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The highest form of human intelligence is the
ability to observe without judgingKrishnamurti
The intuitive mind is a sacred gift and the
rational mind is a faithful servant. We have
created a society that honors the servant and has
forgotten the giftAlbert Einstein The mind
is everything,what you think you becomeBuddha
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U6115 Climate WaterFriday, July 11 2003

• Precipitation
• Condensation, rainfall (spatial temporal)
• Streams Floods
• Nature and cause of floods
• Definitions
• The hydrograph
• Discharge vs. time
• Flood prediction
• Flood routing
• Flood frequency analysis

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• 1) Precipitation
• Most of the precipitation falling on Continental
  USA originates from bordering oceans (up to
  30-40 of precipitation over large land is
  derived from local evaporation)

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1) Precipitation

• Spatial distribution dependent on
• Latitude
• Elevation
• Distance from moisture source
• Position within continental land mass
• Prevailing winds
• Relation to mountain ranges
• Relative Tº of land and bordering oceans

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1) Precipitation

• Point measurements (depth)
• How do you measure precipitation?
• How do you extrapolate specific point
  measurements to an overall area?

• Non-recording vs. recording gages
• Weighing
• Tipping bucket
• Requires averaging of data over selected
  temporal/spatial scales

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1) Precipitation

• However, record at any given point tends to be
  tremendously variable in time!
• Temporal record (hourly, daily) of precipitation
  ? hyetograph

? Precipitation is commonly organized into
discrete storm events of varying intensity and
duration! ? Our ability to forecast temporal
variation is limited to within a few hours
(depending on the system), and is almost zero for
a few days in advance!
? Event-based processes uniformitarianism vs
catastrophism
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1) Precipitation

• Temporal/Spatial variability!

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1) Precipitation
Temporal variability ? Need for averages
(graphical or numerical)
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1) Precipitation
Precipitation intensity ? rate of precipitation
over a specific time period (precipitation depth
divided by time over which the depth was
recorded) ? Average precipitation intensity
depends, by necessity, on the time period of the
computation (longer time, lower intensity) ?
Relative measure of the likeliness of certain
magnitudes of precipitation (probabilistic
approach only appropriate under certain
conditions).
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1) Precipitation
Precipitation intensity (Temporal characteristic
of precipitation) hydrologists apply a technique
called frequency analysis to describe the
temporal characteristics of precipitation we
assume that precipitation data are samples of a
random variable characterized by a probability
density function only mean annual precipitation
appears to be normally (or Gaussian) distributed
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1) Precipitation
Precipitation intensity (Temporal characteristic
of precipitation) precipitation can be described
by a mean and a standard deviation this
information is useful to determine the exceedance
probability (the probability that a certain
annual precipitation value is exceeded in a given
year) or the return period - the inverse of the
exceedance probability).
determination of exceedance probability using
standard deviation, mean and the normal
distribution
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1) Precipitation
determination of exceedance probability using
standard deviation, mean, the normal
distribution, and the normalization of the data
What is the probability that precipitation will
exceed 1m in Seattle? Mean 941 mm Std Dev 176
mm
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1) Precipitation
What is the probability that precipitation will
exceed 1m in Seattle? Mean 941 mm Std Dev 176
mm Z 0.34
The cumulative distribution function (cdf) for a
chosen value is the probability that a random
process (x) will be less than or equal to the
chosen value
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1) Precipitation
What is the probability that precipitation will
exceed 1m in Seattle? Mean 941 mm Std Dev 176
mm Z 0.34
? 37 chance of exceedance Treturn 1/exceedance
then Tr 3yrs
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1) Precipitation
What is the 100-year rain event in Seattle? cdf
0.99 Z 2.33 Mean 896 mm Std Dev 183 mm X
1322 mm 1900-2002 ? Once!
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Fate of Precipitation

1. Interception
2. Infiltration
3. Runoff
4. Evaporation

Infiltration is influenced by type of soil and
vegetation
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Nature and Cause of Floods
Fate of Precipitation ? runoff Rivers respond to
precipitations Basic quantity to be dealt with is
river discharge (as related to rain events) ?
rate of volume transport of water (L3/t) What is
river discharge and how do you measure it? Both
river discharge and depth (stage) change with
time.
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1) Nature and Cause of Floods
A river discharge is (usually) not measured
directly ? inferred from stage (height) hydrograph
Rating curves typically are nonlinear and often
are approximated using power functions Q
76.5(stage)4.1 e.g. If stage peaks at 0.35m
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Nature and Cause of Floods
Rating curves typically are nonlinear and often
are approximated using power functions Q
76.5(stage)4.1 e.g. If stage peaks at 0.35m (at t
6 hours), then the corresponding peak discharge
is Q 76.5(0.35)4.1 1.0 m3.s-1
This way, a continuous measurement of river stage
is used, in conjunction with established rating
curve, to determine discharge as a function of
time (almost all discharge hydrographs are
determined this way)
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Nature and Cause of Floods
The nature of each hydrograph depends upon
watershed and storm characteristics ? strong
relationship between hyetograph (precipitation)
and hydrograph (stream runoff)
-) The resulting peak in the hydrograph is called
a flood regardless of whether the river actually
leaves its banks and causes damage! -) Background
discharge between floods is called baseflow and
is supplied by inflow of groundwaters (Sta Cruz
river in AZ)
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Nature and Cause of Floods

• in rivers, floods and low flows are expressions
  of the temporal variability in rainfall or
  snowmelt interacting with river basin
  characteristics (basin form, hillslope
  properties, channel network properties)
• flooding may also be the result of sudden
  release of water from dams or lakes, ice jams
• floods cause the biggest natural hazard damage
  in the US, example Mississippi flood, 1993
  Honduras, Hurricane Mitch

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Movement of flood wave

• Flood ? may be thought as wave that propagates
  downstream.
• In an ideal channel (frictionless fluid) flood
  wave travels with no change
• However
• Mechanical energy is lost (dissipated) due to
  friction (roughness of bed)
• Water also stored in pools, wetlands, and
  backwaters, and is subsequently released (delay)

Thus magnitude of flood wave is reduced and its
transfer is delayed as it travels
downstream Attenuation by friction and storage
(normalization is critical practice)
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Flood Routing

• flood routing prediction of downstream
  hydrograph, if the upstream hydrograph is known
• How quickly a flood crest travels downstream
• How the height of the crest changes as it travels
  downstream

flood routing in rivers and by reservoirs dV/dt
I-O
Typically, in hydrology problems like these
cannot be solved by differentials but must be
solved numerically? transforming the equation
into one or more algebraic equations that can be
solved more easily.
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Flood Routing

• Prediction of downstream hydrographs requires
• An estimate of speed of wave crest
• An estimate of the volume added by inflow
• Influence of friction
• A complete understanding of hydrology
  hydraulics of drainage basin

• The 2 most important variables
• Depth
• velocity
• dV/dt I-O

Solving this equation requires 2 equations -)
statement of conservation of mass -) conservation
of momentum Need numerical method to transform
DFQ into algebraic one Vn1 - Vn/Dt In In1/2
- OnOn1/2
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Flood Routing

• Reservoirs size and volume affect the routing
  very rapidly. When reservoirs increase in size
  (and volume) ? store more water and rise in water
  (h) is smaller ? increase in outflow is smaller
  (delay and reduction of O).
• A flood wave in rivers, on the other hand, must
  move through a long stretch of river before peak
  discharge is reduced as much as moderate-size
  reservoirs can accomplish in a relative short
  distance

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Flood Frequency Analysis
simplest approach use worst event on record
past record key for the future? Statistical
techniques use the following approach highest
discharges recorded in each year are listed the
floods are ranked according to magnitude, the
largest flood is assigned a rank 1, the second
largest rank 2, etc
The flood statistics are estimated graphically by
plotting the logarithm of discharge for each
flood in the annual series against the fraction
of floods greater than or equal to that flood
this fraction is given by r/(n1), where r is the
rank of the particular flood
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Flood Frequency Analysis
The return period, the average span of time
between any flood and one equaling or exceeding
it, is calculated as Treturn 1/(exceedance
probability). The 100 year flood can then be
estimated from the graph Normal distribution
works often well with precipitation data and ln
normal for discharge Problems not
deterministic, based usually on non-adequate
data, climate and terrestrial environment is
variable