Precipitation

ENV* K245 Water Resources Engineering home

• the starting point of the hydrological flow through a watershed; it is the source of our freshwater
• rain or snow is the important form depending on climate
• if we’re going to know something about water management, we may as well start at the beginning

• Volume-Duration-Frequency
• Volume is the total amount of water that falls, usually expressed as an equivalent depth in inches or millimeters.
• Duration is the time for which precipitation occurs.
• Intensity is volume divided by duration, usually in inches per hour (or metric units).
• Frequency is how often or how likely a storm with a given volume and duration occurs.
• Can be expressed as either a return period, e.g., a 20-year storm, or as an exceedance probability, e.g., p=.05
• Note that these are inverse of one another: p = 1/T
• See p. 183
• Storms with greater volume and/or greater intensity occur with lower frequency
• There are tables that give expected volume for a given volume and duration (e.g., 24 storms for Connecticut) and tables or graphs that give intensity-duration-frequency relationships (e.g., idf for Hartford; see also Figure 4.4 on p. 187)
• These are location dependent.

• The rain rate is not constant.
• A graph of rainfall volume versus time is called a hyetograph.
• These are often simple bar graphs such as Figure 4.1 on p. 180.
• These are drawm from gage data, e.g., Table 4.1 on p. 181.

• the take home lesson here is that the amount of water vapor that the air can hold is determined by the temperature of the air
• if you put a wet sock around the bulb of a thermometer, the water will evaporate and cool the thermometer down to the temperature that corresponds to the saturation point for the moisture in the air
• this is also called the dew point or wet-bulb temperature
• a device with two thermometers, one covered with wet cloth, is called a psychrometer
• relative humidity can be obtained from the wet-bulb and dry bulb temperatures either using a table or the following formula:

where T is in °C

• What is the relative humidity for a wet bulb temperature of 16 C and a temperature of 20 C? (78%)

• small proportion of the atmosphere in comparison with the major gases: nitrogen, oxygen, argon
• the source of water that precipitates; it in turn derives from evapotranspiration
• most of the precipitation in the US is water evaporated from the ocean and moved by the prevailing air currents
• the presence of water vapor affects evaporation
• water vapor follows the gas laws within a range of pressures and temperatures encountered in practical situations
• an exposed water surface has a vapor pressure as does the water vapor in the air (the vapor pressure of the air is also called the partial pressure of the water vapor)
• if the vapor pressure of the water is higher than the partial pressure, there will be net evaporation
• if the partial pressure is higher than the vapor pressure, there will be net condensation
• if the two are equal, there is equilibrium
• at this point there is no net evaporation and the air is said to be saturated with water vapor
• Measures of Atmospheric Moisture
• these include:
• e = vapor pressure (millibars, pascals)
• the product of the volume percent of a gas and the overall pressure of the gas mixture
• r _v = absolute humidity (mass of water vapor per volume of moist air) (g/m³) (also known as the vapor density)
• q = specific humidity (mass of water vapor per mass of moist air) (g/g)
• r = mixing ratio (mass of water vapor per mass of dry air) (g/g)
• relative humidity (percent)
• dew point temperature (degrees)
• Amount of Precipitable Water
• this is simply all the water in a column of air of unit area:

• we say that area=1, so if r _v were constant, we could just say that m_w = r _v * D z; but alas in real life we have to use calculus:
<



(ouch!)

• we would need r as some function of z to integrate this and in fact we have the hydrostatic equation: dp = -r g dz
• the mass of water is usually converted to an equivalent depth by dividing by the density of water and the area (=1); thus precipitable water is usually given in inches; in theory, this is the maximum amount of rain that could possibly fall

• Variations in Precipitable Water
• the amount of precipitable water in the air depends on wind, temperature and atmospheric pressure
• there is more precipitable water near the ground, near the equator and near the ocean; however, the amount of precipitable water in the air does not necessarily indicate the amount of precipitation

• Condensation
• the formation of liquid water from water vapor
• can occur without precipitation (eg, clouds, fog...)
• caused by cooling:
• dynamic or adiabatic (expansion of air)
• mixing of warmer air with cooler air
• contact of warmer air with a cooler surface
• radiational cooling
• dynamic cooling is the most important for precipitation, the others are slower
• the last two are associated with dew, fog and frost
• water vapor will condense into cloud droplets on condensation nuclei
• these are 0.0004 inches in diameter, too small to fall (0.02 in. would be needed)
• hygroscopic materials like salt or acid particulates work best for this process
• overall the process is too slow to contribute substantially to precipitation
• Formation of precipitation
• fast enough processes include the ice crystal process and the coalescence process
• if you have water droplets and ice crystals mixed in the air (which you can have down to about -40°), the vapor pressure is lower next to an ice crystal than next to a water droplet, so additional vapor tends to condense onto the ice crystals
• ice crystals or water droplets fall faster the bigger they are (the terminal velocity is proportional to the square of the radius
• big droplets or crystals tend to catch up with and bump into the smaller ones, forming even bigger droplets or particles
• big big droplets can split up into littler ones which fuel the coalescence of bigger particles
• if one adds nuclei to clouds (such as silver iodide crystals) precipitation can be induced
• not a precise technique
• timing
• location
• ethical and legal as well as practical issues to be worked out
• hydrologic design to the present has been based on the assumption that precipitation is randomly distributed
• has been used to wash-out fogs near airports (but again legal issues abound)
• Types
• as air rises, it expands and undergoes adiabatic cooling (the amount of heat in the air mass remains the same, since the volume increases with decreasing pressure the average heat per unit volume = temperature decreases)
• this vertical motion is responsible for most of the cooling that leads to precipitation-causing condensation
• the type of vertical motion is used to classify the type of precipitation
• convective precipitation
• air masses are heated close to the earth’s surface; typically one area is heated faster than the surrounding area (eg, pavement and roofs); it then becomes a convection cell
• close to the surface, air also picks up moisture
• the heated air undergoes convection cycling
• as it rises it undergoes dynamic condensation (which releases latent heat driving the mass up still further)
• typical of the tropics; the rain may be light or intense as in a thunderstorm
• orographic precipitation
• air that rises over a mountain or similar feature can undergo dynamic condensation leading to orographic precipitation
• if all other factors are equal, rainfall will be proportional to elevation
• for such an area, a topographic map is also an isohyetal map (ie, the contours are lines of equal precipitation)
• the downwind side of a mountain may be a desert
• cyclonic precipitation
• air moves from areas of high pressure (anticyclones) to areas of low pressure (cyclones)
• the cyclones, which are hundreds of miles across, migrate to the east and into the temperate latitudes
• there they encounter colder air masses moving down from the polar regions
• when the warm and the cold collide, fronts are formed
• frontal precipitation
• warm air lifts up and over a mass of cold air
• if the warm air is moving, pushing along the cold, there’s a warm front; the rain travels 200-300 miles ahead of where the front touches the ground
• if the cold air is moving, pushing up the warm, there’s a cold front; the boundary tends to go up more vertically so the zone of precipitation is narrower (about 100 miles ahead to a little behind the front)
• cold fronts tend to move faster and produce heavier rain, especially right at the surface front; usually followed by clear and cold weather
• if the masses are not moving horizontally, there’s a stationary front
• nonfrontal precipitation
• as air spirals into low pressure areas, it pushes against itself and up, expanding...
• Thunderstorms
• severe convective storms are often associated with lightning (and thunder)
• these may not be significant contributors to longterm average levels of rainfall; but in a short period of time rain can fall at rains of 1 in. per hour or more
• rainfall at such a high rate can have a higher than normal rate of runoff, doubly contributing to local flooding
• T-storms develop in three stages:
• the cumulus stage
• intense surface heating or some topographic feature causes a strong updraft
• the rising air draws in moisture laden air from the sides
• the rising air produces rapid dynamic condensation
• this condensation is visible as cumulus clouds, which extend up to about 25,000 feet
• the mature stage
• after about 15 minutes, rain, snow and ice start to form at the top of the cloud
• rain becomes heavy in the center of the storm
• the falling snow and ice rapidly cool the air below; so while the rapid condensation may be forming violent updrafts at the top of the cloud, downdrafts form lower down
• the falling air creates outward gusts
• the dissipating stage
• after about 15 to 30 minutes of heavy rain, the storm has run its course
• the energy driving the updraft has been spent
• with no new air reaching the upper levels, the top of the storm begins to blow away
• the downdraft continues, but the falling air is being compressed and warm so the downdraft fades
• precipitation moderates and stops

• Data
• obtained using rain gauges
• recorded by the Environmental Science Service Administration, National Weather Service, USDA SCS (now NRCS), state and local agencies and by some other entities
• Substantial precipitation data is available online from http://www.ncdc.noaa.gov/oa/climate/climatedata.html
• Variability
• spatial
• precipitation varies regionally (see maps on p. 185)
• can vary locally, but it’s hard to tell when small scale variations represent differences in precipitation or in measurements
• wind and nearby obstructions tend to lower the readings at gauges

• the more gauges that are used, the more reliable the readings
• see Fig 2.8, p 29
• more gauges are needed to assess a larger area; but the number of gauges needed per area is smaller
• the number of gauges necessary increases roughly with the square root of the area to be assessed (see Tab 2.3, p30)

• within an area, the average rainfall is something less than the maximum rainfall at the center of the storm (see Fig 2.7, p 27; see also areal precipitation below)

• temporal
• time course of rainfall during a storm can affect runoff
• measured using a recording rain gage
• seasonal variations can be important for farming or outdoor activities

• the extent of precipitation at a single location is determined directly using a rain gauge (a variety of them is pictured on p 31)
• if the point of interest was not checked with a gauge, we can estimate the precipitation at that point by taking a weighted average for nearby points
• the weighting factor is one over the distance squared between the measurement point and the point of interest
• you sum the measurements * the weighting factors and divide by the sum of the weights:

• point precipitation data is used to draw up intensity-duration-frequency curves (see fig 2.9)
• these are used for flood control planning

• a crude estimate of precipitation for an area can be obtained by taking the reading a a single point in the area or by averaging several points
• generally, a single point estimate is better for:
• points near the middle of the area
• for smaller areas
• for longer periods of time
• We can take an arithmetic average of the gauge readings
• Isohyetal method
• a better approach is to draw up an isohyetal map; the countours on this map are used to separate the area into isohyetal segments (where P = the mean of the value for the boundary contours)
• the precipitation for the area is then given as:

• Theissen method
• the same formula is used, but the segments are drawn by bisecting the lines drawn between stations; the bisecting lines are connected to form a network of polygons
• not suitable for mountainous regions
• Accuracy
• for any method the spacing and location of the gauges will affect the accuracy of the estimate for the area or any point within it

• we often speak of the 2 year storm or the 10 year storm or the 25 year flood etc
• the T-year storm or flood is the storm or flood of intensity that will on the average be met or exceeded once in T years
• we can also talk about an T-year drought or low Q_N which would be the conditions equaled or gone less than on the average once in T years
• T is called the recurrence interval or return period
• these things are surprisingly easy to calculate from a series of yearly data
• generally speaking we want at least 10 years of data or T/2 whichever is greater (eg, we can estimate the 100 year storm from 50 years of data)
• the general idea is to draw up a plot of intensity versus frequency or probability (on probability paper) and read off the intensity that corresponds to 1/T
• to do this:

• we are assuming that we’re looking for rare high values

1. plot each item above its probability
2. sketch the line that fits the points and find the rainfall, etc, that corresponds to P=1/T

• a very similar thing could be done mathematically:

1. find the mean and standard deviation of the items:

mean = X = å x/n


2. look up in a table of z values (ie, the normal distribution) the z value corresponding to P=1/T, call this value K (the z value for the
   entry=0.5-P)
3. our T-year event is then given by:

• this is an estimate of worst-case rainfall expected for an area
• it is based on the assumption the each variable that contributes to rainfall is simultaneously at its most extreme value

• the amount of precipitation that ends up as runoff is sometimes called net precipitation or excess precipitation
• its defined at total precipitation less interception, ongoing evaporation, depression storage, and infiltration

• as the rain comes down, it can encounter several fates: interception, depression storage, overland runoff, infiltration
• water intercepted by leaves and other obstacles will either continue down or evaporate
• water in depressions will eventually evaporate or infiltrate
• infiltrated water may become soil moisture, evaporate, travel a short distance as interflow, or join groundwater
• early in a storm, interception and depression storage get the water, infiltration peaks next after which overland flow rises
• the infiltrated portion follows its own time course as well
• soil moisture is replenished first, after that interflow and groundwater recharge and flow occur
• the actual amount and rate of runoff for a particular event depend on a number of factors including:
• vegetation
• soil type and condition
• type, quantity and time of precipitation
• soil moisture conditions
• land use
• topography and geology of basin
• conditions of stream channels
• a distinction is made between large and small basins
• small basins, which can actually be up to 100 mi², show the effects of short high intensity storms and land use

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Anthony G Benoit  abenoit@trcc.commnet.edu
(860) 885-2386

Revised