Annual cycles in deformation Einar Ragnar Sigurðsson

Leveling lines: monitoring of Katla Eysteinn Tryggvason in two time periods: Monitoring of underground processes preceding eruption in Katla Ref. Tryggvason, 1973

Signal from leveling observation Amount of yearly tilting 1.4 to 4.5  rad Direction changing every year Ref. Tryggvason, 1973

Possible causes of annual variations Atmosphere changes Soil moisture and groundwater variation Temperature variations nontidal ocean loading Variation in ice and snowload Ref. Tryggvason, 1973 and Geirsson et al, 2006

Simple model for variable snow load Use of various data Precipitation data from the nearest weather stations Increased precipitation with elevation Temperature profile same as measured at Keflavik clear correlation Little or none time delay Calculated R coefficient for correlation: highest for 0 days delay, R=0.63 Elastic plate over a liquid substratum modeling gave plate thicknes 6.8 to 8.5km 99% confident the seasonal leveling is true and not caused by magmatic movements Ref. Tryggvason, 1973 and Tryggvason, 2000

GPS network First station in year 1995 Monitoring of crustal movements related to: Plate spreading Magmatic movements Earthquakes They show annual cycles in deformation as well. Ref. Geirsson et al, 2006

A cosinus model for crustal displacement The varying position, function of time in years: y(t) Initial position: a Linear trend: b*t Annual factor for cycles in deformation: Amplitude: A period: 2  t phase:  Ref. Geirsson et al, 2006 Skrokkalda (SKRO) rel. to REYK, uplift Year mm

Elastic half space and Green’s functions For an elastic halfspace after having convolved Green’s functions with the load we have the horizontal and vertical displacement as: at a point ȓ. The variables are  for the density of a load with thickness h integrated over the area R making the load. Poisson ratio is taken to be = 0.25 and g is the gravity acceleration Ref. Grapenthin et al, 2006

Snow load on each glacier Constant load over each glacier Vatnajökull, Mýrdalsjökull, Hofsjökull and Langjökull Good data of snow (water equivalent) thickness Raster size for modeling area of glaciers: 50x50m Ref. Grapenthin et al, 2006

The variable snow load the snow load is taken to be of constant thickness over each glacier but varying with time. So the ice load thickness at a point ȓ‘ at time t is: where t hm is the phase for maximum ice thickness and h m is the maximum ice thickness and With this equation for h and the other two for displacement used with data for displacement from CGPS stations, the only unknown, free parameter will be the Young modulus E. Ref. Grapenthin et al, 2006

Young modulus E Ref. Grapenthin et al, 2006

The model fit Ref. Grapenthin et al, 2006 HÖFN-REYKSAUD-REYK SOHO-REYK SKRO-REYK

Annual displacement cycle according to the model Maximum vertical displacement in center of Vatnajökull: 37mm Maximum horizontal displacement on east end of Vatnajökull: 6mm Note the low horizontal displacement areas on the three smaller glaciers on side to Vatnajökull Ref. Grapenthin et al, 2006

Possible improvements of the model The uniform thickness of snow load on glaciers The same melting and accumulating time -> cosinus function is not the best model Other seasonal causes of deformation Ref. Grapenthin et al, 2006 Ref. Veðurstofa Íslands, 2013

References Geirsson, H., T. Árnadóttir, C. Völksen, W. Jiang, E. Sturkell, T. Villemin, P. Einarsson, F. Sigmundsson, and R. Stefánsson (2006), Current plate movements across the Mid- Atlantic Ridge determined from 5 years of continuous GPS measurements in Iceland, J. Geophys. Res., 111, B09407, doi: /2005JB Grapenthin, R., F. Sigmundsson, H. Geirsson, T. Árnadóttir, and V. Pinel (2006), Icelandic rhythmics: Annual modulation of land elevation and plate spreading by snow load, Geophys. Res. Lett., 33, L24305, doi: /2006GL Tryggvason, Surface Deformation and Crustal Structure in the Mýrdalsjökull Area of South Iceland. Journal of geophysical research, vol 78, No 14, p – Tryggvason, Ground deformation of Katla: Result of precision levellings Jökull No 48, p. 1-8 Vedurstofa Íslands, downloaded http://brunnur.vedur.is/myndir/harmonie/