New developments in WRF-SFIRE

Jan Mandel, Jonathan D. Beezley, Adam K. Kochanski, Volodymyr Y. Kondratenko, Martin Vejmelka

University of Colorado Denver, University of Utah, CERFACS, Czech Academy of Sciences

Research supported by NSF EGS-0835579, NSF DMS-1216481, NSF CNS-0821794, NIST 60NANB7D6144, and NASA Fire program

Numerical Wildfires, Cargese May 2013

Acknowledgements

UCD: Minjeong Kim, Bedrich Sousedik

NCAR: Janice Coen, John Michalakes, Ned Patton

WRF developers at NCAR and the WRF community

University of Utah: Mary Ann Jenkins, Erik Anderson, Joel Daniels, Chris Johnson, Eric Jorgensen, Bigyan Mukherjee, Emanuele Santos, Claudio Silva, Lin Zhang, Mavin Martin, Paul Rosen

Bulgarian Academy of Sciences: Nina Dobrinkova, Georgi Jordanov

Weather It Is, Inc., Israel: Barry Lynn and Guy Kolman

See www.openwfm.org/wiki/WRF-Fire#Contributors for further details.

What are WRF-Fire and WRF-SFIRE?

• WRF-Fire as currently included in WRF release is SFIRE from November 2010, with some features removed, minor edits, and some renaming. See http://www.openwfm.org/wiki/Fire_code_in_WRF_release for details.

• WRF-SFIRE is available at openwfm.org. New features from 2010 include:• vertical wind interpolation from logarithmic boundary layer• diagnostic outputs for fire danger rating• built-in fuel moisture model• standalone executable running from WRF output files with atmosphere state• coupling with WRF-Chem• assimilation of RAWS fuel moisture data (under development)• changing the fire perimeter/perimeter ignition (under development)• level set function based on minimal arrival time (time of ignition)

                                                                     SFIRE

Coupled model WRF-SFIRE-moisture-Chem

Atmosphere  model  WRF

Surface  fire  spread  model

Wind

Heat  and  vapor  fluxes

Fuel  moisture  model

Surface  air  temperature,  rela@ve  humidity,rain

Chemical  transport  model  WRF-­‐Chem

Fire  emissions  (smoke)

Representa@on  of  the  fire  area  by  a  level  set  func@on

• The  level  set  func@on  is  given  on  center  nodes  of  the  fire  mesh• Interpolated  linearly,  parallel  to  the  mesh  lines• Fireline  connects  the  points  where  the  interpolated  values  are  zero    

Evolving the fireline by the level set method

Level  set  func@on L

Level  set  equa@on

Fire  area:   L<0

Right-­‐hand  side  <  0  →  Level  set  func@on  goes  down  →  fire  area  grows

R = R0(1 + cwv↵ + csg�)

• R0 – spread rate with no wind�

• v – wind speed

• g – terrain slope

• R0, cw, cs,↵,� – coe�cients from fuel properties

R = R0(1 + cw(w · n)↵ + cs (rh · n)�)

Fire area = {x : L (x) < 0} represented

by the level set function L, advanced by

the level set equation

@L

@t= �R k5Lk

1

The fire model: fuel consumption

igni@on

fuel

@me

Time  constant  of  fuel:30  sec  -­‐  Grass  burns  quickly

1000  sec  –  Dead  &  down  branches(~40%  decrease  in  mass  over  10  min)

Integrating fuel left over mesh cells, with submesh fire region representation

Coupling with WRF-ARW

• WRF-ARW is explicit in time

• Physics packages including fire are called only in the last Runge-Kutta substep

• Fire module inputs wind, outputs heat and vapor flux

Chapter 3

Model Discretization

3.1 Temporal Discretization

The ARW solver uses a time-split integration scheme. Generally speaking, slow or low-frequency(meteorologically significant) modes are integrated using a third-order Runge-Kutta (RK3) timeintegration scheme, while the high-frequency acoustic modes are integrated over smaller timesteps to maintain numerical stability. The horizontally propagating acoustic modes (includingthe external mode present in the mass-coordinate equations using a constant-pressure upperboundary condition) are integrated using a forward-backward time integration scheme, and ver-tically propagating acoustic modes and buoyancy oscillations are integrated using a verticallyimplicit scheme (using the acoustic time step). The time-split integration is similar to that firstdeveloped by Klemp and Wilhelmson (1978) and analyzed by Skamarock and Klemp (1992).The time-split RK3 scheme is described in general terms in Wicker and Skamarock (2002).The primary di⌅erences between the descriptions found in the references and the ARW imple-mentation are associated with our use of the mass vertical coordinate and a flux-form set ofequations, along with our use of perturbation variables for the acoustic component of the time-split integration. The acoustic-mode integration is cast in the form of a correction to the RK3integration.

3.1.1 Runge-Kutta Time Integration Scheme

The RK3 scheme, described in Wicker and Skamarock (2002), integrates a set of ordinarydi⌅erential equations using a predictor-corrector formulation. Defining the prognostic variablesin the ARW solver as ⇤ = (U, V,W, ⇥, ⇥⇥, µ⇥, Qm) and the model equations as ⇤t = R(⇤), theRK3 integration takes the form of 3 steps to advance a solution ⇤(t) to ⇤(t + �t):

⇤� = ⇤t +�t

3R(⇤t) (3.1)

⇤�� = ⇤t +�t

2R(⇤�) (3.2)

⇤t+�t = ⇤t + �tR(⇤��) (3.3)

where �t is the time step for the low-frequency modes (the model time step). In (3.1) – (3.3),superscripts denote time levels. This scheme is not a true Runge-Kutta scheme per se because,

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Runge-­‐Ku[a  order  3  integra@on  in  @me  

4.1. Variables and equations

The model is formulated in terms of the hydrostatic pressure vertical coordinate �, scaled and shifted so that � = 1at the Earth surface and � = 0 at the top of the domain. The governing equations are a system of partial differentialequations of the form

d⇤

dt= R (⇤) , (20)

where ⇤ = (U, V,W,⌅�,⇥, µ�, Qm). The fundamental WRF variables are µ = µ (x, y), the hydrostatic componentof the pressure differential of dry air between the surface and the top of the domain, written in perturbation formµ = µ + µ�, where µ is a reference value in hydrostatic balance; U = µu, where u = u (x, y, �) is the Cartesiancomponent of the wind velocity in the x-direction, and similarly V and W ; ⇥ = µ⇥, where ⇥ = ⇥ (x, y, �) is thepotential temperature; ⌅ = ⌅ (x, y, �) = ⌅ + ⌅� is the geopotential; and Qm = µqm is the moisture contents of theair. The variables in the state ⇤ evolved by (20) are called prognostic variables. Other variables computed fromthem, such as the hydrostatic pressure p, the thermodynamic temperature T , and the height z, are called diagnosticvariables. The variables that contain µ are called coupled. The value of the right-hand side R (⇤) is called tendency.See (Skamarock et al. 2008, pp. 7-13) for details and the form of R.

The system (20) is discretized in time by the explicit 3rd order Runge-Kutta method

⇤1 = ⇤t +�t

3R�⇤t

⇥

⇤2 = ⇤t +�t

2R (⇤1)

⇤t+�t = ⇤t +�tR (⇤2) (21)

where only the third Runge-Kutta step includes tendencies from physics packages, such as the fire module(Skamarock et al. 2008, p. 16). In order to avoid small time steps, the tendency in the third Runge-Kutta stepalso includes the effect of substeps to integrate acoustic modes.

4.2. Surface schemes

In real cases, non zero sf sfclay physics should be selected to enable the surface model, allowing forproper interaction between the atmosphere and the land surface. In idealized cases, users have an option ofthe basic surface initialization, intended to be used without the surface model, or the full surface initialization(sfc full init=1). The latter allows for using all standard land surface models even in idealized cases. Foridealized cases with full surface initialization, land surface properties like roughness length, albedo etc., are definedthrough the land use category. The surface scheme utilizes a gridded array containing the number of landusecategory, defined in a text file (LANDUSE.TBL), which specifies the roughness length and other surface properties,both for the real and idealized cases. The land use categories may be also defined directly trough the namelistvariables or read in from an external file containing a 2D landuse matrix (see also Sec. 7).

5. COUPLING OF THE FIRE AND THE ATMOSPHERIC MODELS

The terrain gradient is computed from the terrain height at the best available resolution and interpolated to the firemesh in preprocessing. Interpolating the height and then computing the gradient would cause jumps in the gradient,which affect fire propagation, unless high-order interpolation is used.

In each time step of the atmospheric model, the fire module is called from the third step of the Runge-Kuttamethod. First the wind is interpolated to a fixed height zf above the terrain (currently, 6.1m following BEHAVE),

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The fire model is running on a finer mesh than the atmosphere model

Wind  interpola@on• Spread  rates  for  different  fuels  depend  on  wind  at  “midflame”  height  given  by  the  fuel  5me

• Linear  interpola@on  of  wind  as  a  func@on  of  log(height/roughness  height).  Exact  if  the  wind  profile  is  exactly  logarithmic  (just  like  piecewise  linear  interpola@on  is  exact  for  linear  func@ons)  independently  of  the  ver@cal  mesh  spacing

• If  there  are  no  WRF  nodes  under  6m,  mathema@cally  equivalent  to  the  BEHAVE  wind  reduc@on  factors.  

• It  gets  tricky– The  heights  of  the  nodes  are  computed  from  the  geopoten@al,  which  is  a  part  of  the  solu@on

– The  geopoten@al  varies  a  lot  near  the  fire– The  atmospheric  and  fire  mesh  have  different  resolu@ons– The  result  depends  on    the  roughness  length.– Take  the  roughness  length  from  LANDUSE  or  fuels?

wind speed

roughness height

midflame height

WRF mesh level 1

WRF mesh level 2

Structure of the coupled WRF-SFIRE code

Core:  @me  step  for  the  level  set  equa@on,  compute  fuel  loss.  

Dimensionless.

Phys:  sensible  and  latent  heat  fluxes  from  fuel  loss,  fire  rate  of  

spread  

Driver:    get  grid  variables,  get  flags,  interpola@on  calls,  OpenMP  loops,  DM  halos

WRF:    call  sfire_driver  

U5l:  interpola@on,  WRF  stubs,  debug  I/O,…

Atm:  one  @le:  temperature  and  moisture  tendencies  from  heat  

fluxes

wind

Model:  one  @me  step,  one  @le:  winds  in,  heat  fluxes  out

WRF:    error  messages,    log  messages,  constants,…

WRF:      add  tendencies  

heat  and  moisture  tendencies

Standalone Sfire code

Core:  @me  step  for  the  level  set  equa@on,  compute  fuel  loss.  

Dimensionless.

Phys:  sensible  and  latent  heat  fluxes  from  fuel  loss,  fire  rate  of  

spread  

U5l:  interpola@on,  WRF  stubs,  debug  I/O,…

Model:  one  @me  step,  one  @le:  winds  in,  heat  fluxes  out

Wrf_fakes:    error  messages,    log  messages,  constants,…

MAIN

WRF parallel infrastructure - MPI and OpenMP

• Distributed memory (DM): halo exchanges between grid patches: each patch runs in one MPI process; programmer only lists the variables to exchange

• Shared memory (SM): OpenMP loops over tiles within the patch

• Computational routines are tile callable.

• Fire model executes on the same horizontal tiles as the atmosphere model, in the same threads

MPI

OpenMP threads,multicore

Example: 2 MPI processes 4 threads each

The parallel infrastructure constrains the algorithms used.

patch

halo

tile

Parallelism in WRF-Fire: implementing a PDE solver in WRF physics layer, meant for pointwise calculations

Parallel performance

101

102

103

10!1

100

101

Number of cores

Exe

cutio

n t

ime

/Sim

ula

tion

tim

e

Parallel scaling (total)

actualideal

101

102

103

10!2

10!1

100

Number of cores

Exe

cutio

n t

ime

/Sim

ula

tion

tim

e

Parallel scaling (fire only)

actualideal

• 2009 Harmanli fire (Bulgaria), satellite data. Janus cluster, University of Colorado/NCAR. Intel X5660 processors. 180x180x41, 221x221x41 atmosphere grids 50m, fire mesh 5m. Time step 0.3 s.

• Faster than real time on 120 cores.

Crime and punishment

• Euler equations require inflow velocity boundary conditions only. Yet WRF imposes lateral boundary conditions (from global weather state) all around

• WRF makes it up by only nudging at the boundary, and artificial viscosity and smoothing in a layer around the boundary...it’s a balancing act. Ideal runs are fine.

• We are using WRF in a regime it was not meant for: up to 1MWm-2 fire heat flux, very fine meshes

color: vertical wind component + firearrows: horizontal windall wind at level 18 (approx. 2km altitude)2009 Harmanli fire, Bulgariamodel setup: Georgi Jordanov, Nina Dobrinkova, Jon Beezley

smoothed strip

red dot = instability

Diagnos@c  outputs• Heat  flux  (reac@on  intensity)  (J/m2/s)• Rate  of  spread  (m/s)• Fireline  intensity  

–Byram(J/m/s)–new  fireline  intensity  (J/m/s2)

• For  an  ongoing  fire  modeled:  at  the  fireline  only• For  a  fire  danger  ra5ng:  everywhere,  with  the  rate  of  spread  taken  as  the  maximum  rate  in  any  direc@on.

Fireline  intensityByram’s: heat per unit length of the fireline from all available fuelburning in 1s, regardless how far, does not depend on the speed of burning (J/m/s)

1m

New: heat per unit length of the fireline from the newly burning fuel only the fireline moves over in a small unit of time (J/m/s2)

1m

Documentation and user support: openwfm.orgEveryone is welcome to get an account!

Coupling with WRF-Chem

Talked about already.

Fuel  moisture  model• Equilibrium  -­‐  @me  lag  model  for  moisture  m

• Equilibrium  E  from  air  rela5ve  humidity,  temperature,  and  pressure,  different  drying  and  wemng  equilibria  when  approaching  equilibrium  from  above  and  from  below

• Runs  on  the  atmosphere  grid  for  all  fuel  components  (1h,  10h,  100h,...)    independently  of  any  fuel  maps

• Numerical  method:  2nd  order,  adap@ve  switching  to  exponen@al,  exact  up  to  rounding  for  constant  coefficients  and  any  @me  step

• Components  moisture  are  then  combined  in  propor@ons  specified  by  fuel  type  and  interpolated  to  the  fire  grid.

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dmdt

= E −mT

Gentle  rain  moisture  model

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• In  rain,  large  equilibrium  E=250%  and  variable  @me  lag  from  rain  intensity  r.  Parameters:  

• asympto@c  wemng  @me  lag  T for  very  strong  rain• Satura@on  rain  intensity              ,  when  1-­‐1/e    of  the  asympto@c  rain-­‐wemng  @me  T  is  reached

• Rain  under  threshold                        ignored

dmdt

= E −mT

1− exp − r − r0rs

⎛⎝⎜

⎞⎠⎟

⎛

⎝⎜⎞

⎠⎟

rs

r < r0

Calibra@on  of  rain  response

• The  empirical  Canadian  fire-­‐danger  ra@ng  model  gives  final  fuel  moisture  aqer  24  hours  from  the  ini@al  moisture  and  the  rain  accumula@on

• The  @me-­‐lag  model  calibrated  at  @me  lag  14h  and  satura@on  rain  intensity  8mm/h24

Fine  fuels  moisture  model  response

• The  drying  and  wemng  equilibria  are  computed  from  the  WRF  state.  The  fuel  moisture  contents  does  not  change  when  it  is  between  the  two  equilibria.  The  red  ver@cal  lines  correspond  to  periods  of  rain,  where  the  equilibrium  is  2.5  (above  the  range  shown).  The  fuel  moisture  contents  increases  during  rain.

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Assimila@on  of  fuel  moisture  data

• extended  Kalman  filter  applied  to  the  extended  fuel  moisture  state  at  every  grid  node  separately

• observa@on  func@on:  10h  fuel  moisture  at  the  node• state  covariance  at  each  node  will  couple  the  moisture  of  all  fuel  types  and  affect  affect  also  those  not  measured

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m = (m1,m2,…,mn ,ΔE,ΔS)wheremk is the moisture in fuel type kΔE is common change in drying and wetting equilibriaΔS is the change in the soaking equilbrium (from 250%)

Measurements• RAWS  measure  the  moisture  of  10  hours  fuel  (shown  for  Santa  Ana  fires  near  San  Diego)

• Need  to  transport  the  data  and  the  uncertainty  to  all  grid  nodes

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!

Transport  the  moisture  data  values  and  variances  to  grid  nodes

Data  analysis  shows  some  spa@al  covariance  structure  between  RAWS  in  California,  but  none  in  Colorado  Rocky  Mountains.  Can’t  do  kriging,  trend  surface  modeling  instead.  First  a  linear  regression:

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RAWS data = Xsβ + e, e N(0,γ 2I +σ 2I )γ 2I = stations error cov (assumed known, more generally diagonal Γ)σ 2 = microscale variance (unknown)RSSn − k

= unbiased estimate of γ 2 +σ 2, max likelihood at RSSn − k − 2

n = number of stations (measurements)k = number of columns of β (covariates)Different station variances more complicated - EM method

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Fitting RAWS data = Xsβ + error

Choice of the covariates = columns of Xrows = locations on the whole domain, Xs is the matrix of rows for the locations of the data− All ones− Current forecast from the moisture model− T2 - temperature at 2m − P2 - pressure at 2m− Current rain intensity− Latitude, longitude, elevation

Transpor@ng  the  values  and  variances  from  the  regression  to  the  nodes

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Regression: data = X sβ + e, e N (0,Γ +σ 2I )

get estimated σ 2 and β. Approximation at an arbitrary location t:value at t estimated as x(t)β where x(t) is the t-th row of the covariate matrix X recall that X s is the submatrix of the rows of X for the data locations

variance at t estimated as σ 2 + x(t) X sT Γs +σ

2I( )−1X s( )−1

x t( )T

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!

Data  assimila@on  results

The  mean  square  differences  between  non-­‐assimilated  and  assimilated  fuel  moisture  state  es5mates  and  RAWS  observa5ons  (top)  and  microscale  variability  variance  es5mates  as  a  func5on  of  5me  (boVom)  for  the  Southern  California  test.

Assimilated  10hr  moisture

32

!

Perimeter  igni@on  and  moving  the  fire  in  data  assimila@on

• Models  start  from  igni@on  point.  But  oqen  only  a  developed  perimeter  is  available.

• Cannot  light  up  the  whole  area  at  once  -­‐  too  much  energy.  Cannot  ignore  the  inside  either.

• For  the  proper  circula@on  to  develop,  the  heat  need  to  be  release  gradually

• Evolve  the  fire    back  in  @me  and  compute  the  igni@on  @mes  everywhere.  Then  replay  the  igni@on  @mes  to  release  the  heat  gradually.

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2007  Santa  Ana  fires

34

35

Given  fire  perimeter Simula@on  from  igni@on  points

Burned  area  at  20:00:00  10-­‐22Witch  and  Guejito  fire  2007

Evolving  the  given  perimeterback  in  @me

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Propaga@on  forward  and  back  in  @me  by  hybrid  automata-­‐level  set  method

• repeated  update  of  igni@on  @me  at  neighbors• related  to  minimal  arrival  @me  and  Fast  Marching  Method• stable  for  mosaic  fuels  -­‐  ROS  varies  on  cell  scale• level_set_func0on  =  igni0on_0me    -­‐    0me_now• level  set  func@on  give  submesh  scale  gradual  heat  release

• to  go  back  in  @me:  subtract  @me  not  add,  max  not  min37

t

min t + distanceROS

⎧⎨⎩

⎫⎬⎭

Burned  area  at  20:00

38

Original  simula@on  from  igni@on  pointsFrom  ar@ficial  igni@on  @me

39

Given  fire  perimeter Original  simula@on  from  igni@on  points

Difference  

Con@nuing  the  simula@on  aqer  the  given  perimeter  @me

40

Given  fire  perimeter Original  simula@on  from  igni@on  points

Used  opera@onally  in  Israel

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Future  plans• Fire  danger  24  hrs  forecast  website  for  Colorado  Front  Range  (using  wind,  RH,  fuels  maps,....)

• Have  model,  can  go  back  to  data  assimila@on  as  planned  10  yrs  ago–  spectral  ensemble  methods  (FFT  wavelets,  polynomial  chaos,...)– Outputs  -­‐  visualize  probability,....

• Assimila@on  of  satellite  and  airborne  data–  es@ma@on  of  vegeta@on  moisture–  fire  spread  -­‐  change  state  and  parameters  in  coupled  model

• Simultaneous  assimila@on  of  fire  and  standard  meteo  data•  Support  other  spread  model  (Balbi,...),  use  TKE• Crown  fire• Improve  emissions  model  -­‐  depends  on  stage,  flame  vs.  smoldering• Intermediate  CFD  model  between  surface  fire  and  mesoscale  weather  model...

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