Data Analysis Project Patricia Sánchez April 26,2012

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Power Spectrum Analysis: Analysis of the power spectrum of the stream- function output from a numerical simulation of a 2-layer ocean model. Data Analysis Project Patricia Sánchez April 26,2012

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Power Spectrum Analysis: Analysis of the power spectrum of the stream-function output from a numerical simulation of a 2-layer ocean model. Data Analysis Project Patricia Sánchez April 26,2012. Motivation. We have study Q-G systems Many assumptions Leads to set of equations of motions - PowerPoint PPT Presentation

Transcript of Data Analysis Project Patricia Sánchez April 26,2012

Data analysis project

Power Spectrum Analysis:Analysis of the power spectrum of the stream-function output from a numerical simulation of a 2-layer ocean model.Data Analysis ProjectPatricia Snchez April 26,2012MotivationWe have study Q-G systems Many assumptionsLeads to set of equations of motionsHow to solve them??? Numerical SolutionsQuantify the Instabilities How they vary in timeGFD2 Project !!Background Dataset:Numerical Model: solve the Q-G PV equation.Two-layer with thickness H1 and H2Uniform background current of speed Uo in top layer and 0 in the bottom layerOutput: PSI (x,y,t) of each layer.

Latitude (512 gridpoints)Longitude(256)HeightLayer #1MethodPower Spectrum:An often more useful alternative is the power spectral density (PSD), which describes how the power of a signal or time series is distributed with frequency. Here power can be the actual physical power, or more often, for convenience with abstract signals, can be defined as the squared value of the signal,

Fourier Transform has units of utimepower spectral density has units of u2time2/time

ExperimentWhat do we want?Previous work: The estimation of the frequency-wavenumber power spectral density is of considerable importance in the analysis of propagating waves by an array of sensors . (Capon,J, 1969)

Analyze the power spectrum density in terms of wavenumber. Example:http://www.weizmann.ac.il/eserpages/kaspi/jets/jas07_1.htm

Data: Output PSI (x,y,t) snapshots of each layer. Raw DataSnapshots: every 100 daysAnimation

Time:17000Time:100Time:2400Steady StateSmall Scale featuresLarge Scale features but with small scale(x,y,t) Stream function Animation

Power density Spectrum

Time:100Time:9100Time:15100Key Features:Power Spectrum analysis at each snapshotVariation in amplitude and slope at different times.Almost all the power (variance) is at lower wavenumber.But, how low are these dominant wavenumbers?Next.

Next step:Since we know that most of the power is concentrated in lower wavenumbersAnalyze the wavenumber where the power spectrum is maximum.How changes over time?Analysis of Kmax results

2nd Step: Evaluate the KmaxRemember, what do we wantNot clear interpretation of the results .Too much variability We need to define a new way/method to analyze the dataHow to Interpret the Result:From power spectrum, we can see:It changes in amplitudeIt changes where is the kmax and how steep is the slope

Time:15100Refine the resultsFrom 1:Calculate how the total (maximum) cumulative power changes with time.From 2:Approach: Locate the wavenumber at which half the power is in lower wavenumbers.Cumulative PowerIn an analogy to the energy signals, let us define a function that would give us some indication of the relative power contributions at various frequencies, as Sf (), or in this experiment, wavenumbers Sk(k).

NormalizedFrom 0-1 of all cumulative powerWavenumber 1-50Cumulative Power

Time:5100Time:15100Time series of total of cumulative Power

Tendency: to decrease for the first half of the time series.When the flow is more perturbed the maximum cumulative power increases.

K1/2 AnalysisThe wavenumber at which half the power is in lower wavenumbers)We know that the most of the total variance is contributed by the lower wavenumbers.We want to quantify how of these wavenumbers vary with time.

With this result, we could guess what is the scale of the flow. It includes the signal (that your eye already told you so you believe it), but clean and objectiveSummaryPower Spectrum Density: Transform the signal from space (x,y t) domain to frequency/wavenumber domain. The power spectrum show a concentration of power at low frequencies. It varies in amplitude and slope.Hypothesis: The small scale perturbations could have more power than the larger scale features (Kamenkovich)Cumulative Power Spectrum:In snapshot: shows how low wavenumber dominatesIn time series: We could determine the scale of the signal

Future work:Apply same analysis for: a different latitude to compare how different are the results.Instead of latitude-cross, try with longitude-cross, i.e. meridional wavenumber l analysis.Another experiment (model output)We could determine the fastest growing mode.