Damiano Pasetto

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  • Laboratory of ecohydrologyEcole polytechnique federalede Lausanne

    Data assimilation for distributed models:an overview of applications with CATHY

    Damiano Pasetto

    Workshop on coupled hydrological modelingPadova, 24 Sept. 2015

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Table of Contents

    Table of Contents

    1 Introduction

    2 Data assimilation methods

    3 Hydrological applications

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Introduction Motivations

    State-space model

    {x(t) = f (x(t), , q(t), t) + w(t) t [0,] transient modelyk

    yk = h (x, tk) + vk k = 1, . . . observation model

    yk observationsx(t) state variables

    p (x(t)) parameters p()q(t) ATM forcingsx(0) initial conditionw(t) model structural errorvk measurement error

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Introduction Motivations

    State-space model

    {x(t) = f (x(t), , q(t), t) + w(t) t [0,] transient modelyk

    yk = h (x, tk) + vk k = 1, . . . observation model

    yk observationsx(t) state variables

    p (x(t))

    parameters

    p()

    q(t) ATM forcingsx(0) initial conditionw(t) model structural error

    vk measurement error

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Introduction Motivations

    State-space model

    {x(t) = f (x(t), , q(t), t) + w(t) t [0,] transient modelyk yk = h (x, tk) + vk k = 1, . . . observation model

    yk observationsx(t) state variables

    p (x(t))

    parameters

    p()

    q(t) ATM forcingsx(0) initial conditionw(t) model structural errorvk measurement error

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Introduction Motivations

    State-space model

    {x(t) = f (x(t), , q(t), t) + w(t) t [0,] transient modelyk yk = h (x, tk) + vk k = 1, . . . observation model

    yk observationsx(t) state variables p (x(t)) parameters

    p()

    q(t) ATM forcingsx(0) initial conditionw(t) model structural errorvk measurement error

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Introduction Motivations

    State-space model

    {x(t) = f (x(t), , q(t), t) + w(t) t [0,] transient modelyk yk = h (x, tk) + vk k = 1, . . . observation model

    yk observationsx(t) state variables p (x(t)) parameters p()q(t) ATM forcingsx(0) initial conditionw(t) model structural errorvk measurement error

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Introduction Motivations

    MotivationsHydrological forecasting is subject to many sources of uncertainty

    Initial conditionForcing termsModel parameters(Model itself?)

    Data Assimilation (DA)Correct the model forecast considering the measurements

    State . . . xk1 xk xk xk+1 . . .

    Observations . . . yk y

    k . . .

    Forecast pdf: (x(tk) | y1, . . . , yk1)Filtering pdf: +(x(tk) | y1, . . . , yk1, yk)

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Introduction Motivations

    MotivationsHydrological forecasting is subject to many sources of uncertainty

    Initial conditionForcing termsModel parameters(Model itself?)

    Data Assimilation (DA)Correct the model forecast considering the measurements

    State . . . xk1 xk xk xk+1 . . .

    Observations . . . yk y

    k . . .

    Forecast pdf: (x(tk) | y1, . . . , yk1)

    Filtering pdf: +(x(tk) | y1, . . . , yk1, yk)

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Introduction Motivations

    MotivationsHydrological forecasting is subject to many sources of uncertainty

    Initial conditionForcing termsModel parameters(Model itself?)

    Data Assimilation (DA)Correct the model forecast considering the measurements

    State . . . xk1 xk xk xk+1 . . .

    Observations . . . yk y

    k . . .

    Forecast pdf: (x(tk) | y1, . . . , yk1)Filtering pdf: +(x(tk) | y1, . . . , yk1, yk)

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Introduction A simple example with CATHY

    Example: application to CATHY (CATchment HYdrology)

    Coupled surface/subsurface modelRichards equation:

    Sw()Ss

    t+

    Sw()

    t= [KsKrw(Sw()) ( + z)] + qss(h)

    1-D path-based surface routing:

    Q

    t+ ck

    Q

    s= Dh

    2Q

    s2+ ckqs(h, )

    BC-switching/forcing algorithm

    State variables: x = {,Q}.Measures: piezometric head, soil moisture, streamflow, electricpotential (ERT).

    (Camporese et al. 2010, WRR)Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Introduction A simple example with CATHY

    Example: application to CATHY (CATchment HYdrology)

    Coupled surface/subsurface modelRichards equation:

    Sw()Ss

    t+

    Sw()

    t= [KsKrw(Sw()) ( + z)] + qss(h)

    1-D path-based surface routing:

    Q

    t+ ck

    Q

    s= Dh

    2Q

    s2+ ckqs(h, )

    BC-switching/forcing algorithm

    State variables: x = {,Q}.Measures: piezometric head, soil moisture, streamflow, electricpotential (ERT).

    (Camporese et al. 2010, WRR)Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Introduction A simple example with CATHY

    DA: example on the V-catchment

    3 m soil depthAssimilation of streamflow

    Uncertainty:Initial conditionsATM forcings

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Introduction A simple example with CATHY

    Forecast considering model uncertainties (open loop)

    0 1800 3600 5400 7200 9000 10800 12600 144000

    1

    2

    3

    4

    5

    6St

    ream

    flow

    (m

    3 /s) TRUE

    ObservationsOpen Loop

    0 1800 3600 5400 7200 9000 10800 12600 14400Time (s)

    1.939

    1.940

    1.941

    1.942

    1.943

    1.944

    Wat

    er S

    tora

    ge (

    106

    m3 )

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Introduction A simple example with CATHY

    Assimilation of measurement of streamflow

    0 1800 3600 5400 7200 9000 10800 12600 144000

    1

    2

    3

    4

    5

    6St

    ream

    flow

    (m

    3 /s) TRUE

    ObservationsSIR

    0 1800 3600 5400 7200 9000 10800 12600 14400Time (s)

    1.939

    1.940

    1.941

    1.942

    1.943

    1.944

    Wat

    er S

    tora

    ge (

    106

    m3 )

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Data assimilation methods EnKF and SIR

    Forecast step: MC simulation

    xi0 p(x0), i = 1, . . . , N Initial samplesxi,k = f(x

    ik1,

    i, qik, tk) + wik Forecast

    Analysis stepEnsemble Kalman filter (EnKF, Evensen 1994): Kalman gain

    xik = xi,k +Kk

    (yk h(x

    i,k )

    )

    Sequential Importance Resampling (SIR):weighted realizations

    (xik,

    ik

    )update weights with the likelihood and normalize

    ik = Cik1L(yk |x

    i,k )

    duplicate particles that have largest weights.

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Data assimilation methods EnKF and SIR

    Forecast step: MC simulation

    xi0 p(x0), i = 1, . . . , N Initial samplesxi,k = f(x

    ik1,

    i, qik, tk) + wik Forecast

    Analysis stepEnsemble Kalman filter (EnKF, Evensen 1994): Kalman gain

    xik = xi,k +Kk

    (yk h(x

    i,k )

    )

    Sequential Importance Resampling (SIR):weighted realizations

    (xik,

    ik

    )update weights with the likelihood and normalize

    ik = Cik1L(yk |x

    i,k )

    duplicate particles that have largest weights.

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Data assimilation methods EnKF and SIR

    Forecast step: MC simulation

    xi0 p(x0), i = 1, . . . , N Initial samplesxi,k = f(x

    ik1,

    i, qik, tk) + wik Forecast

    Analysis stepEnsemble Kalman filter (EnKF, Evensen 1994): Kalman gain

    xik = xi,k +Kk

    (yk h(x

    i,k )

    )Sequential Importance Resampling (SIR):

    weighted realizations(xik,

    ik

    )update weights with the likelihood and normalize

    ik = Cik1L(yk |x

    i,k )

    duplicate particles that have largest weights.

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Data assimilation methods EnKF and SIR

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Hydrological applications 1. Geophysical coupled inversion

    1. Geophysical coupled inversion: Electrical Resistivity Tomography

    (Rossi et al. 2015, AWR)Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Hydrological applications 1. Geophysical coupled inversion

    Iterative particle filter

    (Manoli et al. 2015, JCP)Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Hydrological applications 1. Geophysical coupled inversion

    Damiano Pasetto DA for distributed models Padova - 24 September 2015

  • Hydrological applications 2. Landscape Evolution Observatory (LEO)

    2. Landscape Evolution Observatory (LEO)

    Three convergent landscapes

    30 m long, 11 m wide, 1 m soil

    10 degrees average slope

    Environmentally controlledgreenhouse facility

    Landscape instrumentation

    rainfall simulator(3-45 mm/h)

    10 load cells

    6 flow meters forseepage faceoutflow

    1,835 sensorsembedded in thesoil

    Damiano Pasetto DA for distributed