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Transcript
Hydrologic Impacts of Climate
Change : Scale Issues and
Uncertainties
P P Mujumdar
Dept. of Civil Engineering &
Divecha Center for Climate Change, IISc.
Organisation of the Talk

Introduction – Hydrologic Processes

Climate Change Impacts : Scope of Research

Scale Issues & Uncertainties
 Meteorologic droughts
 River basins : water availability
 River Water Quality
 Urban flooding

Summary
21 July 2011
Asian Climate Change
2
Hydrologic Processes in a
Catchment
Source: http://hydrogeology.glg.msu.edu/research/active/modeling-and-monitoring-hydrologicprocesses-in-large-watersheds
21 July 2011
Asian Climate Change
3
•Air Temperature
•Net Radiation
•Wind Speed
•Vapour Pressure
•Relative Humidity
•Soil Moisture
•Type of Vegetation/Crop
•Season of Vegetation/Crop Growth
21 July 2011
Asian Climate Change
Source for figure : http://eoedu.belspo.be/en/applications/evapcontexte.asp?section=4.1
Factors affecting Evapotranspiration
4
Physical
characteristics
affecting runoff
21 July 2011
Rainfall intensity
Rainfall amount
Rainfall duration
Distribution of rainfall over the basin
Antecedent moisture content
Credit : USGS
Asian Climate Change
RUNOFF
Land use
Vegetation
Soil type
Drainage area
Basin shape
Elevation
Topography
Drainage network
patterns
Ponds, lakes,
reservoirs etc. in the
basin
Hydro - meteorological factors affecting
runoff
5



Increasing Temperatures
 Evapotranspiration
 Water Quality
Change in Precipitation Patterns
 Streamflow; Water availability
 Intensity, Frequency and
Magnitude of Floods and
Droughts
 Groundwater Recharge
Rise in Sea Levels
 Inundation of coastal areas
 Salinity Intrusion
21 July 2011
Asian Climate Change
6
Fig. Source: ww.engr.uconn.edulanboG229Lect111SWIntru.pdf
Climate Change – Hydrologic Implications
Research Issues of Interest
•Water availability
•How do water fluxes vary on catchment scale
in response to global climate events?
•Impacts on Water Quality
•Change in Frequency and Magnitude of
extreme events
•Design storm intensities - Urban Flooding
•Delays in onset of monsoon
•Impact on agriculture
•Over-year storage policies
•Real-time adaptive decisions
•Water Demands
• Evapotranspiration
• Municipal and Industrial Demands
•Salinity Intrusions & Coastal flooding
•Robust & Resilient water management policies
Source for the map:
to offset adverse impact due to climate change www.mapsofIndia.com
21 July 2011
Asian Climate Change
7
Hydrologic impact assessment
Spatio-temporal
scale mismatch
Accuracy of
tropospheric vs
surface
variables
Source: Xu C.Y., Water Resources Management 13: 369–382, 1999.
21 July 2011
Asian Climate Change
8
Need for downscaling
A schematic diagram describing the statistical downscaling approach. GCMs provide
useful predictions for large-scale atmospheric patterns (lower part). Details contained within a
grid box (upper part) are influenced by local features beyond the resolution of current global
climate models.[Source: http://www.bom.gov.au/info/GreenhouseEffectAndClimateChange.pdf ]
21 July 2011
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9
Downscaling the GCM outputs
to the river basin scales
21 July 2011
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Downscale
Global climate models (GCM: resolution coarser than 20) ; Size of grid box: Tens of
thousands of square kilometers.
GCM Grid
(~2.50)
Grid size of
interest in
hydrology
(~0.20 – 0.5100)
Projecting Climate Change Impacts on Hydrology
Climate Change Projections
(precipitation, temperature,
radiation, humidity)
Topography, Landuse Patterns; soil
characteristics;
Downscaling
Hydrologic Model
Possible Future Hydrologic
Scenarios on Basin Scale
21 July 2011
(Streamflow, Evapotranspiration, Soil
Moisture, Asian
Infiltration,
Groundwater
Climate Change
11
Downscaling
Downscaling: to model the hydrologic variables (e.g., precipitation) at a
smaller scale based on large scale GCM outputs.
Dynamic Downscaling: uses complex algorithms at a fine grid-scale
(typically of the order of 50 Km × 50 Km) describing atmospheric process
nested within the GCM outputs; commonly known as Limited Area
Models (LAM) or Regional Climate Models (RCM).
Statistical Downscaling: produces future scenarios based on statistical
relationships between large scale climate features and hydrologic variables.
Assumption- Statistical relationships hold good in future for changed
climate scenario.
Advantage- computationally simple.
Climate Predictors : Must be reliably simulated by GCMs; readily available from archives
of GCM outputs and strongly correlated with the surface variables of interest
21 July 2011
Asian Climate Change
12
Climate change effects in the Colorado river basin
Source: Christensen et al. (2004), Climatic Change 62, 337–363
Naturalized: effects of water
management removed
Colorado River basin with 1/8degree VIC routing network
and major system of reservoirs
Drainage Area : 6,30,000 sq. km; Serves 7 states; 12 major reservoirs – water supply, hydropower
and flood control ; 70% runoff from Snow pack; Average Annual Runoff : 18.6BCM
Current demands in the basin are not much lower than the mean flow. A mere 10%
reduction in mean annual flow has major implications for the reservoir system
performance; Reliability of a reservoir system decreases rapidly as the demands
approach the mean flow;
21 July 2011
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13
Climate change effects in the Colorado river basin
Downscaled temperature and precipitation from Parallel Climate Model
(PCM) – 105 year simulations
21 July 2011
Asian Climate Change
Source: Christensen et al. (2004), Climatic Change 62,
337–363
HIST : Historical (observed) : 1950-1999
CTRL : Control Climate Simulation (1995 greenhouse gas levels)
BAU: Business as usual scenario for periods 1–3: 2010–2039, 2040–
2069 and 2070–2098
14
Downscaling GCM Simulations to Precipitation : Orissa
Meteorological Sub-division
• Coastal Area
GCM Grids Surrounding
the Case Study Area
• Increase of
hydrologic
extremes in
recent past
21 July 2011
• Increase in
temperature:
1.10C/century,
whereas in
average increase
in India:
0.40C/century.
Asian Climate Change
15
NCEP grid points surrounding the
meteorological sub-division Orissa
Statistical downscaling
(Principal component analysis, fuzzy
clustering, transfer functions)
Climate Predictors:
MSLP and 500 hPa
geopotential height
Data Used : Rainfall : 1950-2003 (source : IITM Pune)
Climate Predictors : from NCEP Reanalysis Project
21 July 2011
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16
Projected Rainfall
CCSR/NIES GCM with B2 Scenario
Increase
decrease
21 July 2011
Asian Climate Change
17
GCMs and Scenarios Used
21 July 2011
Asian Climate Change
18
Projections of SPI (Drought Indicator)
21 July 2011
Asian Climate Change
19
pdfs of Drought Indicator


Water Resources Research , No. 43, (2007)

All
scenarios
are equally
possible
Projections
from all
GCMs are
equally
likely to be
realized.
Time series
generated
by a
downscaled
GCM
simulation
with one
scenario is
considered
as one
realization.
21 July 2011
Asian Climate Change
20
Projections with A1B Scenario
21 July 2011
Asian Climate Change
21
Weights for A1B Scenario
Assignment of weights :
Reliability Ensemble
Averaging Algorithm
Two reliability criteria :
(a) Performance of the
model in reproducing
the present-day
climate (“model
performance”)
(b) Convergence of
simulated changes
across models
(“model convergence”)
21 July 2011
Asian Climate Change
22
Projected Rainfall
(Weighted Mean CDF; A1B scenario)
Limitation Reducing the present knowledge about climate sensitivity to a single
probability distribution would clearly mis-represent the scientific disagreement
( Hall et al., 2007).
21 July 2011
Asian Climate Change
23
Imprecise Probability
Provides an envelope of probability distribution
21 July 2011
Asian Climate Change
24
Bounds for Probability of Drought
Journal of Geophysical Research, 114
(2009)
21 July 2011
Asian Climate Change
25
Mahanadi River Basin - Streamflow
Hirakud Dam
Predictand:
Predictors
2m Surface Temperature
Geopotential Height at 500 hPa
Specific Humidity
Mean Sea Level Pressure
21 July 2011
Asian Climate Change
Monsoon Streamflow
of Mahanadi River at
Hirakud Dam
26
Selection of Predictors

Streamflow: result of rainfall, evaporation and infiltration.

Monsoon: insignificant infiltration compared to streamflow.

Rainfall: consequence of Mean Sea Level Pressure (MSLP)
(Bardossy and Plate, 1991; Bardossy et al., 1995; Hughes and
Guttrop, 1994), Geopotential Height (Stehlik and Bardossy, 2002)
and Specific Humidity (Crane and Hewitson, 1998).

Evaporation: mainly guided by temperature and humidity (Wilby and
Harris, 2006)

Predictors selected: 2m surface air temperature, MSLP, geopotential
height at 500 hPa and surface specific humidity
21 July 2011
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27
Observed and Predicted Streamflow
(from NCEP/NCAR reanalysis data)
Observed
Predicted
7332 Mm3
7384 Mm3
Std. Dev 5996 Mm3
4607 Mm3
Mean
Nash-Sutcliffe coefficient, E = 0.67
21 July 2011
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28
Possibilistic Approach

Assumptions of earlier models on GCM and scenario
uncertainty: equal possibility and equi-probability of all the
scenarios.

With the passage of time, it is relevant to assess the
effectiveness of the GCMs in best modeling climate change
and also to judge which of the scenarios best represent the
present situation under climate forcing.

Scope of the study: assignment of possibility distribution to
different GCMs and scenarios, measured in terms of their
ability in modeling climate change based on their performance
in the recent past (years 1991-2005) under climate forcing
21 July 2011
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29
Possibility Distribution of GCMs and Scenarios
Water Resources Research , No. 44,
(2008), AGU
Model Uncertainty is greater than Scenario
Uncertainty
Possibility assigned to GCM : possibility with which the future hydrologic scenario is
modeled best by the downscaled output of the GCM ; Possibility assigned to a scenario :
possibility with which the scenario best represents the climate forcing in the study area
21 July 2011
Asian Climate Change
30
Projected Streamflow CDF
21 July 2011
Asian Climate Change
31
Projections for future monsoon inflows
to Hirakud Reservoir
Reduction in
‘normal’ (middle
level) flows
Range of projected future flow duration curves at Hirakud
21 July 2011
Asian Climate Change
32
Projected Irrigation Water Demand :
CGCM2; A2 ; Source : Asokan and Dutta
(2009)
Projected Peak and Average Discharge;
CGCM2; A2; Source : Asokan and Dutta
(2009)
Flood Storage
Dam
Live Storage
Hydropower
21 July 2011
Asian Climate Change
Irrigation
33
Hirakud Reservoir : Serves Flood Control, Hydropower
and Irrigation
Gross Storage : 5896 Mm3
Live Storage : 4823 Mm3
Installed Capacity : 347.5 MW
Firm Power
: 134 MW
Adaptive Operating Policies : Derived
with Stochastic Dynamic Programming,
with tradeoffs between flood control,
hydropower and irrigation, with an
objective of maximising hydropower in
future years.
2045-65
21 July 2011
Asian Climate Change
34
Impacts: Performance measures
Adaptive Policy using SDP (Policy 1)
Reliability-power
0.604
Current (1959-2005)
A1B
0.5
2045-65
MIROC3.2
0.453
CGCM2
0.502
GISS
A1B
2075-95
MIROC3.2 0.366
0.276
CGCM2
0.403
GISS
Resiliency-power
0.229
Current (1959-2005)
A1B
2045-65
MIROC3.2 0.214
0.218
CGCM2
0.215
GISS
A1B
2075-95
MIROC3.2 0.155
0.123
CGCM2
0.178
GISS
21 July 2011
A2
0.484
0.523
0.515
A2
0.286
0.146
0.423
B1
0.462
0.471
0.514
B1
0.382
0.294
0.458
A2
0.215
0.224
0.221
A2
0.159
0.103
0.175
B1
0.206
0.202
0.213
B1
0.177
0.255
0.18
Reliability-irrigation
0.834
A1B
0.799
MIROC3.2
0.796
CGCM2
0.802
GISS
A1B
0.592
MIROC3.2
0.544
CGCM2
0.599
GISS
Vulnerability-power
0.688
A1B
0.824
MIROC3.2
0.956
CGCM2
0.911
GISS
A1B
1
MIROC3.2
0.952
CGCM2
0.878
GISS
Asian Climate Change
A2
0.798
0.802
0.801
A2
0.497
0.447
0.614
B1
0.795
0.801
0.801
B1
0.601
0.535
0.634
A2
0.895
0.75
0.873
A2
0.933
1
0.883
B1
0.931
0.935
0.903
B1
0.966
1
0.865
Reliability-Flood Control
0.907
A1B A2
MIROC3.2 0.906 0.921
0.961
0.95
CGCM2
0.899 0.905
GISS
A1B A2
0.93
MIROC3.2 0.944
0.95 0.988
CGCM2
0.916 0.902
GISS
Deficit ratio-power
0.311
A1B A2
0.41
MIROC3.2 0.395
0.429 0.381
CGCM2
0.381 0.377
GISS
A1B A2
0.65
MIROC3.2 0.558
0.677
0.8
CGCM2
0.525 0.501
GISS
B1
0.939
0.955
0.897
B1
0.916
0.984
0.894
B1
0.43
0.395
0.371
B1
0.571
0.673
0.466
35
35
Rule curve for adaptive policies
194
192
Reservoir level (m)
Curr rule curve min
190
Curr rule curve max
188
SDP 2045-65
186
Adaptive policy 1
Adaptive policy 2
184
Adaptive policy 3
182
SDP 1959-2005
180
178
1-Jul
1-Aug
1-Sep
2-Oct
Date
21 July 2011
Asian Climate Change
36
Advances in Water Resources (2010)
Rule curve at Hirakud for adaptive policies
Impacts on River Water Quality
Non-point source of pollution
21 July 2011
Asian Climate Change
37
Schematic Diagram of Tunga-Bhadra River
Shimoga City Sewage
Tunga
Shimoga
4
4
MPML VISL
3
3
Bhadra
Lakavalli
1
1
Tunga - Bhadra River
5
5
6
Honnali City Sewage
2
Harlahalli
6
2
Kumudavathi
7
7
Honnali
16
8
BhadravathiCity
Head Water Flow
Point Load
8
9
Kuppelur
Reach
Reach End point
Check point
MPM VISL HPF -
21 July 2011
15
12
9
14
Harihar City Sewage
10
13
11
10
11
12
13
HP
14
Dhavangere
City Sewage
Byladahalli
Haridra
Mysore Paper Mill
Vishveshwaraya Iron and Steel Limited
Harihara Poly Fibers
Asian Climate Change
38
Temperature
Station
Variable
Air
Temperature
Shimoga
Water
Temperature
Air
Temperature
Honnali
Water
Temperature
Air
Temperature
Kuppelur
Water
Temperature
21 July 2011
Period
1988 – 1999
To
2000 - 2006
1988 – 1999
To
2000 - 2006
1988 – 1999
To
2000 - 2006
1988 – 1999
To
2000 -2006
1991 – 2001
To
2002 - 2006
1991 – 2000
To
2002 - 2006
Annual Mean Change
Streamflow
Increase by 0.215 oC
Increase by 0.599
oC
Increase by 0.315
oC
Increase by 3.34 oC
Increase by 1.39 oC
Station
Period
1971 – 1991 To 1992 2006
1980 – 1990 To 1991 Honnali
2006
1991-1999 To 2000Kuppelur
2006
Byladahal 1985 – 1995 To 1996 li
2005
Shimoga
% Reduction
in Annual
Mean Flow
3.1
12.26
16.8
24.16
Increase by 1.79 oC
Asian Climate Change
39
Climate Change Impact Assessment ;
Adaptive Policies
Climate Change Projections
Statistical Downscaling
River Water Quality Simulation
Model
Water Quality Responses
21 July 2011
Optimal Effluent Treatment Levels
(Fuzzy Effluent Load Allocation
AsianModel)
Climate Change
40
40
Observed and CCA Predicted Projections from MIROC 3.2 GCM
(A1B) at Shimoga along Tunga River
Average Air Temperature
Maximum Air Temperature
Observed
Predicted
(A)
30
25
35
20
30
25
Observed
Predicted
(A)
40
35
26
2010-2040
2040-2070
(B)
60
Observed
(A)
Predicted
80
75
70
65
Monthly Wind Speed in kmph
Monthly Relative Humidity
80
40
24
22
2040-2070
(B)
2010-2040
2070-2100
Wind Speed
Relative Humidity
100
Predicted
(A)
18
2010-2040
2070-2100
Observed
20
30
22
15
8
35
6
30
4
2
Observed
2040-2070
(B)
2070-2100
River Water Temperature
Predicted
(A)
6
4
Water Temperature in degree C
20
40
Monthly Minimum Air
Temperature in degree C
25
Monthly Maximum Air
Temperature in degree C
Monthly Average Air
Temperature in deg C
30
Minimum Air Temperature
25
20
Observed
Predicted
(A)
35
30
25
2
2010-2040
2040-2070
(B)
21 July 2011
2070-2100
20
2010-2040
2040-2070
(B)
2070-2100
2010-2040
2040-2070
(B)
2070-2100
41
Asian Climate Change
41
21 July 2011
Asian Climate Change
42
Present and Future Estimates of DO Levels at Various Check
Points along Tunga-Bhadra River
Check Point 11
7.00
6.50
6.00
Dissolved Oxygen mg/L
Dissolved Oxygen mg/L
Check Point 1
6.72
6.06
5.50
5.55
5.00
4.50
4.89
4.00
3.50
present
7.00
6.50
6.00
5.50
5.82
5.00
4.50
5.24
4.96
4.70
4.00
3.50
present
2010-2040 2040-2070 2070-2100
2010-2040 2040-2070 2070-2100
Dissolved Oxygen mg/L
Check Point 14
21 July 2011
6.50
6.00
5.50
5.00
5.41
4.85
4.50
4.44
4.00
4.30
3.50
present
2010-2040 2040-2070 2070-2100
Asian Climate Change
43
Current and Projected Treatment Policy
Fractional Removal Levels
1
0.9
Current
0.8
0.7
2010-2040
0.6
2040-2070
0.5
2070-2100
0.4
0.3
1
2
3
4
5
6
7
8
Discharger
21 July 2011
Asian Climate Change
44
Urban Flooding
Urbanisation alters the hydrology of a region; rainfall – runoff
relationships get affected; quicker and higher peak flows ; more
runoff
After Urbanization
Before
Urbanization
Q
21 July 2011
Asian Climate Change
t
45
Bangalore Floods
How do the short
term intensities of
rainfall respond to
the climate change?
21 July 2011
Urban Flooding
Asian Climate Change
Likely changes in IDF
(Intensity-DurationFrequency) relationships
due to climate change
46
Toronto
Source : Simonovic, 2005
Precipitation Intensity (mm/hour)
95
2090
90
85
2050
80
75
1985
70
65
60
55
50
21 July 2011
10
20
30
40
50
60
70
Extreme precipitation recurrence time (Years)
Asian Climate Change
80
47
Bangalore City – Change in the IDF
Relationships
Comparison of IDF for return period of 10 years
100
Rainfall Intensity (mm/h)
90
80
90.174
1969-2003
76.789
1969-1986
1987-2003
70
60
62.672
59.653
53.898
50
43.471
40
33.651
30
26.968
20
19.124
15.25
9.5709
17.45
10
0
1
2
6
12
24
Duration (hours)
Results not conclusive, because of the small sample of data available
21 July 2011
Asian Climate Change
48
Summary






Climate change is likely to impact most hydrologic
processes
Impacts need to be assessed at regional/riverbasin and
smaller scales
GCMs are the most credible tools available today for
impact assessment
Scale issues and uncertainties are addressed in recent
studies
Results from the studies are useful in developing
adaptive responses (e.g., long term reservoir operating
policies; modifications in hydrologic designs; change in
cropping patterns; water use adjustments etc.)
Similar results may be used in developing IntenstyDuration-Frequency (IDF) relationships and FlowDuration curves, accounting for Climate Change.
21 July 2011
Asian Climate Change
49
THANK YOU
21 July 2011
Asian Climate Change
50
Kernel Density Estimation
• Basic Equation
fˆ x   nh 
1
fˆ  x 
n
h
n
 K x  X  h
l
l 1
- kernel density estimator of a pdf at x
- number of observations
- smoothing parameter known as bandwidth
Selection of bandwidth - an important step in kernel estimation method.
Conventional Method
(Silverman, 1986):
21 July 2011
h0  1.587 n
1
3
 IQR 
  min S ,

 1.349 
Asian Climate Change
51
Kernel Density Estimation:
Drawbacks

A large sample can give a better estimate of kernel density
estimator. In the present analysis, the sample size is small
only having the downscaled SPI of the available GCM
output, which may not lead to accurate results

The bandwidth is estimated by assuming the actual density
as normal, which may not be the actual case. In such cases
the estimate may be inaccurate.
21 July 2011
Asian Climate Change
52
Orthonormal Series Method

Orthonormal series: series of functions of an orthonormal
system

Properties:
  x  x dx  0 s  j
 x  dx  1
s

Used to determine the nonparametric PDF of a small sample
s
j
2

s
(Effromovich, 1999).

f J  x    j  j  x 
J
or
j 0

f J  x    j  j  x 
j 0
Series Used: Cosine System
 0 x   1
 j x   2 cosjx
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j0
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Determination of Coefficients
Estimation of j
j 


f ( x) j  x  dx

From probability methods:
E j x  

 f x  x dx
j

It can be said
 j  E j x 
or
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1 n
 j    j xl 
n l 1
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Algorithm for pdf Estimation with Orthonormal Series
Determination of
bounds/support
of the data set
Scaling of
data set
Determination of
functions of
orthonormal series
Determination
of smoothing
parameter
Determination
of cut-off
Determination of
Fourier
coefficients
Modifications for
smoothness, area,
negative values
Determination of
pdf of scaled
data
Determination of
final pdf of
unscaled data
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Objectives of the Possibilistic
Approach

Assumptions of earlier models on GCM and scenario
uncertainty: equal possibility and equi-probability to all the
scenarios.

With the passage of time, it is relevant to assess the
effectiveness of the GCMs in best modeling climate change
and also to judge which of the scenarios best represent the
present situation under climate forcing.

Scope of the study: assignment of possibility distribution to
different GCMs and scenarios, measured in terms of their
ability in modeling climate change based on their performance
in the recent past (years 1991-2005) under climate forcing
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Theory of Possibility Distribution
X: variable in the universe , and is not possible to
measure precisely
Possibility that X can take a value x:
X(x):   [0,1]
X(x)=0: Denotes X=x is impossible
X(x)=1: Denotes X=x is possible without any restriction
 X  x   1,
x 
: Interpreted as complete ignorance
about X
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Modeling GCM and Scenario
Uncertainty with Possibility Theory



Assignment of possibility to GCMs and scenarios: based on
system performance in recent past (1991-2005) when climate
forcings are visible.
System performance measure: Deviation of the predicted
CDF from the observed CDF.
System performance measure (C): similar to Nash-Sutcliffe
coefficient.
2
Q

C  1
 Q
F
F

OF
OF
 QPF 
 QO

2
Normalization of C values to obtain possibility distribution
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Graphical models



Combine probability theory and graph theory
Family of probability distributions that factorize according
to an underlying graph G=(V,E). Vertices ~ random
variables, edges ~ statistical dependencies
Directed graph (Bayesian Network)

Variable is conditionally independent of all other variables given its
parents

Undirected graph (Markov Random Field / Markov
network)

Variable is conditionally independent of all other variables given its
neighbors
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Change
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Do2011
not impose acyclicity constraint
/ constraints
on causality
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Graphical models (contd.)
Factor graph representation


Every undirected model can be represented as a factor graph
Distribution over a large number of random variables represented as
product of local functions
Where
is a global normalizing constant.
are clique potentials, functions from sets of nodes to nonnegative
reals.
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Generative vs discriminative models

Generative model : Based on joint distribution p(y,x)


Simplifying independence assumptions, else has to
account for correlated features of input
Eg: Naïve Bayes classifier
Task: Predict class variable y (say, whether an email is spam / not spam)
given a vector of features x = (x1,x2,...xk) (say, from address in
predetermined list, contents more than certain size, subject contains
word from predetermined list, etc). Model of joint distribution is
K
p ( y, x)  p ( y ) p ( x k | y )

k 1
Discriminative model : Based on conditional distribution p(y|x)





Does not need model for p(x)
Sufficient for classification tasks
Model does not need to account for complex dependencies
among input variables.
Better suited to include rich, overlapping features
Eg: Logistic regression (maximum entropy)
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K
1
p ( y | x) 
exp{
AsianClimate
Change
y  
y, j x j }
Z ( x)
j 1
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HMMs vs linear chain CRFs
HMMs
Linear chain CRFs
Type of Bayesian Network
Markov random field globally conditioned on input
(observation) variables x
Generative model
Discriminative model
Assigns a joint probability to paired observation and
label sequences
Assigns a conditional probability to label sequences
given observation sequence
Parameters trained to maximize joint likelihood
Parameters trained to maximize conditional log
likelihood
Joint distribution may have many forms, one of which
is an HMM
Conditional distribution is a linear chain CRF which
includes features only for the current input variable xt
(at time t)
Graphical model representation of an HMM
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One of the many graphical model representations of a
linear chain CRF
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IPCC SRES (2001)
Scenarios(40)
A1
A1F
Fossil fuel
Scenario
family
World order
Ecologically
friendly
Population
Economic
growth
Technology
growth
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A2
A1B
B1
B2
(family)
(group)
A1T
Balanced Non fossil fuel
A1
A2
B1
B2
Integrated
Divided
Integrated
Divided
No
No
Yes
Yes
Increases till
2050 and then
declines
Rapid
Continuously
increasing
Same as A1
Increasing but
lower than A2
Regionally
oriented
Rapid (serviceoriented)
Intermediate
Rapid
Slower
fragmented
Rapid
Slower
fragmented
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IPCC Scenarios
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Climate change projections
Source:Meehl et al., Climate Change
2007: The Physical Science Basis, WG I,
Asian Climate Change
AR4, IPCC
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