Beta effect

The Beta Effect

First, a mea culpa: in my last post I showed a diagram of the Coriolis deflection of an inertial circle in the counterclockwise direction - so that the cyclone would avoid the West Coast of India. Well, that's wrong. The rotation is clockwise in the Northern Hemisphere as can be seen in the Figure below (taken from one of Anders Persson's papers, I think):

So, having got that out of the way, let me meander a bit into some background, on the way to the beta effect - which actually explains the northwestwards (NW) motion of cyclones in the Northern Hemisphere (NH), which causes cyclones to avoid India's West Coast - and prefer to hit the East Coast (to disastrous effect).

Without going into the derivation (which could vary in length depending upon the level of rigour), the Coriolis force, which arises in a rotating frame, such as the Earth itself, is given by:

                                                F = 2m w ´ v

where the Coriolis force F results from the vector cross-product of the angular velocity w and the linear velocity v, all three vectors pointing along 3 perpendicular axes (as given by the right hand rule, w along the thumb, v along the forefinger and F along the middle finger). For the right-hand rule, see the website:

http://phys420.phas.ubc.ca/p420_12/tony/Coriolis_Force/Home.html

For the Earth, the angular velocity vector points through the poles, the velocity is along the surface of the Earth at some given latitude j, and the force F deflects the cyclone in a direction perpendicular to its motion (v). For horizontal motion, the magnitude of the Coriolis force is given by:

                                                F = 2m w v sin(j)

and so its magnitude is exactly zero at the Equator.

Since the Coriolis force acts to deflect any moving object perpendicular to its motion, that motion is likely to become a vortex or a circle. Specifically, the motion is clockwise (CW) in the Northern Hemisphere (NH) and counterclockwise (CCW) in the Southern Hemisphere (SH).

Equating the Coriolis force to the centripetal force mv²/r, the radius of the inertial circle is:

                                                R = v/(2wsin(j))

The latitude of Kanyakumari is 8.1°, of Mangalore is 12.9° and of Mumbai is 19.1°. Corresponding values of sin(j): 0.141, 0.223 and 0.327. The angular velocity of the Earth is w = 7.29x10^-5 rad/sec and so the radius of the inertial circles at these points, assuming that the cyclone speed is 50 m/s (180 km/hr) is: 2,437 kms (KK), 1,537 kms (Man), and 1048 kms (Mum). 

Tabulated:

	Latitude	Sin(l)	Radius of inertial circle (kms)
Kanyakumari	8.1°	0.141	2,437
Mangalore	12.9°	0.223	1,537
Mumbai	19.1°	0.327	1,048

Due to the latitudinal variation, the radius of the inertial circle is much greater closer to the Equator.

The fact that the Coriolis force deflects westwards is not obvious  – considering that the motion in the NH is clockwise, and circular motion along inertial circles should just keep on regularly returning the moving mass back to its pre-existing path - and the explanation is the beta effect (see below for a  sketchy description).

The equations that deal with this are discussed in the website quoted below, for a particle moving with a velocity vector (V₀ cos(q), -V₀ sin(q ), 0 ) with z = 0 along the surface of the Earth, and q = 0  as the reference direction, pointing north:

http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node58.html

The end result of solving the equations of motion, assuming that w is small,  is:

V_x = V₀ cos(q + 2wt sin(l))

And

 V_y = -V₀ sin(q + 2wt sin(l))

Which means that the angle q changes at the rate:

(dq/dt) =  2w sin(l)

Since this quantity is positive, the angle q increases, and the mass moves in a clockwise direction (in the NH)..

The magnitude of dq/dt is 4.66x10^-5  rad/sec (assuming sin(l) = 0.32), or 2.67x10^-3 deg/sec.

In other words, the cyclone would get deflected by 9.6 deg/hr, or 230 deg/day.

According to a course document on “Inertial Oscillations” by Thompson (Ocean420) in Winter 2005 in a book by Susan Hautala, LuAnne Thompson, and Kathryn Kelly:

The time period of the inertial oscillation is given by: 

T_in = T_E/[2 sin (l)]

Where T_E = Earth’s rotation period (24 hrs), and gives some values at different latitudes: 69 hrs at 10°, 24 hrs at 30° (obviously), and 16.9 hrs at 45°. The radius of the inertial circle is also much greater near the Equator (as shown above).

http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node58.html

The UTexas website makes a number of other things clear:

      a)   In the Northern Hemisphere, cool winds from the North (that move towards the Equator to replace hot air that rises), are deflected in a clockwise direction, giving rise to the trade winds which blow towards the southwest (SW).

b    b)  Cyclones originate because winds that blow from a high pressure area to a low pressure area are deflected clockwise in the NH (as seen in the Figure below, taken from the UTexas website), and this sets up the cyclonic rotation. Note that the winds blowing towards the South are deflected westwards, while the wind blowing to the North is deflected towards the East. 

c    c) The related point – not mentioned by Thompson (in this document) – is that the Coriolis force is too weak near the Equator to set up the cyclonic rotation, which accounts for the fact that cyclones mostly originate at latitudes with l >7°.

http://www.indiaweather.gov.in/?page_id=281

In the North Indian Ocean, a tropical cyclone usually lasts 5-6 days, and they remain at hurricane intensity for 2-4 days (compared to a global average of 6 days).

Another important quantity to evaluate is the dimensionless Rossby number Ro, which is the ratio of inertial to Coriolis forces as mentioned in wiki:

https://en.wikipedia.org/wiki/Coriolis_force

                                       Ro = V/(2w sin(l)L)

Where L is the spatial scale of the system, in this case a cyclone. Only if Ro £ 1, is the effect of Coriolis force significant relative to the inertial force.

http://www.indiaweather.gov.in/?page_id=281

A cyclone with a wind speed of 10-14 km/hr is slow-moving, 15-25 km/hr is a moderate cyclone, and for >25 km/hr it is a fast-moving cyclone.

The size of a cyclone in Indian seas varies between 50 and 2000 kms, but most of them are in the size range of 300-600 kms.

For a cyclone with V = 10 m/s (36 km/hr) in the Bay of Bengal or the Arabian Sea, with a spatial dimension of 500 kms, the dimensionless Rossby number Ro becomes:

                                            Ro = 10/[(2)(7.29x10^-5)(0.32)(5x10⁵)] = 0.43

It seems that the Ro number will be even lower for a larger cyclone (say 1000 kms) or a slower moving cyclone at a higher latitude.

Note that the highly contentious case of water draining out in spiral fashion from a kitchen sink: does it go CW in the NH? The answer is that, whatever happens, it’s not due to the Coriolis force. The Rossby factor for this case is (roughly), assuming L = 0.1 m, V = 1 m/s and in India:

                                               Ro = 1/[(2) )(7.29x10^-5)(0.32)(0.1)] = 2x10⁵

So the Coriolis effect doesn’t have a chance compared to inertial effects!

http://www.indiaweather.gov.in/?page_id=281

“Cyclones that form over the Bay of Bengal are either those develop in situ over southeast Bay of Bengal and adjoining Andaman Sea or remnants of typhoons over Northwest Pacific and move across south China sea to Indian Seas. As the frequency of typhoons over Northwest Pacific is quite high (about 35 % of the global annual average), the Bay of Bengal also gets its increased quota.

The cyclones over the Arabian Sea either originate in situ over southeast Arabian Sea (which includes Lakshadweep area also) or remnants of cyclones from the Bay of Bengal that move across south peninsula. As the majority of Cyclones over the Bay of Bengal weaken over land after landfall, the frequency of migration into Arabian Sea is low.

In addition to all the above the Arabian Sea is relatively colder than Bay of Bengal and hence inhibits the formation and intensification of the system.”

I am currently reading Amitava Ghosh’s “The Great Derangement: Climate Change and the Unthinkable“ (Penguin Random House India, 2016) and he observes that (possibly due to global warming) for the first time, in 2015, the number of cyclones originating in the Arabian Sea was known to be greater in number originating in the Bay of Bengal (p.58). He also notes that: “The cyclones that have struck the west coast of Indiain the past have all traveled upwards on a northeasterly tack, from the southern quadrant of the Arabian Sea” (p.66). He is extremely worried that such a cyclone may hit the highly populated, low-lying coastal megacity of Mumbai, with lethal consequences. With global warming, the intensity of cyclones has been observed to have increased, even though the frequency may not have.

According to Persson, since inertia circles have a lower diameter at higher latitudes (than at lower latitudes), the inertia circles are actually spirals transporting mass westwards, (Anders O.Persson, History of Meteorology 2 (2005)3). Elsewhere in this paper, Persson refers to the phenomenon of beta drift, which explains the northwestward movement (in the Northern Hemisphere) of cyclones. This is complicated but I will summarise what I got out of the flash simulation in the following website:

https://courseware.e-education.psu.edu/courses/meteo241/Images/Section7/beta_drift0704.swf

For an axisymmetric cyclone, the vorticity is conserved (under some reasonable conditions).

The vorticity (vector) is defined as: W = curl(v), where v is the velocity vector. Anyway, there are two components of vorticity: the local vorticity due to the spin of the cyclone around its central axis and the vorticity  f due to the spin of the Earth around its axis. The latter is given by:

f = 2sin(l)

 it is zero at the Equator, and it increases as the latitude increases.

If an air parcel in or near the cyclone moves Northwards, its Earth vorticity increases, and since the total vorticity is conserved, its local vorticity decreases. Similarly, an air parcel that moves South, finds its Earth vorticity decrease and its local vorticity increase. Air parcels that move East or West do not change their latitude or Earth vorticity.

These increases and decreases in local vorticity cause the formation of two secondary (beta) gyres (see the Figure below, from the above website) that rotate in opposite directions: the local vorticity has a minimum that is NE (CW rotation) of the main cyclone vortex (CW rotation), and a maximum SW  (rotating CCW) of the main vortex. These two gyres are much weaker (by orders of magnitude) than the main vortex – and they are not visible in satellite pictures of cyclones.      

At this point, the website unabashedly declares that ‘numerical simulation’ shows that these two gyres displace the main vortex of the cyclone in a NW direction (in the NH), and a speed of, at most, a few metres/sec. Note that the beta effect will displace the cyclone in the NW direction even if it is embedded in ‘calm winds’ (a slow or almost static’ cyclone).

For me, this constitutes a ‘ne plus ultra’ – because I am not about to get embroiled in numerical simulation of meteorology!   

http://ambergriscaye.com/forum/ubbthreads.php/topics/469128/The_Beta_Effect.html

About 10-20% of the storm’s motion arises from the beta effect.

 Please note that you can't observe these circulations on satellite loops because their orders of magnitude are so much smaller than the hurricane's circulation. 

Nonetheless, these circulations associated with the Beta effect are sufficiently large to cause a westward-moving hurricane to drift northwestward. Moreover, the Beta effect is the reason why tropical cyclones flirting with crossing the equator swerve to the northeast before it's too late. 

The Earth vorticity parameter f arises due to the Coriolis force, and the beta effect arises due to the variation of the vorticity f with latitude (X.Liang and J.C.L.Chan J.Atmosph.Soc. (Oct.2005) p.3825)

Bottomline: The beta effect does cause the cyclone to move away from the West Coast of India (although it also causes cyclones to move towards the East Coast), while the frequency of cyclones in the Arabian Sea seems to have gone up in 2015, above that in the Bay of Bengal – according to Amitava Ghosh.

More cyclones hit the East Coast of India

Just by reading the newspapers over the years, one can recall more cyclones hitting the East Coast of India than hitting the West Coast.
I thought that I would check online if somebody else has observed, and explained, this observation.

I found one post which I reproduce below, from an IAS (aspirants/trainees?) discussion forum:

http://discuss.forumias.com/discussion/595/gs-geography-questions


“Why do cyclones strike at the Eastern coast in India and not much in the Western coast. As if we notice it is seen that cyclones typically create much havoc in the Eastern coast rather the Western coast?
The main cause is Coriolis effect.
Since India is in Northern Hemisphere, so in here, due to Coriolis force, winds tend to turn toward their right while moving.
So, whatever cyclones are formed in Bay of Bengal, they turn toward their right, hitting our Eastern coast.When cyclones are formed in Arabian sea, they get deflected away from india.
But, they are exceptions also, since this is not the only factor.”

The explanation seems to be correct - except for the fact that in the Northern Hemisphere (NH) the deflection is towards the left, or the North-West. The diagram below indicates this:

I also put a very rough approximation of the Indian peninsula as a triangle, with the East Coast making a shallower angle of 35°  at Kanyakumari, than the West Coast which makes an angle of 21°.
Also, Kanyakumari is at 8.08° N latitude.

Why does India’s West Coast get hit by cyclones less often than the East Coast? 

a)  Cyclones form over water, because they pick up energy from evaporating water 

b)  Cyclones are mostly observed to originate between 7 and 15 degrees of latitude; they form at latitudes greater than 7 degrees (in the NH), and do not originate at all in the zone of +/- 7 degrees about the Equator.

c)  Cyclones move counterclockwise in the NH because of the Coriolis force

d      The East Coast is at an angle to the cyclone so it tends to miss it. The position of Kanyakumauri at 8 degrees N is significant in view of c).  

     

       Another factor is the frequency of storms in the Bay of Bengal and in the Arabian Sea (4:1):

       .http://www.telegraphindia.com/1091112/jsp/frontpage/story_11731340.jsp

“       "Historical records suggest that for every four cyclones in the Bay of Bengal, there is one in the Arabian Sea,” said Basab Bandopadhyay, a scientist in the cyclone warning division at the India Meteorological Department, New Delhi.

Subtle differences between the way that convective currents behave over the Arabian Sea and over the Bay of Bengal may explain this higher frequency of cyclones forming over the Bay, scientists said."

http://www.indiaweather.gov.in/?page_id=281

Q: Why are there fewer cyclones in the Arabian Sea compared to the Bay of Bengal?

The Arabian Sea is relatively colder than the Bay of Bengal and this inhibits formation of cyclones.

"Bay of Bengal cyclones either originate in situ or come from the South China Sea (also NW Pacific) (the latter has 35% of all global cyclones every year, so this is a large number). Arabian Sea cyclones either originate in situ or are remnants of cyclones that come from the Bay of Bengal overland across the Southern Peninsula (and so have become weaker, and are less in number)." 

Generally storms do not cross the Equator - but this rule is probably not inviolable.

http://www.britannica.com/science/tropical-cyclone

"The developing (storm) system must be at least 500 km (300 miles) away from the Equator. For the development of the rapid rotation characteristic of tropical cyclones, the low-pressure centre must be located at least 500 km (300 miles) away from the Equator. If the initial disturbance is too close to the Equator, then the effect of the Coriolis force will be too small to provide the necessary spin. The Coriolis force deflects the air that is being drawn into the surface low-pressure centre, setting up a cyclonic rotation. In the Northern Hemisphere the direction of the resulting circulation around the low is counterclockwise, and in the Southern Hemisphere it is clockwise".

Note that the distance between Kanyakumari and the Equator is about 900 Kms. This implies that the cyclones that form in the Bay of Bengal and in the Arabian Sea are 'separate' - to some extent - because a cyclone crossing land tends to weaken (as mentioned above), but, again, this is not an insurmountable barrier, so there will be some crosstalk between the two.

A similar phenomenon - the East Coast getting more hurricanes - has been observed in the U.S.:

http://www.aoml.noaa.gov/hrd/tcfaq/G8.html

Why do hurricanes hit the East coast of the U.S., but never the West coast? Contributed by Chris Landsea (NHC)

"Hurricanes form both in the Atlantic basin (i.e. the Atlantic Ocean, Gulf of Mexico and Caribbean Sea) to the east of the continental U.S. and in the Northeast Pacific basin to the west of the U.S. However, the ones in the Northeast Pacific almost never hit the U.S., while the ones in the Atlantic basin strike the U.S. mainland just less than twice a year on average. There are two main reasons. 

The first is that hurricanes tend to move toward the west-northwest after they form in the tropical and subtropical latitudes. In the Atlantic, such a motion often brings the hurricane into the vicinity of the U.S. east coast. In the Northeast Pacific, a west-northwest track takes those hurricanes farther off-shore, well away from the U.S. west coast. 

In addition to the general track, a second factor is the difference in water temperatures along the U.S. east and west coasts. Along the U.S. east coast, the Gulf Stream provides a source of warm (> 26.5°C) waters to help maintain the hurricane. However, along the U.S. west coast, the ocean temperatures rarely get above the lower 20's, even in the midst of summer. Such relatively cool temperatures are not energetic enough to sustain a hurricane's strength. So for the occasional Northeast Pacific hurricane that does track back toward the U.S. west coast, the cooler waters can quickly reduce the strength of the storm."

Ok, so this is where I'm going to stop for today. I'll continue in the next post to add some more details about the Coriolis force. The reason that I have to go into more detail is that the deflection in the Northern Hemisphere is counterclockwise, but a cyclone can last several days, and in this process the continued CCW deflection causes the cyclone to trace a circle (called an inertial circle). So where does this leave us, going round and round? On an average is the motion of the cyclone an undeflected straight line (or whatever it was going to do anyway in the absence of the Coriolis force)?

Just a few add-ons to the previous post: a log-log graph of extra time vs altitude h (in kms):

in which points for Burj Dubai, Mt.Everest and the 12 kms cruising height of commercial jet-liners are indicated. The point to be emphasized is that the extra time is proportional to the square root of the altitude.
Of course, one could increase the altitude beyond 12 kms. At an altitude of 100 kms (the 'edge of outer space'), the extra time is 40.34 mins, and at 400 kms (the mean altitude of the International Space Station), it is 79.17 mins.
At an altitude equal to the Earth's radius, the angle q = 60° (which is easy to verify) and the extra time is 240 mins or 4 hrs.
You need to go infinitely far to get q=90° and a time of 6 hrs.
That's it - I can't think of any reason to bang on about this any more!

Longer Day on Burj Dubai, Mt.Everest and a Plane

This problem is one that I encountered when trekking in the Himalayas. If you are on a mountain with an unobstructed view of the horizon, then your day is extended by a few extra minutes that the Sun takes to drop below the horizon at sunset (or rise above, at sunrise). The geometry is fairly simple, but a few days ago I saw a quote attributed to the astronomer Neal de Grasse Tyson. I tried to verify it, and I did not get the same numbers.

So I checked online, and I got differing answers - which I reproduce below. As well as the simple derivation that I did. Have I got something wrong? Dunno!

a a)    Neal de Grasse Tyson, quoted by the Indian Express in the “Social Intelligence” column, 15^th June 2016:

“Indeed from atop Burj Khalifa in Dubai they get four extra minutes of daylight, two in the morning and two in the evening.”

The top of Burj Khalifa is at about 828 metres height.

b b)  Quote from the following website: assuming a plane flying at an altitude of 12 kms:

http://curious.astro.cornell.edu/about-us/161-our-solar-system/the-earth/day-night-cycle/189-how-do-sunrise-and-sunset-times-change-with-altitude-intermediate

“At most latitudes on the Earth, the effect of increased altitude is the same: it makes the Sun rise earlier and set later than it would at that same location from the ground. To make things simple, let's assume that you are in a plane over the ocean, at the equator at sunset. In that case, straightforward trigonometry indicates that at a typical commercial airplane altitude of 12000 metres, you can see an extra 2 degrees (emphasis added) "around" the Earth. Since the Earth moves around the Sun at a rate of a quarter of a degree a minute, it means that at this altitude, sunset occurs 8 minutes later than it would from the ground. The variation with altitude is approximately linear, (emphasis added) and so we conclude that sunset is later by 1 minute for every 1.5 kilometres in altitude, and that sunrise is earlier by the same amount.

Now, all of this is complicated somewhat by the fact that you don't stay in one place in a plane, but you travel in a given direction: if this direction is predominantly East or West, then the plane's motion will completely change the answer we got above (in particular, travelling West at sunset can lengthen the latter significantly in a commercial jet). So, the results above are valid in a plane if a) the plane is moving rather slowly (like a personal plane) or b) the plane is travelling in the North-South direction.”

c c)   Derived formulas:

 

Mean radius of Earth is R = 6371 kms. The horizon in the above figure is at the point that is tangent to a spherical Earth, so it makes a right angle to the radius (apologies for the figure!).

The angle to the horizon, from a height h above Mean Sea Level, is given by:

                                                cos (q) = R / (R+h)

Approximating for small angles:

                                               cos(q) = 1 – (q²/2) = 1/ [ 1 + (h/R)] = 1 – (h/R)

Thus:

                                                          q = (h/R)^1/2

Let h = 12 kms, and R = 6371 kms, so q = 0.0614 rads = 3.52 degs – instead of 2 degs according to the Cornell blog.

Burj Khalifa is at h = 0.828 kms, so q = 0.0161 rads = 0.924 degs.

Multiplying by 4 mins/deg,as mentioned above, (180° = 12 hours) we get 3.69 mins for Burj instead of 2 mins, and 14 mins for the plane at cruising altitude.

Also, the angle varies as the square root of the altitude – not directly proportional as the Cornell blog b) stated.

cd)   However, the following blog gives values for Burj Khalifa (828 m) and Mt.Everest (8,848 m):

These calculations are in better (but not perfect) agreement with the calculations in c):

http://www.kosherjava.com/2010/03/07/faq-how-much-earlier-is-sunrise-on-mount-everest-due-to-elevation/

“With a height of 828 m (2,717 ft), visible sunrise to someone standing on top of the crown of Burj (something unrealistic) on June 22nd would be at 5:24:56 AM versus 5:29:31 AM on sea level, a difference of 4 minutes and 35 seconds. 

With an elevation of 8,848 Meters (29, 029 feet), sunrise on Mt.Everest would be up to 15 minutes and 31 seconds earlier on Mount Everest than on sea level. The range of the effect is from 15 minutes and 31 seconds on June 22nd, to a “low” of 13 minutes 41 seconds earlier on March 18th.”

This website implies that it is a java-based app based on calculations made by Rabbi Harfenes – that are more detailed because they take both the date as well as the latitude and longitude into account.

The formulas given earlier for Mt.Everest yields: q = 3.02°, which means 12.1 mins. That is: kosherjava gives an answer for Mt.Everest that is 13% higher or 28% higher (depending on the date) than the answer from the formulas above.

So: what gives? How much would the latitude and longitude matter if the Earth is pretty much spherical (about 40 kms more radius at the equator than at the Poles) ?

de) Also see the following site, which gives a low value for Mt.Everest and also again states that the variation is linear with altitude:

http://heimhenge.com/skylights/2014/08/25/the-time-of-sunrise-and-sunset/

ef)    TimeAndDate.com also includes a handy calculator for the times of sunrise and sunset on any date for any location on the planet. As with their Day and Night Map, that calculator assumes a flat and unobstructed horizon. They also assume the observer is at the same elevation (measured from sea level) as the horizon. If you were observing from the top of a tall mountain, sunrise would happen slightly earlier, and sunset slightly later. But it would be a small correction — only about 6 minutes if observing from the top of Mt. Everest. The correction factor is: ΔT = ±1 minute per 1.5 km elevation. Again, assumed linear!

Summary: Extra time:

	Burj Dubai 828 m	Mt.Everest 8,848 m	Plane at 12 kms 12,000 m
Tyson	2 mins
Cornell*	33 secs	5 mins 54 secs	8 mins
Kosherjava	4 mins 35 secs	13 mins 41 secs to 15 mins 31 secs
TimeAndDate.com		~ 6 mins
Calculations	3 mins 41 sec	12 mins 6 secs	14 mins 5 secs

 *Cornell calculations mentioned only the plane; the other two I have calculated assuming that the 1 min per 1.5 km rule is correct – which I seriously doubt!

Full disclosure:

I wrote the last post after reading a couple of chapters of Benedict Anderson's "Imagined Communities" while in the Kashmir Valley. I still haven't finished the book - which is rather dense - but I do plan to do so...

I recently came across the German word 'heimat', which is about the relationship of a human being with a certain 'spatial social unit' that is related to the home(land). It connects to a trinity: birth, community and tradition - including language, earliest experiences or acquired affinity. Naturally, this concept was appropriated by the Nazis, but it has been reclaimed in recent decades by the Green environmental movement. I think this concept is very similar to what I discussed in my last post, and it can range from mild patriotism to rabid Nazi-style hyper-nationalism, including ideas of Lebensraum and  Volk (Germanness).

 It is also clearly connected with the idea of 'in-group' and 'out-group', and can be benign as long as there is respect for - as opposed to targeting of - the 'Other'.

I looked up the index in Anderson's book and the word heimat wasn't there - but it may well be there somewhere in the thickets of the book, implicitly if not explicitly.

I wrote this bunch of reflections when in the Valley, returning after 29 years...

My land

Consider the constant migrations of people all over the world , from the smallest groups to the largest, out of Africa, eddying and swirling across continents, even crossing oceans, and it becomes clear that no particular land ‘belongs’ to any specific group. The flows of genes (Y- and mitochondrial), languages and cultures - all of them continuously changing – have been used to map the migrations, often with contradictory results.

What does it mean to be the ‘original’ inhabitants of Africa, if these autochthons just barely qualify as being (recognizably) ‘human’? Even hunter-gatherer societies are territorial, but with the advent of agriculture and ‘settled’ populations, land ownership became even more of an issue. So, to define ‘original’ inhabitants, do we stop at ‘recorded history’ – or do we carry on digging into the often mythical past?

Plants and animals often seem to be more rooted than humans to particular geographical areas – but even they have travelled extensively, sometimes on their own, most often using birds and insects, and sometimes with human aid.

Still we are tied to the land we live in by quirks of geography, weather and food which affect our customs, clothes and language in odd ways. (Bengalis must have hilsa, mutton for Kashmiris, maple syrup for the Canadian…) There are ‘geographical indicators’ in our genes e.g. the lung capacity of Sherpas and Tibetans and the sickle cell anaemia (malaria-resistant) genes in parts of India and Africa. Other traits may not be so obvious. Some mutations may be neutral.

Although we are ‘tied’, we are not truly bound to a given place: one sibling may stay a whole lifetime in one place, another may land up in some other continent, and yet another may be travel all over the world and never settle anywhere – while eyeing the other planets in insatiable wanderlust. In principle, anyone could live anywhere – but in practice there are many barriers to overcome.

But in what ways does a land alter your perceptions, your language? The story that the Eskimos have 40 words for snow turned out to be an exaggeration. Yet it is true that the seasons and the plants (some of them carried along with us), leave their imprints upon our languages. Landmarks acquire historical overtones and memories that last centuries if not millennia – like Mt. Kailash for Hindus or the Wailing Wall for Jews - even if they have been 'lost'. These can arouse feelings of connection with the land, and feelings of ownership. Most of these seem to be for religious reasons, which would naturally get entrenched in the collective memory of a community or group.

But in many places this sacred feeling can be fixed on a river (the Ganga, the Nile, etc) or a lake, that would mostly be adjacent to a temple. It could be a place of pilgrimage (e.g. the Amarnath Yatra, Kailash Manasrover Yatra - which is a mountain and a lake – or Lake Baikal,…).  Often the river has sufficed to demarcate ‘us’ and ‘them’… but the paths of neither rivers nor men are invariable and stable.

Imagine belonging to a nomadic community that has always gone South in the winter, and returned North in summer, along well-worn paths marked and traced by numerous generations of ancestors, along with ‘their’ herds of reindeer, or cattle, or whatever…

The feeling of being attached to some place could also be related to some purely individual memory: like some place you went to with your parents as a child… or it could be an accretion of memories, just the sights, sounds and smells of the village or town that you grew up in…

For many a Kashmiri Pandit, his or her identity is bound up with temples of Shankaracharya, Martand, Tulla Mulla,.. And with the lakes and gardens of the Valley, the apples, the mulberries, the rainbow trout … yet, it may just be the very quotidian, mundane place you grow up in…it doesn’t have to be a putative paradise! 

But it is very hard to pin it down: why do we have these feelings for our ‘homeland’? For me, the song from the film Kabuliwala, “Ae Mere Pyare Watan…” comes closest to expressing the ineffable feeling of nostalgia and homesickness. I do not relate to the ridiculous anthropomorphism of “Bharat Mata”…

Farmers and fishermen are closest to the land and the sea. They are tuned to the seasons and the soil, and the tides and currents of the sea. Local knowledge is important: take the case of the Turkish farmers who refused to remove stones from their fields, because they – counter-intuitively – boosted their yields. That knowledge, often accumulated over generations, ties farmers to their land.

But this is a paradox: we don’t ‘own’ the land – it doesn’t even need us! – and yet we have this feeling of ownership. And particularly in the Anthropocene, humans have made irreversible changes at the global level, leaving behind detectable residues of plastic, concrete and radioactivity.

Food is sourced from so many countries today that we are in denial of the seasons, of the annual and decadal rhythms of the land. The elites imagine themselves as global citizens – and think that there is no price to be paid for these extravagant, profligate ways of global citizenry.

Does the land ‘belong’ to us? No matter how many fences we weave, how many walls we erect, how many canals we dig, dams we build, whether we map it with rulers, theodolites or GPS – the land does not need us – as in Nevil Shute’s “Earth Abides”, it will be there long after we are dead and gone and long forgotten, both as individuals and as a species, that tends to think too much of itself. We may irrigate the land with water, tears or blood, and we may indeed belong to the land – as do countless other organisms, ranging from bacteria to whales, but it does not belong to ‘us’.