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CLIMATE CHANGE SCENARIO GENERATION USING STATISTICAL DOWNSCALING
A DISSERTATION
Submitted in partial fulfillment of the
requirements for the award of the degree
of
MASTER OF TECHNOLOGY
in
HYDROLOGY
By
NARAYAN PRASAD GAUTAM
DEPARTMENT OF HYDROLOGY
INDIAN INSTITUTE OF TECHNOLOGY ROORKEE
ROORKEE-247 667 (INDIA)
JUNE, 2010
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CANDIDATE’S DECLARATION
I, hereby, certify that the work presented in this dissertation entitled “CLIMATE
CHANGE SCENARIO GENERATION USING STATISTICAL DOWNSCALING” in partial
fulfillment of the requirements for the award of the degree of Master of Technology in
Hydrology, submitted in Department of Hydrology, Indian Institute of Technology Roorkee, is
an authentic record of my work carried out during the period July 2009 to June 2010 under the
supervision of Dr. N.K. Goel, Professor, Department of Hydrology and Dr. Manohar Arora,
Scientist, National Institute of Hydrology, Roorkee.
The matter presented in this dissertation has not been submitted by me for the award of
any other degree.
Date: 29/06/2010 (NARAYAN PRASAD GAUTAM)
IIT Roorkee Candidate’s signature
This is to certify that the above statement made by the candidate is correct to the best of our knowledge.
(Manohar Arora) (N. K. Goel)
Scientist Professor
National Institute of Hydrology Indian Institute of Technology
Roorkee Roorkee
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ABSTRACT
Climate change has been emerging as one of the challenges in the global environment.
Information of predicted climatic changes in basin scale is highly useful to know the future
climatic condition in the basin that ultimately becomes helpful to perform planning and
management of the water resources available in the basin.
Observed warming over several decades has been linked to changes in the large-scale
hydrological cycle such as: increasing atmospheric water vapour content; changing precipitation
patterns, intensity and extremes; reduced snow cover and widespread melting of ice; and changes
in soil moisture and runoff. Precipitation changes show substantial spatial and inter-decadal
variability. The frequency of heavy precipitation events has increased over most areas. There
have been significant decreases in water storage in mountain glaciers and Northern Hemisphere
snow cover. Shifts in the amplitude and timing of runoff in glacier and snowmelt-fed rivers, and
in ice-related phenomena in rivers and lakes, have been observed.
General Circulation Models (GCMs), representing physical processes in the atmosphere,
ocean, cryosphere and land surface, are the most advanced tools currently available for
simulating the response of the global climate system to increasing greenhouse gas
concentrations. Recent interest in global warming has also increased concerns about the possible
changes of flood and drought patterns including the rainfall amount.
This study based on statistical downscaling, provide good example focusing on predicting the
rainfall and runoff patterns, using the input of coarse general circulation model (GCM) outputs.
The outputs of the GCMs are utilized to study the impact of climate change on water resources.
The present study has been taken up to understand the climatic changes, climatic scenario
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generation and their inter-relationships based on the data of Satluj river basin. The findings of
this study can be summarized as follows:
1. Statistical downscaling has been conducted in Bhakra region of Satluj river basin and
predicted the future rainfalls from 2001 to 2100.
2. The predicted rainfalls have shown that there will be decrease in rainfall for winter
season, partially decreases for pre monsoon and post monsoon and increases for monsoon
season in the Bhakra region of Satluj river.
3. Rainfall variability as based on the observed rainfall has indicated that the rainfall values
of December, January, February, March, July and August are on decreasing order and the
rainfall values of remaining six months are on increasing order.
4. Future discharges from 2001 to 2100 have been predicted by rainfall-discharge and
rainfall-temperature-discharge relationships by using ANN and MLR techniques. It has
shown a better relationship by considering rainfall and temperature as inputs in compared
to only rainfall as input.
5. In this study, comparison of the results of the ANN models with MLR for rainfall-runoff
relationships has shown that the ANN model is better than MLR.
6. The predicted rainfalls and discharges for first 30 years from 2001 to 2030 are observed with
having higher rainfall and discharge values in compared to the remaining prediction periods.
7. The Z-statistics of Mann Kendall test has shown that there are no trends in the predicted
rainfalls and discharges from 2001 to 2100 at 5 % significance level. Likewise, there is no trend
found out at 5 % significance level in the observed rainfall, discharge, temperature and predicted
temperature data set used in this study.
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ACKNOWLEDGEMENTS
I would like to express my deep sense of respect and gratitude to my supervisors Dr.
N.K. Goel, Professor, Department of Hydrology, Indian Institute of Technology, Roorkee and
Dr. Manohar Arora, Scientist, National Institute of Hydrology, Roorkee for their keen interest,
valuable guidance and encouragement throughout this research work.
I am also grateful to Dr. Himanshu Joshi, Professor and Head, Department of Hydrology,
Indian Institute of Technology, Roorkee for his encouragement and moral support during the
study. I also take this opportunity to express my sincere thanks to all other faculty members of
the Department of Hydrology for their excellent teachings and inspiration throughout the course.
I am thankful to my colleagues Badri Karki, Kabuya, all friends and research scholars for
their kind suggestion in carrying out the research.
I am highly thankful to my parent department DoM, TU for giving me the opportunity to
attend the course and WMO for their financial support in pursuing the M. Tech. Hydrology
program.
My special thanks go to Mr. A.R. Senthil Kumar, Scientist, NIH and colleague
Muhammed Raneef for their constant support during the course of this research.
I am highly indebted to my parents and all other family members for their blessings and
inspiration. No words would be enough to express my appreciation to my wife Sarita and son
Nischal for their support and sacrifices throughout the study period.
(Narayan P. Gautam)
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CONTENTS
Page No.
CANDIDATE’S DECLARATION i ABSTRACT ii-iii ACKNOWLEDGEMENTS iv CONTENTS v-vii LIST OF TABLES viii LIST OF FIGURES ix-x LIST OF APPENDICES xi
CHAPTER 1
INTRODUCTION 1-14
1.1 GENERAL 1
1.2 IMPACTS OF CLIMATE CHANGE IN GLOBAL CONTEXT 4
1.3 CLIMATE TRENDS IN PARTS OF SOUTH ASIA 6
1.4 IMPACTS OF CLIMATE CHANGE IN ASIAN CONTEXT 6
1.5 SCENARIO 8
1.5.1 Climatic Scenario 10
1.6 GENERAL CIRCULATION MODEL 10
1.7 METHODS OF DOWNSCALING 11
1.7.1 Dynamical Downscaling 12
1.7.2 Statistical Downscaling 13
1.8 IMPORTANCE AND OBJECTIVES OF THE STUDY 13
1.9 CHAPTERIZATION 14
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CHAPTER 2
LITERATURE REVIEW 15-33
2.1 GENERAL 15
2.2 CLIMATE CHANGE IN INDIAN CONTEXT 16
2.3 FUTURE CLIMATIC SCENARIOS FOR INDIA 21
2.4 HYDRO-CLIMATIC STUDIES ON SUTLEJ RIVER BASIN 23
2.5 APPLICATION OF ANN IN RAINFALL-RUNOFF RELATIONSHIP 25
CHAPTER 3
STUDY AREA AND DATA USED 34-40
3.1 DESCRIPTION OF THE STUDY AREA 34
3.2 DATA USED 39
CHAPTER 4
METHODOLOGY 41-55
4.1 GENERAL 41
4.2 STATISTICAL DOWNSCALING 41
4.2.1 Weather Generators 43
4.2.2 Weather Typing 43
4.2.3 Transfer Function 44
4.3 FLOW CHART OF STATISTICAL DOWNSCALING 44
4.4 TOOLS USED 46
4.4.1 MATLAB 46
4.4.2 Principal Component Analysis 46
4.4.3 Standardization 46
4.4.4 Multiple Linear Regression Analysis 47
4.4.5 Rainfall Variability 48
4.4.6 Artificial Neural Network 48
4.4.7 Trend Analysis 54
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CHAPTER 5
RESULTS AND DISCUSSION 56-78
5.1 GENERAL 56
5.2 RAINFALL ANALYSIS 56
5.2.1 NCEP Data Analysis 56
5.2.2 GCM Output Data Analysis 57
5.2.2.1 Monthly distribution of predicted rainfalls for some years 58
5.2.3 Rainfall Variability 60
5.2.4 Trend Analysis of Rainfall 62
5.3 RAINFALL - RUNOFF ANALYSIS 63
5.3.1 Development of ANN model for Stream flow 63
5.3.2 Training of ANN Model 64
5.3.3 Analysis of Results of ANN and MLR Models 68
5. 3.4 Simulation of discharge for future period 77
5.3.5 Trend Analysis of Discharge and Temperature 78
CHAPTER 6
CONCLUSIONS AND SCOPE FOR FURTHER WORK 79-82
6.1 CONCLUSIONS 79
6.2 SCOPE FOR FURTHER WORK 82
REFERENCES 83-93
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LIST OF TABLES
Table No. Title Page No.
1.1 Observed effects of climate change and its observed/possible
impacts on water services in global perspectives 5
1.2 Summary of climate trends in parts of South Asia 6
1.3 Status of recent observed extreme events especially in South Asia 8
1.4 Some of the GCMs and their originating institutions 11
2.1 Climate change projections for the Indian sub-continent 21
3.1 Distribution of glaciers in 5Q Indus basin 35
3.2 Salient Features of Satluj river basin 37
5.1 Regression Coefficients 57
5.2 Rainfall variability obtained from the average rainfall values 60
5.3 Correlation coefficient(R) in different relationships 64
5.4 Results of ANN model considering only monthly rainfall as input 66
5.5 Results of ANN model considering monthly rainfall and monthly
average temperature as input 66
5.6 Results of MLR model considering only monthly rainfall as input 68
5.7 Comparison of results between best ANN and MLR models 68
with only rainfall as input
5.8 Results of MLR model considering monthly rainfall and average
temperature as input 73
5.9 Comparison of results between best ANN and MLR models
with monthly rainfall and average temperature as input 73
5.10 Z-statistics obtained by using Mann Kendall’s Test 78
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LIST OF FIGURES
Figure No. Title Page No.
1.1 Trend of global average surface temperature 2
1.2 Trend of carbondioxide concentration in the earth 3
2.1 All India mean annual surface air temperature anomalies 19
2.2 All India summer monsoon rainfall anomalies 20
3.1 Location map of the Satluj basin up to Bhakra dam with
hydrometeorological stations 34
3.2 First order basins of the Himalayas in India 35
3.3 Glacier map of Sutlej basin 36
3.4 Cumulative isohyetal pattern (10 years) of the Indian part of Satluj
basin upto Bhakra dam 38
3.5 Area–elevation curve for the Satluj River basin (Indian part)
upstream of Bhakra Reservoir 39
4.1 Illustrating the general approach to downscaling 42
4.2 Flow chart of statistical downscaling 45
4.3 A Typical Three-Layered Feed Forward ANN 49
5.1 Predicted rainfalls for future period from 2001 to 2100 58
5.2 Predicted monthly rainfall for 2030 58
5.3 Predicted monthly rainfall for 2050 59
5.4 Predicted monthly rainfall for 2080 59
5.5 Average rainfalls from observed and predicted rain data set 61
5.6 Monthly rainfall variability based on observed rain data set 61
5.7 Scatter plot between monthly averages of observed and predicted rainfalls 62
5.8 Scatter plot for the result of best ANN model with only
monthly rainfall as input during calibration 69
5.9 Scatter plot for the result of best ANN model with only
monthly rainfall as input during validation 69
5.10 Scatter plot for the result of best ANN model with only
monthly rainfall as input during testing 70
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5.11 Scatter plot for MLR model with only
monthly rainfall as input during calibration 71
5.12 Scatter plot for the MLR model with only
monthly rainfall as input during validation 71
5.13 Scatter plot for the MLR model with only
monthly rainfall as input during testing 72
5.14 Scatter plot for the result of best ANN model with monthly
rainfall and average monthly temperature as input during calibration 74
5.15 Scatter plot for the result of best ANN model with monthly rainfall
and average monthly temperature as input during validation 74
5.16 Scatter plot for the result of best ANN model with monthly rainfall
and average monthly temperature as input during testing 75
5.17 Scatter plot for MLR model with monthly rainfall and
average monthly temperature as input during calibration 76
5.18 Scatter plot for MLR model with monthly rainfall and
average monthly temperature as input during validation 76
5.19 Scatter plot for MLR model with monthly rainfall and
average monthly temperature as input during testing 77
5.20 Predicted discharges for future period from 2001 to 2100 78
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LIST OF APPENDICES
Title Page No.
Appendix I Predicted rainfall from 2001 to 2100 94-98
Appendix II Predicted discharge from 2001 to 2100 99-103
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CHAPTER 1
INTRODUCTION
1.8 GENERAL
Climate is one of the key parameters in the earth’s environment. Climate is usually defined as
the average weather and in broad sense, it is the statistical description in terms of the mean and
variability of relevant quantities over a period of time ranging from months to thousands or
millions of years (IPCC, 2008). Human activities that could possibly change the climate include
as a result of emission of gases in the atmosphere, industrial activities, development of extensive
cities, pollution of water ways and cities, creation of thousands of dams and lakes, conversion of
grassland or forest to cropland, agricultural activities (Piechota et al., 2006).
The average global temperature rose by 0.74oC over the last hundred years (1906-2005), with
more than half of these rises, 0.44oC, in the last 25 years (ICIMOD, 2009). Most of the warming
over the last 50 years is very likely to have been caused by anthropogenic increases in Green
House Gases (GHGs). Since 1750, atmospheric concentrations of GHGs have increased
significantly. Carbon dioxide has increased by 31 percent, Methane by 151 percent and Nitrous
oxide by 17 percent (Gautam, 2005). Higher carbon dioxide concentration is caused due to
burning of fossil fuels (coal, oil and natural gas) and deforestation.
Climate change refers to a change in the state of the climate that can be identified by changes
in the mean and/or the variability of its properties and that persists for an extended period, for
decades or still longer. The United Nations Framework Convention on Climate Change
(UNFCC), in its Article 1, defines climate change as ‘a change of climate which is attributed
directly or indirectly to human activity that alters the composition of the global atmosphere and
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which is in addition to natural climate variability observed over comparable time periods’ (IPCC,
2008).
Global warming is a major factor to be climate change. Even a conservative estimate of 10C
increase could have dramatic effects for all aspects of human life. For example, during the
Medieval warming period (1200-1500AD) and during the little Ice Age (1600-1700AD)
temperatures were 0.50C higher and 0.50C lower respectively (on average) than they are today
(Khaliq et al., 1997).
Figure 1.1: Trend of global average surface temperature
Continuous greenhouse gas emissions at or above current rates will cause further warming
and induce many changes in the global climate system during the twenty first century that would
very likely be larger than those observed during the twentieth century (Solomon et al., 2007).
These changes have the potential to greatly impact regional hydrological processes, and affect
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long-term water availability (Fu et al., 2007), the occurrence of droughts or floods (Bronstert et
al., 2007) and water resources management practices (Chiew and McMahon, 2002), particularly
at regional scales (Arnell, 2003; Etchevers et al., 2002). Understanding the potential effects of
climate change on hydrological regimes has thus become a priority area, both for process
research and for water and catchment management strategies (Jones and Woo, 2002).
Figure 1.2: Trend of carbondioxide concentration in the earth
It is a fact that the earth’s climate is dynamic and always changes through natural cycle.
Previously it is assumed that climate change is caused due to natural causes. Some of the
more prominent natural causes affecting in climate change are continental drift, volcanoes,
the earth’s tilt and ocean currents. These changes are being studied through evidence obtain
from tree-rings, pollen samples, ice-cores and sea sediments.
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Among many concepts about the cause of climate change, a group of scientists are not
fully agreed to clearly mention that GHG is the main factor to be climate change. Their
concept is “land-use change impacts regional and global climate through the surface-energy
budget, as well as through the carbon-cycle effects. The surface-energy budget effects may
be more important than the carbon-cycle effects” (Sr Pielke et al., 2002).
1.2 IMPACTS OF CLIMATE CHANGE IN GLOBAL CONTEXT
Impacts of climate change can be categorized through positive and negative aspects. Less
chilly winters and greenery in high altitudinal areas can be considered as some positive
impacts due to global temperature rise. However, the adverse (negative) impacts are seen
very highly in compared to the positive impacts. Some of the adverse impacts caused by
climate change especially related to water in global and Asian context can be categorized as
follows:
• It is seen that the global temperature has on rising trend since mid-20th century.
• Hot days, hot nights have become more frequent in most parts of the world.
• Due to rising temperature, it causes abrupt glacier ablation. The formation of lakes is
occurring as glaciers retreat from several steep mountain ranges, including the
Himalayas. These lakes thus have a high potential for glacial lake outburst floods
(GLOFs).
• Climate change has changes on surface and ground water systems. At the global scale,
there is evidence of a broadly coherent pattern of change in annual runoff. Some regions
like China, higher latitudes regions experiencing an increase, and West Africa, southern
Europe and southern Latin America experiencing decrease in runoff (IPCC, 2008).
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• Many natural systems on all continents and oceans are affected due to global warming.
• Diseases related to warming and mosquito problems are seen even if in high altitudinal
regions.
• Changes in water quantity and quality due to climate change affects on food production
leading to decrease food security.
• It is found that the rate of sea-level rise during the 20th century was about 10 times
higher than average rate during the last 3000 years (Gautam, 2005).
• Sea-level rise is projected to extend areas of salinization of ground water, resulting in a
decrease of freshwater availability for humans and ecosystems in coastal areas (IPCC,
2008).
Table 1.1: Observed effects of climate change and its observed/possible impacts on
water services in global perspectives (IPCC, 2008).
Observed effect Observed / possible impacts
Increase in atmospheric
temperature
• Reduction in water availability in basins fed by glaciers
that are shrinking, as observed in some cities along the
Andes in South America
Increase in surface
water
Temperature
• Reductions in dissolved oxygen content, mixing
patterns and self purification capacity
• Increase in algal blooms
Sea–level rise • Salinisation of coastal aquifers
Shifts in precipitation
patterns
• Changes in water availability due to changes in
precipitation and other related phenomena (e.g.
groundwater recharge, evapotranspiration)
Increase in interannual • Increase the difficulty of flood control and reservoir
utilization during the flooding season
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precipitation variability
Increased
evapotranspiration
• Water availability reduction
• Salinisation of water resources
• Lower groundwater levels
More frequent and
intense extreme events
• Floods affect water quality and water infrastructure
integrity, and increase fluvial erosion, which introduces
different kinds of pollutants to water resources
• Droughts affect water availability and water quality
1.3 CLIMATE TRENDS IN PARTS OF SOUTH ASIA
Table 1.2: Summary of climate trends in parts of South Asia (IPCC, 2007)
Region Change in temperature Change in precipitation
Nepal
0.09°C per year in Himalayas
and 0.04°C in Terai region,
more in winter
No distinct long-term trends
in precipitation records for
1948 to 1994
India
0.68°C increase per century,
increasing trends in annual
mean temperature, warming
more pronounced during post
monsoon and winter
Increase in extreme rains in
north-west during summer
monsoon in recent decades,
lower number of rainy days
along east coast
Tibetan Plateau
0.16 and 0.32°C per decade
increase in annual and winter
temperatures, respectively
Generally increasing in north-
east region
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1.4 IMPACTS OF CLIMATE CHANGE IN ASIAN CONTEXT
• The frequency of occurrence of more intense rainfall events in many parts of Asia has
increased, causing severe floods, landslides, debris and mud flows, while the numbers of
rainy days have decreased (IPCC, 2008).
• The increasing frequency and intensity of droughts in many parts of Asia are attributed
largely to rising temperatures, particularly during the summer.
• On average, Asian glaciers are melting at a rate that has been constant since at least the
1960s. The frequency of glacial lake outburst floods (GLOFs) in the Himalayas of Nepal,
Bhutan and Tibet has increased from 0.38 events / year to 0.54 events / year in the 1990s
(IPCC, 2008).
• The adverse impact of climate change is one of the reasons for creating water shortage
problem in many parts of South Asia. It is because changing in climatic condition affects
on water demand, supply and water quality.
• Decreasing trends in annual mean rainfall were observed in many parts of Asia.
• It is found that production of rice, maize and wheat has declined in many parts of Asia
due to increasing water stress, mainly arising from increasing temperature, reduction in
number of rainy days (IPCC, 2008).
• Due to gradual reduction in rainfall, aridity has increased in central and west Asia in
recent years.
• Spreading of diseases like malaria, viral influenza, encephalitis in many parts of South
Asia are caused in recent years due to temperature rising (Gautam, 2005).
• Drying of wetlands and severe degradation of ecosystems has resulted in delta regions of
South Asian countries caused due to precipitation decline and droughts (IPCC, 2008).
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Table 1.3: Status of recent observed extreme events especially in South Asia (IPCC, 2007)
Region Events
South Asia
Serious and recurrent floods in Bangladesh, Nepal and north-east states of
India during 2002, 2003 and 2004; a record 944 mm of rainfall in
Mumbai, India on 26 to 27 July 2005 led to loss of over 1,000 lives with
loss of more than US$250 million; floods in Surat, Barmer and in
Srinagar during summer monsoon season of 2006; 17 May 2003 floods in
southern province of Sri Lanka were triggered by 730 mm rain
South Asia
Frequency of monsoon depressions and cyclones formation in Bay of
Bengal and Arabian Sea on the decline since 1970 but intensity is
increasing causing severe floods in terms of damages to life and property
South Asia
50% of droughts associated with El Niño; consecutive droughts in 1999
and 2000 in Pakistan and N-W India led to sharp decline in water tables:
consecutive droughts between 2000 and 2002 caused crop failures, mass
starvation and affected ~11 million people in Orissa; droughts in N-E
India during summer monsoon of 2006
India
Frequency of hot days and multiple-day heat wave has increased in past
century; increase in deaths due to heat stress in recent years
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1.5 SCENARIO
According to the IPCC, a scenario is a coherent, internally consistent and
plausible description of a possible future state of the world. A projection may serve as the
raw material for a scenario, but scenarios often require additional information (e.g., about
baseline conditions). A set of scenarios is often adopted to reflect, as well as possible, the
range of uncertainty in projections. Other terms that have been used as synonyms for
scenario are "characterisation", "storyline" and "construction".
The IPCC published a set of emissions scenarios in 2000 for use in climate
change studies is known by Special Report on Emissions Scenarios (SRES). The SRES
were constructed to explore future developments in the global environment with special
reference to the production of greenhouse gases and aerosol precursor emissions. The
SRES are categorized in four main families as A1, A2, B1 and B2. Each scenario
represents different demographic, social, economic, technological and environmental
developments. They can be summarized as follows:
• A1 scenario (family): a future world of very rapid economic growth, global population
that peaks in mid-century and declines thereafter, and rapid introduction of new and more
efficient technologies.
• A2 scenario (family): a very heterogeneous world with continuously increasing global
population and regionally oriented economic growth that is more fragmented and slower
than in other scenarios.
• B1 scenario (family): a convergent world with the same global population as in the A1
scenario but with rapid changes in economic structures, and the introduction of clean and
resource efficient technologies.
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• B2 scenario (family): a world, in which the emphasis is on local solutions to economic,
social, and environmental sustainability, with continuously increasing population (lower
than A2) and intermediate economic development.
1.5.1 Climatic Scenario
A plausible and often simplified representation of the future climate, based on an
internally consistent set of climatological relationships, that has been constructed for
explicit use in investigating the potential consequences of anthropogenic climate change
(Wilby and Dawson, 2007).
1.6 GENERAL CIRCULATION MODEL
The general circulation model is also popular by the name of global climate
model. Considering IPCC, General Circulation Model (GCM) represents physical
processes in the atmosphere, ocean, cryosphere and land surface. It is the most advanced
tool currently available for simulating the response of the global climate system to
increasing greenhouse gas concentrations. It has the potential to provide geographically
and physically consistent estimates of regional climate change which are required in
impact analysis. The atmospheric or oceanic GCMs (AGCM or OGCM) are key
components of GCMs which include land-surface, sea-ice and ocean components.
GCM illustrate the climate using a three dimensional grid over the globe of
having horizontal resolution of 250 and 600 km, 10 to 20 vertical layers in the
atmosphere and as many as 30 layers in the oceans (IPCC, 2009). However, some sub-
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grid scale features like clouds, topography at smaller scale cannot be properly modeled
by GCM due to its coarse spatial resolution (of the order of 50,000 km2)
There are several GCMs operating by different countries in the world. Some of
the widely used GCMs being used for the impact studies are listed in Table 1.1.
Table 1.4: Some of the GCMs and their originating institutions
GCMs Institution and country
CCSR-NIES Climate System Research/National Institute for Environmental Studies, Japan
HadCM2 Climate Model of Hadley’s Centre, UK
BCCR Bjerknes Center for Climate Research, Norway
CCCma Canadian Center for Climate Modeling and Analysis, Canada
AOM Goddard Institute of Space Studies, USA
CNRM Center National de Recherches Meteorologiques, France
CM 3.0 Institute for Numerical Mathematics, Russia
CSIRO-
MK3.0
Australia’s Commonwealth Scientific and Industrial Research Organization,
Australia
ECHAM5-OM Max-Planck Institute for Meteorology, Germany
ECHO-G Meteorological Research Institute of KMA, Korea
BCC-CM1 Beijing Climate Centre, China
SXG 2005 National Institute of Geophysics and Volcanology, Italy
The spatial resolution of CCSR-NIES is 5.5o latitude and 5.625o longitude and it varies from
GCM to GCM.
24
1.7 METHODS OF DOWNSCALING
It is a process of the development of climate data for a point or small area from regional
climate information. The regional climate data may originate either from a climate model or
from observations. Methodologies to model the hydrologic variables (e.g. precipitation) at a
smaller scale based on large-scale GCM outputs are known as downscaling. Usually the two
downscaling techniques are in practice they are dynamic and statistical downscaling.
1.7.1 Dynamical downscaling
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 or Regional Climate Models (RCM). Dynamical
downscaling involves the nesting of a higher resolution Regional Climate Model (RCM)
within a coarser resolution GCM. The RCM uses the GCM to define time-varying
atmospheric boundary conditions, in which the physical dynamics of the atmosphere are
modeled using horizontal grid spacing of 20-50 km (Wilby and Dawson, 2007). Dynamic
downscaling can be further subdivided into one-way nesting and two-way nesting (Anandhi
et al., 2008). The strong features of dynamic downscaling can be summarized as follows:
• It gives better representation of land-use • It can resolve smaller-scale atmospheric features such as orographic precipitation • It generally applied to better representations of tropical cyclones, extreme events, etc.
• It is one of the useful methodologies to carry out study on regional climate change
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RCM is inflexible in the sense that expanding the region or moving to a slightly different
region requires redoing the entire experiment. Besides inflexible in nature, complicated in
design and high computational cost are few more drawbacks associated with dynamic
downscaling and due to these drawbacks it is not being highly used in climate change impact
studies (Mujumdar et al., 2009).
1.7.2 Statistical downscaling
Statistical downscaling involves development of statistical relationship between large-scale
climate variables and local-scale hydrologic variable. Training (calibration) of the statistical
downscaling model requires observed climate data. Statistical downscaling methodologies have
several practical advantages over dynamical downscaling approaches. From the aspects of low-
cost, rapid assessments of localized climate change impacts, statistical downscaling is seen as
highly capable technique. Hence, an attempt has been made to use statistical downscaling
technique in the present research and its details have been given in the chapter on Methodology.
1.8 IMPORTANCE AND OBJECTIVES OF THE STUDY
In the past, very few scientific works relating to climate change by General Circulation
Model (GCM) have been carried out in South Asian region. Therefore, in present research an
attempt has been made for climate change scenario generation by using general circulation
model and statistical downscaling technique. This study will be focused to generate the future
climatic scenario near by the Bhakra region of Satluj river basin. Application of statistical
downscaling technique on GCM output for future climatic scenario generation is at beginning
stage in the Indian context including IITs. Summing up, this kind of research has been initiated
26
to fill up the gap existing in between large scale (GCM level) and local scale (basin level)
variables.
It is a fact that research on climate change is one of the highly useful methodologies to
understand the reality of the climatic condition whether it is at global level or local level. The
predicted future climatic condition will be greatly useful to improve the matters related on
planning, decision making systems, etc scientifically. Hence, realizing the importance of the
matter, broadly the following objectives have been carried out in this study.
• To perform GCM output downscaling at a basin level
• To generate climate change scenarios using the GCM output and observed data
• To identify the relationships between hydro-climatic parameters
1.9 CHAPTERIZATION
This dissertation comprises of six chapters including chapter 1 on introduction.
Chapter 2 deals with review of literature on climate change and application of artificial
neural network (ANN) in rainfall-runoff relationships.
Chapter 3 describes briefly the study area and the data used in the study.
Chapter 4 discusses on methodologies to achieve the goal of the objectives taken in the study
as statistical downscaling, climate change scenario generation and identifying relationships
among hydro-climatic parameters.
Chapter 5 illustrates results and discussion of the study. The results obtained from the study
are discussed in two broad categories as rainfall and rainfall-runoff analyses.
Chapter 6 presents the conclusions of the study. This chapter also gives the suggestions for
future work.
27
CHAPTER 2 •
LITERATURE REVIEW
2.1 GENERAL
In global context, it is observed that the year 2009 is ranked as the fifth warmest year on
record since the beginning of instrumental climate records around 1850. On the decadal
scale, the 2000s decade (2000-2009) was warmer than the 1990s (1990-1999), which in turn
were warmer than the 1980s (1980-1989) and earlier decades (WMO, 2009).
Water distribution is uneven in Asia. It is seen that large areas of Asia are under water
stress. On the other hand, Asia has a very high population that is growing at a fast rate, low
development levels and weak coping capacity. Climate change is expected to intensify the
water scarcity situation in Asia, together with socio-economic stresses (IPCC, 2008)
The Himalayan regions are located in the northern part of Indian sub-continent. Several
types of climatic studies are carried out in the region. The studies have demonstrated
significant rise in air temperatures in the Northwest Himalaya of India, Nepal and Tibetan
Plateau. Himalayan regions are sources of many rivers as well as it dominantly controls
meteorological and hydrological conditions in the Indian sub-continent. It is learned that
even a minor change in their climate has a potential to cause disastrous consequences on the
socio-economic survival of millions of peoples living in the Indo-Gangetic plains (Bhutiyani
et. al., 2007).
Most part of the Hindu Kush-Himalayan (HKH) region is situated in the northern part of
the Indian sub-continent. It is found that the rate of warming in the HKH region is higher
than global average that is 0.74oC over the last hundred years (ICIMOD, 2009). While
28
categorizing the HKH region, as western Himalayas, central Himalayas and Tibetan Plateau,
the central Himalayas (Nepal) and the Tibetan Plateau appear to be considerably higher rates
of temperature rise (that is, 0.04 to 0.09oC per year and 0.03 to 0.07oC per year respectively).
2.2 CLIMATE CHANGE IN INDIAN CONTEXT
In India, several studies are carried out to determine the changes in temperature and
rainfall and its association with climate change. However, investigators used different data
length and now studies have been reported using more than a century data. All such studies
have shown warming trend on the country scale. Estimates of temperature anomaly were
better predicted using long-term data series.
A study conducted by Hingane et al., 1985 have shown increasing trend of annual mean
temperature. During 20th century, an analysis of long term temperature records (1901-1982,
73 stations) has shown increasing trend of mean annual surface air temperatures over India. It
was observed that about 0.4°C warming has taken place on country scale during the period of
8 decades. Studies carried out on regional basis revealed that temperature fluctuations do not
show increasing trend over the entire country. Temperatures show cooling trends in the
northeast and northwest India. Moreover, Hingane et al. (1985) observed that trend of
increase in mean annual temperature over the whole country was a result of rise in the
maximum temperature but later studies carried out by Sinha Ray et al. (1997) have shown
that the changes in mean annual temperature are partly due to rise in the minimum
temperature related to enhanced extent of urbanization. Findings by Mukhopadhyay et al.
(1999) have confirmed that there is clear signal of urbanization in these warming, i.e. there is
a steeper rise in the minimum temperature also in urban locations.
29
Studies related to changes in rainfall over India have shown that there is no clear trend of
increase or decrease in average annual rainfall over the country (Sarker and Thapliyal, 1988,
Thapliyal and Kulshrestha, 1991). The examination of trend of annual rainfall over India has
indicated that 5 year running mean has fluctuated from normal rainfall within ± one standard
deviation (Thapliyal and Kulshreshtha, 1991). Summer monsoon rainfall anomalies for all
India are shown in Figure 2.2. Though the monsoon rainfall in India is found to be trendless
over a long period of time, particularly on the all India scale (Mooley and Parthasarathy,
1984), but there are pockets of significant long-term rainfall changes (Chaudhary and
Abhyankar, 1979).
Studies of historical rates of relative sea-level rise in the South Asian region indicate an
average annual relative sea-level rise of 0.67 mm/yr (Gable and Aubrey, 1990). There were
rising trend in the sea level at Mumbai (Bombay) during 1940-86 and Chennai (Madras)
during 1910-33 (Das and Radhakrishnan, 1991). A rise of sea level by 0.08 m with a
corresponding fall in the pressure was confirmed during 1901-40 as per the studies on the
atmospheric and tide gauge data (Srivastava and Balkrishnan, 1993).
A comprehensive study using the monthly rainfall data for 306 stations distributed over
India was attempted by Rupa Kumar et al. (1992). They showed that area of north-east
peninsula, north-east India and north-west peninsula indicate widespread decreasing trend in
the Indian summer monsoon rainfall. On the other hand, they reported a widespread
increasing trend in monsoon rainfall over the west coast, central peninsula and north-west
India. The decreasing trend ranges between -6 to -8% of the normal per 100 years while the
increasing trend is about 10 to 12% of the normal per 100 years. Though these trends are
statistically significant, but they account for a relatively small part of the total variance in the
30
rainfall.
Examination of long-term variation in the annual mean temperature of highly industrial
and densely populated cities like Bombay and Calcutta have shown increasing trend in
annual mean temperature with Bombay and Calcutta by 0.84°C and 1.39°C per 100 years,
respectively (Hingane, 1995). These warming rates are much higher than the values reported
for the country as a whole.
Pant and Kumar (1997) have analysed the seasonal and annual air temperatures from
1881 to 1997 and have shown that there has been increasing trend of mean annual
temperature by the rate of 0.57°C per 100 years. Trend of all India mean annual surface air
temperature anomalies is shown in Figure 2.1. The trend and magnitude of global warming
over India/Indian sub-continent over last century has been observed to be broadly consistent
with the global trend and magnitude. In India, warming is found to be mainly contributed by
the post-monsoon and winter seasons. The monsoon temperatures do not show a significant
trend in many part of country except for significant negative trend over Northwest India.
Srivastava et al. (1998) have supported the existence of a definite trend in rainfall over
smaller spatial scale.
Mirza et al., (1998) have carried out trend and persistence analysis for Ganges,
Brahmaputra and Meghna river basins. He has shown that precipitation in Ganges basin is by
and large stable. Precipitation in one sub division in the Brahmaputra basin shows a
decreasing trend and another shows an increasing trend. One of three subdivision of the
Brahmaputra basin shows a decreasing trend while another shows an increasing trend.
31
1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990
Years
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Te
mpe
ratu
re a
nom
aly
(o C)
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Linear Trends = 0.57oC/100 yr
Figure 2.1: All India mean annual surface air temperature anomalies (1881-1997)
(Pant and Kumar, 1997)
Lal (2001) and MOEF (2004) reported that rainfall fluctuations in India have been largely
random over a century, with no systematic change detectable on either annual or seasonal
scale. However, areas of increasing trend in the seasonal rainfall have been found along the
West Coast, North Andhra Pradesh and Northwest India and those of decreasing trend over
East Madhya Pradesh, Orissa and Northeast India during recent years.
Sinha Ray and De (2003) have summarized the existing information on climate change
and trends in the occurrence of extreme events with special reference to India. They
concluded that all India rainfall and surface pressure shows no significant trend except some
periodic behavior. The frequency of heavy rain events during the south-west monsoon has
shown an increasing trend over certain parts of the country (Sinha Ray and Srivastava, 1999).
On the other hand, decreasing trend has been observed during winter, pre-monsoon and post-
monsoon season. They have tried to attribute dynamical and anthropogenic causes for this
variation.
32
1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
-30
-20
-10
0
10
20
30R
ainf
all A
nom
aly
(% o
f m
ean)
-30
-20
-10
0
10
20
30
Years
Figure 2.2: All India summer monsoon rainfall anomalies (1871-1999) (Lal, 2001) 2
A study conducted by Bhutiyani et al. (2007) have concluded that North West Himalayas
(NWH) of India has shown rise in air temperature due to rapid increases in maximum as well
as minimum air temperatures, with the maximum temperature increasing more rapidly. They
have also accomplished that there were teleconnections between the precipitation and
temperature variation in the NWH till late 1960s. However, after 1970s, these connections
appear to become weaker. It may be due to presence of other factors like increase in
greenhouse gases in the atmosphere.
Malla et al. (2007) have concluded that all India mean annual temperature has shown
significant warming trend of 0.050C / 10 year during the period 1901-2003. The recent period
1971-2003 has seen a relatively accelerated warming of 0.220C / 10 year, which is largely
due to unprecedented warming during the last decade.
The large scale climatological phenomena like EL-NINO has played crucial role in the
monsoon rainfall of India and Nepal. Although, the total rainfall has not shown any
significant trends related to climate change in the countries, there have been seen changes in
onset and retreat of the monsoon, number of rainy days and frequency of extreme
precipitation events.
33
2.3 FUTURE CLIMATIC SCENARIOS FOR INDIA
Future warming scenarios have been generated for the Indian sub-continent using
General Circulation Models (GCM). It is projected that over the inland regions of the Indian
sub-continent, the mean surface temperature may rise between 3.5°C and 5.5°C by 2080 (Lal,
2001). Future projection of increase in temperature and changes in precipitation over Indian
subcontinent are shown in Table 2.1.
Table 2.1: Climate change projections for the Indian sub-continent (Lal, 2001).
Scenarios
Increase in temperature (°C)
Change in rainfall (%)
Annual 1.00– 1.41 2.16 – 5.97
Winter 1.08 – 1.54 (-)1.95 – 4.36
2020s
Monsoon 0.87 – 1.17 1.81 – 5.10
Annual 2.23 – 2.27 5.36 – 9.34
Winter 2.54 – 3.18 (-)9.22 – 3.82
2050s
Monsoon 1.81 – 2.37 7.18– 10.52
Annual 3.53 – 5.55 7.48 – 9.90
Winter 4.14 – 6.31 (-)24.83 – 4.50
2080s
Monsoon 2.91 – 4.62 10.10 – 15.18
On seasonal basis, the projected surface warming is higher in winter than during summer
monsoon. The spatial pattern of temperature change has a large seasonal dependency. The
spatial distribution of surface warming suggests that north India may experience an annual
mean surface warming of 3°C or more by 2050s. GCM models have simulated peak warming
of 3°C over north and central India in winter. Over much of the southern peninsula, the
warming is likely to be under 2°C during winter season. The surface temperature rise would
be more pronounced over northern and eastern region (~2°C) during the monsoon season.
34
In order to predict the changes in the temporal as well as spatial variability of the
monsoon rainfall in response to increases in radiative forcing of the atmosphere, climate
change scenario over Indian sub-continent under the four new SRES 'Marker' emission
scenarios (namely A1, A2, B1 and B2 scenarios) have been developed based on the data
generated in numerical experiments with A-O GCM of the CCSR/NIES, Japan (Lal, 2001).
These four emission scenarios cover a wide range of the main demographic, technological,
and economic driving forces of future emissions. Each describes a different world evolving
through the 21st century and leads to different greenhouse gas emission concentration
trajectories. Warming is projected to be significant in post-monsoon and winter seasons.
The projected scenarios for rainfall over Indian subcontinent for different seasons by
2020, 2050 and 2080 are given in Table 2.1. The increase in annual mean precipitation over
the Indian sub-continent is projected to be 7 to 10% by 2080s. Winter precipitation may
decrease by 5 to 25% in the Indian sub-continent. An increase of 10 to 15% is projected in
area-average summer monsoon rainfall over the Indian sub-continent. Over northwest India,
during monsoon season an increase of about 30% or more is suggested by 2050s. The
western semi-arid margins of India could receive higher than normal rainfall in the warmer
atmosphere. It is likely that date of onset of summer monsoon over India could become more
variable in future. IPCC (2001) has indicated that variability in Asian summer monsoon is
expected to increase along with changes in the frequency and intensity of extreme climate
events in this region. All climate models simulate an enhanced hydrological cycle and
increases in annual mean rainfall over South Asia (under non-aerosol forcing).
In India, limited studies have been conducted by using the statistical downscaling to
model stream flow at river basin scale. Downscaling is required because General
35
Circulation Models (GCMs) often used in accessing the impact of climate change operate on
a coarse scale and thus the results obtained from GCMs aren’t so useful in a smaller river
basin scale.
Tripathi and Srinivas (2005) have used downscaling of GCMs to access the impact of
climate change on rainfall of India. A study carried out by Ghosh and Mujumdar (2007) have
used statistical downscaling of GCM simulations to stream flow for Mahanadi river basin in
India. Their study has shown decreasing trend in monsoon stream flow of Mahanadi.
Moreover, it can be said that the methodology based on downscaling can be used to model
any hydrologic variable such as precipitation, evaporation etc to access the impact of climate
change on hydrology.
2.4 HYDRO-CLIMATIC STUDIES ON SUTLEJ RIVER BASIN
The Satluj river lies in Northern belt of India and the region is also known by
Northwestern part of India. Singh and Bengtsson (2004) has clarified that the Satluj river
basin is characterized by diversified climatic patterns. The westerly weather disturbances
deposit nearly all the precipitation during the winter months in the upper part and middle part
of the basin and most of the precipitation falls in the form of snow in this season. The major
part of the basin area lies in the greater Himalayas where heavy snowfall takes place. The
monsoon rains have little influence in the greater Himalayan range where the annual rainfall
is about 200 mm. Their study has concluded that an increase in temperature from 1 to 3 °C is
computed to change the stream flow in winter (-2 to -5%), spring (4 to 10%), summer (-6 to -
11%) and autumn (-4 to -6%). On an annual basis, the runoff is expected to be reduced by 4–
6%. It also concluded that the effect of warmer climatic conditions on the annual stream
flow will not be severe, but the seasonal distribution of stream flow is highly affected.
36
Singh et al. (2008) have carried out basin-wise assessment of temperature variability and
trends in the northwest and central India. In this study, seasonal and annual trends of changes
in maximum temperature (Tmax), minimum temperature (Tmin) and mean temperature (Tmean)
have been examined on the basin scale. Longest available records for 43 stations, varying
from 90 to 100 years, over the last century were used in the analysis. The study has been
carried out for 9 river basins in northwest and central part of India. Among them, Indus-
lower has experienced an increasing trend in mean annual temperature over the last century.
The range of increase in mean annual temperature varied between 0.40 to 0.64 °C per 100
years. Satluj is one of the main tributaries of the Indus river.
National Institute of Hydrology (NIH) and Central Water Commission (CWC) has
prepared a preliminary consolidated report on Effect of Climate Change on Water Resources
in June 2008. It is mentioned on the report that Satluj river basin receives contributions from
rain, snow and glacier melt runoff. About 65% of the basin area is covered with snow during
winter, which reduces to about 11% after the ablation period. The results obtained from
different climatic scenarios have shown that there is reduction of water availability during the
summer period due to warming. The reduction in summer runoff which contributes about 60
% to the annual flow may have severe implications on the water resources of the region.
A study carried out by Jain et al. (2009) has concluded that there is an enhanced
precipitation during the monsoon season over the northwestern parts of India. Regarding the
temperature trends into the future, all the models show positive trends indicating widespread
warming into the future and the warming is more pronounced over the northern parts of
India. The stream flow analysis has been carried out for different seasons such as winter
(November–February), spring (March–May), summer (June–August), autumn (September–
37
October) and also on annual basis. Seasonal analysis of stream flow under a warmer climate
suggests that water availability is reduced mainly in summer. An increase of 2 oC in
temperature changes the stream flow marginally. During winter, the stream flow reduces and
while the study has shown increase in stream flow during spring season.
2.5 APPLICATION OF ANN IN RAINFALL-RUNOFF RELATIO NSHIP
The relationship between rainfall and runoff is highly nonlinear and complex and its
determination is very important for hydrologic engineering design and management
purposes. It is dependent on numerous factors such as initial soil moisture, land use,
watershed geomorphology, evaporation, infiltration, distribution and duration of rainfall and
so on. Many of the watersheds are gauged to provide continuous record of stream flow data.
But situations such as high flood season, instrument failure, etc force the engineers or
hydrologists to generate the stream flow records using rainfall by simulation models. Many
rainfall-runoff models such as empirical, lumped and distributed models have been
developed and used for simulating the stream flow at the catchment outlet. Empirical models
estimate the peak runoff from the whole catchment for the purpose of design of storage
structures. Lumped models like unit hydrograph (Chow et al., 1988) have been developed to
estimate the runoff hydrograph from a storm event. Distributed models such as SHE (Danish
Hydraulic Institute, 1988), TOPMODEL (Bevan et al., 1995) consider the hydrologic
processes taking place at various points in space and define the model variables as functions
of the space dimensions. Distributed models can be used to synthesize runoff volumes from
ungauged catchments. Calibration of distributed models requires large quantity of data
compared to lumped models and large computer resources for successful implementation.
Sometimes complexity and less accuracy of these conventional models force the modeler to
38
think of alternative modeling techniques such as ANN, Fuzzy logic which provide better
results. Many applications of ANN in rainfall-runoff modeling are reported. Some of the
applied studies are reviewed in detail.
Hsu et al. (1995) used linear least square simplex (LLSSIM) procedure for identifying the
structure and parameters of three layered feed forward Artificial Neural Network (ANN)
models and demonstrated the potential of ANN models for simulating the nonlinear
hydrologic behavior of watersheds. It was shown that the nonlinear ANN hydrologic model
performed better than linear ARMAX (autoregressive moving average with exogenous
inputs) time series approach and the conceptual SAC-SMA (Sacramento soil moisture
accounting) model. It was concluded that ANN approach could be used as substitute of
conceptual model where modeling of the physical processes in the catchment was not
important.
Raman and Sunilkumar (1995) used artificial neural network for the synthesis of inflows
to two reservoirs Mangalam and Pothundy located in the Bharathapuzha, Kerala. Real
observations were used to train and test the feed forward networks. Feed forward structure
was used to model the ANN. Back propagation algorithm was used to train the data set. It
was remarked that the neural network provided a very good fit with the data. The results of
ANN model were compared with AR model. It was concluded that ANN model could be
used to model the water resource time series in place of multivariate modeling.
Minns and Hall (1996) developed ANN model to simulate runoff from rainfall and
compared with conceptual hydrological model consisting of a single linear reservoir. They
also concluded that increase of hidden layer neuron did not give better results than the one
with less number of neurons.
39
Dawson and Wilby (1998) used artificial neural network approach to rainfall-runoff
modeling in two flood prone catchments in UK using real hydrometric data. The
performance of ANN was compared with conventional flood forecasting systems.
Multilayered feed forward network structure was used to model the flood forecasting system
and back propagation algorithm was used for training the network combinations. It was
concluded from the results that there was considerable scope for the development of a fully
operational ANN flood forecasting system.
Fernando and Jayawardena (1998) used RBFN with Orthogonal Least Square (OLS)
algorithm to model runoff forecasting from rainfall patterns. They found that the training was
faster in RBFN with OLS algorithm and RBFN performed better than the network with back
propagation algorithm and the ARMAX model.
Danh et al. (1999) developed two back propagation neural network models (BPNN) to
forecast the daily river flows in two basins in Vietnam and compared with tank model. It was
found that the developed BPNN models provided satisfactory results in both the basins.
Jain et al. (1999) used artificial neural network for reservoir inflow prediction and the
operation for Upper Indravati Multipurpose project, Orissa. Two ANNs were developed to
model the reservoir inflows. Feed forward structure was used for ANN model. Back
propagation algorithm was used for training the neural networks. An ARIMA model was
constructed to fit the monthly inflow series. It was found that ANN model was suitable to
predict high flows and ARIMA model was suitable to predict low flows. It was concluded
that ANN was a powerful tool for input-output mapping and could be used effectively for
reservoir inflow forecasting.
40
Sajikumar and Thandaveswara (1999) used temporal back propagation neural network
(TBPNN) to model the monthly rainfall-runoff process and was compared with the results of
Volterra type Functional Series Model. They found that TBPNN performed better than the
other model. The model was applied to Thuthapuzha river in Kerala, India and Lee river in
UK.
Tokar and Johnson (1999) developed ANN model to forecast daily runoff as a function of
daily precipitation, temperature and snowmelt for Little Patuxent river watershed in
Maryland and the results compared with statistical regression and conceptual model. They
concluded that ANN model provided more systematic approach and reduced the length of
calibration data and at the same it improved prediction accuracy over the other models.
Zealand et al. (1999) used the artificial neural networks to forecast the short-term stream
flow. The possibility of using ANN over the conventional methods for the forecasting of the
flood was explored. The size of input data and the number, and the size of the hidden layers
of ANNs were examined. Feed forward structure of the ANN was used in the forecasting of
stream flow. Back propagation algorithm was used for the training of the network. The
trained ANN was applied to Winnipeg River System (catchment area 20000 km2) in
Northwest Ontario, Canada. From the results it was concluded that ANN approach might
provide a superior alternative to the time-series approach for developing input-output
simulations and forecasting models.
Elshorbagy et al. (2000) used ANN technique to predict spring runoff in the Red River
Valley, Southern Manitoba, Canada. Feed forward neural network structure was used to
model the spring runoff. Back propagation training algorithm was used to train the network.
Linear and nonlinear regression models were also constructed. It was concluded that ANN
41
models demonstrated superiority in most of the cases. In some situations, the performances
of the other two techniques were comparable.
Imrie et al. (2000) presented two ANN models with different training algorithms to
predict river flow. One was with standard back propagation algorithm and another with
cascade correlation learning architecture with guided system to improve the generalization
during training. The ability of the developed algorithm to generalize on new data was
checked with two case studies and compared with the performance of standard error back
propagation algorithm.
Thirumalaiah and Deo (2000) used artificial neural networks in real time forecasting of
water levels and discharge at a given site continuously throughout the year based on the same
levels at some upstream gauging station and/or using the stage-time history recorded at the
same site. Feed forward neural network structure was used to model the river stage
forecasting system. The network was trained by three algorithms namely, error back
propagation, cascade correlation, and conjugate gradient. The results were compared with
each other. The trained networks were verified with untrained data. It was concluded that the
continuous forecasting of a river stage in real time was possible through the use of neural
networks.
Tokar and Markus (2000) applied ANN technique to model watershed runoff in three
basins with different climatic and physiographic characteristics – the Fraser River Colorado,
Raccoon Creek in Iowa, and Little Patuxent River in Maryland. Three layered feed forward
neural network structure was used to model the watershed runoff process. The network was
trained by the back propagation algorithm. The results of ANN models were compared with
conceptual models. In all cases, the ANN models provided higher accuracy, a more
42
systematic approach, and shortened the time spent in training of the models. They concluded
that ANNs could be powerful tools in modeling the rainfall-runoff process for various time
scale, topography, and climatic patterns.
Zhang and Govindaraju (2000) used modular neural network structure to handle complex
sets of rainfall-runoff data. Different modules within the network were trained to learn
subsets of the input space in an expert fashion. A gating network was used to mediate the
response of all the experts. The three modular architectures used in the study represent the
low, medium and high runoff events. Bayesian concepts were utilized in deriving the
training algorithm. Average monthly rainfall of current and previous months and average
monthly temperatures were treated as network inputs, and monthly runoff was treated as
output. The performance of modular networks in predicting runoff over three medium sized
catchments was examined. It was concluded that modular neural networks predicted extreme
events of runoff better than the singular neural network models.
Deka and Chandramouli (2003) developed ANN model for stage-discharge relationship
and compared with conventional curve fitting. It was found that ANN model for stage-
discharge relationship performed better than the conventional curve fitting technique.
Sudheer et al. (2003) developed a technique to improve the peak flow estimation in river
flow models. They used appropriate data transformation to reduce the local variation in the
function being mapped. They concluded that the model built on the transformed data
outperformed the model built on raw data. The peak flow estimates were improved by data
transformation.
Nagesh kumar et al. (2004) developed recurrent neural networks for forecasting river
flow for Hemavati River in India. A feed forward neural network was also developed and
43
applied to the same river. The training of recurrent neural network was done by using the
method of ordered partial derivatives. The feed forward neural network was trained by
improved back propagation algorithm. They found that recurrent neural network models
gave better results than the feed forward neural network for single step and multi step ahead
forecasting.
Parasuraman et al. (2006) proposed spiking modular neural network (SMNN) to model
the streamflow and compared its result with the regular feed forward neural networks
(FFNN) with case study of a basin in Canada. It was concluded that the SMNNs were
effective in discretizing the complex mapping space into simpler domains that could be learnt
with relative ease.
Raghuwanshi et al. (2006) developed ANN models for predicting runoff on daily and
weekly basis for a small catchment in India. The ANN models were trained by Levenberg-
Marquart back propagation algorithm. Regression models were also developed and
compared with the performance of ANN models. It was concluded that the ANN models
were performed better than linear regression models.
Kisi (2007) developed four different ANN models with training algorithms such as back
propagation, conjugate gradient, cascade correlation and Levenberg-Marquart to forecast
daily streamflow of North Platte River in the United States. The results from the different
algorithms were compared with each other.
Fernando and Shamseldin (2009) modelled the rainfall-runoff process using radial basis
function neural network (RBFNN) to forecast the flow one day ahead with the present day
and antecedent observed discharges as input. The model was applied to two different regions
in the world. It was found that the three nodes in the hidden layer effectively divide the three
44
flows domains-low, medium or high from the base flow, interflow and surface runoff
components of the hydrograph.
Srinivasulu and Jain (2009) used integrated approach to achieve reasonable accuracy in
river flow prediction. The integrated approach consisted of conceptual, ANN, Genetic
algorithm, data-decomposition and model fusion techniques. The performance of integrated
model was compared with time series and conceptual models and it was found that the
integrated approach model performed better than other models.
Yonaba et al. (2010) analyzed performance of different sigmoid transfer functions such
as Elliot sigmoid, bipolar sigmoid and tangent sigmoid functions in multilayer perceptron
neural networks for multistep ahead stream flow forecasting up to 5 days as lead time. The
above methodology was applied in five watersheds with lead times from 1 to 5 days. The
performance of ANN models with different transfer functions deteriorated as time horizon
for the stream flow forecasting was increased. It was found that the performance of ANN
model with tangent sigmoid function was better than the ANN models with other two transfer
functions. The ANN model with Elliot transfer function required less computing time and it
could be used as an efficient tool in operational hydrology. Neural networks with linear
function in the output layer performed better than the nonlinear functions.
In most of the studies the input selection to the ANN model was based on trial and error
procedure. In this study, since monthly rainfall and discharge data are used to develop ANN
model for Satluj basin at Kasol, the input consisting of rainfall, temperature and discharge at
time t is considered. Two types of ANN models are developed considering only rainfall,
rainfall and temperature as input. The ANN modeled series of discharge values are
compared with the discharge simulated by Multiple Linear Regression (MLR) model. The
45
discharge at Kasol includes the contribution from rainfall in the plain area and snowmelt
runoff from hilly area. The ANN models developed are used to simulate the monthly
discharge using the GCM downscaled monthly rainfall values for next hundred years i.e.,
from 2001 to 2100 and to find out the increase or decrease in discharge over next 100 years.
46
CHAPTER 3
STUDY AREA AND DATA USED
3.1 DESCRIPTION OF THE STUDY AREA
This study has been carried out for Satluj (also spelled as Sutlej) river near by the Bhakra
dam within 30045’to 33015’ North latitudes and 76010’ to 79010’ East longitudes. The Satluj
River rises from the lakes of Mansarovar and Rakastal in the Tibetan Plateau at an elevation of
about 4572 m. It is one of the main tributaries of the Indus River. It is found that about 65 % area
of the Satluj river basin has been covered by snow in winter. Considering the snow covered
region as well as source of the river, Satluj has been categorized in the Himalayan river system.
Figure 3.1: Location map of the Satluj basin up to Bhakra dam with hydrometeorological stations
In India, Himalayan river system that is sustained, at the head, by glacier bearing basins, has
been initially classified into three first order basins, 5Q (Indus basin), 5O (Ganga basin) and 5P
(Brahamputra basin).
47
Figure 3.2: First order basins of the Himalayas in India (Raina and Srivastava, 2008)
The glaciers located in Indus basin has been given in Table 3.1.
Table 3.1: Distribution of glaciers in 5Q Indus basin
Basin No. of glaciers Glacier covered Area (km2 Ice volume (km3
Ravi 172 193 8.04
Chenab 1,278 3,059 206.3
Jhelum 133 94 3.30
Beas 277 579 36.93
Satluj 926 635 34.95
Upper Indus 1,796 8,370 73.58
Shyok 2,454 10,810
Nubra 204 1,536
First Order Basins
5 Q: Indus Basin
5 O: Ganga Basin
5 P: Brahamputra Basin
48
Gilgit 535 8,240
Kishenganga 222 163
Total 7,997 33,679 363.10
(Raina and Srivastava, 2008)
Satluj river is the longest of the five rivers that flow through the region of Punjab in
Northern India and it finally mix with Indus in Pakistan. The total catchment area of the River up
to the Bhakra dam is about 56, 500 km2, of which about 22, 305 km2 lies in India (Jain, 2008).
The elevation of the catchment varies from 500 to 7000 m, and only a very small area exists
above 6000 m. The gradient of the river is very steep at its source and it gradually decreases as it
moves downstream. Due to the large differences in seasonal temperatures and the great range of
elevation in the catchment area, the snowline is highly variable. Sometimes the snow line
descends to an elevation of about 2000 m during summer.
49
Figure 3.3: Glacier map of Sutlej basin (Raina and Srivastava, 2008)
In the Tibetan plateau, the river flows through the cold desert area with no rain and
absolutely no vegetation (Jain et al., 2009). Spiti is the largest tributary of Satluj River, which
joins the River in Namigia near Shipki. The Satluj River receives cool, snowmelt water from the
upper basin during the spring and summer months and from monsoon precipitation during July–
September in its lower basin. As the river moves down from Khab, Nathpa to Bhakra,
50
contribution from snowmelt decreases and rainfall increases. The climate and vegetation also
changes from arid to humid. The topographical setting and availability of abundant water of the
river has shown great significance of enormous hydropower generation.
Table 3.2: Salient Features of Satluj river basin
Location Western Himalayas
Basin Area (Indian part) 22,305 km2
Elevation Range 500-7000 m
Mean Elevation 3600 m
Snow Covered Area About 65% after winter
Glacierized Area About 10 %
Important Hydropower Scheme Bhakra Dam (1325 MW)
This river basin is characterized by diversified climatic patterns. The westerly weather
disturbances deposit nearly all the precipitation during the winter months in the upper part and
middle part of the basin and most of the precipitation falls in the form of snow in this season.
The major part of the basin area lies in the greater Himalayas where heavy snowfall takes place.
The monsoon rains have little influence in the greater Himalayan range.
51
Figure 3.4: Cumulative isohyetal pattern (10 years) of the Indian part of Satluj
basin up to Bhakra dam
About 2 % of the total basin area is covered by glaciers. Some of the glaciers like Nagpo
Tokpo, Laroathach, Gara, Gorgarang, Shanegarang, Nardu, Baspa are found in the Satluj basin.
The seasonal snowpack, developed during the winter, starts melting around March and depletes
either fully or partially during the forthcoming summer season depending upon the climatic
conditions over the basin. Snowmelt is the major runoff-producing mechanism in the upper part
of the basin, whereas rainfall contributes largely in the lower part of the basin (Singh and
Bengtsson, 2004). The middle part of the basin has contributions from both rain and snowmelt.
52
Figure 3.5: Area–elevation curve for the Satluj River basin (Indian part) upstream of
Bhakra Reservoir (Singh and Bengtsson, 2004)
3.2 DATA USED
The National Center for Environmental Prediction (NCEP) reanalysis data of the study
area have been taken from 1948 to 2004. Data set of wind speed (uwind, vwind), relative
humidity, mean sea level pressure, geopotential height and air temperature have been considered
to carry out the study. The data have been obtained through the website of NOAA as,
http://www.esrl.noaa.gov. In the absence of adequate observed climatological data, the data
from the National Center for Environmental Prediction / National Center for Atmospheric
Research (NCEP/ NCAR) reanalysis project have been used as a proxy to the observed data.
Reanalysis data are outputs from a high resolution atmospheric model that has been taken from
surface observation stations, upper air stations and satellite observing platforms. These data are
obtained in grid scale.
53
GCM outputs of CCSR/ NIES Japan have been considered from 2001 to 2100 for
projecting future rainfalls. The gridded data sets of mean sea level pressure, specific humidity,
wind speed, air temperature have been used as GCM outputs. The gridded data sets of A2
scenario have been used in the study. The GCM data are available in the website of IPCC as,
http://www.mad.zmaw.de/IPCC_DDC/html/ddc_gcmdata.html.
Mean monthly rainfall of Kasol from 1977 to 2004 have been used as observed rainfall
and mean monthly discharge of Kasol and average temperature of Satluj basin from 1987 to
2000 have been considered as observed discharge and temperature data set.
54
CHAPTER 4
METHODOLOGY
4.1 GENERAL
Hydrologic impacts of climate change are usually assessed by downscaling the GCM
output of large-scale climate variables to local-scale hydrologic variables. In this research, data
set of wind speed (uwind, vwind), relative humidity, MSLP, geopotential height, air temperature
of the study area are used as predictor and rainfall as predictand. The predictors for the
downscaling should be (i) reliably simulated by GCM outputs (ii) readily available from the
archieves of GCM outputs and (iii) strongly correlated with surface variables of interest.
In the absence of adequate observed climatological data, the NCEP reanalysis data are
used as a proxy to the observed data. Standarization is performed prior to principal component
analysis and downscaling to remove systematic bias in mean and standard deviation of the GCM
simulated climate variables. Finally principal components are used as regressors to predict the
discharges of satluj in regression. Two-third of the data set have been used in training and rest of
the data have used in testing of the model. The statistical relationship developed is then used on
the standardized output of the GCMs as A2 (future changed scenario).
4.2 STATISTICAL DOWNSCALING
Statistical downscaling gives quantitative relationship between large-scale atmospheric
variables (predictors) and local surface variables (predictands) (Wilby et al., 2004). Statistical
downscaling, produces future scenarios based on statistical relationship between large-scale
climate features and hydrologic variables like precipitation. One of the most important steps in a
downscaling exercise is to select appropriate predictors, or characteristics from GCMs. Wilby et
55
al. (1999) proposed that there are three main factors constraining the choice of predictors: (1)
whether the predictors were reliably simulated by the GCM; (2) how readily available the GCM
output data; and (3) the correlation strength with the surface variables of interest. Generally there
are three inherent assumptions associated with statistical downscaling. These are like (i)
predictors are realistically modeled by host GCM, (ii) empirical relationship is valid under
altered climatic conditions and (iii) the predictors fully represent the climate change signal
(Ghosh and Mujumdar, 2007).
Figure 4.1: Illustrating the general approach to downscaling (Wilby and Dawson, 2007)
56
Easy to use, cheap and readily transferable are some of the strengths and predictor-
predictand relationships are often non-stationary, choice of predictor variables affects the results
are some of the limitations associated with the statistical downscaling.
Statistical downscaling methodology can be broadly classified into three categories as
follows:
4.2.1 Weather Generators
Weather generators are statistical models of observed sequences of weather variables.
They are also known by stochastic weather generators. They can also be regarded as complex
random number generators, the output of which resemble daily weather data at a particular
location There are two fundamental types of daily weather generators, based on the approach to
model daily precipitation occurrence: the Markov chain approach and the spell-length approach.
In the Markov chain approach, a random process is constructed which determines a day at a
station as rainy or dry, conditional upon the state of the previous day. In case of spell-length
approach, instead of simulating rainfall occurrences day by day, spell-length models operate by
fitting probability distribution to observed relative frequencies of wet and dry spell lengths.
4.2.2 Weather Typing
Weather typing approaches involve grouping of local, meteorological variables in
relation to different classes of atmospheric circulation. Future regional climate scenarios are
constructed either by resampling from the observed variable distribution (conditioned on the
circulation pattern produced by a GCM), or by first generating synthetic sequences of weather
pattern using Monte Carlo techniques and then resampling from the generated data. The mean or
57
frequency distribution of the local climate is then derived by weighting the local climate states
with the relative frequencies of the weather classes.
4.2.3 Transfer Function
The most popular approach of downscaling is the use of transfer function which is a
regression based downscaling method. The transfer function method relies on direct quantitative
relationship between the local scale climate variable (predictand) and the variables containing the
large scale climate information (predictors) through some form of regression. Individual
downscaling schemes differ according to the choice of mathematical transfer function, predictor
variables or statistical fitting procedure. To date, linear and nonlinear regression, Artificial
Neural network (ANN), canonical correlation, etc. have been used to derive predictor–predictand
relationship. Among them, ANN based downscaling techniques have gained wide recognition
owing to their ability to capture nonlinear relationships between predictors and predictand.
The main strength of transfer function downscaling is the relative ease of application. The
main weakness is that the models often explain only a fraction of the observed climate variability
(especially in precipitation series). Transfer methods also assume validity of the model
parameters under future climate conditions. The downscaling is highly sensitive to the choice of
predictor variables and statistical form. Furthermore, downscaling future extreme events using
regression method is problematic since these phenomena, by definition, tend to lie at the limits or
beyond the range of the calibration data set (Wilby et al., 2007).
4.3 FLOW CHART OF STATISTICAL DOWNSCALING
A schematic diagram of statistical downscaling has been shown in the Figure 4.2.
58
Standardization
Interpolation
Standardization
Principal Principal Component Directions Analysis
Model Training
Figure 4.2: Flow chart of statistical downscaling
GCM Output
Standardized GCM Output Predictors
NCEP Data
GCM Output at NCEP Grid Points
Standardized NCEP Data: Predictors
Principal Components of GCM Output Principal
Components
Trained Linear Regression Model Linear Regression
Future Hydrologic Variable
Observed Hydrologic Variable
59
4.4 TOOLS USED
4.4.1 MATLAB
MATLAB (meaning "MATrix LABoratory") is a special purpose computer program
optimized to perform engineering and scientific calculations. MATLAB program implements the
MATLAB language and provides a very extensive library of predefined functions to make
technical programming tasks easier and more efficient. Due to such wide variety of functions
make it easier to solve technical problems in MATLAB than in other languages such as
FORTRAN or C. MATLAB is also known by the language of technical computing or the fourth
generation programming language. In the present research, an attempt has been done for
applying Principal Component Analysis with the help of MATLAB.
4.4.2 Principal Component Analysis
Principal Component Analysis (PCA) involves a mathematical procedure that transforms
a number of possibly correlated variables into a smaller number of uncorrelated variables called
principal components. Principal components are also known by generation of a new set of
variables by PCA, and they have a linear combination of the original variables.
In this study, due to large dimensionality of predictor variables, it may computationally
unstable. Hence, PCA is performed to reduce the dimensionality of the predictor variables. PCA
is also used to downscale GCM outputs of large-scale climatic variables to sub divisional level.
60
4.4.3 Standardization
Standardization is performed for both NCEP and GCM output data set. It is applied by
the relationship as, . Standardization has been carried out to change the scale
of measurement of each test variable with a mean of ‘zero’ and standard deviation of ‘one’
4.4.4 Multiple Linear Regression Analysis
Regression is one of the most powerful tools of statistics. It uses for the estimation of the
strength of the relationship between variables (Gautam, 2000). It refers to the method by which
estimates are made of the values of one variable from knowledge of the values of one or more
other variables.
Multiple linear regression analysis is used to find the degree of inter-relationship among
three or more variables. The least square regression analysis can be extended to cases where
there are more than one independent variables (Reddy, 1998). Let y the dependent variable and
x1, x2,…xp be the independent variables. The multiple linear regression equation is then written
as
y = d0 + d1x1 + d2x2 +……+dpxp (4.1)
Where d0, d1, ……dp are the regression constants (coefficients) to be determined. Denoting the
observations on the variable as (yi, x1i, x2i, …., xpi), the sum of the squared deviations is given by
S = ∑ (yi – d0 – d1x1i – d2x2i - …… -dpxpi)2 (4.2)
Where the summation runs from i = 1 to i = n, n being the number of observations. Equating the
partial derivatives of this sum with respect to the regression constants to zero, we get the
following normal equations.
∑yi = ∑d0 + d1∑x1i + d2∑x2i + ……+ dp∑xpi (4.3)
∑yix1i = d0∑x1i + d1∑x1i2 + d2∑x2ix1i + ……+ dp∑xpix1i (4.4)
61
… … … … … … … …
… … … … … … … …
∑yixpi = d0∑xpi + d1∑x1ixpi + d2∑x2ixpi + ……+ dp∑xpi2 (4.5)
The solution of Equations (3), (4) and (5) yields the values of d0, d1, … dp.
In present study, multiple linear regression analysis has been performed among the principal
components and observed rainfalls.
4.4.5 Rainfall Variability
It has been conducted to find out the variability in rainfall between observed and
predicted rainfall values. In this study, monthly variations of rainfall have been obtained by
taking averages of each months of observed and predicted rainfalls based on the average of
observed rainfall. Mathematically, it can be expressed in percentage for the month of January as,
* 100.
4.4.6 Artificial Neural Network
Artifical Neural Networks (ANNs) are a form of computing inspired by the functioning
of the brain and nervous system and are discussed in detail in a number of technical papers
published in hydrologic and water resources journals The architecture of a feed forward
ANN can have many layers where a layer represents a set of parallel neurons. The basic
structure of ANN usually consists of three layers: the input layer, where the data are
introduced to the network; the hidden layer or layers, where data are processed; and the
output layer, where the results of given outputs are produced. The neurons in the layers are
interconnected by strength called weights. A typical three-layered feed forward ANN is
shown in Figure 4.3.
62
Input layer Hidden layer Output layer
Bias Bias
Network
Input Network
X Output
Y
Figure 4.3: A Typical Three-Layered Feed Forward ANN
In general, a neuron can have n inputs, labeled from 1 through n. For example, neuron 3 in
the hidden layer shown in Figure 4.3, has n= 2. In addition, each neuron has an input that is
equal to 1.0, called bias. Each neuron j receives information from every node i in the
pervious layer. A weight (wji) is associated with each input (xi) to node j. The effective
incoming information (NETj) to node j is the weighted sum of all incoming information,
otherwise known as the net input, and is computed as:
xin
iw jiNET j ∑
==
0 (4.6)
Where x0 and wj0 are called as the bias term (x0 = 1.0) and the bias respectively. Equation
(4.6) applies to the nodes in the output layer and hidden layer(s). The weighted sum of input
information is passed through an activation function, called transfer function, to produce the
output from the neuron. The transfer function introduces some nonlinearity in the network,
which helps in capturing the nonlinearity present in the function being mapped. The
1
1 1
2
2
3
63
commonly employed transfer function is the sigmoid function (ASCE, 2000a) and is given as
follows:
e NET jOUT j −+
=1
1 (4.7)
The interconnected weights are adjusted using a learning algorithm such that the output from
the ANN model is very close to the observed values by minimizing the error through a
mathematically formulated procedure. This procedure is called training of network (ASCE,
2000a).
Using a set of examples from a given problem domain, comprising inputs and their
corresponding outputs, an ANN model can be trained to learn the relationship between the
input-output pairs. The feed forward ANN is generally adapted in all studies because of its
applicability to a variety of different problems (Hsu et al., 1995). However, there are no
guidelines in developing an effective ANN architecture, though some researchers have
reported suggestions that can be implemented while developing an ANN model. For instance,
Maier and Dandy (2000) have reported that not more than one hidden layer is required in
feed forward networks because a three-layer network can generate arbitrarily complex
decision regions. Also, the appropriate input vector to the ANN model can be identified
according to the procedure of Sudheer et al. (2002).
Normalization of Input Data
The input values should be normalized to the range between 0 and 1 before passing into a
neural network since the output of sigmoidal function is bound between 0 and 1. Minns and
Hall (1996), Dawson and Wilby (1998), Sajikumar and Thandaveswara (1999), and Burian et
al. (2001) have emphasised the importance of the normalisation of data and have given the
64
procedure to normalise. The output from the ANN should be denormalised to provide
meaningful results. In this study, following equation is used to normalize the data set:
MiniMaxi
MiniRiNi −
−= (4.8)
where Ri is the real value applied to neuron i; Ni is the subsequent normalized
value calculated for neuron i; Mini is the minimum value of all values applied to neuron i;
Maxi is the maximum value of all values applied to neuron i.
Training of ANN
Training a network is a procedure during which an ANN processes training set
(input-output data pairs) repeatedly, changing the values of its weights, according to a
predetermined algorithm and the environment in which the network is embedded. The
main objective of training (calibrating) a neural network is to produce an output vector
),....,,(21
yyyYp
= that is as close as possible to the target vector (variable of interest or
forecast variable) ),....,,( 21 tttT p= when an input vector ),....,,( 21 xxxX p= is fed to
the ANN. In this process, weight matrices W and bias vectors V are determined by
minimizing a predetermined error function as explained as follows:
∑∑ −=P p
ty iiE )(2
(4.9)
where ti is a component of the desired output T; yi is the corresponding ANN
output; p is the number of output nodes; and P is the number of training patterns.
Back propagation is the most popular algorithm used for the training of the feed
forward ANNs (Hsu et al., 1995; Dawson and Wilby, 1998; Sajikumar and
65
Thandaveswara, 1999; Tokar and Jhonson, 1999; Zealand et al., 1999; Thirumalaiah and
Deo, 2000; ASCE, 2000a; Elshorbagy et al., 2000; Maier and Dandy, 2000; Burian et al.,
2001; Nagy et al., 2002; Deka and Chandramouli, 2003; Jain and Srinivasulu, 2004;
Keskin and Terzi, 2006; Kisi, 2007; Jain, 2008; Fernando and Shamseldin, 2009). Each
input pattern of the training data set is passed through the network from the input layer to
output layer. The network output is compared with the desired target output, and an error
is computed based on the equation (4.9). This error is propagated backward through the
network to each neuron, and the connection weights are adjusted based on the equation
)1(**)( −∆+∂∂−=∆ nE
n www ijij
ijαε (4.10)
Where )(nwij∆ and )1( −∆ nwij are weight increments between node i and j
during nth and (n-1)th pass, or epoch (ASCE, 2000a). A similar equation is written for
correction of bias values. In the equation (4.10), ε and α are called learning rate and
momentum respectively. The momentum factor can speed up training in very flat regions
of the error surface and help prevent oscillations in the weights. A learning rate is used to
increase the chance of avoiding the training process being trapped in local minima
instead of global minima. The literature by Rumelhart et al. (1986) can be referred for the
details of the algorithm.
Performance Evaluation of ANN Model
The whole data length is divided into two based on statistical properties of the
time series such as mean and standard deviation, one for calibration (training) and
another for validation of ANN model. The performance during calibration and validation
66
is evaluated by performance indices such as root mean square error (RMSE), model
efficiency (EFF) (Nash and Sutcliffe, 1970) and coefficient of correlation (CORR). They
are defined as follows:
Root mean square error (RMSE) K
K
kyt∑
=−
= 1)( 2
(4.11)
Efficiency (EFF) ∑ −
∑ −−=
)(2
)( 21
tt
yt (4.12)
Coefficient of Correlation (CORR) ∑ ∑
∑=YT
TY
22 (4.13)
where K is the number of observations; t is the observed data; y is computed data; ttT −=
in which t is the mean of the observed data; and yyY −= in which y is the mean of the
computed data.
Advantages and disadvantages of ANN models
Each of the following advantages of a neural network can be usefully exploited in
constructing models of the hydrological processes (Thirumalaiah et al., 1998):
a. Neural networks are useful when the underlying problem is either poorly defined or not
clearly understood.
b. Their application does not require knowledge of the underlying process beforehand.
c. They are advantageous when specific solutions do not exist to the problem posed.
d. Neural networks are most suitable for dynamic forecasting problems because the weights
involved can be updated when fresh observations are made available.
67
e. A small amount of errors in the input does not produce significant change in the output
because of distributed processing.
f. They save on data storage requirements because it is not necessary to keep all past data in
memory.
g. They do not require any exogenous input other than a set of input-output vectors for training
purpose.
ANNs have several drawbacks for some applications. They may fail to produce
satisfactory results if the data set is insufficient in size or the function is not able to learn the
process of the data set. The optimum network geometry as well as the optimum internal network
parameters are problem dependent and generally have to be found using a trial and error process.
ANNs cannot cope with major changes in the system because they are trained (calibrated) on a
historical data set and it is assumed that the relationship learned will be applicable in the future.
If there were any major changes in the system, the neural network would have to be adjusted to
the new process. Some researches have been reported in the literature to evolve better algorithms
for the generalization of ANN model i.e., to estimate the extreme events. Imrie et al. (2000)
added a guidance system to a training algorithm and found that the new algorithm performed
better in estimating the extreme events. Guidance system includes cross-checking of the model
performance, selection of output transfer function and fixing of the range of normalization.
4.4.7 Trend Analysis
A steady and regular movement in a time series, through which the values are on the
average increasing or decreasing, is termed as trend (Goel, 2009). Trend analysis is one of the
important tools to be performed in a hydrologic series. In this study, Mann Kendall test is
68
applied to find out trend in the observed and predicted data set. Short description of the test is
given below.
Mann-Kendall Test
The MK test is based on the test statistic S defined as follows:
S= ∑∑−
= +=
−1
1 1
)sgn(n
i
n
ijij xx
(4.14)
Where the xj are the sequential data values, n is the length of the data set, and
Sgn (θ )= (4.15)
Mann (1945) and Kendall (1975) have documented that when n ≥ 8, the statistic S is
approximately normally distributed with the mean and the variance as follows:
E(S) = 0 (4.16)
V(S) = 18
)52)(1()52)(1(1∑
=
+−−+−n
ii iiitnnn
(4.17)
where ti is the number of ties of extent i. The standardized test statistic Z is computed by
ZMK = (4.18)
The standardized MK statistic Z follows the standard normal distribution with mean of
zero and variance of one.
In this test, if the result of the Z-statistics is within ±1.96, then the series is random (i.e.,
without trend) otherwise it may have rising or falling trend at 5 % significance level.
69
CHAPTER 5
RESULTS AND DISCUSSION
5.1 GENERAL
Matlab program with principal component analysis, ANN, multiple linear regression and
trend analysis have been performed to get results from the study. The study-findings are
categorized in two main headings as rainfall analysis and rainfall-runoff analysis. Two sub-
headings like NCEP data analysis and GCM output data analysis have been carried out in rainfall
study. Similarly, two types of rainfall-runoff analyses have been carried out firstly considering
only rainfall as input and secondly rainfall and temperature as input to get rainfall-runoff
relationships.
5.2 RAINFALL ANALYSIS
5.2.1 NCEP Data Analysis
Air temperature, geopotential height, MSLP, specific humidity, uwind and vwind data
have been used as predictors in the NCEP data set. Observed rainfalls of 1977-2004 have been
used for establishing a relationship with NCEP data set. Standardization has been performed by
the relationship of . The study area has been categorized within 30 to 35
degree North latitudes and 75 to 80 degree East longitudes.
Principal component analyses have been carried out from the NCEP data set within the
period of 1977 to 2004. In present study, with the application of PCA, 98 % variability was
explained by 9 components. Then regression coefficients are obtained with the relationship
between PCA of NCEP data and observed rainfalls as given in Table 5.1.
70
Table 5.1: Regression Coefficients
Then using these 9 principal components (pci1, pci2…pci9) and 9 regression coefficients (d0, d1,
d2…d9); rainfall at time t have been obtained through the equation as:
Raint = d0 + (5.1)
The predicted rainfalls have been taken out with the relationship between regression
coefficients obtained from NCEP data set and PCA obtained from GCM output.
5.2.2 GCM Output Data Analysis
GCM output data analysis has been performed for the data set of A2 scenario. GCM data
of 2001 to 2100 have been considered for the study in predicting future rainfall for the next 100
years. During the analysis, standardization has been conducted and principal components have
been taken out with 98 % variability. Then the relationship between regression coefficients
obtained from NCEP data and principal components, future rainfall values for 2001 to 2100 are
obtained. The predicted rainfall values are given in Appendix I.
Regression Coefficients
d0 d1 d2 d3 d4 d5 d6 d7 d8 d9
Values 109.911 17.4775 -12.0145 33.5482 7.360 4.8876 -16.618 -15.2995 -13.1086 -31.181
71
Figure 5.1: Predicted rainfalls for future period from 2001 to 2100
5.2.2.1 Monthly distribution of predicted rainfalls for some years
Figure 5.2: predicted monthly rainfall for 2030
72
Figure 5.3: Predicted monthly rainfall for 2050
Figure 5.4: Predicted monthly rainfall for 2080
Figure 5.1 has been drawn for the predicted rainfalls from 2001 to 2100. It is observed
from the Figure that for the first 30 years, i.e., from 2001 to 2030, the maximum monthly
rainfalls are above 325 mm in many years. The same trend is not observed during the remaining
period of the prediction. Figures 5.2, 5.3 and 5.4 have been drawn on the predicated monthly
73
rainfalls for the years 1930, 1950 and 1980 respectively. All the Figures have shown that there
will be no rainfall in the months of December and January. The amount of rainfall will be very
high in June, July and August in compared to the remaining months. Hence, it is finalized that
future rainfalls will highly decrease for winter season, partially decreases for pre monsoon and
post monsoon and increases for monsoon season in an annual basis. These results signified a fact
that due to probable decreasing rainfall in winter, water conservation practices to be carried out
in monsoon season for future use. Proper water management is needed for considering the future
climatic condition of the Satluj river especially nearby the Bhakra region.
5.2.3 Rainfall Variability
Average monthly rainfalls from 1977 to 2004 as well as from 2001 to 2100 have been
taken to get rainfall variability within the same month of observed and predicted rainfall data set.
That is, the variability has been taken from the observed average rainfall of January with the
predicted average rainfall of January and so on. The average rainfall values and variations are
shown in the Table 5.2.
Table 5.2: Rainfall variability obtained from the average rainfall values
Month Average rainfall from observed rain data set (mm)
Average rainfall from predicted rain data set (mm)
Rainfall variation based on observed rain data set (%)
Jan 59.20 5.35 -90.96
Feb 55.96 17.51 -68.71
Mar 62.81 38.36 -38.93
Apr 38.81 89.28 130.07
May 58.17 202.13 247.48
Jun 147.95 281.61 90.34
74
Jul 337.79 250.08 -25.97
Aug 358.36 208.19 -41.91
Sep 125.92 142.98 13.55
Oct 28.52 94.26 230.54
Nov 14.86 47.98 222.94
Dec 30.60 10.95 -64.21
Diagrammatic representation of average rainfalls of observed and predicted rainfall data set
is given in Figure 5.5 and its percentage variability has been given in Figure 5.6.
Figure 5.5: Average rainfalls from observed and predicted rain data set
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Figure 5.6: Monthly rainfall variability based on observed rain data set
It is obtained from Figure 5.5 that the average rainfalls of observed rain data set are
higher than predicted rain data set in the months of January, February, March, July, August and
December. Likewise, average rainfalls of predicted rain data set are higher than observed rain
data set in the months of April, May, June, September, October and November. It has shown
clearly in Figure 5.6 that there is a condition of positive rainfall variability in the months of
April, May, June, September, October and November. Reversely, it has shown the negative
rainfall variability for the months of January, February, March, July, August and December.
Further analyzing the results obtained from Figure 5.6, it can be said that rainfall values of six
months are highly decreasing and rest six months are on highly increasing order. It has shown
that rainfall values of December, January and February are on highly decreasing and the rainfalls
of May, October and November are on highly increasing order based on the observed data set.
A scatter plot has been drawn between average observed rainfall and predicted rainfall
values. It is given in Figure 5.7, which shows that lower and medium rainfall values are highly
correlated in comparison to the higher values.
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Figure 5.7: Scatter plot between monthly averages of observed and predicted rainfalls
5.2.4 Trend Analysis of Rainfall
Mann-Kendall test has been applied to check the trend on the observed and
predicted rainfalls. The test statistics (Z-statistics) are -0.18 and 0.17 for observed and predicted
rainfalls respectively. Both the test statistics being within the range of it has shown
clearly that there is no trend in the observed and predicted rainfall data set at 5 % significance
level.
5.3 RAINFALL - RUNOFF ANALYSIS
5.3.1 Development of ANN model for Stream flow
The following sections describe the development of ANN model for simulating the discharge
at Kasol using the monthly data of rainfall, temperature and discharge given in the Chapter 3.
Availability of Data
The discharge at Kasol is natural flow from different small tributaries and snow melt
runoff from the hilly region of the catchment. The monthly rainfall data at Kasol is available
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from 1977 to 2004. But the temperature and discharge data are available only from 1987 to
2000.
Input vector to ANN model
In any basin, the monthly discharge at t has relationship with monthly rainfall, average
temperature at t and not with lagged monthly time series of rainfall and average temperature.
So the input vector to ANN model consists of monthly rainfall and average monthly
temperature at t only and output vector is observed average monthly discharge at Kasol. The
ANN model is represented as
Q(t)= f( r(t), T(t) ) (5.2)
In which Q, r and T are average monthly discharge (cumecs), monthly rainfall (mm) and
average monthly temperature (0C) at Kasol respectively. The input vector to ANN model
consists of data available from 1987 to 2000.
5.3.2 Training of ANN Model
The ANN models are trained using back propagation algorithm. The whole data set are
divided into three sets for the calibration, validation and testing purpose of the ANN model.
The data from 1994 to 2000 are considered for the training of the model since it contains the
extreme values of discharge. The data from 1987 to 1990 are considered for the validation of the
model. The data from 1991 to1993 are considered for the testing of the model. The software
used for the training of the ANN model for discharge is MATLAB. The performance of the
ANN models during calibration, validation and testing are evaluated with the performance
indices mentioned earlier. The number of the neurons in the hidden layer is found by a trial and
error procedure as mentioned in the literature since there is well tested procedure for fixing the
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hidden neurons. Two ANN models are developed, one with only monthly rainfall and the other
with rainfall and temperature as input vector. The correlation coefficient between rainfall and
discharge for calibration, validation and testing set data are 0.83, 0.74 and 0.69 respectively.
The correlation coefficient between temperature and discharge for calibration, validation and
testing set data are 0.83, 0.86 and 0.81 respectively. It clearly indicates that temperature has
greater influence on discharge at Kasol.
Table 5.3: Correlation coefficient(R) in different relationships
Relationships R for Calibration R for Validation R for Testing
Rainfall - discharge 0.83 0.74 0.69
Temperature-discharge 0.83 0.86 0.81
Initially the ANN model is trained with one hidden neuron and the performance of the
model is evaluated by performance indices for calibration, validation and testing data set. The
training of the ANN model is continued with the increase in the number of hidden neurons and
their performances are evaluated. The ANN model with high coefficient of correlation and
model efficiency, low RMSE is selected as the best model for simulating the discharge at Kasol.
The results of ANN model with only monthly rainfall as input is given in Table 5.4.
The results from the Table 5.4 clearly indicate that the performance of the ANN model during
calibration is better than during validation and testing. The increase in hidden neurons does not
yield significant improvement over the performance of the model. The performance indices
remain constant throughout the training process except slight change in RMSE.
The model ANNDIS12 is performed better over other ANN models during calibration
(CORR=0.87, RMSE=187.049, EFF=75.0 %); validation (CORR=0.73, RMSE=270.53,
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EFF=52.0 %) and testing (CORR=0.76, RMSE=248.69, EFF=56.0 %) and the optimum structure
of the ANN model is found to be 2 neurons in the hidden layer.
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Table 5.4: Results of ANN model considering only monthly rainfall as input
Table 5.5: Results of ANN model considering monthly rainfall and monthly average temperature as input
Calibration Validation Testing Model No Epochs ANN Structure CORR RMSE EFF% CORR RMSE EFF% CORR RMSE EFF%
ANNDIS11 42 1-1-1 0.87 186.75 75.0 0.74 269.67 52.0 0.75 249.08 55.0
ANNDIS12 35 1-2-1 0.87 187.04 75.0 0.73 270.53 52.0 0.76 248.69 56.0
ANNDIS13 245 1-3-1 0.87 187.22 75.0 0.73 270.68 52.0 0.76 248.83 56.0
ANNDIS14 230 1-4-1 0.87 187.32 75.0 0.73 270.72 52.0 0.76 248.84 56.0
ANNDIS15 288 1-5-1 0.87 187.32 75.0 0.73 270.72 52.0 0.76 248.83 55.0
ANNDIS16 788 1-6-1 0.87 187.45 75.0 0.73 270.75 52.0 0.76 248.82 55.0
ANNDIS17 661 1-7-1 0.87 187.48 75.0 0.73 270.76 52.0 0.76 248.81 55.0
Calibration Validation Testing Model No Epochs ANN Structure CORR RMSE EFF% CORR RMSE EFF% CORR RMSE EFF%
ANNDIS21 19 2-1-1 0.96 109.27 91.0 0.96 131.67 89.0 0.92 151.21 84.0
ANNDIS22 151 2-2-1 0.96 109.75 91.0 0.96 132.91 89.0 0.92 151.96 84.0
ANNDIS23 505 2-3-1 0.96 110.55 91.0 0.96 133.35 88.0 0.92 152.78 83.0
ANNDIS24 134 2-4-1 0.96 108.73 92.0 0.96 133.06 89.0 0.92 151.63 83.0
ANNDIS25 205 2-5-1 0.96 108.72 92.0 0.96 133.10 89.0 0.92 151.59 83.0
ANNDIS26 292 2-6-1 0.96 108.69 92.0 0.96 133.21 88.0 0.92 151.51 83.0 ANNDIS27 425 2-7-1 0.96 108.71 92.0 0.96 133.13 88.0 0.92 151.55 83.0
81
A Multiple Linear Regression (MLR) model is developed for the prediction of discharge
using the monthly rainfall as input vector considered in the development of ANN model. The
equation of MLR model is represented by
DISt = 2.25Rt+164.33 (5.3)
Where DIS is the monthly average discharge at t and R is the monthly rainfall at t.
The results of ANN model with monthly rainfall and monthly average temperature as
input is given in Table 5.5. Here also the performance of the ANN models remains constant with
the increase in the number of hidden neurons except slight change in RMSE. It is observed that
the performances of ANN models are drastically improved by including the monthly temperature
as input and it is evidenced from the Table 5.5.
The model ANNDIS26 is performed better over other ANN models during calibration
(CORR=0.96, RMSE=108.69, EFF=92 %); validation (CORR=0.96, RMSE=133.21, EFF=88.0
%) and testing (CORR=0.92, RMSE=151.51, EFF=83 %) and the optimum structure of the ANN
model is found to be 6 neurons in the hidden layer.
Another Multiple Linear Regression (MLR) model is developed for the prediction of
discharge using monthly rainfall and monthly average temperature as input vector considered in
the development of ANN model. The equation of MLR model is represented by
DISt = 1.42Rt+25.55Tt-66.61 (5.4)
Where DIS is the monthly average discharge at t , T is average monthly temperature at t and R is
the monthly rainfall at t.
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5.3.3 Analysis of Results of ANN and MLR Models
The performances of best ANN model with only monthly rainfall as input for the
prediction of discharge during calibration, validation and testing are presented in Figures 5.8,
5.9 and 5.10 respectively along with the corresponding observed discharge. The scatter plots
clearly demonstrate that the ANN model is capable of predicting low discharge values better
than medium and high discharge values. The performance of the MLR model during
calibration, validation and testing is given in Table 5.6. The performances of MLR model for
the prediction of discharge during calibration, validation and testing are presented in Figures
5.11, 5.12 and 5.13 respectively along with the corresponding observed discharge. The
scatter plots and performance indices indicate that performance of ANN models is better than
MLR during calibration, validation and testing.
Table 5.6: Results of MLR model considering only monthly rainfall as input
Calibration Validation Testing CORR RMSE EFF% CORR RMSE EFF% CORR RMSE EFF%
0.84 204.35 70.0 0.74 266.60 54.0 0.69 273.53 46.0
The comparison of results of the calibration, validation and testing of the best ANN and MLR model in
terms of various statistical indices are presented in the Table 5.7.
Table 5.7: Comparison of results between best ANN and MLR models with only rainfall as input
ANN model MLR model
Calibration Validation Testing Calibration Validation Testing
Coefficient of
Correlation
0.87 0.73 0.76 0.84 0.74 0.69
Model efficiency
(%)
75.0 52.0 56.0 70.0 54.0 46.0
83
RMSE 187.049 270.53 248.69 204.35 266.60 273.53
Figure 5.8: Scatter plot for the result of best ANN model with only
monthly rainfall as input during calibration
84
Figure 5.9: Scatter plot for the result of best ANN model with only monthly rainfall as input during validation
Figure 5.10: Scatter plot for the result of best ANN model with only
monthly rainfall as input during testing
The coefficient of correlation of MLR model during testing is much lower than ANN model.
The RMSE values of MLR model, which is residual variance, during calibration and testing,
are higher than the values of ANN model. The same trend is not observed during the
validation of the models. The model efficiency of MLR is much deteriorated during the
testing. But overall performance of ANN model is better than MLR Model.
85
Figure 5.11: Scatter plot for MLR model with only
monthly rainfall as input during calibration
Figure 5.12: Scatter plot for the MLR model with only
86
monthly rainfall as input during validation
Figure 5.13: Scatter plot for the MLR model with only
monthly rainfall as input during testing
The performances of best ANN model with monthly rainfall and average temperature as
input for the prediction of discharge during calibration, validation and testing are presented in
Figures 5.14, 5.15 and 5.16 respectively along with the corresponding observed discharge.
The scatter plots clearly demonstrate that the ANN model is capable of predicting low and
medium discharge better than high discharge values. The inclusion of monthly average
temperature in the input improved the performance of ANN model drastically and it is
evidenced from the Figures 5.14, 5.15 and 5.16 and Table 5.5. The RMSE during calibration,
validation and testing has decreased to almost half of the ANN models with only monthly
rainfall as input. The high discharge values are much deviated from the observed discharge
values during the testing of ANN model. The percentage increase in coefficient of
correlation during calibration, validation and testing are 10.34, 31.54 and 17.39 respectively.
87
The percentage increase in model efficiency during calibration, validation and testing are
22.67, 69.23 and 48.21 respectively. The percentage decrease in RMSE during calibration,
validation and testing are 41.89, 50.76 and 39.08 respectively. The performance of the MLR
model during calibration, validation and testing is given in Table 5.8. The performances of
MLR model for the prediction of discharge during calibration, validation and testing are
presented in Figures 5.17, 5.18 and 5.19 respectively along with the corresponding observed
discharge. The performance of MLR model is also drastically increased by including the
monthly average temperature input. But, the scatter plots and performance indices indicate
that performance of ANN models is better than MLR during calibration, validation and
testing.
Table 5.8: Results of MLR model considering monthly rainfall and average temperature as input
Calibration Validation Testing
CORR RMSE EFF% CORR RMSE EFF% CORR RMSE EFF%
0.93 136.64 87.0 0.91 163.32 83.0 0.87 187.12 75.0
The comparison of results of the calibration, validation and testing of the best ANN and
MLR model in terms of various statistical indices are presented in the Table 5.9.
Table 5.9: Comparison of results between best ANN and MLR models
with monthly rainfall and average temperature as input
ANN model MLR model
Calibration Validation Testing Calibration Validation Testing
Coefficient of
Correlation
0.96 0.96 0.92 0.93 0.93 0.87
Model efficiency
92.0 88.0 83.0 87.0 83.0 75.0
88
(%)
RMSE 108.69 133.21 151.51 136.64 163.32 187.12
Figure 5.14: Scatter plot for the result of best ANN model with
monthly rainfall and average monthly temperature as input during calibration
89
Figure 5.15: Scatter plot for the result of best ANN model with
monthly rainfall and average monthly temperature as input during validation
Figure 5.16: Scatter plot for the result of best ANN model with
monthly rainfall and average monthly temperature as input during testing
The coefficient of correlation of MLR model during calibration, validation and testing is
lower than ANN model. The RMSE values of MLR model, which is residual variance,
during calibration, validation and testing, are higher than the values of ANN model. The
model efficiency of MLR is much deteriorated during the testing. Hence it can be said that
overall performance of ANN model is better than MLR Model.
90
Figure 5.17: Scatter plot for MLR model with monthly rainfall and
average monthly temperature as input during calibration
Figure 5.18: Scatter plot for MLR model with monthly rainfall and
average monthly temperature as input during validation
91
Figure 5.19: Scatter plot for MLR model with monthly rainfall and
average monthly temperature as input during testing
5.3.4 Simulation of discharge for future period
The monthly rainfall and average temperature for the future period from 2000 to 2100 are
computed by taking future different meteorological parameters such as relative humidity,
wind speed, temperature, mean sea level pressure obtained from GCM model. The best
ANN model, selected based on the performance indices, is used to simulate the discharge
from 2001 to 2100 using future monthly rainfall and average temperature. The Figure 5.20
represents the simulated discharge for the future period and these values are given in
Appendix II. It is observed from the Figure for the first 30 years, i.e., from 2001 to 2030, the
maximum discharges are above 1000 cumecs in many years. The same trend is not observed
during the remaining period of the simulation.
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Figure 5.20: Predicted discharges for future period from 2001 to 2100
5.3.5 Trend Analysis of Discharge and Temperature
To find out the trend in the observed and predicted discharge and temperature, Mann
Kendall test has been performed. The test statistics (z statistics) for observed and predicted
discharges are 0.62 and 0.00 respectively. Likewise, the test statistics (z statistics) for observed
and predicted temperatures are 0.99 and 0.48 respectively. All the test statistics being within the
range of it has shown clearly that there is no trend in the observed and predicted
discharge as well as the observed and predicted temperature data set at 5 % significance level.
93
Table 5.10: Z-statistics obtained by using Mann Kendall’s Test Z-statistics (test statistics) Result at 5 % significance level Value
Observed Predicted Observed Predicted
Rainfall -0.18 0.17 no trend no trend
Discharge 0.62 0.00 no trend no trend
Temperature 0.99 0.48 no trend no trend
CHAPTER 6
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CONCLUSIONS AND SCOPE FOR FURTHER WORK
6.1 CONCLUSIONS
The main objectives of the study are to perform statistical downscaling, to generate future
climate change scenarios and to get relationships between the hydro-climatic parameters of the
study area. The climatic parameters such as relative humidity, wind speed (u wind, v wind),
temperature and mean sea level pressure which are reanalysis data set introduced by NCEP/ NCAR from
1948 to 2004 are used to develop the relationship with observed monthly rainfall at Kasol. The
relationship is developed by regression analysis. The developed relationship is used to predict the
monthly rainfall using the climatic parameters obtained from GCM outputs. The CCSR-NIES GCM of
Japan has been used in present study. Statistical downscaling has been carried out for the rainfall at
Kasol in Bhakra region of Satluj river basin within the area of 30045’ to 33015’ North latitudes
and 76010’ to 79010’ East longitudes.
The observed monthly rainfall and average temperature are used to develop ANN and MLR
models for predicting the discharge at Kasol. The future discharge from 2001 to 2100 is predicted using
the monthly rainfall and average temperate obtained from GCM model for the location of Kasol. Trend
analyses have been carried out to find trend in the observed and predicted rainfall, discharge and
temperature.
Based on this study, the following conclusions are made. The conclusions from 1 to 6 are
concerned with the rainfall analysis. The conclusions from 7 to 13 are concerned with rainfall-discharge
relationship.
95
1. A relationship between NCEP and observed data sets has been established by the
regression coefficients. The regression coefficients are obtained with the relationship
between PCA of NCEP and observed rainfalls of Kasol and they are given in Table 5.1.
2. Future rainfall from 2001 to 2100 has been obtained by the relationship between PCA of
GCM output and regression coefficients using the equation, Raint = d0 + .
The predicted rainfalls for the 100 years are given in Appendix I and its diagrammatic
representation has been given in Figure 5.1.
3. It is observed from the future rainfall that the maximum amount of rainfalls are above
325 mm in many years for the first 30 years and the same trend is not observed during the
remaining period of the prediction.
4. Diagrammatic representations of three predicted years have been drawn in Figures 5.2,
5.3 and 5.4. Based on the monthly prediction, it can be said that there will be no rainfall
in the months of December and January. The amount of rainfall will be very high in June,
July and August in compared to the remaining months. Thus, it can be finalized that
future rainfalls will highly decrease for winter season, partially decreases for pre
monsoon and post monsoon and increases for monsoon season in an annual basis.
5. Rainfall variability has been obtained by taking averages of observed and predicted
monthly rainfalls. Its result has been given in Table 5.2 and Figure 5.6. Analyzing the
results obtained from Figure 5.6 that rainfall values of six months are highly decreasing
and the remaining six months are highly increasing. It has shown that rainfall values of
December, January and February are on highly decreasing and the rainfalls of May,
October and November are on highly increasing order based on the observed data set.
96
6. Mann-Kendall test has been performed to know the trend in the observed and predicted
rainfalls. There is no trend in both data sets at 5 % significance level.
7. The comparison of the results of the ANN models with MLR for rainfall-discharge show
the potential of ANN model in modeling the process with only monthly rainfall as input.
8. ANN model is capable of predicting low discharge values better than medium and high
discharge values in case of monthly rainfall as input.
9. The inclusion of monthly average temperature as one of the inputs improves the
performance of ANN drastically.
10. The ANN model with monthly rainfall and average temperature is capable of predicting
low and medium discharge values than the high discharge values.
11. The predicted discharges for first 30 years from 2001 to 2030 are observed above 1000 cumecs at
many months. The predicted values are given in Appendix II and its diagrammatic representation
has been given in Figure 5.20.
12. The Z-statistics of Mann Kendall test has shown that there is no trend in the predicted
discharge from 2001 to 2100. Likewise, there is no trend found out at 5 % significance level in
the observed discharge, temperature and predicted temperature used in the study.
13. Summarizing all, it can be said that prediction of future rainfall and runoff is one of the
challenging tasks. Many climatic, hydrologic as well as physical parameters are involved
to establish rainfall- runoff relationship in a basin. Furthermore, the results obtained from
this study may be crucial in water resources planning and management of Satluj River
especially nearby the Bhakra region.
97
6.2 SCOPE FOR FURTHER WORK
1. Such type of study can be carried out by using additional climatic parameters like
evaporation, evapotranspiration, water temperature as predictors including MSLP,
relative humidity, air temperature and wind speed.
2. Data from other scenarios can also be applied to study the climate change in the Satluj
river basin.
3. Downscaling can be performed by other techniques like Relevance Vector Machine,
Support Vector Machine etc.
4. A better rainfall-runoff relationship will obtain by using daily rainfall-runoff data.
5. More observed rainfall, discharge and temperature data are needed to get better result in
pursuing such a climate change study.
6. Outcomes of this study has signified that due to probable decreasing rainfall in winter,
water conservation practices to be carried out in monsoon season for future use especially
nearby the Bhakra region.
7. Results obtained from this study can be used for proper planning and management of the
water-related projects especially nearby the Bhakra region in Satluj river basin.
8. The predicted rainfalls obtained from this study can be compared with the predicted
rainfalls from IITM.
9. Such type of study can be carried out with different scenarios for Nepal river basins too.
98
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109
Appendix I
Predicted rainfall from 2001 to 2100
Date Rainfall
(mm)
Date Rainfall
(mm)
Date Rainfall
(mm)
Date Rainfall
(mm)
Date Rainfall
(mm)
Jan-01 0.00 Jan-21 0.00 Jan-41 12.08 Jan-61 20.74 Jan-81 23.08
Feb-01 0.00 Feb-21 0.00 Feb-41 15.98 Feb-61 19.89 Feb-81 97.17
Mar-01 0.00 Mar-21 0.00 Mar-41 63.53 Mar-61 44.04 Mar-81 86.50
Apr-01 54.95 Apr-21 0.00 Apr-41 169.76 Apr-61 81.26 Apr-81 69.50
May-01 98.59 May-21 227.58 May-41 180.67 May-61 266.57 May-81 213.90
Jun-01 356.71 Jun-21 360.06 Jun-41 286.64 Jun-61 253.83 Jun-81 296.38
Jul-01 370.24 Jul-21 330.20 Jul-41 215.21 Jul-61 204.92 Jul-81 229.38
Aug-01 256.33 Aug-21 304.10 Aug-41 170.84 Aug-61 200.02 Aug-81 210.03
Sep-01 175.51 Sep-21 140.14 Sep-41 147.38 Sep-61 121.26 Sep-81 138.61
Oct-01 146.52 Oct-21 43.54 Oct-41 86.07 Oct-61 96.62 Oct-81 83.33
Nov-01 84.66 Nov-21 36.98 Nov-41 26.89 Nov-61 40.83 Nov-81 57.79
Dec-01 0.00 Dec-21 23.84 Dec-41 11.30 Dec-61 23.60 Dec-81 0.00
Jan-02 0.00 Jan-22 0.00 Jan-42 1.58 Jan-62 4.69 Jan-82 27.34
Feb-02 0.00 Feb-22 0.00 Feb-42 4.04 Feb-62 0.00 Feb-82 84.19
Mar-02 0.00 Mar-22 0.00 Mar-42 60.09 Mar-62 48.17 Mar-82 56.75
Apr-02 98.09 Apr-22 21.59 Apr-42 179.44 Apr-62 99.59 Apr-82 49.11
May-02 201.60 May-22 179.00 May-42 203.65 May-62 198.71 May-82 239.93
Jun-02 331.72 Jun-22 435.43 Jun-42 299.95 Jun-62 166.19 Jun-82 253.98
Jul-02 344.82 Jul-22 388.04 Jul-42 216.48 Jul-62 198.83 Jul-82 161.80
Aug-02 249.77 Aug-22 223.04 Aug-42 200.05 Aug-62 204.25 Aug-82 197.54
Sep-02 177.09 Sep-22 196.25 Sep-42 133.84 Sep-62 112.49 Sep-82 145.48
Oct-02 115.88 Oct-22 34.15 Oct-42 99.22 Oct-62 153.35 Oct-82 141.61
110
Nov-02 82.07 Nov-22 17.95 Nov-42 52.64 Nov-62 28.97 Nov-82 48.07
Dec-02 0.00 Dec-22 16.25 Dec-42 0.00 Dec-62 40.93 Dec-82 45.29
Jan-03 0.00 Jan-23 0.00 Jan-43 0.00 Jan-63 18.65 Jan-83 0.00
Feb-03 0.00 Feb-23 0.00 Feb-43 23.33 Feb-63 32.36 Feb-83 13.08
Mar-03 0.00 Mar-23 8.64 Mar-43 24.63 Mar-63 31.16 Mar-83 85.53
Apr-03 41.72 Apr-23 47.02 Apr-43 125.92 Apr-63 71.77 Apr-83 89.00
May-03 139.52 May-23 199.84 May-43 224.30 May-63 184.24 May-83 224.53
Jun-03 330.93 Jun-23 355.31 Jun-43 251.72 Jun-63 234.28 Jun-83 266.58
Jul-03 322.50 Jul-23 344.46 Jul-43 260.13 Jul-63 232.63 Jul-83 201.31
Aug-03 242.37 Aug-23 305.75 Aug-43 142.25 Aug-63 158.12 Aug-83 182.01
Sep-03 234.40 Sep-23 139.78 Sep-43 125.19 Sep-63 131.82 Sep-83 145.71
Oct-03 148.32 Oct-23 90.40 Oct-43 102.64 Oct-63 148.19 Oct-83 117.09
Nov-03 48.22 Nov-23 35.26 Nov-43 35.56 Nov-63 70.64 Nov-83 50.86
Dec-03 5.91 Dec-23 9.83 Dec-43 0.12 Dec-63 0.00 Dec-83 36.14
Jan-04 0.00 Jan-24 0.00 Jan-44 0.00 Jan-64 20.77 Jan-84 21.37
Feb-04 0.00 Feb-24 0.00 Feb-44 41.98 Feb-64 74.55 Feb-84 47.87
Mar-04 0.00 Mar-24 0.00 Mar-44 37.32 Mar-64 15.35 Mar-84 50.68
Apr-04 63.82 Apr-24 42.78 Apr-44 129.79 Apr-64 177.39 Apr-84 102.50
May-04 227.02 May-24 229.95 May-44 224.75 May-64 132.33 May-84 230.60
Jun-04 431.56 Jun-24 345.84 Jun-44 298.55 Jun-64 213.95 Jun-84 216.60
Jul-04 313.78 Jul-24 291.25 Jul-44 189.25 Jul-64 201.56 Jul-84 172.32
Aug-04 237.38 Aug-24 201.57 Aug-44 187.01 Aug-64 187.39 Aug-84 200.69
Sep-04 185.77 Sep-24 112.40 Sep-44 113.62 Sep-64 128.19 Sep-84 144.17
Oct-04 107.31 Oct-24 81.61 Oct-44 128.78 Oct-64 73.46 Oct-84 124.92
Nov-04 0.00 Nov-24 30.69 Nov-44 114.53 Nov-64 55.78 Nov-84 93.51
Dec-04 0.00 Dec-24 0.00 Dec-44 1.44 Dec-64 64.94 Dec-84 1.94
111
Jan-05 0.00 Jan-25 0.00 Jan-45 0.00 Jan-65 0.00 Jan-85 43.31
Feb-05 0.00 Feb-25 0.00 Feb-45 0.00 Feb-65 11.21 Feb-85 15.40
Mar-05 7.77 Mar-25 0.00 Mar-45 83.56 Mar-65 162.88 Mar-85 18.04
Apr-05 81.04 Apr-25 0.00 Apr-45 140.77 Apr-65 64.07 Apr-85 145.78
May-05 270.84 May-25 138.86 May-45 186.62 May-65 153.45 May-85 190.69
Jun-05 400.82 Jun-25 385.23 Jun-45 265.32 Jun-65 219.74 Jun-85 186.92
Jul-05 350.27 Jul-25 322.15 Jul-45 198.46 Jul-65 234.06 Jul-85 210.77
Aug-05 245.14 Aug-25 285.58 Aug-45 150.21 Aug-65 178.69 Aug-85 171.01
Sep-05 137.62 Sep-25 127.20 Sep-45 171.36 Sep-65 139.05 Sep-85 113.92
Oct-05 59.61 Oct-25 114.53 Oct-45 69.56 Oct-65 92.84 Oct-85 121.34
Nov-05 0.00 Nov-25 40.31 Nov-45 68.52 Nov-65 30.18 Nov-85 106.88
Dec-05 0.00 Dec-25 10.33 Dec-45 0.00 Dec-65 15.49 Dec-85 0.00
Jan-06 0.00 Jan-26 0.00 Jan-46 0.00 Jan-66 11.15 Jan-86 0.00
Feb-06 0.00 Feb-26 19.93 Feb-46 1.99 Feb-66 22.94 Feb-86 0.00
Mar-06 7.92 Mar-26 25.81 Mar-46 41.64 Mar-66 81.29 Mar-86 15.06
Apr-06 17.33 Apr-26 40.71 Apr-46 151.17 Apr-66 86.30 Apr-86 115.76
May-06 233.30 May-26 170.43 May-46 238.36 May-66 157.16 May-86 217.85
Jun-06 384.22 Jun-26 383.48 Jun-46 269.66 Jun-66 189.84 Jun-86 280.49
Jul-06 354.98 Jul-26 307.50 Jul-46 252.65 Jul-66 210.22 Jul-86 229.31
Aug-06 267.69 Aug-26 266.08 Aug-46 146.10 Aug-66 230.18 Aug-86 172.87
Sep-06 131.31 Sep-26 163.81 Sep-46 138.94 Sep-66 152.06 Sep-86 114.19
Oct-06 146.76 Oct-26 150.24 Oct-46 135.40 Oct-66 90.50 Oct-86 104.98
Nov-06 72.72 Nov-26 28.24 Nov-46 18.04 Nov-66 87.12 Nov-86 57.71
Dec-06 26.30 Dec-26 19.20 Dec-46 0.00 Dec-66 33.74 Dec-86 40.49
Jan-07 17.55 Jan-27 0.00 Jan-47 0.00 Jan-67 12.44 Jan-87 0.00
Feb-07 0.00 Feb-27 0.00 Feb-47 21.35 Feb-67 42.47 Feb-87 0.00
112
Mar-07 25.02 Mar-27 14.41 Mar-47 28.82 Mar-67 61.04 Mar-87 18.13
Apr-07 13.36 Apr-27 33.74 Apr-47 42.25 Apr-67 100.66 Apr-87 140.34
May-07 197.08 May-27 149.08 May-47 202.98 May-67 177.23 May-87 194.15
Jun-07 369.01 Jun-27 292.33 Jun-47 249.95 Jun-67 276.64 Jun-87 256.60
Jul-07 319.73 Jul-27 314.60 Jul-47 214.60 Jul-67 190.58 Jul-87 205.30
Aug-07 200.50 Aug-27 273.62 Aug-47 204.83 Aug-67 177.43 Aug-87 192.72
Sep-07 157.05 Sep-27 104.57 Sep-47 139.86 Sep-67 141.80 Sep-87 148.28
Oct-07 21.13 Oct-27 33.65 Oct-47 71.98 Oct-67 101.48 Oct-87 118.67
Nov-07 0.00 Nov-27 0.00 Nov-47 84.78 Nov-67 49.36 Nov-87 11.30
Dec-07 0.00 Dec-27 0.00 Dec-47 0.00 Dec-67 1.03 Dec-87 0.00
Jan-08 0.00 Jan-28 0.00 Jan-48 0.00 Jan-68 0.00 Jan-88 0.00
Feb-08 0.00 Feb-28 0.00 Feb-48 21.96 Feb-68 11.15 Feb-88 14.27
Mar-08 23.36 Mar-28 0.00 Mar-48 37.88 Mar-68 38.63 Mar-88 78.51
Apr-08 59.87 Apr-28 68.91 Apr-48 119.38 Apr-68 87.91 Apr-88 87.94
May-08 190.66 May-28 171.32 May-48 160.25 May-68 210.50 May-88 210.37
Jun-08 368.22 Jun-28 394.55 Jun-48 215.32 Jun-68 262.39 Jun-88 256.81
Jul-08 347.12 Jul-28 267.46 Jul-48 205.03 Jul-68 228.07 Jul-88 283.96
Aug-08 288.17 Aug-28 287.40 Aug-48 164.54 Aug-68 210.12 Aug-88 209.28
Sep-08 193.84 Sep-28 177.76 Sep-48 145.88 Sep-68 127.18 Sep-88 134.16
Oct-08 26.42 Oct-28 48.98 Oct-48 147.96 Oct-68 64.60 Oct-88 70.40
Nov-08 20.76 Nov-28 43.51 Nov-48 45.03 Nov-68 55.09 Nov-88 52.29
Dec-08 0.00 Dec-28 0.00 Dec-48 10.22 Dec-68 0.00 Dec-88 0.00
Jan-09 0.00 Jan-29 0.00 Jan-49 0.00 Jan-69 2.81 Jan-89 0.00
Feb-09 0.00 Feb-29 0.00 Feb-49 4.55 Feb-69 0.00 Feb-89 12.01
Mar-09 0.00 Mar-29 0.00 Mar-49 27.03 Mar-69 69.29 Mar-89 26.15
Apr-09 61.64 Apr-29 41.22 Apr-49 182.37 Apr-69 131.78 Apr-89 118.61
113
May-09 219.50 May-29 207.52 May-49 232.90 May-69 190.79 May-89 225.94
Jun-09 371.63 Jun-29 357.98 Jun-49 282.66 Jun-69 218.05 Jun-89 257.06
Jul-09 368.42 Jul-29 266.85 Jul-49 214.32 Jul-69 196.19 Jul-89 177.64
Aug-09 248.71 Aug-29 351.99 Aug-49 193.09 Aug-69 204.55 Aug-89 163.79
Sep-09 139.41 Sep-29 146.26 Sep-49 131.10 Sep-69 111.21 Sep-89 152.93
Oct-09 55.82 Oct-29 56.26 Oct-49 92.09 Oct-69 94.63 Oct-89 99.68
Nov-09 13.78 Nov-29 2.20 Nov-49 81.98 Nov-69 63.90 Nov-89 42.11
Dec-09 0.00 Dec-29 0.00 Dec-49 29.44 Dec-69 5.98 Dec-89 37.39
Jan-10 0.00 Jan-30 0.00 Jan-50 1.50 Jan-70 0.00 Jan-90 0.00
Feb-10 0.00 Feb-30 0.00 Feb-50 29.67 Feb-70 57.77 Feb-90 80.10
Mar-10 0.00 Mar-30 12.58 Mar-50 0.00 Mar-70 69.97 Mar-90 91.74
Apr-10 22.92 Apr-30 70.12 Apr-50 138.62 Apr-70 78.96 Apr-90 62.56
May-10 231.89 May-30 202.53 May-50 187.92 May-70 207.48 May-90 163.84
Jun-10 372.26 Jun-30 364.92 Jun-50 282.84 Jun-70 224.03 Jun-90 257.67
Jul-10 384.00 Jul-30 293.25 Jul-50 188.99 Jul-70 208.89 Jul-90 196.31
Aug-10 251.06 Aug-30 314.42 Aug-50 188.10 Aug-70 182.29 Aug-90 154.64
Sep-10 215.82 Sep-30 179.44 Sep-50 127.48 Sep-70 128.10 Sep-90 130.95
Oct-10 24.26 Oct-30 119.26 Oct-50 81.19 Oct-70 92.85 Oct-90 110.29
Nov-10 35.74 Nov-30 48.18 Nov-50 34.65 Nov-70 52.15 Nov-90 59.44
Dec-10 0.00 Dec-30 0.00 Dec-50 0.00 Dec-70 0.00 Dec-90 38.16
Jan-11 0.00 Jan-31 0.00 Jan-51 0.00 Jan-71 5.47 Jan-91 14.56
Feb-11 0.00 Feb-31 0.00 Feb-51 0.00 Feb-71 2.32 Feb-91 55.08
Mar-11 0.00 Mar-31 69.87 Mar-51 42.31 Mar-71 78.97 Mar-91 110.76
Apr-11 71.58 Apr-31 86.61 Apr-51 66.44 Apr-71 93.81 Apr-91 126.97
May-11 243.69 May-31 113.05 May-51 239.70 May-71 206.90 May-91 160.34
Jun-11 333.54 Jun-31 186.51 Jun-51 269.24 Jun-71 239.39 Jun-91 221.37
114
Jul-11 343.44 Jul-31 222.18 Jul-51 252.03 Jul-71 157.34 Jul-91 215.33
Aug-11 299.25 Aug-31 209.99 Aug-51 188.17 Aug-71 175.45 Aug-91 177.97
Sep-11 211.06 Sep-31 124.88 Sep-51 126.24 Sep-71 187.42 Sep-91 128.80
Oct-11 59.96 Oct-31 133.69 Oct-51 113.95 Oct-71 102.31 Oct-91 118.80
Nov-11 0.00 Nov-31 1.18 Nov-51 48.54 Nov-71 49.73 Nov-91 36.93
Dec-11 49.60 Dec-31 0.00 Dec-51 0.00 Dec-71 0.00 Dec-91 10.31
Jan-12 0.00 Jan-32 0.00 Jan-52 4.95 Jan-72 0.00 Jan-92 0.00
Feb-12 0.00 Feb-32 0.00 Feb-52 25.37 Feb-72 72.25 Feb-92 35.61
Mar-12 40.22 Mar-32 26.35 Mar-52 0.00 Mar-72 39.80 Mar-92 73.59
Apr-12 45.45 Apr-32 107.00 Apr-52 105.03 Apr-72 79.05 Apr-92 78.58
May-12 195.59 May-32 232.95 May-52 194.09 May-72 200.39 May-92 238.75
Jun-12 366.31 Jun-32 267.10 Jun-52 203.08 Jun-72 305.27 Jun-92 262.45
Jul-12 386.04 Jul-32 263.68 Jul-52 215.02 Jul-72 195.18 Jul-92 217.12
Aug-12 222.33 Aug-32 193.21 Aug-52 183.17 Aug-72 187.01 Aug-92 170.93
Sep-12 117.96 Sep-32 138.46 Sep-52 126.88 Sep-72 115.83 Sep-92 147.74
Oct-12 101.22 Oct-32 87.70 Oct-52 91.36 Oct-72 100.27 Oct-92 95.55
Nov-12 76.80 Nov-32 62.90 Nov-52 8.56 Nov-72 28.37 Nov-92 81.51
Dec-12 27.37 Dec-32 2.01 Dec-52 18.74 Dec-72 27.15 Dec-92 47.51
Jan-13 0.00 Jan-33 0.00 Jan-53 28.66 Jan-73 36.07 Jan-93 11.13
Feb-13 0.00 Feb-33 0.00 Feb-53 32.70 Feb-73 1.39 Feb-93 0.68
Mar-13 0.00 Mar-33 51.38 Mar-53 69.99 Mar-73 0.00 Mar-93 54.66
Apr-13 23.68 Apr-33 88.86 Apr-53 46.58 Apr-73 132.67 Apr-93 133.48
May-13 298.54 May-33 217.54 May-53 169.25 May-73 186.66 May-93 253.85
Jun-13 383.90 Jun-33 282.96 Jun-53 237.54 Jun-73 256.50 Jun-93 246.43
Jul-13 293.35 Jul-33 286.97 Jul-53 212.21 Jul-73 224.10 Jul-93 198.01
Aug-13 238.38 Aug-33 162.51 Aug-53 188.55 Aug-73 186.05 Aug-93 161.18
115
Sep-13 152.48 Sep-33 111.16 Sep-53 150.12 Sep-73 133.99 Sep-93 170.26
Oct-13 47.58 Oct-33 90.55 Oct-53 99.17 Oct-73 95.34 Oct-93 68.58
Nov-13 70.51 Nov-33 55.18 Nov-53 37.13 Nov-73 74.24 Nov-93 79.37
Dec-13 0.00 Dec-33 0.00 Dec-53 0.00 Dec-73 0.00 Dec-93 0.00
Jan-14 0.00 Jan-34 0.00 Jan-54 20.85 Jan-74 0.00 Jan-94 7.79
Feb-14 0.00 Feb-34 0.00 Feb-54 65.86 Feb-74 15.22 Feb-94 0.00
Mar-14 3.39 Mar-34 2.23 Mar-54 93.47 Mar-74 45.70 Mar-94 91.76
Apr-14 50.35 Apr-34 125.27 Apr-54 37.75 Apr-74 102.28 Apr-94 91.15
May-14 250.08 May-34 157.40 May-54 219.06 May-74 203.54 May-94 254.86
Jun-14 405.63 Jun-34 233.27 Jun-54 244.01 Jun-74 217.50 Jun-94 314.74
Jul-14 324.04 Jul-34 255.74 Jul-54 176.99 Jul-74 227.46 Jul-94 190.55
Aug-14 268.31 Aug-34 177.79 Aug-54 203.82 Aug-74 221.83 Aug-94 163.68
Sep-14 140.84 Sep-34 148.06 Sep-54 125.35 Sep-74 137.34 Sep-94 110.41
Oct-14 72.73 Oct-34 85.88 Oct-54 125.87 Oct-74 99.49 Oct-94 62.61
Nov-14 91.28 Nov-34 37.06 Nov-54 25.65 Nov-74 42.46 Nov-94 53.95
Dec-14 0.00 Dec-34 0.00 Dec-54 0.00 Dec-74 0.00 Dec-94 19.99
Jan-15 0.00 Jan-35 0.00 Jan-55 0.00 Jan-75 0.00 Jan-95 0.00
Feb-15 0.00 Feb-35 0.00 Feb-55 52.09 Feb-75 20.01 Feb-95 0.00
Mar-15 4.67 Mar-35 28.16 Mar-55 50.63 Mar-75 42.47 Mar-95 45.16
Apr-15 62.28 Apr-35 104.53 Apr-55 153.85 Apr-75 73.68 Apr-95 83.66
May-15 204.58 May-35 235.03 May-55 179.89 May-75 181.70 May-95 217.39
Jun-15 340.36 Jun-35 243.03 Jun-55 187.91 Jun-75 296.25 Jun-95 200.74
Jul-15 329.77 Jul-35 225.49 Jul-55 239.22 Jul-75 232.82 Jul-95 217.19
Aug-15 299.58 Aug-35 230.97 Aug-55 206.48 Aug-75 193.64 Aug-95 181.51
Sep-15 174.77 Sep-35 109.72 Sep-55 120.20 Sep-75 155.81 Sep-95 123.16
Oct-15 79.81 Oct-35 133.28 Oct-55 110.69 Oct-75 55.71 Oct-95 90.79
116
Nov-15 0.00 Nov-35 78.24 Nov-55 63.46 Nov-75 68.69 Nov-95 40.77
Dec-15 0.00 Dec-35 0.00 Dec-55 0.00 Dec-75 23.19 Dec-95 14.48
Jan-16 0.00 Jan-36 0.00 Jan-56 42.32 Jan-76 0.00 Jan-96 26.20
Feb-16 0.00 Feb-36 23.93 Feb-56 25.33 Feb-76 45.51 Feb-96 20.65
Mar-16 0.00 Mar-36 75.31 Mar-56 74.49 Mar-76 0.00 Mar-96 81.12
Apr-16 12.32 Apr-36 99.07 Apr-56 166.69 Apr-76 112.66 Apr-96 184.48
May-16 227.96 May-36 191.75 May-56 166.84 May-76 226.80 May-96 208.80
Jun-16 261.67 Jun-36 213.33 Jun-56 247.73 Jun-76 202.79 Jun-96 241.69
Jul-16 271.35 Jul-36 223.30 Jul-56 260.17 Jul-76 210.98 Jul-96 233.38
Aug-16 288.32 Aug-36 204.16 Aug-56 166.76 Aug-76 193.48 Aug-96 184.79
Sep-16 139.34 Sep-36 113.75 Sep-56 130.24 Sep-76 117.10 Sep-96 122.33
Oct-16 39.73 Oct-36 116.54 Oct-56 98.93 Oct-76 52.37 Oct-96 75.71
Nov-16 40.96 Nov-36 58.85 Nov-56 35.33 Nov-76 36.34 Nov-96 24.81
Dec-16 0.00 Dec-36 20.15 Dec-56 0.00 Dec-76 22.09 Dec-96 0.00
Jan-17 0.00 Jan-37 0.00 Jan-57 0.00 Jan-77 0.00 Jan-97 0.00
Feb-17 0.00 Feb-37 71.37 Feb-57 30.20 Feb-77 95.66 Feb-97 24.75
Mar-17 0.00 Mar-37 87.97 Mar-57 8.04 Mar-77 113.83 Mar-97 87.68
Apr-17 62.61 Apr-37 32.92 Apr-57 109.48 Apr-77 133.88 Apr-97 69.92
May-17 102.47 May-37 153.79 May-57 269.94 May-77 195.34 May-97 228.84
Jun-17 359.17 Jun-37 234.12 Jun-57 236.00 Jun-77 253.49 Jun-97 224.83
Jul-17 307.40 Jul-37 225.20 Jul-57 227.20 Jul-77 262.03 Jul-97 191.92
Aug-17 211.71 Aug-37 178.70 Aug-57 180.14 Aug-77 185.25 Aug-97 167.89
Sep-17 178.15 Sep-37 166.25 Sep-57 122.60 Sep-77 143.11 Sep-97 124.96
Oct-17 71.27 Oct-37 109.04 Oct-57 119.05 Oct-77 108.10 Oct-97 118.84
Nov-17 39.16 Nov-37 39.22 Nov-57 37.15 Nov-77 61.65 Nov-97 48.04
Dec-17 0.00 Dec-37 0.00 Dec-57 0.74 Dec-77 0.00 Dec-97 27.68
117
Jan-18 0.00 Jan-38 7.83 Jan-58 0.00 Jan-78 14.84 Jan-98 8.38
Feb-18 0.00 Feb-38 17.40 Feb-58 0.00 Feb-78 29.09 Feb-98 0.00
Mar-18 0.53 Mar-38 61.09 Mar-58 1.32 Mar-78 72.57 Mar-98 0.36
Apr-18 75.28 Apr-38 118.24 Apr-58 50.08 Apr-78 126.54 Apr-98 146.77
May-18 226.63 May-38 221.85 May-58 187.47 May-78 225.49 May-98 221.32
Jun-18 362.11 Jun-38 326.87 Jun-58 229.81 Jun-78 286.78 Jun-98 250.09
Jul-18 272.28 Jul-38 204.18 Jul-58 207.23 Jul-78 248.87 Jul-98 196.02
Aug-18 264.80 Aug-38 202.34 Aug-58 184.40 Aug-78 191.29 Aug-98 217.80
Sep-18 161.06 Sep-38 119.54 Sep-58 104.58 Sep-78 122.14 Sep-98 147.67
Oct-18 70.33 Oct-38 111.52 Oct-58 96.59 Oct-78 107.35 Oct-98 117.41
Nov-18 42.72 Nov-38 60.49 Nov-58 90.76 Nov-78 71.97 Nov-98 19.27
Dec-18 23.78 Dec-38 0.00 Dec-58 9.15 Dec-78 10.89 Dec-98 20.35
Jan-19 0.00 Jan-39 0.00 Jan-59 0.00 Jan-79 0.00 Jan-99 51.72
Feb-19 0.00 Feb-39 1.14 Feb-59 20.29 Feb-79 55.24 Feb-99 16.03
Mar-19 0.00 Mar-39 45.31 Mar-59 44.44 Mar-79 62.78 Mar-99 79.54
Apr-19 21.00 Apr-39 77.50 Apr-59 124.88 Apr-79 172.45 Apr-99 125.58
May-19 281.43 May-39 234.64 May-59 171.76 May-79 157.99 May-99 173.02
Jun-19 384.09 Jun-39 206.13 Jun-59 326.77 Jun-79 309.31 Jun-99 192.99
Jul-19 304.66 Jul-39 249.69 Jul-59 242.28 Jul-79 210.82 Jul-99 246.91
Aug-19 245.03 Aug-39 154.28 Aug-59 219.80 Aug-79 140.44 Aug-99 165.07
Sep-19 139.43 Sep-39 171.91 Sep-59 149.86 Sep-79 127.86 Sep-99 160.51
Oct-19 55.88 Oct-39 91.82 Oct-59 108.82 Oct-79 131.90 Oct-99 93.06
Nov-19 12.14 Nov-39 59.02 Nov-59 41.78 Nov-79 105.21 Nov-99 31.32
Dec-19 13.19 Dec-39 0.00 Dec-59 46.41 Dec-79 16.83 Dec-99 59.46
Jan-20 6.97 Jan-40 8.25 Jan-60 0.00 Jan-80 0.00 Jan-00 0.00
Feb-20 25.10 Feb-40 0.00 Feb-60 0.00 Feb-80 49.28 Feb-00 0.00
118
Mar-20 0.00 Mar-40 0.00 Mar-60 85.98 Mar-80 23.59 Mar-00 85.30
Apr-20 64.04 Apr-40 107.31 Apr-60 90.33 Apr-80 125.96 Apr-00 126.65
May-20 215.45 May-40 197.92 May-60 185.57 May-80 179.07 May-00 187.64
Jun-20 294.80 Jun-40 231.20 Jun-60 228.65 Jun-80 208.38 Jun-00 220.17
Jul-20 297.26 Jul-40 182.56 Jul-60 286.69 Jul-80 230.57 Jul-00 182.51
Aug-20 212.39 Aug-40 190.46 Aug-60 217.75 Aug-80 168.15 Aug-00 156.44
Sep-20 185.13 Sep-40 122.20 Sep-60 159.24 Sep-80 141.57 Sep-00 167.33
Oct-20 44.22 Oct-40 64.46 Oct-60 161.39 Oct-80 107.19 Oct-00 91.57
Nov-20 15.54 Nov-40 80.43 Nov-60 19.61 Nov-80 68.19 Nov-00 127.61
Dec-20 0.00 Dec-40 0.00 Dec-60 34.72 Dec-80 0.00 Dec-00 0.00
119
Appendix II
Predicted discharge from 2001 to 2100
Date Discharge
(cumec)
Date Discharge
(cumec)
Date Discharge
(cumec)
Date Discharge
(cumec)
Date Discharge
(cumec)
Jan-01 140.82 Jan-21 141.11 Jan-41 130.95 Jan-61 125.47 Jan-81 124.60
Feb-01 141.01 Feb-21 138.36 Feb-41 127.81 Feb-61 126.23 Feb-81 131.53
Mar-01 136.13 Mar-21 134.19 Mar-41 122.94 Mar-61 119.60 Mar-81 139.01
Apr-01 125.25 Apr-21 138.18 Apr-41 305.26 Apr-61 223.96 Apr-81 174.01
May-01 219.93 May-21 571.75 May-41 461.35 May-61 705.86 May-81 593.48
Jun-01 981.46 Jun-21 1033.54 Jun-41 869.59 Jun-61 841.73 Jun-81 966.17
Jul-01 1020.82 Jul-21 960.96 Jul-41 664.86 Jul-61 709.34 Jul-81 741.59
Aug-01 770.88 Aug-21 896.47 Aug-41 548.74 Aug-61 660.30 Aug-81 767.41
Sep-01 435.39 Sep-21 343.28 Sep-41 393.74 Sep-61 352.66 Sep-81 381.93
Oct-01 251.96 Oct-21 136.85 Oct-41 176.05 Oct-61 211.87 Oct-81 200.88
Nov-01 136.95 Nov-21 120.02 Nov-41 121.33 Nov-61 122.22 Nov-81 135.21
Dec-01 139.68 Dec-21 124.03 Dec-41 129.04 Dec-61 123.99 Dec-81 133.92
Jan-02 141.07 Jan-22 138.46 Jan-42 136.80 Jan-62 136.52 Jan-82 121.83
Feb-02 136.15 Feb-22 135.31 Feb-42 133.31 Feb-62 136.17 Feb-82 127.51
Mar-02 132.08 Mar-22 130.45 Mar-42 129.94 Mar-62 120.95 Mar-82 121.45
Apr-02 172.96 Apr-22 128.70 Apr-42 351.56 Apr-62 215.99 Apr-82 181.18
May-02 495.75 May-22 439.27 May-42 560.03 May-62 563.32 May-82 671.67
Jun-02 950.76 Jun-22 1128.11 Jun-42 902.82 Jun-62 558.06 Jun-82 886.67
Jul-02 974.55 Jul-22 1060.89 Jul-42 716.71 Jul-62 626.51 Jul-82 686.68
Aug-02 706.68 Aug-22 686.59 Aug-42 661.09 Aug-62 608.29 Aug-82 694.37
Sep-02 432.89 Sep-22 476.36 Sep-42 363.95 Sep-62 321.95 Sep-82 481.68
Oct-02 223.96 Oct-22 141.37 Oct-42 199.54 Oct-62 273.88 Oct-82 292.98
120
Nov-02 128.59 Nov-22 123.01 Nov-42 122.63 Nov-62 121.80 Nov-82 123.37
Dec-02 141.11 Dec-22 128.63 Dec-42 134.47 Dec-62 118.80 Dec-82 118.27
Jan-03 141.20 Jan-23 141.31 Jan-43 137.60 Jan-63 125.90 Jan-83 138.58
Feb-03 141.31 Feb-23 138.25 Feb-43 123.09 Feb-63 120.54 Feb-83 128.73
Mar-03 132.59 Mar-23 129.49 Mar-43 122.99 Mar-63 121.81 Mar-83 138.86
Apr-03 128.47 Apr-23 139.52 Apr-43 242.93 Apr-63 166.10 Apr-83 204.65
May-03 334.02 May-23 525.48 May-43 606.70 May-63 542.54 May-83 587.06
Jun-03 967.27 Jun-23 1014.66 Jun-43 763.56 Jun-63 765.69 Jun-83 895.43
Jul-03 933.83 Jul-23 992.21 Jul-43 801.26 Jul-63 671.53 Jul-83 733.01
Aug-03 715.84 Aug-23 862.49 Aug-43 495.35 Aug-63 495.89 Aug-83 665.92
Sep-03 630.94 Sep-23 384.97 Sep-43 376.47 Sep-63 376.06 Sep-83 478.85
Oct-03 262.11 Oct-23 172.01 Oct-43 192.88 Oct-63 278.56 Oct-83 242.28
Nov-03 119.26 Nov-23 120.08 Nov-43 121.07 Nov-63 129.86 Nov-83 124.65
Dec-03 135.45 Dec-23 131.26 Dec-43 137.84 Dec-63 138.16 Dec-83 119.45
Jan-04 141.05 Jan-24 138.08 Jan-44 136.97 Jan-64 124.95 Jan-84 125.43
Feb-04 139.95 Feb-24 140.59 Feb-44 118.35 Feb-64 115.94 Feb-84 117.09
Mar-04 132.63 Mar-24 131.18 Mar-44 122.47 Mar-64 123.79 Mar-84 120.92
Apr-04 136.28 Apr-24 129.40 Apr-44 306.32 Apr-64 294.83 Apr-84 235.53
May-04 546.11 May-24 641.88 May-44 661.58 May-64 316.04 May-84 715.31
Jun-04 1122.69 Jun-24 974.20 Jun-44 923.58 Jun-64 674.53 Jun-84 784.91
Jul-04 875.53 Jul-24 826.09 Jul-44 682.58 Jul-64 635.13 Jul-84 589.24
Aug-04 700.51 Aug-24 564.03 Aug-44 666.03 Aug-64 624.60 Aug-84 673.12
Sep-04 463.57 Sep-24 289.42 Sep-44 395.03 Sep-64 364.40 Sep-84 424.31
Oct-04 195.52 Oct-24 175.29 Oct-44 262.24 Oct-64 180.89 Oct-84 250.12
Nov-04 130.98 Nov-24 120.27 Nov-44 168.58 Nov-64 124.01 Nov-84 149.93
Dec-04 140.03 Dec-24 139.51 Dec-44 137.93 Dec-64 116.67 Dec-84 132.32
121
Jan-05 140.50 Jan-25 140.97 Jan-45 141.21 Jan-65 138.75 Jan-85 118.20
Feb-05 136.98 Feb-25 141.31 Feb-45 135.77 Feb-65 129.08 Feb-85 126.98
Mar-05 126.83 Mar-25 135.34 Mar-45 144.97 Mar-65 237.93 Mar-85 123.78
Apr-05 169.02 Apr-25 129.41 Apr-45 241.66 Apr-65 133.65 Apr-85 333.99
May-05 695.44 May-25 305.04 May-45 450.18 May-65 399.00 May-85 600.84
Jun-05 1072.83 Jun-25 1058.81 Jun-45 848.25 Jun-65 737.00 Jun-85 666.49
Jul-05 981.00 Jul-25 922.48 Jul-45 602.08 Jul-65 807.75 Jul-85 737.28
Aug-05 677.66 Aug-25 805.91 Aug-45 489.79 Aug-65 594.18 Aug-85 610.64
Sep-05 314.51 Sep-25 317.19 Sep-45 437.97 Sep-65 407.89 Sep-85 403.88
Oct-05 140.28 Oct-25 200.63 Oct-45 170.83 Oct-65 209.84 Oct-85 264.45
Nov-05 131.08 Nov-25 119.11 Nov-45 126.19 Nov-65 123.15 Nov-85 163.03
Dec-05 140.46 Dec-25 130.72 Dec-45 139.23 Dec-65 126.44 Dec-85 137.34
Jan-06 141.32 Jan-26 140.23 Jan-46 141.30 Jan-66 130.82 Jan-86 139.13
Feb-06 138.04 Feb-26 125.81 Feb-46 136.89 Feb-66 123.44 Feb-86 131.85
Mar-06 129.20 Mar-26 121.25 Mar-46 120.62 Mar-66 138.50 Mar-86 127.83
Apr-06 134.09 Apr-26 136.50 Apr-46 268.68 Apr-66 184.51 Apr-86 303.63
May-06 565.68 May-26 361.67 May-46 645.41 May-66 518.72 May-86 653.70
Jun-06 1049.83 Jun-26 1055.73 Jun-46 827.18 Jun-66 657.16 Jun-86 906.93
Jul-06 975.19 Jul-26 874.46 Jul-46 806.38 Jul-66 687.74 Jul-86 843.39
Aug-06 789.63 Aug-26 732.27 Aug-46 498.83 Aug-66 725.02 Aug-86 669.24
Sep-06 339.46 Sep-26 413.33 Sep-46 397.59 Sep-66 412.66 Sep-86 411.82
Oct-06 274.70 Oct-26 272.97 Oct-46 243.72 Oct-66 194.95 Oct-86 260.44
Nov-06 128.01 Nov-26 120.76 Nov-46 122.80 Nov-66 139.75 Nov-86 134.83
Dec-06 122.97 Dec-26 126.49 Dec-46 137.34 Dec-66 120.12 Dec-86 118.86
Jan-07 126.54 Jan-27 140.72 Jan-47 138.80 Jan-67 131.03 Jan-87 137.99
Feb-07 141.31 Feb-27 140.37 Feb-47 123.81 Feb-67 118.37 Feb-87 136.46
122
Mar-07 123.03 Mar-27 125.14 Mar-47 120.99 Mar-67 122.84 Mar-87 124.50
Apr-07 130.23 Apr-27 123.10 Apr-47 164.34 Apr-67 196.54 Apr-87 297.03
May-07 479.93 May-27 316.43 May-47 510.63 May-67 509.73 May-87 588.76
Jun-07 1021.62 Jun-27 849.11 Jun-47 787.75 Jun-67 872.36 Jun-87 916.31
Jul-07 957.66 Jul-27 908.69 Jul-47 735.03 Jul-67 672.35 Jul-87 723.71
Aug-07 643.11 Aug-27 786.86 Aug-47 708.64 Aug-67 621.61 Aug-87 613.35
Sep-07 359.39 Sep-27 303.20 Sep-47 405.72 Sep-67 403.24 Sep-87 417.09
Oct-07 134.72 Oct-27 146.55 Oct-47 166.26 Oct-67 227.61 Oct-87 232.95
Nov-07 131.03 Nov-27 130.66 Nov-47 139.60 Nov-67 122.95 Nov-87 126.22
Dec-07 140.09 Dec-27 139.42 Dec-47 135.34 Dec-67 138.22 Dec-87 132.24
Jan-08 141.34 Jan-28 141.34 Jan-48 139.99 Jan-68 138.82 Jan-88 133.11
Feb-08 140.06 Feb-28 140.24 Feb-48 124.90 Feb-68 130.80 Feb-88 124.26
Mar-08 123.21 Mar-28 133.94 Mar-48 119.77 Mar-68 121.84 Mar-88 147.74
Apr-08 135.14 Apr-28 135.35 Apr-48 207.98 Apr-68 207.71 Apr-88 235.44
May-08 470.60 May-28 369.49 May-48 398.65 May-68 582.82 May-88 634.55
Jun-08 1037.47 Jun-28 1062.55 Jun-48 688.86 Jun-68 843.53 Jun-88 795.89
Jul-08 994.03 Jul-28 796.14 Jul-48 692.71 Jul-68 722.18 Jul-88 903.42
Aug-08 849.53 Aug-28 813.80 Aug-48 600.19 Aug-68 640.14 Aug-88 679.50
Sep-08 512.72 Sep-28 452.06 Sep-48 425.02 Sep-68 379.81 Sep-88 405.03
Oct-08 137.13 Oct-28 152.91 Oct-48 284.00 Oct-68 201.47 Oct-88 198.48
Nov-08 122.11 Nov-28 120.82 Nov-48 120.89 Nov-68 127.83 Nov-88 124.89
Dec-08 139.50 Dec-28 138.82 Dec-48 129.11 Dec-68 135.06 Dec-88 134.48
Jan-09 141.34 Jan-29 138.72 Jan-49 139.69 Jan-69 136.36 Jan-89 138.19
Feb-09 141.27 Feb-29 136.16 Feb-49 133.29 Feb-69 133.02 Feb-89 125.96
Mar-09 133.23 Mar-29 129.47 Mar-49 123.21 Mar-69 145.19 Mar-89 127.07
Apr-09 150.67 Apr-29 130.33 Apr-49 361.00 Apr-69 277.60 Apr-89 302.74
123
May-09 503.28 May-29 547.88 May-49 596.63 May-69 539.68 May-89 668.40
Jun-09 1028.11 Jun-29 1013.31 Jun-49 881.76 Jun-69 774.57 Jun-89 873.16
Jul-09 1029.77 Jul-29 781.42 Jul-49 689.93 Jul-69 681.19 Jul-89 650.93
Aug-09 754.17 Aug-29 997.27 Aug-49 653.98 Aug-69 690.19 Aug-89 587.27
Sep-09 350.21 Sep-29 377.54 Sep-49 380.66 Sep-69 370.02 Sep-89 419.86
Oct-09 140.78 Oct-29 161.67 Oct-49 190.05 Oct-69 214.01 Oct-89 218.77
Nov-09 125.54 Nov-29 128.93 Nov-49 135.42 Nov-69 128.48 Nov-89 124.30
Dec-09 141.18 Dec-29 138.40 Dec-49 121.64 Dec-69 134.83 Dec-89 119.39
Jan-10 141.33 Jan-30 140.14 Jan-50 138.31 Jan-70 138.94 Jan-90 135.46
Feb-10 140.69 Feb-30 136.15 Feb-50 121.46 Feb-70 117.87 Feb-90 129.55
Mar-10 134.35 Mar-30 125.67 Mar-50 129.64 Mar-70 132.89 Mar-90 151.12
Apr-10 134.00 Apr-30 166.61 Apr-50 275.98 Apr-70 188.27 Apr-90 174.62
May-10 561.47 May-30 514.45 May-50 511.23 May-70 604.38 May-90 507.89
Jun-10 1034.90 Jun-30 1032.44 Jun-50 875.71 Jun-70 730.93 Jun-90 845.53
Jul-10 1047.00 Jul-30 829.82 Jul-50 615.59 Jul-70 717.68 Jul-90 670.24
Aug-10 752.26 Aug-30 874.08 Aug-50 631.91 Aug-70 580.33 Aug-90 609.54
Sep-10 589.98 Sep-30 455.94 Sep-50 392.58 Sep-70 404.03 Sep-90 470.43
Oct-10 134.76 Oct-30 216.27 Oct-50 189.62 Oct-70 203.77 Oct-90 246.62
Nov-10 119.51 Nov-30 121.47 Nov-50 121.43 Nov-70 123.93 Nov-90 138.01
Dec-10 139.32 Dec-30 137.91 Dec-50 136.95 Dec-70 134.01 Dec-90 119.08
Jan-11 140.63 Jan-31 141.22 Jan-51 138.67 Jan-71 135.49 Jan-91 129.59
Feb-11 137.18 Feb-31 137.77 Feb-51 137.03 Feb-71 131.42 Feb-91 118.75
Mar-11 130.29 Mar-31 125.74 Mar-51 119.60 Mar-71 136.21 Mar-91 159.98
Apr-11 181.45 Apr-31 156.49 Apr-51 175.37 Apr-71 197.52 Apr-91 227.31
May-11 659.03 May-31 315.06 May-51 632.94 May-71 582.04 May-91 455.16
Jun-11 973.41 Jun-31 581.87 Jun-51 813.09 Jun-71 807.61 Jun-91 773.39
124
Jul-11 1012.37 Jul-31 713.08 Jul-51 779.26 Jul-71 644.33 Jul-91 659.60
Aug-11 909.23 Aug-31 675.03 Aug-51 610.28 Aug-71 646.11 Aug-91 605.34
Sep-11 576.42 Sep-31 361.34 Sep-51 345.26 Sep-71 480.33 Sep-91 409.13
Oct-11 149.74 Oct-31 248.17 Oct-51 205.18 Oct-71 216.43 Oct-91 251.98
Nov-11 131.42 Nov-31 129.10 Nov-51 119.95 Nov-71 124.11 Nov-91 127.15
Dec-11 113.90 Dec-31 139.00 Dec-51 136.30 Dec-71 132.57 Dec-91 127.28
Jan-12 141.33 Jan-32 138.68 Jan-52 136.37 Jan-72 136.32 Jan-92 134.30
Feb-12 138.22 Feb-32 136.54 Feb-52 122.33 Feb-72 121.26 Feb-92 119.53
Mar-12 118.96 Mar-32 121.35 Mar-52 131.22 Mar-72 121.68 Mar-92 132.45
Apr-12 129.43 Apr-32 211.97 Apr-52 224.74 Apr-72 201.73 Apr-92 222.00
May-12 518.09 May-32 622.76 May-52 515.88 May-72 580.59 May-92 720.43
Jun-12 1028.33 Jun-32 861.60 Jun-52 680.93 Jun-72 935.30 Jun-92 898.52
Jul-12 1074.41 Jul-32 844.69 Jul-52 735.70 Jul-72 755.83 Jul-92 729.05
Aug-12 681.72 Aug-32 624.43 Aug-52 648.71 Aug-72 691.47 Aug-92 586.91
Sep-12 350.48 Sep-32 403.40 Sep-52 366.34 Sep-72 426.32 Sep-92 484.99
Oct-12 178.65 Oct-32 176.76 Oct-52 208.81 Oct-72 277.26 Oct-92 218.46
Nov-12 129.28 Nov-32 126.95 Nov-52 126.16 Nov-72 127.65 Nov-92 149.79
Dec-12 122.49 Dec-32 133.28 Dec-52 125.43 Dec-72 121.53 Dec-92 118.47
Jan-13 140.80 Jan-33 141.11 Jan-53 121.93 Jan-73 119.40 Jan-93 130.78
Feb-13 140.70 Feb-33 138.33 Feb-53 120.42 Feb-73 135.23 Feb-93 134.62
Mar-13 133.80 Mar-33 121.17 Mar-53 127.42 Mar-73 132.04 Mar-93 128.63
Apr-13 142.28 Apr-33 187.72 Apr-53 139.97 Apr-73 266.75 Apr-93 292.81
May-13 812.98 May-33 524.16 May-53 429.09 May-73 608.51 May-93 720.20
Jun-13 1042.57 Jun-33 789.19 Jun-53 813.01 Jun-73 837.74 Jun-93 861.29
Jul-13 833.15 Jul-33 853.69 Jul-53 699.23 Jul-73 764.56 Jul-93 691.45
Aug-13 728.48 Aug-33 505.55 Aug-53 590.72 Aug-73 604.65 Aug-93 616.10
125
Sep-13 381.49 Sep-33 311.72 Sep-53 385.48 Sep-73 395.08 Sep-93 565.32
Oct-13 143.77 Oct-33 187.25 Oct-53 188.80 Oct-73 206.12 Oct-93 203.47
Nov-13 127.19 Nov-33 121.92 Nov-53 121.39 Nov-73 136.93 Nov-93 148.03
Dec-13 140.13 Dec-33 139.61 Dec-53 137.76 Dec-73 136.64 Dec-93 132.64
Jan-14 141.08 Jan-34 140.02 Jan-54 125.76 Jan-74 139.57 Jan-94 130.17
Feb-14 140.84 Feb-34 140.14 Feb-54 113.76 Feb-74 126.57 Feb-94 130.31
Mar-14 129.25 Mar-34 132.27 Mar-54 133.23 Mar-74 126.59 Mar-94 158.92
Apr-14 130.15 Apr-34 227.70 Apr-54 149.11 Apr-74 226.33 Apr-94 254.88
May-14 647.64 May-34 385.59 May-54 562.29 May-74 540.51 May-94 791.51
Jun-14 1092.15 Jun-34 682.55 Jun-54 763.23 Jun-74 735.33 Jun-94 966.90
Jul-14 922.79 Jul-34 755.24 Jul-54 606.23 Jul-74 796.32 Jul-94 696.97
Aug-14 801.09 Aug-34 534.58 Aug-54 625.35 Aug-74 735.30 Aug-94 609.08
Sep-14 368.86 Sep-34 410.62 Sep-54 358.41 Sep-74 416.46 Sep-94 422.81
Oct-14 155.68 Oct-34 185.70 Oct-54 240.72 Oct-74 215.84 Oct-94 193.44
Nov-14 140.25 Nov-34 120.25 Nov-54 121.43 Nov-74 123.14 Nov-94 130.30
Dec-14 140.79 Dec-34 140.90 Dec-54 136.64 Dec-74 132.78 Dec-94 123.73
Jan-15 140.36 Jan-35 139.05 Jan-55 139.27 Jan-75 135.69 Jan-95 138.37
Feb-15 140.07 Feb-35 141.34 Feb-55 117.93 Feb-75 124.30 Feb-95 134.06
Mar-15 131.59 Mar-35 120.68 Mar-55 122.44 Mar-75 124.50 Mar-95 121.54
Apr-15 140.77 Apr-35 223.73 Apr-55 264.97 Apr-75 207.06 Apr-95 217.83
May-15 519.87 May-35 613.85 May-55 470.80 May-75 535.77 May-95 696.25
Jun-15 982.48 Jun-35 713.94 Jun-55 638.90 Jun-75 943.66 Jun-95 730.37
Jul-15 944.67 Jul-35 661.33 Jul-55 773.34 Jul-75 769.07 Jul-95 707.41
Aug-15 874.05 Aug-35 720.56 Aug-55 705.44 Aug-75 637.19 Aug-95 638.44
Sep-15 447.17 Sep-35 318.81 Sep-55 390.74 Sep-75 455.62 Sep-95 404.09
Oct-15 170.54 Oct-35 228.12 Oct-55 217.59 Oct-75 180.32 Oct-95 226.07
126
Nov-15 130.31 Nov-35 130.04 Nov-55 125.58 Nov-75 136.97 Nov-95 128.54
Dec-15 138.97 Dec-35 140.56 Dec-55 138.27 Dec-75 123.68 Dec-95 125.18
Jan-16 139.60 Jan-36 140.82 Jan-56 116.88 Jan-76 140.65 Jan-96 123.02
Feb-16 134.58 Feb-36 123.83 Feb-56 123.22 Feb-76 117.88 Feb-96 124.57
Mar-16 130.93 Mar-36 132.66 Mar-56 126.11 Mar-76 129.69 Mar-96 137.54
Apr-16 137.43 Apr-36 179.50 Apr-56 302.31 Apr-76 286.38 Apr-96 362.64
May-16 616.30 May-36 482.05 May-56 391.24 May-76 615.50 May-96 572.33
Jun-16 837.18 Jun-36 683.97 Jun-56 692.84 Jun-76 767.41 Jun-96 814.48
Jul-16 869.92 Jul-36 642.34 Jul-56 763.49 Jul-76 714.07 Jul-96 796.10
Aug-16 830.47 Aug-36 620.70 Aug-56 526.97 Aug-76 651.42 Aug-96 681.34
Sep-16 410.94 Sep-36 320.00 Sep-56 384.88 Sep-76 367.03 Sep-96 436.32
Oct-16 147.84 Oct-36 214.36 Oct-56 209.25 Oct-76 183.52 Oct-96 205.51
Nov-16 119.40 Nov-36 126.30 Nov-56 121.87 Nov-76 124.68 Nov-96 126.20
Dec-16 138.11 Dec-36 125.96 Dec-56 138.98 Dec-76 123.44 Dec-96 130.59
Jan-17 137.92 Jan-37 141.20 Jan-57 136.57 Jan-77 135.96 Jan-97 136.67
Feb-17 138.60 Feb-37 110.42 Feb-57 121.15 Feb-77 135.30 Feb-97 121.66
Mar-17 131.75 Mar-37 124.39 Mar-57 126.66 Mar-77 171.50 Mar-97 152.98
Apr-17 140.61 Apr-37 138.79 Apr-57 227.35 Apr-77 247.87 Apr-97 210.45
May-17 267.85 May-37 388.87 May-57 682.08 May-77 522.57 May-97 721.01
Jun-17 1019.79 Jun-37 712.80 Jun-57 730.50 Jun-77 814.57 Jun-97 724.97
Jul-17 907.95 Jul-37 747.27 Jul-57 714.33 Jul-77 839.66 Jul-97 651.24
Aug-17 614.58 Aug-37 565.24 Aug-57 592.77 Aug-77 584.59 Aug-97 623.92
Sep-17 496.55 Sep-37 418.67 Sep-57 381.94 Sep-77 427.21 Sep-97 441.57
Oct-17 170.39 Oct-37 198.04 Oct-57 227.61 Oct-77 222.81 Oct-97 316.24
Nov-17 120.49 Nov-37 119.47 Nov-57 121.38 Nov-77 126.93 Nov-97 129.10
Dec-17 141.28 Dec-37 138.39 Dec-57 138.59 Dec-77 134.11 Dec-97 120.69
127
Jan-18 141.03 Jan-38 134.70 Jan-58 139.71 Jan-78 128.34 Jan-98 130.60
Feb-18 137.88 Feb-38 124.85 Feb-58 137.56 Feb-78 121.01 Feb-98 133.26
Mar-18 129.16 Mar-38 126.89 Mar-58 128.82 Mar-78 132.16 Mar-98 130.50
Apr-18 156.79 Apr-38 225.37 Apr-58 210.45 Apr-78 293.12 Apr-98 349.71
May-18 551.55 May-38 587.90 May-58 609.77 May-78 678.74 May-98 635.11
Jun-18 998.78 Jun-38 925.12 Jun-58 757.67 Jun-78 935.49 Jun-98 856.28
Jul-18 794.72 Jul-38 652.69 Jul-58 713.10 Jul-78 787.35 Jul-98 731.72
Aug-18 763.43 Aug-38 605.22 Aug-58 613.54 Aug-78 595.27 Aug-98 733.98
Sep-18 389.40 Sep-38 371.13 Sep-58 348.78 Sep-78 367.80 Sep-98 482.32
Oct-18 168.77 Oct-38 203.27 Oct-58 230.47 Oct-78 225.86 Oct-98 270.79
Nov-18 119.57 Nov-38 124.17 Nov-58 145.07 Nov-78 136.10 Nov-98 128.64
Dec-18 123.73 Dec-38 140.63 Dec-58 129.70 Dec-78 127.65 Dec-98 122.26
Jan-19 140.38 Jan-39 140.07 Jan-59 138.34 Jan-79 135.47 Jan-99 117.62
Feb-19 136.65 Feb-39 139.23 Feb-59 123.61 Feb-79 119.05 Feb-99 125.20
Mar-19 129.44 Mar-39 120.58 Mar-59 123.23 Mar-79 134.45 Mar-99 149.67
Apr-19 140.88 Apr-39 178.19 Apr-59 216.22 Apr-79 354.03 Apr-99 310.21
May-19 747.86 May-39 626.74 May-59 467.70 May-79 463.43 May-99 646.09
Jun-19 1055.38 Jun-39 717.10 Jun-59 965.86 Jun-79 940.58 Jun-99 793.00
Jul-19 865.07 Jul-39 810.76 Jul-59 711.95 Jul-79 671.82 Jul-99 843.32
Aug-19 718.70 Aug-39 491.76 Aug-59 731.96 Aug-79 504.13 Aug-99 542.01
Sep-19 341.49 Sep-39 430.96 Sep-59 465.71 Sep-79 431.57 Sep-99 441.05
Oct-19 150.17 Oct-39 183.34 Oct-59 222.28 Oct-79 284.60 Oct-99 222.04
Nov-19 125.19 Nov-39 124.74 Nov-59 123.11 Nov-79 168.29 Nov-99 127.44
Dec-19 129.21 Dec-39 139.31 Dec-59 118.91 Dec-79 125.16 Dec-99 118.37
Jan-20 135.31 Jan-40 134.35 Jan-60 139.87 Jan-80 138.13 Jan-00 130.03
Feb-20 123.42 Feb-40 133.71 Feb-60 134.09 Feb-80 117.81 Feb-00 133.56
128
Mar-20 132.14 Mar-40 129.42 Mar-60 142.08 Mar-80 121.57 Mar-00 205.30
Apr-20 148.78 Apr-40 252.08 Apr-60 185.03 Apr-80 294.17 Apr-00 444.32
May-20 589.28 May-40 546.64 May-60 534.40 May-80 612.42 May-00 766.79
Jun-20 854.97 Jun-40 737.51 Jun-60 803.14 Jun-80 766.24 Jun-00 1089.78
Jul-20 881.34 Jul-40 626.95 Jul-60 928.10 Jul-80 886.68 Jul-00 1099.40
Aug-20 647.95 Aug-40 616.26 Aug-60 689.74 Aug-80 630.69 Aug-00 1036.33
Sep-20 456.00 Sep-40 346.83 Sep-60 456.84 Sep-80 431.54 Sep-00 862.22
Oct-20 143.33 Oct-40 171.80 Oct-60 319.87 Oct-80 250.81 Oct-00 346.47
Nov-20 124.07 Nov-40 134.77 Nov-60 125.55 Nov-80 136.93 Nov-00 210.09
Dec-20 140.14 Dec-40 139.36 Dec-60 119.85 Dec-80 133.05 Dec-00 129.58
