Exploring the Weather on Mars by
Data Assimilation: An Overview
Luca Montabone – LMD, Paris, France (and University of Oxford, UK)

Contributors
T. (LJ) Ruan, D. Mulholland, P. L. Read - Univ. of Oxford, UK
S. R. Lewis, L. Steele - The Open University, UK
S. Greybush – University of Maryland, USA
J. Wilson – GFDL, USA
M. Richardson – Ashima Research Center, USA
T. Navarro –	  LMD,	  Paris,	  France
CPS workshop -4th February 2013

Basic principle

Courtesy	  of	  R.	  Young,	  Univ.	  of	  Oxford	  Objectives
Data Assimilation aims to:Ø Produce a regular, physically consistent, four dimensional
representation of the state of a system• from a heterogeneous array of in situ and remote instruments
which sample imperfectly and irregularly in space and time

• e.g. to initialize a model prediction/forecastØ Enable reconstruction of state variables that are not measured
directly• Accessing data-sparse areasØ Identify and characterize systematic model errors and biases• from statistics of misfit to measurements

Strategies
DA has its origin in:Ø (Least square) curve fitting• Given a “model” y = M (x;a, b) := ax + b and observations(xi , yi ), i = 1,..., M, the optimal estimate of model parametersa, b is provided by minimizing: J = ∑ (yi − (axi + b))

2iØ Bayes’ theorem• Given inexact and incomplete observations y and a deterministic
model M connecting x and y, the probability of state x, given yand M is:prob(y | x, M)prob(x | M) Prior	  prob(x | y, M) =prob(y | M) Support	  of	  y	  to	  Posterior	  イメージを表示できません。メモリ不足のためにイメージを開くことができないか、イメージが破損している可能性があります。コンピューターを再起動して再度ファイルを開いてください。それでも赤い x が表示される場合は、イメージを削除して挿入してください。

x	  • The optimal estimate of state x is provided by maximizing prob

Strategies
Several Categories of DA Strategies:Ø Sequential (or “real time”)• Treats measurements in chronological order or from the past &present onlyØ Non-sequential• Can use measurements from both past, present and futureØ Intermittent• Produce analysis at coarsely discrete intervals
Ø Continuous• Assimilates measurements when they become available

Strategies

Strategies
DA general strategy:Ø General form of sequential estimator: x a = x b + W(y − H[x b ])• xa - Analysis• xb - Background or a priori (e.g. earlier model prediction)• y - Observations• W - Matrix of weights• H - Observation operatorØ Other useful quantities• xt – True state• B – Covariance of background errors (xb – xt)• R – Covariance of observation errors (y – H[xt])• A – Covariance of analysis errors (xa – xt)

Strategies
DA general strategy:Ø The “Best Linear Unbiased Estimator” (BLUE) analysis (or “optimalinterpolation” analysis) is the state xa which minimizes the cost function:

J(x) = (x − x b )T B−1 (x − x b ) + (y − H[x])T R −1 (y − H[x])Ø If background and observation errors are Gaussian, then xa is a “maximumlikelihood estimator”.
Ø Different sequential schemes compute/approximate covariances and PDFs indistinctive ways:• Ensemble Kalman Filter – Estimates covariances by a Monte Carloensemble of perturbed model simulations• 3D-Var – Avoids computing weights by iteratively minimising J(x) (atfixed time):	  ∇J(x) = 2B−1 (x − x b ) − 2HT R −1 (y − H[x])• 4D-Var – Iteratively minimises J(x) evaluated over a finite time intervalAnalysis Correction

Ø A pragmatic approach to data assimilation, used by the UK Met Office(1988-1999) and developed by Lorenc et al., 1991.	  	  Ø Take first guess (‘background’) field: x[0]=xb & observations y[0]=yoØ Use iterations

x(n +1) = x(n) + WQ[y(n)− H[x(n)]]• W – Matrix of weights (assumed diagonal) based on distance between
model points and observations

Q•– Normalisation, based on observation density & error statistics• .x(n) → x a (BLUE) as n → ∞	Analysis Correction

Courtesy	  of	  R.	  Young,	  Univ.	  of	  Oxford	  Analysis Correction
Goal: find analysis (xa)at each model grid point

Observa2ons	  Model	  Grid	  Points	  Ø Analysis at a given grid point:background at that point (xb)	  plus
a weighted sum (W) ofobservation increments (y-H[xb])within a localization radius.
Ø Analysis increment at a given
grid point is based on only one
realization.
Ø Background, or forecast, errors
are usually deterined a priori andmight or might not evolve withthe flow.

Ensemble Kalman Filter

Ensemble Kalman Filter

Ensemble Kalman Filter

Ensemble Kalman Filter

Ensemble Kalman Filter

Ensemble Kalman Filter

Ensemble Kalman Filter
Goal: find analysis (xa)at each model grid point

Observa2ons	  Model	  Grid	  Points	  Ø Analysis at a given grid point:background at that point (xb)	  plus
a weighted sum (W) ofobservation increments (y-H[xb])within a localization radius.
Ø Analysis increment at a given
grid point is a local linear
combination of ensemble
perturbations.
Ø Background, or forecast, errors
are described by an ensemble of
MGCM states , and evolve withthe flow (an important advantageof ensemble data assimilationmethods).

DA for Mars (so far…)
Data Assimilation for Mars is a worldwide effort:
Strategy
Analysis
Correction

Ensemble
Kalman filter

DA Scheme

GCM Model

State/Mainpurpose

Oxford UniversityACand The Open (Lorenc et al.
University (UK)1991)

LMD-UK
MGCM(Spectral)

TES and MCS
Reanalyses

GFDL(Spectral)

TES Reanalysis /OSSEGroup

University ofMaryland(MA, USA)

LETKF(Hunt et al.
2007)

AshimaResearch(CA, USA)

DART
MarsWARF Initial TES Reanalysis /(Anderson @ (Finite Differences) model bias studyNCAR)

LMD(Paris, France)

LETKF(Hunt et al.
2007)

In preparation/Quasi
LMD MGCM(Finite Differences) real time Exomars
TGO assimilation

UK Mars DA
UK “Mars Analysis Correction
Data Assimilation” (MACDA)
Model: LMD-UK Mars
General Circulation Model

Observations (so far):Temperature,
Dust Optical Depth*Water vapour*Water ice

Mars Global Surveyor*In progress

Assimilation Scheme:
Analysis Correction(Lorenc et al., 1991)

Mars Reconnaissance
Orbiter

Courtesy of J.-B.
MadeleineUK Mars DA

500

Horizontal
Correlation
Scale

450
400
350km

Information
TimeFactor-1h Now

1h2h

3h

4h5h

UK Mars DA: A bit of history" First attempts:
Lewis & Read (1995), Lewis et al. (1996, 1997)" First development of AC scheme for Mars:
Lewis et al. (2007)" Implementation and validation of TES assimilation:
Montabone et al. (2006)" Science based on TES assimilation:
Variability of dust storms: Montabone et al. (2005)
Thermal tides: Lewis & Barker (2005)
Weather at Beagle 2 atmospheric entry: Montabone et al. (2006)
Radiative effects of tropical clouds: Wilson et al. (2008)
2001 planet encircling dust storm: Martinez-Alvarado et al. (2009)
Atmospheric predictability: Rogberg et al.(2010)

UK Mars DA: Present studies" Science based on TES assimilation:
Solstitial pause in baroclinic wave activity: Lewis et al.
Boundary layer studies: Lewis et al.
Super-rotating equatorial jets: Ruan et al.
Non-local effects of dust storms: Montabone et al.
Dynamics and variability of polar vortices: Montabone et al.

" Science based on TES and MCS assimilation:
Dust cycle and variability of dust storms: Ruan et al.
Water ice clouds: Lee et al.

" Science based on assimilation of future observations:
Ozone photochemistry: Holmes et al.

UK Mars DA: TES 3-year reanalysis

MarsAnalysis
Correction
DataAssimilation(so far, for MGS/TES)

PUBLICLY AVAILABLE ONLINE
Search	  for	  “MACDA”	  at	  	  http://badc.nerc.ac.uk/
search/	  LMD-UK Mars GCM
Dynamical Core:(Semi-) spectral(adapted from University of Reading,
Hoskins et al. 1974, and ECMWF improvements)
Physical Parameterizations:
LMD / University of Oxford / The Open University /Istituto de Astrofisica de Andalusia
Typical resolutions:
5°x5° degrees in horizontal (down to ~1°x1° degrees)
25 layers in vertical (σ-coordinates) or more (up to 200)

Observations
Spacecrafts, Instruments and Availability
MY 24

MY 25

Ls=102 °

MY 26

MY 27

MY 28

MY 29

Ls=80 °

MGS
TES
MRO
MCS

Ls=128 °MY 30

Observations: MGS/TES# Dust Retrievals (☼)

MY24

MY25

MY26

Mars Global Surveyor

Thermal Emission
Spectrometer# Temp. Retrievals (☼)

MY27

MY24

MY25

MY26

MY27

Nadir Temperature profiles (below ~ 40 km)
Total dust optical depth* Water vapour* Water ice* In progressObservations: MRO/MCS# Retrievals (☼)# Retrievals ( )

MY28

MY29

MY30

MY28

MY29

MY30

Mars Reconnaissance
Orbiter

Limb Temperature profiles (below ~ 80 km)

Mars Climate Sounder* Limb dust optical depth profiles

Column integrated dust optical depth* In progress

Selection of past results
Mars Global Surveyor spacecraft
MOC camera

Variability ofdust storms
20 June 2001

Averages over Ls =195º–225º
31 July 2001

Montabone et al., 2006

Wilson et al., 2008

Selection of past results

Radiative effectsof tropicalclouds

Selection of present results
Solstitial pause in baroclinic wave activity
62.5°N, MY24

Transient Temperature at 50 Pa, ~25 Km (TES data assimilation)

Transient Surface Pressure (TES data assimilation)
Lewis et al., in preparation

Selection of present results

RMS	  Temperature	  (TES	  data	  assimilation)	  	  	  	  	  	  (2.5	  km	  altitude)	  Selection of present resultsRMS	  Meridional	  Wind	  (TES	  data	  assimilation)	  	  	  	  	  	  (2.5	  km	  altitude)	  Theore&cal	  conﬁrma&on	  of	  sols&cial	  pause	  :	  Near-­‐surface	  baroclinic	  waves	  ac&vity	  in	  LMD/UK	  GCM	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  (RMS	  of	  Temperature	  at	  2.5	  km)	  Non	  ac&ve	  clouds	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  Ac&ve	  clouds	  tau	  	  =	  0.2	  	  	  	  	  	  	  	  	  MY	  24	  	  Scenario	  Mulholland	  et	  al.,	  in	  preparation	  Work inspired by results inKuroda et al. , 2008

Selection of present results
Work in progress( by “LJ” Ruan)

Time series at ~55 km altitude (~0.04 mbar)

Zonal wind(semi-annual oscillation)
Zonal mean, daily averages

Work inspired by results inLewis & Read, 2003

Selection of present results

Zonal wind(Westerly equatorial jet)
Zonal mean, daily averages

Selection of present results
Latm
s=−1 > 0Local super-rotation index: Mars
Lrest

Selection of present results
Latm
s=−1 > 0
Local super-rotation index: Mars
Lrest

Autumn (LS = 195°—225°) in MY24 and MY25

Selection of present results
Latm
s=−1 > 0
Local super-rotation index: EarthLrest

Mars	  (Past)	  Earth	  B.	  Harris	  (Ph.D.	  
thesis,	  2009)	  “Nothing is Perfect,Nothing is Finished,Nothing Lasts.”(“Wabi-Sabi” aesthetic)

Everything Evolves!
(…after Darwin)

Dust assimilation
Old scheme (dust is not transported)Dust assimilation
New “2D” scheme (dust is transported,column opacity is assimilated)

So far, only
one dust
size istrasported(1 µm)

Dust assimilation
New “3D” scheme (dust is transported,full dust opacity profile is assimilated)Dust assimilation
MCS temperature + dust opacity profile assimilation,
MY 28, Ls=262.5° (Northern winter), nighttime

Dust assimilation
MCS temperature + dust opacity profile assimilation,
MY 28, Ls=262.5° (Northern winter)

Dust assimilation
MCS temperature + dust opacity assimilation,
28, Ls=330.5° (Northern winter)

MYUK AC assimilation: Data impact