Applied Hydrology Climate Change and Hydrology

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Applied HydrologyClimate Change and Hydrology

• Professor Ke-Sheng Cheng
• Department of Bioenvironmental Systems
  Engineering
• National Taiwan University

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Global Circulation Models (GCMs)

• Computer models that
• are capable of producing a realistic
  representation of the climate, and
• can respond to the most obvious quantifiable
  perturbations.
• Derived based on weather forecasting models.

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Weather forecasting models

• The physical state of the atmosphere is updated
  continually drawing on observations from around
  the world using surface land stations, ships,
  buoys, and in the upper atmosphere using
  instruments on aircraft, balloons and satellites.
• The model atmosphere is divided into 70 layers
  and each level is divided up into a network of
  points about 40 km apart.

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• Standard weather forecasts do not predict sudden
  switches between stable circulation patterns
  well. At best they get some warning by using
  statistical methods to check whether or not the
  atmosphere is in an unpredictable mood. This is
  done by running the models with slightly
  different starting conditions and seeing whether
  the forecasts stick together or diverge rapidly.

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• This ensemble approach provides a useful
  indication of what modelers are up against when
  they seek to analyses the response of the global
  climate to various perturbations and to predict
  the course it will following in the future.
• The GCMs cannot represent the global climate in
  the same details as the numerical weather
  predictions because they must be run for decades
  and even centuries ahead in order to consider
  possible changes.

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• Typically, most GCMs now have a horizontal
  resolution of between 125 and 400 km, but retain
  much of the detailed vertical resolution, having
  around 20 levels in the atmosphere.
• Challenges for potential GCMs improvement
• Modeling clouds formation and distribution
• Tropical storms (typhoons and hurricanes)
• Land-surface processes
• Winds, waves and currents
• Other greenhouse gases

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GCMs
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• From GCMs to hydrological process modeling
• Study of hydrological processes requires spatial
  and temporal resolutions which are much smaller
  than GCMs can offer.
• Downscaling techniques have been developed to
  downscale GCM outputs to desired scales.
• Dynamic downscaling
• Statistical downscaling

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Weather Generator of daily rainfall simulation

• Markov chain for rain day/no-rain day simulation
• Exponential distribution for daily rainfall
  simulation.

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Effect of climate change on storm characteristics

• Storm types
• Convective storms
• Typhoons
• MCS (Mei-yu)
• Frontal systems
• Assessed based on MRI high-resolution outpots
  (dynamic downscaling)

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• TCCIP Team 3
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MRI-WRF-5km??? (??1979-2003)
??????? (??1979-2003)
MRI-WRF-5km?????????????????
MRI-WRF-5km??? (???2015-2039)
MRI-WRF-5km??? (???2075-2099)
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????????(????)

• ???????????,?????????
• ?????1 ????????0.5mm???????
• ??????

???? ?? ??
??? (??) 5?-6? ???? gt 3?? ??? gt 0.5 mm/hr
??? (??) 7?-10? ???? gt 8?? ??? gt 2.5 mm/hr
??? (??) 7?-10? 3 ?? gt ???? 8?? ??? gt 2.5 mm/hr
??? (??) 11???4? ???? gt 4?? ??? gt 0.5 mm/hr
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????

• ????
• ??1979-2003???
• ??84?
• MRI-WRF-5km
• ????? 5km
• 1979-2003
• 2015-2039
• 2075-2099 ???

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???
??? (??) 7?-10? ???? gt 8?? ??? gt 2.5 mm/hr
?? ??????(??) ?????
??(1979-2003) - 3.04
1979-2003 3.52 3.39
2015-2039 3.24 3.39
2075-2099 3.28 3.32
Gauges
MRI-WRF ??
???
???
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????
??? (??) 7?-10? ???? gt 8?? ??? gt 2.5 mm/hr
Gauges
MRI-WRF ??
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??? (??) 7?-10? ???? gt 8?? ??? gt 2.5 mm/hr
Gauges
MRI-WRF ??
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??? (??) 7?-10? ???? gt 8?? ??? gt 2.5 mm/hr
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??? (??) 11???4? ???? gt 4?? ??? gt 0.5 mm/hr
?? ?????
??(1979-2003) 7.58
1979-2003 6.94
2015-2039 7.15
2075-2099 8.37
????gt4hrs ???gt0.5mm
????gt4hrs ???gt2mm
Gauges
MRI-WRF ??
???
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????
??? (??) 11???4? ???? gt 4?? ??? gt 0.5 mm/hr
????gt4hrs ???gt0.5mm
????gt4hrs ???gt2mm
Gauges
MRI-WRF ??
???
???
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??????
??? (??) 11???4? ???? gt 4?? ??? gt 0.5 mm/hr
????gt4hrs ???gt0.5mm
????gt4hrs ???gt2mm
Gauges
MRI-WRF ??
???
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????
??? (??) 11???4? ???? gt 4?? ??? gt 0.5 mm/hr
????gt4hrs ???gt0.5mm
????gt4hrs ???gt2mm
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???
??? (??) 5?-6? ???? gt 3?? ??? gt 0.5 mm/hr
?? ?????
??(1979-2003) 6.51
1979-2003 7.16
2015-2039 6.89
2075-2099 7.55
????gt3hrs ???gt0.5mm
????gt3hrs ???gt2mm
Gauges
MRI-WRF ??
???
???
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????
??? (??) 5?-6? ???? gt 3?? ??? gt 0.5 mm/hr
????gt3hrs ???gt0.5mm
????gt3hrs ???gt2mm
Gauges
MRI-WRF ??
???
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??????
??? (??) 5?-6? ???? gt 3?? ??? gt 0.5 mm/hr
????gt3hrs ???gt0.5mm
????gt3hrs ???gt2mm
Gauges
MRI-WRF ??
???
???
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??? (??) 5?-6? ???? gt 3?? ??? gt 0.5 mm/hr
????gt3hrs ???gt0.5mm
????gt3hrs ???gt2mm
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???
??? (??) 7?-10? 3??lt???? 8?? ??? gt 2.5 mm/hr
?? ?????
??(1979-2003) 3.10
1979-2003 6.75
2015-2039 6.51
2075-2099 6.36
Gauges
MRI-WRF ??
???
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??? (??) 7?-10? 3??lt???? 8?? ??? gt 2.5 mm/hr
Gauges
MRI-WRF ??
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??? (??) 7?-10? 3??lt???? 8?? ??? gt 2.5 mm/hr
Gauges
MRI-WRF ??
???
???
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• MRI-WRF-5km?????????????????????????????????,?????
  ??????????

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??????

• ?MRI-WRF-5km??????????????MRI-WRF-5km??????
• ??MRI-WRF-5km??????????????
• ????????????????

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Stochastic storm rainfall simulation model (SSRSM)

• Occurrences of storm events and time distribution
  of the event-total rainfalls are random in
  nature.
• Physical parameters based
• of events in a certain period
• Duration
• Event-total depths
• Time distribution (hyetograph)
• Rainfall intermittence

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Modeling occuerrences of storms

• Number of storm events in a certain period
• Occurrences of rare events like typhoons can be
  modeled by the Poisson process.
• Inter-event-time has an exponential distribution.
• Occurrences of other types of storms which are
  more frequently occurred may not be well
  characterized by the Poisson process.

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Duration and total depth

• Generally speaking, storms of longer durations
  draw higher amount of total rainfalls.
• Event-total rainfall (D) and duration (tr) are
  correlated and can be modeled by a joint
  distribution.
• (D, tr) of typhoons are modeled by a bivariate
  gamma distribution.
• Bivariate distribution of different families of
  marginal densities may be possible.

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Simulation of bivariate gamma distribution A
frequency factor based approach

• Transforming a bivariate gamma distribution to a
  corresponding bivariate standard normal
  distribution.
• Conversion of BVG correlation and BVN correlation.

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Gamma density
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Rationale of BVG simulation using frequency factor

• From the view point of random number generation,
  the frequency factor can be considered as a
  random variable K, and KT is a value of K with
  exceedence probability 1/T.
• Frequency factor of the Pearson type III
  distribution can be approximated by

Standard normal deviate
A
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• Assume two gamma random variables X and Y are
  jointly distributed.
• The two random variables are respectively
  associated with their frequency factors KX and KY
  .
• Equation (A) indicates that the frequency factor
  KX of a random variable X with gamma density is
  approximated by a function of the standard normal
  deviate and the coefficient of skewness of the
  gamma density.

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Flowchart of BVG simulation (1/2)
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Flowchart of BVG simulation (2/2)
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Time distribution of event-total rainfall

• The duration is divided into n intervals of equal
  length. Each interval is associated with a
  rainfall percentage.
• Based on the simple scaling assumption, rainfall
  percentages of the i-th interval (i 1, , n) of
  all events (of the same storm type) form a random
  sample of a common distribution.
• Rainfall percentages of individual intervals form
  a random process.
• Gamma-Markov process

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Modeling the dimensionless hyetograph

• Rainfall percentages can only assume values
  between 0 and 100.
• The sum of all rainfall percentages should equal
  100.
• Constrained gamma-Markov simulation
• Gamma distribution will generate random numbers
  exceeding 100.
• Truncated gamma distribution (truncated from
  above)
• The truncation threshold (cut off value) is
  significantly lower than 100.

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• Observations of rainfall percentages are samples
  of truncated gamma distributions.
• Determining parameters of the truncated gamma
  distributions.
• Scale parameter, shape parameter and the
  truncation threshold.
• Gamma-Markov simulation is based on simulation of
  a bivariate truncated-gamma distribution.
• Determing the correlation coefficient of the
  parent bivariate gamma distribution.