Hydrology

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Hydrology

• Probability, Risk and Uncertainty analysis for
  Soil and Water Engineering
• Acad. year 2001-2002
• FLTBW

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Hydrologic processes

• Observed in timeseries population are all
  possible occurences of that proces
• Partly realised in the past
• Partly will be in the future and
• A part will never occur but is possible
• Limited lifetime of a hydrologic system geologic
  changes, climatic fluctuations, human
  interferences etc.
• Sample a (very) limited observation period in
  the past during the limited lifetime of the
  system

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Observation-period
past
future
Observation- window
now
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Example of record

• Dependency is a characteristic of the runoff data
• Extremum or sum of longer period are less
  dependent

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Population ltgt sample

• Relative frequency
• The number of observations of an event in a
  sample divided by the total number of
  observations within the sample
• Number from 0 to 1

• Chance (probability)
• The chance of an event to be realized within the
  population
• Number from 0 to 1

• Continuous variables intervals of values
• Discrete variables relative number

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See Table 10.1.1 pag 310

• Moments (kth central)
• With f(x) the probability density function (pdf)
• Coefficient of skewness

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Several prob distributions required in hydrology

• Normal or Gaussiangtsymmetrical no skewness from
  -? to ?
• Lognormalgt non-negative 0 to ?
• Relation between moments see pag 313
• Extreme value ( strength of a chain is the
  weakest link is extreme value distributed)
• Log Pearson type I (USA niet te kennen)

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Hydrologic design

• Design scale
• (Average) Return period average period between
  two exceedances of a level
• Hydrologic Risk Risk of exceedance of a critical
  level during a given period
• Hydrologic data series

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(Average) Returnperiod

• P(F) chance that F (ex rainfall gt 50mm in a day,
  discharge gt 20m³/s on a river) is exceeded in any
  particular year
• T1/P(F) (average) return period
  (terugkeer-periode) is the average time between
  two exceedances of F
• chance that F is
  not exceeded in any particular year

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Risk chance to exceed F during a period of n year
Assumption every year is independent
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Coincidence or not?

•  Recent  floods at Leuven
• 1891
• A series 1939 1940 1942 and 1947 (WWII?)
• Since no floods, hopefully not but who knows

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Returnperiod and risk(sensitive and emotional
issue!)
A project has an (economic) liftime Number of
years n (e.g. a dam)
E.g. the average returnperiod T 390 years for
the design flood F means that there is a 5
chance of failure during a lifetime of n 20 year.
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Hydrologic design

• Normally we need extreme values ( a flood a high
  rainfall similar to the strength of a chain is de
  weakest link the maximum or minimum out of N)
• Sometimes a population has many zeros and some
  positive values ( e.g. daily rainfall in an
  arid-climate)
• Inductive approach we might expect a
  probability distribution but the data-fitting
  process decides.

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Hydrologic design scale

• See figure 10.3.1 (page 315)
• Cost
• Safety
• Estimating limiting value (ELV)
• PMP (probable maximum preciptation)
• PMF (probable maximum flood)
• Table 10.3.1 choice of design Flood (Fd)
• Several scenarios without damage (ltFd) and with
  controlled/acceptable damage (gtFd but lt PMF)
• Gebrek aan zon scenarios was een van de grote
  ontwerp-gebreken bij wachtbekkens

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Composite risk (conceptueel geen berekeningen)

• Hydrologic risk F gt Fd
• Hydraulic risk failing under stress
• Loading magnitude of the flood
• Resistance flow carrying capacity
• Reliability probability of the resistance to
  exceed the loading
• Safety margin

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Rarely is the observationperiod long a enough
extrapolation required

• Central limit theorem the probability
  distribution of the average in a sample with n
  observations from a population with wathever
  probabiltiy distribution but with average ? and
  variance ?² is normally distributed with average
  ? and variance ?²/?n
• Most classical statistics are based on normal
  distribution..

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Regular probability distributions

• Normal distribution e.g. yearly rainfall in a
  humid climate
• Extreme value distribution (Gumbel) e.g. the
  yearly maximum 24 h rainfall
• Lognormal distribution e.g. possibly monthly
  rainfall in a semi-arid climate
• Remark many fysical parameters are non-negative
  and can be log normal e.g. hydraulic
  conductivity of a soil.
• USA (log-pearson niet te kennen ).

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Graphical method

• Plot individual observations (plotting position)
  on probability paper
• Draw a line based on moments
• Judge "goodness of fit line versus observations
• Mathematical method requires at least 30 years
  (Kolmorgov-Smirnov-method)

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Inductive fitting process

• Estimate the chance on the basis of the sample
  and fit the data on a probability distribution
• Estimator of the chance (called plotting
  position)
• With r the rank (r1 voor het grootste) and N the
  number of years in the sample

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Moments
Average (1st moment)
Standard deviation (2nd central m)
Skewnes (3nd central moment - lognormal or
exteme value)
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Line-fitting by moments
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Example normal distributed
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Normal distribution QQ-plot
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Example extreme value distributed
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Gumbel plot
100 years
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IDF intensity duration frequency curves

• Summary of all rainfall observations
• For a number of ?t prepare all maximum rainfall
  in every year (e.g. max 30 min rainfall of every
  year during 20 years)
• Frequency analysis
• Bring in one graph
• IDF intensity of rainfall
• RDF rainfall duration frequency

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IDF curves
Woluwe
Beauvechain
200 jaren
Beauvechain
2 jaren
IDF-Gembloux