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AOM 4932 - Atmospheric Water and Precipitation
Distribution of atmospheric moisture in space and time. In general:
1
- water vapor by volume (% of total) decreases with elevation (most within 5
km, > 8 km approximately none)
2
- specific humidity = v/moist increases and decreases seasonally with
temperature (warm air can hold more water vapor)
3
- specific humidity is highest in the tropics and lowest in the poles (for same
reason as 2)
4
- relative humidity = v/moist shows peaks both in tropics and in poles -minimum at high pressure regions (30 - 40)
low moist.
low temp
qv
high moist
high temp
Rn
low moist
intermed. temp.
high press
anti cyclone
90 N
0
90 S
90
60
90 S
Sahara
Mojave
30 N 0
30
60
Australia
Peruvian-Andea
n desert
Knowledge of vertical and horizontal spatial distribution of moisture allows computation of
potential precipitable water in an area. However, for precipitation to occur atmospheric
moisture must condense. In the atmosphere this typically occurs when air temperature is
lowered when the air mass is forced to rise.
Formation of Precipitation Requires:
1 - Cooling of air to  dew point temperature (requires a lifting mechanism)
2 - Condensation of water vapor onto nuclei (dust, ions) to form droplets
3 - growth of droplets so that
a) terminal velocity  updraft velocity
b) sufficient mass of liquid to survive evaporation on way down
4 - Importation of water vapor into cloud to replace precipitation and sustain process
1 - Lifting Mechanisms
Three meteorological situations which lead to vertical uplift of air masses:
a) uplift due to convergence
 Nonfrontal convergence of air masses with equal temperature to a low pressure
point (i.e. at ITCZ due to convergence of NE/SE tradewinds).
Generates moderate rainfall over long duration.
 Frontal convergence of air masses of different air temperature. Produces cold
fronts/warm fronts.
warm front - Occurs when warm air impinges on cold. Two air masses do not mix. Warm
moist air is less dense, rises over cold air at relatively gentle slope. Warming occurs gradually
resulting in more moderate storms which last longer. See high clouds first
cold front - Cold air impinges on warm air. Again do not mix but cold air moves under warm
forcing it upward. Get a steeper sloped interface. Rapid cooling, stronger storms of shorter
duration. See low clouds first
b) uplift due to convection
Convective cells are initiated by heating of lower air mass by ground surface. Cause instability
of air column because of density differentials (  T,  ). Lower air density rises and cools and
condenses (releases heat  sustains process) leads to thunderstorms. High intensity, short
duration events which occur mainly in the tropics. Typically originate over land mass in central
Florida during summer when ground heats rapidly during the day.
c) uplift due to orography
Occurs when air mass is forced to rise over air obstruction such as a mountain. Pronounced on
central west coast of N. America where moist winds off the Pacific hit series of mountain ranges
parallel to coast. In most regions of world mean precipitation increases with elevation.
2 - Condensation/Nucleation Mechanisms
Initiation of condensation typically requires a seed or condensation nucleus around which the
water molecules can attach to overcome high activation energy 9activation energy is surface
energy related to interface of coexisting phases). Impurities in the air (dust, salt, ions, ice
crystals, volcanic material, smoke, clay) act like catalysts and reduce activation energy so that
condensation will occur (cloud condensation nuclei - CCN)
 Without nuclei, condensation rates will be very low even for e  4es. Air usually contains
lots of particles that can act as nuclei ( 10-4 mm, attract H2O via H bonds) so get condensation at
e  es.
Sometimes water management agencies try cloud seeding. Fly over and distribute silver iodide
in atmosphere to induce droplet formations. Not particularly effective since concentration of
CCN not usually limiting factor for rainfall.
3 - Droplet growth
Before falling, condensed droplets must grow to size and weight capable of overcoming (1)
updraft velocities in the cloud and (2) evaporation.
Growth occurs by coalescence as raindrops collide on the way down. Big drops fall faster than
little ones so they catch up, hit them and absorb them.
4 - Importation of Water Vapor
Concentration of liquid water and/or ice in most clouds is in the range of 0.1 to 1 g/m3. Even if
all this water in a very tall cloud were to fall as rain the total depth of precipitation would be
small.
(10,000 m tall cloud) * (0.5 g/m3) = 5000 g/m2
 0.5 cm per unit area
Final requirement for occurrence of significant amount of rainfall is that a continuous supply of
water vapor must be imported into cloud to replace what falls out.
Inflow of moisture is provided by winds that converge on rain producing clouds.
Analysis of Rainfall Data
Storms are classified by “exterior” and “interior” characteristics.
Exteriors are a set of characteristics which define general storm properties, i.e.
a) total storm depth
b) duration
c) time between storms
d) areal extent
These characteristics are generally accepted to be probabilistic in nature.
Interior characteristics refer to time and space distribution of a particular storm,
a) hyetograph - plot of rainfall depth or intensity vs. time
intensity
or depth
time
b) cumulative hyetograph - sum of rainfall depth vs. time
% cumulative
rainfall or inches
cumulative
rainfall
time
Max. intensity (depth) recorded in a given time interval, as interval , max. intensity . Index of
storm severity.
Calculate running totals of depth (or average intensity) for time interval of interest, select max.
value  indicator of storm severity.
c) isohyetal maps - contour map showing lines of equal rainfall depth
4
8
6
4
2
Important design criteria:
average depth of rainfall
over an area.
 area,  depth (intensity)
Rainfall measurements almost always taken at a point or several points in a drainage basin. Two
accuracy problems:
1) how accurate are point measurements
2) how accurately can point measurements be converted to areal estimates
Long term studies have shown that errors due to evaporation, wind currents, obstructions, and
reading errors in point rainfall measurements vary from 5% to 15% for long-term data and as
high as 75% for individual storms:
 Most accurate - Weighing recording gage which continuously collects rainfall and records
weight over time. $$$$
 Least accurate - Standard rain gage. Measures accumulated depth at a point. Get only
volume rain since last reading accuracy  1/10th inch  evaporation problems
 Most common - Tipping bucket rain gage. Records number of tips of bucket with known
volume over time. Intermediate cost and accuracy. Often under-records during heavy
rainfall events.
Estimation of Areal Precipitation from point measurements
Most often interested in quantifying rainfall over an entire watershed. Has to be inferred from
some sort of weighted average of available point measurements P(xi)

N
P    i P ( xi )
point
measurement
i 1
weight (depends
on method)
Several methods to determine weights. All require
0  i  1
 i  1
Weighting Methods
a) Arithmetic average:
i 
1
N
all weights equivalent

1
 P( xi )
N
Method OK if gages distributed uniformly over watershed and rainfall does not vary much in
space.
P
b) Theissen Method
 i - Measure of rain-gage contributing area. Assumes rain at
any point in watershed equal to rainfall at nearest station.
To determine  i :
1. draw lines between locations of adjacent gages
2. perpendicular bisectors drawn for each line
extend to form irregular polygon areas
A1 P1

A2
 P2



P    i P ( xi ) 
A3
 P3
P4
A4
area polygon contributing to i Ai
i 

total area of watershed
A

1
 Ai P( xi )
A

More accurate than arithmetic mean method for irregularly spaced rain gauges but does not
account for possible systematic trends in rainfall distribution such as those caused by orography.
A2
P  1 12 in.
c) Isohyetal Method:
area between isohyets
i 
total watershed area

P    i P ( xi )
mean precipitation
between two isohyets
(1/2(Pi-+Pi+))


4 in.
1 in.


3 in.
2 in.



This is most accurate method if have a sufficiently dense gage network to construct an accurate
isohyetal map. Can account for systematic trends, i.e., orography, distance from coast.
Hydrologic Frequency Analysis
Extreme rainfall (and flood/drought) events are typically of concern in engineering hydrology
[dams, bridges, culverts, flood control structures].
Magnitude of an extreme event is inversely related to its frequency of occurrence.
Frequency analysis of historic data relates the magnitude of extreme events to their frequency of
occurrence through the use of probability distributions.
Return period (T) of an event is the average time (recurrence interval) between events greater
than or equal to a particular magnitude.
For example, 25 year return period storm occurs on average once every 25 years and has a
probability of 1/25 of occurring in any one year.
1
1
Mathematically,
T    
 P x  x T  
P
T
time between
storms
probability storm
PP PPxx  xxTT   probability
storm  specified
specifiedvalue
value
What is probability T-year return period will occur once in N years?
Probability does not occur P(x < xT)=(1-P)N
(never occurs in 10 years)
N
Probability occurs at least once in N years = 1 - (1-P)
= 1 - (1-1/T)N
For example, 10 year return period storm has prob. of occurrence 0.1 in any 1 year. How
probable once in 10 years?
T = average recurrence interval for event is 10 years
Probability of occurrence in any one year = 1/T
Probability = 1 - (1-1/10)10 = 0.651 at least once in ten years
How to estimate return period from flood rainfall records
1 - Select annual maximum rainfall of a particular duration from rainfall record to form annual
maximum series.
2- Rank annual maximum from largest to smallest.
rank
3 - Prob.(x > xm) =
m
N 1
probability of
exceeding storm
with magnitude xn
or
T
N 1
m
total number
years of record
(data points)