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Rain shadows are dry areas on the lee side of mountains. Due to humid air condensing and precipitating as they are lifted up and over the mountains, they lose moisture by the time they reach the lee side, forming a relatively dry area.
What factors affect the size of this dry area, and how?
Of course, first you will need a collision zone where moist air collides with dry air - and therefore you will need to consider a considerable air flow in the opposite direction to the flow responsible for the rain shadow.
For example, in Eurasia, the Himalayan rain shadow extends up to the Kazhak steppes, until regional climatic effects of the Black Sea and Caspian Sea moderate the dryness. The Russian heartlands are blessed with the Dvina-Sukhona river; which starts at the lake Kubenskoye; which is blessed from Baltic Airs, still under the effects of the westerlies: thus you do not directly have a moist airstream colliding with the dry air from the opposite direction, but from the side.
In contrast, the German northeast, Mecklenburg-Vorpommern is within the rain shadow of the central German Harz mountains - but the river Oder is also inside the rain shadow. This brings us to the second point: topological relief. Is it sloping towards the rain shadow, such that the rain water from the other side drains into the rain shadow?
In this case, sooner or later you will form rivers - and lakes, unless the river meets the sea very quickly (as in the case of Germany and the Baltics). As soon as you have lakes, the rain shadow will be moderated.
Taking yet another example, the Kalaharis: east of Namibian Great Escarpment, and west of Highveld/Drakensberg. Thus Kalahari lies within a rain shadow from both east and west - and despite the river Okawango flowing in it, the climate is not moderated.
So there are uncountably many factors that contribute to your question.
Following the asymptotic model developed by Roe and Baker (2006) there are essentially four parameters that govern the dynamics:
$R_0 \to$ Vertically integrated condensation rate in a windward column of air.
$\Theta_{W,L} \to$ Ratio of the raindrop trajectories slope to the orographic slopes.
$\mu \to$ Ratio of mountain height to moisture scale height.
$\Psi_{W,L} \to $Ratio of mountain length to the formation length scale (of falling hydrometeors).
What affects the amount of precipitation on the leeward flank is a combination of all these parameters, the full expression is found in Roe and Baker (2006) and it is rather complicated. However, if we consider the limits $\Psi_{W,L}, \Theta_{W,L} >>1$, that is, steep trajectories of falling hydrometeors and large orogen size then asymptotically we can estimate the precipitation on the windward side
$$P_w = \frac{R_0}{\mu}(1-e^{-\mu})$$
and on the leeward side
$$P_L = \frac{R_0}{\Theta_L\mu}(e^{-\mu}).$$
The latter says that, for large orogen size as compared to moisture scale height (large $\mu$), the precipitation on the leeward side vanishes, $P_L \to 0$. This is because on the windward flank, the average precipitation approaches a finite upper bound as it depletes all moisture in the air column.
