Hydrological Perspective of Climate
Change Impact Assessment
Distinguished Lecture - Hydrological Sciences Section
Professor Ke-Sheng Cheng
Dept. of Bioenvironmental Systems Engineering
National Taiwan University
Outline
• The scale issue of climate change studies
• An example of climate change impact
assessment focusing on changes in design
storms.
07/28 - 08/01, 2014
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The scale issue
• Climate changes have had profound impacts
on climate and weather of our lives.
• The impacts of climate change vary with the
scales of interest.
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• As scientists, we can assess the impacts of
climate changes on all scales of variables of
interest. However, practical actions for coping
with climate changes are almost exclusively
implemented in country and regional/local
scales.
• Although hydrologists and climatologists may
conduct studies in similar scales, there are also
scales which are of unique interests to
hydrologists.
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Scales for flood risk assessment
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• Climatologists focus on climate-scale changes.
– Changes in annual or long-term average rainfalls of
global to regional scales.
• Hydrologist are more concerned about the
impacts of climate change on hydrological
extremes such as floods and droughts.
– Such hydrological extremes are results of extreme
weather events.
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• Studies related to climate changes usually
involve multiple disciplines.
• Terminologies commonly used by one
discipline may not be familiar to other
disciplines and, in some cases, terminologies
actually cause misunderstandings or
misinterpretations of the research results.
• Effective and good communications are
important in disseminating research outputs.
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• Climatologists focus on climate-scale changes.
– Changes in annual or long-term average rainfalls of
global to regional scales.
– Impact of Climate Change on River Discharge
Projected by Multimodel Ensemble (Nohara et al.,
2006, Journal of Hydrometeorology)
• At the end of the twenty-first century, the annual mean
precipitation, evaporation, and runoff increase in high
latitudes of the Northern Hemisphere, southern to
eastern Asia, and central Africa.
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Mean annual flow is the average daily flow for the individual year or multiyear period of interest.
[http://streamflow.engr.oregonstate.edu/analysis/annual/]
– Future changes in precipitation and impacts on
extreme streamflow over Amazonian sub-basins
(Guimberteau et al., 2013, Environ. Res. Lett.)
• Hydrological annual extreme variations (i.e. low/high
flows) associated with precipitation (and evapotranspiration) changes are investigated over the Amazon
River sub-basins.
• Evaluating changes in mean annual flow (MAF), high flow
(highest decile of MAF), low flow (lowest decile of MAF)
over the 1980 – 2000 period and two periods of the 21st
century.
This study investigated changes in hydrological extremes which
were associated with an annual resolution.
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– Temperature dependence of global precipitation
extremes (Liu et al., 2009, Geophysical Research
Letters)
• For Taiwan, the top 10% heaviest rain increases by about
140% for each degree increase in global temperature.
– The top 10% bin rainfall intensity was defined as 13 mm/hr
which was calculated based on long-term average daily rainfall
intensities.
• The above climatological rainfall extreme is much lower
than the 79 mm design rainfalls (for 90-minute duration
and 5-year return period) of the Taipei City.
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Example
•
Contours of the 100-year return period daily rainfall depth based on observed data
and high-resolution downscaled rainfalls.
(A)
Based on site observations
(B)
Based on high-resolution downscaled rainfalls.
Contours exhibit higher degree of spatial
continuity.
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Climate change impact assessment
focusing on changes in design
storms in Taiwan
Cheng, K.S., Lin, G.F., Chen, M.J., Wu, Y.C, Wu, M.F.
Hydrotech Research Institute, NTU
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Scale mismatch in climate projection
and hydrological projection
• In assessing the impact of climate change,
hydrologists often are interested in changes in
rainfall extremes, such as rainfall depths of
high return periods (i.e., design storms such as
rainfall depth of 24-hour, 100-year).
• Such rainfall extremes are results of extreme
weather events which are characteristic of
relatively small spatial and temporal scales
and cannot be resolved by GCMs.
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24 GCMs
Projections in coarse
spatial and time scales.
(200 – 300 km; monthly)
RCM
Projections in finer spatial scale.
(5km; monthly)
From GCM outputs to design
storm depths – a problem of scale
mismatch (both temporal and
spatial)
Design rainfall depths
For example, 24-hr, 100-year rainfall depth
Characteristics of extreme storm events
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• Rainfall extremes represent quantities of high
percentiles.
– Predicting extreme values is far more difficult than
predicting the means.
• We may have reasonable confidence on
climate projections (for example, long-term
average seasonal rainfalls), whereas our
confidence on extreme weather projections is
generally low.
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• Characteristics of storm events
•
•
•
•
Number of storm events
Duration of a storm event
Total rainfall depth
Time variation of rainfall intensities
• These characteristics are random in nature and
can be described by certain probability
distributions.
• Although the realized values of these storm
characteristics of individual storm events
represent weather observations, their
probability distributions are climate (long term
and ensemble) properties.
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• A GCM – stochastic model integrated approach
– Climatological projection by GCMs
• Changes in the means of storm characteristics
• For examples,
– Average number of typhoons per year
– Average duration of typhoons
– Average event-total rainfall of typhoons
– Hydrological projection by a stochastic storm rainfall
simulation model
• Generating realizations of storm rainfall process using
storm characteristics which are representative of the
projection period.
• Preserving statistical properties of the all storm
characteristics.
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24 GCMs
Projections in coarse
spatial and time scales.
(200 – 300 km; monthly)
Projections in finer spatial scale.
(5km; monthly)
RCM
Weather Generator
(Richardson type)
Projections in finer time scale.
(5km; daily)
Conceptual flowchart
ANN
Stochastic
storm
rainfall
simulation
Projections in point
(spatial) and hourly
(time) scales.
1
2
3
4
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Characteristics of storm events
Number of storm events
Onset of storm occurrences
Duration of a storm event
Total rainfall depth
Time variation of rainfall intensity
Design rainfall depths
For example, 24-hr, 100-year rainfall depth
Characteristics of extreme storm events
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Climate change scenarios and
GCM outputs
• Emission scenario: A1B
• Baseline period: 1980 – 1999
• Projection period
– Near future: 2020 – 2039
– End of century: 2080 – 2099
• GCM model: 24 GCMs statistical downscaling
• Hydrological scenario: changes in storm
characteristics
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Changes in monthly rainfalls (Statistical downscaling,
Ensemble average with standard deviation adjustment)
Taipei area
Near future (2020 – 2039)
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Near future (2080 – 2099)
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Annual counts of storm events estimated by ANN
Frontal
Maiyu
Typhoon
Convective
North
Center
South
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Storm characteristics (average duration of typhoon)
Gauge observations
MRI (1979 - 2003)
Source:
NCDR, Taiwan
Department of Bioenvironmental Systems Engineering,
MRI
(2075
- 2099)
National
Taiwan
University
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2014
MRI
(2015 – 2039)
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Storm characteristics (average event-total rainfalls of typhoon)
Gauge observations
MRI (1979 - 2003)
Source:
NCDR, Taiwan
Department of Bioenvironmental Systems Engineering,
MRI
(2075
- 2099)
National
Taiwan
University
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2014
MRI
(2015 – 2039)
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Stochastic storm rainfall process
Storm characteristics
•Duration
•Event-total depth
•Inter-arrival(or inter-event) time
•Time variation of rain-rates
Inter-arrival time
Inter-arrival time
Rainrate
Total
depth
Department
of BioenvironmentalDuration
Systems Engineering,
Duration
Duration
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Duration
Time(hr)
24
Season-specific storm characteristics
Rainfalls (mm)
Frontal
Jan- April
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Storm type
Period
Frontal
Nov - April
Mei-Yu
May - June
Convective
July - October
Typhoon
July - October
Mei-Yu
May - June
Convective,
Typhoon
Frontal
July - October
Nov - Dec
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Stochastic Storm Rainfall Simulation Model
(SSRSM)
• Simulating occurrences of storms and their rainfall
rates
• Preserving seasonal variation and temporal
autocorrelation of rainfall process.
• Duration and event-total depth
• Inter-event times
• Percentage of total rainfalls in individual intervals
(Storm hyetographs)
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• Simulating occurrences of storm events of
various storm types
– Number of events per year
• Poisson distribution for typhoon and Mei-Yu
– Inter-event time
• Gamma or log-normal distributions
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• Simulating joint distribution of duration and
event-total depth
– Bivariate gamma distribution (e.g. typhoons)
– Log-normal-Gamma bivariate
– Non-Gaussian bivariate distribution was
transformed to a corresponding bivariate standard
normal distribution with desired correlation matrix.
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Bivariate gamma (X,Y)
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• Simulating percentages of total rainfalls
in individual intervals (Simulation of
storm hyetographs)
– Based on the simple scaling property
• Durations of all events of the same storm types are
divided into a fixed number of intervals (e.g. 24 intervals).
• For a specific interval, rainfall percentages of different
events are identically and independently distributed (IID).
• Rainfall percentages of adjacent intervals are correlated.
• The simple scaling leads to the Horner equation fitting
of the IDF curves.
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Simple scaling (Random fractal)
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Modeling the storm hyetograph
Probability density of x(15)
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Taking all the above
properties into account,
we propose to model
the dimensionless
hyetograph by a
truncated gamma
Markov process.
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Truncated gamma
density (parameters
estimation,
including the
truncation level)
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Effect of modeling truncated data with
an untruncated density
f X ( x)
f XT ( x) 
,   x  vc
FX ( x )
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Parameters estimation
Truncated gamma distribution
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Kt 
Xt  

E[ K t ] 
E[ X t ]  
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
Var[ K t ] 
Var[ X t ]
2
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Stochastic simulation
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• Example 1
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• Example 2
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• CHECK
• Validation by stochastic simulation
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– Rainfall percentages should sum to 100%
• Truncated gamma distributions
• Conditional simulation is necessary
• 1st order Markov process
– Conditional simulation of first order truncated
gamma Markov process
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Each simulation run yields an annual sequence
of hourly rainfalls. 500 runs were generated for
each rainfall station.
Time of storm occurrences
(Duration, total depth) bivariate simulation
first-order Truncated Gamma-Markov simulation
Rainrate
Hourly rainfall
sequence
Total
depth
Time(hr)
Duration
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Duration
Duration
Duration
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Examples of hourly rainfall sequence
(Kaoshiung)
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Validation of the simulation results
using baseline period observations
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Hyetograph Simulation results (Typhoons)
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Time-to-peak and peak rainfall percentage
(Typhoons)
• Empirical cumulative distribution functions
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Application of simulation results
• Extreme rainfall assessment
– Annual maximum rainfall depth
– Hydrologic frequency analysis
• Seasonal rainfall assessment
• Water resources management
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Impact on design storm depths
Tainan
Kaoshiung
(Projection period: 2020-2039)
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Summary
• Changes in storm characteristics were derived
using monthly rainfall outputs of multiple
GCMs and an ANN model.
• The SSRSM is highly versatile.
– Can provide rainfall data of different temporal
scales (hourly, daily, TDP, monthly, yearly)
– Can facilitate the data requirements for various
applications (disaster mitigation, water resources
management and planning, etc.)
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• References
Wu, Y.C., Hou, J.C., Liou, J.J., Su, Y.F., Cheng, K.S., 2012. Assessing the
impact of climate change on basin-average annual typhoon rainfalls with
consideration of multisite correlation. Paddy and Water Environment, DOI
10.1007/s10333-011-0271-5.
Liou, J.J. Su, Y.F., Chiang, J.L., Cheng, K.S., 2011. Gamma random field
simulation by a covariance matrix transformation method. Stochastic
Environmental Research and Risk Assessment, 25(2): 235 – 251, DOI:
10.1007/s00477-010-0434-8.
Cheng, K.S., Hou, J.C., Liou, J.J., 2011. Stochastic Simulation of Bivariate
Gamma Distribution – A Frequency-Factor Based Approach. Stochastic
Environmental Research and Risk Assessment, 25(2): 107 – 122, DOI
10.1007/s00477-010-0427-7.
Cheng, K.S., Hou, J.C., Wu, Y.C., Liou, J.J., 2009. Assessing the impact of
climate change on annual typhoon rainfall – A stochastic simulation approach.
Paddy and Water Environment, 7(4): 333 – 340, DOI 10.1007/s10333-0090183-9.
Cheng, K.S., Chiang, J.L., and Hsu, C.W., 2007. Simulation of probability
distributions commonly used in hydrologic frequency analysis. Hydrological
Processes, 21: 51 – 60.
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Conclusions
• Physical processes + uncertainties
• Climate extremes vs weather/hydrological
extremes
• Support changes and their interpretations
• Coping with uncertainties by using multiple
model ensembles
• Different meanings of the same terminology in
different fields.
• Importance of communications
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• Communications
– We should not evaluate the performance of GCMs
by making a point-to-point comparison of their
outputs of the baseline (present-day) period to
observed data of the same period.
– Ii is also not appropriate to compare projected data
of GCMs to observations when they become
available. Projected data of GCMs were generated
under certain scenarios which may not be fully
realized in the future.
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Thanks for your patience!
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