Morphing and wavelet EnKF data assimilation - UC Denverjmandel/slides/psu2011_jm.pdf · Morphing EnKF Spectral and wavelet EnKF Applications Morphing and wavelet EnKF data assimilation
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Morphing EnKFSpectral and wavelet EnKF
Applications
Morphing and wavelet EnKF data assimilation
Jan Mandel
Based on joint work with J. D. Beezley, L. Cobb, A. Krishnamurthy, A. K.Kochanski, K. Eben, P. Jurus, and J. Resler
Center for Computational MathematicsDepartment of Mathematical and Statistical Sciences
University of Colorado Denver
Supported by NSF grant AGS-0835579
Penn State, November 3, 2011
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Outline
1 Morphing EnKFData assimilation and EnKFAutomatic image registrationThe morphing transformation
2 Spectral and wavelet EnKFState covariance approximationFFT and waveletsExamples
3 ApplicationsWildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
Data assimilation – continuous Bayesian view
Modelmust support the assimilation cycle: export, modify, andimport statethe state must have metadata: what, when, wheremust support meaningful continuous adjustments to thestate – no discrete datastructures
Datamust have error estimatemust have metadata: what, when, where
Observation functionconnects the data and the modelcreates synthetic data from model state to compare
Data assimilation algorithmadjusts the state to match the databalances the uncertainty in the data and in the stateit is not the purpose to minimize the error
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
The Ensemble Kalman Filter (EnKF)
uses an ensemble of simulations to estimate modeluncertainty by sample covarianceconverges to Kalman Filter (optimal filter) in largeensemble limit and the Gaussian caseuses the model as a black boxadjusts the state by making linear combinations ofensemble members (OK, locally in local versions of thefilter, but still only linear combinations)if it cannot match the data by making the linearcombinations, it cannot track the dataprobability distributions close to normal needed for properoperation
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
The Ensemble Kalman Filter (EnKF)
X a = X f + K(Y − HX f ), K = P f HT (HP f HT +R)−1
X a: Analysis/PosteriorensembleX f : Forecast/PriorensembleY : Data
K : Kalman gainH: Observation functionP f : Forecast samplecovarianceR: Data covariance
Basic assumptions:
Model and observation function are linearForecast and data distributions are independent andGaussian (if not, EnKF routinely used anyway)
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
A simple reaction-diffusion wildfire model
0 200 400 600 800 1000300
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1000
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Tem
pera
ture
(K)
X (m)
1D temperature profile 2D temperature profile
Solutions produce non-linear traveling waves and thin reactionfronts.
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
An example in 2D: non-physical results
Forecast ensemble Data Analysis ensemble
Forecast ensemble generated by random spatialperturbations of the displayed imageAnalysis ensemble displayed as a superposition ofsemi-transparent images of each ensemble memberIdentity observation function, H = IData variance, 100 K
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
What went wrong?
The Kalman update formulacan be expressed as
X a = A(X f )T ,
so X ai ∈ spanX f, where the
analysis ensemble is made oflinear combinations of theforecast.
0 500 1000 1500Temperature (K)
Prob
abilit
y de
nsity
Non-Gaussian distribution:Spatial perturbations yieldforecast distributions with twomodes centered aroundburning and non-burningregions.
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
Solution: morphing EnKF
(picture Gao & Sederberg 1992)
Need correction of location, not justamplitudeSolution:
Use morphs instead of linearcombinationsDefine morphing transform, carriesexplicit position informationIn the morphing space, probabilitydistributions are much closer toGaussian, standard EnKF succesfullInitial ensemble: smooth randomperturbation of amplitude and location
Applicable to any problem with movingfeatures (error in speed causes error inlocation), not necessarily sharp
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
Image morphing
A morphing function, T : Ω→ Ω defines a spatialperturbation of an image, u.It is invertible when (I + T )−1 exists.An image u “morphed” by T is defined asu = u(x + Tx) = u (I + T )(x).
u I + T = u
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
Automatic image registration
Goal: Given two images u and v , find an invertible morphingfunction, T , which makes u (I + T ) ≈ v , while ensuring that Tis “small” as possible.
Image registration problem
Ju→v (T ) = ||u (I + T )− v ||R + ||T ||T → minT
||r ||R = cR||r ||2||T ||T = cT ||T ||2 + c∇||∇T ||2cR, cT , and c∇ are treated as optimization parameters
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
Automatic registration procedure
Avoid getting trapped in local minimaMultilevel method
Start from the coarsest grid and go upOn coarse levels, look for an approximate global match,then refineSmoothing by a Gaussian kernel first to avoid locking thesolution in when some fine features match by an accidentwhile the global match is still poor
On all levelsmap out the solutions space by samplingiterate by steepest descent from the best match
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
Minimization by sampling
Probe the solution space by moving thecenter to sample points and evaluating theobjective function and taking the minimum.Morphing function on grid pointsdetermined by some sort of interpolation.Refine the grid and repeat until desiredaccuracy is reached.When using bilinear interpolation,invertibility is guaranteed when all gridquadrilaterals are convex.Smoother interpolation... invertibility morecomplicated
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
Grid refinement
The objective function need only be calculated locally, withinthe subgrid, allowing acceptable computational complexity,O(n log n).
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
Image smoothing
A smoothed temperatureprofile (in blue) withbandwidth 200 m.
Gaussian kernel with bandwidth h
Gh(x) = ch exp−xT x
2h
Smoothing by convolution with Gh(x)improves performance of steepestdescent methods applied to Ju→v (T ).
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
The morphing transformation
Augment the state by an explicit information about spacedeformation:
Morphing transformation
Given a reference state u0
Mu0ui =
Ti The registration mapri = ui (I + Ti)
−1 − u0 Residual (of amplitude)
M−1u0
[Ti , ri ] = ui = (u0 + ri) (I + Ti) The inverse transformui,λ = (u0 + λri) (I + λTi) intermediate states for 0 < λ < 1
Linear combinations of [ri ,Ti ] give intermediate states. ApplyMu0 to the ensemble and the data, run the EnKF on thetransformed variables, and apply the inverse transformation toget the analysis ensemble.
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
Linear combinations of transformed states are now physicallyrealistic.
The first and the last state are actual simulation states, those inbetween are generated automatically by morphing. Both theposition and the amplitudes are interpolated.
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Data assimilation and EnKFAutomatic image registrationThe morphing transformation
Morphing transform makes distribution more Gaussian
0 500 1000 1500Temperature (K)
Prob
abilit
y de
nsity
−400 −200 0 200 400Temperature (K)
−150 −100 −50 0 50 100 150Perturbation in X−axis (m)
(a) (b) (c)
Typical pointwise densities near the reaction area of the originaltemperature (a), the residual component after the morphingtransform (b), and (c) the spatial transformation component inthe X-axis. The transformation has made bimodal distributioninto unimodal.
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
State covariance approximationFFT and waveletsExamples
Ensemble Kalman Filter (EnKF)
Uses an ensemble of solutions ukNk=1 to estimate modelerrors.
Forecast step:
uk ← M(uk )
Analysis step:
KN ← QNHT (HQNHT + R)−1
uk ← uk + KN (d + ek − Huk ) , ek ∼ N (0,R)
The forecast covariance (Q) is approximated by the samplecovariance (QN ). But, the sample covariance is just anapproximation; why not use a different approximation?
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
State covariance approximationFFT and waveletsExamples
Sample covariance
u ← 1N
N∑k=1
uk
QN ← 1N − 1
N∑k=1
(uk − u) (uk − u)T
Simple formula to estimate covariance from an ensembleWell known convergence behaviorHas rank at most N − 1Usually creates spurious long range correlations, but canestimate the diagonal well
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
State covariance approximationFFT and waveletsExamples
Covariance tapering
Artificially eliminate long range correlations using a taperingfunction.
Large samplecovariance (N = 1000)
Small samplecovariance (N = 10)
Tapered small samplecovariance (N = 10)
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
State covariance approximationFFT and waveletsExamples
Fast Wavelet Transforms
An orthogonal change of basis like the fast Fourier transform,but uses localized waveforms.
Advantages over FFT:
Fast (O(n) rather than O(n lg n))
Can handle localized features
Little to no Gibbs effect fromdiscontinuities
Wide range of waveforms tochoose from for different kinds offeatures
Coiflet octave 2
Coiflet octave 4
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
State covariance approximationFFT and waveletsExamples
Spectral covariance estimation
Basic idea: Do the sample covariance in spectral space andthrow away off diagonal terms.
uk ← S(uk )
diag QN ← 1N − 1
N∑k=1
(uk − uk )2
QN is the covariance in spectral space. We can convert backto model space for diagnostics.
QN ← S−1(I)QnS(I)
We can handle covariances between multiple variables bycomputing blocks of the covariance independently.
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
State covariance approximationFFT and waveletsExamples
A simple 1D model
Consider a two variable model with solutions generated by
vk ← hk exp(− (x − ck )2 /w2
k )
hk ∼ N (1.0, 0.12)
ck ∼ N (0.3, 0.12)
wk ∼ N (0.1, 0.012)
wk ← 0.3vk +n∑
j=1
λjk
j2 sinjx2π
λjk ∼ N (0, 1).
vk is a Gaussian bump with random center, width, and height.wk is a smooth field with a small correlation to vk .
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
State covariance approximationFFT and waveletsExamples
Comparison of covariance estimates
Large sample (N = 1000) Small sample (N = 10)
FFT covariance (N = 10) Wavelet covariance (N = 10)
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
State covariance approximationFFT and waveletsExamples
Spectral EnKF
EnKF using only the diagonals of the covariances in spectralspace.
For one variable (where C(·, ·) is the diagonal of the samplecovariance):
uk ← S(uk )
Huk ← S(Huk )
K ← C(uk , Huk )(C(Huk , Huk ) + R)−1
uk ← uk + K (S(d) + ek − Huk ), ek ∼ N (0,R)
uk ← S−1(uk )
Each variable in the model is updated individuallyAll computations are done on diagonal matricesFaster than EnKF with localization similar to tapering
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
State covariance approximationFFT and waveletsExamples
The spectral EnKF—1D model revisited
Comparison using an observation of the first variable. Shown isthe first ensemble member for each method.
EnKF FFT EnKF Wavelet EnKF
v1
w1
Forecast: black dashed line Data: red dotted line Analysis: blue solid lineJan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
Morphing EnKF for a reaction-diffusion PDE fire model
X (m)
Y (m
)
0 100 200 300 400 5000
100
200
300
400
500
X (m)
Y (m
)
0 100 200 300 400 5000
100
200
300
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500
X (m)
Y (m
)
0 100 200 300 400 5000
100
200
300
400
500
Data Forecast Analysis
High fire heat areas in propagating surface fire. Forecastensemble members are have their fire areas spread over thesimulation domain. Analysis brings the ensemble closer to thedata and moves the fire areas.
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
WRF coupled with wildfire spread
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
Data assimilation for the coupled WRF and fire model
Data source No assimilation
Standard EnKF Morphing EnKF
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
A real coupled WRF and fire run
Surface fire heat flux shown in Google Earth. Slower fuels keepburning behind the fireline. Data assimilation coming soon.
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
Assimilation of precipitation radar data
OPERA radar data givenevery 15 minutes for 20hours over WesternEurope, processed to bedirectly comparable withthe RAIN field.WRF simulation showingincorrect precipitation.The precipitation field inWRF is diagnostic only.Data assimilation must relyon correlation betweenRAIN and other fields.
model
radar
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
To test morphing on an operational system:Registration used to compute a morphing function thatmoves the model RAIN field to the radar data.Morphing function applied to standard fields: wind (U, V ,W ), temperature (T ), pressure (PH), humidity (MU). Noamplitude changes yet.Restart model from the morphed WRF output file and runnext 15 minutes.Repeat.
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 00_15 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 00_30 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 00_45 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 01_00 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 01_15 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 01_30 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 01_45 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 02_00 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 02_15 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 02_30 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 02_45 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 03_00 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 03_15 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 03_30 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 03_45 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 04_00 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 04_15 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 04_30 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 04_45 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 05_00 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 05_15 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 05_30 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 05_45 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 06_00 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 06_15 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 06_30 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 06_45 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 07_00 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 07_15 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 07_30 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 07_45 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 08_00 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 08_15 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 08_30 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 08_45 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 09_00 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 09_15 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 09_30 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 09_45 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 10_00 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 10_15 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 10_30 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 10_45 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 11_00 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 11_15 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 11_30 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 11_45 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
no morphing radar
small morphing large morphing
Time 12_00 : RAIN at surface
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
Conclusions from morphing test:Morphing standard fields over land causes artifacts in themodel due to conservation laws, esp. the large morphing.With this setup, very small modifications are necessary, butit is unclear if it actually helps.Our collaborators will try different combinations of morphedvariables.Need to look at WRF-Var’s change of variables (streamfunctions, etc).Need to look at HWRF’s use of a simple linear map tomove the vortex and change the hurricane size, with aconservation adjustment.
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
Other possible applications of morphing
Forecasting in geosciencesprecipitation, storms, squall lineshurricanespollution transportlocation of ocean currents
Forecasting in sociology and political sciencespread of epidemics (pilot project funded by NIH)spread of social networks and memesspread of behavior patterns and social strata (criminality,abuse, gentrification)
Anything where movement of features in space isimportant, especially when the features reinforcethemselves instead of dissipatingWe are looking for applications and collaborators!
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
Assimilation of point data (near future)
Our current morphing software is limited to raster data over allor a big part of the domain, such as images. Extension to pointobservations by matching lines in timespace - assimilate intomany time levels at once. Also to handle delayed observations.
Spacetime morping EnKF will match the dotted line - a timeseries of observations at a fixed location - by a deformation of
the space at the analysis time (upper left edge).
Jan Mandel Morphing and wavelet EnKF
Morphing EnKFSpectral and wavelet EnKF
Applications
Wildfire reaction-diffusion modelWRF coupled with wildfire spreadAssimilation of precipitation radar data to WRF
References
J. D. BEEZLEY AND J. MANDEL, Morphing ensemble Kalmanfilters, Tellus, 60A (2008), pp. 131–140.
J. D. BEEZLEY, J. MANDEL, AND L. COBB, Wavelet ensembleKalman filters, in Proceedings of IEEE IDAACS’2011, Prague,September 2011, vol. 2, IEEE, 2011, pp. 514–518.
J. MANDEL, J. D. BEEZLEY, J. L. COEN, AND M. KIM, Dataassimilation for wildland fires: Ensemble Kalman filters incoupled atmosphere-surface models, IEEE Control SystemsMagazine, 29 (2009), pp. 47–65.
J. MANDEL, J. D. BEEZLEY, AND A. K. KOCHANSKI, Coupledatmosphere-wildland fire modeling with WRF 3.3 and SFIRE2011, Geoscientific Model Development, 4 (2011), pp. 591–610.
Jan Mandel Morphing and wavelet EnKF
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