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).


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


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


-  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

⌧


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


Injection time

Exit time ιt

Time⌧


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


Injection time

Exit time ιt

Time⌧

p(Tr|t) ⌘ p(t� ⌧ |t) := s(t, ⌧)

S(t)[T�1]

pQ(t� ⌧ |t)

pET (t� ⌧ |t)


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


Injection time

Exit time ιt

Time⌧

�Q(t)pQ(t� ⌧ |t)�AEt(t)pET (t� ⌧ |t)

pQ(t� ⌧ |t) := !Q(t, ⌧)p(Tr|t)


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


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(⌧)


Life expectancy 11-18

Travel time T


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)


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


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


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


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]


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]



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


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


Thank you!

Thank you!

18-18


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