Predicting The Runoff From Storm Rainfall - Provided As A Handout At 6 .
U. S. DEPARTMENT OF COMMERCECHARLES SAwYER, SecretaryWEATHER BUREAUF- W. RMIcEChiefmEDRYSI,RESEARCH PAPER NO. 34PREDICTING THE RUNOFF FROMSTORM RAINFALLby M. A. KOHLER and R.-K. LINSLEYL"7.-' September 1951For sale by the Superintendent of Documents, 1. S.,overnment Printing Office, Washington 25, D. C.-Prime 5 cents
WEATHER BUREAU RESEARCH PAPERSNo. 1 *ProgressReport on Development of an Electronic Anemometer. W. R. Thickstun, July 1943.No. 2 *A Project to Test the Potential Usefulness of Pressure Patternsfor Forecasting. E. W. Norton, G. W.Brier, and R. A. Alien, January 1944.No. 3 *Preliminary Report on Duration of Stormy Periods at Selected Localities and Intervals Between Periods.L. L. Weiss, January 1944.No. 4 *Some Relationships Between Five-Day Mean Surface Maps and Their Component Daily Maps. C. B.Johnson, January 1944.No. 5 *Improvement of Trend Methods of Forecasting. 1P. F. Clapp, July 1943.No. 6 (Unassigned)No. 7 *Formationof New Moving Centers South of Deep Lows. R. C. Gentry, January 1944.No. 8 *An Investigation of a Trajectory Method of Forecasting Flow Patterns at the 10,000-Foot Level. H. G.Dorsey and G. W. Brier, January 1944.No. 9 *Preliminary Report on Stagnant Highs Over Greenland, Iceland, and England, and Over the Bering Seaand Alaska in July and August. R. C. Gentry and L. L. Weiss, January 1944.No. 10 *Persistence in London Temperatures. H. W. Norton and G. W. Brier, January 1944.No. 11 *Skill in Selecting the "Best" Forecast. G. W. Brier, January 1944.No. 12 Notes on Interdiurnal Pressure and Temperature Changes in the Upper Air. R. C. Gentry, January1944. (Unpublished.)No. 13 Investigation and Practical Use of a Method for Constructing Six-Hour Isallobars on Upper LevelCharts. E. M. Cason and P. F. Clapp, January 1944. (Unpublished.)No. 14 Weight Changes for the Atmosphere Divided Into Three Layers. L. L. Weiss, February 1944. (Unpublished.)No. 15 *Some Notes on Forecasting for Atlanta. and Miami Districts (North and South Carolina, Georgia, andFlorida). Grady Norton, February 1944.No. 16 *Verification of a Forecaster's Confidence and the Use of Probability Statements in Weather Forecasting.G. W. Brier, February 1944.No. 17 *PressurePatterns Accompanying Cyclonic Activity in the Azores Area. R. L. Pyle, March 1944.No. 18 *Normal Mean Virtual Temperatures and Weights of the Air Column Between Sea Level and 10,000Feet. Staff, Extended Forecast Section, July 1944.No. 19 *Temperature Changes During Formation and Dissipation of West Coast Stratus. Morris Neiburger(University of California at Los Angeles), July 1944.No. 20 Empirical Studies of the Motion of Long Waves in the Westerlies. P. F. Clapp, July 1944. (Unpublished.)No. 21 *A Collection of Reports on the Preparation of Prognostic Weather Charts. J. IL. Fulks, H. B. Wobus,and S. Teweles, Edited by C. P. Mook, October 1944.No. 22 *Relationship Between Surface Temperature and Mean Virtual Temperature in the .Lower Troposphere.W. M. Rowe, November 1944.No. 23 *Forecastingthe Time of Formation of Stratus Cloud Ceiling at Oakland, California, Airport. EdwardM. Vernon, April 1946.No. 24 *Investigationof Polar Anticyclogenesis and Associated Variations of the Zonal Index. Jerome Namias,September 1945.5 C.No. 25 *Progress Report on Objective Rainfall Forecasting Research Programfor the Los Angeles Area. J.Thompson, July 1946.No. 26 A Study of Quantitative Precipitation Forecasting in the TVA Basin. Glen W. Brier, November 1946. O.25No. 27 Objective Methods of Forecasting Winter Minimum Temperatures at Washington, D. C. C. P. Mook and 0.36Saul Price, August 1947.No. 28 *Possibility of Long Range Precipitation Forecasting for the Hawaiian Islands. Samuel B. Solot,January 1948.No. 29 An Objective Method of Forecasting Five-Day Precipitationfor the Tennessee Valley. William H. Klein, 0.30July 1948No. 30 First Partial Report on the Artificial Production of Precipitation:Btratiform Clouds-Ohio, 1948. 0.30Richard D. Coons, R. C. Gentry, and Ross Gunn, August 1948.*Out o1 print.Note.-Nos. 2, 3, 4, 7, 8, 9,10, and 11are included In one publication under the title A Collection of Reporta on .neded Forecoatiin R2eaearch,Weather Breau, 1044.
PREDICTING THE RUNOFF FROM STORM RAINFALL'M. A.R.RoiTIFR AND1K.L NSLEY2'Division of Climatological and Hydrologic Services, U. S. VWather Bureau, 'Washington, D. C.ABSTRACT'The estimation of the volume of runoff to be expected from a given volume of rainfallis a fundamental problem in flood forecasting. Such estimates are necessary before theunit ihydrograph [1) or other techniques can be used to predict the streamflow hydrograph.The authors describe the technique now used at the River Forecast Centers of the U. S.Weather Bureau for evaluating the effect of season, antecedent conditions, duration ofrainfall and rainfall *amountin determining the portion of the rainfall contributing to storm-runoff 12j. Special -problems encountered in flood forecasting are emphasized. The tech* nique, developed and tested over several years, yields a high degree of accuracy in estimatedrunoff. Although prepared by empirical procedures, the close agreement between relationsfor basins of similar hydrologic characteristics suggests that rational parameters have beenadopted. The similarity between relations also simplifies the work required for theirpreparation.METHOD OF APPROACH7Many articles have appeared in the technicalliterature describing the application of infiltrationtheory to the problem of estimating storm runoff [3]. This is considered by many hydrologiststo be the rational approach and, when consideringheavy, intense rainfall over a small homogeneousarea, it can be used to advantage for some specialized purposes. However, the hydrologic characteristics of a natural basin exceeding .a few acresin area are so variable as to make such a rationalapproach exceedingly complex. When the usualvariations in storm characteristics are superimposed, the solution becomes virtually impossibleunless an unusually dense network of precipitationstations exists. Moreover, the direct applicationof the infiltration theory can be utilized to determine only the surface-runoff component of theflood hydrograph. River forecasting requires thatthe total flow, including interfiow and groundwater flow, be estimated and these two lattercomponents constitute a major portion of. theflood hydrographs for some basins. An evenmore important consideration in forecasting, however, is speed. Time is not available for the detailed consideration of large basins by the rationaliAnltration approach.'rajerpresentedst the 30th.Annml Meeting.ofthemoiaUnion, Washington, -I). C., A.prl 21, 1949.Now with Dept. of Civil .Engineering, Stanlord University, Pala Alto,0811.The difficulties encountered in treating large natural basins in strict accordance with the infiltration theory have led to the use of infiltration indices such as the 0- and W-indices [3]. Sincethese indices must be correlated empirically tofactors representing moisture deficiency of thebasin, their use cannot be considered rational.There is no advantage in the use of such indicesover a direct correlation of runoff -with appropriatefactors. The use of such arbitrary indices forcomputing runoff complicates the solution -without enhancing the accuracy or rationalizing theapproach. After extensive study the WeatherBureau has adopted a graphical correlation ofrunoff with selected parameters as the most satisfactory approach for forecasting purposes.SELECTION OF PARAMETERSThe most important problem in developing atechnique for forecasting runoff is the selection ofthe proper parameters to be used. Runoff is thefactor which-is required in the preparation of riverforecasts. However, since runoff is the residualafter the demands of -interception, infiltration, anddepression storage have been satisfied, there issome logic in using the difference between rainfalland runoff as the dependent variable. This differ-ý&Meepysmnce is 6f encfeiaeRfj'"'r6s,"Tu eai f h"basin recharge."Knowing the basin rechargeIambiguity of this term the authors prefer the t
.4and the rainfall, runoff can be computed by directsubtraction,For the purpose of forecasting, runoff is assumedto fall into two classes.-(I) base or groundwaterflow, and (2) direct runoff. Many methods havebeen suggested for the separation of these twocomponents in the hydrograph. The selectionof method is not as important as the consistentuse of a single, method throughout the study.The method used by the Weather Bureau isshown in figure 1. The curve AB represents anextension of the recession existing prior to thestorm, point B being directly under the peak. Thestraight line BC intersects the hydrograph at apoint n-days after the crest or after the end ofrunoff-producing rainfall. The value of n isassumed constant for any basin, but is variedaccording to drainage area. While basin slopeand other factors should be considered, the valueof n is not particularly critical. If the derivedrelation is to be used in conjunction with a unitgraph, then the same time base should, of course,be used in both analyses. The area boundedby the hydrograph and ABC converted to inchesdepth over the basin is considered to be the stormrunoff. The basin recharge data are computedby direct subtraction of runoff from rainfall.The amount of basin recharge resulting from agiven storm depends upon (1) the moisturedeficiency of the basin at the beginning of rainfall,and (2) the storm characteristics such as rainfallamount, intensity, etc. While storm characteristics can be determined from an adequatenetwork of precipitation stations, the directdetermination' of moisture conditions throughouta basin is extremely difficult. Reliable pointobservations of soil moisture are possible, butan integrated value (over area and throughoutdepth) is required in a medium recognizedfor its marked physical discontinuities, furtheremphasized by cultivation and vegetal cover.Moreover, conditions above the soil surfacemust be considered, i. e., storage capacity ofdepressions and vegetal cover' (interception).Numerous measureable factors have been usedas indices to moisture conditions, notably (1)days since last rain, (2) discharge at beginning ofthe storm, and (3) antecedent precipitation. Thefirst of these is obviously insensitive and shouldnot be used if accurate results are required. Thesecond, base flow, is a reasonably good index inhumid and sub-humid regions, but it is affected by'season and it does not necessarily, reflect changescaused by rains during the previous week. Ante*cedent precipitation is universally applicable andyields good results provided the index is properlyderived and is used in conjunction with season ofthe year or temperature.The antecedent precipitation index is generallydefined by an equation of the typeI b1 .P1 -b2P2 baP2 .-.blp(1)Where Pi is the amount of precipitation whichoccurred i days prior to the storm under consideration, bi is a constant which is assumed to be somefunction of time such as bh 1/i, and the number ofterms is arbitrarily selected. If a day-to-dayvalue of the index I is required, as is the case inriver forecasting, there is considerable advantagein assuming that b, decreases with time (prior tothe storm of interest) -according to a logarithmicrecession rather than as a reciprocal. In otherwords, during periods of no precipitation,Z 10 k'(2)where t is the number of days between I, and theinitial index Io. Letting t equal unity,J kIoTIMEFlouaE l.-Method of hydrograph separation2(3)Thus, the index for any day is equal to that of theprevious day multiplied by the factor k. If rainoccurs on any day, the amount of rain observed isadded to the index as is shown in figure 2. Sincestorm.runoff does not, of itself. add to the residualmoisture of the basin, it is evident that an antecedent index of "precipitation minus runoff," orbasin recharge, should be more satisfactory thanprecipitation only. This refinement requires con-
-.siderably more computations, however, and itsa .question immediately arises regarding snowfall.If the water equivalent of snowfall is added touse is probably not justified.the ýindex at the time of its occurrence, its effectThe effect of a given amount and distributionof antecedent precipitation upon storm runoff on a subsequent rain .storm will be over-emphaobviously depends upon the extent to which itsized if removed from the basin through evaporahas been dissipated through evaporation, trantion and underestimated if melted at a later date.spiration, etc. While k could be assumed to varyIn the usual sequence of events, evaporation fromas a function of pan evaporation, air temperature,the snow surface is not far different from surfaceevaporation following a rain and, consequently,dewpoint or vapor pressure deficiency, much ofthe variation in evapo-transpiration is of a seasonalsnowfall can probably best be considered to havenature and the introduction of season (or week ofbeen applied to the basin on the day it meltedyear) into the correlation has been found highlyrather than when it-'fell.satisfactory. There is an added advantage inPREPARATION OF DATAusing season as a parameter in that it reflects.In general, extended complex storms should bevariations in surface conditions as related to farmbrokeninto as many short, unit storms as can sucing practices, vegetation, etc.cessfully be accomplished through hydrographTheoretically, the value of the recession factork should also be -a function of the physiographiccharacteristics of the basin, but experi ence hasshown that the factor is not critical-values rangefrom 0.85 to 0.90 over most of the eastern andcentral portions of the United States.The antecedent precipitation index can be computed either (1) from average daily values overthe basin, or .(2) from daily precipitation at thevarious stations, and then averaged.To utilize the advantages of the logarithmicrecession, the computation of the index must becarried forward throughout the period of recordbeing analyzed. The index value for any daytheoretically depends upon antecedent precipitation over an infinite period. However, if somereasonable initial value is assumed, the computedFiGuaz 2.-Variation of antecedent index with dailyindex will closely approach the true value withinprecipitation.several weeks. It has been the practice either(1) to begin the computations at the end of a dryspell (prior to the first storm analyzed) with anassumed low value of the index, or (2) to beginthe computations two or three weeks in advanceof the first storm with an assumed value equal tothe normal 10-day precipitation. for the season(which approximates the average index value forthe area). In computing the data for a particular storm,the index at the beginning of the first day of-rainis used. For example, an index value of 1.8would be used for the storm of the 9th and 10thin figure 2. The computation can be rapidlyperformed with the aid of a chart (fig. 3), orcomparable table. By enteringL the chart withan initial index, the value t days later (assumingno rainfall) can be read directly.In any discussion of antecedent precipitation,960594--51-2- -F64INITIAL INDEX (ncihes)ioaua5673.-Chart for computing antecedent precipitationindex.3
family of curves representing the various weeks.analysis. iHaving decided upon the storm periocChart B, for plotting computed vs. observed basinthe amount and duration of rainfall are computeiJrecharge, is placed with horizontal scale (comand tabulated for each storm. While data ar cputed) matching that of Chart A to facilitategenerally insufficient to accurately determine th eplotting. Points labeled with duration are thenaverage duration of rainfall over a basin, thi splotted in Chart B at the observed recharge on thefactor is not critical and can be adequately derivecIvertical scale and at a computed value on theby examination of available six-hourly rainfal Ihorizontal scale corresponding to that determineddata. In the development of the relations to bidescribed, the duration was defined as the sum o:C by entering Chart A with antecedent index andweek number. A smooth family of curves is thenthose six-hourly periods with more than 0.2 miedrawn which represent the effect of duration uponof rain plus one-half the intervening periods witlbasin recharge. The combination of Charts A andless than 0.2 inch. While experimental infiltrationB constitutes a graphical relation for estimatingdata indicate rates commonly in excess of 0.10 inchrecharge from antecedent index, week, and stormper hour after saturation, relations developed toduration. Storm precipitation is then introduceddate consistently show that the portion of basin(Chart C) by (1) plotting computed rechargerecharge which seems to be correlated with dura(from Charts A and B) vs. observed recharge (ontion takes place at rates in the order of 0.01 inchhorizontal scale), (2) labeling the points with rainper hour. The difference between these rates isfall amount, -and (3) fitting a family of curves.largely accountable to interflow, intercorrelations,Charts A, B, and C constitute the first approximaand the method of hydrograph separation.tion of the relation involving the selected parameCOAXIAL GRAPHICAL CORRELATIONters, Chart D, a plotting of observed.rechargeANALYSISvs. that computed from Charts A., B, and C, isshown to indicate the over-all correlation of theIn the previous discussion reasons were adrelation.vanced for the selection of five variables to beSince the parameters are intercorrelated andincluded in the correlation-basin recharge, antesince the first charts were developed independentcedent precipitation index, season or week of year,of factors subsequently introduced, tests should bestorm duration, and storm rainfall. While analyofmadeto determine if revisions of the charts couldtheexistencetical correlation could be used,improvethe relation, i. e., the process is necessarilyjoint functions complicates the problem to such ansuccessiveapproximations. To check theoneofextent that the selection' of an appropriate equaA,the assumption is made thatcurvesofCharttion is extremely difficult. Ezekiel [4] describes athe other charts are correct. Therefore, themethod of graphical correlation which yields'horizontal coordinate for an adjusted point (inexcellent results for some problems, but the coaxialChart A) can be determined by entering Chnarts Bmethod is more flexible and yields correspondinglyand C in reverse order with observed recharge,better results for runoff correlations because of therainfall amount and duration. The ordinate forjoint relations involved.the adjusted point corresponds to the observedThe coaxial method [2] of gTaphical correlation isantecedent precipitation index. In other words,based on the prem is'e that if any important factor isthe week-curves must be revised to fit the pointomitted from a relation then the scatter of pointsadjusted in this manner if the relation is to yield ain a plotting of observed values of the dependentcomputed value equal to the observed. Thevariable vs. those computed by the relation will becurves for duration yat least partiallyandall subsequent approximastormprecipitationareIn other words, if the points of such a plottinginasimilarmanner. In each casetionsaremadelabeled with corresponding values of the omittedbyentering the chart sepoints,areplottedthefactor, a family of curves fitting the data can beobserved values tobothendswithquencefrom-used to modify or correct the values computeddetermine the adjusted coordinates.from the original relation.-.T.he ometho do-of perfor mmogthe correlation-pre.ý.In-applying the-coaial--metho d-to-the selected sented in previous paragraphs is of general appliparameters, a three-variable relation is first decation and can be used as described. In developveloped (fig. 4, Chart A) by (l) plotting antecedenting the relation for basin recharge,. however, cerprecipitation vs. basin recharge, (2) labeling thetain modifications simplify the procedure and repoints with week number, and (3) fitting a smooth4IJ
a)Ti .!4'Ii0 132If rLlL:U2OBSERVED0 RECHARGE (inches)-BASIN2.UMPUTED 40123BASIN RECHARGE (Inches)0-14 COMPUTEDý-\I,.0 5'.}.*I.Ii4FIGuRE 4.-Basin recharge relation for the Monocacy River at Jug Bridge, Md.sult in the derivation of the final relation withinitial moisture conditions in the first chart-afewer approximations.decided'advantage in forecast application.Since storm precipitationis extremely important, the first plotting of ChartA will show so little correlation that the construction of the curve family is extremely diffi6ult. Introducinng storm rainfall in the first plotting would-improve the correlation, but there is also an iaportant advantage in having this parameter in thelast chart of the sequence-namely, the possibilityof computing. runoff in excess of rainfall and ofC7Moreover, the arrangement shown in figure 4 results in the determination of. a unified index ofIf the first plotting in Chart . is limited to thosestorms having an amount of rainfall within a specified class interval (2 to 4 inches, for example),the construction of the curves is simplified provided there are sufficient data. Actually, onlylimited data are required since the general typeof curvature and convergence can be determinedfrom theoretical reasoning. Moreover, the rela'i iiiffiiianyg;ý1'area, and once such a relation is developed, allcurve-families but one can be used as the firstS
Vote: To corect positiveapproximation curves for any other basin in thearea. In fact, a single relation has been found.iet;right.20"applicable to as many as sin or eight tributarydrainages within a river basin.As stated previously, correlations made to date-indicate that storm duration, as determined in anarbitrary manner, is not particularly effective indetermining basin recharge. An assumed spacingof one to two hundredths inch per hour generallyproves satisfactory, but the assumed curves shouldbe checked by plotting after the curve families ofCharts A and C have been finally determined.Examination of figure 4 will show that the errorsof the points with little runoff (recharge approaching precipitation) are considerably magnifiedwhen routed back through the chart sequence asrors sh.ft .0.0* c.snopolive *rfor to Mhe. is1.40.30*70 -.7.4.,.,.10 isS*r.!0. ,,tyfs,.so?r,an.15aso.,,1J O* 10'.7003.002.001.00ANTECEDENT PRECIPITATION INDEX4.00FiGunE 5.-Illustration of method for revision ofweek curves.runoff depths from accumulated precipitation updescribed for the development of the second-apto the termini of the designated periods, and subproximation curves. Therefore, if this approachtracting successive values of runoff. As an alteris used, it will be found that the curves can benative, all precipitation prior to the period ofmore readily determined if low-runoff points areinterest can be considered to be antecedent preomitted in the plotting. As an alternate apcipitation, and the storm rainfall for the periodproach, the required revisions of the curves canused to compute the corresponding increment ofbe determined qualitatively by labeling therunoff. For forecast purposes, -where time is ofpoints of Chart D with week number or durationthe essence, the first method may be preferable.to determine if there is any residual correlation.The second method, on the other hand, ore sigonificance to time variations of rainfallin figure 5, where the errors of the relation areintensity and may, therefore, provide for moreplotted against antecedent precipitation withoftheseaccurate computations. However, the relativeEithernumberasaparameter.weekaccuracies of the two techniques. are also dependsupplementary plottings indicate in which direcent upon the adequacy of the assumed weightstion the curves should be shifted. For example,for antecedent precipitation, since the first methodfigure 5 indicates that weeks numbered about 5is in accord with the analysis used in developingthrough 8 should be shifted to the right for highthe basin relation.antecedent index and to the left for low. TheSince it is impossible to segregate the waterdegree of shift indicated by the .plottings can bepassing the gaging station according to thereflected back through the chart sequence toportion of the basin in which it fell, statisticallydetermine approximately how much the curvederived runoff relations must necessarily beshould be shifted.determined from basin averages of the parameters.Unfortunately, because of the higher order andAPPLICATIONS OF DEBR-IED RELATIONSjoint functions involved, a relation which isbased on storms of uniform areal distributionIn preparing river forecasts, runoff is the conwillyield runoff values which are too low whenSincebasinrecharge.thanratherfactortrollingto storms with extremely uneven' distriappliedhowever,runoff,determinerainfall and rechargebution. This can be demonstrated by computingthe curves of Chart C in figure 4 can be convertedthe runoff for four, six, and eight inches of stormto read runoff directly as shown in figure 6.precipitation, assuming all other factors to remainMoreover, the charts can be superimposed .fig.constant. 7hile six is the average of four and7) to conserve space without reducing the scale.eight, the runoff depths computed from thesecatin of thepTh epi er three values of precipitation do not 'bear a correquires that runoff increments be estimated forresponding redation. An uneven distribution ofsuccessive time periods throughout an extendedantecedent precipitation produces similar results.storm. This can be accomplished by computing6
SII. ---L- 1-z.d-- 0-7Lwznhz2hz,wzzizzwzi 2 zSTORM RUNOFF (Inches)7v//71*-e- - -Ab-c1o II 1I27 III/I,2 i/ V i/.1 Z-4/[/Y 1/ 1 I IIJLIIW/I/if/H H,/ I .1- /4- IIII.FGauRE 6.-Runoff relation for Monocacy River at Jug Bridge, Md.If, however, the runoff relations are based on datarepresenting reasonably uniform conditions, theycan properly be used to compute the runoff in thevicinity of each' of the rainfall stations. Theaverage of such computed values will, in general,more nearly approach the observed runoff. Inother words, if either storm or antecedent precipitation is highly variable from one portion ofthe basin to another, then computed runoff'-Cep-s,pFaveraged,DEFICIENCIES OF DERIVED RELATIONSRelations of the type described yield highcorrelation for most basins and provide a simplemethod of computing runoff, but they, nevertheless, have certain deficiencies which shouldnot be overlooked. First, rainfall intensity isomitted; second, frozen soil obviates their directuse; and third, snowfall has not been considered.Sin& Brai3Ef h-mo6ut- add-adura tiojf e-considered, average intensity for the entire storm7--
STORM RUNOFF(Inches)0zFIaM 7.-Runoff relation for Monocacy River at Jug Bridge, Md., with curve-families superimposed.8
the estimated water equivalent can be sub* period is an integral part of the relations. Howtracted from the observed storm precipitation.ever, the computed runoff for a 5-inch, 24-hourstorm is independent of intensity variationsSnow on the ground at the beginning of thestorm should be included in the storm precipwithin the period. As mentioned previousJy,itation (rather than antecedent precipitation)the storm can be treated as several short periodsof rainfall, considering all rainfall occurring priorif it is dissipated during the storm.to any specific period as antecedent precipitation.REFERENCESWhile intensity variations can be given consider1. L. K. Sherman, "Streamflow from Rainfall byation in this manner, neglecting intensity apthe Unit-graph Method," Engineering Newsparently causes serious error in total stormRecord, vol. 108, No. 14, April 7, 1932, pp.runoff only when intensities are so great through501-505.out the entire storm that rainfall runs off too2.R.E. Linsley, M. A. Kohler, and J. L. H.ofdeficiencyrapidly to alleviate the moisturePaulhus,Applied Hydrology, McGraw-Hill,the basin. Experience has shown that theNew York, 1949.relations yield fair results during frozen conditions,3. H. L. Cook, "The Infiltration Approach to theprovided that the weekly curve representingCalculation of Surface Runoff," Transactions*manmuin runoff conditions is used, regardless ofof the American Geophysical Union, vol. 27,the date of the storm. Storms which are preNo. 5, Oct. 1946, pp. 726-747.dominantly snow present an entireJy different4. M. Ezekiel, Methods of Correlation Analysis,problem and are not considered here. If only a2d ed., Wiley, New York, 1941.slight snow cover remains at the end of the storm,9
N,WEATHER BURLEAU RESEARCH PAPERS(Continued from inside self cover)Second Partial Report on the Artificial Production of Precipitation: Cumuliform Clouds--Ohia, 1948. 0.30Richard D. Coons, Earl L. Jones, and Ross Gunn, January 1940. 0.30No. 32 FurtherStudies in Hawaiian Precipitation. Samuel B. Solot, January 1950.No. 33 Artificial Production of Precipitation. Third Partial Report: Orographic Stratiform Clouds-California,1949. Fourth Partial Report: Cumuliform Clouds--Gulf States, 1949. Richard D. Coons, Earl L.Jones, and Ross Gunn, September 1949.No. 34 Predicting the Runoff From Storm Rainfall. M. A. RKhler and R. K. Linsley, September 1951. 0.40No. 31I"Weather Bureau Research Papers for sale by Superintendent- of Documents, U. S. Government PrintingOffice, Washington 25, D. C.10U. S. GOVERNMENTPRIINTINGOFFICE. 1251
U. S. DEPARTMENT OF COMMERCE CHARLES SAwYER, Secretary WEATHER BUREAU F- W. RMIcE mEDRYSI, Chief RESEARCH PAPER NO. 34 PREDICTING THE RUNOFF FROM STORM RAINFALL by L" 7. -M. A. KOHLER and R.-K. LINSLEY ' September 1951 For sale by the Superintendent of Documents, 1. S. ,overnment Printing Office, Washington 25, D. C. -Prime 5 cents
May 02, 2018 · D. Program Evaluation ͟The organization has provided a description of the framework for how each program will be evaluated. The framework should include all the elements below: ͟The evaluation methods are cost-effective for the organization ͟Quantitative and qualitative data is being collected (at Basics tier, data collection must have begun)
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Chính Văn.- Còn đức Thế tôn thì tuệ giác cực kỳ trong sạch 8: hiện hành bất nhị 9, đạt đến vô tướng 10, đứng vào chỗ đứng của các đức Thế tôn 11, thể hiện tính bình đẳng của các Ngài, đến chỗ không còn chướng ngại 12, giáo pháp không thể khuynh đảo, tâm thức không bị cản trở, cái được
v Agriculture Handbook 590 Ponds—Planning, Design, Construction Tables Table 1 Runoff curve numbers for urban areas 14 Table 2 Runoff curve numbers for agricultural lands 15 Table 3 Runoff curve numbers for other agricultural lands 16 Table 4 Runoff curve numbers for arid and semiarid rangelands 17 Table 5 Runoff depth, in inches 18 Table 6 I a values for runoff curve numbers 21
v Agriculture Handbook 590 Ponds—Planning, Design, Construction Tables Table 1 Runoff curve numbers for urban areas 14 Table 2 Runoff curve numbers for agricultural lands 15 Table 3 Runoff curve numbers for other agricultural lands 16 Table 4 Runoff curve numbers for arid and semiarid rangelands 17 Table 5 Runoff depth, in
