Pressure Gradient Breakthrough

I decided to investigate the Cordova-Anchorage pressure gradient a little more given the relatively weak correlation compared to the intuitively strong association, as well as the lag that exists between strong wind events and the time of the maximum gradient.

I realized that the change in the gradient over time might have a better physical connection as it would account for the isallobaric wind. Without pulling any new data, I just used the gradient at the time of the report and the maximum gradient to determine the change over time. I plan on trying to analyze the pressure gradient change centered around or just prior to the wind report next.

The result was a 0.56 correlation to the wind magnitude. This was a notable increase from the maximum gradient correlation. More importantly, when replaced in the empirical formula, it makes a significant difference.

In addition, I have rerun the pressure gradient program to be able to pull data from one event that was missing from the initial database. This is the weakest case, and thus an especially important case.

First of all, it actually reverses the dominant group ... the pressure correlation is 0.61 for the wet class and 0.54 for the dry class. The new correlation for the bestfit values is 0.84 overall, which is excellent ... 0.85 for the wet class, and 0.83 for the dry class. This is a huge improvement. Case-by-case, this also removes the biggest outlier! There are two cases with error greater than 10kt. The average error is 4.4kt or 6.0%

Splitting cases into wet and dry events

Following the information I found from the mid level (3.5km) dew point, I split the cases into wet and dry events, using -30C as a benchmark.

I reanalyzed all of the variables in the empirical formula given the class of the event (wet/dry), for a new average, standard deviation, and correlation to the actual data.

In addition, I added the dew point variable itself into the formula given that especially the dry cases show a strong correlation to the wind magnitude (drier mid levels = stronger winds).

The latest formula incorporates the following variables:

• Cordova-Anchorage SLP gradient
• Depth of the mid-level temperature inversion
• 2.5-5km shear magnitude
• Change in low-level cross-barrier flow over time
• 3km temperature
• 3.5km dew point

The results are very good. Of most significance, the new formula reduces the error of the outliers.

For the wet cases: Correlation = 0.73, Error = 5.0kt, 6.7%

For the dry cases: Correlation = 0.83, Error = 3.9kt, 5.2%

Overall: Correlation = 0.75, Error = 4.6kt, 6.1%

The 0.83 correlation for the dry cases is excellent.

Dew point

Examining the vertical profile of dew point in the Anchorage soundings, there is significantly greater variance than with temperature. The most interesting feature in the composites is between 3000m and 4000m where there is a dry layer in the strong cases and a relatively more moist layer in the weak cases.

I plotted 3500m dew point against the magnitude of the wind event. The huge variance is clear but what stands out the most is that there are two very distinct groups of dew point values. There is a moist group and a dry group. I went ahead and split the data accordingly (color coded on the graph), and analyzed them separately. For both there is a negative correlation between dew point and the wind events ... drier mid levels are conducive to stronger wind events. The correlation is much greater for the dry events (-0.40) then the moist events (-0.22).

Together, there is actually very little correlation between the dew point and wind magnitude, as both the moist and dry classes span a wide spectrum of wind speeds. It's when they're split that we can better identify possible relationships.

This poses the question: Should all events be initially identified as dry or moist before any further analysis be done? Next plan is to redo some of the previous analysis split into these two categories.

Below I have included sounding composites for the dry (red) class and moist (blue) class. These classes also maintain themselves through the 12-24 hour period leading up to the event. So for instance a dry event in this classification maintains a dry profile during the time of the event itself.

Up Next

Whittier to Anchorage pressure gradient

Empirical formula improvement

Investigate physical basis behind 3km temperature correlation

Cross-barrier flow

Cross-barrier flow was one of the parameters I investigated in the individual soundings from each event. As I mentioned here, this parameter exhibited a negative correlation to the wind gust magnitude which goes against intuition. This correlation was largest around 18 to 24 hours prior to the event, and then weakened toward the time of the event at which point it became slightly positive.

From this information, I chose to investigate the change in the cross-barrier flow over time in relation to the wind events. As suggested by the initial statistics, increasing cross-barrier flow correlates with stronger wind events. This at least makes more sense intuitively. The result is a +0.29 correlation. 

Below I have graphed the wind reports against the d(Cross-barrier flow)/dt parameter. I have included this parameter in the empirical function, which made very slight improvements on the correlation and error. It currently has a correlation of +0.69 with an average error of 4.8kt or 6.5%. The contribution from each component of the function is also plotted. 

The third graph is the current best fit plot which adjusts for the same standard deviation as the wind event database, and thus it is perfectly averaged around the y=x line on the plot of obs versus empirical values. There are three events for which the empirical value has an error greater than 10kt and eight events with a percent error greater than 10%.

Empirical Formula Formulation

So far I have used the 3000m temperature (correlation = -0.64), the maximum ACV-ANC pressure gradient (+0.40), the depth of the temperature inversion aloft (+0.27), and the 2500-5000m shear (+0.49).

Using these variables weighted by their correlation, I have created an empirical formula with a correlation of +0.68 to the observed winds, and an average error of 4.8kts or 6.5%.

Hodograph composites

The graph below displays the magnitude of vertical wind shear from Z height to 5000m for strong cases (on x-axis) versus weak cases (on y-axis). The greater the distance from the y=x (45deg) line (gray line on graph), the more uniqueness there is between the strong and weak cases. The strong cases exhibit greater vertical wind shear throughout the entire column, but this difference is maximized in the mid levels (can also be seen in the length of the composite hodographs above).

The second graph displays the angle the <strong, weak> vector. The greater the difference from 45 degrees, the more unique the two classes are. We can see that this is maximized at 2500m. More specifically, the 2500m-5000m layer shear exhibits the greatest difference between the strong and weak classes, and thus is the best layer at distinguishing between the two.

Also I created a histogram and density graph of the wind events for future reference in comparing to empirical results:

More on 3000m temperature

As I showed yesterday, there seems to be a strong clustering of the strong case soundings around -16.5C at 3000m, while there is significant spread in the weak cases at this level. I went ahead and pulled temperature data for all 41 cases, and plotted the wind report against the absolute difference from T3000m=-16.5C. The result was a -0.52 correlation ... very impressive for a seemingly arbitrary variable.

From here, I molded this variable to maximize the correlation, and then standardized it to the mean and variance of the actual wind reports. The result was a 0.64 correlation, with an average error of 7.7kts or 10.4%. Again, this is impressive for a single variable, and shows promise for the construction of a useful predictive empirical formula.

First round of various sounding results

So far, the results of spaghetti plot and composite soundings have shown that there is considerable variance in the height and amplitude of pertinent features. Averaging smooths these features down to essentially a constant lapse rate sounding. From the previous tests, the primary inversion layer is generally found near and above 2000m, which can be seen in the spaghetti plot.

To supplement the average, I also plotted the standard deviation of the temperature at each level. This has interesting results. The spread of the weak cases generally increases with height, while the strong cases actually significantly converge around -16.5C at 3000m, at which point the standard deviation drops to near just one degree C. This is around the height that an inversion or stable layer is most likely to be present, and thus the lapse rate is very small or negative.

The plots below are for 18 hours from the time of the event report. Other times are being analyzed now, and show similar results.

Plans for week 3

I have finished the sounding composite program. The averaging tends to smooth much of the detail out of the soundings, so to supplement the composite, I'll include each case sounding overlaid on the same plot. This will give some idea of the spread and common features. I will do this for the top 10 strong cases and bottom 10 weak cases.

Download NARR data for top 5-10 cases and bottom 5-10 cases to initialize WRF. Model should be run 18 hours from the time of event to 6 hours after, each for 24 hours.

From the model data, I am interested in finer time resolution soundings and locations of features that I have pointed out in the synoptic composites.

From this information, combined with the Anchorage-Cordova pressure gradient, and the sounding parameter data, I can construct an empirical predictive formula. I have already ran a few tests that return a greater than .50 correlation and only only a 7% error.

Sounding Parameters

Using a program to pull sounding data from the U Wyoming archive, I was able to isolate certain characteristics of each case sounding. I focused on three primary supporting features of high wind events:

• Low level cross-mountain flow
• Critical level where cross-mountain flow drops to zero
• Inversion or stable layer aloft

To produce quantitative data, I averaged the sfc-850mb wind for cross-mountain flow, yielding an average direction, average speed, and the component crossing the mountain from the southeast. I calculated the height of the critical level by the level at which the component of the wind cross the mountain dropped below 5kt. I tested for the existence of an inversion layer between 850mb and 500mb, and determined the height of the bottom of the inversion as well as the vertical depth of the inversion.

These six variables were then compared to the magnitude of the wind report in each event. The inversion and critical level data was promising: The stronger events more frequently had an inversion present, with the bottom at a lower height than for weak events, and the depth of the inversion larger than for weak events.

The critical level was also generally at a lower height for strong events and higher, or not present at all during weak events.

Interestingly, the cross-mountain flow shows a small negative correlation to the magnitude of the wind event, which I'm not sure what to make of ... weaker events tended to have stronger low level cross-mountain flow...

Quantitative Data

Beginning with the Anchorage-Cordova pressure gradient, I want to look at more quantitative data in order to develop an empirical forecast method. The composite maps give excellent qualitative information on the synoptic situation. One possibility is to pull the prevalent features from the composites to produce usable data. My current project is to examine sounding data, generating quantitative information for each case on the important features (Case Soundings). I have begun writing a program to pull this data from the UWyoming archive.

Anchorage-Cordova Pressure Gradient

The gradient at the time of the report shows little correlation to the magnitude of the report. The maximum gradient within 18 hours of the report exhibits more of a positive correlation (+0.40).



The time difference shows a positive correlation to the magnitude of the report (+0.31). This suggests that the maximum pressure gradient tends to lead weaker events and lag stronger events.



Possible plan:
Develop an empirical formula for forecasting high wind events.


Important, quantitative factors...

Plan for tomorrow...

Complete Anchorage-Cordova pressure gradient program, including empirical calculation of TAJ.

Generate graphs of gradient over time and note the time of the high wind report.
...time of peak gradient relative to the time of the report correlate with the magnitude of wind?

Use both peak gradient and gradient at the time of the report to correlate to the magnitude of the wind report.

Explore GrADS more.

Individual case soundings. ...composites in GrADS?

Analysis of change composites

This is analysis for the composite maps in the previous post

These change composites returned some interesting results.

In the strong cases, the greatest magnitude SLP change is -22hPa over southwest Alaska associated with the low. The maximum change is +12hPa around Juneau associated with the downstream high. This produces a strong isallobaric wind from the east centered around Anchorage. In the weak cases, the greatest magnitude SLP change is +15hPa near 50N/170W associated with the upstream high. The pressure tendency with the low is much weaker and more diffuse than in the strong cases, and the downstream high only has a +5hPa change. The strongest isallobaric wind in this domain is thus over the Aleutians between the upstream high and the low, rather than around Anchorage between the low and the downstream high.

The 500hPa has similar results. The strong class has the greatest change couplet from the trough and downstream ridge, while the weak class has the greatest change couplet from the upstream ridge and trough. The couplet is also much stronger in the strong class: -180m to +150m versus +90m to -80m in the weak class. The differences in height tendency with the downstream ridge is the most significant result. The strong class features a +150m change in the northern GOA, while the weak class has only a +90m change further southeast. As a result, there is also a significant contrast in height change specifically over Anchorage. In the strong class, heights rise 80m, and in the weak class, heights are about constant.

Another point is that the strong class exhibits well defined maxima and minima in height change, with a predominant negative tilt. The weak class has more elongated maxima and minima that are predominantly positively tilted. What this and the above observations suggest is an amplifying wave pattern in the strong class and a more progressive pattern in the weak class.

Much of the evidence here points to the strong cases featuring a much more intense low that remains the dominant feature in the domain. The weak cases exhibit a weaker low that is clearly also undergoing secondary development to the southeast. This weakens the pressure gradient and re-orients it more toward the NE-SW over Anchorage. The dominant feature becomes the upstream high over the northern Pacific.

The tendency in the lifted index shows a significant increase in stability in the strong class versus only a small rise in the weak class. Over Anchorage, the LI increases 5C in the strong class and 1C in the weak class.

Composites of variable derivatives

The top ten strongest wind events in the NCDC storm reports were compared to the weakest ten events. Composites were made of the 24-hour change in: 500hPa height, sea level pressure, SB lifted index, and 850hPa omega.

850hPa Wind

Sea level pressure

500hPa heights

SB lifted index

Plans for next week:

• Analyze variable derivatives ✓
• Quantify gradients: Cordova to Anchorage for each case
• Case by case SLP and LLJ
• More in depth with soundings

Case soundings

ANC Soundings from the nearest 12-hour increment PRIOR to the high wind report. These four soundings are from some of the strongest events, and include well defined specific features favorable for windstorms. These features include:

• Strong low level southeasterly winds
• Winds veering with height, becoming southwesterly in the mid levels
• Conditionally unstable mixed boundary layer
• Mid level temperature inversion or stable layer
• Conditionally unstable layer above the inversion

Future ideas: Create composite soundings for strong versus weak classes. Compare these specific features in the composites.