A travel time model for estimating the water budget of complex catchments

A travel time model for water budget of complex catchments

Candidate: Supervisors: Marialaura Bancheri Prof. Riccardo Rigon Matr.: 169091 Eng. Giuseppe Formetta

Doctoral School in Civil, Environmental and Mechanical Engineering - 29°Cycle

A travel time model for water budget of complex catchments

Getting the right answers for the right reasons: toward many

“embedded” reservoirs.

Age-rankedhydrologicalbudgetsandatravel6medescrip6onofcatchment

hydrology

JGrass-NewAge: a replicable

hydrological model

Bancheri M., A travel time model for the water budgets of complex catchments

Overview

Travel time T

Residence time Tr Life expectancy Le

Injection time tin

Exit time tex

tTime

Travel time: the time a water particle takes to travel across a catchment

T = (t� tin

)| {z }Tr

+(tex

� t)| {z }Le


Travel times as random variables

dS(t)

dt= J(t)�Q(t)�AET (t)

S(t) =

Z min(t,tp)

0s(t, tin)dtin AET (t) =

Z min(t,tp)

0aeT (t, tin)dtin

J(t) =

Z min(t,tp)

0j(t, tin)dtin Q(t) =

Z min(t,tp)

0q(t, tin)dtin

ds(t, tin)

dt= j(t, tin)� q(t, tin)� aeT (t, tin)


“Bulk” water budget VS “age-ranked” water budget

Backward probability conditioned on the actual time t

Travel time T

Exit time tex

tTimeInjection

time tin

Looks backward to tin

Travel time T

Exit time tex

tTimeInjection

time tin

Looks backward to tin


Backward probabilities

Time

Time

J(t)

S(t)

S(t)

Residence time

ttin

s(t, tin)Residence timebackward probabilities

pS(t� tin|t) :=s(t, tin)

S(t)[T�1]

Bancheri M. , A travel time model for the water budgets of complex catchments


Time

J(t) ttin

TimeResidence time

Q(t)

Q(t)

Travel timebackward probabilities

q(t, tin)

pQ(t� tin|t) :=q(t, tin)

Q(t)[T�1]



On the shape of the backward pdfs

Z min(t,tp)

0pQ(t� tin|t)dtin = 1

•  Time-variant

• 

•  not always true for other classical distributions , e.g., Z min(t,tp)

0

(t� tin)↵+1e(t�tin)

�

�↵�(↵)dtin 6= 1

8t⇤ 2 [0,min(t, tp)]



After the previous definitions and some proper substitutions, the water budget equation for the control volume can be written as:

d

dtS(t)pS(Tr|t) = J(t)�(t� tin)�Q(t)pQ(t� tin|t)�AEt(t)pET (t� tin|t)

obtaining a linear ordinary differential equation that can be solved exactly, once assigned the SAS values :

d

dtS(t)pS(Tr|t) = J(t)�(t� tin)�Q(t)

SASz }| {!Q(t, tin) pS(Tr|t)| {z }

pQ(t�tin|t)

�AEt(t)

SASz }| {!ET (t, tin) pS(Tr|t)| {z }

pET(t�tin|t)



The formalism developed is applicable, in principle to any substance, say indicated by a superscript i.

If the substance is diluted in water, it is usually treated as concentration in water, which is known once the concentration of the solute in input is known together with the backward probability:

d

dtSi(t)p(t� tin|t) = J i(t)piJ(t� tin|t)�Qi(t)!Q(t, tin)p(t� tin|t)

Ci(t) =

Z t

0p(t� tin|t)Ci

J(tin)dtin


Passive solute transport

Forward probability conditioned on the injection time tin

Travel time T

Exit time tex

tTimeInjection

time tin

Looks forward to t

Travel time T

Exit time tex

tTimeInjection

time tin

Looks forward to t


Forward probabilities

Thanks to Niemi’s relationship (Niemi, 1977) we can connect the backward and forward pdfs:

Where:

We can also define the forward travel time pdfs as:

pQ(t� tin|tin) :=q(t, tin)

⇥(tin)J(tin)

⇥(tin) := limt!1

⇥(t, tin) = limt!1

VQ(t, tin)

VQ(t, tin) + VET (t, tin)

Q(t)pQ(t� tin|t) = ⇥(tin)pQ(t� tin|tin)J(tin)


Forward probabilities


Getting the right answers for the right reasons: toward many “embedded” reservoirs.

R S

Ssnow

M

SCanopy

E

Tr

SRootzone

TRZ

SRunoff

TR

Re

SGroundwater

QR

QG

U

R S

Ssnow

M

SCanopy

E

Tr

SRootzone

TRZ

SRunoff

TR

Re

SGroundwater

QR

QG

U

The entire model is based on the assumption that the water budget has been solved and the fluxes are known.

Flux Expression

Tr(t) H(Scanopy

(t)� Imax

)ac

Scanopy

(t)

E(t)S

canopy

S

Canopy

max

(1� SCF )ETp

U(t) pSRootzone

TRZ

(t) S

Rootzone

S

Rootzone

max

ETp

Re

(t) Pmax

S

Rootzone

S

Rootzone

max

QR

(t) ARt

0 uW (ut� ⌧)↵(⌧)Tr

(⌧)d⌧

TR

(t)S

Runoff

S

Runoff

max

ETp

QG

(t) aSGroundwater

Process Component Geomorphological model setup Jgrastools

Meteorological interpolation tools KrigingIDW, JAMI

Energy balance Shortwave radiation balance

Clearness IndexLongwave radiation balance

Evapotranspiration Penmam-Monteith

Priestley-TaylorFao-Etp-model

Snow melting Rain-snow separationSnowmelt and SWE model

Runoff production Adige "Embedded" reservoirs

Travel times descriptionBackward travel times pdfsForward travel times pdfs

Solute trasport

Automatic calibration LUCA

Particle swarmDream

Geomorphological model setup

Meteorological interpolation tools

Energy balance

Evapotranspiration

Runoff production and Snow Melting

Travel times and passive solute transport

Automatic calibration

JGrass-NewAge


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

Adige model Snowmelt and SWE model

LUCA Particle swarm Dream

“Embedded”reservoirs

Backward travel times pdfs

Forward travel times pdfs

Solute transport Bancheri M. , A travel time model for the water budgets of complex catchments

JGrass-Newge: hydrological modelling with components

•  Rewrote according to the Java object orienting programming;

•  Increased their flexibility using design patterns;

•  Gradle integrated;

•  Travis CI integrated;

•  Documentation wrote to obtain a variety of modelling solutions;

•  OMS project example published for reproducing the results.

Source code Project examples

Community blog Documentation


Replicability of JGrass-NewAge

http://geoframe.blogspot.com


GEOframe: a system for doing hydrology by computer


Application to real cases: River Net3 for the Posina river case

14HRUsA=36km2

42HRUsA=112km2


Applications: Posina River

0

100

200

300

1995 1996 1997 1998 1999

Pre

cipi

tatio

n [m

m]

0

10

20

30

40

1995 1996 1997 1998 1999Time [h]

Dis

char

ge [m

3/s]

Measured

Simulated



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

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

10

20

1995 1996 1997 1998 1999Pre

cipi

tatio

n [m

m] Precipitation [mm]

010203040

1995 1996 1997 1998 1999

Mea

n TT

[d]

Canopy

0255075100

1995 1996 1997 1998 1999

Mea

n TT

[d]

Rootzone



0.25

0.50

0.75

1.00

Gen 1994 Apr 1994 Lug 1994 Ott 1994 Gen 1995Time

Par

titio

ning

coe

ffici

ent Θ

January

February

March

April

May

June

July

August

September

October

November

Jan 94 Apr 94 Jan 95 Oct 94 Jul 94



Further valida6ons of the travel 6mes theory are required,especiallytotestthesolutetransport.However,sincethelackofdata,itwasnotpossible6llnow.ThereforeIaskedtoadeferralof6monthsofthesubmissionofthethesis.Hopefullytheisotopedataarearrivingintheweeks…(maybewithSanta!)


Research outcomes

Journals paper

Rigon, R., Bancheri, M., Formetta, G., and de Lavenne, A. (2016) The geomorphological unit hydrograph from a historical-critical perspective. Earth Surf. Process. Landforms, 41: 27–37. doi: 10.1002/esp.3855.

Rigon R., Bancheri M., Green T., Age-ranked hydrological budgets and a travel time description of catchment hydrology, in discussion, HESSD, 2016

Formetta, G., Bancheri, M., David, O., and Rigon, R.: Performance of site-specific parameterizations of longwave radiation, Hydrol. Earth Syst. Sci., 20, 4641-4654, doi:10.5194/hess-20-4641-2016, 2016.

Bancheri, M., Serafin, F., Abera, W., Formetta, G., Rigon R., A well engineered implementation of Kriging tools in the Object Modelling Sisytem v.3., in preparation, 2016


Research outcomes

Conference abstract

M. Bancheri, G.Formetta, W.Abera, R. Rigon, Componenti della radiazione solare ad onda lunga: NewAge-LWRB, XXXIV Convegno nazionale di Idraulica e Costruzioni Idrauliche, 2014

W. Abera, G. Formetta, M.Bancheri, R.Rigon, 2014, The effect of spatial discretization on hydrological response, the case of Semi-distributed Hydrological modelling, AGU chapman conference, 2014.

M.Bancheri, W. Abera, G. Formetta, R.Rigon & F. Serafin , Implementing a Travel Time Model for the Entire River Adige: the Case on JGrass-NewAGE, American Geophysical Union, Fall Meeting 2015, abstract \#H11K-03.

M.Bancheri, Rigon, R., Formetta, G. & Green T.R., Implementing a travel time model for water and energy budgets of complex catchments: Theory, software, and preliminary application to the Posina River, Hydrology Days 2016.

Serafin, F., Bancheri M., Rigon R. and David O. "A Java binary tree data structure for environmental modelling." (2016), International Congress on Environmental Modelling and Software, 2016

Bancheri, M., et al. "Replicability of a modelling solution using NewAGE-JGrass.", International Congress on Environmental Modelling and Software, 2016

Bancheri M. and Rigon R. “Implementing a travel time model for the water budget of complex catchment: theory and preliminary results.” , XXXV Convegno nazionale di Idraulica e Costruzioni Idrauliche, 2016

Bancheri M., Formetta G., Serafin, F., and Rigon R. “Rasearch reproduciblity and replicability: the case of JGrass-NewAge”, XXXV Convegno nazionale di Idraulica e Costruzioni Idrauliche, 2016


Research outcomes

Organized meetings

- PhD Days di Ingegneria delle Acque 2015, University of Trento, Italy

- Hydrological Modeling with the Object Modelling System (OMS) International Summer Class Short Course, University of Trento, Italy, July 18-21, 2016

Teaching activity

- Supervision of undergraduates at Hydrology course A.A 2013-2014

- Supervision of undergraduates at Hydraulic Construction course A.A 2013-2014 - Supervision of undergraduates at Hydrology course A.A 2014-2015

- Supervision of undergraduates at Hydraulic Construction course A.A 2014-2015


Thank you

Thank you for your attention!

A travel time model for estimating the water budget of complex catchments

Environment

Transcript of A travel time model for estimating the water budget of complex catchments