*4.1. Data Sources*

The administration areas in Taihu Basin mainly include Jiangsu province, Zhejiang province, and Shanghai city. Taihu Basin is one of the most developed and most modernized region in China. By far, the amount of annual water use has reached 36.5 billion m3, while the amount of the perennial water resources of the basin is only 19.6 billion m<sup>3</sup> Therefore, the gap between supply and demand is great.

At present, in Taihu Basin, water shortage, worsening water pollution, and increasing demand of water resources have imposed undue pressure on the carrying capacities of the water resources and water environment. As a result, in order to promote the sustainable development of the basin, it is an inevitable requirement to clarify the initial provincial water rights and implement the allocation plan of Taihu Basin.

According to the materials of Taihu Basin and Southeast Rivers Water Resources Bulletin [16], some values of indexes for Jiangsu province, Zhejiang province, and Shanghai can be presented respectively as follows (we adopted the annual average values during 2011–2014 as the values of P2, P4, P11, and P12):


The other specific relevant data of Taihu Basin during 2011–2014 are summarized in Table 2.


**Table 2.** Provincial index values of Taihu Basin during 2011–2014.

Notes: Data sources: Taihu Basin and Southeast Rivers Water Resources Bulletin (2011–2014) and Water Quality Bulletin of Taihu Basin and Important Water Function Areas of Southeast Rivers (2011–2014).

### *4.2. Calculation of Initial Provincial Water Right Alloction*

Using the initial data of indexes in Table 2, selecting three typical parameter combinations of parameter *α* and *β* (*α* = 0.4, *β* = 0.6; *α* = 0.5, *β* = 0.5; *α* = 0.6, *β* = 0.4), according to the initial provincial water dynamic projection pursuit allocation model based on the self-adaptive chaotic algorithm in this paper, we can obtain related solutions by MATLAB 7.01 including the value of optimal projection direction *θ* = (*<sup>ω</sup>*1, ...*ω*12, *λ*2, *λ*3, *<sup>λ</sup>*4) and optimal projection value *d*∗(*k*). Using Equation (18), we can acquire the ratios of the initial provincial water rights allocation which are shown in Table 3.

According to the materials of Taihu Basin and Southeast Rivers Water Resources Bulletin, under the three different water frequencies including 50%, 75% and 90%, aiming for the planning year 2030, the distributable total amounts of initial water rights in Taihu Basin are 329.2 hundred million m3, 355.4 hundred million m3, and 392.6 hundred million m<sup>3</sup> respectively.


**Table 3.** Results of initial provincial water rights allocation in Taihu Basin.

According to the results of initial provincial water rights allocation in Table 3, we can acquire the larger weight of index *Pj* and year *Ti*, and also the ranking results of ratios for provincial initial water rights allocation which can be expressed in Table 4.


Consequently, according to the ratio of initial provincial water rights allocation which is shown in Table 3, using Equation (19), we can obtain multiple scenarios of the solutions for initial provincial water rights allocation under three different water frequencies in the planning year 2030 which can be presented in Table 5.

**Table 5.** Multiple scenarios of solutions for provincial initial water rights allocation in Taihu Basin, China (water frequencies of 50%, 75% and 90%, planning year 2030, Taihu Basin).

