Potential systematic errors in pressure altimeter altitudes (Paper II)

௜ୀଵ

(29)

where ݊ is the number of independent errors ߪ. This relation can be used to estimate the overall mass balance error from the independent error contributions of the observations, the spatial extrapolation, the density conversion and the tidewater front fluctuations (Paper II).

5.5.2.Potential systematic errors in pressure altimeter altitudes (Paper II)

An attempt was made to compare the 1983 radio-echo sounding (RES) profiles (Dowdeswell et al., 1986) with recent elevation data from GNSS surface profiles, airborne laser altimetry and ICESat laser altimetry (Fig. 18). Such an analysis requires a good knowledge about potential systematic errors in the data sets. No clear elevation bias was found in the RES data over land surfaces with respect to existing DEMs and ICESat crossovers. This is no surprise since the RES instrument was frequently calibrated over sea level during the survey and most land surfaces are at low elevations. Potential errors in the aircraft pressure altimeter due to temporal pressure variations would also be largely removed by these calibrations. However, one can not exclude the possibility of pressure altimeter

71 biases due to local pressure fields over the ice cap. The local pressure anomaly (ο݌) with respect to a homogeneous pressure field can be calculated from the barometric formula:

ο݌ ൌ ݌_଴൬ ݐ_଴ ݐ_଴െ ܮሺ݄_ଵെ ݄_଴ሻ൰

௚ெ

ோ௅ െ ݌_ଵ (30)

where ݄, ݐ and ݌ refers to the elevation (m), temperature (K) and pressure (kPa) at two stations (0 and 1) separated in space, ܮ is the temperature lapse rate between the two stations (K m^-1), ݃ is the gravity (9.807 m s^-2), ܯ is the molar mass of air (0.02897 kg mol^-1) and ܴ is the universal gas constant for air (8.314 N m mol^-1 K^-1). Such a pressure anomaly will introduce a barometric height error (ο݄) in a temperature-corrected pressure altimeter:

ο݄ ൌ ݄_଴െݐ_଴

ܮ൭ͳ െ ൬݌_ଵ

݌_଴൰

ିோ௅

௚ಾ

൱ െ ݄_ଵ (31)

A simple field experiment was carried out in spring 2008 to test the relative stability of the air pressure at Austfonna with respect to a coastal weather station to the north of the ice cap. Air pressure and temperature were logged at both sites and used to calculate the summit pressure anomaly (Eq. 30) and the corresponding barometric height error (Eq. 31). Mean sea level pressure values from ERA-40 reanalysis data were interpolated to the same sites and used to calculate comparable barometric height errors (Fig. 19). The spatial resolution of ERA-40 is too coarse to capture local pressure fields over a few tens of kilometers, but it gives a good indication of typical horizontal pressure gradients across the ice cap. The barometric height error between the two sites for ERA-40 varies within ~15 m, while the meteorological readings show a larger variation. A positive pressure anomaly of up to 0.1-0.3 kPa was registered at the summit between April 26 and May 30, corresponding to a negative barometric height error of 10-30 m (Fig. 19). This occurred after a marked pressure increase of ~2 kPa combined with a weather transition from stormy and cloudy conditions (“camp weather”) to calm and clear conditions (“work weather”). The 5-day pressure anomaly started and ended with a sharp temperature peak close to 0 ˚C at the coastal station with stable temperatures between -10 and -15 ˚C in the intermediate and subsequent period.

The weather during the RES campaign in April 23-28 1983 was characterized by high sea level pressures (102-104 kPa), low temperatures (-10 to -20 ˚C), calm winds and clear weather (ERA-40 / T. Eiken, pers. com.). Hence, it is not unlikely that a similar local pressure anomaly to spring 2008 was present at the summit during the survey. A negative elevation bias of a few tens of meters could therefore be present in the 1983 surface elevations in the summit region. This might explain the extreme elevation differences between the 1983 data

72

set and recent elevation measurements. Some of the elevation differences in Fig. 18 are definitively due to interior thickening and peripheral thinning, but the exact amount can not be quantified. This uncertainty was the background for comparing ice thickness changes at crossover points between RES profiles in 1983 and 2007 instead (Paper II). Ice thickness measurements are not influenced by potential pressure altitude biases since they are determined from the time delay time between the surface and bedrock echoes, assuming a signal propagation velocity of 169 m μs^-1 for ice (Kristensen et al., 2008). Unfortunately, there are much fewer crossover points between ice thickness profiles (Paper II: Fig. 1d) than surface elevation profiles (Fig. 18), and the precision of ice thickness measurements is also lower than that of surface elevation measurements. It was therefore not justifiable to estimate volume change and mass balance for the period between 1983 and 2003-2008 in Paper II.

Fig. 19. Potential pressure altitude errors during the spring 2008 field campaign at Austfonna.

Temperature and air pressure were logged several times a day at the summit camp while an automatic weather station (AWS) at sea level in Rijpfjorden (45 km northwest of the summit) was recording hourly temperature and air pressure (blue line). These data were then used to calculate the barometric height of the summit. The difference with respect to the true summit elevation yields the barometric height error (solid black line). A similar calculation was done using interpolated pressure values from ERA-40 reanalysis data (dotted line).

The aircraft positioning in 1983 relied on a ranging system to four ground-based transponders. Three of the transponders were precisely positioned to ±2 m using satellite Doppler geoceivers. Two geoceiver locations were re-measured with GNSS in 2008, yielding

73 elevation changes of +10 m close to the summit and -12.5 m at 200 m elevation in Basin 3.

This corresponds to average elevation change rates of +0.4 m y^-1 and -0.5 m y^-1 which fit well with the rough trend between 1983 and 2007 (Paper II: Fig. 3d) and the more precise data from 1996-2002 (Bamber et al., 2004) and 2002-2008 (Paper II: Fig. 3a). The recent interior thickening is thus probably a part of a long term trend related to quiescent glacier dynamics rather than precipitation increase. The net surface mass balance in the summit area is also consistent between 1986-1998/99 (Pinglot et al., 2001) and 2004-2008 (Paper II: Fig. 5).