Station Trends Based on the RRWT Average Correlation Wavelength

I added a new test specimen. I want to compare the group velocity wavelength method versus the average wavelength method. In order to do so I needed data and decided to implement the average wavelength method into a Station Trend output like I currently have for the group velocity method. The forecast data for the average wavelength method can be found here. I will be conducting verification on both methods. On a side note, the average wavelength method acts as a numerical genesis for the Lezak Recurring Cycle and the Doug Heady Pattern cycle length. This means anyone can forecast like Gary or Doug as the LRC/HP cycle length is automatically generated on a daily basis, all year round. If there are any questions, comments, or suggestions on the material presented please let me know.

A Quick Ramble. An Example of Pattern Correlation.

What do I mean when I mention pattern correlation? The chart below shows the H5 for Oakland, CA and the linear connection of two cycles. Top frequencies in the region have hovered in the mid 50s for nearly a month. Oct-12 top frequency for Oakland, CA was 54 days, the correlation result was 0.63.



The H5 values are not supposed to match, but instead parallel each other. If there are any questions, comments, or suggestions on the material presented please let me know. Click on the images for a larger view. Thanks for reading!

A Transient Cycle Length with Multiple Phasing Cycles

So where was I? Ah yes, I dropped the high amplitude and frequency states (ISO short-term component, 10-20 days) from the CONUS output and plotted the 30-90 day correlations exclusively. More

The map below shows the RAOB stations that I collect data from. I don't collect Canada or Mexico and it seems I randomly do not collect in the deep south US. I blame it on laziness. I am super lazy.



My thoughts are not well organized or educated. They are likely difficult to follow. I will attempt to explain them in short detail. The image below shows which region the highest correlations stem from. The range is 0-1. The higher the value, the more high correlations stem from that region. Example; the daily analysis for 2/21 shows region 5 has 9% of it's stations reporting a top 10 value. Region 8 60% and region 9 67% of it's stations in the top 10. This correlation could be considered "east based", where this region shows the most correlation.



These correlations are charted in a heat-map like table form. The image below shows the first 21 days of February. The left most table is the top 10 cycle lengths, listed from left to right, 1 through 10. The table directly to the right is the corresponding correlation values. The 3 tables to the right are mode, median, and average of cycle lengths for the previous 30 days, since December 1st, and since August 1st. The entire table can be found here.



A quick analysis of the heat-maps suggest a transient cycle length with multiple phasing cycles taking place. Similar to a standing wave. If there are any questions, comments, or suggestions on the material presented please let me know. Thanks for reading!

Framework: Use current NOAA/ESRL Radiosonde Database to analyze large-scale upper atmosphere patterns in standing wave notation. Described specifically to harmonics, reflecting the temporal/transient behavior of the frequency wavelengths in correlation and relating Intraseasonal Oscillation to Mid-Latitude recurring weather patterns.

Goal: Forecasting skill of upper-air and surface weather trends.

500mb Intraseasonal Oscillation Correlation - April through June

The correlation of the 500mb flow over the OSNW3 domain. Y axis is correlation coefficient, X axis is days. Analyzing the oscillations we can apply standing wave harmonics to find the recurring weather patterns based on the dominant ISO component.

500mb ISO Correlation Apr-Jun (larger chart)

ISO and Rossby; Harmony 101

An auto-discovery "cycle" duration. Obtainable by finding the dominant ISO component. On a daily basis I am doing just that. A while back I began following a specific feature and tracking it back through the long-term recurring Rossby.

Observations


Short-term ISO on Apr-13


Midwest 500mb Correlations Apr 1-30


What are these charts showing? The correlation of the 500mb flow over the Midwest. Y axis is correlation coefficient, X axis is days. I correlate each station on a daily basis looped 10-80 days backward in time to find the most positive correlation. The change is in days of the ISO translated to the mid latitude Rossby wave. Analyzing the oscillations we can then apply standing wave harmonics to find the recurring weather patterns.

Below is a KMCI MaxT reanalysis based on ISO (r=0.716) and LRC (r=0.017). Out with the old and in with the new?



If there are any questions, comments, or suggestions on the material presented please let me know. Thanks for reading! More to come.

Seeking an Auto Discovery Cycle Duration - Part 4

The patterns are cycling but the season they recur in is likely the missing feedback in the Trend. I am seeking to eliminate this seasonal hiccup. An accurate dominant harmonic correlation must be integrated into the formula. The short-term ISO may allow the trend to latch onto seasonal change and produce a more accurate projection. Testing out a new formula to calculate a dominant harmonic correlation, a recent analysis produced a short-term ISO of 18 days. This number led me to potential analogs at specific harmonics.

~18, 36, 54, 72

Correlations




The primary and second harmonic were the most dominant as there wasn't regional consistency in positive correlation past 40 days (see above images). I chose the second harmonic. Give or take a couple days, 36 days away from mid March was early/mid February. I knew that back on Feb 20 (see tweet below) the atmospheric setup produced a severe weather event that had recurred on two separate occasions in the long-term cycle.

Primary harmonic ~18. Seeing good correlation in the 2nd harmonic. Could this be recurring at the end of March? #ISO pic.twitter.com/pEXlv49uyQ
— Josh Herman (@OSNW3) March 17, 2014

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The SPC had nothing in their D4-8 forecasts on Mar 20 or Mar 22. They did in the D3 on Mar 25 though. Very good.

Just saying. See image. The potential power of knowing the #ISO and the recurring #Rossby it produces. @OSNW3 pic.twitter.com/awCkrgH7bG

— Josh Herman (@OSNW3) March 25, 2014

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The above observation is over a week old and the dominant ISO components have evolved. Below is the Mar 26 run. More to come.

Correlations


If there are any questions, comments, or suggestions on the material presented please let me know. Thanks for reading! More to come.

Seeking an Auto Discovery Cycle Duration - Part 3

I am putting the 500mb sounding correlations to use and seeking the recurring weather pattern. There is talk about severe weather approaching. The SPC probabilistic outlook for 2/20-21 is below. This feature has occurred before.



I want to track this feature back in time through the ISO. I start by seeking the dominant components in the correlations. The listed correlations are the greatest positive correl from the short and long term ISO components. Short-term is on the left, long-term is on the right. Give or take a day or two on each side, I see a consistent short-term component of 20-21 days in the FEB correls. I utilize standing wave harmonics and pin point a long-term component of 60-63 days. I see a consistent long-term component of ~50 days in the DEC correls.

FEB Correlations


DEC Correlations


Observations and Forecasts


Starting with the forecast date of 2/20/14 I subtract ~60 days and find 12/21/13, I then subtract ~50 days from 12/21/13 and find 10/31/13. Simply put, from within the correlations we are seeing the movement of ISO components in relation to the recurring Rossby Wave Train and cyclic weather patterns. If there is interest in the data it can be found here. Another step closer.

Click for FEB observations
500-Millibar Height Contour Map 20140220
Storm Prediction Center Storm Reports 20140220

If there are any questions, comments, or suggestions on the material presented please let me know. Thanks for reading!

Seeking an Auto Discovery Cycle Duration - Part 2

Stemming from seeking an auto discovery cycle duration I started running the sounding correlations on a daily basis. They now begin from the current day and loop 10-80 days backward in time.

When I first began correlating the soundings I started the sample period on 10/1/13. I recall ~15 days being the short-term component from those runs - a consensus on positive correlation from all stations. Beginning from the current day the short-term 10-20 day ISO still holds the top positive correlation, but now ~20 days has the consistent positive correlation. It seems to me that the short-term cycle of the ISO stands out as the dominant component this season.



I am very interested to see what happens to this correlation as the days move along. Should I expect the wave to continue on or will it roll back towards ~15? Am I seeing a seasonal ISO in the 70-80 day range? I should loop to 90 or beyond to get a better glimpse? It's a work in progress, but I think we are very close to finding an index to aid in calculating a daily cycle duration based on a primary harmonic. More to come.

If there are any questions, comments, or suggestions on the material presented please let me know. Thanks for reading!

Translating Tropical ISO to the Midlatitudes

Studies have attempted to identify recurrent modes that contribute to the alternation between active and inactive periods of the Indian summer monsoon and the South China Sea summer monsoon. Generally, two components of variability were found to be dominant on an intraseasonal time scale: the “short-term” component, with a period of less than 1 month, and the “long-term” component, with a period of 1–2 months but apparently less than a season. Both can be referred to as the intraseasonal oscillations (ISOs) since they are clearly separated from the high-frequency synoptic-scale (less than 10 days) features and the slowly varying seasonal cycle as well. - BIN GUAN AND JOHNNY C. L. CHAN

We considered our cycle correlation a step in the right direction. Next was to match the cycle correlation to the "short-term" and "long-term" ISO components. The paper referenced above identified the years 1981, 1984, and 1990 as case studies of when either the 10-20 or 30-60 day ISO was strong. The paper states 1981 is strong in the "short-term" 10-20 day ISO, 1984 is strong in the "long-term" 30-60 day ISO, and 1990 is strong in the seasonal cycle.



For each of the case studies we think our cycle correlation matches their findings. 1981 does favor the "short-term" component. We see positive and negative correlation in the 15 day time period. 1984 does favor the "long-term" component. We see one strong lengthy correlation at days 41-47. The 1990 seasonal cycle is inconclusive, however. We could debate either way, short and long, but would need a wider time scale to make a seasonal cycle determination. What we label as the "harmonic", they label as the "short-term" 10-20 day ISO. What we label as the "cycle", they label as the "long-term" 30-60 day ISO. Because the findings match, we can assume that our cycle correlation method is valid and can piggy back the paper as something significant and scientifically valid.

Tropical intraseasonal oscillation (ISO), especially its dominant component at the equator—Madden–Julian oscillation (MJO), has been extensively studied over the past decades. ISO (or MJO) consists of large-scale coupled patterns in atmospheric circulation and deep convection [...] the influence of MJO can extend to the subtropics and midlatitudes. Associated with enhanced (reduced) tropical convection, the upper-level divergence (convergence) is often accompanied by a subtropical upper-level convergence (divergence) counterpart. - Li LIN-LIN PAN AND TIM LI

Extending the tropical ISO into the midlatitude we are able to find the "short-term" and "long-term" ISO (see image below). Applying our cycle correlation to the h5 pattern since October 1, 2013 we see a strong correlation in the "short-term" component around 15 days. Using principles of standing wave harmonics we can then solve the "long-term" component. Evolution of the sine wave shows peak to peak harmonics of around 15 days. More to come.



If there are any questions, comments, or suggestions on the material presented please let me know. Thanks for reading!

Seeking an Auto Discovery Cycle Duration

A while back I needed a quick way to compare soundings. I coded a few simple VBA instructions to do this. I was happy, I could study daily soundings from many stations and come up with a perceived cycle length. Using this tool became stale however and I felt I was staring and comparing like I had been doing with maps in the past. With some statistical motivation I am now seeking correlation in the sounding data.

Admittedly I had no idea what was going to result from correlating two cycles of sounding data. I gathered the data and looped it through a 30-60 day period. To the surprise of myself and another, it produced a spectacular looking sine wave. The data represent 20 sounding stations throughout the states of ND, SD, NE, KS, MO, IA, MN, WI, MI, IL, OH, PA, NY and MA. Station locations are color coded. Purple represents the region that is farthest west. Red represents the region that is the farthest east. The top chart displays the regional average correlation. The bottom chart displays the individual station correlation. This particular sample time frame begins 10/1/2006.



Taking the absolute value of the correlation coefficient measures the strength of the relationship. A correlation coefficient of 0.50 indicates a stronger degree of linear relationship than one of 0.40. Likewise a correlation coefficient of -0.50 shows a greater degree of relationship than one of -0.40. Thus a correlation coefficient of zero (0.0) indicates the absence of a linear relationship and correlation coefficients of +1.0 and -1.0 indicate a perfect linear relationship.

With this application the positive, zero, and negative values each hold significant meaning in regard to standing wave harmonics. The results prove to me that cycle duration with auto discovery is obtainable. More to come.

If there are any questions, comments, or suggestions on the material presented please let me know. Thanks for reading!