Transcript Lecture 6

“The highest form of human intelligence is
the ability to observe without judging”
Krishnamurti
“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 gift”
Albert Einstein
“The mind is everything,
what you think you become”
Buddha
U6115: Climate & Water
Friday, 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
1) Precipitation
1) 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)
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
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
a. Weighing
b. Tipping bucket
Requires averaging of data over selected temporal/spatial scales
 precipitation
•
•
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
1) Precipitation
•
Temporal/Spatial variability!
1) Precipitation
Temporal variability  Need for averages (graphical or numerical)
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).
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
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:
xx
z
Sx
1) Precipitation
determination of exceedance probability using standard deviation,
mean, the normal distribution, and the normalization of the data:
xx
z
Sx
What is the probability that precipitation will exceed 1m in Seattle?
Mean = 941 mm
Std Dev = 176 mm
1) Precipitation
xx
z
Sx
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
1) Precipitation
xx
z
Sx
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
1) Precipitation
xx
z
Sx
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!
Fate of Precipitation
1)
2)
3)
4)
Interception
Infiltration
Runoff
Evaporation
Infiltration is influenced by
type of soil and vegetation
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.
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
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)
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)
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
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:
a) Mechanical energy is lost (dissipated) due to friction (roughness of bed)
b) 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)
Flood Routing
flood routing: prediction of downstream hydrograph, if the upstream
hydrograph is known
a)
b)
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.
Flood Routing
Prediction of downstream hydrographs requires
a)
b)
c)
d)
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:
a) Depth
b) 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:
Vn+1 - Vn/Dt = In +In+1/2 - On+On+1/2
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
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/(n+1), where r
is the rank of the particular
flood
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