A possible feedback between dynamics and thermodynamics through the background moisture in dictating the ISO rainfall over the Bay of Bengal

Abstract

The northward propagating intraseasonal Oscillation (ISO) is one of the dominant modes of tropical variability during Boreal summers. Several mechanisms have been proposed to explain northward propagation. Yet the factors that decide the ISO rainfall over a particular region remain elusive. This study shows that the ISO rainfall anomalies weaken across the south Bay of Bengal (SBoB) before they re-strengthen over the north Bay of Bengal (NBoB). We use the moisture budget to understand the reason for these weakening-strengthening cycles. We find that the horizontal moisture flux convergence (MFC) predominantly controls the ISO rainfall anomalies over the two regions. The convergence of background moisture by the ISO wind perturbations decides the ISO rainfall structure. Since past literature suggests that the Planetary Boundary Layer (PBL) convergence is caused by barotropic vorticity, we further conduct the vorticity budget to understand the rainfall structure. We find that though vorticity tilting helps generate the positive tendency of the ISO vorticity, the vorticity stretching enhances it. Further splitting of the stretching term helps us conclude that the convergence due to wind perturbations is the predominant term, representing feedback between dynamics and thermodynamics. We hypothesize that the weaker rainfall anomalies in the SBoB result from the weaker background column relative humidity and moisture, which do not allow the initial dynamic perturbations to grow as fast as they do in an environment with stronger background relative humidity and moisture (NBoB). Our study helps us understand the factors that control the ISO rainfall over a particular region and could help improve the model simulations.

Appendices

Appendix A: Conversion of kgm$^{-2}\text {s}^{-1}$ to mmday$^{-1}$

Noting that 1 kg of water occupies a volume of 1000 cm$^3$ which is equal to $10^{-3} \hspace{2mm} \text {m}^3$. A kg of water spread uniformly over an area of $m^2$ will be 1 mm high. Thus, 1 kgm$^{-2}$ of rain is equivalent to 1 mm of rainfall. And noting one day has approximately 86,400 s, Thus, we need to just multiply the value in kgm$^{-2}s^{-1}$ by 86,400 to convert into mmday$^{-1}$.

Appendix B: Relation between pressure vertical velocity and the convergence

Starting from the continuity equation continuity equation $\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}+\frac{\partial \omega }{\partial p} = 0$, noting that both the background and the anomalous components of velocities individually satisfy the continuity, when we integrate the above equation for the ISO winds, between the surface level $p_s$ and any other level p we get:

$$\begin{aligned} \int _{p_s}^{p} \left( \frac{\partial u^{\prime }}{\partial x} + \frac{\partial v^{\prime }}{\partial y} \right) dp = -\int _{p_s}^{p} \left( \frac{\partial \omega ^{\prime }}{\partial p}\right) dp \end{aligned}$$

(B1)

If we assume that vertical velocity at the surface is negligible (which is generally the case), we get:

$$\begin{aligned} \omega ^{\prime }(p) = - \int _{p_s}^{p} \left( \frac{\partial u^{\prime }}{\partial x} + \frac{\partial v^{\prime }}{\partial y} \right) dp \end{aligned}$$

(B2)

Which states that vertical velocity at any pressure level p, is equal to the vertical integral of convergence from the surface pressure ($p_s$)to that level p.

Appendix C: The vorticity budget

The vorticity equation in pressure coordinate system takes the form:

$$\begin{aligned}{} \underbrace{\Biggl \langle \frac{\partial \zeta }{\partial t} \Biggr \rangle }_{Tendency} &= - \underbrace{\Biggl \langle u \frac{\partial \zeta }{\partial x} + v \frac{\partial \zeta }{\partial y} + \omega \frac{\partial \zeta }{\partial p}\Biggr \rangle }_{Advection} - \underbrace{\Biggl \langle \left( f + \zeta \right) \left( \frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}\right) \Biggr \rangle }_{Stretching} \nonumber \\{} & {} \quad -\underbrace{\Biggl \langle \left( \frac{\partial \omega }{\partial x} \frac{\partial v}{\partial p} - \frac{\partial w}{\partial y}\frac{\partial u}{\partial p} \right) \Biggr \rangle }_{Tilting}- \underbrace{{\big \langle \beta v \big \rangle }}_{Beta} \end{aligned}$$

(C3)

where $\zeta = \frac{\partial v}{\partial x} - \frac{\partial u}{\partial y}$ is the z-component of vorticity and “$\Biggl \langle \Biggl \rangle$” represents the vertical integration from the surface pressure $p_s$ to 200 hpa level (Karmakar et al. 2022).