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Considerations for Data Series for Current Practices Scenario November 2006 Update 17 January 2007 B. Contor (New stuff will be in green boxes or on green slides)

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Outline Goals Time series for index How to apply

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Goals AVERAGE STRESS Variability Serial correlation (persistence) Probability distribution

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Goals AVERAGE STRESS – correct endpoint Variability Serial correlation (persistence) Probability distribution correct variability

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How to meet these goals: Candidate data Apply data –Multiple-traces paradigm –Single-trace paradigm Evaluation Reality Check

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1. Candidate Data:

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Candidate Time Series Lewis Lake SNOTEL White Elephant SNOTEL Natural flow at Heise Palmer Index (PDSI)

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They all are similar

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Time Series Lewis Lake SNOTEL White Elephant SNOTEL Natural flow at Heise Palmer Index (PDSI) No data before 1981 Two long-term candidates

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Preference?

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Also consider diversions:

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Increasing variability?

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Change in persistence?

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Average index 1.04 Candidate Years

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New item: Diversions Index The biggest component of recharge is diversions Are diversions correlated to our indices? Remember two goals: –correct end point –correct representation of variability

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Proposal: Eliminate 1997 from Candidate Pool Damage to infrastructure means water-use response is unique, not representative of 1997’s hydrologic condition

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2. Multiple traces paradigm Select data to create representative series Use average of data to create “baseline” run –result after many periods = endpoint –trajectory from start describes how fast adjustment will be Multiple traces of variable series to define probability envelope

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Three methods to select from candidate years: Historical sequence Synthetic Stochastic

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Use Historical Series to Order Candidate Years (Synthetic A) Identify index of each year of record Associate each year of record with one candidate year Adjust to obtain average index ~ 1.0

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I didn’t calculate the diversions implications of Synthetic A

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Synthetic Series Identify combination of years w/ correct average Combine into time series –repeat “actual” order of years (Synthetic B) –adjust order (Synthetic C)

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In either case: Heise Index avg 0.992 DetrendDivIndex 1.019

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Stochastic Series Identify combination of years w/ correct average Combine in random order

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I haven’t analyzed the diversions implications of the stochastic series

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Define Variability Envelope: Repeat Series w/ Different Start

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Multiple-trace representation of variability Graphical: –Envelope defined by multiple traces –No matter the starting condition, envelope will converge to range determined by water- budget ? ?

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Multiple-trace representation of variability Text: “The simulated long-term average discharge of my favorite reach is x cfs. The discharge is expected to exceed z cfs 80% of the time and y cfs 20% of the time. Within aa years, 75% of the adjustment from current discharge would be expected.”

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3: Single-trace Paradigm (Repeat Representative Year) No pretense of predicting future time series Run single stress to get steady-state end point and trend of adjustment from current Stress is a single year or average of group of years Groups of years are in sequential blocks to preserve human or hydrologic serial correlation Obtain knowledge of variability from historical data

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Candidate years or groups of years All Candidate Years w/1999 repeated and 1997 omitted: 0.992

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All candidate years with 1997 omitted and 1999 repeated: Average index = 1.019

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Representation of variability in single-trace paradigm: Represent uncertainty in generating data set by running all three best estimates Represent hydrologic uncertainty by referring to history (Cosgrove 2006, Draft Final Report) (Meinzer 1923, USGS paper 489)

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Proposed Presentation of Results: Range associated with alternate input data sets Range associated with historical variability Single-trace graphical representation of uncertainty:

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Proposed Presentation, Narrative Format: “Simulated long-term discharge of my favorite reach is x to y cfs, depending on the input data set used. Under average conditions and current practices, 75% of the adjustment from current levels is realized within z years. Historical data and prior estimates suggest that discharge can vary by aa cfs over a single season and by bb cfs over a ten-year period.” Single-trace text representation of uncertainty:

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4. Evaluation AVERAGE STRESS Variability –Histogram –Serial correlation (persistence) order of sample years –Visual assessment of trace –Frequency distribution Reality Check

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AVERAGE STRESS = Average Index? I haven’t analyzed the diversions implications of all the options

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Variability I haven’t analyzed the diversions implications of all the options Histogram

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Serial Correlation – Order of Sample Yrs

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Serial Correlation – Visual Assessment I haven’t analyzed the diversions implications of all the options

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Probability Frequency Distribution May be important for both diversions and natural recharge components? I haven’t analyzed the diversions implications of all the options

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Summary Table I haven’t analyzed the diversions implications of all the options Frequency

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Reality Check Correct Average is vital –What if stress is not correlated to indices? –What about climate change? Other characteristics relate to variability –What if the variability has been changing? –What if we can’t match distribution? –What if we get autocorrelation wrong? –What about persistence?

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Reality Check Every time-series option has at least one “BAD” entry! We have another way to deal with variability

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(End)

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