Here is an article written in 2012 that somehow did not get posted. It is now, because we just got a question about this that I thought we had answered, but could not find it, then found this draft, which a bit late now, we post. Thanks to Nathaniel Fairfield for finding this issue mentioned below in our Emergency Nav book and taking the time to tell us.
Refraction of light as it enters the atmosphere is still one of the largest uncertainties in celestial navigation. When starlight leaves the vacuum of outer space and enters the atmosphere it bends down a small amount depending on how high the star is in the sky. This happens because the light is slowed down in the gas of the atmosphere. See Refraction in a Sink.
Thus with our sextants we always measure a star height that is slightly too high. A starlight from stars some 30º above the horizon will bend only some 1' to 2' (if uncorrected yielding an error of some 1 to 2 nmi), but at lower angles the correction can be twice that or more. At higher angles it is less, being only half a mile or so at 60º and 0 by definition for stars overhead.
For perspective, keep in mind that if we do everything right, we can hope to achieve a cel nav position fix accuracy of about ±0.5 nmi. Not much better, especially if the boat is moving, and if we are not careful, the uncertainty will be notably larger. So this refraction issue (on the order of tenths of an arc minute) is right in the same order of magnitude as sextant sight accuracy and nautical almanac accuracy, the other two factors that limit the ultimate accuracy of our fix.... assuming of course that we do everything else right, and if plotting, do so on a large enough scale that small errors don't matter.
There should be no doubt that there is uncertainly associated with refraction. You would not, for example, ever ask that question if you have ever seen a good mirage, which is just abnormal refraction on steroids.
But we do not need to be so qualitative. When we first made our book called Emergency Navigation, throughout the early and mid 80's, the US-UK Nautical Almanac used a value of -34.5' of correction for the lowest stars, those just over the horizon. In other words, this low starlight is bending more than half a degree. But the correction goes down fast. One way we remember it is to note at 5º high the correction is -10', and at 10º high the correction is -5'. We have formulas and jingles in the book to help remember this if you get stuck without an almanac.
But now, in 2012, we take a look at this correction in the official US-UK Nautical Almanac and we see -33.8' of correction instead of 34.5'. Granted, there are things about the immovable, permanent stars that have in fact moved. The Polaris correction used to find latitude from the height of the North Star above the horizon was 49' in 1982, whereas today it is 41'. But this is an entirely different effect and result. This Polaris correction is well understood on the basis of star and earth motions over the years–small as they are, they do add up.
Nothing at all similar has happened to the atmosphere over these years that changes how the starlight bends. Yes, there is global warming and measurable changes to the atmosphere, but these do not change the refraction we are discussing.
This does not mean that navigators in the 80s who knew where they were then, we now know were wrong! In fact, this large shift (0.7 nmi) in the maximum refraction at the horizon has little effect on normal celestial navigation. For one thing, we know there is enhanced refraction uncertainty at low angles, so good texts teach that we should take sights whenever possible above 15º and below 75º. Above 15º the correction and the uncertainty in the correction go down rapidly. (The goal of taking sights below 75º is for an entirely different reason having to do with the math approximations used in basic procedure. These in fact can be overcome with special procedures.)
Below some 15º, the refraction becomes more sensitive to the properties of the atmosphere used, particularly the pressure, temperature, humidity, temperature changes with altitude (lapse rate), and the wavelength (color) of the light ray.
A thorough description of the values used in the Nautical Almanc is given by C.Y. Hohenkerk (Director of HM Nautical Almanac Office) and A.T. Sinclair in "The Computation of Angular Atmospheric Refraction at Large Zenith Angles," Technical Note 63, 1985. This paper explains the origin and assumptions made in obtaining the value of -34.5'. They proposed that as a base reference value that can be used to apply corrections to for various conditions of temperature and pressure, and presumably to be used as a standard that could be improved upon if newer data or analysis becomes available. That value was used then and up until about 2004. After that, almanacs (US-UK, French, Russian) switched to the value of -33.8'.
My question has been, what changed that led to the new value and the above paper sheds much light on that question.
Besides explaining the process, they also compute the sensitivities of the result to the input parameters. First they show that above 60º the result is essentially independent of this input, but at 0º, on the horizon, the effects are large. Summarizing and changing units, they show:
Change in input Change in Refraction on the horizon
Temperature change of 4.5º F - 0.6'
Pressure change of 10 mb +2.6'
These values have then been incorporated into the Table A4 of the Nautical Almanac for adjustments to be made for deviations from the standard conditions they used, namely 50º F and 1010 mb. They also assumed dry air, but showed that changing to saturated air only changed the result by -0.08'.
A difficult challenge of this analysis, however, is not so much the pressure or the temperature effects, but how the temperature changes with altitude, called the lapse rate. This is much more difficult to know in practice and to account for. The earlier almanac computations used a value called the average lapse rate of 3.5º F/1000 ft and showed that a lapse rate change of 1º F causes a horizon refraction change of -0.3'. Actual air mass lapse rates vary from some 2.5 to 5.5, so we are seeing that there are easily factors floating around that could change the value from 34.5 to 33.8 on improved analysis.
In fact, it is rather more complex than even that. Light rays from bodies on the horizon, must skim along the surface of the ocean to get from outer space to our eye and spend some amount of time within the first meter of air above the surface. This first meter above the ocean is a complex region. Water is continually evaporating into it and condensing back to the ocean, there is salt spray there, and its temperature is affected by the sea temperature as well as local air mass temperature. The nature of this air is also dependent on the local wind, which mixes the air, and it depends on the sea state, which is more or less active in interacting with it, and the time of day.
See this article Sunset Science. IV. Low-Altitude Refraction by Andrew Young for more details. He is the expert on this and related subjects.
Tuesday, February 7, 2017
Monday, January 16, 2017
Buys Ballot Law to find wind direction from isobars
Reading wind speed and direction from the lay of the isobars on a weather map is a basic skill in marine weather. We need it because surface analysis maps only contain spot winds from observations and forecast maps only include winds greater than 34 kts. On other parts of both maps we are left to deduce the corresponding wind from the isobars alone.
The ubiquitous use of GRIB formatted weather forecasts has dampened the motivation to learn this skill because looking at one of these forecasts you can turn on and off wind and isobars at will to see the correlation, and if that is all we used we would not need to know more. But that is poor policy to rely on these GRIBs alone; for most effective analysis and forecasting we need to look at the actual maps made by the NWS, and to read these we need this skill. Even with GRIBs at hand, it is valuable to see if the correlation makes sense or not.
The procedures are discussed in Modern Marine Weather and we have several videos on the subject as well.
The most challenging part is usually figuring the speed of the wind, which takes either tables or a formula (Section 2.4 in our text), on top of reading latitudes and distances carefully from the map. The wind direction should in principle be easier to determine, but we have found there are still some cases where the in-principle easy solution can be evasive.
Thus we take here an all new approach to resolving this that relies only on the Buys Ballot Law. This should work in all cases the same way. Normally we started with the rule that wind flows (in the NH) clockwise around Highs and counterclockwise around Lows, and assumed that is all we need to figure the wind direction at any point on a map. But when we do not know where the local Highs or Lows are located it could be distracting.
Here is the short depiction, followed by a (probably longer than needed) video showing it in action.
In the Southern Hemisphere, the wind circles the other direction so the hand are reversed... but don't even think about that now.
Here is then how you can follow up on choosing the wind direction more precisely.
(1) Plot the point you care about on the map.
(2) Through that point sketch in a new isobar that is parallel to the isobars on either side.
(3) Draw a line through the same point that crosses your new isobar at an angle of about 20° pointing toward the lower pressure.
(4) That line is marking with the wind direction. (Put an arrowhead on the end of the line on the low pressure side.)
The ubiquitous use of GRIB formatted weather forecasts has dampened the motivation to learn this skill because looking at one of these forecasts you can turn on and off wind and isobars at will to see the correlation, and if that is all we used we would not need to know more. But that is poor policy to rely on these GRIBs alone; for most effective analysis and forecasting we need to look at the actual maps made by the NWS, and to read these we need this skill. Even with GRIBs at hand, it is valuable to see if the correlation makes sense or not.
The procedures are discussed in Modern Marine Weather and we have several videos on the subject as well.
The most challenging part is usually figuring the speed of the wind, which takes either tables or a formula (Section 2.4 in our text), on top of reading latitudes and distances carefully from the map. The wind direction should in principle be easier to determine, but we have found there are still some cases where the in-principle easy solution can be evasive.
Thus we take here an all new approach to resolving this that relies only on the Buys Ballot Law. This should work in all cases the same way. Normally we started with the rule that wind flows (in the NH) clockwise around Highs and counterclockwise around Lows, and assumed that is all we need to figure the wind direction at any point on a map. But when we do not know where the local Highs or Lows are located it could be distracting.
Here is the short depiction, followed by a (probably longer than needed) video showing it in action.
In the Southern Hemisphere, the wind circles the other direction so the hand are reversed... but don't even think about that now.
Here is then how you can follow up on choosing the wind direction more precisely.
(1) Plot the point you care about on the map.
(2) Through that point sketch in a new isobar that is parallel to the isobars on either side.
(3) Draw a line through the same point that crosses your new isobar at an angle of about 20° pointing toward the lower pressure.
(4) That line is marking with the wind direction. (Put an arrowhead on the end of the line on the low pressure side.)
Sunday, January 1, 2017
Short Survey of Ocean Waves
These three environmental sources surveys cover key resources available to mariners who have not taken our Marine Weather Course, which covers each of these in depth, along with the background needed to use them efficiently. Our goal here is to be sure that you do not leave one of our other courses without at least knowing what the basic tools are and how to find them.
All three surveys (weather, waves, and currents) take advantage of viewing forecasts or actual data in GRIB format using dedicated GRIB viewing software or a navigation program with that functionality. A discussion of those programs and sources of GRIB formatted data are in the Weather Survey, so that one is needed to understand the Currents Survey and Waves Survey.
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For US coastal waters, we have a rough starting point on waves with the statistics in Appendix B to each Coast Pilot in a section called Meteorological Data. For all US coastal waters they list the "percent frequency" of winds > 33 kts, seas > 9 ft, and visibility < 2 nmi, with the caution that these data are based on observations from vessels that may have avoided bad conditions, and therefore these are minimum numbers. They do though clearly show how these data vary month to month along the coast, which could help in choosing a voyage time.
For live data we have the occasional buoy, which has to be identified from the NDBC site. There are certainly more buoys with waves than with currents. Here is one example: http://www.ndbc.noaa.gov/station_page.php?station=51000
We can access wave forecasts graphically in the OPC forecast maps called "wind and waves." There is a 24h, 48h, and 96h forecasts. See near bottom of this page for the Pacific. The 24h forecasts cover different regions than the 48h and 96h, which is the same with weather forecasts.
https://ocean.weather.gov/Pac_tab.php
and this page for the Atlantic
https://ocean.weather.gov/Atl_tab.php
Farther down the page they show color graphics, which are direct model outputs.
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| Sample from the OPC site |
Wave maps can be received by HF radio wxfax (or direct internet download). The schedule and links to products are at at this page:
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| Sample from interactive fax schedule |
Also at the bottom on the OPC page mentioned above you will see color graphics of wave forecasts from the WW3 model (Wave Watch III). They choose to show just one map (primary wave period and direction), but there are more, and you can see others at
Click WW3 to show regions available, select a region, then the model runtime, then the time span of interest. There are three parameter combinations to choose from.
Wave definitions
Here is a good place for a reminder about sea state definitions. The word "waves" can mean anything, i.e. any one of the following specific types, or even combinations of them, which makes it obvious that if we want to be clear in our communications we should chose these words carefully.
Wind waves are those caused by the existing wind. Generally they move in the same direction as the wind, but for new wind shifts it can take half a day or more for them to get in alignment… and for a moving system they may indeed stay out of alignment to some extent.
There is always a statistical distribution of wave heights, wave periods, and wave lengths, and wave widths—meaning the horizontal extend of a wave in the direction perpendicular to the way it is moving.
Wind wave distributions are characterized by the significant wave height, defined as the average height of the highest one third of all waves. The table below shows how other stats can be tied to the SWH. Wind wave forecasts are generally given in terms of SWH.
Swell waves are those caused by distant storms. They have out run the systems that created them and they proceed across the ocean. As they proceed from their source they get organized into a near constant height and length, and as they proceed the height gets lower the length gets longer. Longer waves means longer periods, being the time peak to peak time it takes one to pass. Average wind wave periods are some 7 seconds; swells are longer, up to twice that or more.
Combined seas means wind waves plus swells. SWH can also be applied to the combined seas.
(There are different ways that is computed, but you can think of it as the sum of the SWH of the wind waves and height of the swells computed as square root of the sum of the squares, and then figure the SWH of that new distribution.)
Capillary waves, called cat’s paws or ripples, are waves on the surfaces of wind waves or swell waves. They are restored to flat by surface tension, as opposed to wind waves and swell which are diminished by gravity. These ripples reflect the direct, transient action of the wind. These do not enter into navigation, other than our using them to spot the true wind direction from their pattern on the surface of the waves below them. (We are grateful for these little guys, because they are the ones that scatter the microwaves back to scatterometers on satellites that measure wind speed and direction, as noted briefly in the Weather Survey.)
As you look over the WW3 forecast images, you will see wind waves and swells forecasted. Check out their heights and periods across the maps to see how all this works. A look to the corresponding weather maps shows the sources of the waves.
Besides these graphic image forecasts, for ocean sailing we also have the digital wave forecasts from ocean models, which are more precise and easier to use. (Not necessarily more accurate than the graphic data, which is from the same model, but available more often than the standard map times. )
As is the case with ocean current models, noted in the Currents Survey, there are internationally several models providing sea state forecasts, but there is one dominant one, made here in the US that is the most popular for global coverage, the WW3 model. This is essentially the only one we need.
As with RTOFS current forecasts, you can get the WW3 wave forecasts from within zyGrib, LuckGrib, or OpenCPN, or request them directly by email from saildocs. Here would be a sample request to saildocs
send WW3:43N,20N,83W,50W|0.5,0.5|6,12,18|HTSGW,WVDIR,WVPER
This brings you the digital GRIB data for the parameters listed (see bellow) for the Lat-Lon window shown, for the times 06, 12, and 18z. There are many wave parameters computed by WW3. The ones available from most servers are:
HTSGW = SWH of the combined seas (wind waves and swells)
WVDIR = direction of motion of the wind waves
WVPER = period of the wind waves.
Samples of the these data are shown above. WW3 is updated every 6h, and gives forecasts out to 7 days, starting at every 3h, then in larger steps. Resolution is 0.5º, but we may not need that and can ask for 1º to save air time.
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For those who do not have time for our full Marine Weather Course, we have available our textbook Modern Marine Weather and our Weather Workbook for study on your own.
Short Survey of Ocean Currents
These three environmental sources surveys cover key resources available to mariners who have not taken our Marine Weather Course, which covers each of these in depth, along with the background needed to use them efficiently. Our goal here is to be sure that you do not leave one of our other courses without at least knowing what the basic tools are and how to find them.
All three surveys (weather, waves, and currents) take advantage of viewing forecasts or actual data in GRIB format using dedicated GRIB viewing software or a navigation program with that functionality. A discussion of those programs and sources of GRIB formatted data are in the Weather Survey, so that one is needed to understand the Currents Survey and Waves Survey.
* * *
We have a page dedicated to ocean and coastal currents at http://www.starpath.com/currents. It is extensive, but not well organized as an introduction, and it covers more than we need now. So we make this list.
Climatic averages
(1) Climatic ocean currents are given on pilot charts, which you can download from links at http://www.starpath.com/navpubs, monthly by ocean.
( http://www.opencpn.org offers these charts as RNC echarts that can be loaded in any nav program. )
Pilot charts are historically the mariners first guess of what current to expect.
(2) A survey of the various global current patterns in given in Bowditch (starpath.com/navpubs)
(3) A short pictorial description is at http://www.srh.noaa.gov/jetstream/ocean/currents_max.html
(4) for more detail on each system see http://oceancurrents.rsmas.miami.edu
Live Current Forecasts
There are several models that do global ocean current forecasts, but we will stick with the most popular one RTOFS, which is likely as good as any of them.
(1) See graphic forecasts online at https://ocean.weather.gov/Current_fcasts.php Note that this site gives NCOM as well for adjacent US waters, and they only show RTOFS for the Northern Hemisphere, but you can use RTOFS for all waters. And that is good, because the RTOFS digital data is readily available, and only special programs can access the NCOM data.
(2) You can request and view digital RTOFS current forecasts in Zygrib, LuckGrib, OpenCPN, and other programs. Most ECS, and indeed most ECDIS programs will display this data. For the ECDIS apps you may have to provide the data yourself, see (3) below.
(3) The data are also available directly from saildocs (see Weather Survey). For example, you would send this email to query@saildocs.com
send RTOFS:34N,43N,77W,68W|0.08,0.08|0,3..72|CUR,WTMP
This gets you the currents and seawater temps in 3-hr steps out to 72 hr, for the lat-lon box indicated. the 0.08 part is a fixed notation for the resolution. See saildocs.com for more specs. You can request and get this file now, but you need a grib viewer to see it. if using Zygrib or LuckGrib you can ask for this from within the program and do not need this external email.
(4) To view historic images and animations of global currents see this comprehensive Navy Link.
Generally this link will require you to give your browser permission, so say yes every where, then you have a real encyclopedia of currents around the world.
Live coastal current measurements
(1) See the HF radar data coordinated at this link: http://cordc.ucsd.edu/projects/mapping/maps/
These installations are mostly in US coastal waters, but there are a few stations overseas as well.
For those who do not have time for our full Marine Weather Course, we have available our textbook Modern Marine Weather and our Weather Workbook for study on your own.
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