Wednesday, January 16, 2019

Southern Hemisphere Weather Maps by Email

Our main source of NWS weather maps for the Atlantic, Pacific, and Gulf of Mexico and Caribbean is the FTP folder located at https://tgftp.nws.noaa.gov/fax/.

What may not be so well known is this folder also includes weather maps for the Central Pacific that extend all the way to Australia. Below is a sample map followed by the file names for these maps. How to access them is discussed below that.



WIND/WAVE CHARTS - CENTRAL PACIFIC                              NAME

00Z Pacific Wind/Wave Analysis 30S-30N, 110W-130E   PJFB89.TIF
12Z Pacific Wind/Wave Analysis 30S-30N, 110W-130E  PJFD89.TIF
    Pacific Wind/Wave Analysis (Most Current)  PJFB10.TIF

24HR Pacific Wind/Wave Forecast VT00Z 30S-30N, 110W-130E  PWFE82.TIF
24HR Pacific Wind/Wave Forecast VT12Z 30S-30N, 110W-130E  PWFE84.TIF
24HR Pacific Wind/Wave Forecast (Most Current)      PWFE11.TIF

48HR Pacific Wind/Wave Forecast VT00Z 30S-30N, 110W-130E   PJFI89.TIF
48HR Pacific Wind/Wave Forecast VT12Z 30S-30N, 110W-130E PJFI91.TIF
48HR Pacific Wind/Wave Forecast (Most Current)                 PJFI10.TIF

72HR Pacific Sea State Forecast VT00Z 30S-30N, 110W-130E  PJFK89.TIF
72HR Pacific Sea State Forecast VT12Z 30S-30N, 110W-130E  PJFK91.TIF
72HR Pacific Sea State Forecast (Most Current)     PJFK10.TIF



SURFACE CHARTS - CENTRAL PACIFIC

00Z Pacific Surface Analysis EQ-50N,  110W-130E       PPBA88.TIF
06Z Pacific Surface Analysis EQ-50N,  110W-130E      PPBA89.TIF
12Z Pacific Surface Analysis EQ-50N,  110W-130E    PPBA90.TIF
18Z Pacific Surface Analysis EQ-50N,  110W-130E  PPBA91.TIF
    Pacific Surface Analysis (Most Current)     PPBA11.TIF

00Z Pacific Streamline Analysis 30S-30N, 110W-130E    PWFA90.TIF
06Z Pacific Streamline Analysis 30S-30N, 110W-130E    PWFA91.TIF
12Z Pacific Streamline Analysis 30S-30N, 110W-130E   PWFA92.TIF
18Z Pacific Streamline Analysis 30S-30N, 110W-130E   PWFA93.TIF
    Pacific Streamline Analysis (Most Current)  PWFA11.TIF            


03Z Significant Cloud Features 30S-50N, 110W-160E     PBFA99.TIF
15Z Significant Cloud Features 30S-50N, 110W-160E      PBFC99.TIF
    Significant Cloud Features (Most Current)         PBFA11.TIF

24HR Pacific Surface Forecast VT00Z 30S-50N 110W-130E PYFE87.TIF
24HR Pacific Surface Forecast VT12Z 30S-50N 110W-130E  PYFE88.TIF 
24HR Pacific Surface Forecast (Most Current)         PYFE11.TIF

48HR Pacific Surface Forecast VT00Z 30S-50N 110W-130E   PYFI87.TIF
48HR Pacific Surface Forecast VT12Z 30S-50N 110W-130E   PYFI88.TIF 
48HR Pacific Surface Forecast (Most Current)          PYFI11.TIF

72HR Pacific Surface Forecast VT00Z 30S-50N 110W-130E   PYFK87.TIF
72HR Pacific Surface Forecast VT12Z 30S-50N 110W-130E PYFK88.TIF 
72HR Pacific Surface Forecast (Most Current)       PYFK11.TIF

Note that there is no surface analysis offered for below the equator, just above it, but there is a 24h, 48h, and 72h forecast, plus an interesting streamline map.

There are several ways to obtain these maps.

(1) Direct internet link:  https://tgftp.nws.noaa.gov/fax/PYFE11.TIF

(2) Use NWS FTPmail. That means sending an email to NWS.FTPMail.OPS@noaa.gov with the following lines of text, where you replace the file name with ones you want. You can ask for one or more.

open
cd fax
get PYFE11.TIF
get PYFI11.TIF

quit

(3) Use Saildocs. Send an email to query@saildocs.com with this message in body of the text
send PYFE11.TIF
send PYFI11.TIF

Again, you can ask for one or more as shown.  

Saildocs offers a special service on these in that they will automatically reduce the file size by 50% to save wireless transmission times. These reduced files are still perfectly legible. FTPmail sends them in their native size, 31 kb in this case; saildocs will send that one at about 15 kb.

If you want the full size image from saildocs, then send a request for the URL, namely send https://tgftp.nws.noaa.gov/fax/PYFE11.TIF


====  BOM Maps ====

We can also request the maps from the Australian Bureau of Meteorology. Below is a sample and then a list of the maps available.  We get these from saildocs as explained below.



These charts are available in the following form:
http://www.bom.gov.au/difacs/IDX0854.gif  

These are the maps they broadcast by radio fax; the times on the left are the broadcast times; file names are made up from the IDcode on the right by adding .gif

 
Time (UTC) Description of Item and Current Chart                       IDcode    
0015-0030 VMC/VMW Schedule Page 1 of 2                                IDX0468    
0030-0045 VMC/VMW Schedule Page 2 of 2                                IDX0469    
0045-0100 VMC/VMW Information Notice                                  IDX0467    
0100-0130 IPS Recommended Frequencies for VMC (Charleville            IDX0470    
0130-0200 IPS Recommended Frequencies for VMW (Wiluna)             IDX0473    
0200-0215 Australian MSLP Prog (H+36) Valid 0000                      IDX0104    
0245-0300 Australian MSLP Anal (Manual) Valid 0000                    IDX0102    
0300-0315 Australian 500 hPa Anal Valid 0000                          IDX0099    
0315-0330 Voice Broadcast Information for VMC and VMW                 IDX0461    
0400-0415 Australian 500 hPa (H+24) Prog Valid 0000                   IDX0090    
0430-0445 Australian MSLP 4-day forecast, Days 1 and 2                IDX0041    
0445-0500 Australian MSLP 4-day forecast, Days 3 and 4                IDX0042    
0600-0622 Asian (Part A) Gradient Level Wind Anal (Manual) Valid 0000 IDX0965    
0623-0645 Asian (Part B) Gradient Level Wind Anal (Manual) Valid 0000 IDX0966    
0645-0700 Asian MSLP Anal (Manual) Valid 0000                         IDX0016    
0730-0745 Indian Ocean MSLP Anal (Manual) Valid 0000                  IDX0033    
0745-0800 Australian Wind Waves Ht(m) Prog Valid 0000 (H+24)          IDX0049    
0800-0815 Australian Swell Waves Ht(m) Prog (H+24) Valid 0000         IDX0050    
0830-0845 South Pacific Ocean MSLP Anal Valid 0000                    IDX0032    
0845-0900 Australian MSLP Anal (Manual) Valid 0600                    IDX0354    
0900-0915 Australian MSLP Prog (H+36) Valid 0000                      IDX0104    
0915-0930 Australian MSLP 4-day forecast, Days 1 and 2                IDX0041    
0930-0945 Australian MSLP 4-day forecast, Days 3 and 4                IDX0042    
1015-1030 Casey Eastern and Western High Seas (H+24) valid 0000       IDX1087    
1030-1045 S.H. 500 hPa Prog (H+48) Valid 0000                         IDX0004    
1045-1100 S.H. MSLP Prog (H+48) Valid 0000                            IDX0003    
1100-1115 Casey Eastern and Western High Seas (H+36) valid 0000       IDX1088    
1115-1130 S.H. 500 hPa Anal Valid 0000                                IDX0008    
1130-1145 Asian Sea Surface Temp Anal (Weekly)                        IDX0084    
1145-1200 VMC/VMW Information Notice                                  IDX0467    
1200-1215 Australian MSLP Prog (H+36) Valid 1200                      IDX0011    
1215-1230 VMC/VMW Schedule Page 1 of 2                                IDX0468    
1230-1245 VMC/VMW Schedule Page 2 of 2                                IDX0469    
1245-1300 Indian Ocean MSLP Prog (H+36) Valid 1200                    IDX0002    
1315-1330 South Pacific Ocean Total Waves (H+48) Valid 0000           IDX0949    
1330-1345 Indian Ocean Total Waves (H+48) Valid 0000                  IDX0948    
1345-1400 Pacific Ocean Sea Surface Temps (Weekly)                    IDX0942    
1400-1415 Indian Ocean Sea Surface Temps (Weekly)                     IDX0946    
1415-1430 Casey Eastern and Western High Seas (H+48) valid 0000       IDX1089    
1430-1445 Australian MSLP Anal (Manual) Valid 1200                    IDX0602    
1500-1515 Australian 500 hPa Anal Valid 1200                          IDX0099    
1515-1530 Australian MSLP Prog (H+36) Valid 1200                      IDX0604    
1600-1615 Australian 500 hPa Prog (H+24) Valid 1200                   IDX0090    
1630-1700 IPS Recommended Frequencies for VMC (Charleville)           IDX0470    
1700-1730 IPS Recommended Frequencies for VMW (Wiluna)                IDX0473    
1800-1822 Asian (Part A) Gradient Level Wind Anal (Manual) Valid 1200 IDX0967    
1823-1845 Asian (Part B) Gradient Level Wind Anal (Manual) Valid 1200 IDX0968    
1915-1930 Indian Ocean MSLP Anal (Manual) Valid 1200                  IDX0533    
1930-1945 Australian Wind Waves Ht(m) Prog (H+24) Valid 1200          IDX0049    
1945-2000 Australian Swell Waves Ht(m) Prog (H+24) Valid 1200         IDX0050    
2000-2015 South Pacific Ocean MSLP Anal (Manual) Valid 1200           IDX0532    
2015-2030 Casey Eastern and Western High Seas (H+24) valid 1200       IDX1087    
2030-2045 Australian MSLP Anal (Manual) Valid 1800                    IDX0854    
2215-2230 Casey Eastern and Western High Seas (H+36) valid 1200       IDX1088    
2230-2245 S.H. 500 hPa Prog (H+48) Valid 1200                         IDX0004    
2245-2300 S.H. MSLP Prog (H+48) Valid 1200                            IDX0003    
2300-2315 S.H. 500 hPa Anal Valid 1200                                IDX0008    
2315-2330 Casey Eastern and Western High Seas (H+48) valid 1200       IDX1089    
2330-2345 Australian MSLP Prog (H+36) Valid 0000                      IDX0011    
2345-0000 Indian Ocean MSLP Prog (H+48) Valid 1200                    IDX0006    

You can view these online from the link below or request them from saildocs with the request:

send http://www.bom.gov.au/difacs/IDX0854.gif  and replace the file name with the ones desired.  One line for each  map.

====  South America Surface Analysis ====

The Brazilian Navy offers a great analysis map at 00z and 12z. A sample is below, followed by instructions for getting it underway. This map is a good test for model forecasts and includes several unique pieces of information as we explain in our textbook Modern Marine Weather, 3rd ed.



You can view this map online at https://www.marinha.mil.br/chm/dados-do-smm-cartas-sinoticas/cartas-sinoticas, keeping in mind that it is sometimes a slow link to respond. 

To obtain the map from saildocs, send this form of request:

send https://www.marinha.mil.br/chm/sites/www.marinha.mil.br.chm/files/cartas-sinoticas/c19011600.jpg

where the filename is CYYMMDDhh.jpg   and hh is either 00 or 12.

There are other maps available from JMA, FiJi Met Office, and the South African Weather Service. Samples are below. 

I will come back later to add details on getting these by email.












Wednesday, January 9, 2019

Florida Gulf Stream: An Exercise in Sources

... Well, that title is going to upset some folks right a way. Many feel that the name of the strong current off the east coast of Florida should be called the Florida Current. However, navigation and marine weather publications that make the claim to that name, very shortly move on to call it the Gulf Stream themselves—just as we will, and just as Benjamin Franklin did when he named the current system, 200 years ago.

We consider here a detail (our speciality!) of this current flow that stems from questions that came up in our online class about Question 16 in our online Weather Course Quiz 3: When sailing from West Palm Beach Florida toward Grand Bahama Island located some 70 nmi to the east, how far offshore would you expect to first run into the Gulf Stream Current?  And we give a Hint that such information is in the Coast Pilot, among other sources, including charts, and weather maps, and that we were not talking about the axis of the current, but rather when would we first start to experience notable current flowing north... and we might here go further to say notable means 1.5 to 2 kts or more.  Your choices are A) about 2 nmi; B) about 10 nmi; C) about 20 nmi; D) about 60 nmi.

Gulf Stream (GS) Currents Discussed in the Coast Pilot
Our motivation of this question has always been very simple: We want students to get used to using the Coast Pilot. It is an amazing resource and does indeed include information of this type, which is often more useful than other sources.  That question is some 25 years old now, and on checking our answer I find it refers to Coast Pilot No. 4, Chapter 10, paragraph 192. The numbering of the paragraphs in each chapter is their convenient way to cross reference items, and it this case helped me find this in the latest edition. It is now paragraph 260, but the wording has not changed:


So the answer is 2 nmi, which all seems easy enough, but that is not the end of the story. We have to address now why it is easy to come up with different answers to this question.

Our problem now is too many resources! It is easy to see why conscientious students are starting to stumble on this question. We now have many ways to locate the Gulf Stream, and even though many focus on the axis or center of the path of current rather than its edges, there are many ways to look into both of these properties, including forecasted current strengths.  And sure enough, they do not all agree, even some from the same agency do not agree.

My goal for now is to look into these various ways the Florida Gulf Stream is specified, showing which are more dependable than others, what the uncertainties are, and to show at least one trick play for displaying forecasted boundaries of this most famous of all current systems. For this note we are concentrating on the southern run along the Florida coast, but similar resources cover the full current from within the Gulf of Mexico, up and around Cape Hatteras and on into the complex flow into the Atlantic.

Keeping true to our standards, we have to think of the Coast Pilot as the generic place to start, and indeed it has almost all of the best Gulf Stream (GS) sources referred to, if just indirectly in some cases. There are custom sources, which I will list at the end, but basic navigation training would take us to the Coast Pilot as the place to start for nav info on the coastal waters.

US Coast Pilot No 4 is a free download as a pdf. It can be stored in the cellphone of any mariner plying the waters of the East Coast. Store it as an iBook or Kindle book for quick access,  searching, and personal annotations.  Then search under Gulf Stream to start learning about the recommended resources.

GS Data in the Coastal Waters Zone Forecasts
The first find will be Chapter 1, paragraph 243. It says  "GS locations are given in the NAVTEX broadcasts from the Miami and Portsmouth stations." This is an unfortunate start, because this is not true. It was maybe true at one point, but not now.  If we want to find GS info in a zone forecast report we cannot even use the coastal zones or the offshore zones, we have to use the groups of coastal zones called "coastal waters," and find the reports in coastal waters forecast (CWF), such as CWF for South FL, a link that will show you values that apply when you look at it.

In this example, I am studying data for Dec. 3, when we got this dated 434 PM EST, MON Dec 3 2018:

We learn several things from this. First, it does not agree with the climatic forecast of the Coast Pilot (CP) that called for 2 nmi offshore. This forecast puts the left edge of the current band (called west wall) farther east—using Lake Worth, it is about 10 nmi farther east (called 12 nmi instead of 2 nmi). One of the purposes of this note is to show evidence that this description of the current location is wrong.


NAVY Gulf Stream Features Analysis
We also note a subtlety here. This is described as Navy data. The Navy GS data are available every 36 hr, but they do not publish data on weekends or holidays. If the expected next release is on the weekend, we have to wait till the next scheduled cycle.  In our case, the last run was 12z, Fri, Dec 1, so the next run would have been 00z on Sunday, Dec 3,  You will see this weekend effect also in their important color images of the GS (north part, south part).  Below is a sample of the south part we have from some time ago.  We cannot see them live now because of the stupid government shutdown.

There is also a B&W version that shows the SST across the image. This is an old one, but also from the winter.  In the summer, the bottom half of this image can be solid red. Our textbook Modern Marine Weather has an extended section on the interpretation of these plots, issued every 36 hr.

The OPC relies on the Navy for their GS data, so this can propagate into other forecasts, as we shall see. Normally a few days does not matter too much with the GS as it wanders around very slowly, and furthermore it is more restricted off FL than farther north, but it does wander around. Nevertheless,  my guess is this location of the west wall is too far off shore in any event... and not consistent with other data we can get for this time.

GS Data In NOAA Tidal Current Tables
The next hit in the CP search for GS is Chapter 4, paragraph 369.  This is a reminder that there is GS data in the NOAA Tidal Current Tables for the Atlantic.  These Tidal Current Tables are not online, but we made a copy of these GS pages for reference.  It is an interesting set of notes. Here is a part we care about for now.


They tell us the axis where we care about, but not the inner edge, only pointing out that it "lies very close to the shoreline." This we are falling back to the coast pilot to mean about 2 nmi.

Extensive General Discussion of GS in the Coast Pilot
Returning to the Coast Pilot, the next hit in the search is Chapter 3, paragraph 122, which is their main discussion of currents for all of Vol. 4. This is the start of a 3 page discussion, which is one of the best general discussions of the GS available to us. We see that the abbreviated notes in the Tidal Current Tables were reproduced from these, in that the same note on current very close to the shoreline is there in paragraph 138. This discussion is more in depth than in the Tidal Current Tables.

GS Data on Nautical Charts
This currents section has various general notes about the GS that are crucial to anyone sailing in those waters, but the first reference to specific data is in paragraph 140, which tells us which nautical charts have GS data on them. So this is another source, namely four specific (RNC) nautical charts include GS data. Samples of how this shows up on charts is shown below.

 RNC and paper chart 11009 showing climatic location of west wall and GS main axis.  The west wall is closely correlated with the 100 fathom line that marks the edge of the continental shelf.

ENC chart US3FL30M shows the GS axis but not the inner wall, which is also missing farther north where it does show on the RNC.  The ENC can show much more such data than an RNC, but this one has just not been updated with that info.


GS Data on NOAA Weather Radio
Then in paragraph 142 we get to specific references to live forecasts of the GS.  It starts with reminding us that the 24-hr coastal NOAA Weather Radio VHF broadcasts give us distance to the wall (our main interest in this article) and to the axis of the stream relative to local navigation aids, and then in Appendix A it lists these stations.  It also warns that because this data is based on satellite SST measurements, it may not be available in the summer months when all the water is very warm in this region.

You can hear one of these broadcasts online (Daytona Beach, KIH26), but they are essentially the same as the coastal waters forecast (CWF), which are based on the RTOFS model (presumably using the SST data, referred to in the Coast Pilot). As we shall note below, the RTOFS model is not as dependable as the Navy NCOM model for this region.

Ocean Model Forecasts of GS Data
The Coast Pilot tells us about model forecasts for the GS in paragraph 143.  They are not specific, but send readers to this page ecowatch.ncddc.noaa.gov, which is not accessible at the moment due to the government shutdown. In place of that, all the model data can be found at the main NOMADS link.

There are three numerical forecasts for the GS. Two are very easy to access, RTOFS and OSCAR. The first is the Real Time Ocean Forecast System, whose GRIB formatted data is available on just about any navigation program. This model is tuned up for the GS, but it is not as good for the near coastal region as is the Navy's Near Coastal Ocean Model (NCOM). Not all 3rd party sources offer the NCOM data selectable by time slots and Lat-Lon windows;  LuckGrib is one source for Mac and iPad and Expedition is one source for the PC. Alternatively, you can download the grb2 files directly from NCEP but you must take the full 29 MB for the US East Coast Region.  Below are two samples for comparison.


RTOFS model data (Resolution 0.4º) viewed in Expedition. 


NCOM model data (Resolution 0.08º) viewed in Expedition. 

The cursor location did not show up in the screen caps, but the read out showing in both pictures is at a cursor click right on the beach in the areas we are investigating. The Lat lines showing are 10 nmi apart, so we see strong current right on the beach.  We have to stress this, because this is official data and we can see other official forecasts below that do not agree.

GS Data on the OPC 24-hr Wind & Wave Forecast
The Coast Pilot does not tell us this, but we also get GS data from the OPC plotted right on the 24-hr wind and wave forecast map. A sample is shown below.

The green line is the west wall of the GS. This is the 24 -hr wind and wave forecast from OPC

We can also get this green line as a track line that can be loaded into our nav programs as a gpx file... and this can be valuable. For example, right now we cannot get the US Navy GS Features Analysis because of the government shut down, but we can still get this version of the west wall from this indirect link from the OPC.  We have a video on how to download this data and convert it to a gpx file.

Below is a sample of loading the gpx version of the west wall into Expedition.

The red lines are the GS boundaries according to the NAVY link given above, converted to gpx file and loaded into Expedition. We see this forecast has the wall well with 2 nmi of the coast at this location.

GS Data From HF Radar Current Measurements
Along many of the coastal waters of the US there are several HF Radar stations that can measure the speed and direction of the coastal currents out to some 50 nmi from the antennas.  These data are linked from several sources but to me the best source is the CORDC presentation.

Below is a sample from just now... this article was started in Dec, but the "now" part has evolved to Jan 9.

Sample of HF radar current measurements. The time history option shows the variation is speed and direction over the past hours and weeks, which reflects a strong influence of tidal flow.

For now we just leave this as a note that there are these real-time current measurements along the coast including within the GS off the coast of FL.  We have an earlier in-depth study of currents measured this way compared to NCOM and RTOFS forecasts. Please refer to that for details.

In the model discussion above I have for now omitted the OSCAR currents: Ocean Surface Currents Analysis in Real-time, because these are blocked in the government shutdown... which shows what a sham this is.  These are all automated computations that take no personal attention at all.  Someone has gone out of their way to block the links just to cause inconvenience to others. Maybe those employees that have such an attitude will lose their jobs so we can say there was some benefit to the shutdown.

OSCAR currents are 10-day averages issued every 5 days with 0.33º resolution. As such they generally predict weaker flows than are actually observed, but in several cases they do a better job on identifying the boundaries of the currents.  We find this to be the case in the areas of Equatorial Countercurrents, for example. With the GS, however, we are better off with NCOM.

So we will leave this here for now.  The answer to our quiz question is the GS starts on average about 2 nmi offshore near Fort Pierce,  and to that we have added an overview of sources of info on the GS.  There are other popular compilations of GS resources; we keep a list of these on our ocean currents web page starpath.com/currents.



Friday, January 4, 2019

Navigation Exercise: Crossing Currents

In an ongoing article about crossing the Equatorial Countercurrent (to be posted shortly) we confront a classic navigation exercise in optimal routing through and across currents. More often than not, there are external factors that dominate how we choose to cross a current, but it is valuable to have in mind the fundamental results for comparison.

The problem is illustrated below. The situation looks idealized, but as it turns out, the values are fairly realistic—we are for now disregarding the performance of the vessel (assuming a constant speed on any heading) and also ignoring the constant equatorial currents of 1.0 kts flowing the other direction on each side of the countercurrent. We will come back to that reality, but as first guess we assume that does not affect our solution to this problem.  The vessel in this case is a custom single-handed rowboat, on its way to Cairns, AU, after departing from Neah Bay, WA about 5 months earlier.



Figure 1. Pacific Equatorial Countercurrent of 1.0 kts spreads over a band about 200 nmi wide. In some parts of the ocean in some seasons it could be twice this wide. Sometimes it does not exist.

We start the computation from a position along the rhumb line route that is 300 mi off the top edge of the current band, and ask for the fastest time to get to the finish line, which is defined here as any point on the line shown that is equidistant from Cairns, or more generically, on the line perpendicular to the course line, since Cairns is indeed more than 4,000 miles away from this point!

Assume the vessel can take any route, but maximum speed is 2.0 kts.  We are looking for an answer that is a number of days, hours, and minutes, plus the actual route proposed. It will take some review of current sailings, but that is by no means a hint.

Standing by for answers by comment or email to helpdesk@starpath.com.
__________

Here are a couple starting points.
If there were no countercurrent at all, the trip would be 300 mi to the current edge, then staying on the rhumb line (RL) course at 240T, means we are on a 30º right triangle with the sides of the current  so there are various ways to compute the distance across, but there is no point in doing that. We can layout this route and current band in a nav program such as OpenCPN and just read off these values. Or plot it on a piece of paper at some random scale and measure it that way. How we come up with the distances does not matter.

In this case the RL distance across the current is 400 nmi for a total distance of 700. At 2 kts, this takes 350 hr = 14 days 14 hr.

The time to get across the current is going to be longer, so the question is how much longer and how does this depend on our heading while crossing.  There are several choices.

(1) You can drive up to the current following the RL (300 nmi) then crab acoss the current heading into the current the right amount to make good the RL course. This means we will be still be going 1.5 kts through the water, but at some up current heading that lets us make good some slower speed but keeps us tracking along the RL. This is a standard vector problem in navigation. Find heading and resulting SMG that yields a CMG = RL course.  There are analytical as well as graphic solutions.

(2) Another choice would be to just enter the current when we hit it without changing course. We will then get set down stream by some amount and after we emerge from the current we  have to make it back to the finish line.  This is also a standard problem: how much do I get set in a know current; that is, given speed and heading as well as current set and drift, find SMG and CMG.  Then DR back to the finish line.

(3) A kayaker might first think of computing the total set during a straight-across paddle, then head for a point that far up stream from where the RL enters the stream and the paddle straight across. You will then get set right down to your RL track when you exist the current.

(4) And there could be other solutions... maybe some combination of these pure solutions.

The reader's goal now is to choose a method and solve for the total time, and see what you come up with for the shortest time?  Give your time precise to the minute as we will likely get more than one right answer, and it might come down to precision of computation.

The winner will receive a signed copy of Emergency Navigation.

We will wait until Feb 1 to see what answers we get, then post our solutions.  Note that even if you are wrong, if you are the only submitted answer you win!

Later we can also think on whether our answer depends on the speed of the boat or the speed of the current, or the ratio of the two, or is the fastest approach true for any circumstance?  Observation: there is at least one national sailing organization certification exam that believes there is only one answer!

Another part of this query, since we already know of at least three different approaches, is to ask if there is some general principle that directs us to the right solution, which would then save us testing the numerical values of the other solutions?  This would presumably be some argument from math or physics.

Spoiler alert!  Some comments may have answers in them.