SUSTAINABLE AG SYSTEM
SUSTAINABLE AG SYSTEM AOM 4932
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AOM 4932 Evaporation and Transpiration Evaporation change of water from its liquid to its vapor phase Potential Evaporation climatically controlled evaporation from a surface when the supply water to the surface is unlimited Transpiration evaporation occurring from plant s leaves through stomatal openings Function of stomata is to provide a place where C02 can dissolve into water and enter plant tissue Evaporation unavoidable in this process driven by same process as evaporation Ratio of water transpired to that used to form plant matter very large gt 800 Potential transpiration Transpiration which would occur if water supply to plant roots and through vascular system to stomata was unlimited Controlled by climate and plant physiology Two main forces in uencing evaporation rate are 1 Supply of solar energy to provide the latent heat of evaporation 2 Ability to transport evaporated water away from surface gt affected by wind velocity and vapor gradient Transpiration affected by above plus ability of plant to extract and transmit water from soil to stomata We will discuss four methods of estimating evaporation from free water surfaces or completely saturated soil 1 energy balances methods 2 mass transfer or aerodynamic methods 3 combination of energy and mass transfer Penman 4 pan evaporation data 1 Energy Balance Method Assumes energy supply the limiting factor Consider energy balance on a small lake with no water inputs or evaporation pan sensible heat net energy used in transfer to air radiation evaporation f H5 R f Q V heat stored in system heat conductec o ground typically neglected Energy balance in ows out ows assuming water temperature does not change no ow into or out of lake Rn Q6 HS G RnR1 ARl1 Al Rb are atim e eEw evaporatlon rate energymass depthtime or density of water volum eareatime m assvolume HS sensible heat ux to atmosphere by convection and G heat conducted to ground are typically small and difficult to measure Neglect G and HS and substitute equation of Q6 Rn Qe Epre E R evaporation rate pre depthtime Note Assumes 1 no water in owout ow to lake 2 no change in water temperature of lake 3 neglects sensible heat transfer to ground and atmosphere 4 neglects heat energy lost with water which leaves system as vapor 2 Mass Transfer or A J 39 Method Mass transfer methods are based on the concept that rate of turbulent mass transfer of water vapor from evaporating surface to atmosphere is limiting factor u T qv satura Mass transfer is controlled by l vapor gradient and 2 wind ve ogi typgxlghich determines rate at Whi alpdfalpagig esr earned away39 Pressure measured vapor coefficient pressure E B es 62 0 102u Alternative forms of the 2 111ZV vapor transfer Zn coefficient Bu Many empirical vapor transfer coefficients have been developed by tting this model to local data 3 Combination Methods P I quot can be r J by J 39 method when energy supply not limiting and energy method when vapor transport not limiting 3 Typically both factors limiting so use combination of above methods First proposed by Penman 1948 a E LE L E A 7 A 7 evaporation weighting computed from factor for E aerodynamic method evaporation weighting computed from faCtOT for Ea energy In ethod Weighting factors sum to 1 Deviation of weighting factors is based on physics esesz T z A gradient of saturated vapor pressure curve at air temperature Called vapor pressure deficit Tabulated or approximated by equation saturated vapor 40988S pressure at T in Pascals 2373 T8 C PascalsOC psychometric constant y 668Pa0 C Combination method is most accurate and most commonly used method if meteorological information is available Particularly good for small wellmonitored areas Need net radiation air temperature humidity wind speed If all this information is not available can use PriestlyTaylor Approximation EaAE Ay r l3 Based on observations that second term in Penman equation typically 30 of first This is better for large areas All equations suitable for daily time intervals or longer 4 Direct Measurement from Pan Evaporation Since expensive to maintain weather stations required to use Penman equation evaporative pans are o en used to directly measure evaporation Standard Class A Evaporative Pans are built of unpainted galvanized iron 4 ft diameter 10 inches deep set on a platform 12 inches above ground Water level in pan recorded daily with high precision micrometer Evaporation determined by mass balance AS I 0 V2 V1 P E 3 E P P V2 V volume at precipitation beginning At since last pan reading volume at end Pans measure more evaporation than natural water bodies because 1 less heat storage capacity because smaller volume water 2 heat transfer through pan sides 3 wind effects caused by pan itself Typically estimate E K FE p pan factor m 07 Pan factor varies with season and location Should be calibrated at each site Set up complete weather station gt calculate Penman E and Ep Kp EP Evapotranspiration Same factors which govern water evaporation from water surfaces govern evapotranspiration because essentially transpiration is mainly due to evaporation from stomata Also plant physiology plants can control size of stomata and resistance to ow through roots and vascular systems and soil moisture conditions resistance of ow to roots play a role reference potential Recommended equation Evaporatlon actual Et 2 KSKCE evapotranspiration crop coef cient soil coefficient 02 lt Kclt 13 0 3 K5 5 1 depends on stage of depends 9n Son growth and type of crop m01sture and sell type Blaney Criddle monthly crop Empirical formula to estimate PET coefficient PET Kf PET or monthly consumptive use consumpnve in inches use factor mean monthly monthly fraction of daylight hours temperature OF as of yearly total depends on tp latitude f 7 calculate as hrs daylight in mth 100 hrs daylight in yr Consumptive use coefficients K for crops alfalfa beans 065 corn 075 pasture 075 AOM 4932 Surface Water Surface runoff P 391 quot quot or quot which moves across the land surface ultimately channelizing into streams or rivers or discharging into lakes Watershed Land area which contributes surface runoff to a speci ed point of interest gt typically stream outlet Note entire area within watershed may not contribute runoff due to depressions detention ponds etc Watershed divide Imaginary lines delineating adjacent watersheds Normally follow ridges and can be delineated with topographical maps Relationship between precipitation and runoff is in uenced by various storm and basin characteristics Storm Basin or Watershed intensity area shape slope duration soil vegetation geology areal extent stream patterns length degree of branching uniformity Initially large portion of precipitation goes into surface storage initial abstraction then soil moisture storage governed by infiltration equations Both of these types of storage can be classified as either i retention storage long term depleted by evaporation ii detention storage short term depleted by out ow After detention storage volume begins to fill out ow begins to occur Can be 1 groundwater ow all can ultimately 2 unsaturated ow end up as stream ow 3 overland ow 4 channel ow Stream ow Hydrograph Plot of volumetric ow rate vs time at a particular point in stream or river Typically at outlet of watershed Gives spatially and temporally integrated measure of runoff production at a point in stream Annual stream ow hydrograph shows long term balance of precipitation evaporation and stream ow Individual storm hydrograph most widely used method of evaluating surface runoff Shows relationship between peak stream ow s and individual storms Hydrographs are used to predict peak ow rates so that hydraulic structures can be designed to accommodate ow safely and to evaluate water quality effects associated with surface runoff Also integrating hydrograph over time gives volumes needed to design reservoirs detention ponds etc Typical Storm Hydrograph if crest segment stabilizes and crest segment 4 plateaus ma storage atta1ned re ects mostly in ow out ow storm characteristics falling limb re ects Q mostly basin geometry m3S rising limb entire drainage stored water drains area contrlbutes next Storm to runoff but still b egins storage remains to be filled I A R first arrival of runoff from tune nearby regions gt may be furthest point delay from onset of storm due begins to drain no due to rainfall absorbed by soil runOff re eas and transmission time base ow Components of hydrograph channel rainfall rainfall J J begms ellds 1 direct surface runoff Horton and Dunne direct 1 2 inter ow lateral ow at shallow depths Q surface 3 groundwater base ow runoff 4 channel precipitation linterflow groundwater flow baseflow tim e Direct surface runoff can be generated by two mechanisms 1 Hortonian Overland Flow Occurs when rainfall exceeds infiltration capacity of the soil Saturation of soil occurs from land surface down applicable for impervious surfaces in urban areas Low permeability soils 2 Dunne Overland Flow also called Saturation Overland Flow All rainfall infiltrates and results in a raising of the watertable saturation overland flow V increased out ow to 1 stream a If rains long enough saturation of soil occurs from below Get no more in ltration gt Overland ow Occurs in shallow water table atwoods regions of Florida First in low lying areas near streams and wetlands How do we determine when Dunne runoff will occur Total available soil moisture storage in inches of rain total porosity water content at beginning of stormdepth to water table at beginning of storm Therefore time to onset of Dunne runoff total available soil moisture storagerainfall rate Before onset of Dunne runoff runoff rate0 all rainfall in ltrates to fill storage After onset of Dunne runoff runoff raterainfall rate AOM 4932 Evaporation and Transpiration Evaporation change of water from its liquid to its vapor phase Potential Evaporation climatically controlled evaporation from a surface when the supply water to the surface is unlimited Transpiration evaporation occurring from plant s leaves through stomatal openings Function of stomata is to provide a place where C02 can dissolve into water and enter plant tissue Evaporation unavoidable in this process driven by same process as evaporation Ratio of water transpired to that used to form plant matter very large gt 800 Potential transpiration Transpiration which would occur if water supply to plant roots and through vascular system to stomata was unlimited Controlled by climate and plant physiology Two main forces in uencing evaporation rate are 1 Supply of solar energy to provide the latent heat of evaporation 2 Ability to transport evaporated water away from surface gt affected by wind velocity and vapor gradient Transpiration affected by above plus ability of plant to extract and transmit water from soil to stomata We will discuss four methods of estimating evaporation from free water surfaces or completely saturated soil 1 energy balances methods 2 mass transfer or aerodynamic methods 3 combination of energy and mass transfer Penman 4 pan evaporation data 1 Energy Balance Method Assumes energy supply the limiting factor Consider energy balance on a small lake with no water inputs or evaporation pan sensible heat net energy used in transfer to air radiation evaporation f H5 R f Q V heat stored in system heat conductec o ground typically neglected Energy balance in ows out ows assuming water temperature does not change no ow into or out of lake Rn Q6 HS G RnR1 ARl1 Al Rb are atim e eEw evaporatlon rate energymass depthtime or density of water volum eareatime m assvolume HS sensible heat ux to atmosphere by convection and G heat conducted to ground are typically small and difficult to measure Neglect G and HS and substitute equation of Q6 Rn Qe Epre E R evaporation rate pre depthtime Note Assumes 1 no water in owout ow to lake 2 no change in water temperature of lake 3 neglects sensible heat transfer to ground and atmosphere 4 neglects heat energy lost with water which leaves system as vapor 2 Mass Transfer or A J 39 Method Mass transfer methods are based on the concept that rate of turbulent mass transfer of water vapor from evaporating surface to atmosphere is limiting factor u T qv satura Mass transfer is controlled by l vapor gradient and 2 wind ve ogi typgxlghich determines rate at Whi alpdfalpagig esr earned away39 Pressure measured vapor coefficient pressure E B es 62 0 102u Alternative forms of the 2 111ZV vapor transfer Zn coefficient Bu Many empirical vapor transfer coefficients have been developed by tting this model to local data 3 Combination Methods P I quot can be r J by J 39 method when energy supply not limiting and energy method when vapor transport not limiting 3 Typically both factors limiting so use combination of above methods First proposed by Penman 1948 a E LE L E A 7 A 7 evaporation weighting computed from factor for E aerodynamic method evaporation weighting computed from faCtOT for Ea energy In ethod Weighting factors sum to 1 Deviation of weighting factors is based on physics esesz T z A gradient of saturated vapor pressure curve at air temperature Called vapor pressure deficit Tabulated or approximated by equation saturated vapor 40988S pressure at T in Pascals 2373 T8 C PascalsOC psychometric constant y 668Pa0 C Combination method is most accurate and most commonly used method if meteorological information is available Particularly good for small wellmonitored areas Need net radiation air temperature humidity wind speed If all this information is not available can use PriestlyTaylor Approximation EaAE Ay r l3 Based on observations that second term in Penman equation typically 30 of first This is better for large areas All equations suitable for daily time intervals or longer 4 Direct Measurement from Pan Evaporation Since expensive to maintain weather stations required to use Penman equation evaporative pans are o en used to directly measure evaporation Standard Class A Evaporative Pans are built of unpainted galvanized iron 4 ft diameter 10 inches deep set on a platform 12 inches above ground Water level in pan recorded daily with high precision micrometer Evaporation determined by mass balance AS I 0 V2 V1 P E 3 E P P V2 V volume at precipitation beginning At since last pan reading volume at end Pans measure more evaporation than natural water bodies because 1 less heat storage capacity because smaller volume water 2 heat transfer through pan sides 3 wind effects caused by pan itself Typically estimate E K FE p pan factor m 07 Pan factor varies with season and location Should be calibrated at each site Set up complete weather station gt calculate Penman E and Ep Kp EP Evapotranspiration Same factors which govern water evaporation from water surfaces govern evapotranspiration because essentially transpiration is mainly due to evaporation from stomata Also plant physiology plants can control size of stomata and resistance to ow through roots and vascular systems and soil moisture conditions resistance of ow to roots play a role reference potential Recommended equation Evaporatlon actual Et 2 KSKCE evapotranspiration crop coef cient soil coefficient 02 lt Kclt 13 0 3 K5 5 1 depends on stage of depends 9n Son growth and type of crop m01sture and sell type Blaney Criddle monthly crop Empirical formula to estimate PET coefficient PET Kf PET or monthly consumptive use consumpnve in inches use factor mean monthly monthly fraction of daylight hours temperature OF as of yearly total depends on tp latitude f 7 calculate as hrs daylight in mth 100 hrs daylight in yr Consumptive use coefficients K for crops alfalfa beans 065 corn 075 pasture 075 AOM 4932 Subsurface Water Subsurface water Water occurring below land surface Groundwater Water under positive pressure in the saturated zone of earth materials constitutes approximately 30 earth s fresh water approximately 99 liquid fresh water Overall residence time for global groundwater reservoir is centuries to millenia because rate of groundwater movement is generally slow lt l mday This is in contrast to 9 day residence time for atmospheric water 3 completely different time scales Classification of soilrock profile A soil water p lt atm 6S 7 UNSAT D intermediate vadose water ZONE capillary water p lt atm 639 71 water table p atm 639 n SAT D groundwater p gt atm a n ZONE mmmyw mumm s tt halmhm volume water water content s01l m01sture content 639 V W er water content soil moisture content 639 total volume soil water Ground surface to bottom of root zone depth depends on soil type and vegetation May become saturated during periods of rainfall otherwise unsaturated soil pores partially lled with air Plants extract water from this zone Evaporation occurs from this zone intermediate vadose zone Between soil water zone and capillary fringe Unsaturated except during extreme precipitation events Depth of zone may range from centimeters to 100s of meters capillag zone Above saturated zone Water rises into this zone as a result of capillary force Depth of this zone is a function of the soil type Fractions of a meter for sands mm to meters for ne clays All pores lled with H20 p lt 0 Effect seen if place bottom of dry porous media soil or sponge into water Water will be drawn up into media to a height above water where soil suction and gravity forces are equal saturated zone All pores filled with water p gt 0 Formations in this zone with ability to transmit water are called aquifers Unsaturated Zone Water can exist in all its phases in the unsaturated zone Liquid water occurs as o hygroscopic water adsorbed from air by molecular interaction Hbonds o capillary water held by surface tension due to viscosity of liquid 0 gravitational water Hygroscopic and capillary waters are held by molecular electrostatic forces between polar bonds and particles surface tension in thin films around soil particles 3 drier soil smaller pores T hygroscopic and capillary forces 1 Hygroscopic water unavailable held at 31 to 10000 bars 2 Capillary water Held at 033 to 31 bars More water filling pores but discontinuous except in capillary fringe This water can be used by plants permanent wilting point Tension suction negative pressure above which or level of dryness above which plant root system cannot extract water Depends on type of vegetation typically 15 bars field capacity Maximum amount of water soil can hold against gravity Tension above which or level of dryness above which water cannot be drained by gravity due to hygroscopic and capillary forces Depends on soil type somewhere between 0 and 033 bars 3 Gravitational water Water in unsaturated zone in excess of field capacity which percolates downward due to gravity ultimately reaching saturated zone as recharge Note 1 bar 105 Pa approximately 1020cm water approximately 1 atmosphere Typical Moisture Pro les a rain after a long dry period moisture content t 13900 zone directlon of E moisture movement depth Wil ing point field capacity hygroscoplc saturatlon l 4 gt typical wetting path b drylng process T evapotranspiration I moisture depth field capacity saturation l 5 gt typical drying pattern 2 Drying in upper layers by ET 3 Bottom part of wetting front continues L Upper part continues to dry 4 At some point T and L movement results in no moisture gradient 5 Dry front established Lower zones are being depleted to satisfy PET at surface Drying continues until capillary forces are unable to move water to surface Flow in unsaturated porous media governed by a modified Darcy s law called Darcy Buckingham law 0 qz Kgg l D ow in z direction But now total head 1 x Z gravitational ppg head 1 suction head capillary head or negative pressure head Energy possessed by the uid due to soil suction forces still P pg but negative Suction head varies with moisture content T 9 9 gt 0 P gt 0 KG hydraulic conductivity is a function of water content T 9T KG because more continuously connected pores more space available for water to travel through until 9 n Kn K531 7 3910 Ksat Soil Suction T mm or KT 10391 I Soil Suction 1 head measured with tensiometers Airtight ceramic cup and tube containing water Soil tension measured as vacuum in tubes created when water drawn out of tube into soil Comes to equilibrium at soil tension value h1100cm65cm35cm hz50cm50cm0cm hl 21 KPI KPI negative 65 cm 21 100 cm h 22 KPZ 7 KPZ negative 2 0 22 7 50 ml 50 cm Estimate Darcy ux in vertical direction from tensiometer measurements 5 i hlh2 7 350m 0cm K Pim K P 7 K P qz z 21 22 100071 506 Look up K041 for soil type at the moisture content corresponding to the average tension Flow is in negative direction ie down Look at components of gradient 6122441 h1h2K 1P T1Zi P2ZzK P Pi T2K 2122 2122 2122 65 50 KiPl K P 100 50 J m 15 KTlmKm Capillary gradient cause upward ow gravitational gradient causes downward ow Net ux is down What would it take to get net ux upward Saturated Zone recharge area for pOtemlometrlc confined aquifer surface recharge in ltration unconfined aquifer aquitard confining layer confined aquifer confining layer aquiclude aguifer saturated soil or geologic unit with ability to transmit water aguiclude saturated soil unable to transmit water aguitard saturated soil transmits water very slowly aguifuge has no water therefore does not transmit impermeable con ned aguifer Saturated zone between two impermeable layers Fed by exposed recharge area recharge areas can be remote 3 con ned aquifer then contains fossil water deposited in past geologic times No free water surface except in recharge area and in some cases recharge through leaky upper con ning layer Well in con ning layer water will rise to piezometric level above upper con ning layer sometimes above ground surface equal to elevation above datum and pressure in aquifer No free water surface except in recharge area uncon ned aguifer Also called phreatic or water table aquifer Water in well in uncon ned aquifer will rise to water table level which de nes piezometric surface or head of system Uncon ned aquifers have free water surface Water comes from direct rainfall over the aquifers connections with surface waters or other aquifers Whether rock or soil formation is an aquifer aquifuge or aquiclude depends on its geologic origins and history unconsolidated sediments gravel coarse sand gt aquifer silt clay gt aquiclude or aquitard consolidated 139 J quot J 39 quot gt aquifer shale siltstone basalt gt aquifuge Flow in saturated porous media is governed by Darcy s law dh 1D ow In X39dlrecnon 9x K dx piezometric head measured as height above arbitrary datum to which water Darcy flux or spec1f1c d1scharge rises in a tube connecting the point V01ume rate 0f ow Per unlt area being measured to the atmosphere UT hppgz L K saturated hydraulic conductivity LT function of uid and porous media K 10396 cmsec clay 10393 cmsec sand 10 cmsec gravel 1910 21100 hl h100 p0 2290 h290 A h h K10393 cmsec qx K 2 I a x2 xl qx 20 x lUUUm 39 PPgZz 1 ZO p1 pg21 h2 22 90 20 hzl100 h h 100 90 qK 10 3 u 10 53Jmyear x2 x1 sec lOOOm sec Water table in surficial aquifer typically re ection of topography Flow from topographic highs to lows Groundwater often can be assumed hydrostatic but not always ie not in recharge and discharge areas l 2 3 4 5 6 h1gthzgth3 h4gth5gth6 downward ow upward ow recharge discharge h1 h2 h3 gt h4 h5 h5 ow from recharge to discharge 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 gt 8 km approximately none 2 speci c humidity pvpmoist increases and decreases seasonally with temperature warm air can hold more water vapor 3 speci c humidity is highest in the tropics and lowest in the poles for same reason as 2 4 relative humidity pvpmoist shows peaks both in tropics and in poles minimum at high pressure regions 30 40 low moist high moist low temp high temp qv Rn low moist intermed temp high press anti cyclone 90 N 0 90 S 90 60 30 N 0 0 60 90 S Australia Sahara PeruvianAndea Ojave 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 A A Formation ofP Reuuires39 l Cooling of air to m 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 gt updraft velocity b suf cient 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 0 Nonfrontal convergence of air masses with equal temperature to a low pressure point ie at ITCZ due to convergence of NE SE tradewinds Generates moderate rainfall over long duration 0 Frontal convergence of air masses of different air temperature Produces cold frontswarm 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 rst 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 rst 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 T L p Lower air density rises and cools and condenses releases heat 3 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 orogpaphy 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 Paci c hit series of mountain ranges parallel to coast In most regions of world mean precipitation increases with elevation 2 CondensationNucleation 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 3 Without nuclei condensation rates will be very low even for e gt 4es Air usually contains lots of particles that can act as nuclei gt 10394 mm attract H20 via H bonds so get condensation at e m 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 l 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 01 to l gm3 Even if all this water in a very tall cloud were to fall as rain the total depth of precipitation would be small 10000 m tall cloud 05 gm3 5000 gm2 3 05 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 In ow 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 ie 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 tim e b cumulative hyetograph sum of rainfall depth vs time cumulative rainfall or inches cumulativ e rainfall t1me Max intensity depth recorded in a given time interval as interval T maX intensity L Index of storm severity Calculate running totals of depth or average intensity for time interval of interest select maX value 3 indicator of storm severity c isohyetal Imps contour map showing lines of equal rainfall depth J 6 Important design criteria 4 average depth of rainfall over an area T area i 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 longterm data and as high as 75 for individual storms 0 Most accurate Weighing recording gage which continuously collects rainfall and records weight over time 0 Least accurate Standard rain gage Measures accumulated depth at a point Get only volume rain since last reading accuracy 1 10th inch 3 evaporation problems 0 Most common Tipping bucket rain gage Records number of tips of bucket with known volume over time Intermediate cost and accuracy Often underrecords during heavy rainfall events F timation ofAreal P 39 quot quot from point Most often interested in quantifying rainfall over an entire watershed Has to be inferred from some sort of weighted average of available point measurements PXi A N P 213 x t lpoint 7 measurement weight depends onme 0 Several methods to determine weights All require 0 s 2 s 1 Z A 1 Weighting Methods a Arithmetic average it all weights equivalent A l P W Z Px Method OK if gages distributed uniformly over watershed and rainfall does not vary much in space b Theissen Method 2L Measure of rain gage contributing area Assumes rain at any point in watershed equal to rainfall at nearest station To determine 2L I draw lines between locations of adjacent gages 2 perpendicular bisectors drawn for each line extend to form irregular polygon areas area polygon contributing toz39 A 1 total area of watershed A 19 221 24m 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 c Isohyetal Method area between isohyets total watershed area i P Z 111399 mean precipitation between two isohyets 12P This is most accurate method if have a sufficiently dense gage network to construct an accurate isohyetal map Can account for systematic trends ie orography distance from coast Hydrologic Frequency Analysis Extreme rainfall and ooddrought events are typically of concern in engineering hydrology dams bridges culverts ood 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 125 of occurring in any one year Mathematically T Eh i 3 Px 2 xT P time between f storm 5 r PEWE xgr probability stem W r tmlme What is probability Tyear return period will occur once in N years Probability does not occur Px lt xTlPN never occurs in 10 years Probability occurs at least once in N years l lPN 1 1 1TN For example 10 year return period storm has prob of occurrence 01 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 lT Probability l lllO10 0651 at least once in ten years How to estimate return period from ood 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 gt 3 Probx xm m or T N l N l m probability of total number exceeding storm years of record with magnitude xn data points AOM 4932 Atmospheric Processes From last time Distribution of solar radiation over earth in space and time leads to an energy imbalance Meteorologic and hydrologic processes originate to redistribute energy Water in both liquid and vapor forms plays a major role in this energy redistribution from equator to poles 23 transfer of energy occurs via atmosphere water vapor 13 occurs through oceans liquid water quot39 Characteristics of 39 80 N2 20 Oz treated as perfect gas 100 km Thermosphere upper 39 Mesosphere 50 km A A Alt1tude km lower Stratosphere atmosphere sharp change in temp and pressure produce Jet Streams T 8 16 km r r poles J Troposphere I I equator I I I I 80 60 40 20 0 20 Temperature C Lower atmosphere extends up to 50 km Plays primary role in weather determination Upper atmosphere doesn t play much of a role Lower atmosphere most active part of atmosphere where most of the mass and energy transfer occurs It is divided into two parts distinguished by their temperature distribution the troposphere and the stratosphere Troposphere characterized by Variable thickness 8 km poles 16 km equator Decreasing temperature with elevation linear Well de ned pressure gradients maX pressure at bottom nonlinear Well de ned distribution of moisture and suspended particles maX at bottom Sharp air velocity gradient At earth s surface velocity is zero noslip condition and velocity increases over 2700 m thick boundary layer according to a logarithmic velocity pro le U39HeP NH 112 Stratosphere no well de ned pro les Temperature Distribution Temperature distribution follows radiation distribution both in time ie daily and space ie distribution over earth In time 10 4 pm peak 5 clear day 0 cloudy day clouds buffer in 5 and outgoing solar radiation because H20 absorbs heat 10 6 12 18 24 Air temperature rises during day and falls at night following solar radiation Peak temperature lags peak solar radiation occurs at noon by several hours due to heating effects on earth s back radiation which lags solar radiation incoming solar radiation ener ufy outgoing longwave radiation from earth 6 am noon 4 pm mid Clouds absorb incoming and outgoing radiation gt attenuate diurnal uctuations Similarly diurnal uctuations not as great near ocean as inland because ocean absorbs and distributes heat more efficiently throughout its uid mass than land masses H20 higher heat capacity than earth because when energy added much of it used to break H bonds rather than increase rate of molecular vibration which increases T This makes it possible for warmblooded organisms to regulate temperatures gt prevents large rapid temperature uctuations Seasonally Temporal distribution Air temperatures also follow cycle of incoming solar radiation Again peak temperature July August lags peak radiation June 22 because of effect of earth s back radiation Lag is more signi cant near oceans near oceans in Northern hemisphere maX min gt Aug Feb inland in N hemisphere maX min gt July Jan In space Spatial distribution horizontal Same trend in horizontal distribution of temperatures over globe Time averaged temperature distribution follow latitude lines which receive equal solar radiation Highest temperatures just northsouth of equator due to extensive cloud cover in this region intertropical convergence zone Similarly air over oceans tends to stay warmer in winter colder in summer than air over land due to high heat capacity of ocean ie same change in heat energy produces a smaller temperature change for oceans versus land Vertical Distribution of T T r r39 shows wellde ned linear relationship of temperature with height above earth surface in an average sense Tz To otz Z ambient lapse rate 6 10 OCkm To T C humid cloudy conditions or gt 6 Ckm saturated adiabatic lapse rate dry clear conditions or gt 10 Ckm dry adiabatic lapse rate 98 Why Under humid conditions water vapor in air condenses as it rises and cools Heat is released from water to surrounding air when vapor condenses This slows the rate of cooling Ambient lapse rate dictates the stability or instability of air masses Air can only rise and thus lead to condensation and precipitation if it is warmer than surrounding air Get unusually stable weather ie no precipitation when have a temperature inversion ie when temperature increases with elevation locally Air can t rise no rainfall thus pollution problems Most likely to happen over continental land masses after calm dry nights with clear skies Land cools faster than upper air Pressure Distribution Horizontal Daily pressure distribution at sea level is variable and unstable However if looking at average pressure distributions over long time periods semipermanent patterns emerge polar easterlies low pressure westerlies high pressure NE Tradewinds low pressure SE Tradewinds high pressure westerlies polar easterlies low pressure 0 These pressure belts migrate northward in June July and southward in JanFeb following solar radiation distribution gt ie are of thermal origin 0 Horizontal pressure gradients are the driving force for winds Wind direction and circulation however is also affected by l The rotation of the earth which produces the apparent Coriolis force apparent force which causes moving object to deviate right in N hemisphere and left in S hemisphere Results from perception of observer on rotating earth looking at unattached moving mass 2 Friction of lower air masses with earth s surface The net effects of these forces are N 5 Convergent equatorial winds of easterly origin tradewinds or doldrums Converge in low pressure belt called intertropical convergence zone ITCZ 3 cloudy showery weather Prevailing westerly winds at midlatitudes Associated with high pressure centers little precipitation Highly variable polar easterly winds not wellcharacterized Poleward circulation of air masses is broken up into 3 cells forming banded structure around the earth Winds shift northsouth with radiation intensity Pressure Distribution Vertical Vertical pressure distribution is also highly variable and weather dependent To obtain a representative profile commonly assume atmosphere is hydrostatic pressure K dP gravitational constant dz Must also account for the fact that density of air is dependent on pressure Assume air follows the ideal gas law Ideal gas law for Ppil RT ambient air unrt mass temp K dry air gas pressure of constant air w 287 Jkg K mass air 288E6 cmZsz K Combine these two equations to get g distribution of T a z E pressure with height 313230 in troposphere a Nonlinear due to linear variation of temperature with height and ideal gas law and hydrostatic assumption Distribution of Water Vapor Water vapor humidity is the most variable atmospheric component and the most important in determining climate Most within 2 4 km of earth s surface Water vapor good absorber of radiation therefore its movement and phase changes which absorb and release heat play a major role in heat and energy balance Liquid and solid precipitation of vapor also drives land based portion of hydrologic cycle When air is saturated with water vapor ie holding maximum amount of water vapor at that particular r and I and quot are occurring at equal rates water vapor behaves like an ideal gas absolute temperature of water vapor assumed e pvRvT same as air temp vapor pressure air gas millibars Vapor densnyj constant 100 Nmz kg watercm cmZSZOK 100 kgm 52 moist air RV is related to universal gas constant R0 19857 cal K mole through the following equation universal gas constant dry air gas 110 RD constant R R R v VAZVMVMVMV vapor gas constant molecular weight water 0828 0232 288 vapor M ef 67MV5VTR 7 l llg vTR TVapor Pressure 18 VMV M28 Vapor density Also V Pv ejRT called absolute humidity Note This equation indicates density of water vapor is 0622 density of dry air at that e same Tand Pe pa E E If you have a mixture of dry air and water vapor Dalton s law of partial pressure Total pressure of mixture 2 partial pressure of constituents pmix pd e vapor Dressure dIV air pressure pmix pd pv P e pressure due to dry an F pressure mixture moist air e vapor pressure Dressure le Vapor pressure P e 0622e pm RT RT 1 0378e 3 Moist air is less dense than dry air at same temp and pressure If moist and dry air converge moist air will rise and cool 3 precipitation Some definitions vapor density pv sat39d va or densz39 relative humidity Rh r p ty p5 vapor pressure sat d vapor pressure es saturated vapor pressure es partial pressure at which additional vapor would cause net condensation 3 max amount of vapor system can hold 3 function of temperature approximate empirical equation 1727 T S 611 exp Pascals Nmz 39 0c 1b 105 Nm2 lmb 100 Nm2 dew point temperature Td temperature to which air must be cooled to just become saturated at a given vapor pressuredensity mass water absolute humidity pv volume moist air speci c humidity q W piv absolute humidity V unit mass moist air pmix denSitY mOiSt air 0622 T N 0622e P 0378e N AT P humidity measured with a psychrometer instrument with two thermometers one is wetbulb thermometer covered by cloth saturated with water other is dry Psychrometer is ventilated by rotation to induce evaporation from wet bulb Temperature of wet bulb lowered because during evaporation water absorbs heat from air to break H bonds Amount of evaporation controlled by humidity Dry bulb reads ambient temperature Change between wet bulb dew point temperature and dry bulb temperatures is called wet bulb depression related to relative humidity 3 tabulated or empirical equations e g at climate station suppose T 20 C ambient temperature wa 16 C wet bulb temperature What is relative humidity max vapor 1727T pressure at 20 C 6 T20 6llex S plz373r J 2339Pa actual v apor ressure at 20 C P eacteSTl6 6116XP1819DQ e Rh act 1819Pa 278 es 2339M AOM 4932 In ltration In ltration is the process by which water penetrates from ground surface into the soil In ltration rate is governed by rainfall rate conductivity of soil surface and vegetative cover at top of soil pro le and ability of deeper soil pro le to store and transmit incoming water Overall goal predict in ltration rate f LT rate at which water enters soil surface or cumulative in ltration F L The remainder of the nonin ltrating water becomes runoff which ultimately contributes to stream ow In general there are three conditions that should be distinguished No ponding In ltration equals rainfall rate and is less than or equal to the soils ability to in ltrate water ie in ltration capacity Saturation from above Ponding occurs because rainfall rate exceeds that in ltration rate In this case in ltration rate equals the in ltration capacity Saturation from below Ponding occurs because the water table has risen to or above the land surface and the entire soil is saturated In this case in ltration rate is zero In ltration is measured with a ring in ltrometer A ponded condition is created by ooding the surface or by applying a high rate of simulated rainfall The rate of in ltration is obtained by l measuring the rate at which the level of ponded water decreases or 2 measureing the rate at which water has to be added to maintain a constant level of ponding General observed in ltration behavior time to ponding rainfall rate f infiltration rate in ltration rate runoff darcy ux at typlcally grOund surface exponential decay qz0 after ponding Km t if rainfall rate lt Km all infiltrates no ponding soil never becomes sat d For rainfall rates less than saturated conductivity of soils all rainfall will in ltrate no runoff will occur gt soil never becomes saturated For rainfall rates gt K531 but less than the soils maximum in ltration capacity initially all water will in ltrate Since rate gt K531 all water cannot be transmitted down water storage in soil will increase until soil is saturated When soil becomes saturated rate of in ltration will decrease because only will take in water which can be transmitted down No more storage to ll gt called time to ponding After ponding in ltration rate decreases approximately exponentially initially driven by both capillary gradients and gravitational gradients gt when moisture approximately uniformly distributed through pro le capillary gradients gt 0 in ltration driven by gravity gradients gt asymptotic value Ksm For rainfall rates greater than maximum in ltration capacity get immediate ponding and exponential decay from maximum in ltration capacity toward minimum in ltration capacity H01t0n In ltration Model one of earliest in ltration equations developed 1933 and the most common empirical equation used to predict in ltration if ponding occurs from above Instantaneous In ltration f0 fc f0 mexp k t Cumulative In ltration Ft jfrdr fct 0 exp KI 0 Note this equation has been xed since the lecture period on 61598 fc minimum in ltration capacity approximately saturated hydraulic conductivity f0 maximum in ltration capacity function of saturated conductivity and soil tension k constant representing exponential rate of decrease of in ltration All are empirical parameters which must be t to each soil type using data from a ring in ltrometer experiment f0 F0 rate of decay governed by k f0 increase k increase rate of decay analogous to Km fc t time after ponding This equation is only valid after ponding Therefore all water the soil has potential to in ltrate is available at soil surface Ponding will only occur if i gt ft Should only be used during very high intensity precipitation events Example Suppose that the parameters for Horton s equation are fc 10 cmhr f050 cmhr and k2 hr391 Determine the in ltration rate and cumulative in ltration after 00510 15 20 hours if the rainfall rate is 6 cmhr Plot as a function of time What would be the in ltration rate if the rainfall rate were 06 inhr There are many other physically based models to predict in ltration from particular storm events when upper soil ponding is the limiting factor Horton s equation is just an example A common alternative empirical method is the SCS method SCS Method Generally applied to total rainfall event not time distribution of rainfall Predicts total volume of in ltration and total volume of runoff not rate over time Most often used to predict effects of land development on runoff from quotdesign stormsquot for permitting purposes Based on cont1nu1ty pr1nc1ple continuing abstraction water retained in watershed total rainfall P P9 Ia Fa after runoffbegjns depth excess rainfall initial abstraction depth direct amount of rainfall which no runoff will occur Assume equal to 20 total storage in basin 1391113910 SCS method assumes no theoretical basis 1 actua storage actual runoff Pg i S P a max potential runoff max potential storage Insert Ia 0ZS Solve for Fa and plug into continuity P 02S2 e P 08S Problem How to get S Total storage in basin depends on antecedent moisture conditions soil type and land use Again studying many experimental watersheds SCS developed a relationship between basin storage and curve numbers which depend on land use antecedent conditions and soil type 1000 S 7 0 CN impervious surface and water surface CN 100 S 0 natural surfaces CN lt 100 CN 30 meadow CN 70 residential Curve numbers for various land uses are tabulated 552 for normal antecedent moisture conditions AMC 11 Depend on soil type Group A deep sand allFlorida soils B sandy loam classified according moreasmgLCN C clay loam t0 hydmlogic group therefore S D heavy clay in county soil survey Look at 5 day antecedent rainfall lt 05 in dormant seasonl4 in growing season AMC I gt 11 in dormant season 21 in growing season AMC 11 For extremely dry conditions modify CN AMC I 42 CN CNd 10 058 CNn For extremely wet conditions AMC III 23 CNn CNW 10 013 CNn For mixed land uses compute a weighted curve number based on percent area in that land use ZAiCNi ZAi percent area with CN Now have generated volume of excess rainfall which contributes to runoff gt have to get it to outlet to predict stream ow hydrograph