Distortion and Improvement Method of Location Quotient in Water Consumption Evaluation

Location quotient (LQ) is a widely used model to evaluate the spatial aggregation of water consumption. The conventional view is that all the domains of the LQ values in different water-using departments are [0, +∞). The larger the LQ is, the higher the degree of water consumption concentration is. With the water consumption structure evaluation of Northwest China as an illustration, this study shows the following: (i) The conventional LQ has a distortion phenomenon. The agricultural water consumption of Xinjiang Province accounts for more than 70.4% of the total water consumption in the whole study area, indicating that this department plays a dominant role. However, its conventional LQ is only 1.06, which is much less than the conventional LQs of the industrial and domestic water consumptions of Gansu Province and Shaanxi Province. (ii) The mathematical essence of this distortion in the conventional LQ model is that the conventional view that all the domains of the LQ values in different water-using departments are [0,+∞) is not tenable. The actual domain of the i-th department in the j-th province is [dij, dij−1], where dij is the water consumption proportion of this department accounting for the whole study area. For the department with high water consumption, the upper limit of its LQ is too small. Thus, the conventional LQ values of different water-using departments are not directly comparable. (iii) An improved LQ model is designed by introducing the standardization procedure. The improved LQ values of different water-using departments are [0, L], making them directly comparable. The improved LQ of the agriculture department in Xinjiang Province is 1.56, which is the most significant of all. This finding indicates that the water consumption in Northwest China is significantly concentrated in the agriculture department in Xinjiang. The evaluation results of the improved LQ model are more realistic and more suitable for the government’s water resources management than those of the conventional model.