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# Scatter Plot Laplacian time

CDF: large every other point

Scatter Plot Laplacian time

I will post still screenshots of the full data.

You see these 2 humps at the end, they are due to padding, I do not believe they are in the original data, I will fiddle with padding later on.

Generally it is a rectangular volume along time, fairly evenly scattered.

Notes:

1. The data had to be normalized for splines to work
2. Therefore what you see is the diffeomorphism of the original data (I love to throw in those manifold theory buzzwords, for once something useful came out of all those courses).

D

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Scatter Plot Laplacian time, screenshots

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edited August 2014

Hi Dara. Could you share the raw data as a csv with columns (laplacian, dT/dt, x, y, t)?

thanks Daniel

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To include the x, y the volume data is too huge to post online, I could try if you really need x,y . However I got you the list (laplacian, dT/dt, t) which is still large

scatter data 2010

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Meanwhile I am making stremplots and posting to youtube, since the actual volumetric data is too large

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Hello Daniel

I made the volumetric data sliced thru time and make a video of the Slicer:

Scatter Plot Double

Surface Temperatures 2010

Each streamline vector has x= dT/dt, y=Laplacian

Top plot: Length of the stream vector is proportional to y=Laplacian Bottom plot: Length of the stream vector is proportional to x= dT/dt

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Caveat: the scatter plots and stream line/vectors are approximate and the original data is sparse to start with. So the observed properties (not conclusions) require more investigations

Observations:

ONE. The direction of the (laplacian, dT/dt) is more or less fixed and the stream line vectors kinda vibrate around a fixed directions

TWO. Both coordinates could reach small proportions in comparison to the other

THREE. There seems to be a wave-like propagation perpendicular to direction of stream lines/vectors

Dara

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For better quality video

Scatter Plot Double video file

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Dara, I am trying to get oriented WRT the last scatter plot video.

Is it an altitude cross-section along one zone?

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No it is a time slice i.e. per day of the year. So imagine the volume grid, slice it each day and then inside each slice plot the 2D vector (laplacian, dT/dt) at each node on the grid. Then vary the length of that vector proportionally by laplacian and then by dT/dt, this way you could visualize the laplacian / (dT/dt) as a quotient, which was what Daniel was concerned about.

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Dara, Pardon my confusion. Whenever I try to juggle the 4 dimensions of xyz and time together with a metric based on a spatio-temporal derived quantity, I will often will get disoriented.

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my fault actually need to write you more tools for visualization.

Problem is we are used to 1D and 2D functions and image processing, so when we are given volumetric data find it hard to even start looking at them. It is an educational situation, hopefully John will help us to overcome.

For that matter, I am making these videos and CDFs so we could get use to volumetric data and run the algorithms on volumes vs. 1D or 2D setups.

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Paul I did some visualizations for some slices of time:

vector plot

Stream plot

I don't seem to see any problem in the code. I added the lm linear regression and it is kinda deceptive to come up with a a regression line for this data.

Daniel asked me to take the derivatives on the non-normalized coordinates, I will hack that code tonight sometime.

Dara

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Here is the non-normalized version, it looks a lot more reasonable now. So any scaling or truncation of the numbers might overly simplify the field lines in the streamplots:

Stream Plot Laplacian dT/dt non-normalized

Generally we could have any dimension volumetric data and spline along the axes and take derivatives.

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This is the meta data for the data:

{"Conventions" -> "COARDS", "title" -> "mean daily NMC reanalysis (2010)", "history" -> "created 2009/12 by Hoop (netCDF2.3)", "description" -> "Data is from NMC initialized reanalysis (4x/day). These are the 0.9950 sigma level values.", "platform" -> "Model", "references" -> "http://www.esrl.noaa.gov/psd/data/gridded/data.ncep.reanalysis.\ html"}

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Dara, This is hot off the press

"Quasi-resonant circulation regimes and hemispheric synchronization of extreme weather in boreal summer" http://www.pnas.org/content/early/2014/08/06/1412797111.abstract

They say

"Two mechanisms have recently been proposed that could provoke such patterns: (i) a weakening of the zonal mean jets and (ii) an amplification of quasi-stationary waves by resonance between free and forced waves in midlatitude waveguides."


Then

"The spread in the zonal mean zonal wind reflects,in the first place, the seasonal cycle with weaker jets and hence slower wave propagation in summertime. Therefore, in boreal summer, a significant fraction of synoptic waves, notably with k = 6, have a phase speed close to zero (quasi-stationary) or are even traveling westward."


Interesting the mention of waveguides.

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Dara, regarding your question on Figure 3 and 4 in the Boreal Summer paper above, they might be looking at dispersion of wind velocities at altitude.

I did some perhaps related analysis of this a few years ago based on high resolution data collected by airplanes flying at altitude.

http://theoilconundrum.blogspot.com/2013/03/spatial-and-temporal-correlations-of.html

It is hard to get a handle on the spatial and temporal scale involved since these effects can occur at so many scales.