## Mass Streamfunction

Mass Streamfunction

Sandro Wellyanto Lubis

Graduate Student of Leipzig Institute for Meteorology, University of Leipzig, Germany

[ All computations are made using NCAR Command Language (NCL)]

2012

Mass streamfunction $\Psi$ was computed using pressure coordinates from the ERA-Interim dataset 1989 – 2007. The streamfunction was determined  by normalization of the inverse gravity and latitudinal belt using the equation of  : $\frac{1}{acos\phi}\frac{\partial}{\partial\phi}\left(\left[\bar{v}\right]cos\phi\right)+\frac{\partial\bar{\omega}}{\partial p}=0$ . By defining the mass flux streamfunction $\Psi$ as the vertically integrated northward mass flux at latitude φ from pressure level p to the top of the atmosphere, the analytical solution for $\left [\bar{v}\right]$ can be obtained as $\frac{g}{2\pi acos\phi}\frac{\partial\psi}{\partial p}$ . Assumption that the streamfunction at the top of intergration is equal to zero, streamfunction $\Psi$ can be directly calculated from the observed $\left [\bar{v}\right]$.

Figure 1. Zonal-mean cross section of the mass streamfunction in Tg/s for annual

In general, the mass streamfunction is commonly known as meridional overturning circulation (further, known as Hadley, Ferrel or polar cells depending on the latitudes) with unit 10^9 kg/s or Mt/s or Tg/s, the positive values (negative values) always denote to the clockwise (anticlockwise) rotation. The meridional overturning velocities are related to $\Psi$ by v and $\omega$. There is a strong seasonal dependence of the streamfunction. In DJF, the rising motion is just south of the equator (in the southern or summer hemisphere) around 10S and sinks in the subtropics of NH around 30N. In JJA, the rising motion is fairly north of the equator, nearly at 20N and sinking in the subtropics of the SH, 30S. These shifted circulations are induced by the Asian summer monsoons and displacement of  ITCZ.  The strong upward motions occur on the summer hemisphere of equator where the huge covection and rising motion are intensively trigged by warm surface. Meanwhile, the strong downward air masses take place in the winter hemisphere of the equator. The annual mean (by averaging these values) produced two cells which are symmetric about the equator (the center is roughly around 5N). The center of these two symmetric cells denote the wet region in equator with  high of cloud cover (further analysis using the OLR data).

Figure 2. Zonal-mean cross section of the mass streamfunction in Tg/s for DJA (Winter), MAM (Spring), JJA (Summer), and SON (Autumn)

-Sandro –

[computed by Sandro, data was obtained from the course of Global Climate Dynamic, Leipzig Institute for Meteorology, Germany]