Precipitation The beginning of the hydrologic problem Just

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Precipitation

• The beginning of the hydrologic problem
• Just as a watershed accepts precipitation as the
  beginning of its terrestrial cycle,
  hydrologists work with precipitation data at the
  beginning of analysis
• Classic problem Where does the rain go?
• Current research focuses on
• Measurement techniques
• Assessing spatial and temporal variability
• Very little recent work on process in hydrologic
  literature

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Precipitation

• The starting point for water resource analysis
• How much snow is in the foothills?
• What is the magnitude and intensity of rainfall
  that produces the 100 yr flood?

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Precipitation

• Our approach
• Formation of precipitation
• Appendix D 586-592, Chapter 4 pp 94-105
• Basic concepts
• Adiabatic cooling
• Mechanisms of uplift
• Atmospheric stabity
• Measurement and data analysis, Chapter 4 105-140
• Point measurement techniques
• Spatial variability and mean areal precipitation
• Temporal variability and probability
• Global distribution on your own
• Climatology on your own

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Formation of Precipitation

• Vapor to Liquid Transformation
• Moisture laden air must lower T, increase P, or
  reduce V

PV nRT Or K PV/T
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Formation of Precipitation

• 4 steps to form precipitation
• Air must cool to Dew Point
• Condensation nuclei must be present
• Droplets must grow
• Continuous import of vapor

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Formation of Precipitation

• Cool to Dew Point
• Absolute Humidity (Vapor density) ??
• Mass concentration of water vapor in a volume of
  air
• Vapor Pressure e
• Partial pressure of water in atmosphere

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Formation of Precipitation

• Cool to Dew Point
• Saturation Vapor Pressure e
• Maximum vapor pressure that is thermodynamically
  stable (??)
• What happens to e as the temperature of an air
  mass drops?
• What happens when e e

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Formation of Precipitation

• Cool to Dew Point
• Temperature at which e e
• Relative Humidity Wa
• Wa e/e
• What happens to Wa as temperature drops?
• What happens to e as the temperature drops?
• What is Wa at the dew point?

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Formation of Precipitation

• Cool to Dew Point
• Relative Humidity
• Calculate vapor pressure if relative humidy is
  36 and Ta is 15 C
• Relative humidity given Ta 5C and vapor
  pressure 0.6 kPa
• Dewpoint temperature if Ta 20C and Wa 52.4

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Formation of Precipitation

• 2. Condensation nuclei
• Fig D-7
• Water can not condense on itself except in very
  cold temperatures
• Basis behind cloud seeding
• http//www.hcountryrcd.org/cloud20seeding.htm
• http//www.usnews.com/science/articles/2009/11/19/
  modifying-weather-cloud-seeding-has-some-new-belie
  vers.html

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Formation of Precipitation

• 3. Droplets must grow
• Clouds are composed of water droplets too small
  to fall and survive evaporation
• Mostly ice in our lattitude
• Growth by
• Collision
• Vapor migration
• 4. Importation of water vapor
• A large cumulonimbus cloud would raing about 0.5
  cm onto the area it covers

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Formation of Precipitation

• 4 steps to form precipitation
• Air mass must cool to Dew Point
• Condensation nuclei must be present
• Droplets must grow
• Continuous import of vapor

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Whats an Air Mass

• A mass of air that contains relatively
  homogeneous temperature and density properties
• Size ranges from small convective masses to
  continental fronts

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How does an air mass cool?

• Radiation to a cooler surrounding
• Conduction to a cool surface
• Mixing with cold air
• Adiabatic cooling by horizontal movement
• Adiabatic cooling by vertical uplift

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Cooling an air mass

• Radiation, conduction, mixing, horizontal
  movement may form dew and fog

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Cooling of an Air Mass

• 5. Adiabatic cooling by vertical uplift is the
  only significant cooling mechanism for
  precipitation
• Adiabatic
• change in temperature without external forcings
  (no addition or removal of heat)
• Heating or cooling of a gas from pressure changes
• See figure D-6

• See Figure D-6

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Cooling an Airmass

• Adiabatic Lapse Rate
• Dry ALR occurs without condenstation and is
  constant at -1 c/100 m
• Wet ALR occurs during condensation is variable
• More or less cooling?

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Nest of lists

• Steps to form precipitation
• Air mass must cool to Dew Point
• Adiabatic cooling by uplift
• Uplift by
• Convergence of fronts
• Convection
• Orographic effects

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Lifting an Airmass

• Convergence of Fronts (boundaries between air
  masses)
• Air masses move to low pressure zones, or zones
  of convergence

• Air masses with different properties collide
• Cause extratropical cyclones
• Our main source of precip

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Lifting an Airmass

• Frontal convergence
• Cold Front
• Rapidly moving COLD mass collides with warm mass
• Steep snout rapid uplift

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Lifting an Airmass

• Frontal convergence
• Warm Front
• Slow moving WARM mass collides with cold mass
• Rises of over gentle tail of cold mass - slow
  uplift

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Lifting an Airmass

• 2. Convection
• Solar radiation heats surface rapid uplift

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Lifting an Airmass

• 3. Orographic Effect

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Atmospheric Stability

• Previous discussions assume that air masses CAN
  be lifted
• Atmospheric Stability A property of the
  atmosphere that promotes or inhibits vertical
  motion
• Stable vertical motions are suppressed
• Unstable vertical motions are promoted
• Depends or relationship between adiabatic lapse
  rate and ENVIRONMENTAL lapse rate

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Lapse Rates

• Environmental LR is the actual vertical
  temperature distribution in atmosphere
• Hold your hand out the window going up Bogus
  Basin Road
• Adiabatic LR is what happens inside a parcel of
  rising air
• Hold a balloon out the window

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Stable or Unstable
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Calculation

• Suppose a parcel of air initially at z 0, T 6
  C, and W 56 is forced over a mountain with an
  elevation of z 1600 m.
• What is the temp and Wa of the parcel of air at
  1600 m?

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Precipitation Measurement

• Hydrologists generally want to know
• How much (L)
• How long (t)
• Intensity (L/t)
• Where?
• Rain or Snow?
• Probability

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Precipitation Measurement

• Data Sources
• Several different agencies
• For real-time and forecasts
• National Weather Service
• http//www.nws.noaa.gov/
• What do Radar and Satellite data tell us?
• Data Archives
• http//www.wrcc.dri.edu/
• http//mesowest.utah.edu/index.html

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Precipitation Measurement

• Conventional data collected from Bucket Gauges

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Raw Precipitation Data
Discrete
Cumulative
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Precipitation Measurement

• Data Quality Issues
• How accurate are the point measurements?
• How do point measurements relate to larger areas?
• Spatial Variability
• How do instantaneous measurements relate to
  longer timescales
• Temporal Variability

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Precipitation Measurement

• What errors might you expect at the point of
  measurement?

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Precipitation

• Wind is a HUGE problem

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Spatial Distribution

• How do we estimate the spatial average

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Spatial Distribution
963 mm 77 Snow
Precipitation (mm)
335 mm 32 Snow
Rain
Snow
2008 Water Year
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Spatial Variability in Iowa
https//www.crops.org/publications/cs/articles/48/
4/1545
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Spatial Averaging

• How do we estimate the total precipitation over a
  large area with few gages?

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Spatial Average Methods

• How do we weight the importance of individual
  gages?
• Weighted Average
• Direct Average
• Theissen Polygon
• Surface Fitting
• Isohytetal
• Hypsometric

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Direct Average
-All gauges receive equal weight
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Theissen Polygon

• Weights are assigned by proximity to other
  stations
• agarea represented by gage g, A total area

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Spatial Average Methods

• Theissen Polygon
• Accounts for uneven distribution of gages

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Spatial Average Methods

• Surface Fitting Methods
• Contoured surface of spatially distributed
  precipitation
• Isohyetal methods
• Eyeball method
• Kriging
• Weights are assigned using precip data rather
  than station proximity

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Isohyetal Method
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Gauges are replaced by isohyetal
zones Precipitation in a zone is determined by
average of bounding contours
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Spatial Average Methods

• Hypsometric method
• Useful when topography has a significant effect
  on precipitation
• How much area is in any given elevation band?

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Hypsometric Method
P145047 cm
A1400-1500/A 0.13
Gauges are replace by elevation
zones Precipitation in an elevation zone is
determined from P-Z relationship
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Spatial Average Methods

• How do we measure representative areas?
• Geographic Information System
• Grid paper

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Temporal Variability

• Hydrologists are often asked to predict the
  response to design storms, or storms that have
  a certain probability of occurrence
• How will a river react to a 100-yr storm?
• What does a 100 yr storm mean?
• Lets review some probability concepts

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Basic Probability Concepts

• Probability
• Statistics
• Sample
• Population
• Independent
• Probability Function
• Probability Density Function
• Probability Models

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Basic Probability Concepts

• Discrete Probability
• What is the probability of rolling any given
  number on a die?
• Plot the probability function (eqn c4 and c5)

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Continuous Probabilities

• What is the probability that the total annual
  precipitation at a site is 300 mm?
• Requires continuous probability, or the
  probability that a variable is greater or less
  than a value
• PDFs and CDFs are use to estimate probabilities
  of continuous random variables

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Frequency Analysis

• The values of annual precipitation in College
  Station, Texas, from 1911 to 1979 are shown in
  the attached excel file.
• What is the probability that the annual
  precipitation R in any year will be less than 35
  in?
• Calculate Exceedence Probabilities for each value
• EPx(X)Pr(Xgtx)
• Pr(Xgtx) 1-Fx(x)
• How do we calculate Fx(x)?
• What is the return period of a total annual
  precipitation exceeding 45?
• T 1/EP

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Frequency Analysis

• For College Station, what is the value of the
  total annual rainfall with a return period of
• 2 years
• 25 years
• 50 years
• 100 years
• How do we estimate storm magnitudes with return
  periods greater than the length of our sample?

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Frequency Analysis

• In the previous example we interrogated the
  sample to answer questions about the population.
• What do we do when we want to estimate extreme
  values outside the sample?

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Frequency Models

• Fit a probability distribution model of the
  population to the sample
• Use statistics of sample (mean, standard
  deviation) to build a model of the population
• See table C-1, page 554
• Can use model of population, rather than sample,
  to extend the tails, or estimate extremes.

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Example Frequency Model The Normal Distribution

• Estimate the 100 yr annual P assuming that the
  population is normally distributed
• Fit Normal Distribution equation (C36) to the
  sample
• Calculate Z for each value
• C38
• Equation C36 is a model of the underlying
  population that we drape over the sample
• Graphically estimate 100 yr magnitude by
  plotting the model Normal CDF model
• OR, obtain Z for the probability of interest,
  calculate X.

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Normal Distribution

• Commonly applied to the Z standard variate
• Z (X-Xave)/stdev
• Mean 0, STDEV 1
• f(x-STDEV) 0.16
• f(xSTDEV) 0.84

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Depth Duration Frequency Curves

• In the previous example, we considered annual
  total P
• We can do the same for storms of specific
  durations
• Depth-Duration-Frequency Curves
• Describes the probability that a storm of a given
  depth and duration will occur in a year
• http//www.wrcc.dri.edu/CLIMATEDATA.html