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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 PPxx 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)