Nonpoint Source Pollution
Nonpoint Source Pollution CIVE 440
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CE 440 Basic Concepts of Diffuse Pollution Lecture Notes on Chapter 3 Text Reading pp 104132 Watersheds and Drainage Networks De ne watershed stream order thalweg oodplain Important table from Leopold Wolman and Miller 1964 on stream orders in US Mean Average Total Drainage Cumulative Strahler Length Length Area sq Total Cumulative Total t0tal Order Number km km km Length t0tal length number number 1 1570000 16 2526547 25897353 48 48 78 78 2 350000 37 1295459 12171756 25 73 17 95 3 80000 85 682329 59563913 13 86 4 99 4 18000 193 347601 28228115 7 93 1 100 5 4200 451 189250 13414829 4 97 0 100 6 950 1030 97843 6370749 2 98 0 100 7 200 2366 47312 30299904 1 99 0 100 8 41 5439 22301 14398929 0 100 0 100 9 8 12504 10003 68369013 0 100 0 100 10 1 28967 2897 32371692 0 100 0 100 Perennial vs intermittent vs ephemeral ow Geomorphic oodplain vs regulatory 100yr oodplain Effluent dominated streams Types of Diffuse Pollution Loads and Transport Routes Water pollution requires both a source of a contaminant and moving water to transport the contaminant The moving water can be either surface water or ground water or both See bullets describing sources on pp 108109 To characterize pollutant loadings from a given source both surface runoff and percolation to ground water must be estimated Mass load per time concentration X ow rate Generally ows are estimated using a mass balance for a de ned system or control volume for example a watershed aquifer agricultural eld mine parking lot or any region with carefully de ned system boundaries A storage in ow out ow Unit Loads Export Coef cient Concept starts on page 110 A unit load UL is a mass or weight of pollution per unit area per capita day or per unit length of curb CL Field measurements and typical unit loads from urban areas are given in Figure 35 and on page 115 references differ appreciably Edge of eld or edge of site loads vs delivery Be careful 7 some export coef cients include background Sediment Delivery Ratio DR De nition Enrichment Ratio ER De nition The overall enrichment is a combination of the mineral soil and organic matter enrichment ratios We do not have well established ERs for organic matter For annual loads a ruleofthumb type number to use for overall enrichment is ER 2 Loading Calculations Load of adsorbed pollutant Concentration on sediment X Sediment load Load of dissolved pollutant Dissolved concentration X Water ow rate Concentration on sediment Concentration on soil X ER Mass of pollutant in runoff pollutant emissions from source areas X enrichment during overland ow attenuation in the watershed background sources Load of pollutant in runoff DR X UL if UL doesn t include background Load of adsorbed pollutant in runoff DR X ER X soil erosion masstime X Cssoi1 Statistical Quality Characteristics of Urban Runoff The NURP study USEPA 1993 produced data on 28 urban sites around the country Runoff is often characterized by Event Mean Concentrations EMC s EMC Mass of pollutant transported during eventTotal ow during event 29c 29 So each storm has a particular EMC for each water quality variable EMC At a given site one can monitor EMC s for a few seasons to determine their statistical characteristics Such as shape of distribution histogram summary statistics percentiles return periods of various EMC s 2 N N Sample Mean EMC Tc u Zm W Sample Standard Dev1atlon S T m 7 For normally distributed data 23 of the population or of random observations are within i 1 standard deviation of the mean 95 of the population are within i 26 of the mean S The coefficient of variation CV x E u The median is the 501h percentile of the distribution Estimating Percentiles from data First rank the data from smallest to largest The rank of the 100pth percentile is MpN l where p is the fraction of the population below the percentile of interest The value of p is sometimes called the non exceedence probability lp would be the exceedence probability Example For the 90Lh percentile p09 If we have N100 observations then M09101909 To find the 90Lh percentile rank the data and interpolate between the 901h and 91st largest observations Try p09 and n10 Then M99 Try p095 and n10 Then M104 won t work Oops we can t estimate the 951h percentile with only 10 data points using this estimator This actually makes sense we should not be able to estimate extreme percentiles p close to 00 or 10 unless you have a sufficiently large sample size Extreme percentiles are more difficult to estimate than those close to the median but estimates of all percentiles will bene t from larger sample sizes An alternative estimator is MpN which will never result in MgtN This sounds good but it will not provide estimates which are as good as those from the other estimator and it still has the problem that N can be lt 1 This is bad because you can t interpolate below the smallest value Return Periods The return period of a given event such as a rainfall depth or EMC observed from a single storm is defined as lthe exceedence probability of that event based on annual maximum data 1 1 p Let s say for example that lp0 1 meaning that there is a 10 chance that the event in question will be exceeded in any given year Also p 09 meaning that there is a 90 chance that the event will not be exceeded in any given yearThen Tr l0l 10 years T To calculate return periods from a data set of rainfall amounts or EMC s first find the annual maximum for each year rank those and then find M N 1 position Then calculate the return period Tr as above Interpolate as necessary p from the ranked data This equation is known as the Weibull plotting Values of p and return periods can also be calculated based on an assumed distribution such as normal or lognormal distribution De ne a lognormal distribution What does the histogram look like This would be called a parametric approach since a particular distribution is assumed The above method based on ranks is a nonparametric approach No particular distribution is assumed NURP Results NURP results suggest that EMC s are often lognormally distributed Geographic location land use runoff volume are poor predictors of EMC s There is a signi cant difference between urban and nonurban or open sites Statistical results overall sites are given in tables 814 medians and 815 means For lognormal data the meangtmedian This shows up here CSO s It is useful to know the critical rainfall intensity at which over ow occurs This can then be used to determine how often a CSO will occur Typical values are l mmhr Calculation of percentiles based on normal or lognormal distribution parametric method For the normal distribution the 100pth percentile is given by p ch where Zp is the value of the stande normal distribution with nonexceedence probability or lefttail area p which can be found from tables To use the lognormal distribution first convert each observation to its log and then proceed as with the normal distribution That is find the mean and standard deviation of the logs etc Study Boxes 31 through 34 Management and Targeting Critical Areas Source controls vs change runoff characteristics vs interception of pollutants Standard Normal Distribution 0 039 10 Commonly Used Values of Zp 2 Zn 099 2327 0975 196 0950 1645 0900 1282 085 1037 084 100 080 0842 075 0675 050 0000 025 0675 020 0842 016 100 015 1037 010 1282 005 1645 0025 196 001 2327 p 1p ZO Zp CE440 Erosion and Sedimentation Lecture Notes on Chapter 5 Text Reading pp 205242 Important terms Erosion Removal of granular material sediment The major mechanisms include water wind ice and gravity A geologist might prefer the narrower de nition that refers to the breaking of the bond between sediment grain and the underlying material formation of the grain itself Sedimentation Deposition of sediment quotSedimentationquot is often used to describe both erosion and deposition Denudation Geomorphology Aggradation Degradation Sheet erosion r39ill erosion gully erosion Washload bed material load Suspended load bedload Delivery ratio Enrichment ratio Shear stress Dimensionless shear stress Erosion and sedimentation requires 0 Gravity o Fluid we focus exclusively on water 0 Topography o Erodible material Two fundamental controls 0 the transport capacity of the ow 0 the availability of material to transport CE440 Page 1 Lecture Notes on Chapter 5 Erosion and Sedim entation Variables that in uence quantity and quality of sediment vs variables that in uence capacity Quantity and quality of sediment geology topography watershed network characteristics magnitude intensity duration distribution and season rainfall soil type condition vegetation land uses such as agriculture urbanization grazing etc surface erosion bank cutting and channel erosion others Capacity uid properties slope roughness depth or hydraulic radius discharge velocity velocity distribution turbulence tractive force shear size and gradation of the sediment others Two primary sources of sediment 0 material from the watershed and stream banks and o bed material that makes up the stream bed Sources of sediment and practices resulting in excessive erosionisee pages 213215 Impacts of erosion and sedimentation why do we care Eutrophicationiwhy Habitat lossiexamples Transport of pesticides PCB s and other organics to receiving waters Reduced recreation Reduced reservoir life Loss of productivity from of sedimentiexample Channel scour from lack of sedimentiexample Aquatic life ecological integrity Others CE440 Page 2 Lecture Notes on Chapter 5 Erosion and Sedimentation USDA soil textural triangle 7 be sure you know how to get sand silt and clay for different soil types Estimating sediment yield for a watershed pages 218235 Measurements 7 event oriented Bed material loadidifficult to sample Wash load Reservoir sediment surveys Representative storms Used to develop rating curves Models Most highly empirical Rating curves see gure 510 on page 252 USLE and delivery ratio Some more physically based Estimating Erosion using the Universal Soil Loss Equation A RKLSCP A annual soil loss in metric tons acre R rainfall energy factor K soil erodibility factor LS slope length factor C crop management factor F erosion control practice factor Rainfall erosivity factor Annual values in Fig 512 Single storm values equation 53 on page 220 Modification of USLE for soil detachment by overland ow equation 55 Dimensionsless Adjustment Factors Soil Erodibility Factor K found in Figure 514 or Table 53 pages 223224 Slope Length Factor LS adjusts for length and steepness LS 1 for 22m length and 9 slope Equation 56 and Figure 515 on pages 224225 Crop Management Factor C C 1 for continuous fallow Values in Tables 5455 on pages 225227 Table 55 has C values for construction sites and mulch practices CE440 Page 3 Lecture Notes on Chapter 5 Erosion and Sedimentation Erosion Control Practice Factor P Tables 56 and 57 on pages 228229 and handouts Work through Boxes 52 and 53 on pages 230232 Modi cations ofthe USLE MUSLE RUSLE WEPP Sediment Delivery Ratio De nition Rough annual values may be obtained from Figure 516 based on watershed area However sitespeci c values will vary greatly Note the quote from Wolman near the top of page 234 Some computer models include sediment routing capability which considers the sediment carrying capacity of overland andor stream ow and accounts for deposition of sediment in excess ofthis capacity Enrichment Ratio De nition from Chapter 2 Enrichment by clay see equation 524 on page 288 Relationship to delivery ratio see gure 525 and equation 525 on page 290 If 525 holds then the net result is pretty much a wash for clay This implies that if a chemical is largely adsorbed on clay then most of what is eroded would be delivered to the outlet of the watershed Obviously the mass of clay delivered to the outlet of the watershed must be the same or less than the amount eroded and the total amount of any chemical adsorbed on the clay that is delivered to the outlet must be the same or less than the total amount eroded Enrichment by organic matter we do not have a good relationship with delivery ratio for OM The overall enrichment is really a combination of the two enrichment ratios For annual loads a ruleof thumb type number to use for overall enrichment is ER 2 Sediment Transport in Streams CE440 Page 4 Lecture Notes on Chapter 5 Erosion and Sedim entation Sediment is transported by rolling sliding or skipping on the bed bed load or contact load or by suspension via the turbulence of the stream Three ways to classify modes of sediment transport lWhere and how it moves bed load vs suspended load 2Where it came from bed material load vs wash load 3Whether it s measured on not measured vs unmeasured Total Load Bedload Suspended Load Bed Material Load Washload Measured Load Unmeasured Load Sand and coarser material may move as bedload For practical purposes gravel and coarser sediments are only transported as bedload exceptions in the case of gravel might occur in mega events As a general approximation particles coarser than about 1 mm almost always move as bedload particles smaller than 01 mm predominately move as suspended load and particles from 011 mm are frequently transported in both modes Washload is not transported at the capacity of the stream and is not functionally related to measurable hydraulic variables Instead washload depends on the supply of fine sediments There is no sharp demarcation between washload discharge and bed sediment discharge Washload is often assumed to be silt and clay fractions 61 lt00625 mm or sizes less than the d10 ofthe bed material Dimensional Analysis 0 Shear stress dimensionless shear stress 0 Shields diagram CE440 Page 5 Lecture Notes on Chapter 5 Erosion and Sedim entation More on Sediment Measurement Varies tremendously in time and space Measurement accuracy and precision are affected by discharge antecedent conditions pulse stochastic phenomena hydrograph hysteresis rising vs falling limb sampler design efficiency effects on ow Bedload Helley Smith sampler traps bags Suspended pointintegrated depthintegrated siphon bottles grab samples pump samplers eg ISCO Even after many years of observation estimates of suspended load and bedload typically involve 2550 and 50100 uncertainty respectively even for the same location and discharge If G 265 then 1 mg liter of sediment corresponds to roughly 90 particles of very fine sand 90000 particles ofmedium silt 90000000 particles of fine clay Implications for turbidity and aquatic biota At the sediment concentrations commonly found in many rivers lt10000 ppm 1 ppm is equivalent to 1 mgl for practical purposes per Homework 2 Sediment rating curves Often a relationship of the form QsaQb or qsaqb Logarithmic transformation of data induces systematic error there are many correction techniques CE440 Page 6 Lecture Notes on Chapter 5 Erosion and Sedimentation Chapter 4 Hydrologic Considerations Text Reading pp 134159 161177 180187 191201 The Hydrologic Cycle NPS pollution is a waterdriven process In order to understand and manage NPS pollution we need to understand how water and to a certain extent air moves in the environment For nonpoint sources we are concerned about water movement largely in natural systems which are more complex than manmade systems for water transport Of course it is usually human alteration of natural systemsthrough agriculture urbanization mining timber harvest etcthat causes the pollution The natural movement of water in the environment is called the hydrologic cycle List the most important primary processes in the cycle in the space below Throughout the cycle water moves as a result of energy gradients Radiant energy from the sun is the ultimate source of energy driving the cycle via the evaporation of water One might think of the hydrologic cycle as a complex hydraulic network with the sun as a pump Since the rate of ow in the network is proportional to the magnitude of the energy gradient and inversely proportional to resistance we often describe the ow processes using various forms of the diffusion equation Darcy39s Law governing the ow of water in soils is the most obvious example of such an equation q K9dhdx where q is the mass ux of water K is the hydraulic conductivity a function of water content 9 and the term in brackets is the potential gradient in the x direction The ow of water in plants is also governed by a complex set of energy gradients and resistances to ow In other parts of the system the diffusion analogy is not so obvious In all parts of the Chapter 4 page 1 hydrologic cycle though the ow processes are difficult to model accurately and are the subjects of continuing research Basic processes and principles Precipitation Rainfall depth and intensity Actual storms and design storms Characterizing storms o Hyetograph o Volume Duration Frequency o Intensity Duration FrequencyilDF curves available for most locations See attached curves for Fort Collins Exceedence probability probability that a storm of a given magnitude and duration will be exceeded at a given location in a given year Return period lExceedence probability Discuss public s failure to understand the concept ofa lOOyear storm Go through an example of how to calculate return periods given a set of annual maximum lhr or 24hr rainfall data Procedure 1 Rank the data from largest to smallestlargest gets rank 1 smallest rank N 2 Compute the exceedence probability for each rank P ranldNl 3 Return period l P Return Period Calculation Example Given 10 years of annual maximum 1hour rainfall find the 2 and 10year design storms Year Maximum 1hr Rank Exceedence Return Period Rainfall PranklN1 1IP cm years 1991 54 1 009 1100 1994 52 2 018 550 1996 51 3 027 367 1992 48 4 036 275 1999 48 5 045 220 1998 47 6 055 183 1993 44 7 064 157 Chapter 4 page 2 1997 43 8 073 138 2000 41 9 082 122 1995 4 10 091 110 To find the 2year storm interpolate between the storms for 183 and 220 years or approximately 475 cm The 10 year storm is interpolated between values for 550 and 110 years or about 536 cm Characterizing pollutant loadings Water pollution requires both a source of a contaminant and moving water to transport the contaminant The moving water can be either surface water or ground water or both To characterize pollutant loadings from a given source both surface runoff and percolation to ground water must be estimated Mass load per time concentration X ow rate Generally ows are estimated using a mass balance for a de ned system or control volume for example a watershed aquifer agricultural field mine parking lot or any region with carefully defined system boundaries A storage in ow out ow Observe the schematic representation of watershed hydrology on page 200 Many possible systems of interest can be defined The relative importance of the various processes often depends on the size of the time scale of interest as we shall see Write mass balance equations for runoff inter ow and ground water ow Often a block diagram of the processes and storage components as shown in Figure 412 can be helpful in formulating and understanding the mass balance Note that evapotranspiration ET does not appear in a mass balance for event scale surface runoff but does appear in a mass balance for inter ow Why How might you calculate ET for a field or watershed using a mass balance Another way to write a mass balance for runoff is Runoff rainfall 7 initial abstractions 7 infiltration Initial abstractions include both depression storage and interception Soil moisture storage not well covered in the text Chapter 4 page 3 Soil moisture storage is most often expressed on a volume basis Soil water content 9 cm of water cm of soil Soil water storage as a depth of water or volumeunit area 9D where D is the depth of soil of interest often the root depth Water is stored in the soil under tension or negative pressure Soils vary in their water holding characteristics which include Porosity I or saturated water content 95 Field capacity about 03 bars tension suction Wilting point about 15 bars tension suction Water contents may be related to tensions negative pressures via a soil water characteristic curve for a particular soil which depends on the soil texture particlesize distribution Imagine a static column of soil and water at equilibrium The water contents and pressures would look something like this 1 5 bars Wilting Point 1 l3 bar Field Capacity Water table Water Content 9 One bar 1 atmosphere Water holding characteristics for soils over a range of textures are shown in Figure 414 on page 152 For a given tension nertextured soils hold more water than coarser teXtured soils For very ne soils a large fraction of the water in storage is held at high tensions above the wilting point and is thus not available for plant uptake page 152 In ltration Capacity Limited by either rainfall rate or the infiltration capacity of the soil that is the ability of the soil to transmit water permeability under the available energy pressure gradient Thus in ltration into coarse soils and dry soils can occur more rapidly than into ne soils and wet soils Runoff Potential Since permeability and in ltration capacity are directly related permeability and runoff potential are inversely related See the SCS Hydrologic Groups A B C D on page 150151 Table 42 Which represents the highest runoff potential Highest in ltration capacity Soil Surveys classify most ofthe soils in the US 4000 soils in Colorado alone Variation of in ltration rate with time Ponding occurs when the rainfall rate exceed the in ltration capacity of the soil Under nonponded conditions in ltration rates vary with the rainfall rates Under ponded conditions infiltration rates decrease with time because the energy gradient decreases as the soil gets wet Under ponded conditions and long times the infiltration rate approaches the saturated hydraulic conductivity Km of the soil because the gradient in Darcy s Law approaches one Alternative Mathematical Models for Infiltration Capacity Horton Holtan Phillips GreenAmpt equations pages 152156 There are several others including the Kostiakov equation All show an exponential decay with time see Fig 415 on page 153 Let s focus on a few examples Horton equation Phillip s equation Green Ampt Note the parameters in each of these equations How would you obtain values for these parameters What is the effect of initial soil moisture content Chapter 4 page 5 Given the above equations how would you estimate the total in ltration which had occurred up to a certain time What if the soil were not ponded the entire time Evapotranspiration Evaporation is an important component of the overall hydrologic budget Evaporation estimates are especially important in estimating annual water yield from watersheds losses from lakes and reservoirs and irrigation demands of crops In Colorado irrigation is by far the largest use of water accounting for 8090 of the total At times it is important to distinguish between evaporation from a water or wet soil surface and transpiration from plants However the two are often lumped together as evapotranspiration ET 0r Et The physics of evaporation are the same whether or not plants are involved However plants add a resistance to water ow which can make estimates a bit more complicated Evaporation and Et can be measured indirectly using a water balance or budget and can be estimated using predictive equations which have the factors affecting evaporation as inputs These equations can be empirical physically based or a combination of the two Physically based models are based on an energy budget Predictive equations may be designed to estimate evaporation from a freewater surface or from a wellwatered reference crop such as clipped grass or alfalfa The latter is called reference Et It is important to make sure that the equation you are using is predicting what you think it is Evaporation from a freewater surface grass reference Et and alfalfa reference Et are all different Actual Et from a crop or native vegetation will be different as well and will depend on the type of crop or plant cover the stage of growth or canopy density and the availability of soil water Generally reference Et is the starting point for estimating plant water use with adjustments for the other factors Factors affecting evaporation 0 Temperature 0 Vapor pressure or relative humidityRelative humidity is the ratio of actual vapor pressure to saturation vapor pressure at that temperature Saturation vapor pressures are given by Table 41 on page 136 0 Solar radiation 7 incoming short wave minus re ected short wave and reradiated long wave 0 Wind speedia function of height and generally measured at a height of 2 meters 0 Soil moisture if soil is dry Chapter 4 page 6 Water Budget Evaporation is often estimated using a water budget or mass balance especially for ponds lakes and reservoirs Predictive Equations There are many predictive equations for evapotranspirations for a wide variety of conditions and uses Several probably not most as Novotny suggests have a form similar to 48 on page 157 The Penman Equation The Penman Equation along with its variations is a physically based and potentially highly accurate method of estimating evaporation andor Et using measurements of weather variables Even though the method is based on an energy balance there are still model parameters which required local calibration for best results The Penman Equation is often used for time steps of one day and is sometimes used for time periods of less than one day Generally as the time period increases the accuracy of estimation increases as well There are several forms of the Penman Equation Generally they are very similar to equation 48 with the addition of a net radiation term RustLp missing from 4 8 plus weighting factors for the two terms The required input weather variables are temperature solar radiation relative humidity and wind speed The equation has two main terms or components The missing term represents the energy input from net radiation and the second term equation 48 represents the evaporative capacity of unsaturated air The second term increases with increasing wind speed and is zero if the air is saturated but is not zero if the wind speed is zero It is interesting to note that the first term is not zero if the air is saturated How can evaporation occur into saturated air Note that the latent heat of vaporization of water L which relates the net energy ux to the evaporation rate is a function of temperature and is given by an equation on page 157 Simpler empirical equations For evapotranspiration reference Et estimates the JensenHaise equation using solar radiation and temperature is often used in the western US to provide estimates of alfalfa reference Et The JensenHaise method should be used for weekly or longer time intervals The BlaneyCriddle equation based on temperature only is used worldwide to provide seasonal Et estimates for specific crops and should be used for time intervals no shorter than one month Chapter 4 page 7 Evaporation Pans Evaporation may be measured directly using an evaporation pan the most common of which is a Us Weather Bureau Class A pan However evaporation from pans is greater than that from a free water surface or a wellwatered reference crop Thus pan evaporation must be adjusted by means of a pan coefficient to obtain lake or crop Et Pan coefficients are presented in the reference cited below and are specific to the type of pan the type of Et to be predicted freewater alfalfa or grass reference and the local conditions surrounding the pan Actual Evapotranspiration for a particular crop or vegetative cover can be estimated by multiplying a crop coefficient time the reference Et see page 158 However the appropriate coefficient to use depends on the method used to obtain the reference value Tables of crop coefficients will work only for specific intended applications and exist for adjusting Penman Et JensenHaise Et etc in addition to pan or lake evaporation to obtain actual Et Reference Jensen ME R D Burman and R G Allen editors 1990 Evapotranspiration and Crop Water Requirements ASCE Manuals and Reports on Engineering Practice No 70 332 p Snowmelt Predictions of snowmelt can be either physically based purely empirical or some combination of the two Physically based models base predictions on the energy available for snowmelt compared to the energy required Energy can be supplied by solar radiation or by heat transfer from the air soil or precipitation The energy requirement is the latent heat of fusion of water What is the numerical value of the latent heat of fusion of water Degree day methods relate snowmelt to temperature These methods assume that snowmelt starts at base value of mean daily temperature usually 0 deg C and increases linearly thereafter eqn 410 The slope CD can be estimated by regression or taken from Figure 312 or other literature values Energy balance methods are based on equations of the form 412 on page 160 similar in concept to a Penman equation for evaporation Runoff and Peak Discharge Analysis and Design Possible design requirements Chapter 4 page 8 1 Total runoff volume 2 Peak runoff rate 3 Runoff rate as a function of time The NRCS Curve Number Equation for total runoff volume page 162 Assumes that a rainfall event may be separated into an initial abstraction actual retention and direct runoff The actual retention will be somewhat less than the potential maximum retention denoted as S S should be a function of land use interception infiltration depression storage and antecedent moisture The overall equation is Q P 7 02 S2P 08S eqns 416 and 417 IfP lt 02 S then assume that Q 00 This equation gives the runoff depth in terms of the rainfall depth P and one unknown S Runoff volume is simply the depth of runoff times the watershed area S is found from the SCS NRCS curve number CN which is an index representing the combination of soil hydrologic group AD cover complex good fair poor and antecedent moisture conditions Hydrologic group can be found in soil surveys or field tests of the minimum longterm infiltration rate see table 45 S is related to the CN as follows S 25400CN 7 254 eq 420 Curve numbers are tabulated in table 39 and adjustments for antecedent moisture condition are in tables 310 and 311 Weighted curve numbers can be used for urban areas with given fraction of impervious surface Study Boxes 44 and 45 Peak discharge The rational method QCiA eq 422 Define the variables in this equation What is a reasonable choice for duration of the design storm De ne time of concentration tc See page 171 Weighted average C values for nonhomogeneous watersheds see eq 423 Be sure to read the footnote in Table 48 pg 1 72 on calculating C values for rural watersheds Don39t just use the value in the right column Chapter 4 page 9 Study Box 46 on page 174175 Distribution of runoff with time from a 1 rainfall hyetograph we wish to construct an 2 excess rainfall hydrograph and to then convert this into a 3 direct runoff hydrograph Construction of excess rainfall hyetographs from rainfall hyetographsiinflltration losses and surface storage losses are removed For any storm the volume of excess rainfall must equal the volume of direct runoff If we are analyzing a measured event in order to evaluate watershed response unit hydrograph we will have measurements of discharge at some stream gage location If runoff is observed in addition to rainfall then the difference between the runoff and the rainfall is equal to the infiltration plus surface storage losses These losses can be distributed over time in a variety of ways the simplest of which is to assume a uniform loss rate When the losses are subtracted from the rainfall hydrograph what is left is the excess rainfall hydrograph Construction of direct runoff hydrographs from stream ow measurements Often the available measurements are of stream ow rather than runoff directly Thus there may be ow present even when it has not recently rained Base ow separationTo extract direct runoff only from an observed discharge hydrograph it is necessary to remove base ow or groundwater flow Several methods for accomplishing this are available All are somewhat subjective The simplest is a straightline method When the baseflow has been removed from a streamflow hydrograph following a storm event what is left is the direct runo hydrograph When runoff is not observed the infiltration losses can be estimated by one of the infiltration capacity equations we have seen earlier In ltration capacity Infiltration capacity can be estimated by Horton s Holtan or Phillip s equations and other similar exponential decay equations Kostiakov GreenAmpt with parameters which can be locally calibrated or roughly approximated using tables NRCS soil surveys etc If the rainfall rate exceeds the infiltration capacity then the difference will be the excess rainfall If the rainfall rate is less than the infiltration capacity the excess rainfall is zero Chapter 4 page 10 For cases in which the rainfall rate does not initially exceed the in ltration capacity the in ltration capacity will not decay as fast as the Horton equation predicts There are several options and much debate about how to proceed The simplest approach is to ignore the problem realizing that you will underpredict infiltration and overpredict excess rainfall as a result Now suppose that we have obtained an excess rainfall hydrograph by some method and we need to convert it into a runoff hydrograph Unit Hydrographs The transfer function that converts an excess rainfall hydrograph into a runo hydrograph is the unit hydrograph Recall the definition of hydrograph Remember that volumes and depths are interchangeable For most analyses depths are more convenient Why are runoff hydrographs needed Why can t we base designs and management on peak discharges alone De nition A unit hydrograph is the direct runo hyalrograph which results from a single unit 1 inch or 1 cm of excess rainfall in a stated time period T Unit hydrographs depend on watershed characteristics and may be obtained by direct observation of rainfall and runoff or any of several synthetic unit hydrographs may be used 431 and 432 on page 178 or the NRCS dimensionless unit hydrograph on pages 180185 Let s suppose now that we have a workable unit hydrograph How do we use it Using Unit Hydrographs to Predict Runoff from Excess Rainfall Recall the definition of a unit hydrographithe direct runoff response or output of a given watershed to a unit input of excess precipitation over a given interval of time T The time interval is the effective duration of the unit hydrograph and can be anything including zero The response in this extreme case is called the unit impulse hydrograph instantaneous unit hydrograph IUH or the kernel function The most convenient interval T is the same as that for which we have an excess rainfall hydrograph as we shall see Unit hydrographs may be used to determine the watershed response to any time pattern of excess rainfall if we can assume that the system behaves linearly In other words if we double the input we double the response the time pattern of response to a given input Chapter 4 page 11 does not depend on when the input occurs and responses to multiple inputs can be added See the discussion of linearity on page 176 The relationship between the excess rainfall hydrograph the instantaneious unit hydrograph and the runoff hydrograph is given by equation 426 on page 176 We can extend this example to the general case of discrete inputs and unit hydrographs as follows ya Z xJ39Ut J39 1 In this equation U is the discrete unit hydrograph ordinate for time with an effective duration T equal to the discretization interval for both excess rainfall and runoff and x is the excess rainfall for time 0 This equation is called a convolution equation and the continuous form 329 is called the convolution integral The use of the convolution equation is illustrated very well in Figure 421 on page 176 Work an example dealing with unit hydrographs The SCS NRCS Unit Hydrographiparticular shape based on analysis of many data sets Both triangular and curvilinear forms are available The triangular form is obviously simpler and we shall work with it There is a single parameter of the NRCS unit hydrograph either the time to peak or time of concentration Either determines the entire unit hydro graph For the triangular form the time to peak tp is 23 to The total time of runoff is 83 tp Thus the recession limb tr 53 tp or 109 tc From geometry the total runoff volume would be 12 qp tp tr For a unit hydrograph this volume must 10 so qp 2tp tr see equation 438 The effective duration of the excess rainfall pulse T or D 0133 tc These relationships are portrayed in Figure 424 on page 181 So all you really need to construct the NRCS triangular unit hydrograph for a given watershed is the time of concentration and the above relationships The rest of the equations are unnecessary The time base D 0133 tc eq 442a All computations are performed using this time interval or closest rounded value Thus the excess rainfall Chapter 4 page 12 hydrograph must be expressed using a discretization interval of T for convolution with the NRCS Unit Hydrograph To nd the time of concentration for a given watershed a number of methods can be used A method suggested in the text is equation 342 on page 160 to nd a lag time t1 which is related to the time of concentration by tc 1666t1 The lag time may be adjusted for urban watersheds using equation 343 Study Box 47 Ground Water Systems Conceptualization See Figures 430 431 and 432 on pages 197 198 and 200 Water balance equations 451 452 and 453 on page 200 Chapter 4 page 13
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