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Implementing a travel time model for the Adige River: the case of Jgrass-NewAGE

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I contains 2015, dec 14 presentation give at AGU Fall Meeting in S. Francisco and covers our research on travel time distribution

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Implementing a travel time model for the Adige River: the case of Jgrass-NewAGE

  1. 1. Implementing a travel time model for the Adige River: 
 the case of NewAGE-JGrass Bancheri M., Abera, W., Rigon R., Formetta G., O.David and Serafin F.
  2. 2. Outline •  Introduction: GIUH theories, limitations and evolution; •  Travel times as random variables; •  NewAge-JGrass & Adige River; •  Preliminary results: Posina River; •  Conclusions.
  3. 3. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE Introduction: Geomorphological Instantaneous Unit Hydrograph Rodriguez-Iturbe & Valdès, 1979 Rinaldo et al., 1991 D’Odorico & Rigon, 2003 3-18 Rigon et al. "The geomorphological unit hydrograph from a historical‐critical perspective." Earth Surface Processes and Landforms (2015).
  4. 4. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE But… •  These theories are event-based and time invariant •  Do not include evapotranspiration therefore… We should consider a new modelling approach, which takes into account: •  The traditional theory of the hydrological response •  Tracers measurements and their transport •  The modelling of all the elements of the hydrological cycle, at various scale . Introduction: limitations 4-18
  5. 5. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE Introduction: a novel approach The novel approach of the GIUH must then be based on a more general theory, which has been presented in various paper: Benettin et al., 2013 Harman, 2015 Botter at al., 2011 5-18
  6. 6. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE -  No deep losses and recharge t e r m s s u p p l y i n g d e e p groundwater; Travel time: the time water takes to travel across a catchment Travel times as random variables Travel time T Residence time Tr Life expectancy Le Injection time Exit time ιt Time 6-18 ⌧
  7. 7. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE The (bulk) water budget of the control volume is: We can decompose all the previous quantities in their sub-volumes, i.e.: And obtain the age-ranked water budget (Harman, 2015): dS(t) dt = J(t) Q(t) ET(t) S(t) = Z t 0 s(t, ⌧)d⌧ ds(t, ⌧) dt = j(t, ⌧) q(t, ⌧) aeT (t, ⌧) Time-ranked water budgets 7-18 Travel time T Residence time Tr Life expectancy Le Injection time Exit time ιt Time ⌧
  8. 8. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE Based on the definitions above, it is easy to define the probability densities of residence times: And analogously: Backward probabilities 8-18 Travel time T Residence time Tr Life expectancy Le Injection time Exit time ιt Time ⌧ p(Tr|t) ⌘ p(t ⌧|t) := s(t, ⌧) S(t) [T 1 ] pQ(t ⌧|t) pET (t ⌧|t)
  9. 9. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE After the above definitions, the age-ranked equation can be rewritten as: But we need further assumptions for each of the outputs: d dt S(t)p(Tr|t) = J(t) (t ⌧) Backward probabilities 9-18 Travel time T Residence time Tr Life expectancy Le Injection time Exit time ιt Time ⌧ Q(t)pQ(t ⌧|t) AEt(t)pET (t ⌧|t) pQ(t ⌧|t) := !Q(t, ⌧)p(Tr|t)
  10. 10. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE Thanks to Niemi’s relationship (Niemi, 1977) we can connect the backward and forward pdfs: Where: We can also define: Forward probabilities 10-18 Travel time T Residence time Tr Life expectancy Le Injection time Exit time ιt Time ⌧ pQ(t ⌧|⌧) := q(t, ⌧) ⇥(⌧)J(⌧) ⇥(⌧) := lim t!1 ⇥(t, ⌧) = lim t!1 VQ(t, ⌧) VQ(t, ⌧) + VET (t, ⌧) Q(t)pQ(t ⌧|t) = ⇥(⌧)pQ(t ⌧|⌧)J(⌧)
  11. 11. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE Life expectancy 11-18 Travel time T Residence time Tr Life expectancy Le Injection time Exit time ιt Time ⌧ Eventually, we can consider the life expectancy pdfs: since: T = (t ⌧) | {z } Tr + (◆ t) | {z } Le pQ(t ⌧|t) = p(Tr|t) ⇤ p◆(◆ t|t)
  12. 12. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE Even in the new formalism we can think the sub-catchment as a part of the system : Q(t) = A X 2 p (Je ⇤ p 1 ⇤ · ⇤ p ⌦ )(t) 12-18From one to n HRUs
  13. 13. Monitoring points Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE NewAge-JGrass & Adige River Adige River- Italy A = 12200km2 Geomorphological model setup Meteorological interpolation tools Energy balance Evapotranspiration Runoff production and Snow Melting Channel routing Automatic calibration uDig-Jgrasstools-Horton Machine GEOSTATISTICS Kriging DETERMNISTICS IDW,JAMI SHORTWAVE (SWRB) Iqbal+Corripio model Decomposition LONGWAVE(LWRB) Brutsaert with 10 parametrizations Penmam-Monteith Priestley-Taylor Fao-Etp-model Hymod model Duffy model Snowmelt and SWE model Cuencas LUCA Particle swarm Dream Water Budget and Travel Time theory NewAge-JGrass Abstraction of the network and the parallel execution of the components for independent HRUs. 13-18 Average elevation
  14. 14. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE Preliminary results: Posina River-Italy Beta(↵, ) : prob(x|↵, ) = x↵ 1 (1 x) 1 B(↵, ) B(↵, ) = Z 1 0 t↵ 1 (1 t) 1 dt 14-18 T ω Uniform preference: α=1,β=1 1 T ω 1 Preference for new water α=0.5,β=1 T ω 1 Preference for old water α=3,β=1 0 5 10 15 20 1995 1996 1997 1998 1999 Rainfall[mm] Upper layer 0 50 100 150 1995 1996 1997 1998 1999 MeanTT[d] ω Preference for new water Uniform preference Preference for old water
  15. 15. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE Beta(↵, ) : prob(x|↵, ) = x↵ 1 (1 x) 1 B(↵, ) B(↵, ) = Z 1 0 t↵ 1 (1 t) 1 dt 15-18 T ω Uniform preference: α=1,β=1 1 T ω 1 Preference for new water α=0.5,β=1 T ω 1 Preference for old water α=3,β=1 Preliminary results: Posina River-Italy 0 5 10 15 20 1995 1996 1997 1998 1999 Rainfall[mm] Upper layer 0 50 100 150 1995 1996 1997 1998 1999 MeanTT[d] ω Preference for new water Uniform preference Preference for old water 0.0 0.2 0.4 0.6 1995 1996 1997 1998 1999 Drainage[mm] Lower layer 0 100 200 300 1995 1996 1997 1998 1999 MeanTT[d] ω Preference for new water Uniform preference Preference for old water
  16. 16. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE Conclusions To sum up, the goals of the work are: •  Reformulate the equations for the age-ranked storages and fluxes; •  Rederive the relationship between backward and forward travel time distributions; •  Provide a tool, integrated in the hydrological model NewAge- JGrass, for easy and fast computation of the travel times for a catchment of any size. 16-18
  17. 17. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE Conclusions Further details: Theory: http://www.slideshare.net/CoupledHydrologicalModeling/adige-modelling http://www.slideshare.net/GEOFRAMEcafe/giuh2020 Components: https://github.com/formeppe/NewAge-JGrass https://github.com/geoframecomponents General info: http://geoframe.blogspot.com 17-18
  18. 18. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE Thank you! Thank you! 18-18
  19. 19. Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE References -  Benettin, Paolo. "Catchment transport and travel time distributions: theoretical developments and applications." (2015). -  Botter, G., E. Bertuzzo, and A. Rinaldo (2011), Catchment residence and travel time distributions: The master equation, GEOPHYSICAL RESEARCH LETTERS, VOL. 38, L11403, doi:10.1029/2011GL047666 -  D'Odorico, Paolo, and Riccardo Rigon. "Hillslope and channel contributions to the hydrologic response." Water resources research 39.5 (2003). -  Calabrese, Salvatore, and Amilcare Porporato. "Linking age, survival, and transit time distributions." Water Resources Research (2015). -  Formetta G., Antonello A., Franceschi S., David O., Rigon R., "The informatics of the hydrological modelling system JGrass-NewAge" in 2012 International Congress on Environmental Modelling and Software Managing Resources of a Limited Planet, Sixth Biennial Meeting, Manno, Swizerland: iEMSs, 2012.Atti di: 6th 2012 International Congress on Environmental Modelling and Software Managing Resources of a Limited Planet, Leipzig, Germany, 1-5 July 2012. -  Harman, Ciaran J. "Time‐variable transit time distributions and transport: Theory and application to storage‐dependent transport of chloride in a watershed." Water Resources Research 51.1 (2015): 1-30. -  Niemi, Antti J. "Residence time distributions of variable flow processes." The International Journal of Applied Radiation and Isotopes 28.10 (1977): 855-860. -  Rigon, Riccardo, et al. "The geomorphological unit hydrograph from a historical‐critical perspective." Earth Surface Processes and Landforms (2015). -  Rinaldo, A. and Rodriguez-Iturbe, I., Geomorphological theory of the hydrologic response, Hydrol Proc., vol 10, 803-829, 1996 -  RODRiGUEZ-lTURBE, I. G. N. A. C. I. O., and Juan B. Valdes. "The geomorphologic structure of hydrologic response." Water resources research 15.6 (1979): 1409-1420.

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