Data Assimilation in a Coupled LandBoundary Layer System

1
Data Assimilation in a Coupled Land-Boundary
Layer System Dara Entekhabi MIT Steve
Margulis UCLA David Flagg York University
GLASS/GABLS Workshop 19-21 September 2005
2
Motivation Capability to monitor and map surface
turbulent fluxes (LE and H) are lacking. Need to
develop techniques to extract information content
of existing data on states.

• Specific Questions
• Can we estimate model structural errors?
• What are mapped (versus point) key parameters of
  turbulent flux?

3
Data Assimilation or State Estimation of Dynamic
Systems

• Definitions
• State variables -- dependent variables of
  system differential equations, also called
  prognostic variables.
• Forcing variables input variables from outside
  the system that do not depend on the system
  state.
• Measurements -- variables that are observed (with
  measurement error) and can constrain state
  variables.
• Output variables derived variables that depend
  on state and input variables, also called
  diagnostic variables.

Rethink system boundaries
4

• Synthetic experiment
• Generate synthetic observations with known model
  error and initial conditions (allows for testing
  of algorithm)
• Application to FIFE
• Tested for 20-day window at FIFE site
• First 10 days marked by strong advection (model
  error) and atmospherically-controlled evaporation
  rate
• Second 10 days marked by low advection and
  soil-controlled evaporation

5
Basic Components of a Data Assimilation Problem
The System Equation describes the evolution of
system states (y) through time
The Measurement Equation describes the
relationship between states and measurements (Z)
a and u are parameter and forcing vectors and w
and n are model and measurement errors
6
The system equation is the set of prognostic
equations for the coupled land surface-atmospheric
boundary layer
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Atmospheric Boundary Layer Model Mixed-layer
Energy and Moisture Budgets Mixed-layer
growth and ABL-top inversions
8
Land Surface Model Canopy and Soil Energy
Budgets Soil Moisture Budget
9
Estimation of ABL and Land Surface States,
Fluxes, and Model Error using a Variational
Approach
Motivating Question Can we estimate unknown land
surface states and fluxes by merging readily
available observations and a coupled land
surface-ABL model?
System Observations Radiometric surface
temperature (Ts) Standard reference-level
micrometeorology (Tr, qr)
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In Variational data assimilation, measurements
are merged with the model by minimizing a least
squares penalty function over a specified
assimilation window t0 tf
The problem is solved iteratively, by integrating
the state equation (forward model) followed by
the adjoint model and update equations for the
parameters and model error
11
c
)
-1
(kg kg
r
q
Day
Synthetic Experiment Prior (dashed black
line) Posterior (magenta line) Observations
(blue dots)
12
305
300
295
290
285
0
1
2
3
4
5
f
(K)
g
T
Day
Synthetic Experiment Prior (dashed black
line) Posterior (magenta line) Observations
(blue dots)
13
Synthetic Experiment Prior (dashed blue line)
Posterior (solid blue line) True model error
(dashed blue)
14
FIFE Observations
)
-1
(kg kg
r
q
Day of Year
15
FIFE application Prior (dashed black
line) Posterior (magenta line) FIFE observations
(blue dots)
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FIFE application The assimilation provides a
posterior estimate of advection-related model
errors. Note the large advection event (cool/dry
air) centered on Day 193. By definition the
prior (dashed magenta line) estimate is zero.
17
FIFE application Prior (dashed black
line) Posterior (magenta line) FIFE observations
(blue dots)
18
2000
c
1500
h (m)
1000
500
0
193
Day of Year
FIFE application Prior (dashed black
line) Posterior (blue line) FIFE observations
(circles)
19
Summary

• Methodology shows ability to estimate land
  surface states and fluxes from readily available
  observations
• Coupled model reduces needed auxiliary forcing
  data and allows for inclusion of observations
  which would otherwise be used as forcing
• Estimation scheme may be used to diagnose
  structural model errors

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2. What are mapped (versus point) key parameters
of turbulent flux?
Tower-Based Measurements Neither Reveal
Dependencies Nor Allow Mapping Fa Ca U (
Asurf - Aair ) Scaling Parameter Ca is Key
Unknown.
What is Ca at Mapping Resolutions? How Does Ca
Depend on Landscape Characteristics? Does Ca
Respond to Climate Anomalies Through Vegetation?
Is This a Feedback?
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Thermal Signature and Atmospheric Impact
May 10 Dry soil. Clear with scattered to broken
cirrus May 20 Moist soil. Mild winds and clear.
May 18-19 90 mm Rain
H/LE1
H/LElt1
CASES97, BAMS, 81(4), 2000.
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Impact of the Efficiency of Turbulent Exchanges
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Impact of the Surface Moisture Availability
WET
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Estimation of Surface Conditions from
Satellite-Based Land Temperature
Dynamic approach
Divergence of G is Heating Rate
When State Observations T are Noisy, the Tendency
Term Cannot Be Constructed
Static (Empirical) Approach (e.g. SEBAL, ALEXIS,)
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G/Rn
Local Hour
Empirical Approach Fails. Causes Major Phase
Errors.
(Santanello and Friedl, 2003)
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System Equation
Surface Medium Heat Diffusion
Constant During Month
E
L
EF

s

H
Constant During Daytime
E
L
Evaporative Fraction
Uses No Information About Land Cover and
Vegetation
27
(No Transcript)
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Measurement Equation
Radiometric Land Surface Temperature State
M
Lower
res.
Higher
res.
observations
observations
(e.g. GOES
-
8
(e.g. AVHRR)
SSM/I)
State
Vector
T
s
Tobs M TR ?
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Example of assimilation of multi-scale/multi-senso
r LST estimates (SGP 97)
GOES 8
AVHRR
GOES 8
GOES 8
AVHRR
GOES 8
GOES 8
AVHRR
GOES 8
GOES 8
AVHRR
GOES 8
SSM/I
SSM/I
SSM/I
SSM/I
AVHRR
AVHRR
AVHRR
AVHRR
Model LST
Model LST
Air Temperature
Air Temperature
Radiation
Forcing
Radiation
Forcing
Estimated
Heat
Flux
Estimated
Heat
Flux
Wind
Speed
Wind
Speed
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Variational Adjoint-State Assimilation System
Minimize a Multi-scale Penalty Function
State Misfit Penalty
Parameter Estimation Error Penalty
Adjoint Physical Model
EF varies daily, Ch vary on a monthly time scale
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Ch
NDVI (Not Used)
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Very Poor Quality Flux Data For Evaluation at
SGP. Better FIFE Data Used Extensively Earlier
(But Not Multiscale and Mapping)
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Results fluxes estimation
LE Wm-2
Half-hour fluxes
r RMSE Wm-2 LE 0.92 56.19 H 0.90
31.18
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Assesment of the assimilation algoritm FIFE 1987
DAILY AVERAGE LATENT HEAT FLUX
500
modelled
measured
400
300
200
100
0
150
160
170
180
190
200
210
220
230
240
Julian day (1987)
DAILY AVERAGE SENSIBLE HEAT FLUX
250
modelled
measured
200
150
100
50
0
150
160
170
180
190
200
210
220
230
240
Julian day (1987)
Daily average fluxes
r RMSE Wm-2 LE 0.98 19.77 H 0.99
9.87
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Summary Wealth of Existing LST Measurements
May be Used Effectively to Constraint an
Estimation System With Minimal Model and
Auxiliary Data Requirements Example...Possibilit
y of Mapping Key Unknown and Problematic
Parameter of Land Surface Models (e.g., z0h)
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Estimation of ABL Growth Entrainment Ratio
using an Ensemble-Variational Approach
Motivating Question Can we estimate the
entrainment ratio AR for FIFE IFC days using a
data assimilation framework? Daytime
mixed-layer growth is governed (with uncertain
parameter ch) by
Forced convection term
Free convection term
The entrainment ratio is strongly coupled to this
growth rate
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A primary drawback of the traditional variational
approach is that it provides no error bounds on
the posterior parameter estimate which may be
extremely sensitive to model inputs (initial
conditions, parameters, forcing, etc.) Here we
develop an ensemble-variational approach, where
the variational algorithm is run for an ensemble
of uncertain model inputs to obtain a posterior
distribution of the entrainment parameter (ch)
and entrainment ratio (AR) estimates.

• Method is applied to nine Intensive Field
• Campaign (IFC) days at FIFE
• Observations used for assimilation
• Radiosonde obs. q obs, qobs, hobs
• Micrometeorology obs. Trobs, qrobs

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Estimates of the entrainment parameter ch and
average daytime surface and entrainment fluxes
for each analysis day. The entrainment ratio AR
is computed from the equation shown above. The
error bounds correspond to /- one standard
deviation from the posterior estimate ensemble.
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0.7
0.6
0.5
-
0.4
R
A
0.3
0.2
0.1
140
150
160
170
180
190
200
210
220
230
240
Julian Day
Estimates of entrainment ratio AR at the FIFE
site for the nine Intensive Field Campaign (IFC)
days examined.
40
Surface and ML-top entrainment fluxes Posterior
(magenta line) FIFE observed (blue circles)
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b
R
A
2
R
0.21
-1
U
(m s
)
m
Dependencies of AR The results show a small
correlation between entrainment and wind,
indicating additional factors may be responsible
for the variability in AR.
42

• Key Conclusions
• Data assimilation methodology allows for
  estimation of ABL growth and entrainment from
  radiosonde and micrometeorology data
• Ensemble-Variational approach yields estimates
  of both mean and uncertainty
• Mean estimate of AR0.40 /- 0.11 at FIFE site
  (much larger than early literature values of 0.2)