CVEEN 4410: Engineering Hydrology Topic: Frequency Analysis General .
FrequencyAnalysis ICVEEN 4410: Engineering HydrologyTopic: Frequency AnalysisLearningObjectivesGeneral Goal: Use frequency analysis of historical data to forecast hydrologicevents, e.g., specific flood magnitudes, annual runoff values, etc.RandomVariablesSpecific goals/outcomes for this presentation: define random variables define PDFs and PMFs define Method of Moments define what is a probability distribution PDFsandPMFsMethod ofMomentsuse general (non-graphical) frequency analysis to forecast the probabilityof a given size flood in cfs(specifically: an example problem is assigned here, and you are tasked with working through thisproblem at home; we will then work through this example problem together in class)Probabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysisOcean
FrequencyAnalysis IConsider: Peak intensity (in in/hr) of next rainfall event in SLC Peak streamflow (in cfs) of next year in EmigrationCreek Snowmelt runoff volume (in ac-ft) in thod ofMomentsTake 1 minute and estimate these valuesThink about these values and decidewhether we can predict these values withcertainty!Values that cannot be predicted withcertainty are called random variablesFrequency Analysis ICVEEN 4410 Engineering HydrologyProbabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysis2
FrequencyAnalysis ILearningObjectivesIs a coin flip outcome a random variable?RandomVariablesIs the outcome of a roll of a die a randomvariable?PDFsandPMFsMethod ofMomentsYes!Probabilitydistributions These types of random variables that canonly take on values from a specifieddomain of discrete values are calleddiscrete random variablesFrequency Analysis ICVEEN 4410 Engineering Hydrologysome criticalaspectsGeneral (nongraphical)FrequencyAnalysis3
FrequencyAnalysis ILearningObjectives Hydrologic random variables can take on valuesfrom a domain of continuous values –continuous random variables If continuous data are assigned to intervals(quantiles), then data are said to be quantizedcontinuous (e.g., histograms)RandomVariablesPDFsandPMFsMethod ofMomentsProbabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysisFrequency Analysis ICVEEN 4410 Engineering Hydrology4
FrequencyAnalysis ILearningObjectivesSpend 1 minute (pause this video) and thinkabout how you would quantify the probabilityof streamflow exceeding 16,000 cfs in a riverany given yearRandomVariablesPDFsandPMFsMethod ofMomentsAnalysis of Historical Data!Probabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysisFrequency Analysis ICVEEN 4410 Engineering Hydrology5
FrequencyAnalysis ILearningObjectivesPDFs (and PMF, the discrete equivalent):RandomVariablesPDFsandPMFsMethod ofMomentsProbabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysisFrequency Analysis ICVEEN 4410 Engineering Hydrology6
FrequencyAnalysis IMethod of Moments:LearningObjectives Hypothesize underlying ethod ofMomentsProbabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysisFrequency Analysis ICVEEN 4410 Engineering Hydrology7
FrequencyAnalysis IMethod of Moments:LearningObjectives Hypothesize underlying ethod ofMomentsProbabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysisFrequency Analysis ICVEEN 4410 Engineering Hydrology8
FrequencyAnalysis IMethod of Moments:LearningObjectives Hypothesize underlying probabilitydistribution Obtain sample; compute sample momentsRandomVariablesPDFsandPMFs Equate sample moments and parameters ofthe proposed density functionMethod ofMoments Construct frequency curve Check data fit to frequency curveProbabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysisFrequency Analysis ICVEEN 4410 Engineering Hydrology9
FrequencyAnalysis ILearningObjectivesSample Moments: the first three moments arethe mean, standard deviation, and skew:RandomVariablesPDFsandPMFsMean:Method ofMoments2ùé 1S êXi - X úåë n - 1 i 1ûnStandard Deviation:nStandardized Skew:Frequency Analysis Ig ((n å Xi - Xi 1))Probabilitydistributionssome criticalaspects3( n - 1) ( n - 2 ) S 3CVEEN 4410 Engineering Hydrology0.5General (nongraphical)FrequencyAnalysis10
FrequencyAnalysis ITwo Methods (in general) ofFrequency Fs1. Method of Moments2. Graphical MethodsMethod ofMomentsProbabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysisFrequency Analysis ICVEEN 4410 Engineering Hydrology11
FrequencyAnalysis ILearningObjectivesDifferent Probability Distributions forFrequency AnalysisRandomVariables1. NormalPDFsandPMFs2. Log-normalMethod ofMoments3. BinomialProbabilitydistributions4. Exponentialsome criticalaspects5. Gamma6. Log-Pearson Type IIIToday -- we’ll discuss applications that assume the normal distributionFrequency Analysis ICVEEN 4410 Engineering HydrologyGeneral (nongraphical)FrequencyAnalysis12
FrequencyAnalysis IMethod of Moments forAssumed Normal DistributionLearningObjectivesRandomVariables1. Assume random variable has a normaldistribution with population parameters and 2. Equate the sample moments to the populationparametersPDFsandPMFsMethod ofMomentsProbabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysisFrequency Analysis ICVEEN 4410 Engineering Hydrology13
FrequencyAnalysis ILearningObjectivesSome critical aspects:RandomVariablesThe cumulative distribution function, or CDF:PDFsandPMFsF(x) P(X x) 1 - 1/T; note that T 1 / (1 - F)Return Period T 11 1- (non - exceedance probability) exceedance probabilityThe CDF represents the probability that a randomvariable X takes on a value less than or equal to x. T isthe return period -- an annual maximum event has areturn period of T years if its magnitude is equaled orexceeded once, on average, every T years. F is alsothe NON-EXCEEDANCE PROBABILITY.Frequency Analysis IMethod ofMomentsCVEEN 4410 Engineering HydrologyProbabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysis14
FrequencyAnalysis ILearningObjectivesSome critical aspects:RandomVariablesThe frequency factor:PDFsandPMFsx-xK SxMethod ofMomentsWhere the variables in the numerator are the randomvariable and its mean, respectively, and Sx is thestandard deviationProbabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysisFrequency Analysis ICVEEN 4410 Engineering Hydrology15
FrequencyAnalysis ILearningObjectivesSome critical aspects:RandomVariablesThe frequency factor K also corresponds to thevariable “z”, also called the “standard normalvariate”:z x-msSee Appendix D of text NormalDistribution Table, includingtabulation of frequency factors(standard normal variate, z)PDFsandPMFsMethod ofMomentsProbabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysisFrequency Analysis ICVEEN 4410 Engineering Hydrology16
FrequencyAnalysis ILearningObjectivesSome critical aspects:RandomVariablesThe magnitude of a random variable x for a givenreturn period is given by:PDFsandPMFsx x z iSxMethod ofMomentsProbabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysisFrequency Analysis ICVEEN 4410 Engineering Hydrology17
FrequencyAnalysis IGeneral (non-graphical) Frequency Analysisusing a normal distribution:LearningObjectivesRandomVariables1. Assume random variable has a normaldistribution with population parameters and 2. Compute the sample momentsand SPDFsandPMFs3. For the normal distribution, the parameters andsample moments are related by and S4. Calculate the CDF: F(z) 1 - 1/T5. Obtain the standard normal variate “z” frompublished tables of values (Appendix D of text)6. Use x x z iSx to calculate magnitudeWith these steps, you can calculate how frequent an event is likelyto occur, and what the magnitude of that event might be.Frequency Analysis ICVEEN 4410 Engineering HydrologyMethod ofMomentsProbabilitydistributionssome criticalaspectsGeneral (nongraphical)FrequencyAnalysis18
In-Class Exercise: The normal distribution is fit todischarge data for the Siletz River. What is the 100 year flood magnitude?What is the probability that a flood will beless than or equal to 30,000 cfs?Please review this problem at home, and be prepared towork through it in-class (as an “in-class” exercise).Frequency Analysis ICVEEN 4410 Engineering Hydrology19
Ocean General Goal: Use frequency analysis of historical data to forecast hydrologic events, e.g., specific flood magnitudes, annual runoff values, etc. Specific goals/outcomes for this presentation: define random variables define PDFs and PMFs define Method of Moments define what is a probability distribution use general (non-graphical) frequency analysis to forecast .
Physical Hydrology Second Edition S. Lawrence Dingman University of New Hampshire . Introduction to Hydrologic Science 1.1 Definition and Scope of Hydrology 1 1.2 Development of Scientific Hydrology 1 1.3 Approach and Scope of This Book 5 Basic Hydrologic Concepts 2.1 Physical Q
Stanford University, the University of Arizona and Wisconsin. The Hydrology Program at NM Tech now offers an on-line 15-Credit Graduate Certificate and a 30-Credit coursework only Professional Masters Degree Hydrology. The hydrology faculty who teach distance education classes are listed below in Table 1.
Chapter 7 HYDROLOGY 7.1 HYDROLOGIC DESIGN GUIDELINES Manual, hydrology will address estimating flood magnitudes as The following sections summarize ODOT practices that relate to hydrology.
with the LACDPW Hydrology Manual. The soil type used is No. 10 and the 50year, 24hour ‐‐ isohyet is 5 inches per Appendix B Sheet 1H1.7 of‐ LACDPW Hydrology Manual (2006). The isohyets for WQV and 25year storms are converted by multiplication factors per Table 5.3.1 of ‐ LACDPW Hydrology Manual.
This edition includes new sections on wetlands hydrology and snowmelt hydrology, an expanded section on arid lands hydrology, corrections of minor errors, and inclusion of dual units. 17.
Topic 5: Not essential to progress to next grade, rather to be integrated with topic 2 and 3. Gr.7 Term 3 37 Topic 1 Dramatic Skills Development Topic 2 Drama Elements in Playmaking Topic 1: Reduced vocal and physical exercises. Topic 2: No reductions. Topic 5: Topic 5:Removed and integrated with topic 2 and 3.
Timeframe Unit Instructional Topics 4 Weeks Les vacances Topic 1: Transportation . 3 Weeks Les contes Topic 1: Grammar Topic 2: Fairy Tales Topic 3: Fables Topic 4: Legends 3 Weeks La nature Topic 1: Animals Topic 2: Climate and Geography Topic 3: Environment 4.5 Weeks L’histoire Topic 1: Pre-History - 1453 . Plan real or imaginary travel .
the tank itself, API standards prescribe provisions for leak prevention, leak detection, and leak containment. It is useful to distinguish between leak prevention, leak detection and leak containment to better understand the changes that have occurred in tank standards over the years. In simple terms, leak prevention is any process that is designed to deter a leak from occurring in the first .
