GPS based surface displacements – a proxy for discharge and sediment transport from the Greenland Ice Sheet

The elastic respond of the Earth’s surface to mass changes has been measured with Global Positioning System (GPS). Mass loss as accumulated runo ﬀ and sediment transport from a 10 000 km 2 segment of the Greenland Ice Sheet (GrIS) correlated very well ( R 2 = 0.83) with GPS measured uplift. Accumulated winter precipitation cor- 5 related fairly well with surface depression ( R 2 = 0.69). The relationships are based on seven years of runo ﬀ and sediment transport observations from the Watson River (2007–2013), winter precipitation from Kangerlussuaq Airport and GPS observations at Kellyville. GPS recordings of surface subsidence and uplift from 1996–2013 are used to calculate 18 years time series of annual runo ﬀ , sediment and solute transport and 10 winter precipitation. Runo ﬀ and related transport of sediment and solutes increase over the period, while winter precipitation (land depression) tends to decrease. Based on the entire GPS record (1996–2013), it is shown that until 2005–2006 the mass balance of this segment of the GrIS was rather stable – since then there has been an increasing loss of mass, culminating in 2012. 15


Introduction
This study focuses on vertical and horizontal surface displacements due to mass loss from the Greenland Ice Sheet (GrIS) at the GPS station located at Kelyville (KELY). KELY (longitude = 50.9448 • W, latitude = 66.9874 • N) has been operating continuously since 1996 (Wahr et al., 2001;Khan et al., 2008) and detect a fairly regular pattern 20 of annual depression with a maximum in April-July and uplift of the land surface with a maximum in October-January, which however is showing an increasing accumulated uplift recently. This pattern could be interpreted as an elastic response to the weight of accumulated snow during the winter and loss by runoff caused by melting during the summer. Introduction Discharge and sediment transport have been measured in Watson River, draining a 10 200 km 2 catchment, whereof 94 % is covered by a segment of the GrIS, Hasholt et al. (2013). Meteorological observations covering the period have been carried out at Kangerlussuaq Airport by the Danish Meteorological Institute (DMI). The GPS station at Kellyville, is located close to the outlet from Watson River.

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Because of this favourable combination of data, it was decided to test if the recorded surface changes could be related to the recorded mass changes. The aim of this presentation is to investigate the possible correlation, and if found significant, to use the relationships to calculate previous runoff and sediment and solute transport, 1996-2006.

Methodology
The present-day unloading of ice causes the Earth to respond elastically (Farrell, 1972), resulting in both vertical and horizontal elastic surface displacement of the crust (Dietrich et al., 2005;Jiang et al., 2010;King et al., 2012;Bevis et al., 2012;Fu et al., 2013;Wahr et al., 2013;Yang et al., 2013;Khan et al., 2014;Groh et al., 2014 The magnitude of the displacement is proportional to the mass of the load and inversely proportional to the distance between the load and the observing point (Nielsen, 2012). If a load is removed, the observing point uplifts and moves away from the load (Wahr, 2013). The present-day unloading along the margin of the GrIS is detectable using GPS observations (Khan et al., 2010;Bevis et al., 2012;Nielsen et al., 2013).

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To estimate site coordinates from GPS measurements, we follow the procedure of Khan et al. (2010). Data is sampled every 30 s, however, there are few gaps; sometimes up to three months of observations are missing. Within the test period values are missing in 2009 and 2010, however, the missing values do not have any influence of the calculated depression and uplift for the two years.
Discharge is measured at the bridges just south of the airport, Fig. 1. Stage is recorded by pressure transducers located upstream the bridges. Discharge is measured by use of the velocity × area method at the bridges and a rating curve is established in order to calculate the discharge continuously, the estimated accuracy of the accumulated annual discharge is −15 % to +45 % for the study period. The upper un- Precipitation is recorded by DMI with a Hellman rain gage at the airport, Fig. 1. Winter precipitation falls as snow (October-April) and summer precipitation is often convec-20 tive. Here we use uncorrected precipitation as an indicator of the winter precipitation, being aware that it probably underestimates the precipitation significantly (Allerup et al., 2000).
Annual uplift is determined by subtracting the annual (calendar year) minimum surface elevation from the annual maximum elevation. Annual depression is determined 25 by subtracting maximum surface level from the previous year from minimum surface of the calendar year. Because this is a difference measure, the accuracy of each surface observation of ±0.8-2 mm, will cause higher uncertainties at the low uplift and depression values than at the high ones. Average "error" was 1 mm, implicating that a surface Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | change of 6 mm (minimum recorded) has an uncertainty of ±33 % while a change of 23 mm (maximum recorded) has an uncertainty of ±10 %. The correlation between accumulated discharge and sediment transport and uplift is shown in Figs. 2 and 3. Related statistics is shown in Table 1. It is seen that the correlation is highly significant and the relationship can therefore be used to calculate 5 previous discharge and sediment transport. The correlation between accumulated winter precipitation and surface depression is shown in Fig. 4. The correlation is lower, but significant. It confirms that surface depression is related to deposition of snow, but a calculation of winter precipitation using this relationship is less accurate.

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The entire GPS record is shown in Fig. 5. It is observed that the record is nearly horizontal until 2005-2006, thereafter the record moves upward indicating an increased uplift. The horizontal surface displacement for the entire period is shown in Fig. 6. It is observed that there is a displacement towards west and north, also starting around [2004][2005][2006]. Annual uplift, depression and uplift minus depression from the preceding 15 winter are plotted in Figs. 7, 8 and 9. It is seen that the uplift has an increasing trend over the period while the depression has a decreasing trend. The net effect, Fig. 9, indicate an increasing mass loss during the 17 year period.
The calculated annual accumulated discharge and sediment transport is shown in Figs. 10 and 11. Averages of discharge, sediment transport, transport of solutes and 20 winter precipitation over the entire period are shown in Table 2. Figure 6 shows relative horizontal displacements. In general, horizontal displacements are dominated by tectonic plate motions. To overcome this problem, we remove the 1996-2004 trend and study changes in horizontal displacements rather than absolute Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | displacement. The horizontal displacements after 2004, suggest surface motion away from the Watson River drainage, confirming that the observed uplift at KELY is due to mass loss centred at the Watson River drainage. The correlation functions between accumulated precipitation and discharge and respectively depression and uplift can be described as linear as expected because of the elastic response of the surface upon 5 the weight changes. Slightly better R 2 values can be obtained when using exponential or power functions, however, they are not significantly different from the R 2 values for the linear functions, and therefore we use the simple linear functions. The good correlation between uplift and sediment transport could be expected because the sediment transport is well correlated to the discharge, R 2 = 0.95. Also the solute transport is 10 strongly correlated to the discharge. Because of the good correlation with discharge at this location, it is reasonable to calculate sediment and solute transport from the GPS record, although it should be kept in mind that the weight component of these two transport forms is less than 2 per mille of the weight of the accumulated discharge. It is observed that the trend lines are not passing through the origo. When the depres-15 sion or the uplift is zero, then the winter precipitation and the discharge are negative. This indicates that the measured mass changes do not include all mass changes. The winter precipitation used is uncorrected and from a dry area, it is therefore too low. The total mass loss during the melt season includes the measured runoff and an unmeasured evapotranspiration which may explain part of the deviation from origo. A possible 20 underestimation of the discharge will have the same effect. The actual evaporation and sublimation may add to the uncertainty of the actual mass loss that is to be compared with the GPS "balance" reading. An important point is that in this catchment, there is no mass loss because of calving, which could elsewhere blur the response because of the released melt water alone, this implicate a possibility for calculating calving indi-25 rectly by use of the GPS readings elsewhere if the melt loss is known. The calculated "winter precipitation" represents only the uncorrected precipitation at Kangerlussuaq, a point value that has to be calibrated before being used in mass balance studies. The