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Models and Modelling in FEWS Part II


Models and Modelling in FEWS Part II Micha Werner Deltares & UNESCO-IHE Error correction ARMA & ADJUST-Q Improving the Forecast Output Processing This can be done ... – PowerPoint PPT presentation

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Title: Models and Modelling in FEWS Part II

Models and Modelling in FEWS Part II
  • Micha Werner
  • Deltares UNESCO-IHE

Error correction ARMA ADJUST-Q
In this section we will discuss two methods used
for correcting the outputs of a hydrological
model. The method used widely in the NWS is
ADJUST-Q, which typically requires manual
interaction during the forecast run. The second
is the ARMA method in FEWS. This is a statistical
error model that is widely used in forecasting.
This does not need interaction during the
forecast process
Improving the Forecast
A Input correction B State Updating (data
assimilation) C Parameter Updating D
Postprocessing (including Error Correction)
Output Processing
  • This can be done using very simple approaches as
    well as with more complex methods that canb also
    provide an estimate of uncertainty
  • Simple methods
  • Adjust Q (correction at start forecast)
  • AR or ARMA type error correction
  • More complex methods
  • Quantile regression
  • Bayesian Output Processor (HUP)

Overview of error correction models/methods
  • Available methods for error correction in FEWS
  • Internal
  • AdjustQ type operation
  • ARMA Error correction method
  • External (models) run using the adapter
  • MCRM/DODO Error Correction approach
  • CEH ARMA Module
  • PDM Error correction/State updating
  • Implementations of Quantile Regression HUP

Overview of available error correction methods
  • ADJUST-Q Empirical error correction
  • Parameter steps determines convergence speed
  • steps may be changed interactively during

Example simple model with constant bias
Overview of available error correction methods
  • Statistical model of error
  • Time series modeling
  • ARMA Auto Regressive Moving Average
  • Concept
  • Error is typically highly correlated in time
  • Establish model of error predict future error
  • Correct model simulation in forecast period with
    predicted error

Model Order
Model Parameters
ARMA module Delft-FEWS - 1
  • Autoregressive Moving Average Models used for
    forecasting of stationary timeseries in this
    case applied to modelling the time evolution of
    the model error
  • AR This part of the model describes how each
    observation (error) is a function of the previous
    k observations (errors). For example, if k 1,
    then each observation is a function of only one
    previous observation. That is,
  • where Qres(t) represents the observed residual
    (error) value at time t, Qres(t-1) represents the
    previous observed residual (error) at time t - 1,
    e(t) represents some random error and c and a1
    are constants. Other observed values of the
    series can be included in the right-hand side of
    the equation if k gt 1

ARMA module Delft-FEWS - 2
  • MA This part of the model describes how each
    observation is a function of the previous y
    errors. For example, if y 1, then each
    observation is a function of only one previous
    error. That is,
  • Here e(t) represents the random error at time t
    and e(t-1) represents the previous random error
    at time t - 1. Other errors can be included in
    the right-hand side of the equation if y gt 1.

ARMA Model
Example of error correction using ARMA. Corrected
time series (red) will converge to uncorrected
time series (pink) as lead time increases
ARMA Model
  • Simple example of ARMA model

See also spreadsheet
AR module Delft-FEWS - 3
  • What is required for setting up an ARMA Model
  • Simulated trace (typically SQIN)
  • Observed trace (typically QIN)
  • Parameterisation of error model
  • - Model Order
  • - Model parameters
  • Three ways of defining error model in FEWS
  • - Automatic Establish both order parameters
    dynamically (AR only)
  • Defined order Order defined by user Dynamic
    parameter identification
  • Define all Order parameters defined by user

Establishing ARMA model order and parameters
Window length
Statistical behavior of error in window of
defined length used to identify order and/or
parameters of error model. Rule of thumb Window
should be gt 50 x order of AR model
Establishing ARMA model order and parameters
  • Length of window will influence the estimation
    of AR parameters. As window increases
    autocorrelation of errors will decrease for most
    hydrological time series

Window length
When estimating order of model Define maximum
order Typical AR orders vary in range 1-3
Error Correction using FEWS ARMA model
  • FEWS ARMA Error model
  • Additional Features
  • Error correction using AR and MA
  • pre-processing methods to normalize errors (Log,
    Box-Cox etc)
  • Additional options
  • Interpolation of observed data to remove small
  • Data hierarchy for simulated inputs
  • Constraints on outputs
  • Constraints on inputs

Error Correction using FEWS ARMA model
  • Options for ARMA model

Free order Free parameters This allows the error model to establish both order parameters dynamically Fixed order Free parameters Order is now fixed but parameters dynamically - order established/calibrated offline
Free order Fixed parameters not applicable Fixed order Fixed parameters Everything is now fixed parameters order established/calibrated offline
Error Correction using FEWS ARMA model
  • Options for ARMA model pros and cons

Free order Free parameters Pro may utilize full potential Con statistical optimization with many degrees of freedom small risk of coming unstuck Con behavior with strange data/bad model unpredictable Fixed order Free parameters Pro utilize potential of dynamic orders Con very small risk of coming unstuck Con behavior with strange data/bad model unpredictable Con need to establish - order. 3 is good working max.
Free order Fixed parameters not applicable Fixed order Fixed parameters Pro controlled, predictable, behavior Con need to establish order parameters. Calibration required
Error Correction using FEWS ARMA model
  • Notes on inputs to Error model
  • 2 Traces are required
  • Simulated trace shoud cover historical
    forecast period
  • Observed trace normally ends at T0
  • When there is missing data in simulated time
    series failure ?
  • Error correction module allows multiple simulated
    time series to be allocated
  • Simulated Forecast
  • Simulated Historical
  • Simulated Backup (use in case problems with
    cold start!)

Error Correction using FEWS ARMA model
  • Additional options manipulating inputs
  • Range check on input can be defined (min/max)
  • This is like validation values beyond range
    become Missing
  • Better to apply a more stingent validation
    berfore going in to error model (e.g rate change
    checks etc)
  • Interpolation of input data
  • Avoid spurious results due to small gaps
  • Same function as in InterpolationModule Linear
    Interpolation for defined gap length
  • Ignore Doubtfull. Doubtfull data can be set to be
  • Be very careful as rated flows often doubtful
    beyond range of rating but we do want these to
    be used

Error Correction using FEWS ARMA model
  • Additional options manipulating outputs
  • Range check on outputs can be defined (min/max)
  • This is NOT a validation values are constrained
    to min-max
  • Typically used for constraining discharge values
    to zero (or a minimum flow, e.g. as input to HD

Application of Error correction
  • General notes
  • Error correction is a form of modeling!
  • Careful thought of the nature of errors being
  • Calibration validation
  • Calibration required if orders are fixed
  • Validation required in both cases !

  • Typical application of error model
  • Rainfall-runoff model calculates flow to
    catchment outlet (C)
  • Error correction applied to flow at C
  • Routing-model calculates propagation of flow in
    steep river
  • Uses error corrected flow as input
  • Error correction applied to flow at B
  • HD model calculates levels flows in reach from
    B to A
  • Uses error corrected flow as input

  • Error model cannot be applied to tidal signal as
  • Periodic signal requires different approach
  • Approach 1 Correction of surge residuals
  • Possible but
  • Forecast surge may be very different from
    observed surge (bias)
  • Approach 2 Correction Frequency domain
  • Significant training periods (several months
  • If to be considered integrate as external

Setting up the ARMA Model in FEWS
  • Configuration when using automatic estimation
    methods is very easy
  • Identify inputs and outputs
  • If fixing order - set order of AR to e.g. 3
    (typically maximum order)
  • Typically MA can be ignored as AR dominates
  • If fixing both order AND parameters Recommended
  • Set up models ARMA in UpdateStates workflow
  • Configure ARMA to estimate parameters
  • Run UpdateStates for extended period (e.g. 1
  • Run ARMA in DEBUG mode for 1 year of data
    (through e.g. cold state selection).

  • ARMA model run in DEBUG mode allow parameters
    to be estimated
  • Read AR (and MA values if relevant from DEBUG
  • Copy values as fixed

Comparison of ADJUSTQ to AR
Blending steps 100
Blending steps 1
Blending steps 12
Comparison of ADJUSTQ to AR
Blending steps 100
Blending steps 12
Blending steps 30
Blending steps 1
Calibrating and Validating ARMA models
  • Calibration of ARMA models using e.g. FEWS
    inernal routines, or other statistical packages
  • Validation
  • Run series of hindcast runs
  • Plots of lead time accuracy

Calibrating and Validating ARMA models
  • FEWS can be easily applied in setting up such
    hindcast runs

  • Pros
  • ARMA allows for an automated approach to
    adjusting errors reduces need for interactivity
  • ARMA makes statistical sense errors typically
    have structure
  • ARMA provides an objective method can be
    verified using hindcasts
  • ADJUST-Q supports changing interactively when not
    behaving properly
  • Cons
  • ARMA is a statistical model not a hydrological
    model statistical sanity is not always
    hydrologically correct
  • ADJUST-Q is subjective difficult to apply in

Routing models in FEWS Hydrodynamic models
In this section we will discuss the application
of routing models in FEWS focusing primarily on
the use of hydrodynamic models such as HEC-RAS.
Some of the particular aspects of using HD models
in real time are discussed.
Routing models
  • Objective Calculate propagation of flood wave
    through river system
  • Simple Hydrological Routing (KW, Lag-K,
    Muskingum, )
  • Complex with 1-D hydrodynamic model (ISIS,
    Mike11, SOBEK, HEC)
  • Potentially more complex 2D models (Delft3D,
    Telemac, Flow2D etc)

Routing models linked to FEWS (Examples)
Hydrological LAG-K TATUM Kinematic Wave (KW) 2-Lyr Muskingum NWS NWS CEH-Wallingford Deltares US US England Wales, Scotland -
Hydrodynamic SOBEK-1D ISIS Mike-11 HEC-RAS Delft3D SOBEK-1D2D Deltares HR Wallingford/Halcrow DHI USACE Deltares Deltares Rhine basin, Waterboards England Wales, Scotland England Wales, Italy, Spain US, Italy, Sudan Scotland Thailand
Differences between model approaches
  • Kinematic Wave
  • Diffusive Wave
  • Dynamic Wave (all other cases) Full Equations

Most models are derivations of the shallow water
equations ignoring different terms that are
insignificant Depends on the hydraulic situation
Hydrodynamic vs. Hydrological Models
  • Typical set-up

Simple routing often in hydrological model e.g.
Hydrological routing e.g. LAG-K, Kinematic Wave
Hydrodynamic routing e.g. HEC-RAS
Hydrodynamic vs. Hydrological Models
  • Pros
  • Hydrodynamic routing provides more realistic
    simulation of flood wave propagation
  • Deals well with backwater effects, change in
    flood wave propagation when flow goes out of bank
  • Allows incorporation of structures and control of
  • Allows outputs at intermediate locations (not
    gage ? gage)
  • Cons
  • More complex models, data intensive
  • Computationally more demanding
  • Risk of instability

Hydrodynamic vs. Hydrological Models
  • Apply HD models only when really required
  • Extensive floodplains
  • Reaches with structures
  • Tidal Reaches
  • Confluences
  • Mixing models
  • Hydrological ? Hydrodynamic
  • Hydrodynamic ? Hydrological

HD model in a forecast workflow
Exchange between HD models FEWS
  • All HD models integrated with FEWS using standard
    adapter approach
  • Inputs (typical)
  • Flows at upstream boundary and tributary inflows
  • Level at downstream boundary may be a tidal
  • (not required when internal rating curve
    boundary is used)
  • Inputs (less common)
  • Gate settings
  • Temperature
  • Outputs (typical)
  • Water Level Flow (point or longitudinal)

Exchange between HD models FEWS
  • Location of boundaries needs careful thought to
    avoid reading a defined boundary as the result
    of a HD model

Reach influenced by d/s boundary condition
Ignore results from this point
Upstream boundary Q(t)
Downstream boundary Q-h
Flow direction
Exchange between HD models FEWS
  • Tidal boundaries offer a specific problems
  • Astronomical constants to derive astronomical
  • Difficult to work with harmonic constants
  • Work with surge residuals (interpolate, ARMA
    modeling etc) then add back to astronomical
  • ADJUST-T (NWS operation addresses similar issue)
  • Other option link with coastal shelf model (see
    case study)

Hydrodynamic models Error correction
  • Hydrodynamic models typically cover long reaches
    of river, which means that intermediate gages are
    not utilized for error correction
  • Options
  • State updating e.g. Ensemble/Extended Kalman
    Filter Particle Filter)
  • Particle filter applied in Rhine for updating
  • Simple nudging techniques
  • Available in Mike11 ISIS
  • ? These are computationally intensive
  • Splitting model in sections use error
    correction at each gage
  • Assumes rating curve is reliable!

Model cascades
  • Hydrodynamic Hydrodynamic model cascade
  • Complex interaction
  • State in d/s hydrodynamic model affects state in
    u/s hydrodyanic model
  • Overlap models

Region of influence of d/s boundary
Model 1
Model 2
Model cascades
  • Connecting two hydrodynamic models
  • Error correction on flow from u/s model
  • Note that this does assume rating curve is
    reliable!! May not include hysterisis

Gauge u/s of model transition Calculate error
Add error to flow at d/s boundary Model 1 u/s
boundary Model 2 Read Levels from d/s model!!!
Model 1
Model 2
Burn-in profiles
  • Avoid abrupt shock on startup
  • Mainly relevant to HD modules (stability)
  • Only applied when starting from a cold state
  • Identify start value in cold state
  • Gradual climb to actual value

Burn-in section
Inundation Mapping
  • Inundation maps provide spatial view of extent of
  • Two main approaches in integrating these maps in
  • Running external (2D) hydrodynamic model
    importing resulting grid data to view dynamic
    inundation profile
  • HEC-RAS (ID Interpolation)
  • TUFlow
  • SOBEK-1D2D
  • Running a 1D hydrodynamic model
  • Export levels at cross sections to FEWS Flood
    Mapping Module
  • Interpolate water surface profile in GIS
  • Import dynamic flood map to FEWS

Inundation Mapping using a 2D model
  • Model runs through General Adapter as does any
  • Time series of grid data returned map stack
  • Imported to FEWS database displayed as any
    other grid

Example SOBEK 1D2D model of the Barotse
Floodplain Zambezi River, Zambia DEM extent 303
x 541 cells 720m resolution (resampled from 90m
SRTM data) SOBEK model using 1D for main stem
Inundation Mapping using a 1D model
Example Modeling of bifurcation/Confluence 1D
Modeler decides division 2D Division depends on
water level
Forecasting using 1D 2D HD models in the Firth
of Clyde, Scotland
Low Pressure
increased tide levels
Forecasting using 1D 2D HD models in the Firth
of Clyde, Scotland
  • Firth of Clyde (FoC) Flood Forecasting Model
    setup in Delft3D-FLOW
  • Hydrodynamics module of Delft3D framework,
    applied for the modelling of surface water
  • FoC Model provides
  • Tidal surge forecasts at locations distributed
    in Firth of Forth
  • Downstream boundary to 1D river models

Firth of Clyde model development
  • Model setup - computational grid
  • Orthogonal curvilinear grid, aligned with local
    geometric features
  • Spatially varying resolution (1 km 100 m)
  • Run in 2D, 3D effects are secondary
  • Based on a time step of 1 minute, a 1 day
    simulation takes approximately 6 minutes
  • Model does not run often (4x per day) when
    forcings are updated. Provides d/s boundary for
    river models
  • Runs on dedicated server to avoid conflicting
    with other resources

Firth of Clyde model development
  • Model setup - boundary forcing
  • Tidal boundary conditions (harmonic
    constituents) for 50 tidal components
  • External surge conditions by time-varying,
    spatially uniform water level elevation
  • Meteorological forcing by time-varying,
    spatially uniform wind speed and direction
  • Assuming one-way coupling at rivers (model
    provides d/s level boundary), no river discharge
    taken into account

Wrap up of models in FEWS
  • Variety of different types of models available
    for running in FEWS
  • All integrated using the same adapter concept
  • Models can be mixed in a single workflow
    extremely useful for creating integrated
    modeling structures
  • Increasing use of distributed physically based
    models in forecasting
  • Issues speed, database sizes, complexity,
  • Variety of models adapters available and used
  • Actual availability depends on model supplier
  • Adapters to new models can be readily developed