Simultaneous estimation of groundwater recharge and hydrodynamic parameters for groundwater flow modeling

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Simultaneous estimation of groundwater recharge and

hydrodynamic parameters for groundwater flow

modeling

F. Hassane Maina, P. Ackerer, Olivier Bildstein

To cite this version:

F. Hassane Maina, P. Ackerer, Olivier Bildstein. Simultaneous estimation of groundwater recharge and hydrodynamic parameters for groundwater flow modeling. SAMO 2016 - International Conference on Sensitivity Analysis of Model Output, Nov 2016, Le Tampon, France. �cea-02435102�

SIMULTANEOUS ESTIMATION OF

GROUNDWATER RECHARGE AND

HYDRODYNAMIC PARAMETERS

FOR GROUNDWATER FLOW

MODELING

29/09/2016 1

Fadji HASSANE MAINA (Université de Strasbourg)

Philippe ACKERER (Université de Strasbourg)

INTRODUCTION

INTRODUCTION

29/09/2016

 Groundwater (aquifers): 3rd _{freshwater reservoir on the planet}

 Replenished essentially by precipitation through groundwater recharge





.

_s

H

S

K H

q

t



_{ }

_

_



q

  

K H

.

_s

H

S

q

q

t



  



2

INTRODUCTION

29/09/2016

 Groundwater (aquifers): 3rd _{freshwater reservoir on the planet}

 Replenished essentially by precipitation through groundwater recharge  The main available water resources for many countries

 Threatened by pollution and over-exploited

 Usually described by models Simulations of piezometric levels (Hydraulic heads)

 Physical Models are widely used

1. Continuity equation (mass conservation):

2. Darcy’s law (computation of fluxes):

Diffusivity equation

(flow equation):

Values of H knowing S, K and q

_s

 S and K are constant, q

_s

includes

groundwater recharge





.

_s

H

S

K H

q

t



_{ }

_

_



q

  

K H

.

_s

H

S

q

q

t



  



2

29/09/2016

 Groundwater flow models: Sophisticated and

accurate

 Recharge modeling:

Challenge

o Complex hydrological component

Groundwater recharge depends on:

 Climatic conditions  Vegetation

 Soil and root zone  Unsaturated zone

GROUNDWATER RECHARGE

Recharge : water transfer from precipitation to groundwater

BRGM

29/09/2016

 Groundwater flow models: Sophisticated and

accurate

 Recharge modeling:

Challenge

o Complex hydrological component

Groundwater recharge depends on:

 Climatic conditions  Vegetation

 Soil and root zone  Unsaturated zone

Values can not be directly measured

Estimation

 Direct methods: lysimeters, TDR  Empirical methods

 Tracers

 Mathematical models

GROUNDWATER RECHARGE

Recharge : water transfer from precipitation to groundwater

BRGM

RECHARGE ESTIMATION:

COUPLED MODEL

29/09/2016

Simulation of flow in both unsaturated and saturated zones

4

Runoff

Precipitations, Evapotranspiration

Infiltration

Flow in the Unsaturated Zone

Interactions between

Atmosphere and Soil

and Hydrodynamic in

the Unsaturated Zone :

Nash

Groundwater Flow:

Diffusivity equation

Recharge

Flow in the Saturated Zone

Coupling

NASH MODEL

Hydrodynamic in the unsaturated zone





_{ }

      t Rn Taue t Tau t Tau Rn    _  _      1 1

Root

Zone

_{1 1} 1



₁



0 Recharge k k n _t n k n t k Pe  t  d     





 

Nash parameters: RUMAX, RN, TAU

Water transfer in the unsaturated zone: delay and spreading

Modeling : propagation of a unit pulse signal

Threshold : RUMAX

ET Rainfall

if RUMAX is reached

the excess water (Pe) goes into the unsaturated zone

5 Infiltration Recharge Time Water Level ET depends on soil saturation

 Model uses constants called parameters

 Aquifers are highly heterogeneous



Parameters are not known accurately or even

unknown in natural environments

PARAMETERS ESTIMATION

 Model uses constants called parameters

 Aquifers are highly heterogeneous



Parameters are not known accurately or even

unknown in natural environments

 Available data: meteorological and piezometric levels

PARAMETERS ESTIMATION

6 0.00 50.00 100.00 150.00 200.00 250.00 300.00 294 296 298 300 302 304 306 308 Ra inf a ll ( mm) Hy d raulic Heads ( m)

 Model uses constants called parameters

 Aquifers are highly heterogeneous



Parameters are not known accurately or even

unknown in natural environments

 Available data: meteorological and piezometric levels

PARAMETERS ESTIMATION

Simultaneous estimation of groundwater flow and recharge parameters from hydraulic heads

variations

Recharge is estimated by calibrating piezometric levels

6 0.00 50.00 100.00 150.00 200.00 250.00 300.00 294 296 298 300 302 304 306 308 Ra inf a ll ( mm) Hy d raulic Heads ( m)

GLOBAL SENSITIVITY ANALYSIS

 Correlation between recharge and storage capacity (S and qs)

Recharge and storage capacity lead to the same effect

29/09/2016

q

  

K H

Determine q et K knowing H !

 Calibration is performed over time and space

 But… recharge is variable over time while the storage capacity is constant When   Determination of K

When  Determination of q knowing K  Global sensitivity analysis

Assess the calibration approach and guide the parameter estimation

Recharge Storage capacity

0

  

K H

0

q

q





0

High recharge and high storage Low recharge and low storage

7

Uncertain parameters: variability ranges known Quantify the effects of parameters uncertainty Global sensitivity analysis: focuses on the output uncertainty over the entire range of values of

the input parameters both single and in combination with one another

GLOBAL SENSITIVITY ANALYSIS

29/09/2016

Variance based approach:

Sobol Indices

Surrogate model: Chaos polynomial expansion

8

q

  

K H

q

and

K

are parameters and

H

the state variable

q

and

K

are unknowns



0.0 0.5



  q K_105 101_

n

simulations with different values of

q

and

K

n values of H

Study the effects of variations of q and K on H

29/09/2016

SOBOL INDICES :

CHAOS POLYNOMIAL EXPANSION

Let us consider a model with y as output and n input parameters, X the parameters vector  ANOVA decomposition :

Orthogonality of f

Sensitivity (Sobol) Indices :

Computation of f Polynomial expansion

 Chaos polynomial expansion

 









0 1,2,..., 1 2 1 1

,

...

,

,...,

n n i i ij i j n n i j

y

f

f x

f

x x

f

x x

x

 















 

 

 









0 s K RN RN K,

,

S K,

,

....

H



H



f

S



f

K



f

RN



f

RN K



f

S K



;

ij i i ij

V

V

S

S

V

V







1



0

,...,

j j n j

y

a



x

x

 





1,...., 1 1

...

n n i ij n i j

V

V

V

V

 



 







f_i : contribution of single parameter i to the output

f_ij : contribution of the combined effect of parameters i and j to the output

x : variable

𝚿 : orthogonal polynomial (Legendre, Hermite)

GLOBAL SENSITIVITY ANALYSIS

29/09/2016

 A subdomain of the Upper Rhine alluvial aquifer widely studied at Université de Strasbourg

 Average rainfall per year: 1100 mm

 Average of evapotranspiration per year: 900 mm

 Simulate variations of piezometric levels during 1500 days  Sensitivity analysis performed over the last 450 days

 Investigate spatial and temporal variations of sensitivity indices

 1500 simulations of Quasi Monte Carlo

Field based sensitivity analysis

GLOBAL SENSITIVITY ANALYSIS:

NASH MODEL

 Nash parameters for recharge: RUMAX, RN, TAU  Aquifer parameters: K and S

 Parameters defined by zones (Zonation) 20 parameters

Mean and Variance of the hydraulic head

RN and TAU _{Permeability Storage capacity}

11

GLOBAL SENSITIVITY ANALYSIS:

NASH MODEL

29/09/2016

 Nash parameters for recharge: RUMAX, RN, TAU  Aquifer parameters: K and S

 Parameters defined by zones (Zonation) 20 parameters

170 165 160 155 150 145 140 10 km 6 8 9 2 1 4 10 5 3 7 11 12 13 14 15

Frame 00131 Mar 2015Zonation

100.1 90.1 80.1 70.1 60.1 50.1 40.1 30.1 20.1 10.1 0.1 10 km 6 8 9 2 1 4 10 5 3 7 11 12 13 14 15 Frame 00108 Jun 2016Zonation

Mean and Variance of the hydraulic head

Mean _Variance

 Hydraulic heads range between 140 and 165 m

 Variance ranges between 0 and 100: the imposed boundaries have the lowest variance

0

100

200

300

400

500

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

Total Sensitivity Indices

Time (days)

S1

K3

RN3

RUMAX1

Point 1

29/09/2016

GLOBAL SENSITIVITY ANALYSIS:

NASH MODEL

Influential parameters: S, K, RUMAX, RN

12

29/09/2016

GLOBAL SENSITIVITY ANALYSIS:

NASH MODEL

Influential parameters: S, K, RUMAX, RN

0 100 200 300 400 500 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

Recha

rge (mm/day)

Time (days)

Recharge

12 0 100 200 300 400 500 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

Total Sensitivity Indices

Time (days) S1 K3 RN3 RUMAX1 Point 1 0 100 200 300 400 500 140,6 140,8 141,0 Hydrau lic He ads (m) Time (days)

H

29/09/2016

GLOBAL SENSITIVITY ANALYSIS:

NASH MODEL

Influential parameters: S, K, RUMAX, RN

0 100 200 300 400 500 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

Recha

rge (mm/day)

Time (days)

Recharge

12 0 100 200 300 400 500 0,1 0,2 0,3 0,4 0,5 0,6

Total Sensitivity Indice of K3

Time (days)

S

_K3 0 100 200 300 400 500 0,1 0,2 0,3 0,4 0,5 0,6

Total Sensitivity Indice of S1

Time (days)

S

_S1

Decrease of piezometric level

Decrease of the influence of

permeability 0 100 200 300 400 500 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

Total Sensitivity Indices

Time (days) S1 K3 RN3 RUMAX1 Point 1 0 100 200 300 400 500 140,6 140,8 141,0 Hydrau lic He ads (m) Time (days)

H

Temporal variation of sensitivity indices at point 1

Increase of piezometric level

Increase of the influence of

29/09/2016

GLOBAL SENSITIVITY ANALYSIS:

NASH MODEL

0 100 200 300 400 500 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

Recha

rge (mm/day)

Time (days)

Recharge

0 100 200 300 400 500 0,0 0,1 0,2 0,3 0,4 0,5

Total Sensitivity Indice of RN

Time (days)

S

_RN

13

Temporal variation of sensitivity indices at point 1

RN: water transfer in the unsaturated zone

(delay and spreading)

29/09/2016

If RU>RUMAX

Decrease of the sensitivity

of RUMAX

Increase of the recharge

Increase of the sensitivity of

RN

GLOBAL SENSITIVITY ANALYSIS:

NASH MODEL

0 100 200 300 400 500 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

Recha

rge (mm/day)

Time (days)

Recharge

0 100 200 300 400 500 0,0 0,1 0,2 0,3 0,4 0,5

Total Sensitivity Indice of RN

Time (days)

S

_RN 0 100 200 300 400 500 0,00 0,05 0,10 0,15 0,20 0,25 Ru Rumax Water Level (m) Time (days)

Temporal Variation of RU and RUMAX

13 0 100 200 300 400 500 0,0 0,1 0,2 0,3 0,4 0,5

Total Sensitivity Indice of RUMAX Time (days)

SRUMAX

Temporal variation of sensitivity indices at point 1

RN: water transfer in the unsaturated zone

(delay and spreading)

29/09/2016

GLOBAL SENSITIVITY ANALYSIS:

NASH MODEL

0 100 200 300 400 500 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

Recha

rge (mm/day)

Time (days)

Recharge

0 100 200 300 400 500 0,0 0,1 0,2 0,3 0,4 0,5

Total Sensitivity Indice of RN

Time (days)

S

_RN

13

Temporal variation of sensitivity indices at point 1

RN: water transfer in the unsaturated zone

(delay and spreading)

29/09/2016

If RU>RUMAX

Decrease of the sensitivity

of RUMAX

Increase of the recharge

Increase of the sensitivity of

RN

GLOBAL SENSITIVITY ANALYSIS:

NASH MODEL

0 100 200 300 400 500 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

Recha

rge (mm/day)

Time (days)

Recharge

13

Temporal variation of sensitivity indices at point 1

RN: water transfer in the unsaturated zone

(delay and spreading)

29/09/2016

Sensitivity maps over time

GLOBAL SENSITIVITY ANALYSIS:

NASH MODEL

S1

RUMAX3

₁₄

RUMAX3: sensitive from the

1

st _to

₁₈₅

th _day

S1: influential between the

185

th _{and the}

₃₄₆

th _day

Weak or even negligible correlations between the 185th _{and the 346}th _day

Identification of S

During the first days

 Determination of influential parameters

Nash: RUMAX and RN Groundwater flow: K and S

 Temporal variation of parameter sensitivity

Nash: saturation of the 1st _{reservoir (RUMAX) and recharge (RN)}

Permeability: decrease of the hydraulic heads Storage capacity: increase of the hydraulic heads

 Weak interactions between aquifer and recharge parameters

Confirmation of the feasibility of simultaneous estimation of recharge and

groundwater flow parameters

29/09/2016

q

  

K H

K constant, q variable  q=0, détermination of K

GLOBAL SENSITIVITY ANALYSIS:

CONCLUSION

Thank you for

GLOBAL SENSITIVITY ANALYSIS

29/09/2016

Parameters Interactions

Nash model

Richards model

14 0 100 200 300 400 500 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 Varian ce Temps (jour) RUMAX3 RN1 RN2 RN3 RN4 K3 S1 S2 Variance Point 4 0 100 200 300 400 500 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 Ind ices d e Sen sibilité d 'Or dr e 2 Temps (jour) K3&S1 RN3&S1 RN2&K3 RU3&S1 RUMAX3&K2 RUMAX3&RN2 Point 4 0 100 200 300 400 500 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 Varian ce Temps (jour) KS1  K3 S1 Variance Point 1 0 100 200 300 400 500 0,00 0,05 0,10 0,15 0,20 Ind ices d e Sen sibilité d 'Or dr e 2 Temps (jour) K3&S1 HE1&S1 HE1&K3 S1 KS1&S1 KS1&K3 Point 1 0 100 200 300 400 500 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Varian ce Temps (jour) RUMAX3 RN1 TAU1 K2 S2 S3 Variance Point 2 0 100 200 300 400 500 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 Ind ices d e Sen sibilité d 'Or dr e 2 Temps (jour) K2&S3 RN1&S3 RN1&K2 RN1 & TAU1 RUMAX3&RN1 Point 2

PARAMETER ESTIMATION

29/09/2016

Diffusivity equation (Transient state with recharge )

Steady state without recharge

Steady state with recharge

Transient state without recharge

14





.

_s

H

S

K H

q

t



 











.

0



K H









.



K H





q

_s





.

0



_{ }

_

_



H

S

K H

t

OVERESTIMATION OF RECHARGE

29/09/2016

14

If the hydraulic heads decreases, the imposed pressure decreases, and the flux calculated is positive and strong

If the hydraulic heads increases, the imposed pressure increases, and the flux calculated is negative

Assumption of constant hydraulic head over decade

1 1 2 ( )  1           _{ }  _  _{ }  _ n n n i i i i i h h q K h z K h z z

RESOLUTION OF RICHARDS

EQUATION

29/09/2016

14 Pression à l’état initial

M étho de s it ér a ti v es : P ica rd o u N ew to n Ajustement des paramètres Ajustement du pas de temps Calcul du pas de temps Résolution du système : Calcul de la pression Calcul du pas de temps suivant Calcul des paramètres Calcul des paramètres Calcul du pas de temps Résolution du système : Calcul de la pression Vérification des critères de convergence Vérification des critères de convergence M étho de s n o n ité ra tiv es

Pression au pas de temps suivant h=f(K,θ), K= f(h,θ) et θ = f(h)