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Damiano Pasetto

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

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Damiano Pasetto

  1. 1. Laboratory of ecohydrology ´Ecole polytechnique f´ed´erale de Lausanne Data assimilation for distributed models: an overview of applications with CATHY Damiano Pasetto Workshop on coupled hydrological modeling Padova, 24 Sept. 2015 Damiano Pasetto DA for distributed models Padova - 24 September 2015
  2. 2. 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
  3. 3. Introduction Motivations State-space model ˙x(t) = f (x(t), λ, q(t), t) + w(t) t ∈ [0, ∞] transient model y∗ k y∗ k observations x(t) state variables Damiano Pasetto DA for distributed models Padova - 24 September 2015
  4. 4. Introduction Motivations State-space model ˙x(t) = f (x(t), λ, q(t), t) + w(t) t ∈ [0, ∞] transient model y∗ k y∗ k observations x(t) state variables λ parameters q(t) ATM forcings x(0) initial condition w(t) model structural error Damiano Pasetto DA for distributed models Padova - 24 September 2015
  5. 5. Introduction Motivations State-space model ˙x(t) = f (x(t), λ, q(t), t) + w(t) t ∈ [0, ∞] transient model y∗ k ↔ yk = h (x, tk) + vk k = 1, . . . observation model y∗ k observations x(t) state variables λ parameters q(t) ATM forcings x(0) initial condition w(t) model structural error vk measurement error Damiano Pasetto DA for distributed models Padova - 24 September 2015
  6. 6. Introduction Motivations State-space model ˙x(t) = f (x(t), λ, q(t), t) + w(t) t ∈ [0, ∞] transient model y∗ k ↔ yk = h (x, tk) + vk k = 1, . . . observation model y∗ k observations x(t) state variables p (x(t)) λ parameters q(t) ATM forcings x(0) initial condition w(t) model structural error vk measurement error Damiano Pasetto DA for distributed models Padova - 24 September 2015
  7. 7. Introduction Motivations State-space model ˙x(t) = f (x(t), λ, q(t), t) + w(t) t ∈ [0, ∞] transient model y∗ k ↔ yk = h (x, tk) + vk k = 1, . . . observation model y∗ k observations x(t) state variables p (x(t)) λ parameters p(λ) q(t) ATM forcings x(0) initial condition w(t) model structural error vk measurement error Damiano Pasetto DA for distributed models Padova - 24 September 2015
  8. 8. Introduction Motivations Motivations Hydrological forecasting is subject to many sources of uncertainty Initial condition Forcing terms Model parameters (Model itself?) Data Assimilation (DA) Correct the model forecast considering the measurements State . . . ˆxk−1 → x− k ˆxk → x− k+1 . . . ↓ ↑ ↓ Observations . . . y− k ↔ y∗ k . . . Damiano Pasetto DA for distributed models Padova - 24 September 2015
  9. 9. Introduction Motivations Motivations Hydrological forecasting is subject to many sources of uncertainty Initial condition Forcing terms Model parameters (Model itself?) Data Assimilation (DA) Correct the model forecast considering the measurements State . . . ˆxk−1 → x− k ˆxk → x− k+1 . . . ↓ ↑ ↓ Observations . . . y− k ↔ y∗ k . . . Forecast pdf: π−(x(tk) | y1, . . . , yk−1) Damiano Pasetto DA for distributed models Padova - 24 September 2015
  10. 10. Introduction Motivations Motivations Hydrological forecasting is subject to many sources of uncertainty Initial condition Forcing terms Model parameters (Model itself?) Data Assimilation (DA) Correct the model forecast considering the measurements State . . . ˆxk−1 → x− k ˆxk → x− k+1 . . . ↓ ↑ ↓ Observations . . . y− k ↔ y∗ k . . . Forecast pdf: π−(x(tk) | y1, . . . , yk−1) Filtering pdf: π+(x(tk) | y1, . . . , yk−1, yk) Damiano Pasetto DA for distributed models Padova - 24 September 2015
  11. 11. Introduction A simple example with CATHY Example: application to CATHY (CATchment HYdrology) Coupled surface/subsurface model Richards equation: Sw(ψ)Ss ∂ψ ∂t + φ ∂Sw(ψ) ∂t = · [KsKrw(Sw(ψ)) ( ψ + ηz)] + qss(h) 1-D path-based surface routing: ∂Q ∂t + ck ∂Q ∂s = Dh ∂2Q ∂s2 + ckqs(h, ψ) BC-switching/forcing algorithm (Camporese et al. 2010, WRR) Damiano Pasetto DA for distributed models Padova - 24 September 2015
  12. 12. Introduction A simple example with CATHY Example: application to CATHY (CATchment HYdrology) Coupled surface/subsurface model Richards equation: Sw(ψ)Ss ∂ψ ∂t + φ ∂Sw(ψ) ∂t = · [KsKrw(Sw(ψ)) ( ψ + ηz)] + qss(h) 1-D path-based surface routing: ∂Q ∂t + ck ∂Q ∂s = Dh ∂2Q ∂s2 + ckqs(h, ψ) BC-switching/forcing algorithm State variables: x = {ψ, Q}. Measures: piezometric head, soil moisture, streamflow, electric potential (ERT). (Camporese et al. 2010, WRR) Damiano Pasetto DA for distributed models Padova - 24 September 2015
  13. 13. Introduction A simple example with CATHY DA: example on the V-catchment 3 m soil depth Assimilation of streamflow Uncertainty: Initial conditions ATM forcings Damiano Pasetto DA for distributed models Padova - 24 September 2015
  14. 14. Introduction A simple example with CATHY Forecast considering model uncertainties (open loop) 0 1800 3600 5400 7200 9000 10800 12600 14400 0 1 2 3 4 5 6Streamflow(m 3 /s) TRUE Observations Open Loop 0 1800 3600 5400 7200 9000 10800 12600 14400 Time (s) 1.939 1.940 1.941 1.942 1.943 1.944 WaterStorage(10 6 m 3 ) Damiano Pasetto DA for distributed models Padova - 24 September 2015
  15. 15. Introduction A simple example with CATHY Assimilation of measurement of streamflow 0 1800 3600 5400 7200 9000 10800 12600 14400 0 1 2 3 4 5 6Streamflow(m 3 /s) TRUE Observations SIR 0 1800 3600 5400 7200 9000 10800 12600 14400 Time (s) 1.939 1.940 1.941 1.942 1.943 1.944 WaterStorage(10 6 m 3 ) Damiano Pasetto DA for distributed models Padova - 24 September 2015
  16. 16. Data assimilation methods EnKF and SIR Forecast step: MC simulation xi 0 ∼ p(x0), i = 1, . . . , N Initial samples xi,− k = f(xi k−1, λi , qi k, tk) + wi k Forecast Damiano Pasetto DA for distributed models Padova - 24 September 2015
  17. 17. Data assimilation methods EnKF and SIR Forecast step: MC simulation xi 0 ∼ p(x0), i = 1, . . . , N Initial samples xi,− k = f(xi k−1, λi , qi k, tk) + wi k Forecast Analysis step Ensemble Kalman filter (EnKF, Evensen 1994): Kalman gain ˆxi k = xi,− k + Kk y∗ k − h(xi,− k ) Damiano Pasetto DA for distributed models Padova - 24 September 2015
  18. 18. Data assimilation methods EnKF and SIR Forecast step: MC simulation xi 0 ∼ p(x0), i = 1, . . . , N Initial samples xi,− k = f(xi k−1, λi , qi k, tk) + wi k Forecast Analysis step Ensemble Kalman filter (EnKF, Evensen 1994): Kalman gain ˆxi k = xi,− k + Kk y∗ k − h(xi,− k ) Sequential Importance Resampling (SIR): weighted realizations xi k, ωi k update weights with the likelihood and normalize ωi k = Cωi k−1L(y∗ k | xi,− k ) duplicate particles that have largest weights. Damiano Pasetto DA for distributed models Padova - 24 September 2015
  19. 19. Data assimilation methods EnKF and SIR Damiano Pasetto DA for distributed models Padova - 24 September 2015 −x ,N−1 { }π − k 1:k−1 (x |y ) k
  20. 20. 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
  21. 21. Hydrological applications 1. Geophysical coupled inversion Iterative particle filter (Manoli et al. 2015, JCP) Damiano Pasetto DA for distributed models Padova - 24 September 2015
  22. 22. Hydrological applications 1. Geophysical coupled inversion Damiano Pasetto DA for distributed models Padova - 24 September 2015
  23. 23. 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 controlled greenhouse facility Landscape instrumentation rainfall simulator (3-45 mm/h) 10 load cells 6 flow meters for seepage face outflow 1,835 sensors embedded in the soil Damiano Pasetto DA for distributed models Padova - 24 September 2015
  24. 24. Hydrological applications 2. Landscape Evolution Observatory (LEO) First experiment at LEO (18 February 2013) Experiment setup: Unsaturated initial conditions Imposed rainfall: ≈12 mm/h With homogeneous soil, steady state expected after 36 h After the experiment: the rainfall was stopped after 22 h due to the occurrence of overland flow. Damiano Pasetto DA for distributed models Padova - 24 September 2015
  25. 25. Hydrological applications 2. Landscape Evolution Observatory (LEO) Synthetic scenario reproducing Experiment 1 at LEO Assumption: Y = log(KS) is a Gaussian random field with exponential covariance function. E[KS] = 10−4 m/s with coefficient of variation 100% (µY = −9.56, σY = 0.83) Test case 1 (TC1): λx = λy = 8 m; λz= 0.5 m Test case 2 (TC2): λx = λy = 4 m; λz= 0.25 m Number of grid cells: 60×22×20= 26400 Sensor failure analysis The assimilation is repeated decreasing the number of measurements, from m=496 to m= 21 active sensors. (Pasetto et al. 2015, AWR) Damiano Pasetto DA for distributed models Padova - 24 September 2015
  26. 26. Hydrological applications 2. Landscape Evolution Observatory (LEO) −5 0 5 5 10 15 20 25 d= 0.00÷0.05 m x (m) y(m) −5 0 5 5 10 15 20 25 d= 0.15÷0.20 m x (m) −5 0 5 5 10 15 20 25 d= 0.30÷0.35 m x (m) −5 0 5 5 10 15 20 25 d= 0.50÷0.55 m x (m) −5 0 5 5 10 15 20 25 d= 0.80÷0.85 m x (m) −5 0 5 5 10 15 20 25 d= 0.95÷1.00 m x (m) 10 −5 10 −4 10 −3 KS  (m/s)  True   −5 −2 0 2 5 5 10 15 20 25 d= 0.00÷0.05 m x (m) y(m) −5 −2 0 2 5 5 10 15 20 25 d= 0.15÷0.20 m x (m) −5 −2 0 2 5 5 10 15 20 25 d= 0.30÷0.35 m x (m) −5 −2 0 2 5 5 10 15 20 25 d= 0.50÷0.55 m x (m) −5 −2 0 2 5 5 10 15 20 25 d= 0.80÷0.85 m x (m) −5 −2 0 2 5 5 10 15 20 25 d= 0.95÷1.00 m x (m) 10 −5 10 −4 10 −3 KS  (m/s)  m=  496   True and estimated spatial distributions of KS in TC2. Damiano Pasetto DA for distributed models Padova - 24 September 2015
  27. 27. Hydrological applications 2. Landscape Evolution Observatory (LEO) 0 0.5 1 1.5 OverlandFlow(m 3 /h) Ensemble Ensemble Mean True 90% C.I. TC1 (long correlation length) 0 0.5 1 1.5 SeepageFaceFlow(m 3 /h) 0 4 8 12 16 20 24 28 32 36 Time t (h) 40 60 80 100 120 WaterStorage(m 3 ) TC2 (short correlation length) 0 4 8 12 16 20 24 28 32 36 Time t (h) Open loop: model response with 200 random realizations of the prior distribution of Y = log(KS) without data assimilation. Damiano Pasetto DA for distributed models Padova - 24 September 2015
  28. 28. Hydrological applications 2. Landscape Evolution Observatory (LEO) 0 0.5 Overland(m 3 /h) True m= 496 m= 196 m= 46 m= 21 TC1 (long correlation length) 0 0.5 1 1.5 Seepage(m 3 /h) 40 60 80 100 120 Storage(m 3 ) 0 4 8 12 16 20 24 28 Time t (h) 0.001 0.01 RMSEonvwc TC2 (short correlation length) 0 4 8 12 16 20 24 28 32 36 Time t (h) Model response with the calibrated saturated hydraulic conductivity Damiano Pasetto DA for distributed models Padova - 24 September 2015
  29. 29. Conclusions Conclusions Data assimilation methods help improve the forecast and reduce the uncertainty of high dimensional hydrological models. Data assimilation methods allow the online estimation of both the state variables and the model parameters. Damiano Pasetto DA for distributed models Padova - 24 September 2015
  30. 30. Conclusions Conclusions Data assimilation methods help improve the forecast and reduce the uncertainty of high dimensional hydrological models. Data assimilation methods allow the online estimation of both the state variables and the model parameters. Work in progress Covariance localization and ensemble inflation to minimize ill-conditioning and filter inbreeding in the EnKF update. Update step performed with a combination of EnKF and SIR (Gaussian Mixture Filters) Surrogate models to accelerate the Monte Carlo simulation. Damiano Pasetto DA for distributed models Padova - 24 September 2015
  31. 31. Conclusions Thank you for your attention References D Pasetto, M Camporese, and M Putti. Ensemble Kalman filter versus particle filter for a physically-based coupled surface-subsurface model, Adv Water Resources, 2012. G Manoli, M Rossi, D Pasetto, R Deiana, S Ferraris, G Cassiani, and M Putti. An iterative particle filter approach for coupled hydro-geophysical inversion of a controlled infiltration experiment, J Comp Phys, 2015. M Rossi, G Manoli, D Pasetto, R Deiana, S Ferraris, C Strobbia, M Putti, G Cassiani. Coupled inverse modeling of a controlled irrigation experiment using multiple hydro-geophysical data, Adv Water Resources, 2015. D Pasetto, G-Y Niu, L Pangle, C Paniconi, M Putti, PA Troch. Impact of sensor failure on the observability of flow dynamics at the Biosphere 2 LEO hillslopes, Adv Water Resources, 2015. Damiano Pasetto DA for distributed models Padova - 24 September 2015
  32. 32. Conclusions Damiano Pasetto DA for distributed models Padova - 24 September 2015
  33. 33. Conclusions Damiano Pasetto DA for distributed models Padova - 24 September 2015
  34. 34. Conclusions Damiano Pasetto DA for distributed models Padova - 24 September 2015
  35. 35. Conclusions Damiano Pasetto DA for distributed models Padova - 24 September 2015

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