Development of theoretical minimal model on glacier flow line with GIS tool, to assess glacier response in climate change scenarios

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1 International Syposiu on The Future of the Glacier Fro the past to the next 100 years Turin, 18th 21st Septeber2014 Developent of theoretical inial odel on glacier flow line with GIS tool, to assess glacier response in cliate change scenarios Moretti M.*, Mattavelli M., DeAicis M., Maggi V. & Provenzale A. Departent of Earth and Environental Sciences (DISAT) University of Milano-Bicocca Project NextData

2 Introduction Recognizes that ountains provide indications of global cliate change through phenoena such as [ ] the retreat of ountain glaciers [ ] UN A/Res/62/196, 2008 IPCC report 2013 Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 02

3 How to study glacier response to CC? CLIMATE FORCING MATHEMATICAL MODELS They reduce a coplex situation to a siple description, using laws of physics. Teperature 2 Precipitation Snow deposition Huidity Radiation balance Lw, Sw Wind speed & direction Atospheric pressure Cloud height GLACIER RESPONSE Glacier terinus variation Area fluctuation Lose or gain volue Increase or decrease of thickness Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 03

4 Minial Glacier Model (Oereleans 2008, 2011) CONTINUITY EQUATION: describes the transport or variation of a conserved quantity. Accuulation area V = H W L Ablation area dv dt = H W dl dt + H L dw dt + W L dh dt = B S PERFECT PLASTICITY PRINCIPLE: first-order estiate of how the thickness of a glacier varies with its horizontal diension. x y The elaboration is based on reconstruction of historical tie series, after have obtained eteoreological, physical and orphological data to start the odel it is possible copare the flow line length variation,the odel results, with real easured variations. Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 04

5 Minial Glacier Model - 2 dl dt = 3α 2(1 + υs) L B S = Wβ(H + b E)L Mass Balance gradient β = h Length variation of glacier terinus on flow line direction Surface balance = db& dz H = + b 0 h b& E L s α υ (1 + υs) 2 L 3 2 s L 1 B W Equilibriu Line Altitude [] Net Mass Balance [ w.e.] S Boundary Condition: B0 = highest elevation [] (β) H = ean thickness [] ( H) b = ean bed elevation [] L = length of the flow line [] s = ean slope GIS Cliate forcing Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 05

6 Minial Model: GISodule for boundary conditions Algorith to calculate and to iterate the GIS operations to obtain Minial Model input, using QGIS and other instruents: GRASS odule and GDAL/OGR-libraries. Input Output Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 06

7 Minial Model: GISodule - 2 GIS process allows to apply spatial approach on deterinistic one, that is Minial Mole equations. DTMs are the basis of GIS analysis, on which we can study the flow line and the polygons to obtain the orphological data set. All the odule results are rely on DTM resolution. Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 07

8 Minial Model: GISodule - 3 Polygons are used to evaluate the length of the flow line and to obtain the DTM statistics for a single year. Flow lines are calculated with Grass r.flow and they are drawn with orphological analysis to choose the ost plausible. Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 08

9 Minial Model: input data In inial glacier odel, the input data set are given by b and ELA. Cliate forcing on glacier Mass balance and ELA are very closely related to the cliate forcing and oscillations. We use a bi-variate fit to describe ass balance and ELA as a functions of suer teperature and winter precipitation, year on year. b& i = ats, i + bpw, i + c Ei = uts, i + vpw, i + Weather values coes fro cliate odel, used to validate the algorith through coparison with real easures and to assess future glacier response. z Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 09

10 Minial Model flow chart Cliate forcing with Input data and transfer function. boundary condition. y = f Ts, Pw ) in = Bn i ; ELA ) i ( i i ( i L = L + i+1 i ( dl )i dt ( dl dt )i Output data: length variation of glacier terinus on flow line direction. Algorith: explicit forulation of Model and Runge-Kutta solutions Model calibration: validation of siulated results with real easureents. Future evaluation: assess glacier response in cliate change scenarios. Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 10

11 Minial Model on Careser glacier Careser glacier ( a.s.l.) - Ortles-Cevedale group Glacier features: - flat bedrock (slope 16%); - ainly exposed to the south; - no accuulation area; - exhibits rapid ass loss and fragentation; - ass-balance and ELA easureents have been carried out since Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 11

12 Minial Model on Careser glacier - 2 We identify in the east section: the 90% of the whole area of the glacier. The elaborations show the slow down of the front retreat since Around 2000 the tendency changes slope and the real values becoes parallel to siulated ones. Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 12

13 Minial Model on Careser glacier - 3 Year = CMIP5 Year = CSIRO Year = 2042 range [ ] PROTHEUS Year = CMIP5 Year = CSIRO Future projection on Careser glacier. L = 200 is the statistic threshold for the disappearance of the studied flow line. GCM [ ] CMIP5 enseble and CSIRO runs in two different Eission scenarios: RCP 4.5 & RCP 8.5. RCM [ ] Regional cliate odel PROTHEUS. Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 13

14 Minial Model on Rutor glacier Rutor glacier ( a.s.l.) Vallone di La Thuile (AO) Glacier features: - surface slope 22%; - ainly exposed to the north; - currently there are three ain flow line; - L Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 14

15 Minial Model on Rutor glacier - 2 We identify three different flow line, but only east and center region have a good dataset that allow the application of Minial Glacier Model coupling with Cliate Model input. The real values are the validation points coe fro GIS analysis by intersection between polygons and flow lines. Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 15

16 Minial Model on Rutor glacier - 3 Initial length (2004) Li = 4398,32 L = (3494, ,09) CMIP5 L = (3551, ,10) CSIRO Future projection on east flow line of Rutor glacier. The different RCP scenarios show a gap of length retreat at about 600. GCM [ ] CMIP5 enseble and CSIRO runs in two different Eission scenarios: RCP 4.5 & RCP 8.5. L = (3318, ,79) CMIP5 L = (3427, ,21) CSIRO Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 16

17 Minial Model on Rutor glacier - 4 Initial length (2004) Li = 4187,53 L = (2745, ,37) CMIP5 L = (2831, ,83) CSIRO Future projection on center flow line of Rutor glacier. The different RCP scenarios show a gap of length retreat at about 300. GCM [ ] CMIP5 enseble and CSIRO runs in two different Eission scenarios: RCP 4.5 & RCP 8.5. L = (2490, ,15) CMIP5 L = (2650, ,25) CSIRO Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 17

18 Conclusions and future developents CONCLUSIONS - Developent of Minial Model algorith to siulate glacier behavior into the past following cliate forcing on Bn and ELA. - Link with GIS analysis to apply spatial approach for the best evaluation of boundary condition and orphological data set. - After validation, we proceed to evaluate future fluctuation of glacier terinus, following cliate data by GCM or RCM. FUTURE DEVELOPMENTS - Iprove the error spreading. - Apply Minial Model on historical series of other glaciers to validate equations. - Apply Minial Model coupling with Global Cliate Model ensebles on eaningful survey of glaciers, to evaluate a retreat trends of entire GAR or specific areas. - Study the difference of response between the use of GCM and RCM on Minial Model. Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. 18

19 References Haeberli W., Hoelzle M. (2012): Application of inventory data for estiating characteristics of and regional cliate-change effects on ountain glaciers: a pilot study with the European Alps. Annals of Glaciol., 21, Haing R.W. (1986): Nuerical Methods for Scientists and Engineers, Unabridged Dover, republication of the 2nd edition published by McGraw-Hill 1973 Linsbauer A., Paul F., Haberli W. (2012): Modeling glacier thickness distribution and bed topography over entire ountain ranger with GlabTop: Application of fast and robust approach. Journal of Geo. Res., Vol. 117, F03007, 2012 Oerleans J. (2008): Minial Glacier Models. Igitur, Utrecht University, 90 pp., 2008 Paterson, W. (1994), The Physics of Glaciers, Pergaon, Tarrytown, N.Y. Carturan L. and Seppi R. (2007): Recent ass balance results and orphological evolution of Careser Glacier (Central Alps). Geogr. Fìs. Din. Quat., 30(1), Carturan L. and Seppi R. (2009): Coparison of current behaviour of three glaciers in western Trentino (Italian Alps). In Epitoe: Geoitalia 2009, Settio Foru Italiano di Scienze della Terra, 9 11 Septeber 2009, Riini, Italy, Vol. 3. Federazione Italiana di Scienze della Terra, 298 Carturan L., Dalla Fontana G. and Cazorzi F. (2009a): The ass balance of La Mare Glacier (Ortles-Cevedale, Italian Alps) fro 2003 to In Epitoe: Geoitalia 2009, Settio Foru Italiano di Scienze della Terra, 9 11 Septeber 2009, Riini, Italy, Vol. 3. Federazione Italiana di Scienze della Terra, 298 Carturan L., Cazorzi F. and Dalla Fontana G. (2012): Distributed ass-balance odelling on two neighbouring glaciers in Ortles-Cevedale, Italy, fro 2004 to Journal of Glaciol., Vol. 58, No. 209, 2012 Carturan, L., Baroni, C., Becker, M., Bellin, A., Cainelli, O., Carton, A. & Seppi, R. (2013). Decay of a long-ter onitored glacier: the Careser glacier (Ortles-Cevedale, European Alps). The Cryosphere, 7(6), General Assebly of the United Nation: Sustainable ountain developent, UN A/Res/62/196, Knutti R., Masson D., and Gettelan A. (2013): Cliate odel genealogy: Generation CMIP5 and how we got there. Geophy. Res. Lett. Jeffrey S., Rotstayn L., Collier M., Dravitzki S., Haalainen C., Moeseneder C., Wong K. and Syktus J. (2012): Australia s CMIP5 subission using the CSIRO-Mk3.6 odel. Austr. Meteo. Ocean. Journ. V Taylor K. E., Stouffer R. J. and Meehl G.A. (2012): An Overview of CMIP5 and the Experient Design. A. Meteo. Soc. DOI:

20 Minial Model: solution ethod dl dt t n+1 = = f t { L, } n P j + t The estiation of solution is obtained by discretization of continuous proble, to approxiate the real results with nuerical ethod. Runge-Kutta ethod: one of the ost refined ethods of integrating ordinary differential equations. We use this ethod to solve Minial Model equations, considering final length as input of new cycle. Moretti M., Mattavelli M., DeAicis M., Maggi V. & Provenzale A. xx