GEOtop 2.0


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This is the presentation (INVITED) for the AGU 2013 Session on High resolution modelling (Dec 10, 2013, session H21M)

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GEOtop 2.0

  1. 1. Gino Severini, Dancer+Sailing+Sea,= Bouquet, 1950 GEOtop 2.0: simulating the combined energy and water balance S. Endrizzi, S. Gruber, M. Dall’Amico and R. Rigon Dec. 10 2013 - AGU Fall Meeting S. Francisco
  2. 2. It is difficult to avoid the impression that a miracle confronts us here, quite comparable in its striking nature to the miracle that the human mind can string a thousand arguments together without getting itself into contradictions, or to the two miracles of laws of nature and of the human mind's capacity to divine them. The inconceivable effectiveness of mathematics in natural sciences. E. Wigner
  3. 3. The basics A theory that describes whole hydrology ? The miracle is hard to see in Hydrology where heterogeneity mixes with complexity, and phenomena across several scales. !3
  4. 4. Catchment hydrology At the catchment scale: ancestors Freeze and Harlan, Jour. of Hydrology, 1969 SHE, Abbot et al. 1986 Horton Overland Flow Dunne Saturation Overland Flow Surface Layer Unsaturated Layer Saturated Layer:! Modified from Abbot et al., 1986 !4 Endrizzi et al.
  5. 5. Endrizzi et al. tRIBS, Ivanov et al, 2004 Catflow, Zehe et al., 2001 Hydrogeosphere, Therrien and Sudicki, 1996 InHM, VanderKwaak, and Loague, 2001 Parflow, Asby an Falgout, 1996 DHSVM, Wigmosta et al., 1994 Cathy, Paniconi and Putti, 1994 Rigon et al, 2006; Bertoldi et al., 2006 Water mass budget In What GEOtop is different ? !5
  6. 6. Endrizzi et al. CLM, Dai et al., 2003 SEWAB, Megelkamp et al., 1999 LSM, Bonan, 1996 Noah LSM, Chen et al., 1996, BATS, Dickinson et al., 1986, Rigon et al, 2006 Energy budget In What GEOtop is different ? !6
  7. 7. Snow and freezing soil: see also me on Thursday talk Snow height, density, temperature) Zanotti et al, 2004; Dall’Amico et al., 2011 Endrizzi et al. Alpine3D, Lenhing et al., 2006 Freezing Soil - Permafrost CROCUS, Brun et al., 1992 In What GEOtop is different ? !7
  8. 8. To study the interactions all is modelled together Many models do the water budget Many models do the energy budget Many model do the snow budget How many models do the whole stuff together ? Obviously is also matter of the degree of physical simplification (i.e. the equations) used. !8 Endrizzi et al.
  9. 9. Endrizzi et al. see also Endrizzi et al. !9
  10. 10. Equations (Monin - Obukov) Snow metamorphism (with some assumptions) Energy budget Radiation Flux-gradient relationship Double layer vegetation Diffusive approximation to shallow water equation Richards equation + van Genuchten parameterization + Mualem derived conductivity !10 Endrizzi et al.
  11. 11. Equations <latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKBcQLKBvoGYCBAibDEMpQZoACoHJDdElMRqiRnpmeQSBCG4e0koahuYNHQGhyStfknfsPQoQZGaHyggyo4BQAVIE48g==</latexit> <latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKBcQLKBvoGYCBAibDEMpQZoACoHJDdElMRqiRnpmeQSBCG4e0koahuYNHQGhyStfknfsPQoQZGaHyggyo4BQAVIE48g==</latexit> <latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKBcQLKBvoGYCBAibDEMpQZoACoHJDdElMRqiRnpmeQSBCG4e0koahuYNHQGhyStfknfsPQoQZGaHyggyo4BQAVIE48g==</latexit> Endrizzi et al. <latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKBcQLKBvoGYCBAibDEMpQZoACoHJDdElMRqiRnpmeQSBCG4e0koahuYNHQGhyStfknfsPQoQZGaHyggyo4BQAVIE48g==</latexit> <latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKBcQLKBvoGYCBAibDEMpQZoACoHJDdElMRqiRnpmeQSBCG4e0koahuYNHQGhyStfknfsPQoQZGaHyggyo4BQAVIE48g==</latexit> <latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKBcQLKBvoGYCBAibDEMpQZoACoHJDdElMRqiRnpmeQSBCG4e0koahuYNHQGhyStfknfsPQoQZGaHyggyo4BQAVIE48g==</latexit> Se = [1 + ( C(⇥) := ⇤ w () Se := ⇤⇥ ~ ~ Jv = K(✓w )r h ⇧ ⇤ K( w ) = Ks Se 1 ⇥) )] m w r ⇥s n r (1 Se ) 1/m ⇥ m ⌅2 !11
  12. 12. Guidelines The “ What Else ?” Principle I said: “Why to use Richards’ equation … do they work at hillslope scale ?” M.P. said: “What else do you want to use (Topmodel) ? ” I went home, and after comparing the alternatives, I decided to use Richards equations ?* The same story applies more or less to the other processes. * See also Cordano and Rigon, 2008, to see that alternatives are indeed often simplifications of RE. See also Endrizzi et al. !12
  13. 13. Guidelines The Occam’s Rasor ? “Lex parsimoniae" It states that among competing hypotheses, the hypothesis with the fewest assumptions should be selected We all either try to formulate laws at one scale by guessing them, using the available knowledge, or try to deduce them by a mix of algebraic treatment of the basic laws of mass, energy and momentum conservation, and educated simplifications. !13 Endrizzi et al.
  14. 14. Is there ! It is Open source Is it feasible ? Is it usable ? Does it works ? We did it ! !14 Endrizzi et al.
  15. 15. Better wrong than “not even wrong” It is useful ? e.g Beven, 2000, 2001 (for instance … but also many of my closest friends) criticized this approach of making models Yes, it is! !15 R. Rigon
  16. 16. A mountain catchment of applications <latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKBcQLKBvoGYCBAibDEMpQZoACoHJDdElMRqiRnpmeQSBCG4e0koahuYNHQGhyStfknfsPQoQZGaHyggyo4BQAVIE48g==</latexit> <latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLA High Resolution Joint Water and Energy Balance Modeling and Observation in a Prealpine Environment by Hingerl, L., Kunstmann, H., Mauder, M., Wagner, S. and Rigon R., submitted to Journal of Hydrometeorology 2013 !16 Endrizzi et al.
  17. 17. A mountain catchment Closing the hydrological budget Hingerl et al., 2013 after (Mauder et al., 2006) Root river in Germany - TERENO experiment Figure 2: The catchment of the Rott with the position of the discharge gauge in Raisting, the TERENO-observatory “Fendt” and the climate stations used for the meteorologic Zacharias et al., 2011 - Endrizzi et al. forcing in the model. !17
  18. 18. A mountain catchment 15 10 0 5 Discharge [m³/s] 20 30 measured simulated 40 Precipitation [mm] Hingerl et al., 2013 25 20 10 0 30 “Traditional approach” by calibrating discharges 11.2009 01.2010 03.2010 05.2010 07.2010 09.2010 11.2010 Figure 5: Simulated and measured discharge at the gauge in Raisting for the hydrologic 25 20 Endrizzi et al. 10 0 30 year 2010. measured !18
  19. 19. Hingerl et al., 2013 Energy fluxes - NO calibration !19 Endrizzi et al.
  20. 20. 0 10 20 simulated 6cm measured 6cm −10 Soil temperature [C°] Temperature is among the prognostic variables 03.2011 05.2011 07.2011 09.2011 11.2011 03.2011 05.2011 07.2011 09.2011 11.2011 03.2011 05.2011 07.2011 09.2011 11.2011 20 10 0 −10 Soil temperature [C°] 01.2011 simulated 21cm measured 25cm 11.2010 01.2011 0 10 20 simulated 51cm measured 50cm −10 Soil temperature [C°] Hingerl et al., 2013 11.2010 11.2010 01.2011 Fig. 9. Simulated soil temperatures for di↵erent depths compared to measurements from the TERENO prealpine observatory Fendt. !20 Endrizzi et al.
  21. 21. We close the budget a) Hingerl et al., 2013 Netto shortwave radiation Netto longwave radiation Sensible heat flux Latent heat flux Soil heat flux c) This is the land-use types coniferous forest (a), and settlements Energy balance forconiferous forest. But there is also pasture pasture (b) and set- !21 c) showingal. Endrizzi et absolute monthly means of simulated energy fluxes and the longwave
  22. 22. Small mountain catchment ecohydrology of applications <latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKBcQLKBvoGYCBAibDEMpQZoACoHJDdElMRqiRnpmeQSBCG4e0koahuYNHQGhyStfknfsPQoQZGaHyggyo4BQAVIE48g==</latexit> <latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKBc Modeling the variability of snow, evapotranspiration and soil moisture along inner alpine elevation gradient   Della Chiesa, S., Bertoldi, G., Niedrist, Obojes, .G., Albertson, J. D., Wohlfahrt,G., Tappeiner U. X - 40 DELLA CHIESA ET AL.: ELEVATION GRADIENT GRASSLAND DRY ALPINE VALLEY Figure 1. Endrizzi et al. Study area is a side slope in the upper Vinschgau watershed in South Tyrol, Italy !22
  23. 23. Small mountain catchment ecohydrology Well, it is not my merit but the guys here added (off-line) a GRADIENT GRASSLAND DRY ALPINE VALLEY DELLA CHIESA ET AL.: ELEVATION dynamic vegetation model and study alpine X - 43 There are effects of temperature and precipitation quantity and phase varying with height, of variable snow cover, climate interannual variability … There is irrigation. ET at 1500 m Endrizzi et al. 450 400 ET cumulative [mm] Della Chiesa et al., 2013 grassland along a transect at varying elevation from 1000 m to 2000 m ET obs ET mod 350 300 250 200 150 100 50 0 Apr/11 May Jun Jul Aug Sep Oct !23
  24. 24. Small mountain catchment ecohydrology Snow Water Equivalent at different elevations Della Chiesa et al., 2013 DELLA CHIESA ET AL.: ELEVATION GRADIENT GRASSLAND DRY ALPINE VALLEY X - 45 What can we observe ? o di↵erent years and elevation gradient on SWE a), cumulative ET ibution ✓ 5cm depth c). The black dashed line represents to water SWC results refer to the snow free period only. !24 Endrizzi et6. E↵ects of the two di↵erent years and elevation gradient on SWE a), cumulative ET Figure al.
  25. 25. Small mountain catchment ecohydrology Della Chiesa et al., 2013 This reflects in different soil moisture distributions Figure 6. E↵ects of the two di↵erent years and elevation gradient on SWE a), cumulative ET differentfrequency distribution ✓ 5cm depth c). The black dashed line represents to water at different elevations and different years b) and SWC limitation point. Notice that SWC results refer to the snow free period only. This has influences on the ecosystems. Details in the paper !25 Endrizzi et al.
  26. 26. So far Could have been used another model instead of GEOtop <latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8 Certainly we needed a model with all the hydrological components simulated. A model where lateral subsurface and surface redistribution is accurately described. A model were snow is modelled. A model were temperature is an explicit prognostic variable… SO … !26 Endrizzi et al.
  27. 27. Going to a conclusion: are the equations right ? (Monin - Obukov) Snow metamorphism (with some assumptions) Energy budget Radiation Flux-gradient relationship Double layer vegetation Diffusive approximation to shallow water Richards equation + van Genuchten parameterization + Mualem derived conductivity !27 Endrizzi et al.
  28. 28. Going to a conclusion: what happens at the interfaces Snow-ABL interactions Vegetation-ABL Surface Water-Groundwater !28 Endrizzi et al.
  29. 29. To sum up our position Some misconceptions about distributed modelling “Distributed model are overparameterised” “Model parameters cannot be identified” “These models require too high computational time” “They cannot be used for ungauged basins” “Reality is simpler than that (and we learn just from simple models)” not completely wrong but not completely true. eat the apple before talking! see also Endrizzi et al. !29
  30. 30. Looking at larger sites !30 Dall’Amico et al.
  31. 31. And operationally Snow height by Mountain-eering More details on the cryospheric processes in session C44B 02 - On thursday Dall’Amico et al. !31
  32. 32. Going ahead Several options for going ahead Making of GEOtop a library Embedding in Object Modeling system vs. 3 Parallelizing it Making easier its use Develop the R and Java (uDig) interfaces Data assimilation and real time !32 Endrizzi et al.
  33. 33. Going ahead Process-wise Re-think the processes schemes Change them, without loosing the old work Test, Test, Test Create a community Actually it includes 4 core research groups: Quebec (was Zurich), Trento (CUDAM and Mountain-eering), Bozen, KIT (Garmisch) and some group !33 Endrizzi et al.
  34. 34. Splitting GEOtop of applications <latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKBcQLKBvoGYCBAibDEMpQZoACoHJDdElMRqiRnpmeQSBCG4e0koahuYNHQGhyStfknfsPQoQZGaHyggyo4BQAVIE48g==</latexit> <latexit sha1_base64="tYHCApFiY8slQcKMwQxwGacE74A=">AAAA+3icSyrIySwuMTC4ycjEzMLKxs7BycXNw8XFy8cvEFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKBcQLKBvoGYCBAibDEMpQZoACoHJDdElMRqiRnpmeQSBCG4e0ko So can we go on ? Formetta et al. to be submitted to EM&S, 2013 !34 Endrizzi et al.
  35. 35. and embedding it in OMS Formetta et al., 2013 Towards GEOtop 3.0 OMS v3 - David et al., 2013 Endrizzi et al. !35
  36. 36. and embedding it in OMS Formetta et al., 2013 Drake river soil moisture Formetta et al. to be submitted to EM&S, 2013 Endrizzi et al. !36
  37. 37. and embedding it in OMS Formetta et al., 2013 Endrizzi et al. !37
  38. 38. presentation available at about Ulrici, 2000 ? Thank you For giving information about hydrology and receiving news about positions, conferences, session, subscribe to Riccardo Rigon !38
  39. 39. Soil Moisture, Water Setention Curves, (Landslides,) and all that Another Application A lab case !39 Rigon et al.
  40. 40. GEOtop in the lab Thanks to Neaples Group: the IWL3 experiment R. Greco1, L. Comegna1, E. Damiano1, A. Guida1,2, L. Olivares1, and L. Picarelli1 1Dipartimento di Ingegneria Civile Design Edilizia e Ambiente, Seconda Università di Napoli, via Roma 29, 81031 Aversa (CE), Italy
 2Centro Euro-Mediterraneo sui Cambiamenti Climatici, via Maiorise, Capua (CE) 81043, Italy !40 Rigon et al.
  41. 41. t GEOtop in the lab Soil Thickness (cm) Slope Length (cm) Initial porosity n0 Rainfall intensity (mm/h) Initial mean s uction (kPa) Duration of test (min) 10.0 100 0.75 55 17.5 36 10.0 120 0.76 56 41.0 30 The inclination of the slope is 40°. ! The test are carried out with constant and spatially homogeneous rainfall intensity. Several devices (tensiometer, pore pressure transducer, TDR and laser !41 Rigon et al.
  42. 42. Analysis of the data Suctions and pressures failure first displacement first displacement . -5 cm ! ! factor of safety here is 1.2 -10 cm !42 Rigon et al.
  43. 43. Analysis of the data Water Content !43 Rigon et al.
  44. 44. Analysis of the data Water Content talks Hydraulic conductivity was measured in the lab. The value given was around one order of magnitude less than the artificial rainfall So we expect an Hortonian flux: saturation at the top and movement downward. Which we do not have! !44 Rigon et al.
  45. 45. Analysis of the data So we expect an Hortonian flux: saturation at the top and movement downward. red line is more ore less what we expect just after the beginning of irrigation in a Hortonian interpretation of infiltration Rigon et al. !45
  46. 46. Questions What about the Darcy scale here ? !46 Rigon et al.
  47. 47. Analysis of the data Water Content talks Is irrigation really stationary ? What happens after the 28th minute ? Lateral flow triggers ? !47 Rigon et al.
  48. 48. Let’s go ! Two hydraulic conductivities One hypothesis we did is that, despite the homogeneity of the preparation of the experiment, hydraulic conductivity (at saturation) at the bottom is different from hydraulic conductivity at the top of the mock-up. Due to packing of particles ? Due to some unavoidable imperfection in preparation ? Due to avoidable imperfection of the preparation ? What else ? !48 Rigon et al.
  49. 49. Which parameters ? Suction talks Both suction and water content data were used to calibrate van Genuchten parameters. Also the hydraulic conductivity is among Se = [1 + ( Se := n ⇥) )] m w r ⇥s r Also hydraulic conductivity at saturation is a calibration parameter K( w) = Ks ⇧ Se ⇤ 1 (1 Se ) 1/m ⇥ m ⌅2 !49 Rigon et al.
  50. 50. Which parameters ? Calibrated Parameters alfa 0.052 n m 1.805 0.445983 Ksat_layer superficiale (0-5cm) = 0.178 mm/s Ksat_layer di fondo (5-10cm) = 0.117 mm/s !50 Endrizzi et al.
  51. 51. Suctions !51 Rigon et al.
  52. 52. Water content Averaging does not get the right result even if water contents are reproduced fairly well until the 21th minute Rigon et al. !52
  53. 53. Who says that we do not learn from comps models ? Lesson Learned The relation assumed between Soil Water Retention Curves and hydraulic conductivity could not be correct : ! • does van Genuchten parameterisation needs to be substituted ? • does Mualem theory really works ? • Well, in some some the model does not work. However, in the science perspective, certainly it does ! !53 Rigon et al.
  54. 54. The Bibliography Journal Papers Bertoldi, G., Notarnicola, C., Leitinger, G., Endrizzi, S., Della Chiesa, S., Zebisch, M., & Tappeiner, U. (2010). Topographical and ecohydrological controls on land surface temperature in an Alpine catchment. Ecohydrology, 3(doi:10.1002/eco.129), 189–204. ! Bertoldi, G., Rigon, R., & Over, T. M. (2006). Impact of Watershed Geomorphic Characteristics on the Energy and Water Budgets. Journal of Hydrometeorology,, 7, 389–403. ! Bertoldi G.; Della Chiesa, S; Notarnicola, C.; Pasolli, L.; Niedrist, G; Tappeiner, U. (2013), Estimation of soil moisture patterns in mountain grasslands by means of SAR RADARSAT 2 images and hydrological modeling, submitted to Journal of Hydrology Dall’Amico, M.; Endrizzi, S., Gruber, S; and Rigon, R. (2011), An energyconserving model of freezing variably-saturated soil, The Cryosphere. Della Chiesa, S.; Bertoldi, G.; Niedrist, Obojes, N.G.; Albertson, J. D.; Wohlfahrt,G.; Tappeiner (2013), Modeling the variability of snow, evapotranspiration and soil moisture along inner alpine elevation gradient , submitted to Ecohydrology. ! Rigon! et al. !54
  55. 55. The Bibliography Journal Papers Endrizzi S. and Marsh P. Observations and modeling of turbulent fluxes during melt at the shrub-tundra transition zone 1: point scale variations, (2010) Hydrology Research Endrizzi S., Gruber S., Investigating the effects of lateral water flow on spatial patterns of ground temperature, depth of thaw and ice content, Peer reviewed proceedings of the 10th International Conference on Permafrost, 25–29 June 2012, Salekhard, Russia, 91–96, 2012 Endrizzi S., Gruber S., Dall’Amico M., Rigon R., GEOtop 2.0.: Simulating the combined energy and water balance at and below the land surface accounting for soil freezing, snow cover and terrain effects, Geosci. Model Dev., 2013 (submitted) Fiddes J., Endrizzi S., Gruber S., Large area land surface simulations in heterogeneous terrain driven by global datasets: a permafrost test case, (2013), The Cryosphere (submitted)    Formetta, G., Rigon R., David, O., Green, T. R., Capparelli, G. (2013), Integration of a spatial hydrological model (GEOtop) into the Object Modeling System (OMS), To be submitted to EM&S      ! ! Rigon et al. !55
  56. 56. The Bibliography Journal Papers  Gubler S., Endrizzi S., Gruber S., Purves R. S., Sensitivity and uncertainty of modeled ground temperatures and related variables in mountain environments, Geosci. Model Dev., 6, 1319–1336, 2013. ! Gebremichael, M., Rigon, R., Bertoldi, G., & Over, T. M. (2009). On the scaling characteristics of observed and simulated spatial soil moisture fields, Nonlin. Processes Geophys., 16, 141–150. ! Hingerl L., Kunstmann H., Mauder M., Wagner S., Rigon R. (2013), High Resolution Joint Water and Energy Balance Modeling and Observation in a Prealpine Environment, 2013, submitted to Journal of Hydrometeorology. ! Rigon, R., Bertoldi, G., & Over, T. M. (2006). GEOtop: A Distributed Hydrological Model with Coupled Water and Energy Budgets. Journal of Hydrometeorology, 7, 371–388. ! ! Rigon et al. !56
  57. 57. The Bibliography Journal Papers Simoni, S., Zanotti, F., Bertoldi, G., & Rigon, R. (2007). Modelling the probability of occurrence of shallow landslides and channelized debris flows using GEOtop-FS. Hydrological Processes, doi: 10.10. ! Zanotti, F., Endrizzi, S., Bertoldi, G., & Rigon, R. (2004). The GEOtop snow module. Hydrol. Proc., 18, 3667–3679. DOI:10.1002/hyp.5794. ! ! ! ! !57 Rigon et al.
  58. 58. Epilogue A fool with a tool is still a fool !58 Rigon et al.