Tuesday, September 10, 2019

Hurricane Eye Size

We recently captured pictures from a NDBC BuoyCAM as hurricane Dorian passed over buoy 41004. We were lucky to catch views inside the eye of the storm, which eventually led us to think about the size of these eyes.  Our motivation is always marine navigation, but in this case we also noted that there were many birds trapped inside the eye, which was another unique observation.

The eye of Dorian was 40 nmi across when it passed over the buoy, and only later did we realize that this was much larger than common values, which we report in our textbook (Modern Marine Weather) are typically 10 to 20 nmi.  We can also look up past studies of hurricane structures that confirm these smaller average values. Two ways to look at this data are shown below.

From "Typhoon Structure as Revealed by Aircraft Reconnaissance. Part II Structural Variability" by Candis Weatherford and William Gray, Monthly Weather Review, Vol 116, 1988.

We see the most common value is less than 20 km, with most between 20 to 40 km.  This corresponds to 11 to 22 nmi (1 nmi = 1.852 km).

So we were double lucky to catch our neat view inside the eye of the storm. But just how lucky were we?  With that question in mind, we took a look at the history of the Dorian eye size compared with other parameters of the storm.  These data are presented below.

Advisories not listed did not include eye diameters. I will discuss these stats in a later video relative to standard hurricane properties we discuss in our textbook.  For now we concentrate on the eye diameter and in particular we look for any correlation of this size with other parameters. Spoiler alert!  We don't see any.

The thin red line is the trace of the eye diameter overlaid on the other data.  We do not see any correlation with any of them. The reference paper cited shows that the size of the eye is based on a lot of complex interactions. No way for mariners to estimate this—if there ever should be any reason to try, which I cannot imagine.

The main thing we see is we were actually more than triple lucky on the buoy pics. We got the picture in the first place, i.e., path went within 4 nmi of the buoy during daylight hours (luck 1 and 2); the eye diameter at the time (40 nmi) was twice the average size for such systems (luck 3); and finally the eye was only blown up to this large size for just over one day of its 10-day life time, and that eye expansion was in place as it crossed the buoy (luck 4).  

Dorian, for example, later on (12z 9/6) passed within 14 nmi of buoy 41025 during daylight, but its eye diameter was just 25 nmi (radius 12.5 nmi), and we do not see any interesting pictures from it. No discernable eye properties to be seen.  

The storm also passed with in 4 nmi of buoy 41013 with an eye diameter of about 35 nmi, but this took place at 0045z, which was pitch dark local time, so this was not a candidate. That is exactly what happened to us last year when we set this up in the first place to watch Florence approach a BuoyCAM. After a lot of preparation and BuoyCAM calibration, it passed over the buoy in the middle of the night.

In short, again, our Dorian pictures at buoy 41004 were very lucky; we will hang on to them!

Sunday, September 8, 2019

Frequency of ASCAT Data at a Specific Position

Wind data from the ASCAT scatterometers on the European satellites Metop-A and Metop-B are the truth meters for ocean forecasting. Each time we get a surface analysis map at sea, a next step is to check to see if there are any ASCAT passes near the time and places of the forecast we care about. If the wind measurements agree with the analysis maps, then we can have more faith in the forecasts. If they do not agree, we have every right to use that forecast with caution. The ASCAT data are presented online in a convenient graphic format.

Methods of obtaining the ASCAT data by email or direct satcom request when underway, along with further details of its use, are covered in our textbook Modern Marine Weather. We use one of the most convenient methods in the procedure outlined below.

The analysis maps are available every 6 hr at the synoptic times 00, 06, 12, 18z. So for starters we are looking for maps at or near one of these times for map comparisons—although we learn about our local conditions from passes at any time that are near us. Second, the satellite pass must cover some region of the ocean we care about.

Estimating the likelihood of such a pass is not simple, because the satellite circles the earth every 104 minutes (1h 44m) going up one side (ascending pass) and down the other side (descending pass) during one orbit.

On top of that, the earth is rotating (toward the east) during this 104m, so the track curves to west ascending and to the east descending during the 30 minutes or so of time it is in view on that pass.

And on top of that, there is a gap in the data just below the satellite (the nadir gap) because this type of scatterometer cannot read data directly below its position. Thus each pass has two 300 nmi wide swaths of data separated by a 240 nmi wide gap.

On top of that, we have two fixed swath widths plotted on a round globe in a mercator projection so the paths are distorted from that as well.

With that in mind, how often will any random point on earth see a pass that provides data within 200 nmi of that position?  That is question 4.14 in our Weather Workbook—which is maybe a little bit unfair, because the only place you get the answer is our own textbook!

That is, until now. I just figured a way to get good data on this; so one can actually measure it, and not rely on our estimates, stated, up until now, without proof.

Here is the procedure.

The key tool will be LuckGrib, which can download ASCAT data in GRIB format. It automatically provides the past 3 days of passes that crossed the users selected area. Needless to say, we are generally looking only to present and future passes, not past ones, but the display of past tracks helps us anticipate the next track since they are evenly spaced on the globe.

We also take advantage of a feature of LuckGrib that lets us import GPX files. So our trick is to use OpenCPN to create routes that mark the circumference of 200-nmi radius circles around 6 random positions. Then we export these routes to LuckGrib, display the circles, download the ASCAT data, and then step through the sequence of satellite passes to see when data appears inside any of these circles.

More specifically, in OpenCPN we drop a mark where we want to look, then add a 200 nmi range ring to that point, then we trace that circumference to make the circular route, then export it as a GPX file. In practice, all 6 are made and stored, and then exported as one combined GPX file.

OpenCPN showing 6 circular routes marking places we will monitor ASCAT passes.

These routes imported and displayed in LuckGrib look like this after we download the ASCAT data for the region shown.

This is the view advanced to the 24th satellite pass (marked on the bottom).
The valid time of the pass is shown in the top right display.

We see that at this time there is data in the Central Atlantic point and in the North Atlantic point. The valid time of the Central Atlantic point is 1248z. Below we zoom in to see this wind data, which is indeed very interesting if we are sailing in this region.

We see light air, reversing direction to the south, and prominent patches of calm.

In this process, we step through each picture starting from the far left, which is 0038 on Sept 5, 2019 in this case. There are some 50 passes to check on Sept 5th, then we do the same thing for Sept 6th.

Another example from a pass on Sept 6. This shows data for the North Pacific (0700) and for the Equatorial Pacific (0645).

The compiled data are shown below.

The 1248 example mentioned above is marked in the table.

Now we can count the passes that have data within 200 nmi of the points selected. First we see what might be obvious; the higher the latitude, the more passes. This comes about because the earth is not rotating very fast (in knots) at high latitudes, so the same place stays within the data swath longer than at the equator.

The published answer in the workbook is "2 or 3 times a day, depending on latitude"—we were not really considering high latitude regions where there is less sailing. With this new study we might reword that answer at next printing to be  2 to 4 times depending on latitude, but this depends a bit on the wording of the question. Two entries above that are within 104 min of each other are likely the two sides of the same pass, either side of the nadir gap. This is indeed new data, but not a new pass.

For a more generic summary, we can offer this to the answer of: How often will we get ASCAT data within 200 nmi of our position?

        For the mid latitudes, expect data 3 or maybe 4 times a day.

        For the equatorial region, expect data 2 or maybe 3 times a day.

        At high latitudes data are available about 5 ± 2 times a day.

Below is a video illustration of the above process.


Sunday, September 1, 2019

BuoyCAMs and Hurricanes, Part 2.

We have an earlier note and video on the use of NDBC BuoyCAMs to watch approaching and passing tropical storms, and indeed detailed info on use of BuoyCAMs in general. We have now renamed that article Part 1, because it is now easier to do what we discussed there, and hence this Part 2.

All the recent TV news about Dorian in the Atlantic led me to look into this again, where I learned of the new shortcuts available now. ( In passing, we have to recommend that the news media should read the Mariners 1-2-3 Rule to realize they were forecasting landfall way too early in the history of the storm, or at least they were doing so without adequate qualifications. At 3 days out the track location* is uncertain by ±300 nmi, and they started calling landfall a week out—not mentioning that the historically most common track does indeed turn north and not go ashore at all. )

To anticipate watching the storm on a BuoyCAM, here is the type of data display we would like to see in Google Earth (GE), and even ideally in our phone versions of GE, and we want this display to be new and updated every time we look at it. This is not a standard GE display; we have to create this ourselves.

Screencap from GE showing NHC track line and cone of uncertainty along with
interactive locations of the NDBC BuoyCAMS. 

When you click a point on the storm track showing in GE you get this type of position report, which will change with each new advisory.

Within GE you can just click a BuoyCAM to see something like this:

This does not tell us too much yet, except there are high seas, which accounts for the misaligned horizons. Get a better view in the computer version of GE by right clicking and choose Open Image.  In a phone version, the image can be tapped then pinch zoomed. To go to the image in the main buoy site just google its number "NDBC 41010," and we can then double zoom to get the max resolution.

Referring back to the top image, we see that this storm could pass right over or very near at least 3 BuoyCAMs as it heads north.  With that said, here is what is new.

We can set up GE now with just a few steps, and it will refresh for us throughout the history of any one storm. The only way we could do this earlier was tweaking the track images individually at every new Advisory, but now the track and cone data are available as KMZ files for both NHC tropical storm zones.

Part 1. Get the BuoyCAM file at NDBC, then on the left click BuoyCAMS, and see on the bottom right of next page a small link to the KML file.

This file when opened in GE (or drag and drop it) plots the interactive buoys on the ocean map of GE. Install once and save; no need to update. This is the easy step. Also this one remains valid for all storms or indeed year round regardless of storm season.

Part 2. The NHC track and cone files are located the NHC site; find them under Analyses & Forecasts / GIS Products menu item.

There are a lot of data on this page. What we want for now is in the top line, by ocean.

A typical link looks like:

With this we see what is new and an improvement, and what remains an issue still calling for custom work.

This file name means:  an Atlantic (AL) storm; in particular storm 05 of the 2019 season, and it is the latest update of the cone of uncertainty data. Storms in the Pacific are labeled EP for Eastern Pacific.

Storm numbers can be determined from the annual lists found in the Archive link at NHC. Find the storm number by just counting down. Dorian is 05 of 2019, Erin is 06. In the EP, Juliette is storm 11. We also need to know these storm numbers to request the text Advisories by email when underway, as explained in our text, Modern Marine Weather. These are the primary and indeed mandatory sources for tropical storm forecasting.

In the previous approach we loaded and georeferenced the NHC image of all active tracks, but then discovered that NHC changes the specs on these images on each Advisory update, so that it was tedious to keep these properly positioned in GE.  This is an improvement in that the mapping is automated so that step is removed, but we are limited to looking at one storm at a time. That is not a problem. The next storm will have a file name AL062019_CONE_latest.kmz.  Note that capitalization matters on these file names.

If we want to see what is going on right now, meaning which buoys are on the storm track in the latest forecast, we can just download the track and cone KMZ files and then open them in GE on our computer or phones and compare to the BuoyCAM locations. But this method will not auto update,  so we cannot just look at our phone anytime later and see the latest configuration.

Here is the tricky part we have to work around.  A KMZ file is just a zipped set of KML files. You can verify this by taking any KMZ file and changing the extension to ZIP and then uncompressing it with whatever tools you use, such as Unstuffit on a Mac, or WinZip or WinRar on a PC.

The NHC KMZ file called "AL052019_CONE_latest.kmz" that looks perfectly generic to the storm, is actually a specific Advisory report on that storm, such as Advisory 37a valid at 2 PM EDT zipped up with the generic name "latest." In short, this file will not update automatically in GE.

So we have to work around this. We know where the file is located that is updated, but we need to automatically fetch that file anew each time we look at the GE presentation. This can be done with a GE menu option called Add / Network Link.

In the Name line you can put anything. Then add the link to to track, as shown, and in the Refresh tab choose hourly and in the View-Based Refresh choose On Request.  Then save and repeat for the cone file. These two files will then auto update each time we open the file, or we can right-click the file name in the My Places list and choose Refresh. I have checked this in both computer and phone and it works. The video at the end here will illustrate the setup in a computer and in a phone or tablet.

That is how we set this up to see the picture at the top of this note in a computer version of GE, which will then auto update.  When you are ready to look at the next storm, either go back to NHC and get the new storm 06 file link, or use the Get Info link on the GE file and change  05 to 07. As it turns out in this case, storm 6 has come and gone (at higher latitudes, but you can still see its track if you like. The next Atlantic storm will be 07.

The other issue that is new as far as I can tell is that the iOS version of GE will now open KMZ files, which are zipped files containing one or more KML files. Unless I was making a mistake last year, they would not open then (only KML), but they do now. Unfortunately, there does not seem to be a way to establish a network link from within the GE phone app, so we have to make it in the computer and then send it to the phone.

Once the track and cone files are in My Places in your computer, right click each and save to your downloads as a KML file.  Then mail these to yourself and open in your phone and assign the attachment to GE. The process is illustrated in the video below. You can then see something like this in a phone, and get the same info you would from a computer display.

In short,  you can tell at a glance where the storm is relative to a BuoyCAM from your phone. The NHC Public Advisories along with new data on the track and cone are updated every 3 hours.

If you want to expedite the process for Dorian (AL storm 05), you can download these three files to your computer and move them into GE, or mail them to yourself and open in a mobile device and copy to GE.




For later storms you can edit the link and name in the Get Info page in GE.

Here is a very nice link to the GOES16  satellite image of the storm.

Demo of the procedures

Pictures captured from the eye of Dorian as it passed over buoy 41004... added Sept 6.

For completeness, I should add that NDBC has a version of what we are doing here on their site. I think this was added after our original proposal from early in the storm season last year.

When you go to the NDBC site you will see the storm icons amongst the buoy icons and if you zoom in you will see the latest track and cone as shown below.

This is almost exactly what we are making for GE, except we are concentrating on the BuoyCAM buoys. If you go to their BuoyCAM display (left side  panel) to limit the view to buoys with cams, then the storm track goes away. They are in a sense pointing out that we learn a lot from the raw buoy data (wind and seas) even when there is no camera, and indeed there are far more buoys without cameras than with them.

This picture also reminds me to add this footnote to an earlier statement on track uncertainty.

* Although the track uncertainty is best thought of as growing at +100 nmi a day, meaning that at 72 hours out the track location is ± 300 nmi, we do not need to consider the forecast any worse than that.  In fact, the models have gotten better and better every year, and we can believe that the center of the storm will indeed stay inside of that cone for the first 72 hr of the forecast, and even more likely be in the center of it than on the edges. If that cone does not go onshore during the next 72 hr of forecast, you can believe the storm center is not going ashore... but that does not mean you don't get the full brunt of the system, albeit the "navigable" side. On land in such cases it is usually the water that causes more damage than wind.

Wednesday, August 28, 2019

Great Circle Sailing with the 2102-D Star Finder

The 2102-D Star Finder is used to identify stars after sighting them or to choose the optimum set of stars before sighting them. It has other uses as well, as we describe in The Star Finder Book: A Complete Guide to the Many uses of the 2102-D Star Finder.

It turns out that this title is not quite true for the 1st and 2nd editions of the book, because the 3rd ed (Sept, 2019) includes a new application—namely great circle sailing solutions; the subject at hand.

We did not invent this new application, and indeed did not think of it ourselves over the years working with this star finder. We learned of it by chance because one of the original 1921 versions  (HO 2102-A) was found by Mike Walker in a garage sale in Rowley, MA. He recognized its historical value and kindly donated it to Starpath. We are in the process of documenting the device, after which we will post it on the Institute of Navigation's  Virtual Museum, and then donate it to a real maritime museum.

The original patent for the device by Capt. Gilbert Thomas Rude (pronounced Roo dee) did not mention this new application (solving for great circle initial heading and total distance), but the instruction sheet included with the actual Navy versions did include a couple sentences outlining the procedure. It seems those instructions are not quite right, but the principle is clear, so we can work around them. The method will definitely work better on the original 2102-A (star disk diameter 14") than on the present 2102-D (disk diameter 8"), but as we show below, and in an accompanying video, the current version that thousands of mariners own does indeed still provide a useable initial heading and total distance for great circle sailing. This technique was not mentioned on the later versions 2102-C (1932) and 2102-D. Obviously, it is not as precise as we get from an app in our phones, but it is one more tool in our bag of tricks that does not require power and can be dropped into water, stepped on, and kicked around, and still work fine.

Let's consider a hypothetical—but not at all random!—case of being located at a waypoint called Deneb and we want the great circle distance and initial heading to a waypoint called Hamal, as shown below.

For comparisons in the following, accurate great circle (GC) and rhumb line (RL) solutions can be computed online at www.starpath.com/calc.

These waypoints happen to be the fixed positions of two navigational stars that are plotted on the white disk of the 2102-D star finder. The GC solution by star finder comes about because the arcs on the blue templates are great circles plotted on the same projection used for the white star baseplate. A sample is below.

We chose Deneb for this example because its declination (N 45º 21.2') nearly matches the Lat 45 N blue template of the star finder. There is a template for every 10º of Lat, up and down from 45. We chose Hamal more or less randomly.

Thus we imagine the earth not rotating and we are at the geographical position of Deneb, meaning it is directly overhead, 90º above the horizon, and we want the initial GC heading and distance to Hamal. The blue lines are all great circles, so we just find the one that goes from Deneb to Hamal, and read that true bearing on the rim of the blue template, which corresponds to the horizon as viewed from Deneb, or more generally from the center of the template, wherever it is located.

In this case, we see the bearing to Hamal is about 078 or 079 T, and the altitude (Hc) of Hamal is about halfway between 20º and 25º above the horizon. We know from cel nav that the distance between them is the zenith distance, or  90º - 22.5º = 67.5º, and each degree is 60 nmi, so the GC distance we read is 4050 nmi.

Thus in this example we get from the star finder disk an initial heading of 079 ±0.5 compared to correct value of 078.5 and a star finder distance of 4050 compared to a correct value of 4063.5.

This GC heading is a whopping 30º north of the RL route in this example,  so this could have a major impact on navigation decisions.  We don't care so much that one route is shorter than the other, even when this difference is large as in this case, because we are dominated by wind and rarely can make good such routes. But knowing that 078 is just as good or even better than 108 gives us some freedom in planning what to do in local winds.

In the real world, our initial latitude will not coincide with a template value, so we have to improvise the process.  We will work two examples.

Example 1. West Coast of US at 45N, 125W to Japan 38N, 142E. For this route the GC distance  is 3962.1 nmi, with an initial heading of 300.6º T. This heading is 36.3º north of the RL heading of 264.3.  The GC distance is 247.1 nmi shorter than the RL distance of 4209.2 nmi.

Example 2. Exit of the Strait of Juan de Fuca at 48N, 125W to HI at 21.5N, 157W.  This is a GC distance of 2210.3, which is just 14.7 nmi shorter than the RL distance of 2225.0. The initial GC heading of 235.3º T is 10.9º north of the RL heading of 224.4.

The question is, how close can we get to these GC values using the 8" disk of the 2102-D star finder?  We see the answers in the video below which works these two examples from scratch.

The procedure 
Illustrated in two videos below for Northern Lat departures

(1) On the N side of the white disk, draw a thin line to mark the departure meridian going through 0º on the rim to the center of the centerpin.  Or perhaps easier, draw in two meridians, one from the precise rim location (0º) to the left of the centerpin, and one to the right of the centerpin, and know the proper location is between those two lines.... all done carefully, with a sharp pencil.

(2) Use the red template scales to plot your departure point on the white disk on the departure meridian.  The celestial equator on the white disk is equivalent to the equator for this plotting. It is likely best to use dividers on the red template to get the right lat spacing, and then transfer that to the white disk. All of this plotting should be done as carefully as possible as the scales involved are all compressed.

(3) Figure the Lon difference (dLon) between departure and arrival, and note if arrival is west or east of departure.  If arrival is to the east, the arrival meridian is just dLon to the right of 0º on the rim. If arrival is to the west, the arrival meridian is located at 360 - dLon to the left of 0º. Again, draw in the arrival meridian carefully as noted in (1).

(4) Set dividers to arrival Lat on the red disk and then plot it on the arrival meridian.

(5) Find the blue template with the closest Lat to your departure Lat. Do not put it on the centerpin, but instead move it above or below the pin (keeping the blue arrowed line on the template coinciding with the departure meridian on the white disk) until the crosshair at the center of the blue template is precisely over your departure point.

(6) Then hold the template in place and carefully read the altitude (Hc) and bearing (Zn) to your arrival point, interpolating as best you can. The initial GC heading is Zn; the total GC distance is approximately (90 - Hc) x 60 nmi.

The answer is in Example 1 we get from the Star Finder initial heading of 302 T (correct is 300.6) and distance of 3900, whereas correct is 3962.

The answer is in Example 2 we get from the Star Finder initial heading of 235 T (correct is 235.3) and distance of 2100, whereas correct is 2225.

The two examples above worked on the star finder.

This method of solving great circle sailings basic data (range and initial heading) is not accurate enough for the USCG exam for unlimited masters. Indeed, we show in another article that the only method that works dependably for all exam questions is to compute the solution directly. See Great Circle Sailing by Sight Reduction.

Monday, August 19, 2019

Inverse Barometer Effect in Puget Sound

We did this analysis in 2008 and just rediscovered it.  We will come back shortly and analyze a few of the pictures. The effect is clear without actual numbers, but I will add some numbers in the next day or so to compare with the predictions.

There are many factors that can cause the observed tide height to differ from the predicted tide heights found in tide books. Atmospheric pressure studied here is only one, and in many circumstances or regions this is not the most important effect. Wind speed and direction creating unaccounted for wind-driven currents is another factor, as is unseasonable river runoff. 

The effect of atmospheric pressure on water level is called the inverse barometer effect (IBE). Pressure is just the weight of the air above us, so when the pressure is higher than normal, the rising tide has more air to lift and so it cannot lift it quite as high as in normal conditions.  When the pressure is lower than normal, the tide rises higher than predicted, because is has less air to raise than was anticipated.  

We show here that this effect can be observed and anticipated in at least one tide station in Puget Sound, Cherry Point, near Edmonds, WA. The theoretical magnitude of the effect is about 1 cm of tide height for each 1 mb of pressure difference from the seasonal mean. 

The effect was known in the 1800s, often stated as "Fog nips the tide" — which was almost right. It is not the fog, however, but the high pressure that usually accompanies the fog that is doing the nipping.

In the data presented we see both the rise in tide height in lower than normal pressure, as well as the lowering of tide height in higher than normal pressures. This simple theory accounts for the observations quite well, considering the large uncertainties of the model. 

The mean surface pressure in Puget Sound is about 1017 ± 1mb throughout the year. So we have looked at pressure incidents that exceed the mean by ± 13 mb. The standard deviation of the mean in Puget Sound is about 5 mb in the summer (June, July) and about 11 mb in the winter (Dec, Jan). The dates covered are Jan 1 to Oct 26, 2008. All incidents that meet these pressure criteria are included.

The IBE is discussed in The Barometer Handbook See also the long list of related articles on barometry at the support link for that book.

Below we show the data in Part I for all 2008 incidents of pressures above 1030 mb at Cherry Pt, Puget Sound, and in Part II, all 2008 incidents of pressures below 1004 mb at Cherry Pt, Puget Sound. The data are from http://tidesandcurrents.noaa.gov.

Part I High Pressures, above 1030 mb

At the peak, 1036.3 mb -1017 = 19.3 mb difference leading to a height difference of 1.2 ft = 15.6 " = 30.5 cm, so peak effect is about 58% higher than expected, based on the prediction of 1 cm/mb. 

Part 2. Low Pressures, below 1004 mb