WIXLIB

Double-Mass Analysis of Point PrecipitationThe double-mass analysis is used to detect if data at a site have been subjected to asignificant change in magnitude due to external factors such as problems withinstrumentation, observation practices, or recording conditions.It consists of plotting cumulative rainfall values at a test station against the cumulativemean rainfall values at surrounding (base) stations. It is assumed that changes due tometeorological factors will affect all stations equally and therefore any breaks in thedouble-mass curve are strictly due to external factors. However, natural variations in thedata can produce apparent changes in slope that need to be investigated further byperforming statistical hypothesis testing analysis.If the data are consistent, the double-mass curve will be a straight line of constant slope.If the data is not consistent, a break in the double-mass curve will be apparent. The ratioof the slopes prior (a) and after the break (b) can be used to adjust the data in two ways:1. The data can be adjusted to reflect conditions prior to the break. This is done bymultiplying each precipitation value after the break by the ratio a/b.or2. The data can be adjusted to reflect recent conditions after the break. This is doneby multiplying each precipitation value prior to the break by the ratio b/a.Applicability: Base stations should be located relatively close to station being tested. Method should not be used in mountainous areas where precipitation can deviatesignificantly for nearby stations. Method should only be used for long-term adjustment of precipitation data but notfor adjusting daily or storm precipitation.12

Double-mass curve analysis100Cumulative rainfall at test stationOriginal dataData adjusted toreflect conditionsprior to the break90807060bbreak501Data adjusted toreflect conditionsafter the break4030a2011010090807060504030201000Cumulative value at surrounding (base) stationsEstimating Missing Point Precipitation DataThe most common methods for estimating missing point precipitation data include: Arithmetic Average Method – Missing precipitation values at a station can beestimated by a simple arithmetic-average of concurrent precipitation at three ormore stations which are close to and evenly spaced around the location wheredata is missing. Use method only if the normal annual precipitation at the threesites do not vary significantly ( 5-10%) from the missing station’s normal annualprecipitation. Normal Ratio Method - Missing precipitation values at a station can beestimated from concurrent observations at 3 or more neighboring stations basedon the normal-ratio method:Px1 n P i N x n i 1 N i Px missing precipitation value at station xNx normal long-term, usually annual, precipitation at station X. Nx could alsobe taken as the long-term average value for a particular month for all years ofrecord.Pi precipitation value at neighboring station i for the concurrent period13

Ni normal long-term precipitation for neighboring station in number of neighboring stations Inverse Distance Squared Method – Missing precipitation values at a stationcan be estimated from concurrent precipitation measurements at the closeststations in each of 4 quadrants (North, South, East, and West). n Pi 2 i 1 d i x Px n 1 2 i 1 d i x Px missing precipitation value at station xdi-x distance from station i to station xPi precipitation value at neighboring station i for the concurrent periodn number of neighboring stations (4: one on each quadrant N, S, E, W)Converting Point Precipitation to Areal PrecipitationThe most common methods of determining rainfall averages for an area based on data fora limited number of precipitation gages include: Arithmetic Average Method – Assigns equal weight to all gages irrespective oftheir relative spacing and other factors. Appropriate if gages are uniformlydistributed over a flat area. Thiessen Polygon Method – Perpendicular bisectors of the lines connecting thegages form polygons around each gauge. The basin average rainfall is thendetermined as a weighted average of the precipitation at each gage, with theweighting factor being the polygon area.NP i 1N i 1Ai PiAiP average precipitation for the areaPi precipitation at gage iAi area of Thiessen polygon enclosing gage iN number of gages or Thiessen polygons Isohyetal Method – It is considered the most accurate method since it considersorographic effects.1. Contours of equal precipitation are drawn.2. The area between successive isohyets is computed and multiplied by thenumerical average of the two contour values.14

3. The sum of #2 is computed and divided by the total drainage area to computethe weighted average precipitation.NP i 1N i 1Ai PiAiP average precipitation for the areaPi average precipitation between two successive contoursAi area between two successive contoursN number of areas between successive contours15

EvapotranspirationEvapotranspiration (actual evapotranspiration, AET) is the combined processes bywhich water is transferred to the atmosphere from open water surfaces and vegetation. Itconsists of evaporation, which is the amount of water vaporized into the atmosphere fromopen water surfaces and land areas, and transpiration, which is the amount of waterabsorbed by plants and crops and eventually discharged into the atmosphere through theplants stomata. The source of water for the plants and crops can be from the unsaturatedand saturated zones.During larger storm events, the intensity of precipitation is much larger than the rate ofevapotranspiration. Therefore, evapotranspiration is commonly ignored or lumped withother abstractions when analyzing the water budget during and immediately following astorm event. For longer and drier periods, evapotranspiration becomes a significantcomponent of the water budget.Potential evapotranspiration (PET) is a measure of how much the atmosphere controlsevapotranspiration independent of the surface hydrologic conditions. It is the quantity ofwater evaporated from an idealized extensive free water surface per unit area, per unittime under existing atmospheric conditions.Moisture deficiency limits the actual evapotranspiration rate, therefore AET PET.Evaporation from an Open-Water BodyAn evaporation pan is usually used to estimate evaporation from an open water body (e.g.lake or reservoir). The pan evaporation is computed based on the difference in theobserved water levels adjusted for any precipitation observed between observations. Theactual evaporation from a real open water body is smaller than that measured from a pan.Therefore, a correction coefficient is applied to the measured pan evaporation:E L KE PEL evaporation from an open water bodyK pan coefficient (0.6-0.8, with an average value of 0.7)EP pan evaporationApplicability: The largest errors in the evaporation pan method are due to the assumed pancoefficient. Therefore, the method is usually useful to provide long-term ballparkestimates of evaporation and to analyze the variability of evaporation.The method is more appropriate for very shallow water bodies. For large waterbodies, it may necessary to adjust for heat storage and energy advection.16

ReservoirsIn an ideal world, the quantity, timing, quality, and distribution of available water wouldmatch human needs. Unfortunately, freshwater is scarce in many parts of the world,threatening human health, limiting agricultural and industrial production, and causingecological degradation. It is estimated that less than 3/4 of a percent of the total volumeof water on Earth is freshwater stored in aquifers, the vadose zone, lakes, streams,wetlands, and the atmosphere. On the other hand, excess water at the wrong time andlocation, can cause catastrophic flooding.Reservoirs serve multiple purposes that are directly related to the quantity, timing, qualityand distribution of water. These include flood control, water supply, water quality,groundwater recharge, sediment control. Secondary purposes include recreation, wildlifehabitat enhancement, etc.Water Supply ReservoirsWater supply reservoirs are used to store water during periods of surplus and provide asource of water during periods of drought. Water supply reservoirs may serve a dualpurpose of flood control.A Rippl diagram is a common method of sizing water supply reservoirs. It consists of agraph of cumulative inflows and cumulative demands from the reservoir with respect totime. Generally a constant demand is assumed, so the cumulative demand will plot as astraight line. The cumulative inflow curve will have a large slope during periods of highinflow, and will flatten out during periods of little or no inflow. If pseudo-demand linesare drawn tangent to a peak and a subsequent trough, the separation between the two linesgives the volume that would need to be stored in the reservoir to satisfy the constantdemand for that period. The reservoir capacity required so that the community served bythe reservoir does not run out of water during a drought condition would be the largestseparation between pseudo-demand lines.17

Rippl diagramCumulative inflowCumulative demand70000Cumulative inflow or demand (ac-ft)60000Minimumrequiredreservoircapacity 32,160 ac-ft5000040000300002000010000Jan9M 6ar-9M 6ay-9Ju 6l -9Se 6pN 96ov-9Ja 6n9M 7ar-9M 7ay-9Ju 7l -9Se 7pN 97ov-9Ja 7n9M 8ar-9M 8ay-9Ju 8l -9Se 8pN 98ov-9Ja 8n9M 9ar-9M 9ay-9Ju 9l -9Se 9pN 99ov-9Ja 9n0M 0ar-0M 0ay-0Ju 0l -0Se 0pN 00ov-000DateRippl Diagram of cumulative inflow and demandReservoirs for Flood Control and Other Uses Detention reservoir/pond/basin, dry pond – Reservoir designed to store watertemporarily as part of a flood control management system. It has no conservationpool. The reservoir is designed to temporarily store a specific volume of runoff,which is usually defined in terms of a return frequency (e.g. 100 year flood).Most are designed to empty out the runoff after the peak of the runoff has passed(usually less than a day) by slowly draining (usually through a bleeder) into anearby flood control conveyance system. If the flow exceeds the storage capacityof the reservoir, an uncontrolled structure (usually a spillway) provides an outletfor the excess water. Retention reservoir/pond/basin – Reservoir that holds water for an extendedperiod of time. It has a conservation pool. Retention ponds usually serve twomain purposes: to contain runoff generated by urban development, and to providelocalized recharge to the groundwater system which would otherwise be limiteddue to imperviousness of urban cover. Other uses include pollution control byfiltering of stormwater, fish and wildlife habitat, sedimentation control, recreationetc. If the flow exceeds the storage capacity of the reservoir, an uncontrolledstructure (usually a spillway) provides an outlet for the excess water.18

Flood Control Analysis and DesignFlood control reservoirs and other flood control facilities are designed to contain excessprecipitation resulting from extreme storms or rapid snowmelt. In designing thesefacilities, it is important to estimate the timing, quantity, distribution and peak flowassociated with extreme storm events. This information is encapsulated in a hydrograph,which is a plot of streamflow as a function of time at a specific location in a streamchannel. In addition, it is important to determine the probability of exceedance of theseevents due to safety and economic considerations.The diagrams below summarize the processes required for estimating a hydrograph at alocation downstream of a stream or reservoir, and the peak flood discharge associatedwith a storm event. These processes are discussed in more detail in the next infallStreamand/orreservoirroutinghydrologic ingDownstreamhydrograph**Not discussed hereProcess for generating an outflow (downstream) hydrograph for a stream orreservoir starting from lModelEffectiveRainfallPeakdischargeProcess for estimating the peak discharge starting from rainfall19

To generate a downstream hydrograph, the rainfall falling on a watershed or contributingarea is converted into effective rainfall by means of an effective rainfall model. Aneffective rainfall model converts the total (gross) precipitation into abstractions andeffective rainfall which eventually reaches a stream channel as direct runoff.The abstractions are the portion of precipitation that does not contribute to direct runoff.They include interception, depression storage, and infiltration. Infiltration is usually themajor abstraction from rainfall during a significant runoff-producing storm. Someabstractions occur immediately after the beginning of a storm prior to the beginning ofrunoff. These are called initial abstractions and include infiltration prior to ponding,depression storage and interception. Infiltration – Movement of water from the land surface to the upper layers of thesoil. It is usually the major abstraction from rainfall during a significant runoffproducing storm. Depression storage – Fraction of precipitation that is trapped in puddles, ditches,and other surface depressions from where it evaporates or infiltrates into the soil. Interception – Fraction of precipitation that is retained on buildings and plants andis eventually evaporated.Effective rainfall (effective precipitation, precipitation excess) is the portion ofprecipitation that is available as overland flow supply. In order for water to start flowingthrough the land surface, first a very thin layer of water needs to be stored on the landsurface to provide continuity of flow en route to a stream. This volume of water is calleddetention storage. The effective rainfall (overland flow supply) travels through the landsurface until it eventually reaches stream channels as direct runoff. Direct runoff – Portion of the total runoff hydrograph at a stream which is causedby and directly following a rainfall or snowmelt event. It consists of: a) overlandflow, and b) quick interflow. It contributes rather quickly to streamflow.To quantify this lag or travel time between effective rainfall and direct runoff, a basinrouting model is used. One such model is a unit hydrograph, which describes the shortterm response of a watershed to a unit volume of effective rainfall applied uniformly overthe entire watershed at a constant rate for a unit time. It includes contributions tostreamflow immediately following a rainfall event (i.e. only includes contribution fromdirect runoff and excludes baseflow). The unit hydrograph is assumed to encapsulate allthe combined physical characteristics of the basin and that of the storm. Based on theeffective rainfall and the basin routing model the direct runoff hydrograph reaching astream is produced. Alternatively, if only the peak of the direct runoff hydrograph is ofinterest, a peak discharge model can be used.In addition to the direct runoff, a stream receives inflows from the subsurface. Thiscomponent of the streamflow hydrograph is known as baseflow or delayed runoff since it20

has a much longer travel time than the direct runoff. The source of this flow is fromwater that infiltrated during previous storm events and percolated down into thegroundwater, where it flowed through the unsaturated and saturated zones until itdischarged into a stream. Baseflow, base runoff, delayed runoff – Portion of the total runoff hydrograph at astream location which is composed of contributions from: a) groundwater runoff,and b) delayed interflow. Baseflow is the result of water fr

Source: Civil Engineering Reference Manual for the PE Exam, 10th Ed. (Lindeburg, 2006) Steel's formula encapsulates these two observations: t b K i Steel formula i intensity (in/hr) t duration (min or hr depending on how K and b are defined) K,b constants empirically derived for a return period and location