Very interesting paper on basin water yields

The very idea of budyko curve and other long term water balance approach is to characterise the basin water yeild capacity, or, the capacity of the basin to generate the discharge at the outlet, for a given precipitation. In other words, how the basin is parttioning the incoming inputs, rainfall, into different outflow (i.e ET and Q). In most studies, the formulations, the main driver that is asumed and explicitly accounted, is the basin energy-budget, in the form of PET. For me, though I didn't review literatures very well, it seems that the mere description and formulation of precipitaion, P, and potentail evapotranspiration, PET, would not explian the dischrage, Q, specially in the so-called a single hydrological year and so. I find that this (Zhou et al)\( ^{1} \) paper published in NATURE COMMUNICATIONS, and, is very promising with easy analytical formulation.
From the simplified water balance equation \[ P=E+R+ \Delta S \] where P is rainfall, E is evapotranspiration, and R runoff and \( \Delta S \) change in storage differences for a given hydrological year. Assuming the \( \Delta S = 0 \) for a given hydrological year, or even better for longer hydrological years, after re-arranging the equation will be:
\[ \frac{R}{P} = 1-\frac{E}{P} \]
From this point, there are some studies on how to estimate the \( E \) from the \( P \) and \( PET \) (e.g. Zeng and Cai, 2015\( ^{3} \) and papers cited therein), defines \( E \) as function of aridity index (\( PET/P \)), \[ E= P(1+ \frac{PET}{P} - (1+(\frac{PET}{P})w)^{\frac{1}{w}})) \]
This \( E \) formulation is substituted, and the reciprocal of the aridity index (\( P/PET \)), wetnes index, is used for analytical simplicity , i.e:
\[ \frac{R}{P}=(1+ (\frac{P}{PET})^{-m})^{\frac{1}{m}}-(\frac{P}{PET})^{-1} \]
which relates annual water yield ( R ) to a wetness index (precipitation/ potential evapotranspiration; P/PET) and watershed characteristics (m). m could be connected to many watershed characterstics, such as soil, vegetation, basin area, geomorphometry.

There is also an intersting efforts by Voepel et'al\( ^{2} \) on the controls of hydrologic partitioning at the catchment scale. One important thing in thier approach is the way they concptualize basin wetting and aridity in relation to the Normalized Difference Vegetation Index (NDVI). This would make the job easy, because it is easy to use NDVI from satellite.
Anyways, what interest me is \( m \) can be assessed with wide ranges of basin characterstics, and, further refine the equation with the dominante physical paramater(s).
References

1. \( ^{1} \) Guoyi Zhou, Xiaohua Wei, Xiuzhi Chen1, Ping Zhou, Xiaodong Liu, Yin Xiao, Ge Sun, David F. Scott, Shuyidan Zhou, Liusheng Han & Yongxian Su: Global pattern for the effect of climate and land cover on water yield.“ Nature Communications 6, Article number: 5918 DOI: 10.1038/ncomms6918
2. \( ^{2} \)Voepel, H., B. Ruddell, R. Schumer, P. A. Troch, P. D. Brooks, A. Neal, M. Durcik, and M. Sivapalan (2011), Quantifying the role of climate and landscape characteristics on hydrologic partitioning and vegetation response, Water Resour. Res., 47, W00J09, doi:10.1029/2010WR009944.
3. \( ^{3} \)Ruijie Zeng, Ximing Cai. (2015) Assessing the temporal variance of evapotranspiration considering climate and catchment storage factors. Advances in Water Resources 79, 51-60.
4. Gerrits, A. M. J., H. H. G. Savenije, E. J. M. Veling, and L. Pfister (2009), Analytical derivation of the Budyko curve based on rainfall characteristics and a simple evaporation model, Water Resour. Res., 45, W04403, doi:10.1029/2008WR007308