Local field does not always decrease!
I am an undergraduate BSc (Hons) Physics student at the University of Mauritius doing my final year project entitled "Geomagnetism studies over the Indian ocean.". I have provided the computer program calculating the local magnetic field intensity F with my location--latitude 20.17 S, longitude 57.33 E and elevation (highest point) 828m. The program gave me values of the total field F (=magnitude of the magnetic vector B) for 1900-2004.
The value of the total field is found to be decreasing during the interval 1900-1997 (from 39834 nT to 36884 nT), but from 1998-2004, there is an increase! (From 36985 nT to 37420 nT). I have read that at present the magnetic field continues to weaken. Then how is it possible that here from 1998 to 2004 we are having an increase? Should there not be a decrease?
I am really stuck at this point and do not know how to explain this. I have applied the program to another location ( 39.25 N, 105.28 W elevation 735m) and there I get a continuous decrease in F for 1900-2004, from 59288 nT to 53390 nT. This suggests a decrease exists over the entire interval. But if so, how can the other result, at my location, be explained?
I would be very grateful to you if you could give an answer to my question.
I do not have the codes which you use and can only guess. What is decreasing all these years is the dipole component of the field. That is the biggest contribution to F and over a long time (such as 1900-1997, almost a century) usually dominates the local trend.
However there exist other terms, such as quadrupole (n=2) and higher. They seem to be increasing (if the total energy of the field is almost constant, as Ned Benton found) and more important, they are not axially symmetric, and slowly migrate. I suggest that they are the cause.
The trouble with F is that it is non-linear, involving the square of the vector field B. I do not know if you can modify your code. If you can, have it calculate separately B1, the dipole (vector) field and B2, the non-dipole field. Then (* is scalar multiplication)
F*F = (B1*B1 + 2 *B1*B2 + B2*B2)
Now track over the same years B1*B1 , which is the contribution to F*F from the dipole alone, and of 2*B1*B2 + B2*B2, roughly the contribution of the higher harmonics (B2*B2 is small, and you can perhaps neglect it). My guess is that the first term declines steadily over 1900-2004, but the second may grow. It may perhaps overtake the decline in 1997, but is probably present even before.
You may also discuss it with your professor.