Friday, December 27, 2013

Google Earth as an Aid to Chart Reading

We have an exercise in our online course on navigation that asks students to choose useful bearing targets when heading east along the south side of the Strait of Juan de Fuca, just passing Freshwater Bay. We have students from all over the world, and most do not know the area. This is not a problem, because we are focusing on chart reading, and that is the same worldwide. Skills you learn from one chart are usually easily transferred to other charts, in other parts of the world.

With that said, there are nuances to chart reading, and sometimes the terrain may be more complex than might appear from a chart. Also some cryptic notes on the chart or in Coast Pilot may not be clear till seen in person.

Thus enters Google Earth, which does indeed let us see coast lines around the world. Here is the example at hand. Below is the chart of Freshwater Bay, and in the background we see two mounts clearly marked. These were part of an answer to our practice question, so we add this new dimension to that answer.

Now turn to Google Earth and find this location (you can type in a lat lon, as one way), and you will get after some zooming, rotating, panning, etc the following view of the bay... looking south from over the water.

The round spit on the left is Angeles Point, which by the way is where the USCG defines the limit of mariner's sea time between coastal and inland. Every mile you log west of there is coastal time; east of there it is inland time.  It is a bit arbitrary.

We can now use Google Earth to look up from here, from a lower perspective. This one is more from a plane than a boat.

Now we begin to see more or less what you would from the water, but it still might be difficult to find the two mounds we are looking for.  So me must get out the binoculars, which we do on Google Earth by holding the shift key and moving the mouse up the screen.

This works very well, but not quite as good as we might hope for.  The two peaks that are charted are there because they are indeed more prominent than shows here.  The graphics cannot quite match the actual shading that is seen in life.  The background behind these would be notably darker so the peaks stood out.

Below is the areal view with push pins set at the lat lon of the two mounds, that shows a bit better why these show up more distinct from the water.

To have more fun with GE, you can also travel inland and look back out the river valley that these mark, as shown below, looking north.

If you have not played with GE in this manner, you might give it a try. It takes a bit of tweaking and practice. You might want to go to Settings (Preferences) and choose the option to exaggerate the vertical scale, and of course have 3D turned on.  I find it works best using a mouse than a touch pad.

Saturday, December 21, 2013

Model Predictions of World Winds

This shows numerical wind predictions from the same programs used by the NWS. You can zoom, click and drag, or click on a point to get Lat-Lon, speed, and direction. You can also click on the word Earth, to get other options, ie look at the winds aloft (500 mb), or change to a Mercator projection etc. Really nice work from Cameron Beccario. The original source is
This concept and an implementation of it has been around for many years. It was originally an art project and was more stylized than realistic, but now it is a working tool that much helps us understand the winds of the world.

Tuesday, December 17, 2013

Starpath Ship Reports Revised

We offer a free email service for mariners with which you can receive by email all the official ship reports of weather and sea state for the past 6 hours from within 300 nmi of your location on any ocean.  This service is described at

It is a powerful service, in that it is essentially a live look at the wind and waves around you, in any ocean at any time of day or night. You could also use it to check your barometer if you forgot to calibrate it before you left. Many vessels these day have email via sat phone or HF/SSB radio.

We have offered this service for almost a year now, but we just noticed that the way enhanced spam filters are now working, along with the increased use of html mail, that we were getting as many rejects as we were valid requests... not counting of course the tons of span that hit the server continuously.

To improve the functionality of this service we have restructured it so that you now use the subject line to send in your latitude and longitude, rather than the way we used to have it when we pulled your location from the body of the message.  Now the body of the text can be anything, in any format and it will not matter.

If you have not tried this, give it a go.  If you live on a coast, it is even a way to get "buoy reports" from offshore waters where no buoys exist.

Or if you are following a friend's voyage across the ocean, you can with an email learn in a minute or two what the actual conditions are where they are.

We have a similar free service for asact wind data at

Monday, December 16, 2013

Local Pressure as a Squall Goes By

We might guess that when a big squall goes by we could detect a drop in pressure if we had an accurate and sensitive barometer on board.  These are local lows, after all–but this measurement might be tricky, and depend on more than we guess.

For example, in our office where we do have numerous instruments like that, we see pressure drops when the wind gusts outside of our leaky front door.  You can test this as well with a good instrument in a car.  Drive along with the windows closed at 30 mph or so, and watch your barometer display carefully.  Then open the window a crack.  You will see a sudden drop.  With a nice recording instrument you can study this in depth.

Thus with the low pressure of the squall, and the venturi effect of sucking out the air from the boat (or house or car) we can expect to see a nice drop when a big squall goes by.

Well... let us think again on this.

Today we have a very specific measurement of such an event. Measured by a sailor underway off the coast of Panama using a precision electronic barograph. The results are shown below.

 I will come back to the normal daily oscillation in tropical pressures, but note the pressure as the squall went through. These folks had been sailing in these waters for several years now, and they described this as the worst squall they have seen. They estimated the winds at 40 kts and it lasted nearly 30 minutes.

And sure enough, the pressure did not go down at all. It went up!  And it stayed up quite a while during the strong wind period.

At this point we can only guess that the wind blowing against the boat pressurized the cabin.  As opposed to opening a car window when moving, if you instead sit in the car watching a good barometer when someone closes the door with all windows closed, you will see something like this, but on a shorter time frame, and more dramatic rise.

We will have to think on this some more, but it was a neat surprise, and it brings to light the great values of an accurate and precise barometer.  In this case the bump could be seen nicely on the 3-hr instrument display and better still in 3-min steps, which are plotted above.

In the tropics the pressure oscillates during the day due to a tidal behavior of the atmosphere. We discuss this in depth in Modern Marine Weather. The picture below is from that book. It shows a clock dial we developed to help remind us of this behavior, and an annotated capture of data from the NDBC, at which you can see this behavior by just clicking some reporting station in the tropics.

The times listed on our clock are solar times, referring to 1200 as local apparent noon. If the peak height of the sun at your location with your clock zone is say 1335, then you would adjust these times by 1h 35m.

Friday, December 6, 2013

Worldwide Shipping Lanes

The following can can be used to update pilot charts with density of worldwide shipping lanes.

Adapted from the original work of Benjamin Halpern et al, ScienceVol. 319. There is a more detailed image available at the UCSB National Center for Ecological Analysis and Synthesis but it is really huge, and we have not figured out how to handle it yet.

Friday, November 22, 2013

One Rombe Wrong, and What Do You Get?

In the brand new edition of our textbook Inland and Coastal Navigation, we use throughout what we call the Small-angle Rule. It is an approximation to the tangent of 6º that says the sides of a 6º right triangle are in the relation of 1:10. This can also be scaled up to about 18º (3:10) or on down as low as you like, ie 3º (0.5:10 = 1:20). We use it to estimate DR errors (ie steering 6º off course, you get 1 mile off your intended track for every 10 you sail); to estimate current sailings; cross track corrections; and other applications. We were proud to have made up this convenient formulation that has so many applications, and is so easy to remember.

Last night, however, I got one more reminder that there is rarely anything truly original in traditional marine navigation. There have just been too many people working on it for too long. Rarely is something without precedent; it is just rediscovered or reformulated. And so is the case with our handy Small-angle Rule.

Below is a page of an early textbook with the unusual title M. Blundevile, His Exercises, published in 1594. This is in one of eight sections, called the Art of Navigation, Chapter 37.  (I am crawling through books like this looking for something very specific, and if I find it, you will be the first to know!)

He is here in a section discussing compasses and related position reckoning and wants (as we do) to offer a way to make estimates of errors. This is the time period when navigators were just learning compass use on a global scale (Columbus had no idea how his compass worked on his famous voyage), and taffrail logs to measure distance traveled through the water were first described just 15 years earlier than this book, in 1580. The reference to Mariner's Card, refers to early form of a Mercator chart.

His angle units here are Rombes, which one learns earlier in the book is what we now call compass points.  In fact, it is books like this where we learn where the concept of compass points (11.25º, 1/32 of a circle) comes from. His units are leagues, and since at this time the English were absorbing navigation from the Spanish as they developed their own, he deals with both Spanish leagues (2857 fathoms) and English Leagues (2500 fathoms), but the units do not matter at this point. (England and Spain were  more or less at war during this period, so there was much competition in navigation.)

Below is a copy of his angle rule for DR errors. It is not directly our Small-angle Rule, but the principle is the same. That is, we skip the trig, and give specific values that can be scaled.  Below this picture is the interpretation of what he means.  In short, if you make good one point wrong from what you steered, you will be 19.6 miles off course for every 100 miles you log.

After running 100 leagues with a course wrong by 1 Rombe, you will be off course by 19 3/5 leagues.

His Small-angle Rule would then be: Tan (11.25º/2) = [(19 3/5)/2]/100 or 

Tan 5.625º = 0.098

which is analogous to our 

Tan 6º = 0.1

See how much easier it is to navigate now than it was 419 years ago.

Sunday, November 10, 2013

Notes on Loran

In updating our new text Inland and Coastal Navigation, 2nd Edition  we finally removed all reference to Loran, though it might indeed be on the uptick in Europe. Here are the notes we removed, which we archive here.

In this section we review other electronic aids that are either new or remain options to small-craft navigation. The technologies are not so far reaching as GPS, but nevertheless impressive in the convenience and precision they offer. Before covering new developments, we briefly review Loran, an electronic navigation system we thought was completely replaced by GPS, but there is now a renewed interest in it, especially in Europe. Keep an eye out for eLoran (e for enhanced).

The oldest of all electronic aids is radio direction finding (RDF), which is covered in Chapter 11 in the High Seas Navigation section. Although this is in an entirely different class of electronic navigation, it will long remain a valuable method to know about since it can be applied with an inexpensive pocket radio using commercial AM radio broadcasts. New high-tech developments in communications are covered in Section 12.16 on Marine Radios.

Loran was definitely on the way out as GPS emerged, but with increased concerns about its vulnerability, Loran is getting another look by some.  It is worth a few notes here for general knowledge. GPS is still cheaper, more accurate, and easier to use, so if you do not have interest in this historical (or maybe future) aspect of navigation, you can safely skip this short section.

Loran is a land-based navigation system operated by the Coast Guard. It has been in operation (with several upgrades) since World War II. It was intended solely for coastal waters, but it has been used extensively and successfully on inland waters for the past decade and was crucial to the fishing industry until GPS came along. The name derives from long-range navigation, which in some senses is an outdated acronym these days.

The system works by determining lines of position from the observed arrival times of radio signals broadcast simultaneously from two stations several hundred miles apart. The lines of position are hyperbolic curves that trace out across the chart the path of all points with the same arrival-time difference between the two signals. The intersection of two such curves (from one master station coordinated with two slave stations) produces the fix. Programming within the individual Loran units then converts this information to latitude and longitude. The precision of this last step varied among the models and manufacturers and from region to region for the same unit.

Regions are covered by separate groups of four or five stations each. The West Coast from Alaska to California, for example, is covered by three such groups. Positions can be determined up to 1,000 miles from the stations, but the stations themselves are often hundreds of miles inland.

Although Loran measures and computes the same things as GPS (position, COG, SOG, XTE, WCV) and uses waypoints in the same manner, there are still very important differences, and these differences are still only slowly being appreciated by new users of electronic navigation. If you know how to use GPS, as outlined above, you automatically know how to use the functions of Loran—although historically the statement should be reversed; all the convenient user interface design applied to GPS was developed with Loran.

But though the outputs are the same, the accuracy of the data and dependability of its operation are different. Loran has, indeed, a high reproducible accuracy (60 to 100 feet), but it has significantly less intrinsic accuracy. That is, if you store a present position as a waypoint and then travel away from it, the unit will guide you back to that precise point very accurately. But if you compared the latitude and longitude of that location read from the Loran with that read from a large-scale chart, you would find the instrument might be off as much as a couple tenths of a mile. This places limits on its use in confined waters and also on the accuracy and immediacy of its derived data, such as COG and SOG.

There are ways around the intrinsic accuracy problem for position navigation, either by relying on repeated routes that have been directly stored when at the site of each waypoint, or by entering fudge factors to offset the errors for specific locations. But there is no way around its influence on COG and SOG, which, again, is the primary information required for careful navigation.

It takes a Loran unit a minute or two and sometimes longer to figure your COG and SOG, because it must average over a longer period to compensate for its lower position accuracy. If you were sailing at a constant rate, in constant current and constant wind for five minutes, then the COG and SOG it shows will be as accurate as that of GPS. But the moment you turn or the current changes, you will get inaccurate readings on the Loran until things have stabilized for a few minutes. In contrast, GPS takes just a few seconds to detect new motion, although even GPS results (without differential corrections) should also be averaged over at least thirty seconds for reliable speed and course information.

Another drawback with the early Loran was its much higher vulnerability to local electromagnetic noise or static. This is not nearly the problem for small vessel use as it is for larger vessels with engines, fluorescent lights, televisions, and so forth, but it still influences operation in some areas because ambient noise levels in the environment outside of the boat depend on location and time of day. Likewise, electrical storms interfere with Loran but have little influence on GPS. There also are other factors that inhibit the use of Loran that can all be traced to the fixed geometry of the land-based transmitting stations. Many of the problems that arise from these factors can in fact be corrected for by user adjustments, but the vast majority of Loran users, on any size vessel, did not get involved in this level of its operation. GPS, on the other hand, provides what most users want—a true black box, with no required tuning or adjustments.

The 2012 Federal Radionavigation Plan does not mention eLoran, but it is much in the 2013 international navigation news and in professional journals. It is definitely something to keep an eye on.

Saturday, October 26, 2013

Print-on-Demand Charts and pdf Charts

NOAA has just announced that the federal government is discontinuing printing of the traditional lithographic paper charts in April, 2014. The reasons given include echarts are becoming more popular, and (more to the point) the NOAA print on-demand (POD) paper charts have gained wide acceptance. Agents who can sell both types of charts sell some 80% more of the POD charts than the litho charts, in large part because when they get back to the ship the navigators know the charts are up to date. "Federal budget realities" was also mentioned, but this is not a predominantly economic decision, even though traditional litho charts have been heavily subsidized.

At the time of writing, this transition is still six months away, so we do not know what options will arise between now and then. But is it clearly a change in a direction that could be expected. Many books are now published in this manner, and the percentage grows steadily. As prices go down and quality goes up, even more books will be printed this way. It also has the virtue, similar to nautical chart printing, that even rarely sold books can now be printed and made available without increased costs, not to mention that each printing is the latest edition or version of the book. Only the master file has to be changed. In contrast, traditional book printing yields warehouses full of books, with or without known errors in them.

At present POD charts cost a few dollars more than litho charts (same as in book publishing), but the masters are updated weekly and the charts are readily available. Granted, there are not many authorized sales agents who have the printing capability in house, so we will not have as many places to walk in and buy them, but they can be purchased by mail order or online from authorized agents. Another trend that is not unfamiliar.

We have already taken one big hit in outlets when the printing of nautical charts was transferred to the Federal Aviation Administration in 2000. In recent years, the FAA proceeded to close all but the largest chart agents. This will be another step in that direction. But we still have need for conscientious chart agents who provide advice on selections and who might stock samples of the charts for us to view in full form–or they guide users through the excellent online chart viewers at NOS. Then after selection, they either print the chart on the spot (if they have the facilities) or they order online to be shipped either to the store or direct to the customer. Chart selection is an important part of navigation, so we look forward to keeping the agent support we have grown accustomed to.

The POD chart process has been long tested, but it can still improve, and it likely will. Up until March of 2012, there was only one NOAA-certified print-on demand provider (, but now there is also East View Geospatial (, which offers not only updated NOAA charts, but also nautical charts from around the world. These two companies, both based in Minneapolis, MN, have different options and also paper choices.

We will have to see how things develop. For now, one sample of an early OceanGraphix POD paper we tested is not as durable as the litho charts. It definitely tears more easily, but it responds to multiple folds in about the same way. Water runs off this POD paper more readily, but it did not respond well after being wet for a long time. Traditional litho charts, on the other hand, can be soaked in saltwater and wadded up, then dried out and ironed, and they look remarkably good. Neither type of chart likes to be rubbed when it is wet, but this sample POD chart  liked it a lot less. You can easily make smears that obscure the printing. If they get wet they should be carefully patted dry and then let dry thoroughly.

The main difference we detect is how they erase. If anything, they take pencil lines even better than the litho charts, but they do not erase well at all. Normally we recommend not erasing past routes as you might go there again and benefit from your past tracks, but we all make mistakes in plotting, and these mistakes are very difficult to remove on a POD chart. Again, I refer to the present paper in use by just one company. Once POD is the only option, we expect the technology will improve. Or maybe someone will invent a special pencil for writing and plotting on POD nautical charts. East View Geospatial has 4 paper options, and we will test these with a follow up report as soon as possible.

The UK and Canada also offer POD charts, and I understand they have also been well received, and may use a different type of paper.

If you have not used one of these charts in the past, you might find it valuable to buy your next chart in that format to see where we are headed. Maybe try a sample from each outlet. If you really want a set of the latest and last litho charts for your region, you may want to buy them now. There is a chance they have already stopped printing some charts and are relying on existing stock, knowing there is no new edition on the horizon. You can stay informed on the chart news by monitoring the excellent website or follow @nauticalcharts.

From a practical point of view for many mariners, paper charts are a back-up to echarts. And it won’t be long until the back-up to an electronic charting system (ECS) is second ECS. NOAA has already begun producing free tablet apps to read their echarts, as well as the GPS and display relevant Coast Pilot data at places of interest. There are numerous commercial ECS apps that do this as well. Nevertheless, mariners are rightfully conservative and do not want to be 100% dependent on electronics, so some form of printed chart will be with us for a long time, and with other new changes at NOAA we have related options.

NOAA now offers free high-res pdf files of the full nautical charts. It is a brand new system and we have to see where this goes as well. But now we have options of our own. In principle we could print our own charts, but large size color printing is very expensive (about $7.25/sq. ft.  or about $80 for a 3 ft. x 4 ft. chart). In lieu of a full chart, we can crop a pdf and just print the part we need. In some cases for local sailing you might need just one corner of the chart. Or print the chart on 11 x 17” paper in sections, and make a booklet.

If you do want the full chart in printable pieces, NOAA has had this option already for several years, though now these are updated automatically, just as the POD charts are. They are called BookletCharts. These are very nice products, and you can print them on letter size or tabloid size (11 x 17) paper and have a nice set of chartlets.

Cover of a BookletChart

Sample page from the BookletChart

On the other hand, if we are thinking of back-ups, then we could use a gray-scale print, and these are more like 75¢ per sq. ft.. A gray-scale  chart would be about $9, much less than they are now in color (about $20). This would not be a good choice for routine navigation, because so much information is in the color, but it would serve as a back-up.

Once we do print our own charts, or buy some that we do not want to replace with every new edition then we should look into the process of updating the charts ourselves. Recreational vessels have this option, but some commercial vessels are required to carry the latest edition, and needless to say we recommend using the latest editions or updating if not.

This is an easy process. The corrections are all online, and well organized by chart number–and by chart edition, if you have to go back several editions. There is also an option to print out a text list of the corrections that you can take with you if you don’t get to the updates before departure. Normally it takes just a few minutes to update a chart from one edition to the next, which is a big savings, and a worthwhile exercise. The more you get involved with the charts you use, the better off you will be when you need them.

The changes listed in the above link are all those made since the last edition. They are incorporated online weekly into the latest pdf or POD chart; they just do not appear on older editions. The changes listed are called critical changes, which relate to safe navigation. New editions, when offered, will also include the accumulated non-critical changes, such as newly surveyed shoreline boundaries in non critical areas, new structures on the land, soundings in non critical areas, or maybe slight compass rose adjustments, and so on.

Sample of chart corrections.

Monday, October 14, 2013

Checking your Compass with the Sun

We have just added this new section to our training materials, which we post here for feedback and comments.  Earlier sections of the text addressed compass checks by simply swinging ship promptly and watching that the shadow bearing does not change. Here we expand the use of the sun with a more versatile and accurate method.

The sun method just described uses several approximations and also calls for changing course to make the checks. Often we are underway and just need to be sure the compass is right on our present heading, and then we will worry about other headings when we can. This comes up, for example, in an ocean yacht race, where some doubt about the steering compass might arise because the electronic heading sensors are reporting other headings; in a race you do not want to stop and swing the ship.

But we do not have to. Here is a quick and easy solution that you can use in the ocean or in your local lake. We are relying now on celestial navigation in a sense, but we do not need any of the details if we are on land and have access to the Internet.  We just assume if you are in the ocean, you have the full tools to solve this with conventional cel nav methods.

We start with the measurement of Figure 12.9-1 where we learned that the compass bearing to the sun was 135 C when the vessel was headed 000 C. Note that this heading does not matter for this application. We just happen to have a nice picture with the compass in that direction. For this method, you measure the sun bearing on whatever heading you happen to be on.

Figure 12.9-1. Reading the sun’s bearing form the reciprocal of the shadow pin bearing. Here the shadow is at 315 C, so the sun’s bearing at the moment is 135 C, when the vessel was headed 000 C. From convenient resources on line we can determine the true bearing of the sun at this time, and from this and the known variation for our location we compute the magnetic bearing of the sun. The difference is then the deviation of the compass on our present heading.

But we do now need more information. We need to know the time accurate to within a minute or so, and we need to know our location. Both you can get from the GPS. Now we need to look up or compute what the true bearing of the sun was at this moment based on cel nav principles, or we just go online and look it up.

Go the for a quick link to the right place at the US Naval Observatory. Then type in the time of the bearing and your Lat-Lon. As example is in Figure 12.9-2, which assumes we were headed north in Chesapeake Bay on Oct 14, 2013, and we recorded the bearing at 0930 EDT, which is 1330 UTC.  The true bearing to the sun at the time was 123.5º.

Figure 12.9-2. Data from the USNO. The true bearing of the sun (Zn) is 123.5º at 0930 EDT from this location in Chesapeake Bay, VA. We also see that the height of the sun at this time (called Hc) was 24º 29.5’ above the horizon, along with other data we are not using. We can convert this true bearing to a magnetic bearing using the local magnetic variation

Next we need the local magnetic variation which we could get from a chart, but for this type of precise compass check we might want to go back online and get the most accurate and up to date value. This you find at the National Geodetic Center ( for specific times and locations. For our example time and location the correct value is 11º 05.3’ W, or about 11.1º W.   
Input screen for online GeoMag. Note you can download a Windows version of GeoMag for your own computer if you like. It makes a nice backup underway. Note too, land navigators call variation "declination," but this is never done in marine navigation, because we have other meanings for that name in marine navigation.

Output screen from online GeoMag

So the proper magnetic bearing of the sun is 123.5 + 11.1 = 134.6 M. The compass showed 135 C, so the deviation on heading 000 C is -0.4º which would be called  0.4º W.

We  have learned that this compass is essentially correct at this heading, as it is difficult to be confident we have read the shadow bearing to this precision. But the main point is, this method has no other approximations in it. The result you get is as accurate as you can read the shadow bearing on the compass card.

This is a very powerful method. It would be instructive to try it once or twice whenever you see a nice shadow on your compass card, no matter where you are.  Just write down the shadow bearing, the time, and the location, and your actual compass heading at the time. Then you can check the compass for that heading when you get back home. If convenient, record the data headed roughly north or south by compass and also roughly east or west by compass, and then you will have a pretty good analysis of your compass with a few minutes of paperwork at home.

Friday, October 11, 2013

Air Temperature Dependence of Sea Level Pressure Conversions

Many electronic electronic barometers offer the option to display sea level pressure, which they compute from the measured station pressure corrected for the elevation of the instrument above sea level. The only user input to this type of conversion is the elevation of the instrument.  In barometry terms, station pressure is called QFE, and sea level pressure corrected for elevation alone is called QNH – it is called the altimeter pressure in aviation.

In the true atmosphere, however, the equivalent sea level pressure measured at a location that is well above sea level is more complex than a simple elevation correction can account for. The more realistic value of sea level pressure, called QFF, is a bit of a tricky concept, in that we wish to know what the pressure would be at sea level measured from the top of a mountain, as if the mountain were not really there.

QFF is the pressure needed by the National Weather Service so they can make maps of the sea level isobars that spread across a landscape that varies in elevation from place to place.  The measured pressures across this landscape are crucial to seeding the numerical weather prediction models that in turn are used to forecast the weather over the region.

Since pressure is the weight of the atmosphere above us, and because cold air weighs more then warm air, we can see that air temperature must be a factor in this correction as well as the elevation. The simple conversions that use only elevation are based on the International Standard Atmosphere, which provides a specific formula for how pressure drops with elevation. It also assumes that the temperature of the air is also following along with that of a standard atmosphere, namely starting at 15º C and dropping at a rate of 0.0065º C per meter.

This turns out to be a reasonable approximation, provided the air temperature at the elevation at which you measure the pressure is about what it would be in the standard atmosphere for that elevation. Thus if I am at 300 m elevation (984 ft) the correction to my station pressure reading (QFE) to get to QNH would be + 35.5 mb, based on elevation alone.  But this correction assumes the outside air temperature where I am is 15º - 0.0065º x 300 = 13.1º C (55.5º F).  Needless to say, all locations in the world that are at 984 ft elevation are not at 55.5º F at all times.

The first ever insights into this issue can be traced to the American meteorologist William Ferrel in a paper from the mid 1800s. He worked at the US Signal Corps at the time (forerunner of the NWS), and his pioneering paper on this subject appeared in the same report that included a paper on the interpretation of smoke signals used by the Apache Chief Geronimo.

Ferrel pointed out that there had to be temperature corrections applied because the average daily temperature range, as well as the average annual temperature range, are notably higher on elevated land than they are at an equivalent elevation in the air, away from the land.

The required corrections for temperature can be notable for elevations above 1000 ft, even at modest temperature ranges.  Notable in the sense of the rate that pressure changes across a typical weather pattern, which is depicted on weather maps with isobars spaced 4-mb apart. Thus a 1-mb discrepancy could shift an isobar by many hundreds of miles in some cases.

Table A2 below shows a list of air temperature corrections based on a simple hydrostatic equation, which accounts only for a difference in air temperature. The far right column shows the expected air temperature based on the ISA as a function of elevation. At these air temperatures, the temperature correction as we present it here would be zero.

As an example, If the barometer is set to report SLP using an elevation of 200 m (656 ft) and it reads 1022.8 mb when the average outside air temperature was 30º C (86º F), then the pressure should be corrected by -1.3 mb to read 1021.5 for comparison to weather map reports for the same time and location.

Likewise in the winter, when the same pressure was measured in outside air temperature averaging 32º F, then the correction would be +1.2 mb for a QFF of 1024.0.

The air temperature correction, however, is not quite as simple as we might want.  Namely the proper air temperature to use is not what you read at the time you read the barometer, but rather we should use the average of the air temperature at the time of observation T(0h) and the value from 12 hours earlier T(-12h):

T (avg) = [ T(0h) + T(-12h) ]  ÷ 2

This 12-hr time average is not an obvious choice. It is also not the result of a mathematical theory, but we can expect that some average is called for. We know the virtual temperature of this virtual air column affects the pressure, and it is reasonable to assume that the the pressure at the base of this column cannot respond instantly to a change in temperature at the top, so we are led to averaging over some time period to reach equilibrium. In other words, the air temperature at the moment is not what we should use to project this pressure down to the sea level, but rather some average of what it has been in the recent past.

Ferrel originally tried a 24-hr average, but found that was too long. The daily changes in air temperature with the rising and setting of the sun distorted the underlying weather pattern pressures. He found that a 12-hour average was the best compromise in that it provided the most systematic results when compared with data from neighboring locations. Recall the main goal of this endeavor is to develop a systematic measure of the sea level pressure pattern that is as independent of local terrain as possible. And he was pretty much right. Ferrel's approach to air temperature has not improved much over the intervening 150 years!

Since this air temperature averaging seems at first a rather arbitrary procedure, we have looked into this in more detail. One way to test Table A2 using present air temp versus using the 12-hr average air temp is to compare the corrections we get with those generated by the AWOS (automated weather observing system) computers located at airports around the country. These computer programs use the most sophisticated analysis available to convert QNH to QFF. They use the latest models for virtual temperature as well as the humidity and even local fudge factors developed over the years,  stemming from what Ferrel originally called Plateau Corrections.

The AWOS generate METARS (a long French phrase meaning airport weather), that include both QNH and QFF along with the air temperature, dew point and other data of interest to aviators. A typical METAR looks like the following. The top line is the METAR code, below it is the translation of the code. The one below was just pulled offline at this writing, along with one from 12h earlier.

METAR text:     KABQ 120052Z 35010KT 10SM CLR 14/M02 A3006 RMK AO2 SLP147 T01441017
Conditions at:     KABQ (ALBUQUERQUE , NM, US) observed 0052 UTC 12 October 2013
Temperature:     14.4°C (58°F)
Dewpoint:     -1.7°C (29°F) [RH = 33%]
Pressure (altimeter):     30.06 inches Hg (1018.0 mb)
[Sea-level pressure: 1014.7 mb]
Winds:     from the N (350 degrees) at 12 MPH (10 knots; 5.2 m/s)
Visibility:     10 or more miles (16+ km)
Ceiling:     at least 12,000 feet AGL
Clouds:     sky clear below 12,000 feet AGL
Weather:     no significant weather observed at this time

METAR text:     KABQ 111252Z 01004KT 10SM CLR 04/M01 A3007 RMK AO2 SLP158 T00391011
Conditions at:     KABQ (ALBUQUERQUE , NM, US) observed 1252 UTC 11 October 2013
Temperature:     3.9°C (39°F)
Dewpoint:     -1.1°C (30°F) [RH = 70%]
Pressure (altimeter):     30.07 inches Hg (1018.4 mb)
[Sea-level pressure: 1015.8 mb]
Winds:     from the N (10 degrees) at 5 MPH (4 knots; 2.1 m/s)
Visibility:     10 or more miles (16+ km)
Ceiling:     at least 12,000 feet AGL
Clouds:     sky clear below 12,000 feet AGL
Weather:     no significant weather observed at this time

Elevation at KABQ = 1619 metres (5312 feet). The only information used from the bottom METAR is the air temperature. 1252 on the 11th is 12h earlier than 0052 on the 12th.

T(0h)   Temperature: 14.4°C (58°F) QFF = 1014.7, QNH = 1018.0  corr = −3.3
T(−12h)  Temperature:     3.9°C (39°F)

So we want to compare the correction for T(0h) = 14.3  with the correction we would get for T(avg) = [14.3 + 3.9)/2] = 9.1.

Unfortunately, we do not have very fine steps in the table shown (we can add more later), so we have something like a triple interpolation to do (ie find the numbers in the blue fields based on the white ones):

There is an interpolator at (sample below), and the free Windows program Celestial Tools by Stan Klein includes such a function, among others valuable to the navigator.

So we see here one data point:  the best AWOS correction was -3.3, and we got -5.8 with present air temp, but got -2.9 with the average air temp.  Still not exactly right, but a huge improvement from the average – it might even have been closer with a computation rather than interpolation.

That example shows the approach we are taking to study this effect.  But not just one case like this but very many. With high and low elevations, hot and cold temperatures.  This example, by the way, is a very high station, and we still got pretty close. Below 2000 ft the table using the right temperature is very good.

Below are a few selected samples of data so far that support very clearly the need for the average temperature and not the current temperature.  They are comparisons done just like the one above but for multiple test cases for different locations.  Needless to say, these are all typical, we have not selected out particular sets, nor omitted any data points, and we have many more examples that behave the same way.

The red lines represent the errors in our corrections using T, and the blue lines are the errors using the T average over past 12h.  Even this rough study is remarkable evidence that we must use the average temperature over the past 12h when correcting QNH to get QFF.

Besides the apparently obvious need for the temperature average, we also see that there are still large discrepancies with the AWOS data for SLP, even at the same average air temp, at the same locations. We can estimate the overall uncertainty in this approach as the spread of values about the blue line. We see no evidence that the need for average is correlated with temperature, but the success of the solution does vary with elevation, which is not a surprise.  This method works pretty well for stations below 2000 ft or so (< 1 mb) but for the very high stations we are still hovering around ± about 1 mb or so.  All and all not bad, but a seemingly large scatter.

The summary is, if you want to compare your pressure with what would be expected at sea level, you must take the recent history of the air temperature into account, and the higher you are, the more important it is.

We are in the process of automating the data collection and analysis in hopes of learning more of the inherent reliability of such conversions to SLP as well as an attempt to develop some empirical modifications to table A2 to account for the discrepancies and scatter. We would like to end up with the blue line centered on 0.0 for all elevations, and to have a better feel for what variations about it are expected.  We do have all of the dew point data, so a small correction for humidity can also be added, but the problem with that is end users will not have such data, so we want to learn how well we can do without it.

A very special thanks to Albert Brown of Garfield HS in Seattle, who carried out the data searches and analysis. 

[Some of the formalism that goes into the AWOS computations of SLP along with historical notes on  Wm. Ferrel's role in the process are covered in the Appendix to The Barometer Handbook.]

Thursday, October 3, 2013

Why Study Celestial Navigation in the Age of GPS?

If you rely solely on GPS to cross an ocean, you will not know if you are right until the last day.

With that said, the real answer to the question is: You have a good chance these days of getting by without celestial navigation.

...In fact, you don't even need a boat to get to Hawaii or Bermuda, or to take a trip around the world. You can do this by plane. It is faster, cheaper, and more comfortable, and it will increase your likelihood of not needing celestial navigation as well.

On the other hand, if you do choose a life on a small boat at sea, then one of the fundamental rules that has been proven so many times we don't have to go over it is you must be prepared to take care of yourself in any contingency. You must be self reliant. Murphy's Law was invented on a small boat at sea. Anything electrical is vulnerable after some time in the salt air, especially when it is being jarred, bumped, banged, and dropped (i.e. going to weather).

To be self reliant, we need some dependable means of navigation, and celestial is that. Needless to say, a hand-held GPS and spare batteries stuffed into a well protected vacuum sealed bag is a pretty good back up these days, but it is not at all bullet proof. Batteries of any kind are not bullet proof. One could even argue that the durability of hand held GPS units is not improving at all with time. They are getting cheaper, and have more functions, but no evidence of more dependable.

Furthermore, you are still dependent on the availability of the signals. In any sort of worldwide military conflict, it is likely you would lose these first thing. (Here is a March, 2016 example of US military shutting it off over hundreds of miles.)  In principle, you could lose the signals in a union dispute. It doesn't really matter.  Or lose them as a result of a "pre-commissioning validation exercise!"

See also question 724 of the USCG Deck License exam questions on GPS.

Keep in mind as well that GPS has always been notoriously easy to jam either maliciously or accidentally, so you could get stuck one day without it.  Here is an example from 2011, and here shows our progress as of 2013. Google GPS jamming for more discussion.  See also this note from Feb 2014: GPS pioneer warns on network’s security.

See also:

And here is a database started in 2015 of GPS jamming events.

There are also numerous examples of GPS failures linked in the comments below.

But quite beyond the numerical likelihood of not having it when you need it, still a very small probability, learning celestial is still a most rewarding venture. It will make you a better navigator even on inland and coastal waters—you must, for example learn how to do a running fix to do celestial, and this could well pay off if you lost the GPS for some reason, and were left with just one light shining through the fog; or you are close in on a coast, but can then only identify one feature on the land (which is not a radar target), etc. Such problems are easily solved with a running fix.

In some areas of the world you can have precise GPS coordinates, but no chart scale adequate to navigate on with Lat and Lon. You have to use basic piloting skills. This is not celestial navigation itself, but the question is, if you choose to not learn celestial because of GPS for worldwide navigation, what else are you prepared to not learn?

But back to the celestial. Once you learn celestial, it is a trivial matter then to check your compass with the bearing to some celestial body, even well away from any land marks and in a strong unknown current. You can't do this with GPS in a dependable manner (in current and leeway), nor any other instrumentation on board, no matter what it cost, and no matter if you are a ship or a sailboat. The only way to truly check your compass at sea is with celestial. And if the boom hits your compass or lightning strikes near by, or–much more likely–you simply realize that it never was checked before, then this is something you will eventually have to do.

In the last 4 or 5 ocean crossings I took part in, we did maybe take a sight or two for practice but we did not feel compelled to do celestial for basic navigation, and it was not needed.  But, we did use cel nav on each of these voyages to check the compass.  Ironically, the more technical the vessels become, the more this need arises.  That is, we now have multiple compasses on board with heading sensors for the other electronics, and inevitably they will not agree, and if this does not get sorted out before leaving the dock, you are left to do it underway.

(In passing, the last ocean crossing that I did that relied solely on celestial navigation was in July 1982. And all the details of that navigation is presented in a new book from Starpath called Hawaii by Sextant.  It is a thorough and enjoyable way to master the subject of celestial navigation with real sights and real logbook entries. See also this article about that book and an overview of cel nav in general.)

And finally, there is a wonderful intellectual satisfaction that comes from learning and practicing celestial navigation. It is a way to see science and math come together in our own hands and mind and do something both tangible and useful.

Learning celestial will make you a better ocean mariner because whether you show it or not, you will be anxious about your navigation if you are depending on something that we (most of us) cannot hope to understand. GPS is the quintessential black box. With nothing else to check it with, you can just hope and pray that it works right, and, again, you will only really know that on the last day, when you either see the right land or do not. And when you are anxious, you are more likely to make a mistake.... and you risk the chance of exposing your anxiety to the crew, which could undermine your leadership, which in turn could lead to all sorts of unpleasantness.  None of that will happen of course so  long as everything is going fine, but if things start to get stressed for any reason (bad weather, broken gear), this factor will just add to the challenge.

In the long run, it is best to learn celestial, even if you are never going to use it. You will know you can use it if you need to, and that alone will make it worthwhile. If you plan to crew on other vessels, then knowing celestial will be an important part of your credentials and will certainly help you find a good position. The majority of skippers will believe they do not need it, but they will be happy to know someone on board does know it.

In contrast to GPS, celestial navigation is completely transparent.  If you are confident that your watch is right, then you must be located at the intersection of the 3 star lines you have plotted. There is no mistake you can make and still get that confirmation.  Likewise, if you make a mistake, it will generally stand out like a sore thumb and you can go back over your work and find the error.  With celestial navigation, you are crossing an ocean with the same confidence you would be sailing from headland to headland on inland waters.  Think of it as sky piloting.

And one last related thought: GPS is (in an abstract sense) another version of SatNav (the Navy Transit System, now long gone) that happens to be a lot easier to use and is more accurate. But in this sense, we have had all-weather global satellite positioning for more than 30 years now. Yet there never was any consideration at all by the USCG to remove the requirement of learning celestial from an ocean license exam. And there is none now. To get a USCG license that is valid offshore you need to know celestial and pass a test on it. Whatever the reasoning behind that decision for ships, it is many-fold increased for small boats at sea.

Still a required part of professional training.

Wednesday, September 4, 2013

Tuesday, August 27, 2013

Open Letter to the America's Cup Rules Committee

Like anyone who has seen the Louis Vuitton Cup races, I stand in awe of the technology of the AC72 yachts, and admire the skill of the sailors and designers who have learned to sail these phenomenal vessels to such high performance. I would praise the crew's courage as well, but most of them have proved that many times over in the Southern Ocean in other boats in even more dangerous conditions.

But these are still sailboats and this is still supposed to be yacht racing, which has stood for the highest standards in sailing and seamanship for more than 100 years. As such they set precedents for the whole sport of sailing that reflect on the concept of seamanship for all mariners.  A hallmark of good seamanship is getting safely where you want to go, and to show up with everyone on board who departed onboard.

In fact, the International Sailing Federation (ISF) Racing Rules require that you cannot finish a race if you do not have onboard everyone who was onboard when you started. It is stated in Rule 47.2.  However in Race 1 of the LV Cup, ETNZ was allowed to win a race after losing two crew members overboard. They were safely rescued by a chase boat, but that is not the issue at hand. The question raised is the change of Racing Rules that allows this to happen without even a penalty charged.

In my opinion this sets a very poor precedent, not to mention that it is not a sustainable rule in the first place. Suppose the two sailors did not survive?  Or look at the ISF Rule 41 clause on outside help.  Would you consider the outside help of the chase boat in saving the lives of two of your crew members as a "significant advantage"?   But the AC Rules committee got around that by just removing that clause from the Rules as well.

Or what if all the crew were washed overboard on a round up at the finish line and the boat went on to cross the line on its own.  Would they still get to count that as a win?

I would propose that the pundits of the race (who by the way are doing a good job of the reporting) devote some air time to this issue and that the Race Committee at least consider some form of penalty to cover cases of crew lost overboard. If there are no consequences for losing crew, the safety factor and image of good seamanship is bound to suffer. 

Here are the related Rules, with italics added to the subjects at hand.

ISF Racing Rules America's Cup Racing Rules


47.1 A boat shall use only the equipment on board at her preparatory signal.

47.2 No person on board shall intentionally leave, except when ill or injured, or to help a person or vessel in danger, or to swim. A person leaving the boat by accident or to swim shall be back on board before the boat continues in the race.

A boat shall not receive help from any outside source, except

(a) help for a crew member who is ill, injured or in danger;

(b) after a collision, help from the crew of the other vessel to get clear;

(c) help in the form of information freely available to all boats;

(d) unsolicited information from a disinterested source, which may be another boat in the same race.

However, a boat that gains a significant advantage in the race from help received under rule 41(a) may be protested and penalized; any penalty may be less than disqualification.


47.1 A yacht shall use only the equipment on board at her preparatory signal.

47.2 A yacht shall not permit any person on board to intentionally leave unless ill or injured. Except as a result of a capsize, a person leaving shall not be accepted back on board nor replaced during the race.

A yacht shall not receive help from any outside    source, except:

(a) help for the removal of an injured or ill person. Once a person has been removed from the yacht, that person shall not be returned or replaced;

(b) after a collision, help from the crew of the other yacht or vessel to get clear;

(c) unsolicited information from a disinterested source, which may be another yacht in the same race;

(d) communication with the Race Officer and Umpires;

(e) after a capsize, help to recover the yacht.

Thursday, August 8, 2013

Tides in Puget Sound

In a recent note I addressed the issue of correcting a barometer to sea level accounting for the tide height. The conclusion was that the barometer elevation to use is the height of the instrument above the water line plus a correction for where mean sea level (MSL) is relative to the height of the water at the time you are choosing to determine an accurate sea level pressure:

MSL correction =  ± dH + (Tide - MHW) + (MWH - MLW)/2,

where dH is the change of the draft relative to your standard waterline, which does not change much in small boats but can in larger vessels. In large vessels the reference is usually the Summer Load Line (SLL). dH can be 15 feet or more in tankers and routinely 5 ft in cargo vessels.

This correction is based on the approximation that MSL is very nearly equal to the Mean Tide Level (MTL, halfway between MLW and MHW). This approximation varies within Puget Sound from 0 to 4.5 cm, but it is plenty close enough for considerations at hand.

The task at hand now is to look at actual tide ranges in Puget Sound to show the relative significance of this barometer correction, and in doing so we learn some about how the tides vary along the length of what is often called Puget Sound, namely Port Townsend (PT) to Olympia (Oly), though this is not a strictly valid name, in that the upper portion of this water way where PT is located is called Admiralty Inlet and Puget Sound starts at the base of Whidby Island––another detail that does not matter for now.

For those less familiar with the region, here is a bathy map of the area.

It is about 90 nmi from PT to Oly by boat.  On the west coast of the US, we have a mixed semi-diurnal tide pattern, which looks like this at Seattle:

We have two highs and two lows and they are typically not equal, giving rise to a higher high water (HHW) and a lower low water (LLW) each day. A sample day's tide in Oly at the time of this writing is given below, which are typical values.

We can find more extreme tides in this area if we look for a new or full moon near a solstice, and without hunting for the best we can get this:

So even though we are not in Alaska, we can get high tide ranges in Puget Sound (- 4 ft to + 16 ft).  At this same time you would also get ranges of -4 to about 12 in Seattle

For the barometer work––and for navigation work––we need to know not just the tides but also the MHW and MLW values.  These vary along the Sound approximately as shown here:

These are numerical computations (real data below) which I show because they are already plotted!  This and other pictures presented here are from a tidal research paper called: Tidal Datum Distributions in Puget Sound, Washington, Based on a Tidal Model, NOAA Technical Memorandum OAR PMEL-122, Nov. 2002, by H.O. Mofjeld, A.J. Venturato, V.V. Titov, F.I. Gonzalez, J.C. Newman.  Their goal was to compute all of these values and compare with the tide gauge data, and they did a good job of it. 

I will show the actual numerical data at the end, but this nice plot shows what is going on.  The left is PT; the right is Oly. Again, the fact that these two places are actually only 166 km apart is not important now!

One could extract the MSL correction from a drawing like this, but the actual computation using real values is not hard, so we do not need that.  But we do see that the deeper you go into a tidal estuary, the higher the tides and the larger the correction.  This example is for Puget Sound, but you would get the same type of data going into San Francisco Bay, or Chesapeake Bay, or New York Harbor.

This plot shows that if you were doing the correction at MHH tide in Oly, you would have a MSL correction of about 2m (6.6 ft, which is 0.2 mb). At LLW it is about 2.5m (8.2 ft = 0.3 mb).

One interesting result that can be pulled from the above plot (or actual data) is shown below:

Throughout the Sound, the MSL is about 60% of the MWH, and that offers a quick way to make the correction. For example, if MHW were 10 ft and the tide is now 13 ft, then the correction is about 13 - 6 = 7 ft. In other words, if your barometer is 5 ft above the water line and the tide is 13 ft in a region where the MHW  is 10 ft, the the height you use to correct to sea level pressure is not 5 ft, it is 12 ft.  The mean sea level is 7 ft under water.

And now at this point I can imagine what might be going through the minds of the reader: Wow!  Why bother with this at all?  That is fair enough. In Puget Sound this is a small effect in all but rare cases, but we would not know that without some analysis... and we can be happy we are in Puget Sound and not near Anchorage, where the tide range can be more like 30 ft, or the Bay of Fundy at 50+ ft.

Each little bit matters if you want to do your best.  That is, if you have a good barometer that can give a dependable pressure to within a couple tenths of a mb, then we do not want to lose accuracy we do not need to––or we do not want to question our good barometer that seems off 0.3 mb at a very low tide when it had been so good in the past.  Likewise we want to know accurately the barometer height above the water line, and not just guess it.  It is analogous to the Height of Eye needed in celestial navigation sights.  Rather than guess it, take the time to measure it once then that uncertainty goes away.

For completeness, below are the actual tide data from Puget Sound and adjacent waterways.  You could piece this together from NOAA data online for any other large tidal estuary.

This compilation is from the same paper quoted above. You can disregard the two geodetic datums listed, which are not related to our discussion.  MHW and MLW are listed on most charts. There is typically a table showing multiple values for a small scale chart.

Saturday, August 3, 2013

"Point Four Four per Floor" –– QFE to QNH to QFF

Several years ago we developed a jingle for making elevation corrections to barometer readings for quick conversions from station pressure measured at some elevation to sea level pressure needed for weather work.

It goes "Point four four per floor," which is intended to remind us the that pressure drops 0.44 mb for every 12 ft we rise above sea level––we are calling 12 ft a floor, which is more or less right for buildings with multiple floors. Needless to say, we chose the word because it rhymes, not because it matches some architectural standard.

If your barometer was 120 ft above sea level and it read 1012.5, then you would increase that by 4.4 mb to read 1016.9 to get the equivalent sea level pressure. More generally, the correction is just (H/12) x 0.44 mb.

This jingle will serve many needs we have in this department.

For example (using info from an earlier note):

The barometer on my boat is, mounted 6 ft above the water. It reads 1015.1 mb.  The tide is 13 ft, MHW = 8 ft, MLW = 2 ft, so mean sea level is (13-8) + (8-2)/2 ft, which equals 8 ft below the surface of the water. So this barometer at this moment is 14 ft above sea level, and thus I need to correct it by: (14/12) x 0.44 = 0.5 mb. The correct SLP at this moment is 1015.6 mb.  If this moment happened to be a synoptic time (i.e. 00, 06, 12, 18z) then I could wait a couple hours for the next weather map that covers this time, and I should see that pressure on the map at my location. Or i can compare this with a local buoy or lighthouse report, which is given every hour (google "nws ndbc").

This jingle will almost always work for computations like that one, even on up to several hundreds of feet, over a broad temperature range.  But this jingle is definitely an approximation, and it is time to address this more specifically so we know what affects the accuracy and how to compensate for variances.

It is an approximation for two main reasons. One, the density of the air decreases with increasing elevation, so it cannot be 0.44 forever as we go up.  Also the conversion of a pressure measured at a high elevation to the best equivalent value at sea level pressure (SLP) at that location and time depends on the outside air temperature as well as the elevation. Worse than that, it also depends on other properties of the atmosphere at the moment and it even depends on the local geography, but the main factor beyond elevation is the air temperature.

The conversion dependence on these factors is a complex one, and even meteorologists from different countries do not agree on the best way to compute it. The best rules for the highlands of Norway are not the same as the best rules for highlands of New Mexico or Colorado.  For an introduction to the conversion process and the factors involved, see Appendix A3, Reducing Station Pressure to Sea Level Pressure in The Barometer Handbook. More details on the issues and challenges are presented in the WMO document CIMO/ET-Stand-1/Doc. 10, Pressure Reduction Formula, Nov, 2012.

To begin, the jingle is an approximation to an approximation, and to clarify that thought we need to use the specific terms for the types of pressures we are dealing with. The short definitions are: QFE = station pressure, QNH = sea level pressure figured from elevation alone (called altimeter in aviation weather),  and QFF = best value of the equivalent sea level pressure taking all known factors into account.

There is a unique and unambiguous way to find QNH from QFE. We assume that QFE decreases with increasing elevation exactly like the pressure drops with elevation in the International Standard Atmosphere (ISA). This average atmosphere was developed originally by aircraft designers who needed some standard to work with. There are tables and formulas online that compute the pressure of the ISA as a function of altitude.  A slick online computer is at, which even lets you create a printable table to your design.

Essentially all electronic barometers on the market that offer the option to display SLP as a function of elevation are presenting QNH and they are using the ISA formulation. Indeed, most of the time we hear or see the phrase sea level pressure the implication is that the elevation dependance is this simple one based on the ISA. If air temperature is not mentioned in the same sentence, then it has to be that one.

And the results (ie QNH) are actually very close in many applications, compared to the best we could do (QFF) if we made a lot of corrections. We have to go to extenuating conditions (high elevations or unseasonal temperatures) to see notable difference, or we have to care for a precision that may be difficult to justify.

So our jingle of point four four per floor is just an approximation of how the ISA pressure drops with altitude over the lower layer of atmosphere, which as noted is itself an approximation of how QFF might drop with elevation. Note I say, "might drop" with elevation.  Throw a big temperature inversion in there and even the best computers will have trouble coming up with a good sea level pressure.

Table below shows how the jingle falls off in accuracy as the elevation increases. Also shown are the ISA air temperatures as a function of elevation. As you go up in the atmosphere, the pressure and the temperature drop.

Elevation (ft)    Jingle factor     ISA air temp (Fº)
0                       0.44                 59
100                   0.44                 59
500                   0.44                 57
750                   0.44                 56
1500                 0.43                 54
3000                 0.42                 48
6000                 0.40                 38

So the first thing we see is our jingle is good up to 750 ft, and still ok within a couple percent to 1500 ft.          

But the underlying assumption of using this conversion (QFE to QNH as an approximation of QFF) assumes the temperature of the air as a function of elevation matches that of the ISA––in some sense.

This brings up an interesting distinction in language that is related to our problem here. The ISA describes the properties of the air as a function of altitude, which is assumed to be distance up in the air, whereas we are dealing with our elevation, which means a height above sea level while still on land. A cloud is at some altitude; a hiker is at some elevation.

In short, we have little reason to think that the air temperature at our elevation is what it would be if there were no land below us.  We know the weight of the air above us, that is QFE which we measured, so a determination of QFF is tied to making some estimate the average temperature of the imaginary air column below us, so we can figure the weight of that, which added to QFE is QFF. 

For practical corrections at sea we have some advantage.  First we are on a uniformly flat surface (water or ice), as opposed to in a mountain range, and second we are not going to be very high.  Thus the NWS Observing Handbook No.1 can include a table for navigators to use to make the correction for elevation and temperature in one step.  Clearly there has to be some empirical nature to the result, because there is not agreed upon theory, and I would guess that in principle the correction depends on the pressure as well, but the main point is everyone uses the same corrections, and that is what the models need for consistency.  Below is the NWS table with some inserts added.

The white background are the actual numbers from the NWS Handbook Table. Thus if the elevation is 110 ft and the outside air temp is 86º F, the correction to get from QFE to QFF would be + 3.8 mb. The yellow number beside it means that of this 3.8, 0.2 is due to the temperature, which caused a lower than normal correction.  Likewise, if the air temp had been a chilly 4º F, the correction at 110 ft would be 4.6 mb, of which 0.6 mb was due to the air temp, and this caused a higher than normal correction.

These yellow numbers come from just computing what the elevation correction alone would be using our 0.44 jingle, and then subtracting it.  In a sense, the yellow numbers reflect the difference between QNH and QFF.  We see from this that air temperature is not a big factor for low elevations, even with rather extreme temperatures, but since we do have this good approximation, we are better off using it than not.

At higher elevations, however, these corrections are quite large. We will post here some results on that as soon as completed.  These we have to compute.

Our  next step then––the truth meter––will be to compare our results with the differences seen in metar reports for various elevations and temperatures around the county.