1. Improved synthesis data products
using multiple constraints model
data assimilation
Prof Damian Barrett, Luigi Renzullo, Anthony Almarza
University of Queensland
CSIRO

2. Background
• Synthesis products key output of TERN
• Need robust methods to combine high volume
datasets in computationally efficient manner &
provide quantitative estimates of uncertainty
• Model Data Assimilation: A synthesis analysis
of information contained two satellite datasets:
1. Diagnose canopy conductance (gc)
2. Prognose soil moisture (qA & qB)
• Only possible by linking TERN AusCover and
NCRIS National Computational Infrastructure
(ANU) within eMAST Facility

3. ‘Traditional’ biophysical modeling
Vegetation &
soil classes
Parameters
BIAS!
300
250
q
200
m
z SEB TS 150
100
50
0
T V TS 300
0 100 200 300 400 500 600
250
q Sm1 Microwave RT TB 200
150
100
50
0
0 100 200 300 400 500 600
M

4. Model Data Assimilation: (1) Inverse model
IceSAT r , n
300
250
200
150
100
50
0
0 100 200 300 400 500 600
Forward Model Veg Height Op RT-1
LAI
300
250
q TS q z 
200
m
z SEB TS 150
100
50
0
T V TS 300
0 100 200 300 400 500 600
TB qS1 
250
q Sm1 Microwave RT TB 200
150
100
50
0
0 100 200 300 400 500 600
H= M-1

5. Model Data Assimilation: (2) Assimilating observations
IceSAT r , n
300
250
200
150
100
50
0
0 100 200 300 400 500 600
Assimilation
Forward Model Veg Height Op RT-1
LAI
300
250
q TS q z 
200
m
z SEB J TS 150
100
50
0
T V TS 300
0 100 200 300 400 500 600
TB qS1 
250
q Sm1 Microwave RT J TB 200
150
100
50
0
0 100 200 300 400 500 600
H
q za
gc
q Sa1
0.15
Infiltration/Runoff 0.1
Diagnostics
0.05
0
0 10 20

6. Gain Matrix
• K is a function of model sensitivities and model + observation covariances
1. Provides spatial information on where observations maximally inform model
2. ‘Smears’ information spatially from where observation are to where they are not
3. Allows calculation of prediction errors for analysis variables
• H is the ‘tangent linear operator’: sensitivity of model to states/parameters
• Two large computational steps: Calculating covariances (H B HT + R) and then inverting it
é ù
ê ¶H ¶H
 ú
ê ¶x1 ¶x2 ú
ê x1 x1
ú
ê ¶H ¶H ú
H =ê  ú
ê ¶x1 x2
¶x2 x2 ú
ê ú
ê    ú
ê ú
ë û

7. Covariances: (H B HT + R)
Covariance matrix (441 x 441) Spatially correlated grid (21 x 21)
1.9 x 105 elements Exp lag correlation

8. Error covariance matrix: (H B HT + R)
Region: 550 x 460 km
Matrix size:
4 x 253,000 x 253,000 Jan 2003 – Dec 2011
= 2.56 x 1011 elements
5 km grid cells:
4 x 10,120 x 10,120
= 20,240 x 20,240
= 4.10 x 108 elements
Computation:
9 years daily data
24 hours wall time
20 CPU cores
+ GPU routines for QR
decomposition to yield
Inverse & generate K 20
0 5 10 15 25 30
covariance units (K2)

9. Error covariance matrix: (H B HT + R)
Shows:
1. Length scale correl.
2. Similar veg behavior
3. Info ‘smearing’
4. Source analysis errors
0 5 10 15 20 25 30
covariance units (K2)

10. Inferred canopy conductance based on obs TS & TB
Mean gc [Range 0.1 – 11.1 mm/s] s gc [Range 0.01 – 10 mm/s]

11. Analysis corrections (Qanalysis – Qopen loop)
A Horizon [Range 0.14 – 20 mm] B Horizon [Range 0.14 – 20 mm]

12. Summary
• Synthesis products key output of TERN
• MDA provides a rigorous mathematical
framework to generate synthesis products
through the combination of multiple datasets
and biophysical models
• The move away from classification data to
continuous variables reduces bias introduced
into biophysical model output leading to better
model prediction
• TERN and NCRIS infrastructure have
provided the mechanism by which
computationally intensive synthesis products
can be generated from fundamental satellite
observations and models