As mentioned in the ZIP Codes and Zmanim – Use With Care article, using ZIP codes to geolocate your position for zmanim can be problematic when the zip code is large. With large zip codes, zmanim on the west side of the zip code can be quite a bit later than zmanim on the east side of the zip. Recently, Lazer Guttman created an SMS based zmanim service at (914) 409-9394 that provides a warning when zmanim are requested for large zip codes. This approach is probably the best that can be done. I would recommend that any zmanim service that is zip code based (and does not have a map to allow zeroing in to a precise location), use this data to to provide a warning whenever the zip codes is wider than 0.5° of longitude. A degree of longitude spans 4 minutes (regardless of the latitude), so half of a zip code with half of a degree would span 2 minutes (one minute east or west of the center). It should be noted that Canadian postal codes are much smaller than zip codes (usually covering one side of a city block), and most likely do not face the same issue. A spreadsheet listing all zip codes with the maximum longitude and latitude distances (in degrees), was generated by Avraham David Gelbfish from OpenDataDE that is based on US Census data. His Python source code is below.
jsonfile = open("tl_2019_us_zcta510/out2.geojson")
zipcodes = json.load(jsonfile)
def getop(geolist, operation, longitude = None, latitude = None):
if isinstance(geolist, list):
answers = [getop(geo, operation) for geo in geolist]
for answer in answers:
lat, lng = answer
if latitude is None:
latitude = lat
if longitude is None:
longitude = lng
latitude = operation(latitude, lat)
longitude = operation(longitude, lng)
return latitude, longitude
with open("out2.csv", "w") as csvfile:
zwriter = csv.writer(csvfile)
zwriter.writerow(["Zip", "Latitude max distance", "Longitude max distance"])
for zipcode in zipcodes["features"]:
zip = zipcode["properties"]["ZCTA5CE10"]
geometry = zipcode["geometry"]["coordinates"]
maxlat, maxlng = getop(geometry, lambda x, y: x if x > y else y)
minlat, minlng = getop(geometry, lambda x, y: x if x < y else y)
dlat = abs(maxlat - minlat)
dlng = abs(maxlng - minlng)
zwriter.writerow([zip, dlat, dlng])
Determining zmanim times while on an airline flight is rather complex compared to calculating it for a fixed location. Some of the complexity involves:
Where you are currently located
Direction of travel / flightpath
The above 3 variables impact the calculation of what the zmanim are in your current location and where you will likely be when various zmanim are met.
Surprisingly, the hardest part is figuring out your current location. The shortest point between 2 points on the globe is the great circle route. Though it is the shortest path, airliners rarely fly this way. To take advantage of prevailing winds such as the Gulf Stream, or to avoid bad weather, airlines often fly much longerroutes and as a passenger you often do not know exactly where you are. Yes, the airline shows you a nice location map, but getting your exact coordinates from the map is not something that they usually supply. From a practical perspective, many people on domestic and short international flights will manage to figure out davening times by themselves. As a general rule of thumb, it is time for Shacharis when the sun rises and time for Maariv when it gets dark. Please keep in mind that most poskim are of the opinion that we use zmanim at sea level elevation, or ground level, and not the 37,000 foot elevation of the flight. This elevation results in a difference of approximately 20 minutes in sunrise and sunset times. Not sure when Mincha time is? Wait until shortly before sunset. Just keep in mind that when flying due east (such as a flight from NY to Israel), you are flying in the opposite direction as the sun and the time for davening is compressed. While you may expect sof zman krias shema to be 1/4 of the way into the day, in this case the davening window is compressed into a much shorter time. The real complexity is in flights that cross the halachic dateline, polar flights and to a lesser degree, cross-Atlantic and Pacific flights. This article will not delve into the halacha of in-flight zmanim, but solely on the technical aspects of figuring out the zmanim times.
Using your phone’s GPS to identify your in-flight location, or even a standalone GPS device will usually not work once you are away from cell towers (where your GPS no longer has the assistance of A-GPS). GPS signals are very weak and your GPS receiver typically does not have an antenna strong enough to pick up the signals in an aluminum or even newer carbon fiber composite airplane like the Airbus A350 and Boeing 787. To receive a signal, an external GPS receiver is usually required and assuming that you can get a signal (it helps if the external receiver is placed by a window), we can proceed. Note that while you would expect that the CFRP body of a Boeing 787 would allow for a much stronger signal than aluminum airliners, the graphite (and probably other materials) in the 787 CFRP in conjunction with the electrochromic windows on the 787, completely block GPS signals. It is this shielding as opposed to GPS jamming that blocks signals on El-Al 787s. In my testing with an external GPS device designed for aviation such as the Dual XGPS 160, the composite A350 and 787 both do not allow enough GPS signal through for a GPS receiver to provide a location fix. It may be surprising that it is easier to receive the weak GPS signal in an aluminum fuselage than a composite one, but keep in mind that carbon fiber is an excellent electrical conductor. Carbon fiber was used as the filament in Thomas Edison’s early light bulbs and does not let RF signals through and effectively acts as a Faraday cage. If you are able to receive a GPS signal, you can accurately calculate zmanim for your current location using tools such as the KosherJava zmanim map. Just change the latitude and longitude to what you see in your GPS in the URL https://kosherjava.com/maps/zmanim3.html?lat=75.74&lng=-63.22&zoom=3. While not an ideal solution, it does work. The same works for the rare airlines whose maps do show accurate GPS coordinates. Please note that Wi-Fi based geolocation will not work on your flight (in my testing it gave the location of the service provider headquarters).
Precalculated Flight Paths
Another way to figure out where you are located when in the air is via a precalculated flight path. This allows programs such as the Chai Tables Chai Air Times program for Windows and Android to work. However, they just calculate a great circle route between the origination and destination locations, something that is not very accurate. Currently MyZmanim’s Inflight charts are the most practical. These charts calculate the average path of the 5 previous flights in an attempt to better estimate your flight path and provide precalculated charts based on the time you take off. While this solution is currently the best that I am aware of, there are a number of issues with it. For one, much of the flight path over the oceans and Arctic that are provided by services such as FlightAware and others (that are used by MyZmanim) are just educated guesses for cross oceanic or Polar flights, since there are no ADS-B receivers in much of this area. As a matter of fact, this terrestrial ADS-B receiver free area comprises 75% of the globe. Even if the previous flight paths were accurate, your current flight may be very different. Flights such as the Cathay Pacific flights from the NY area to Hong Kong fly either east or west depending on wind conditions. MyZmanim deals with this scenario by providing both east and west maps (based on the in-flight map you would use one or the other) and indicating the portion of a flight-path that is unknown, but this is a warning that does nothing to help you accurately calculate zmanim.
Every airliner broadcasts its position, heading, altitude and speed using ADS-B. A technical user can bring an ADS-B-receiver with him on the flight and use it to retrieve the current information on his flight. This would work even when there are no ground based ADS-B receivers. This is something costly and beyond the technical ability of the vast majority of flyers.
Due to issues in tracking flights that came to light with the disappearance of Malaysia Airlines Flight 370, satellite based ADS-B tracking is rolling out and will be mandated. This will make it much easier for services such as MyZmanim to provide more accurate pre-flight estimates, since services such as Flight-Aware will be able to provide more exact historical flight paths. For users who do have in-flight Wi-Fi, services such as FlightAware will be able to provide almost real time location (note that many services have a 5 minute delay and are not really real-time), allowing future Wi-Fi connected zmanim apps to tap into this and provide accurate zmanim.
A primer for this halachic dateline post if you are not familiar with the subject, is the earlier Halachic Date Line Map post about the Jewish date-line. Based on the opinion of the Ba’al Hamaor, the Chazon Ish ruled that the dateline is 90° east of Yerushalayim, and it can’t split a landmass. The concept of graira is used to drag the land past the dateline to the water’s edge. This concept of graira is based on the Yesod Olam, a talmid/disciple of the Rosh. For this reason, according to the Chazon Ish, Korea and Australia follow the local date and not the previous date.
Islands Connected to Mainland by a Bridge
A question touched on in the previous article that was mostly theoretical, was about an island connected by a bridge to the mainland. Would the concept of graira apply to the island? The kollel members in Melbourne and others do not visit Phillip Island on Sundays for this reason, but Chabad chassidim who do not follow the Chazon Ish’s opinion, do visit Phillip Island on Sundays.
Islands in Bays
There are differing opinions whether an island in a bay would also be included in graira. Rabbi Yitzchok Meir Goldstein in his השבת בכל מושבותיכם (pages 85-88) brings the following opinions. Rabbi Shlomo Zalman Auerbach in הליכות שלמה (Moadim, vol. 2, page 70) is of the opinion that an island in a bay would be considered part of the land that partially surrounds it. In the same vein, (but not specifically in reference to a bay), Rabbi Moishe Sternbuch in מועדים וזמנים vol 7, ch. 236 mentions something similar (that the easternmost border of Australia would be a vertical line from north to south at the longitude of Brisbane, the eastern-most point of Australia). What is not clear is how large a bay can be. Rabbi Goldstein mentions that drawing a line from Siberia to Malaysia (thus creating a “bay”), would put Japan on the same side of the dateline as the Asian mainland. The Chazon Ish clearly stated that Japan was past the dateline. Presumably, Rabbi Shlomo Zalman Auerbach and Rabbi Moshe Sternbuch would agree that such a large area would not be included in graira. Given the lack of detail about the size of bays, it is possible that these poskim would only include very small bays (within the techum perhaps). It should be noted that Japan is only in the “bay” if you use a rhumb-line. Drawing a great circle line would result in Japan being out of the “bay”. Rabbi Dov Landau in the פשר חזון, and Rabbi Moshe Heinemann do not include bays as part of the graira zone. Rabbi Sternbuch was asked about bays by Rabbi Goldstein, and he agreed that according to the Chazon Ish, bays would not be included in graira, so Rabbi Sternbuch either reversed his earlier opinion, or he disagrees with the Chazon Ish’s opinion. There are related opinions that bays themselves do not drag islands within them into graira unless land to their east is part of graira. See Rabbi Leib Blum’s קו התאריך בכדור הארץ for details. For example the Sea of Okhotsk is to the west of the Kamchatka Peninsula. This means that they are of the opinion that you can’t have land to the east that is part of graira such as the Kamchatka Peninsula, and have Sea of Okhotsk and Sakhalin Island to the west of it that is considered past the line, (and back again to Siberia that is part of graira). The same would be the case in the portion of the Yellow Sea to the west of the Korean Peninsula and east of the Chazon Ish line, as well as the above mentioned Phillip Island and French island that are in the Western Port Bay near Melbourne. Bays such as Moreton Bay that includes Bribie and other islands near Brisbane, as well as Ulleungdo Island in the Sea of Japan would not be included in graira, since there is no graira land to the east of it.
Incheon International Airport and the Halachic Dateline
In January 2019, the Star-K held a Kashrus training seminar in Shanghai for mashgichim who live or work in Asia. Among the sessions, was a shiur about the halachic dateline by Rabbi Dovid Heber who shared the URL to my halachic dateline map with the participants. One of the mashgichim, Rabbi Yosef Wexler, who travels from Eretz Yisrael to Asia regularly, noticed a potential issue related to the Incheon airport, the main airport in South Korea (near Seoul). The airport is located on Yeongjong Island, that is connected to mainland South Korea by two long bridges. The island is within a Bay (formerly Chemulpo Bay), that is itself within the Yellow Sea that is itself a vary large bay. Ifgraira would not apply here (bridges and bays would not be considered a connection) and you followed the opinion of the Chazon Ish, the airport would observe Shabbos on local Sunday (the same issue faced in Japan). This impacts mashgichim who bypass Japan on Sundays, and regularly fly to Korea on flight KE958 on Motza’ei Shabbos from Israel on their way to China etc. The flight lands at about 3pm Sunday local time, when the airport may be observing Shabbos. It would also impact anyone else who plans on flying in or out of the airport between Motza’ei Shabbos and Sunday night.
Please consult a posek before relying on this for halacha lema’aseh. There are a number of opinions, and I will touch on a few of them.
As per Rabbi Heber, Rabbi Yonasan Weiner (a posek in Ohr Sameach) asked R’ Chaim Kanievsky about Phillip Island (that as mentioned above, has a bridge and is in a bay), and he said that it is ‘צריך עיון’. Based on this, Rabbi Moshe Heinemann ruled that if someone is in the Incheon airport from shkiah on Friday (local day) until it gets dark on Saturday, one should keep regular Shabbos. From when it gets dark on Saturday night until it gets dark on local Sunday deoraisas should be avoided, but derabanans are permissible. This would permit most activities. The following quote in Rabbi Yitzchok Meir Goldstein’s השבת בכל מושבותיכם should be noted:
שמעתי מדודי הגאון רבי משה היינעמאנן שליט״א שאולי גבול היבשה הוא כשיעור תחום שבת מסוף היבשה
Yeongjong Island is at its closest 1,950 meters from mainland South Korea (from the eastern tip of the island to Wolmido, a former island that is now connected to land), and thus beyond tchum Shabbos. It is therefore not within the extended maritime graira zone. This applies to Incheon, but not the Yellow Sea. Rabbi Heber in his note to the Star-K mashgichim stated that melachos deoraisa should not be done within 35 minutes of landing since that is the earliest time the KAL958 flight passes the Chazon Ish line over the Yellow Sea. At this point according to the Chazon Ish it would be Shabbos. This was also mentioned by Rabbi Goldstein as a possible deoraisa. See below for more details.
Permissible Activities on Incheon Island on Sundays
There are many variables and variations in various melachos, so please consult a posek before relying on this for halacha lema’aseh.
Note: This list is only meant for Incheon airport on Sundays (from Motza’ei Shabbos until it turns dark on Sunday night) and other areas where a majority of opinions hold it is a weekday, but an accepted minority hold it is Shabbos. This list should not be used in any other locations or on a day that is accepted as Shabbos.
Traveling as a passenger to and from Incheon airport by plane or car. You do not have to worry about the 12 miltchum Shabbos.
Carrying your belongings more than 4 amos outside the airport, or carrying them into the airport – there is no reshus harabim deoraisa on the island
Walking in the airport including the use of escalators and moving sidewalks.
Triggering automatic sensor doors, sensors in bathrooms etc. (there no need to wait for someone else to activate it).
Scanning boarding or other passes (including to open electronic gates).
Going through security, taking muktzeh out of pockets, and passing through metal detectors.
Electronically signing into a lounge.
If a paper signature or writing is required, try to avoid it. If there is no other option, use your alternate hand (left for a righty, right for a lefty). An ambidextrous person can’t do shinuy by changing hands, and can’t sign or write.
Typing on a computer and typing or calling with cellphones is permissible, but the screen saver or the automated powering down of the monitor has to activate by itself to “erase” your writing. For power saving and security reasons, almost all computers will end up having a screensaver or a monitor power down and clear the screen. If this is not in place, and your “writing” will remain on the screen, it is more of a maaseh ksiva. Saving the document to your hard drive is permissible.
Problematic Activities During This Time
Opening a taxi door that causes the dome light to turn on (ask the driver to open your door, or have him open his door first, thus turning on the dome light)
Writing (with paper and pen).
Showers in the lounge should be avoided since there can be deoriasas involved.
Making coffee should be done the same way you would do it on Shabbos. Instant is fine, brewing fresh in a machine should not be done.
Rabbi Shlomo Miller in his approbation to the above mentioned Hashabbos Bechol Moshvosaichem, mentions that:
… והביא שטה אחת דכדי שיראה הוי בכלל אסטרליא וכן הי׳ דעתי נוטה [כמובן א״א להביא ראיות ברורות בזה] אולם יש להוסיף דלפי הגמ׳ בכורות נ״ד: עד ט״ז מיל הוי שעור כדי שיראה ויש אחרונים שהביאו מזה לגבי היקף מחיצות בשבת במחיצות הנעשות מאליהן דצריך שיהא העומד בתוכו רואה את המחיצות ע״כ עד ט״ז מיל יש מקום להסתפק אפשר שנגרר אחר אסטרליא.
This intuition (that he is unsure of) would potentially remove the questionable status of Incheon airport.
בית שבים: מדקתני בית שבים ובית שבספינה משמע דתרי מילי נינהו דשבים אפילו בנוי על גבי קרקע הים שהביאו אבנים וטיט ושפכו בים עד שנעשה כמין תל ובנו עליו בית אין מטמא בנגעים משום דכתיב ״ארץ״ ולא ים
This implies that the only questionable status is for נגעים, but otherwise, man-made land would have the status of natural land. Rabbi Katz holds that the bridge itself would connect the island and give it the same halacha as the mainland. It should be noted that Rabbi Katz also discussed the issue of The Sea of Okhotsk. His opinion is that the line follows the contour of the land, and the Sea of Okhotsk and Sakhalin Island would not be included in graira, but mentioned that Rabbi Leib Blum felt that it should be included due to it being to the west of land that has graira.
Rabbi Mordechai Kuber in his upcoming book, Crossing the Dateline (expected to be published later this year) strongly feels that there is no problem in Incheon airport on Sundays due to it being in a bay (that is in itself a safek). The question of the bridges, its proximity to land, and the many sandbars between it and the land make it at most a sfaik sfaika, which most poskim should agree is not an issue even according to the Chazon Ish. This sfaik sfeka is in addition to the other opinions who do not agree with the Chazon Ish, and are of the opinion that Incheon is not east of the halachic dateline, and therefore Saturday is Shabbos in Incheon, and not Sunday.
Rabbi Yitzchok Meir Goldstein in a letter to me mentioned that there is a possibility of a deoraisa in flying on a flight that is completely or partially on Shabbos
… this is comparable to one who boards a plane which takes off before Shabbos and lands after Shabbos, which, as the Shailos U’Teshuvos Minchas Yitzchok 2:106, the Shailos U’Teshuvos Tzitz Eliezer 1:21 and the Shailos U’Teshuvos Shraga HaMeir 7:27 write, involves an issur d’oraysa transgressing the chiyuv of “shabosson” which is not fulfilled while on an airplane ride. (However, it could be that there is a sevara to say that there is a difference in the d’oraysa of “shabosson” between flying on an airplane for the whole Shabbos and flying over the Yellow Sea for a short time …). If, indeed, this involves an issur d’oraysa, this creates a problem not only for people who follow the opinion of the Chazon Ish with regard to the dateline, but even for people who refrain from issurim d’oraysa on the Shabbos of the Chazon Ish. If so, regardless of whether or not the sevara of graira applies to Incheon Airport, I would think that people should still not be flying to that airport on Sunday. Second of all, even if I am mistaken in the above comparison and there is no issur d’oraysa to fly over the Yellow Sea while it is Shabbos in the Yellow Sea, it would be worthwhile for you to mention in your article that at least while the airplane is flying over the Yellow Sea one should certainly be careful not to perform any melacha d’oraysa such as writing. I am not trying to offer a psak about these points, but I think there is reason to consult with a poseik whether these issues need to be mentioned in your article.
It should also be noted that on page 83 of השבת בכל מושבותיכם, Rabbi Chaim Kanievsky is quoted with a different psak than the one quoted above by Rabbi Yonasan Weiner. Rabbi Goldstein sent the following question to Rabbi Chaim Kanievsky
שמעתי שבחוף הים של אוסטרליה יש גשרים ובנינים שנבנו בידי אדם שיוצאים מן היבשה לתוך קצה הים, האם גם בנינים אלו וגשרים אלו המחוברים ליבשה נגררים אחר שאר ארץ אוסטרליה או רק הארץ שנעשה שם בידי שמים ולא מה שניתוסף בידי אדם בתוך הים?
Rabbi Kanievsky replied with his typical brevity
I would like to thank Rabbi Dovid Heber, Rabbi Shmuel Meir Katz, Rabbi Yitzchok Meir Goldstein, Rabbi Mordechai Kuber, My father-in-law R’ Feivel Muller and my wife for reviewing this article. This article is published in memory of my mother-in-law Mrs. Helen Muller חיה בת ר׳ יצחק הכהן ע״ה.
There are many zmanim services and apps that use ZIP codes as a location finder for calculating zmanim. While very convenient, there is a potential pitfall in using ZIP codes for geolocation. In general, ZIP code geolocation services will provide the center of the ZIP code and zmanim apps calculate zmanim for that location. The issue arises with large ZIP code areas mostly found in rural areas. Take the following two extreme cases that have very large ZIP code areas. ZIP code 89049 for rural Tonopah, NV, is 195 km (121 mi) from east to west. The eastern boundary of this non-contiguous ZIP code has a longitude of -115.417°, while the western boundary is -117.625°. This means that there are 2.2° of longitude between the eastern and western borders of this ZIP code. The earth rotates 1 degree every 4 minutes, so zmanim at the eastern and western edges of this ZIP code are approximately 8.8 minutes apart. Using the typical center of the ZIP based calculations would mean that zmanim would be about 4.4 minutes different at the edges compared to the center. Moving to something a bit more extreme, is the case of ZIP code 99557 of Aniak, Alaska and its surrounding area. This ZIP code is 415 km (258 mi) from east to west. The longitude of the eastern edge of the ZIP code is -153.032°, and the western edge is -160.783°. Being farther north and therefore having shorter distances between degrees of longitude, this ZIP code stretches across 7.7° of longitude. The zmanim difference from the center to the edges of this ZIP code is 15 and a half minutes (31 minutes across the ZIP). While it is indeed rare to have such large distances, there are 193 US ZIP codes that are over 1° of longitude wide, meaning that the zmanim difference for these ZIP codes are at a minimum 4 minutes apart, or 2 minutes off from the center. There are 1,463 or 4.4% of all ZIP codes with 0.5° or greater distance between east and west (a minimum of a 2 minute zmanim difference between the east and west zide of the ZIP code). zmanim software developers should be aware of this, and take care to alert users of possible inaccuracies when using large ZIP code areas, or require addresses or more specific location information for large zip codes. Let’s contrast the above with Lakewood, NJ. With 0.107° of longitude from east to west, zmanim are 24 seconds later on the west side (the intersection of New Central Ave & N Hope Chapel Rd) than the east side (Shinn Cranes, 1600 Ocean Ave). New York City is larger, and from the western edge of Staten Island to the edge of Glen Oaks, the eastern edge of Queens there is a 2 minute and 11 second difference in zmanim. See the Calculation of Zmanim VS Other Sites post for additional related material. I thank Avraham David Gelbfish for generating the ZIP code longitude range for all 33,093 ZIP codes from the US Census BureauZIP code shape files.
You may have seen disclaimers on zmanim calendars warning of up to a 2 minute inaccuracy due to weather and atmospheric conditions. Atmospheric refraction from the earth’s atmosphere, causes the sun to be visible on average about 3 minutes earlier at sunrise, and about 3 minutes later at sunset (compared to a vacuum) due to the atmosphere bending the sunlight upwards towards the viewer. The 3 minutes is only an average, and it can swing widely due to weather and atmospheric conditions. The typical variance caused by “non-average” atmospheric conditions would usually be within 2 minutes, resulting in the 2 minutes mentioned in the disclaimers. This 2 minute variance is during usual conditions, though there are conditions that would greatly increase this time.
When the sun’s rays traveling through the vacuum of space hit the earth atmosphere, they slow down and bend upwards towards the observer resulting in the sun being visible earlier (than in a vacuum) in the morning, and later at sunset.Refraction of the sun’s rays is not a one stage refraction, but as the sun passes through increasingly dense layers of atmosphere, the amount of refraction increases with each thicker layer. This can be seen in the diagram of refraction at sunset above. The apparent position of the sun near sunset in the image (exaggerated in the image) is height of the sun as it appears to the user, though in reality the sun is below the horizon. Refraction can easily be observed by looking at a straw in a partially filled glass. The straw appears to bend (or be broken) at the point it enters the water. This is due to increased refraction in water versus air.
Complexity in Calculating Refraction
Since the amount of refraction depends on the pressure (the more dense the atmosphere is, the greater the refraction), temperature (hot air is less dense and refracts less) and to a lesser degree humidity (water vapor in the air impacts the refraction) in each layer of the atmosphere, calculating refraction is complex and requires very detailed meteorological information on the current conditions in each layer of the atmosphere in the area being computed. This can’t be done accurately in advance, and even calculations for the current day require readings from weather balloons at multiple elevations for accurate measurement, something not very practical (though the Lakewood vasikin minyan (likely done elsewhere as well) manually adjusts the hanetz hachama time each morning based on the weather). For this reason, zmanim (as well as civil sunrise and sunset) calculations usually use a global average refraction of 34′ of a degree, or 0.5666°. The global average atmospheric refraction accounts for sunrise being between 3:01 minutes earlier (during the solstice), and 2:29 minutes earlier (during the equinox) in Yerushalayim, as opposed to the value in a vacuum (the difference depends on where in the world you are, in Lakewood, NJ the range is 3:29 – 2:57). This average atmospheric refraction is not very accurate but is commonly used since it is complex to calculate local averages. More accurate refraction figures can be calculated for local and seasonal atmospheric models, and these have been shown to be accurate to within 15 seconds 90% of the time in the case of summer and winter subtropical models used in a study in Israel. See Using a Digital Terrain Model to Calculate Visual Sunrise and Sunset Times by Rabbi Chaim Keller and Dr. John K. Hall for additional details.
Inversion and the Novaya Zemlya Effect
Under usual conditions, the atmosphere gets colder at elevation, with the warmest air being closest to earth. An inversion condition is where there is a layer of cold air under a layer of warmer air. When there is an inversion over a large area (greater than 400 km), the solar rays get ducted in the lower colder air layer (see image below) and produce an extreme refraction. This is known as the Novaya Zemlya effect and produces a solar mirage resulting in the somewhat visually distorted sun being visible much earlier than expected (see top image).While typically a phenomena in the polar regions, a study by the University of Calgary showed that refraction can have a significant affect on zmanim even in non-polar areas. In the 2003 study (Variability in the Astronomical Refraction of the Rising and Setting Sun), they observed that the sunrise on January 10, 1991 appeared almost 12 minutes earlier than expected. The paper mentions:
On rare occasions, the Sun appeared to rise much earlier or set much later than predicted by such publications as the Tables of Sunrise, Sunset, and Twilight (USNO 1962). In our study, the sunrise of 1991 January 10 was almost 12 minutes early. This phenomenon is known as the Novaya Zemlya solar mirage (Lehn1979). It appears to be caused by a geographically extensive temperature inversion within the boundary layer of the atmosphere. The resulting vertical density profile causes the sunlight to be ducted around the curvature of the Earth. For the purpose of this study, we defined anomalously large astronomical refraction to be an event with refraction greater than 1°. A total of 12 anomalous events were recorded (2.9%).
While these typically occur in cold areas, they can happen in other areas as well. The study authors mention that
The majority of the anomalous events took place in the cold months. Nine of the 12 events occurred between November 1 and April 30, with January having five events. At the time of the events, the average surface temperature was -10.9°C, and all events occurred with surface-inversion conditions. Surface inversions tend to form with overnight surface radiative cooling through a dry atmosphere. Typically, they persist into the early morning, even after sunrise. Even though most of the events took place in the cold parts of the year, the data suggest that the Novaya Zemlya solar mirage may not be an exclusively cold-weather or polar phenomenon. Four of the events occurred with a surface temperature greater than 0°C. One event took place 2 days after the summer solstice.
Refraction at Sunrise VS Sunset
The University of Calgary study found that extreme refraction is an order of magnitude more common at sunrise than sunset. The reason for the difference between sunrise and sunset is that
This may be because the lower atmosphere is better mixed during the day as a result of solar heating leading to a dry adiabatic lapse rate in the boundary layer. Anomalously large astronomical refraction events the “Novaya Zemlya solar mirage” occurred about 3% of the time and were an order of magnitude more common at sunrise than sunset.
That said, The Novaya Zemlya effect does occur at sunset and in warm climates as seen in this video of sunset in San Francisco. Sadly, the video does not include information on how long it delayed sunset.
Halachically sunrise and sunset times depend on when we can see the sun, and not when it is at the horizon. As mentioned above, the average global refraction of 34′ results in sunrise appearing about 3 minutes earlier and sunset 3 minutes later later than in a vacuum, and this refraction (or other similar refraction values) is what is used in all calendars (both halachic and civil). The fact that there is such potential for variation in weather conditions, and that the global average is likely not what is present where the zmanim are being calculated, is the reason that many luchos (zmanim calendars) have disclaimers about accuracy. Many calendars round off their zmanim without showing seconds due to the inability to accurately calculate zmanim because of refraction variations. Lahalacha the impact of earlier or later sunrise is limited to vasikin minyanim. A separate article may be needed to actually discuss sof zman krias shema and other zmanim’s relation to sunrise and sunset VS the actual position of the sun in the sky (1/4 of the way across its path for sof zman krias shema). The halachic impact of refraction at sunset is much greater since it impacts the day/night boundary, but those are much rarer. Now to the big question, does extreme refraction such as the Novaya Zemlya effect impact zmanim? The fact that it rarely impacts sunset, means that it almost academic since predicting the inversion before a vasikin minyan starts is impractical. In a conversation with one posek a number of years ago, he felt that the Novaya Zemlya Effect should not impact zmanim lahalacha due to the fact that unusual occurrences should not be factored in, and because the distorted sun is not considered the sun as far as zmanim. I would appreciate being notified if anyone receives a psak halacha on this question.