Implementing a travel time model for the Adige River: the case of Jgrass-NewAGE
-
Upload
riccardo-rigon -
Category
Education
-
view
323 -
download
0
Transcript of Implementing a travel time model for the Adige River: the case of Jgrass-NewAGE
Implementing a travel time model for the Adige River:
the case of NewAGE-JGrassBancheri M., Abera, W., Rigon R., Formetta G., O.David and Serafin F.
Outline
• Introduction: GIUH theories, limitations and evolution;
• Travel times as random variables;
• NewAge-JGrass & Adige River;
• Preliminary results: Posina River;
• Conclusions.
Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE
Introduction: Geomorphological Instantaneous Unit HydrographRodriguez-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).
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
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
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
⌧
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
0s(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⌧
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)
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
dtS(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)
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(⌧)
⇥(⌧) := limt!1
⇥(t, ⌧) = limt!1
VQ(t, ⌧)
VQ(t, ⌧) + VET (t, ⌧)
Q(t)pQ(t� ⌧ |t) = ⇥(⌧)pQ(t� ⌧ |⌧)J(⌧)
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)
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) = AX
�2�
p� (Je ⇤ p�1 ⇤ · ⇤ p�⌦)(t)
12-18From one to n HRUs
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
DETERMNISTICSIDW,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
Geomorphological model setup
Meteorological interpolation tools
Energy balance
Evapotranspiration
Runoff production and Snow Melting
Channel routing
Automatic calibration
uDig-Jgrasstools-Horton Machine
GEOSTATISTICS Kriging
DETERMNISTICSIDW,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
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
0t↵�1(1� t)��1dt
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
Mea
n TT
[d]
ω Preference for new water Uniform preference Preference for old water
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
0t↵�1(1� t)��1dt
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
Mea
n TT
[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
Dra
inag
e [m
m]
Lower layer
0
100
200
300
1995 1996 1997 1998 1999
Mea
n TT
[d]
ω Preference for new water Uniform preference Preference for old water
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
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
Bancheri et al.: Implementing a travel time model for the entire Adige River: the case of JGrass-NewAGE
Thank you!
Thank you!
18-18
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.