The geographical extent of the global surface monsoons (the figure above) can be  outlined by the normalized seasonality (Li and Zeng, 2000, 2003, 2005). The global surface monsoons contains three kinds of monsoons:  the tropical, subtropical, and temperate-frigid monsoons, respectively.  The extent of the classical tropical monsoons is surrounded by the positions of the Intertropical Convergence Zone (ITCZ) in summer and winter, which is the result of the two driving forcings of the tropical monsoon, the seasonal variation of the planetary thermal convection and  the seasonal variation of the semi-permanent planetary waves due to the thermal contrast between ocean and continent (Zeng and Li, 2002; Li and Zeng, 2005).

A monsoon index: Dynamical normalized seasonality (DNS) index 

The basics idea of the DNS index is based on intensity of the normalized seasonality of wind field. The monsoons possess very strong seasonal variation, it is therefore rational that strong and weak monsoons may be measured by use of the magnitude of seasonality of wind field. Such the DNS index is given by  

where  and  are the January climatological wind vector and the mean of January and July climatological wind vectors, respectively, V_m,n  the monthly wind vector for the year n and month m. The norm ||A|| is defined as  

||A||=(∫∫_S|A|²dS)^1/2 where S denotes the domain of integration (In calculations at a point (i, j), 

 where  the latitude at the point (i, j), , a is the mean radius of the earth,  and  in radian are resolutions at the meridional and zonal directions, respectively).

Then a large-scale monsoon index (MI) is defined as a measure of the area-averaged DNS given by

MI = {d }                        

where the symbol { } indicates an areal average within certain monsoon domain and d  is the monthly (or seasonal)  value of the DNS at a point and at certain pressure level (generally, taking 850 hPa or 925 hPa level).

Related References :

Li, J. and Q. Zeng, 2005: A new monsoon index, its interannual variability and relation with monsoon precipitation. Climatic and Environmental Research, 10(3): 351-365. Electronic version PDF

Li, J. and Q. Zeng, 2003: A new monsoon index and the geographical distribution of the global monsoons, Adv. Atmos. Sci., 20, 299-302. Electronic version PDF 

Li, J. and Q. Zeng, 2002: A unified monsoon index, Geophysical Research Letters, 29(8), 1274, doi:10.1029/2001GL013874. Electronic version PDF

Zeng, Q. and J. Li, 2002: On the Interaction between Northern and Southern Hemispheric Atmospheres and the Essence of Tropical Monsoon, Chinese Journal of Atmospheric Sciences, 26, 207-226. Full Paper PDF

Li, J., and Q. Zeng, 2000: Significance of the normalized seasonality of wind field and its rationality for characterizing the monsoon, Science in China (D), 43(6): 647-653. Electronic version PDF