CE 385 D Water Resources Planning and Management

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CE 385 D Water Resources Planning and Management

• River Basin Modeling
• Daene C. McKinney

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Water Resources

• Water at
• Wrong place, wrong quantity, wrong time
• What to do?
• Manipulate the hydrologic cycle
• Build facilities? Remove facilities? Reoperate
  facilities?
• Reservoirs
• Canals
• Levees
• Other infrastructure

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Scales

• Time Scales
• Water management plans
• Consider average conditions within discrete time
  periods
• Weekly, monthly or seasonal
• Over a long time horizon
• Year, decade, century
• Shortest time period
• No less than travel time from the upper basin to
  mouth
• For shorter time periods some kind of flow
  routing required
• Flood management
• Conditions over much shorter periods
• Hours, Days, Week

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Processes

• Processes we need to describe
• Precipitation
• Runoff
• Infiltration
• Percolation
• Evapotranspiration
• Chemical concentration
• Groundwater

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Data

• Reservoir losses
• Missing data
• Precipitation-runoff models
• Stochastic streamflow models
• Extending and filling in historic records

• Measurement
• Data sources
• Flow conditions
• Natural
• Present
• Unregulated
• Regulated
• Future

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Yield

• Yield - amount of water that can be supplied
  during some time interval
• Firm yield - amount of water that can be supplied
  in a critical period
• Without storage firm yield is lowest streamflow
  on record,
• With storage firm yield can be increased to
  approximately the mean annual flow of stream

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Regulation and Storage

• Critical period - period of lowest flow on record
  
• having observed an event in past, it is possible
  to experience it again in future
• Storage must be provided to deliver additional
  water over total streamflow record
• Given target yield, required capacity depends on
  risk that yield will not be delivered, i.e., the
  reliability of the system

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Hydrologic Frequency Analysis

• Flow duration curves
• Percent of time during which specified flow rates
  are equaled or exceeded at a given location

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Central Asia
Syr Darya
Naryn River
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Naryn River Annual Flows
Min. flow
Glacier melt
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Random Variables

• Function (X) whose value (x) depends on the
  outcome of a chance event
• Discrete RV
• Takes on values from a discrete set
• of years until a certain flood stage returns
• of times reservoir storage drops below a level
• Continuous RV
• Takes on values from a continuous set
• e.g., Rainfall, Streamflow, Temperature,
  Concentration

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Cumulative Distribution Function
Continuous RV
Discrete RV
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Probability Density (Mass) Functions
Probability density function
Probability mass function
Continuous RV
Discrete RV
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Multiple RVs

• The joint distribution of two RVs, X and Y
• For example, joint distribution of current
  streamflow and previous streamflow

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Independent RVs

• If the distribution of RV X is not influenced by
  the value taken by RV Y, and vice versa, the RVs
  are independent
• For two independent RVs, the joint probability is
  the product of the separate probabilities.

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Marginal Distributions

• Two RVs X and Y can have a joint distribution
• FXY(x,y)
• The marginal distribution of X is the
  distribution of X ignoring Y

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Conditional Distributions

• Conditional distribution of X given that Y has
  taken on a particular value

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Discrete RVs

• Conditional Distribution
• Joint Distribution
• Marginal Distribution

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Expectation
Note (expected value of X Mean of X)
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Variance
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Principle

• Replacement of uncertain quantities by either
  expected, median or worst-case values can grossly
  affect the evaluation of project performance when
  important parameters are highly variable.

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Example

• Elevation of reservoir water surface varies from
  year to year depending on the inflow and demand
  for water.

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Example

• Average pool level

• Average Visitation Rate

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Quantiles

• The pth quantile of a random variable X is the
  smallest value xp such that X has a probability p
  of assuming a value equal to or less than xp

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Quantiles

• X is a continuous RV
• p-th quantile is xp

equally likely to be above as below that value
range of values that the random variable might
assume.
pth quantile is also the 100-p percentile
Floodplain management - the 100-year flood x0.99
Water quality management - minimum 7-day-average
low flow expected once in 10 years 10th
percentile of the distribution of the annual
minima of the 7-day average flows
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Quantiles

• Observed values, sample of size n

• Order statistics (observations ordered by
  magnitude

• Sample estimates of quantiles can be obtained by
  using

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Flow Duration Curve
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Flow Duration Curve

• Flow duration curve - Discharge vs of time flow
  is equaled or exceeded.
• Firm yield is flow that is equaled or exceeded
  100 of the time

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Increase Firm Yield - Add storage

• To increase the firm yield of a stream,
  impoundments are built. Need to develop the
  storage-yield relationship for a river
• Simplified methods
• Mass curve (Rippl) method
• Sequent peak method
• More complex methods
• Optimization
• Simulation

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Simplified Methods

• Mass curve (Rippl) method
• Graphical estimate of storage required to supply
  given yield
• Constructed by summing inflows over period of
  record and plotting these versus time and
  comparing to demands
• Time interval includes critical period
• Time over which flows reached a minimum
• Causes the greatest drawdown of reservoir

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Rippl method
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Rippl Method
Capacity K
Accumulated Inflows, ?Q
Accumulated Releases, ?R
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Sequent Peak Method