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Mapping and Exploring Data
Ana P. Barros
1st Workshop on Understanding Climate Change from Data, University of Minnesota, August 15-16 2011
Water Cycle Extremes and Nonlinearities from Data
Exploratory Data Analysis Detection and Attribution (Understanding)
Predictability Physically-based Data-Driven Models Modeling Myths (Black-Box/Data Assimilation)
Metrics Diagnostics Impacts (Actionable Prognostics)
√
Philosophy –> Method –> System -> Outcomes
Long-Lead Forecasts of Extreme Events for Water Resources Management Drought Forecasting in the Murray-Darling Basin
Ana Barros Gavin Bowden*
Relationship with ENSO
Harmonic analysis of 24-month Log-Normal (LND) percentiles of precipitation
composites for strong ENSO years (Troup SOI < -5) at 345 stations (100 years of data)
Jul(-1)
Jul(0)
Jan(0)
Jan(+1)
X=Xo+ Ci cos(a-ai)
1st harmonic i=1
Phase (a1): 0-2 months after July of current EL Nino year
0.8
Barros and Bowden, 2008
to achieve predictability ….... precursors of ENSO onset
• SST anomalies (SSTAs)
• Zonal OLR monthly anomaly gradients (NOAA,1979-2002,2.5ox2.5o) (Barros and Bindlish 1998)
• Zonal Windstress Anomalies (Western Equatorial Pacific, COAPS)
(Clark&Van Gorder 2001; Curties et al. 2002)
Goal
12 month lead-time areal mean SPI12
1 2 3 4 5 6 7 8 9 10 11 12 ………..24
F1 F2
***Length of Record ***Non-stationarity
12-month
SPI PC
RMSE/R
Calibration
Set
RMSE/R
Validation
Set
1 4.86
0.76
4.65
0.74
2 1.57
0.60
4.63
0.05
3 1.22
0.77
1.13
0.37
SOLO OUTPUTS
Barros and Bowden, 2008
PC 1 72.8% PC 2 7.2% PC 3 5.3% PC1 72.8% PC2 7.2% PC3 5.3%
Barros and Bowden, 2008
-0 .4
-0 .3
-0 .2
-0 .1
0
0 .1
0 .2
0 .3
0 .4
19
61
19
63
19
65
19
67
19
69
19
71
19
73
19
75
19
77
19
79
19
81
19
83
19
85
19
87
19
89
19
91
19
93
19
95
19
97
19
99
-3
-2
-1
0
1
2
3
4
SS
T (
ºC)
W in d s tre s s A n o m a ly - 5 m o n th M A
N IN O 3 .4
Barros and Bowden, 2008
Barros and Bowden, 2008
Summary
What is the right measure of drought in the context of desired (useful) predictability? What is useful predictability?
How can we best use such studies…… to assess data needs? to test and improve physical models? to learn?
A question of pride and prejudice…
Can we afford not to explore such models?
January 2005
Fast Dynamics
Slow Dynamics
Coupled System
1 log()
Uncoupled System λ()
0
50
0
20
40
60
0
20
40
60
PWAT(n)
NARR Trajectory (26.25N,86.13W) Spring 2000
PWAT(n-)
PW
AT
(n-2
)
phase points
start point
end point
0100
200300
0
100
200
300
0
100
200
300
ITMP(n)
ISCCP Trajectory (26.25N,86.13W) Spring 2000
ITMP(n-)
ITM
P(n
-2)
phase points
start point
end point
0 1 20
0.5
1
1.5
2
2.5
3
log()
FS
LE
( )
NARR
ISCCP
100oW 95
oW 90
oW 85
oW 80
oW 75
oW
24oN
27oN
30oN
33oN
36oN
39oN
Spring[Day]
2
4
6
8
10
100oW 95
oW 90
oW 85
oW 80
oW 75
oW
24oN
27oN
30oN
33oN
36oN
39oN
Summer[Day]
2
4
6
8
10
100oW 95
oW 90
oW 85
oW 80
oW 75
oW
24oN
27oN
30oN
33oN
36oN
39oN
Fall[Day]
2
4
6
8
10
100oW 95
oW 90
oW 85
oW 80
oW 75
oW
24oN
27oN
30oN
33oN
36oN
39oN
Winter[Day]
2
4
6
8
10
100oW 95
oW 90
oW 85
oW 80
oW 75
oW
24oN
27oN
30oN
33oN
36oN
39oN
Spring[Day]
20
40
60
80
100
120
140
160
100oW 95
oW 90
oW 85
oW 80
oW 75
oW
24oN
27oN
30oN
33oN
36oN
39oN
Summer[Day]
20
40
60
80
100
120
140
160
100oW 95
oW 90
oW 85
oW 80
oW 75
oW
24oN
27oN
30oN
33oN
36oN
39oN
Summer[Day]
20
40
60
80
100
120
140
160
Figure 3 – Phase-space trajectories of NARR PWAT (a) and ISCCP ITMP (b) in 3D time-delay:
PWAT(n), PWAT(n-_) and PWAT(n-2_) denote each component of the time-delay coordinates; similarly for ITMP(n), ITMP(n-_) and ITMP(n-2_). The delay 2 is the time interval at which the data are available, specifically every three hours.
Figure 4 - FSLE curves for NARR PWAT(black symbols) and ISCCP ITMP (green symbols) spatial
series along a latitudinal transect (35.63o N, Fig 2) for the spring of 2000.
a)
b)
Figure 5 - Moderate-perturbation FSLE fields for NARR PWAT: a) summer, and b) fall
a)
b)
Figure 6 - Large-perturbation FSLE fields for NARR PWAT: a) summer, and d) winter.
a)
b)
Figure 7 - Moderate-perturbation FSLE fields for NARR Cloud Water content for winter: a) 700 hPa; b)
850 hPa.
a)
b)
Figure 8 - Moderate-perturbation FSLE fields for ISCCP ITMP: a) summer, and b) fall.
a)
b)
Figure 9 – Large-perturbation FSLE fields for ISCCP ITMP: a) summer, and b) winter.
a) b)
•d)
Figure 10 – Diurnal cycle of NARR PWATCLM FSLE in the moderate perturbation regime: a) 0300
UTC, and b) 1500 UTC in the summer; and c) 0300 UTC and d) 1500 UTC in the fall.
a)
b)
Figure 11 – ISCCP minimum FSLE fields at the transition between the moderate and large perturbation
regime at 1500 UTC: a) summer; and b) fall.
•b)
•d)
Figure 12 - Localization length fields in the moderate-perturbation regime for NARR PWAT: a)
spring, b) summer, c) fall, and d) winter.
a)
b)
b)
Figure 14 – Spring localization length fields in the large-perturbation regime: a) NARR; b ) ISCCP ITMP.
a)
b)
Figure 15 – Summer localization length fields in the large-perturbation regime: a) NARR; b ) ISCCP
ITMP.
a) b)
•d)
Figure 16 - FSLE vs. Perturbation for ISCCP ITMP and NARR PWAT: a) spring, b) summer, c) fall, and d) winter.
Finite-Size Lyapunov Exponents (place-based)
Tao and Barros 2009, Barros 2010
Tao and Barros,2009 Barros 2010
NARR
ISCCP
100oW 95
oW 90
oW 85
oW 80
oW 75
oW
24oN
27oN
30oN
33oN
36oN
39oN
Summer[Day]
2
4
6
8
10
100oW 95
oW 90
oW 85
oW 80
oW 75
oW
24oN
27oN
30oN
33oN
36oN
39oN
Summer[Day]
2
4
6
8
10
Tao and Barros, 2009
)(~)Pr(
c
1,1
1
exp1
1,
'1
'1
1
)(
CC
CC
c
0 500 10000.98
1
1.02
1.04
1.06
(a) C1=0.1
0 500 1000
1
1.1
1.2
(b) C1=0.2
0 500 1000
1
1.2
1.4
1.6
(c) C1=0.3
0 500 1000
1
1.5
2
2.5
(d) C1=0.4
0 500 1000
1
2
3
4
(e) C1=0.5
0 500 1000
2
4
6
(f) C1=0.6
0 500 1000
2468
1012
(g) C1=0.7
0 500 1000
5
10
15
20
25
(h) C1=0.8
0 500 1000
10
20
30
40
(i) C1=0.9
x
(x)
0.9 1 1.10
20
40
(a) C1=0.1
0.5 1 1.50
5
10
15
(b) C1=0.2
0.5 1 1.5 20
2
4
6
(c) C1=0.3
0 1 2 30
1
2
3
(d) C1=0.4
0 2 4 60
1
2
(e) C1=0.5
0 5 100
1
2
(f) C1=0.6
0 5 10 150
0.5
1
1.5
(g) C1=0.7
0 10 20 300
0.5
1
1.5
(h) C1=0.8
0 20 40 600
0.5
1
(i) C1=0.9
(x)
Pro
babili
ty D
ensity
Multifractal Scaling
0 500 1000
2
4
(a) =0.5
0 500 1000
5
10
15
(b) =0.9
0 500 1000
10
20
30
(c) =1.3
0 500 1000
20
40
60(d) =1.7
x
(x
)
Sun and Barros, 2010
Longitude
La
titu
de
125W 120W 115W 110W 105W30N
35N
40N
45N
50N
-1000m
-500 m
0 m
500 m
1000 m
0
0.5
1
Pa
ram
ete
r V
alu
e
C1
s
NCDC(a)
Multifractal Parameters
C1
s
NARR(b)
C1
s
GPCP(c)
0
0.5
1
C1
s
(d)
C1
s
(e)
C1
s
(f)
Sun and Barros, 2010
Sun and Barros,2010
Mu
ltif
ract
al α
Brunt-Väisäila *
Using Multifractals to develop new subgrid-scale parameterizations of terrain-forced convection
HPC Opportunities “compression”
Model Populations
Nogueira et al. 2011
Kim and Barros, 2001 Barros ,2005
754 km2 8684 km2
1147 km2
Prediction in Ungauged Basins - PUB May 2004
18-hr Forecasts over a 5-year period
Barros,2005
Yoo and Barros,2004
6 radiosondes GOES IR 160 raingauges
Artificial Intelligence
Knowledge Discovery
Data Driven Models Data Mining Methods
Learning and Making Decisions Anchored to the Best Available Information