1
I dream of rainI dream of gardens in the desert
sandI wake in painI dream of love as time runs
through my handI dream of rainI lift my gaze
to empty skies aboveI close my eyes, this rare
perfumeIs the sweet intoxication of her
loveSting Desert Rose
2
U6115 Climate WaterTuesday, Aug. 09 2004

• Precipitation
• Condensation, rainfall (spatial temporal)
• Streams Floods (Nature and cause of floods)
• The hydrograph
• Discharge vs. time
• Flood prediction
• Flood routing
• Flood frequency analysis
• Case Studies
• Spatial variability in streamflow
• Impervious surface area (ISA) and streamflow
• Watershed hydrology and contaminant transport

3
Perturbations Catastrophic Shifts in Ecosystems
Scheffer et al., 2001. Catastrophic shifts in
ecosystems. Nature 413591-596.
4
Hysteresis in a Shallow Lake
Scheffer et al., 2001. Catastrophic shifts in
ecosystems. Nature 413591-596.
5

• Water Precipitation/Evaporation
• Temporal and spatial change in energy of
  atmosphere will affect the amount of moisture and
  thus heat transfer
• Regional water mass balance will be affected.
• Precipitation is the primary input of water to a
  catchment
• Evaporation is (often) the primary output from a
  catchment.

6

• Catchment
• Catchement (drainage basin, watershed) the basic
  unit of volume (control) which is an area of land
  in which water flowing across the land surface
  drains into a particular stream and ultimately
  flows a single point or outlet.

dV/dt p - rso - et 0 on average ? p   rso
et
7
Catchment

• Our concern with precipitation and
  evapotranspiration is in knowing the rates,
  timing, and spatial distribution of these water
  fluxes between the land and the atmosphere.
• dV/dt p - rso - et 0

8
Water in the atmosphere - thermodynamic
properties of moist air

• Describing amounts of water vapor in the
  atmosphere.
• There are a few ways to report the concentration
  of water vapor in the atmosphere.
• 1. Vapor pressure (denoted e) is the partial
  pressure of water vapor molecules in the
  atmosphere.
• 2. Relative humidity is the ratio of actual
  vapor pressure to saturation vapor pressure
• 3. Mixing ratio is the mass of water vapor in
  grams per kilogram of air.
• 4. Dew point temperature the temperature at
  which the vapor in a cooled parcel of air begins
  to condense.

9
Water Vapour Pressure vs. Temperature
Three primary steps in the generation of
precipitable water in atmosphere

1. Creation of saturated conditions
2. Condensation of water vapor
3. Growth of small droplets by collision and
   coalescence

10
Dew Point Temperature
11

• Precipitation/Evaporation
• Why?
• Precipitation ? Supply of freshwater (surface
  water system)
• Evaporation ? Reduction in supply (and effect on
  quality!)

• Water management
• Prediction of precipitation
• Estimates of evaporation (water-agriculture)
• Estimates of runoff

12

• 1) Precipitation
• Creation of saturation conditions (changing Tº)
• Mountain range
• Cold fronts

13

• 1) Precipitation
• Condensation of water vapor into liquid water
• The importance of nuclei (salts, particles, water
  droplets)

14

• 1) Precipitation

• Growth of small droplets
• Condensation only leads to droplets ?m in size
  whereas rain drops are mm is size ? coalescence
  through collision

15

• 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)

16
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

17
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

18
Hydrologic Observations and Parameters
The value of hydrologic observation over time or
location (i.e. precipitation) cannot be known
exactly. Thus virtually all hydrologic
quantities are random variables and hydrologic
observation must be regarded as samples taken
from some probability distribution (which is a
theoretical relation between magnitude and
probability) ? Statistical analysis
(particularly estimation of the probability
distributions that quantify magnitude-frequency
relations) constitutes the principal means by
which hydrologic observations are transformed
into terms that are useful for water-resource
management.
19
1) Precipitation

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

? Precipitation is commonly organized into
discrete storm events of varying intensity and
duration! ? Our ability to forecast temporal
variation to within a few hours is limited
(depending on the system), and is almost zero for
a few days in advance!
? Event-based processes uniformitarianism vs
catastrophism
20
1) Precipitation

• Temporal/Spatial variability!

21
1) Precipitation
Temporal variability ? Need for averages
(graphical or numerical)
22
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).
23
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
24
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
25
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
26
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
27
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
28
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 1900-2003 ? Once!
29
Precipitation Forecasts
International Research Institute for Climate
Change (Lamont)
30
Precipitation Forecasts
International Research Institute for Climate
Change (Lamont)
31
Precipitation Forecasts
International Research Institute for Climate
Change (Lamont)
32
Precipitation Forecasts
International Research Institute for Climate
Change (Lamont)
33
Fate of Precipitation

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

Infiltration is influenced by type of soil and
vegetation
34
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.
35
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
36
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)
37
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)
38
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

39
Nature and Cause of Floods
Floods cause the biggest natural hazard damage in
the US
Bangladesh Monsoon (2004)
Mississippi flood, 1993
Honduras, Hurricane Mitch (1998)
40
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)
41
Streamflow Frequency
As drainage area decreases, greater proportions
of annual discharge occur during smaller amounts
of time. Put another way, the occurrence of
brief, but intense, flood events is a more
important part of annual discharge in watersheds
of decreasing size
Dalzell et al (2005). Biogeoscience.
42
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 differential equations but
must be solved numerically? transforming the
equation into one or more algebraic equations
that can be solved more easily.
43
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
44
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).
45
Flood Routing
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
46
Flood Routing
Folsom Reservoir In 1995, a partial failure of a
spillway gate at Folsom Dam increased flows into
the Lower American River from 6,500 cubic feet
per second to about 40,000cfs.
47
Flood Routing
Folsom Reservoir 1944 Folsom Dam Authorized The
Flood Control Act of 1944 authorized the U.S.
Army Corps of Engineers (Corps) to build a dam on
the lower American River
1956 Record Flood Though engineers had been
predicting it would take a year to fill the
nearly completed Folsom Dam, the second record
storm filled the dam in a week and Sacramento is
saved from flooding. 1964 Record Flood The third
record flood in less than 15 years causes
engineers to re-evaluate storm frequency. They
conclude the storm Folsom is designed to handle
is a 120-year storm not a 500-year storm. 1986
Record Flood The February 1986 storm dumps 10
inches of rain on Sacramento in 11 days. The
American River dumps more water into Folsom than
it is designed to handle. After 2 days of
releases at the design level, (115,000 cubic feet
per second (cfs)), officials boost releases to
134,000 cfs. Folsom performance downgraded to
about a 60-year storm
48
Flood Frequency Analysis

• simplest approach Is the past record the key for
  the future?
• Statistical techniques use worst event on record
• highest discharges (peak flow) 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 and n is the number
of observations (years)
49
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 years flood can then be
estimated from the graph Normal distribution
works often well with precipitation data and peak
discharge Problems not deterministic, based
usually on non-adequate data, climate and
terrestrial environment is variable
50
Flood Frequency Analysis
Not all peak streamflow data are lognormally
distributed ? skewness
51
Impervious Surface Area and Streamflow
The amount of ISA in the conterminous U.S. now
covers an are equivalent to Ohio.
52
Impervious Surface Area and Streamflow
There exists a relationship between increase in
ISA extent and streamflow.
53
Impervious Surface Area and Streamflow
In this case, the increase in streamflow is
independent of rainfall
54
Streamflowand Contaminant Transport