Glacier mass balance

The glacier MB describes the change of mass of a glacier as a whole or a particular part of the glacier over a certain period (Cogley et al. 2011). Generally, this period spans from minimum total mass in one year to minimum total mass in the next year (end of ablation season to end of ablation season) (Hubbard & Glasser 2005). For glaciers on the TP we apply MB years from 1 October to 30 Septem-ber. Elsberg et al. (2001) further divide the glacier-wide MB into a conventional balance that includes topographic feedbacks of the glacier, and into a reference-surface balance that refers to an unchan-ged glacier surface and area over the entire period. In this thesis the reference-surface balance is cal-culated for the various glaciers, respectively. As the reference-surface balance does not incorporate any feedback effects of glacier response to climate, it is more closely related to climate variations than the conventional balance (Cogley et al. 2011). The total MB of a glacier incorporates different components of accumulation and ablation for surface, interior and the base of a glacier (Fig. 1.6). The surface MB includes all mass changes within the layer above the summer surface of the previous year and is largely determined by climate conditions. The internal MB is the change in mass in the interior of the glacier beneath the summer surface, e.g. internal ablation through heat release from percola-ting melt water and internal accumulation through refreezing within the firn or ice. Thus, the internal MB is also influenced by climate conditions. The sum of surface MB and internal MB is therefore called climatic mass balance (Cogley et al. 2011). The basal MB accounts for mass changes at the base of a glacier (Fig. 1.6).

The MB model applied in this thesis calculates the surface MB and to a certain degree also the inter-nal MB (Fig. 1.7). The amount of SWin that penetrates into the snow or glacier ice is explicitly calcula-ted and may lead to subsurface melt (see section 2.3.1). If the subsurface melt happens in layers be-neath the last summer surface, this mass change is part of the internal ablation. The MB model struc-ture allows surface and subsurface melt water to percolate down to the ice surface (see section 2.3.1). In glacier regions where a cold firn layer is present beneath the snow, the refreezing would be part of the internal accumulation. This effect has to be considered especially in the accumulation zones of glaciers with slightly negative or positive MBs and only little precipitation. This is the case for glaciers on the central TP (see chapter 3). Within the applied MB model it is not possible to dis-tinguish properly between surface MB and internal MB.

Fig. 1.6: Components of the mass balance of a glacier. The arrows have arbitrary widths and do not indicate physical pathways of mass transfer. (Cogley et al. 2011)

Fig. 1.7: Glacial mass balance components considered in the MB model applied in this thesis. The arrows have arbitrary widths and do not indicate physical pathways of mass transfer. (modified after Cogley et al. 2011)

In this thesis glacier MB is assessed solely by SEB model calculations and results are evaluated both with observations on point scale and with the results of remote sensing approaches for the total glacier area. The calculation of the MB through SEB models or through statistical approaches (e.g.

temperature-index models) is called indirect method (Kaser et al. 2003, Schöner 2003). Common methods to measure the MB of a glacier are the glaciological method, the geodetic method and the hydrological method. Less common because the requirements are less practicable are the flux

meth-od and the flux-divergence methmeth-od (Kaser et al. 2003). The SEB mmeth-odel applied in this thesis to calcu-late the MB of various glaciers on the TP is explained in detail in section 2.3.1. The integrated MB components are visualized in Fig. 1.7. The evaluation and discussion of the model results is mainly based on MB data obtained by the glaciological and the geodetic method. Therefore, these methods are explained in more detail below.

The glaciological method (or direct method) determines the surface MB in-situ on the glacier surface by repeated point measurements of accumulation and ablation through ablation stakes and snow pits. Therefore, the length of the stake above the surface, the snow depth and the corresponding density is measured at every stake. Through repeat measurements the surface MB is calculated from the relative change in height of both snow and ice surfaces, multiplied by the vertically-averaged density of the snow, firn or ice that has been added or removed. Also the amount of refrozen melt water within the snow and the amount of superimposed ice can be derived. These rates may contri-bute to the internal MB. Nevertheless, per definition the glaciological method only refers to the sur-face MB (Cogley et al. 2011). The result of this method is a point sursur-face MB. A simplified scheme of the measurement and calculation procedure is presented in Fig. 1.8. The change of mass (Δmass) at a point i within a period t1 to t2 can be determined after Dyurgerov (2002) from

2

where ρ is the density of ice or snow/firn, h is the snow height (if any) and z is the distance from the top of the stake to the ice surface. The dimension of MB is [kg] (mass). When the MB is given per unit area, it is termed specific MB and it is generally given in the dimension [kg m^-2] or in [mm w.e.] (milli-metre water equivalent). The units kg m^-2 and mm w.e. are numerically identical because 1 kg of liquid water with a density of 1000 kg m^-3 has a vertical extent of 1 mm when distributed uniformly over 1 m² (Cogley et al. 2011). The glaciological method is the only method that is based on in-situ measurements and is considered to be the most accurate (Kaser et al. 2003). However, it requires re-peated field measurements under sometimes challenging conditions. In this thesis we use measured surface height changes and density measurements of the ablation stake network at Zhadang glacier from 2009 to 2011 to calculate point surface MB that are compared to the MB model (see chapter 2).

Staff from ITP maintains 25 ablation stakes in the ablation zone and accumulation zone of the glacier since 2005. The time span between two consecutive measurements ranges between four days and seven month.

Geodetic methods determine glacier MB by the volumetric change of the ice mass through time from repeated mapping of the surface elevation (Hubbard & Glasser 2005). Repeated high-resolution alti-metry data can be obtained from satellite missions like ICESat, TerraSAR-X and SRTM (e.g. Bolch et al.

2012, Neckel et al. 2013, 2014, Holzer et al. 2014, see chapters 3, 5 and 6). The data is used to inves-tigate spatial patterns of mass thickening or thinning on a glacier or ice cap. Due to the satellite ima-ge resolution the concerned ice mass has to exceed a certain minimum area. The volume chanima-ge can be investigated only for the entire glacier and between the dates given by the available satellite ima-ges (Paterson 1994). The conversion from a volume or elevation change again requires information on the density of the mass that was lost or gained (Cogley et al. 2011). In regions where no in-situ measurements for snow and firn densities are available a mean density has to be assumed (Neckel et al. 2013, 2014). Thus, mass changes in the accumulation areas are difficult to determine accurately (Kaser et al. 2003). The geodetic method does not yield altitudinal gradients of MB but is very useful complementary to the glaciological method and for the evaluation of MB models over longer peri-ods.

When comparing surface elevation changes and associated MB from the geodetic method and the applied SEB/MB model, the effect of mass transition and redistribution between accumulation and

ablation areas through ice flow has to be considered. The vectors of ice movement are not perfectly horizontal to the glacier surface. In the accumulation are there is a small downward component and an upward component in the ablation area. Thus, ice flow balances the elevation changes through accumulation (glacier thickening) and ablation (glacier thinning) (Paterson 1994). Large accumulation or ablation rates increase the flow speed (Bolch et al. 2012). Also the thermal structure of a glacier influences its motion because the viscosity of cold ice is higher than the viscosity of temperate ice (Aschwanden & Blatter 2006). Thus, the presence of cold ice leads to lower velocities. The SEB/MB model applied in this thesis does not account for glacier dynamics. Therefore, it will produce a stee-pening of the surface elevation gradient over time, with increased glacier thickening in the accumula-tion areas and increased glacier thinning in the ablaaccumula-tion areas. Most of the processed glaciers and ice caps are of polythermal or cold thermal regime with relatively small precipitation amounts (see sec-tions 1.3.5 and 1.4), characterized by generally low ice velocities (e.g. Hu et al. 2014). Thus, we as-sume that the derived discrepancies from the neglectance of glacier dynamics are within the calcula-ted model uncertainties.

Fig. 1.8: Stake measurements of seasonal MB in a year of positive (left) and a year of negative (right) surface MB, with no superimposed ice. The z coordinate is positive downwards, with origin z = 0 at the top of the stake. Light shading represents snow; dark shading represents firn or glacier ice. Measurements are made at t₀, the start of the accumulation season; at t_x, the start of the ablation season (strictly, the date when the mass of the column is at its maximum for the MB year); and at t1, the end of the MB year. The quantities measured are: at t0, when by definition there is no snow, the glacier surface height z₀ (the height of the summer surface); at t_x, the glacier surface height z_x and (in a nearby snow pit) the mean snow density ρx; and at t1, the surface height z1 and the mean density ρ1 of the snow (if any). The winter balance bw is the change of mass between t0 and tx. The summer balance bs is the change of mass between tx and t1. It is impractical to measure ρs or ρ1 when the annual balance is ne-gative. In these cases the density of the lost mass is supplied by making an appropriate assumption. At the instant following t1, any residual snow is deemed to become firn and the glacier surface, at z1, becomes the summer surface z0 of the next MB year. Subscript a denotes the annual value for h and b (Möller 2011 after Cogley et al. 2011).