 89 60
Sea level rise in 2050 [cm] 20−50 - -
Cropland [%] 30.0 72.4 29.4
Irrigated cropland [%] 24.1 22.7 3.7
Grassland, savannah and scrubland [%] 46.4 13.4 44.7
Forest [%] 0.4 4.2 18.5
Loss of original forest cover [%] 90.1 84.5 73.3
Wetlands [%] 4.2 17.7 20.7
Dryland area [%] 63.1 58.0 0.0
Basin protected [%] 4.4 5.6 3.7
Urban and industrial area [%] 4.6 6.3 2.4
Glaciated area [%] 2.2 1.0 3.1
Glaciers in source area 5 057 6 696 4 366
Glacial melt in river flow [%] 44.8 9.1 12.3
Hydrological significance of glaciers and snow
Very high High High
alteration, but rather investigate how the future will look like concerning ice and snow in the Himalayas.
Chapter 2
Snow and Ice Physics
2.1 Energy balance
Most of the theory found in this chapter is based on Armstrong & Brun (2008).
Often we find energy balance defined as the energy exchange at an interface. With the presence of snow on the ground, the physical properties of the atmospheric boundary layer (ABL) are changed, and so is the energy balance. Among these changes the influence on the fluxes may be found. In return the state of the atmosphere plays a critical role in determine among others the growth or melting of the snow cover and its structure.
The interface for energy exchange is desired to be infinitesimally thin and having neither mass nor specific heat. This is hardly the fact for snow due to penetration of shortwave radiation into the snowpack, mass movement and phase changes. Therefore it is better to consider a volume balance of fluxes as shown in figure 2.1. Its energy balance for an open and flat snow cover may be written:
−dH
dt =Qs↓+Qs↑+Ql↓+Ql ↑+Qh+Qe+Qp+Qg (2.1) All units are in W m−2. Here horizontal energy transfers and the effects from vege- tation and wind drift of snow have been neglected. −dHdt is the net change rate of the internal energy in the snowpack per unit area. Qs ↓ and Qs ↑ are the downward and reflected shortwave radiation components, respectively. For longwave radiation, Ql ↓ and Ql ↑ represent the downward and upward components, respectively. The turbulent fluxes through the atmosphere are represented by the sensible, Qh, and latent heat, Qe. Qp is the energy flux due to precipitation and blowing snow, carried as sensible and latent heat. The final term, Qg, is the ground heat flux.
A change of internal energy in the snow pack is related to either warming and melting (energy gain) or cooling and freezing (energy loss). Thereby the energy balance is linked
9
Figure 2.1: Energy balance for an open snowpack. Taken from Armstrong & Brun (2008).
to the mass balance. The mass balance of an equivalent snow cover is given as:
dM
dt = ∂M
∂t + ¯u· ∇M
=P ±E−R±A (2.2)
=Pr+Ps+Ec,s+Ec+Aa±Asd−Ee−Es−R−Ac
All units are in kg m−2 s−1. dMdt is here the rate of mass change, made up from the local storage ∂M∂t and advective terms ¯u· ∇M. It is defined positive for accumulation.
The local storage terms come from the precipitation rate P (accumulation), the phase transition rate E (accumulation or ablation) and the runoff rate R (ablation).
These may be divided into the accumulation effects of rainfall, Pr, snowfall, Ps, solid condensation, Ec,s, or condensation, Ec, and the ablation effects of evaporation, Ee, or sublimation, Es. The runoff rate is strongly coupled to the melting rate of isothermal snowpacks1. See figure 2.5 for a schematic representation of the processes.
The advective terms A (accumulation or ablation) are a result of the accumulating effects from avalanches, Aa, or snow drift,Asd, and ablation effects from snow drift, Asd,
1Snow temperatureTs= 0◦C throughout the snowpack
or calving, Ac. Of these, mass advected into the glacier from a possible larger glacier on the plateau above is included in Aa. Similarly, Ac also includes mass advected out of the glacier into the glacier lake or bare ground region in front of it.
Figure 2.2: Mass balance for an open snowpack. Taken from Armstrong & Brun (2008).
2.1.1 Shortwave radiation
In many cases, and most likely in the subtropical belt in which the Himalayas are located, the incoming shortwave radiation (SW) is the most important energy source for a snow cover. This is especially the fact in the melt season. SW is usually defined as the part of the solar spectrum up to 4.0µm.
Initially, SW makes up about 99.2 % of the solar radiation, but then makes its way through clouds, particles and gasses in the atmosphere. Through absorption, scattering and reflection this energy is reduced as it reaches the ground so that the net flux of shortwave radiation is given by:
∆Qs =Qs ↓+Qs↑= (1−αs)Qs↓ (2.3) whereαsis the snow albedo. A definition on the parameter may be found in chapter 2.1.6.
Normally measurements of Qs ↓ are not at hand, hence a parametrization is nec- essary. This is calculated from the solar zenith angle and easier observable quantities, as cloud cover. Generally, Qs ↓ are first calculated for clear skies and then adjusted for cloud cover. Mainly clouds reduce Qs ↓, but for surfaces with a high albedo - like snow or ice - the reflection between the surface and the cloud base may still be vital. A small, but not negligible part of Qs ↓ enters the surface as diffuse radiation. This part becomes more important in the dark season or in steep slopes. Besides, diffuse radiation also comes in as reflection from surrounding topography.
2.1.2 Longwave radiation
Longwave radiation (LW) is the term usually used for wavelengths between 4 to 100µm.
Incoming LW, Ql ↓, is mainly a result of thermal emission from atmospheric gasses and clouds. These are again partly a result of the outgoing LW, Ql↑, which is emitted from the surface. Since water vapor is an effective absorber of LW, Ql↓is mainly determined by conditions in the lower hundred meters in the atmosphere. Thereby it is normally practically acceptable not to use a radiative transfer model, but only measurements near the surface. Using Stefan-Boltzmann equation, Ql ↓ may be parameterized as:
Ql↓=−εef fσSBTa4 (2.4)
where σSB = 5.6697·10−8 W m−2 K−4 is the Stefan Boltzmann constant, Ta the near-surface air temperature and εef f is the ”effective” emissivity for the atmosphere.
The latter is normally a function of cloud cover and air humidity near the surface.
Whereas clouds have emissivity close to unity, meaning that they are very efficient infrared emitters, εef f commonly has a value of about 0.75. In Alpine regions values of εef f may reach as low as 0.55 (Marty, 2000).
The parameterization ofQl ↑ is also based on Stefan Boltzmann’s law, but includes the part of Ql↓ that is not absorbed by the snow. That results in:
Ql↑=−εsσSBTs4−(1−εs)Ql↓ (2.5) Hereεs is the emissivity of the snow andTs the surface temperature of the snow.
2.1.3 Net radiation
Shortwave and longwave radiation may be put together to find the net radiative flux at the surface, Qtot:
Qtot = ∆Qs+ ∆Ql=Qs↓(1−αs) +εs(Ql↓ −σSBTs4) (2.6) Here positive values of Qtot is equivalent with an energy exchange from the atmo- sphere to the snow cover, and the net radiative direction is heavily dependent on αs.
The latter shift with cloud cover, but no manifestation can be made on their interac- tion. For example during times with a very small portion of shortwave radiation (like wintertime), an increase in cloud cover will lead to more energy input to the snow cover.
2.1.4 Turbulent heat fluxes
Turbulent eddies in the surface boundary layer may carry turbulent heat to or from a snow surface (Morris, 1989). These fluxes are either sensible, Qh, or latent heat fluxes Qe, and formally these may be written as:
Qh =ρacp,aw0Ta0 (2.7a)
Qe =ρaLs,iw0q0 (2.7b)
The indexes a and i yield for air and ice, respectively. The fluxes are written as the covariance of fluctuations in vertical velocity, w, with temperature (of air), Ta, for sensible heat flux and with specific humidity,q, for latent heat flux. The overbars denote a time average and the primes stand for deviations from the mean. ρa is the density (of air), cp,a = 1.01·103 J kg−1 K−1 the specific heat (of air) at constant pressure, and Ls,i = 2.838·106 J kg−1 the latent heat of sublimation (for ice) at 0 ◦C.
It is possible to measure these covariances with fast-response instrumentation, but as these are very seldom at hand, the fluxes need to be estimated. This is mostly done through measurements of already mentioned Ta, Ts and q in addition to wind velocity u (Deardorff, 1968):
Qh =ρacp,aCu(Ta−Ts) (2.8a) Qe = Lsρa
pa Mv
MaCu ei[Ta]q−ei[Ts]
(2.8b) where C is a turbulent exchange coefficient, pa is the air pressure, MMv
a the ratio between water vapor and dry air in molecular weight and ei(T) is the water vapor pressure at saturation over an ice surface with temperatureT. The size ofCis discussed, but as a rule of thumb it will depend on the roughness of the surface and the stability of the atmosphere. Monin-Obukhov’s surface layer similarity theory represents the best approximation so far (see for example in Garratt (1994)).
2.1.5 Heat flux between the snow and the ground
Most often there will be a positive energy flux from the ground to the bottom of the snow cover. This is due to the fact that the ground temperature ordinarily is above
the freezing point when the first snow falls. According to Brun et al. (1989) the flux declines during the winter and reduces rapidly at the end of the season when cold melt water cools the ground.
2.1.6 Radiation properties of snow
The white color of the snow is a result of the high reflectivity of snow for shortwave radiation - the most important property of snow. To prevent the photons from being absorbed by the ground, the snow cover has to be sufficiently thick. In most occasions 10 cm is enough.
Albedo is defined as the ratio between reflected and total incoming SW. It is found by integrating the reflectivity over the whole wave spectrum. For snow it may be as high as 0.9. Dependent on the snow type and the spectral distribution of incoming radiation, the albedo highly varies on the cloud cover and the ratio of direct to diffusive radiation. Its variation with impurities and crystal sizes can be found in figure 2.3. Due to the general increase of both grain sizes and level of impurities in the snow by age, the albedo is reduced over time (ONeill & Gray, 1973; Nolin, 1993). This is especially the case during the melt season when the grain grows rapidly and more impurities are revealed. In general during the season, the process of a decreasing albedo is counteracted by the arrival of a new snow fall.
(a) (b)
Figure 2.3: Snow albedo as a function of wavelength. Effect of soot concentration on albedo (a) and albedo for different grain sizes (b). Taken from Wiscombe & Warren (1981).
A parameterization of albedo and the coefficient of absorption cannot be made over the whole spectra. Variations in reflectivity rising from the different grain sizes elimi- nates this option. Instead it is helpful to consider a grouping of spectral bands, as in Brun et al. (1992).
The albedo of a point snowpack and a snow-covered surface may often differ due to its heterogeneity. With the exception of large ice sheets (Greenland and Antarctica), large surfaces generally have a much lower albedo than the snow covering these surfaces.
The main causes are a patchy snow cover due to uneven surface leading, vegetation with a lower albedo and local variations in wind and melting.
Considering longwaves, the snow absorbs nearly all radiation emitted from the at- mosphere or objects in close proximity (Dozier & Warren, 1982; Warren, 1982). This takes place over only the first upper millimetres of the snow cover. Besides, it emits the maximal amount of thermal radiation in regards to the surface temperature. In other words, it is nearly a perfect black body, and its emissivity makes up about 0.98 in average.
2.2 Snow processes
Most of the theory found in this chapter is based on Armstrong & Brun (2008).
The formation of snow crystals is a result of the continuosly changing conditions in the atmosphere. The form it takes, whether it is as a plate or column, is mostly dependent on temperature and air humidity. This dependency is shown in figure 2.4.
The growth of the ice crystals go on the behalf of water droplets as the saturation pressure for ice is lower than for water. Reaching a certain size, the crystal will start falling towards the ground and becomes then what is defined as a snow crystal. On its way down it may collide with supercooled cloud droplets which then freezes on the crystal, or it may adhere on other crystals. In any way, the crystal grows. The crystal may also take form as hail or graupel if several melt-freeze cycles take place.
How the snow crystal finally looks when it settles on the ground, also depends on the wind conditions and the surface temperature. It may then fasten to the other crystals on the ground and constitute a part of the snow cover. For every snowfall the snow cover gets a new layer, which may have properties rather different than the snow underneath.
2.2.1 Snowfall
Fresh snow has a density ranging from 20 to 300 kg m−3, but for dry snow falling under calm conditions it is typically 60−120 kg m−3. To put this number in perspective, wet snow may reach a density of 650 kg m−3 and ice 917 kg m−3. Glacial ice contains air bubbles and has a density of about 850 kg m−3. The snow density usually increases with wind and temperature and thereof water level. In general small crystals that have a simple shape connect more effective and thus have a higher density. The opposite case of the lowest density happens when large, highly dendritic crystals precipitate in calm and cold conditions.
Figure 2.4: Diagram of snow crystal morphology that shows types of snow crystals which grow at different temperatures and humidity levels. Taken from Libbrecht & Rasmussen (2003), originally based on work by Ukichiro (1954).
The snow depth may alternate highly over short distances due to the topography and wind transportation of snow. In the latter case variations in velocity may lead to a removal of snow from the upwind side and accompanying deposition on the lee side of hills or other convex barriers.
2.2.2 General characteristics
How the initial structure of a new snow layer looks like is connected to the shape and size of the snow crystals and the stress applied to the bonds that link them together. In between the ice, pores are found filled with either humid air or, in the case of wet snow, liquid water. Most of the pores are interconnected so that snow may be characterized as a porous media. Porous media often have complex physical properties, and that is certainly the case for snow. In this case the water may exist in solid, liquid and gaseous form simultaneously. This state is called the triple point (see figure 2.5). It is the ther- modynamical relation between these three phases that determines the metamorphism and grain growth.
Figure 2.5: Schematic phase diagram for water near the triple point, T P. P represent pressure, θ temperature and C the depression of the melting point with increased pressure.
Based upon Hooke (2005).
The solid part of the snow continuosly changes, and sometimes rapidly too, due to the high thermodynamic activity around the triple point of water. Thus snow is a unique, dynamical and complex component of the surface of the earth.
2.2.3 Snow classification
The International Commission on Snow and Ice updated the system for classifying snow on the ground (Colbeck et al., 1990). In this way various snow types are described in terms of qualitative indications of form and size of the grains. There is no singular parameter for describing the snow, but through the classification the snow is divided into six main classes. Their name and appearance is found in figure 2.6.
2.2.4 Snow metamorphism
The micro structure of the snow ranges widely. To a certain degree, these are connected to the inequality of the precipitation particles, but much more important are the transi- tions of the snow grains that take place due to the thermodynamical relationships among the water phases. This transition is known as snow metamorphism. The meteorological conditions are the main factor behind the effect and rate of the process, which explains why fresh snow layers develop differently in different weather with the result of stratified snowpacks.
The primary difference in metamorphism comes from the presence of water in the snow, and it is normal to distinguish between dry and wet snow metamorphism. Even
Figure 2.6: The six classification schemes for snow types. Taken from Colbeck et al. (1990).
though the mechanisms in dry and wet snow metamorphism are well understood, the quantifying of the process in numerical models is yet not sufficient.
Dry snow metamorphism
The definition of dry snow is snow that does not contain liquid water. Instead, the pores are filled with air, and this air is commonly saturated with water vapor. Whether a temperature gradient is found in the snow cover or not, principally determines the dry snow metamorphism.
For a nearly uniform temperature in the snow cover, the air around convex crystal surfaces (for example at the points of crystal branches) tends to be at a higher vapor pressure than the air around concave surfaces (for example at the bond between two adjacent crystals). The result is sublimation from convex crystal surfaces and a cor- responding deposition on concave or less convex surfaces. Over time convex surfaces shrink while concave or less convex surfaces grow, and grains become rounded. The re- lationship between area and volume decreases so that the equilibrium phase of a sphere may be reached eventually. The process is therefore known as the equilibrium growth form.
The kinetic growth form takes place where a temperature gradient is present in a snow layer. Then the difference in temperature generates variations in vapor pressure
at saturation and induces vapor diffusion from the warmest crystal surfaces towards the coldest ones. For a sufficiently high temperature gradient, the growth of the coldest surfaces is rapid enough to form facets and even strias, shapes of faceted crystals (class 4) and depth hoar (class 5), respectively (see figure 2.7). Both of these are far from the equilibrium form.
Figure 2.7: Schematic description of the transformation between the main snow classes and metamorphism. Taken from Armstrong & Brun (2008).
Under natural conditions, curvature and temperature gradient effects work together and compete. Newly deposited precipitation particles (class 1) normally get rapidly rounded into decomposing and fragmented particles (class 2). In the situation of a temperature gradient higher than 5 ◦C m−1 at this stage, snow metamorphoses into faceted crystals (class 4) and further into rounded grains (class 3). If the gradient exceeds 15 ◦C m−1, depth hoar (class 5) is formed.
Wet snow metamorphism
Wet snow metamorphism takes place when the snow contains a significant amount of liquid water, typically more than 0.1 % of the volume. Then mass exchanges between all three phases need to be considered to explain snow metamorphism. Convex crystal surfaces have a lower melting point temperature. Consequently give local temperature gradients melting of the most convex surfaces, including the smallest crystals, and re- freezing of liquid water (if it is available) onto the concave or less convex surfaces. As a result rounding takes place and the largest crystals grow on the behalf of the smaller so that there is a net growth. The background for the rapid growth of grains during melt-freeze cycles is the inclusion of liquid meniscus in the adjacent ice grains when wet snow freezes.
2.2.5 Grain size and growth rate
The importance of a quantitative knowledge of metamorphism processes rises due to the influence of the snow texture on most of its physical properties. This yields especially for snow modeling. A major difficulty comes from the lack of a unique parameter to quantitative describe snow texture. Three possible approximations to the quantification are experimental, theoretical and numerical. Different models have different approxi- mations, and an experimental approach is presented in chapter A.6.
2.2.6 Snow compaction
The mixing ratio between ice, liquid water and air is a key parameter to explain a sig- nificant part of the variability in physical and mechanical snow properties. Density is a proper indicator for this mixing ratio when considering dry snow, whereas measure- ments of the amount of liquid water are also needed for wet snow. It is mainly three processes that contribute to the compaction of snow inside or atop a snowpack: snow drift, metamorphism and deformation strain. The two first are described in chapter 2.2.1 and 2.2.4, whereas the latter comes from the pressure the upper layers make on buried layers. In the grain bonds gravity forces are concentrated so that these break, slide, partially melt or wrap. In any case the rheological properties of snow become very complex (Golubev & Frolov, 1998). These processes are particularly active in fresh snow, which settles quickly during and after snowfall.
2.2.7 Thermal behavior of snow
Snow has a relative low thermal conductivity. This leaves the snowpack as a thermal blanket, keeping the earth unaffected by rapid atmospheric temperature changes. But as the thermal properties of snow rely on the micro structure, and this alternates over
time, the thermal properties will change too. The same can be said of the snow density and heat conductivity. In general, a higher density leads to a better heat conductivity.
How swift heat is transferred inside a material depends on the thermal conductivity of the material. In one dimension, the heat flux Qc at a point is given by the Fourier equation as:
Qc=kef f
δT
δx (2.9)
where kef f is the thermal conductivity and x is the spatial coordinate along the direction of the flow. Herekef f is defined as the ”effective” thermal conductivity which includes both the effects of heat conduction through connected grains, through the air space between the grains and transportation of latent heat from sublimation and deposition of water vapor.
Pressure variations due to high wind velocities over the uneven snow surface generate a larger circulation of the air inside the snow. This is due to the chiefly interconnected air spaces, and a transportation of energy (advection) in the snow cover turns out as a result. The temperature profile of the snow layer is regulated by the ratio of the air stream velocity and the heat conductivity. These effects are notable in figure 2.8.
Figure 2.8: [Left] In-snow temperature profiles at intervals of 6 h during a cold, mostly clear and calm day. [Rigth] In-snow temperature profile at a time when the wind speed was7 m s−1. Taken from Armstrong & Brun (2008).
Highly porous snow, like fresh snow and depth hoar, often get advection dominated temperature profiles as these have low heat conductivity. In the opposite case of very
low porosity, like wind packed snow, heat conduction nearly without exceptions controls the temperature profile, even though it may be large air flows inside the snow (Albert
& McGilvary, 1992)
The specific heat capacity of the snow states how much energy that is needed in a certain amount of snow to change its temperature. Snow is a conglomerate of ice, air and liquid water, and so the specific heat comes from a calculation involving the weighted average of the three parts. The specific heat of snow cp,s at 0 ◦C and 1 atmosphere of pressure is given as:
cp,s= ρaΘacp,a+ρiΘicp,i+ρwΘwcp,w
ρs (2.10)
where the indexes a,i andw stands for air, ice and water, respectively. The specific heat constants are cp,a = 1005 J kg−1 K−1, cp,i = 2114 J kg−1 K−1 and cp,w = 4217 J kg−1 K−1, and Θ represents the constituent volume fractions.
2.2.8 Fluid flow behavior in snow
The snow properties of high porosity and low heat conduction does not only make snow a protecting layer against temperature changes, but also easy permeable to air and water. But fluid flow in snow is complicated because of factors like freeze-melt effects, metamorphism and stratification. Therefore, fluid flow throughout the snow cover ranges in velocity, from 1 to 20 cm h−1. An inclusion of both water and air should ideally be made, but as the water volume in snow normally is less than 10 %, the air will not be restrained by the snow (Colbeck, 1978). Water movement in the snow may then be treated as a modified one-phase flow (Scheidegger, 1958). In this case, the flow velocity of the fluid vw may be expressed in terms of the combined pressure and gravitational forces as:
vw = Kw ηw
δpa,w δx
| {z }
pressure force
+ ρwg
|{z}
gravitational force
(2.11) where Kw is the saturated or intrinsic permeability of water in fluid state, ηw the dynamic viscosity,pa,w =pa−pw the capillary pressure andg = 9.81 m s−2 acceleration due to gravity. Fluid continuity then leads to the equation for water flow through the snow:
ρwφδs δt
| {z }
saturation change
=− δ δx
ρwKw
ηw [δpa,w
δx +ρwg]
| {z }
water flux
−ρwφsδvi
δx
| {z }
compaction
+ S
|{z}
melting (2.12)
wheres is the liquid water content,t time, vi the compaction rate of the ice matrix and S a phase shift term.
Capillary forces are here neglected as they rarely contribute to the flow. The outcome is a slight underestimation of the flow rate in equation 2.12. Nevertheless, these forces are important in the formation of capillary barriers and flow fingers. The first occur between layers of fine and coarse snow due to the higher capillary suction in the layer of fine snow (Jordan, 1995). An accumulation of infiltrating water takes thereby place above the limit between fine and coarse snow. Containing much water, these layers may freeze in cold snow and create ice layers, which may prevent later water flow. The effect may be an acceleration of hydraulic pulses by hours or even days in sloping terrain, as water may reach the ground before the bottom of the snowpack in this case.
Permeability
Since the pores in the snow rarely are saturated of water, the division of saturated permeability, K, and liquid permeability, Kw, is made. Both depend on the pore size, but in contrast to K, the size of Kw is limited to the pores that contain water. Kw is also usually much smaller than K because of the restriction of water movement to the smallest pores in the snow cover. Likewise, Kw is a result of how the water filled pores are interconnected. Shimizu (1970) derived a formula for the permeability K in regards of density and grain size, d, on the form:
K = 0.077e−0.0078ρsd2 = 0.077e−7.153(1−φ)
d2 (2.13)
A couple of years earlier, Brooks & Corey (1965) introduced a relative permeability, Kr,w =Kw/K, which gives the permeability as a function of the water level in the snow, s:
Kr,w =
s−si 1−si
ε
(2.14) Here si is the saturation limit turned out from snow type and grain size, typically about 9−10 % of the mass (Denoth et al., 1979). Experimentally, values ofε are found between 2 and 5 (Denoth et al., 1979).
2.3 Ice processes
Most of the theory found in this chapter is based on Hooke (2005).
From the snow processes described in chapter 2.2 a further transformation to ice may take place. At the first phase water molecules diffuse from the points of snowflakes toward their centers, so that the flakes tend to get rounder into a spherical form. A schematic sketch of the process is shown in figure 2.9 (a).
Densification continues in the process of sintering (figure 2.9 (b)). It involves sub- limation and molecular diffusion within grains, nucleation and growth of new grains,
Figure 2.9: Transformation of snow to ice. (a) Modification of snow flakes to a subspherical form. (b) Sintering. (c) Processes during sintering where 1 = sublimation, 2 = molecular diffusion within grains, 3 = nucleation and growth of new grains and 4 = internal deformation of grains. Taken from Hooke (2005), which is based on Kinosita (1962) and Sommerfeld &
LaChapelle (1970)
.
along with internal diffusion of the grain’s transfer material, as seen in figure 2.9 (c).
Sublimation is more important when pore spaces still are large. This process is therefore replaced by internal deformation over time. The latter increases with increasing pressure from burying of the snow. Surface tension may draw grains together when water films form around them, and air spaces may be filled by melt water and refreeze; both affects an accelerated densification process in warmer temperatures.
At a density about 830 kg m−3 pores become closed and thereby forbid air movement through the ice. Where the pores close off, depend on the temperature. The fact is important for studies of atmospheric composition at historic times.
In general, glaciers form either at high elevations or latitude. On some parts of the glacier, snowfall during the winter exceeds melting and other losses during the summer.
This region is called the accumulation area. Lower down on the glacier, a net ablation is observed. The ablation zone looses all winter snow and some of the underlying ice during the summer. In addition to the atmospheric interaction, gravitational forces push ice towards lower elevations. At the end of the season, the line separating the accumulation and ablation zone is relatively easy spotted. This is named the Equilibrium Line Altitude (ELA). Here, melting and snowfall exactly equalize each other. An elevated ELA is thereby equivalent with a higher melt amount.
Figure 2.10 shows the different zones in the accumulation area of a glacier at the end of the melt season. At the top of the glacier where no melting occurs, the dry-snow
Figure 2.10: Variation in snow zones with altitude on a glacier. Horizontal distance from equilibrium line to dry-snow line is tens to hundreds of kilometers. Taken from Hooke (2005), which is based on Benson (1962)
.
zone is found. Some melting can take place in the percolation zone below. Here, the melt water may form lenses or gland-like structures as it percolates downward into the cold snow and refreezes (Benson, 1960; M¨uller, 1962). According to Benson (1962), the boundary between these two zones, the dry-snow line, lies near the elevation which have a mean temperature of −6 ◦C. Lower on the glacier, the summer melting will sufficiently wet the entire snow pack. This is known as the wet-snow zone, and if this water-saturated snow refreezes, it may form ice recognized as superimposed ice. This is the case at even lower elevations, where only this type of ice is present at the end of the melt season. It is thus called the superimposed ice zone. The zone is limited from below by the ELA.
At any given point on the glacier there is also a distinct vertical zonation. This rises from vapor-pressure gradients due to a higher vapor pressure of the warmer autumn snow than the overlying winter snow. Diffusion of molecules from the autumn to the winter snow takes place so that the first becomes coarser and possibly also denser. This is known as depth hoar (see chapter 2.2.3).
2.3.1 Glacier classification
Glaciers are classified in two ways; by shape and by thermal characteristics. The geo- morphology of glaciers leaves two basic types: ice caps or ice sheets and valley glaciers.
A schematic sketch of the two types and their flow lines are shown in figure 2.11. The first are long and narrow glaciers that flow down a valley. Most Himalayan glaciers are thought of having this shape. Cirque glaciers, tidewater glaciers, piedmont glaciers and hanging glaciers are all different types of valley glaciers.
Figure 2.11: Cross sections of (a) a typical polar ice cap or ice sheet and (b) a typical valley glacier. The relation between ELA and flow lines in relative proportions. Taken from Hooke (2005)
.
Ice caps and ice sheets both spread out in all directions from a central dome. It is normal to operate with two present ice sheets on the globe; Greenland and Antarctica.
Ice caps are more numerous, whereof Vatnaj¨okull on Iceland is one example.
In addition, there are transition types of glaciers, like outlet glaciers from ice caps, and also other types which do not fit into one of the two categories. Regenerated glaciers and rock glaciers both have this status.
The thermal classification of glaciers splits glaciers into three groups: polar glaciers, polythermal or subpolar glaciers and temperate glaciers. The first are cold glaciers with a temperature below the melting temperature of ice everywhere in the glacier. It may be frozen to bed or melt water at the bed may prevent this from happening. A polythermal glacier is slightly warmer, containing cold and temperate volumes. The accumulation zone is typically temperate, whereas the snout and the surface layer are cold. In the final case, the entire snowpack of a temperate glacier is at the melting point. Here the conduction of heat is insignificant.
In a continental climate, it is the low temperatures of the relatively dry, but cold areas that make the presence of the glaciers possible. Here mean summer temperature and glacier mass balance are strongly (inversely) correlated. To the contrary, in a warmer and wetter maritime climate the air temperature alone is less important, but so is the winter snow fall.
2.3.2 Mass balance principles
Mass balance may differ widely from glacier to glacier and from year to year. That is why several terms to describe different aspects of the mass balance exist.
A glacier’s winter balance is defined as the amount of snow that accumulates during the winter months. Accumulation may take place as solid precipitation (snow), snow drift, avalanches, refreezing and rime. Conversely, snow and ice is lost during the melt season is known as the summer balance, a negative quantity. Ablation comes from surface melt, evaporation, calving, snow drift and basal melt. However, melting may occur during the winter and snow may fall in the summer.
One balance year is usually taken from the end of the melt season to the end of the next, and the sum of the winter and summer balance over this period is the net balance.
A regular unity of balances are water equivalents (abbreviation w.e.), that is, in terms of the thickness of a layer of water. Specific balances are given in m a−1 or kg a−1 m−2 and refers to a specific place on the glacier. The net specific balance dmdtn may then be given as:
dmn
dt = dmw
dt +dms
dt (2.15)
where dmdtw and dmdts represent winter and summer balance, respectively. The overall balance of the glacier then follows as:
