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Youll find that the only thing you can do
easily is be wrong, and thats hardly worth the
effortNorton Juster The Phantom Tollbooth
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U6115 Climate WaterFriday, July 18 2003

• Water Properties
• Heat capacity, latent heat, saturation vapor
  pressure, etc
• Precipitation
• Condensation, rainfall (spatial temporal)
• Evaporation
• Evaporation, transpiration, mass/energy balance

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• 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 primary input of water to a
  catchment
• Evaporation is (often) the primary output from a
  catchment.

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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) ? they 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
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 years 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
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Fate of Precipitation

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

Infiltration is influenced by type of soil and
vegetation
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Evapotranspiration

• evapotranspiration summarizes all processes that
  return liquid water back into water vapor
• - evaporation direct transfer of water from
  open water bodies
• - transpiration indirect transfer of water from
  root-stomatal system
• water needed as well as solar energy
• of the water taken up by plants, 95 is
  returned to the atmosphere through their stomata
  (only 5 is turned into biomass!)
• potential evaporation (PE), i.e. the evaporation
  rate given an unrestricted water supply -
  different from actual evaporation
• how can the actual evapotranspiration be
  measured?
• water balance
• energy balance
• or combination of both

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Evapotranspiration
Apart from precipitation, the most significant
component of the hydrologic budget is
evapotranspiration. Evapotranspiration varies
regionally and seasonally during a drought it
varies according to weather and wind
conditions Slightly more than 10 of atmospheric
moisture (40,000 bg) is precipitated as rain,
sleet, hail, or snow in the conterminous USA. The
disposition of this precipitation is illustrated
below.
Evapotranspiration 67 (majority of loss
through transpiration) Runoff 29 Groundwater
outflow 2 Consumption 2
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Evapotranspiration
Estimates of average statewide evapotranspiration
for the conterminous United States range from
about 40 of the average annual precipitation in
the Northwest and Northeast to about 100 in the
Southwest. During a drought, the significance of
evapotranspiration is magnified, because
evapotranspiration continues to deplete the
limited remaining water supplies in water bodies
and soils
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Evapotranspiration
Estimation of ET 1) from the water balance this
approach may suffer from the uncertainties in the
numbers, example dV/dt p rsi - rso - et 0
? et   p rsi - rso p 1075x105 m3/y
(5) rsi 1091.5x108 m3/y (15) rso
9.95x1081.5x108 m3/y (15) Here, if we neglect
the groundwater inflows and outflows, we can use
these values to solve for et.
The results, accumulating the errors as we go,
is 1.5x1073x108 m3/y Unrealistic to expect to
be able to quantify accurately all terms in a
water balance for a catchment to solve for et,
especially over short periods where storage
changes are both substantial and difficult to
measure precisely (or predict). Diagnostic ? NOT
predictive approach
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Evapotranspiration
Estimation of ET 2) from the Energy balance First
Law of Thermodynamics conservation of energy
(E) Thermodynamic principles hold that the net
radiant energy arriving across the boundary of a
surface land system (including a very thin top
soil layer, vegetation, and immediate surrounding
air), must be exactly balanced by other energy
fluxes across the boundary and the net change in
energy held within the volume. Total incoming E
Outgoing E any increase in the bodys internal
E (DQ)
dQ/dt Rn-G-H-El Rn net (solar) radiation G
output (conduction) to the ground H output
(sensible heat) to atmosphere El output of
latent heat
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Evapotranspiration
Estimation of ET 2) from the Energy balance All
matter has internal energy (expressed in calories
or joules) a) Specific heat capacity provides a
measure of how a substances internal energy
changes with temperature Cp (dEu/m)/dT Water
has a specific heat of 1.0 cal/g.C or 4.2x103
J/kg.C b) Latent heat is the amount of internal
energy that is released or absorbed during phase
change (no change in temperature), at a constant
temperature. lv 2.5 - (2.18x10-3xDT) x106
J/kg At 20C ? lv 2.45x106 J/kg
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Evapotranspiration
Estimation of ET 2) from the Energy balance The
rate of evaporation can be described, in the
context of the energy balance equation, as an
energy flux dQ/dt Rn - G - H - El or El Rn -
G - H - dQ/dt Since the heat flux is related to
the rate of evapotranspiration (through latent
heat of vaporization) et El/(rwxlv) We can
then substitute this later equation into the
previous one et (Rn - G - H - dQ/dt)/(rwxlv)
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Evapotranspiration
Estimation of ET 2) from the Energy balance When
water is in limited supply, the surface becomes
warmer than in the wet cases and more energy is
removed from the control volume through
conduction in the the soil and heating of the
air. In this case the surface properties, rather
than the atmospheric conditions, are controlling
the rate of evapotranspiration. (eg. Higher winds
and lower saturation will increase evaporation
rate, while reduced solar radiation - clouds -
will reduce evaporation)
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Evapotranspiration
Estimation of ET 2) from the Energy
balance Relationship between surface wetness and
the partitioning of received energy between
evaporation and heating of air and soil
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Evapotranspiration
Estimation of ET 2) from the Energy balance The
rate of et that occurs under prevailing solar
input and atmospheric properties, if the surface
is fully wet, is commonly referred as Potential
Evapotranspiration (PET). For a catchment water
balance, we are interested in the actual et (rate
at which water is actually removed). When a
surface is wet et/PET 1, when it is dry et/PET
0
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Dams

• Reasons for dams building
• Water storage stable source in water quantity
• Reduction in flood risks
• Source of energy (hydroelectricity)
• Recreation
• Fire and farm ponds
• Irrigation (similar to 1)
• Waste disposal (mining, livestock)
• Navigation

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Dams
The US now has the capacity to store the
equivalent of almost a full years runoff in
reservoirs behind 80,000 structures
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Dams
Dams ownership and function
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Dams
Dams distribution in the US (National Inventory
of Dams USACE)
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Colorado Riverhydrograph

• Questions
• When does discharge peak and why?
• The hydrographs were taken at different locations
  of the river, what is the difference in the
  hydrographs and why is there one?

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Colorado River hydrograph

• Hydrographs are variable between years
• Discharge often peaks in late winter or spring,
  snowmelt

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Colorado River hydrograph

• Reservoirs smooth out extremes

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Colorado River

• Role of floods on ecosystems

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Dams

• Dams generate
• Reduction in sediment load

• Factors that control sedimentation
• Relationship between average grain size and
  energy of bottom currents

• Erosion, Transport and Deposition (sedimentation)
  depend on velocity of current and grain size
• Settling rate of suspended particles varies with
  diameter (Stokes Law)

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Dams

• Dams provide
• Stable source in water quantity
• Reduction in flood risks
• Source of energy (hydroelectricity)

• Dams generate
• Reduction in sediment load
• Questionable source in water quality
  (eutrophication, metals, etc)
• Reduction in water flow to coastal systems (Rio
  Grande, Colorado)
• Source of GHG (hydroelectricity)
• Impact on ecosystems (Hg, biodiversity)

• Reasons for removal
• Structural obsolescence
• Safety and Security
• Recreational oportunities
• Water quality and quantity issues
• Ecosystem restoration (and species protection)

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Dams
Dams removed in the US (National Inventory of
Dams USACE)