Based on the multivariate joint probability distribution of the discharge and water quality indicators, this paper analysed the occurrence probabilities and improvement probabilities of combinations of water quality indicators under different discharge conditions and then presented a method for calculating the optimal discharge to seek a balance between the discharge dispatch and water quality improvement. The method was used to construct the relationship curve between the discharge and joint improvement probability used by a copula function and then calculate the critical point on the curve. The proposed method was applied to the Yi River Basin above Gegou Station with data composed of the discharge and main pollution indicators (NH₃-N and COD_Mn) from 1982 to 2015. The results showed that the trivariate joint probability distribution can more reasonably reveal the statistical characteristics of different combinations of discharge and water quality indicators. Furthermore, the optimal discharges and the corresponding improvement probabilities that improved NH₃-N and COD_Mn to different grades were calculated. The calculation method took the interdependence of multiple water quality indicators into account, thereby providing a more reasonable method for using discharge dispatch data to improve the river water quality.

The aim of this study is to reveal statistical characteristics and exceedence probability of discharge under the combined effect of climate change and human activities. The study is conducted in the Xiaoqing River in Jinan, China, based on data of discharge, land-use types and precipitation from the period 1970–2016. A multivariate joint probability distribution of the data is established to test the univariable, bivariable and trivariable change points. These are then used to calculate and analyse the risk probability of discharge exceeding the specific values under different conditions of precipitation and land-use type. The results show that the change point calculated by trivariate joint distribution can reduce the disturbance of the change point obtained with univariable or bivariable approach and reflect the changes of various factors in the hydrological processes more objectively. When the land-use type is taken into consideration, the trivariate distribution can reflect variation of hydrological processes more reasonably.

Discharge and water quality are two important attributes of rivers, although the joint response relationship between discharge and multiple water quality indicators is not clear. In this paper, the joint probability distributions are established by copula functions to reveal the statistical characteristics and occurrence probability of different combinations of discharge and multiple water quality indicators. Based on the data of discharge, ammonia nitrogen content index (NH₄⁺) and permanganate index (COD_Mn) in the Xiaoqing River in Jinan, we first tested the joint change-point with the data from 1980–2016, before we focused on analyzing the data after the change-point and established the multivariate joint probability distributions. The results show that the Gaussian copula is more suitable for describing the joint distribution of discharge and water quality, while the year of 2005 is a joint change-point of water quantity and quality. Furthermore, it is more reasonable to use the trivariate joint probability distribution as compared to the bivariate distributions to reflect the exceedance probability of water quality combination events under different discharge conditions. The research results can provide technical support for the water quality management of urban rivers.

To assess hydrologic regime more comprehensively using the distribution of hydrologic parameters, the probability density function of each parameter is obtained from parameter estimations and goodness-of-fit tests based on the principle of maximum entropy. Then, the Shannon entropy and weights for a multi-attribute decision-making process are used to calculate the degree of hydrologic alteration. This method is applied to the Xiaoqing River in the city of Jinan, China. The results indicate that the diversities of the monthly mean flow and annual extreme flow show decreasing trends that are attributable to human impacts, while the diversities of the timing of annual extreme, high and low flows, and the rate and frequency of flooding show increasing trends. Meanwhile, the overall degree of hydrologic alteration of the Xiaoqing River in Jinan is 0.747, which belongs to a change in the height. Thus, we suggest that the timing and volume of inter-basin water transfer should be reasonably regulated and that the regulation of peak flooding times and peak flow should be strengthened to make them conform to ecological characteristics during the water resource management of the Xiaoqing River.

The paper adopts 17 prefecture-level cities in Shandong Province as geographical unit, selects the indicators concerning regional sustainable development capacity from the perspective of resource, environment, social economy and efficiency support, etc., introduces the concepts of water footprint and evaluates the sustainable development condition of water resource and overall sustainable development condition in these geographical units. It’s indicated that the overall sustainable development capacity of the 17 prefecture-level cities in Shandong Province is ranked in descending order as follows: Weihai, Yantai, Qingdao, Binzhou, Zibo, Dezhou, Jining, Rizhao, Jinan, Laiwu, Linyi, Zaozhuang, Weifang, Dongying, Liaocheng, Taian and Heze. The score of sustainable development capacity achieved by the former nine is larger than 0 and the cities are in a state of sustainable development; while the score of sustainable development capacity achieved by the latter eight is smaller than 0 and the cities are in a state of unsustainable development. On this basis, the geographical units are further divided into four types by means of optimal partition method, i.e., with strong sustainable development capacity, with comparatively strong sustainable development capacity, with comparatively weak sustainable development capacity and with weak sustainable development capacity, and the sustainable development characteristics of each type are analyzed.

Land use optimization is essential for balancing the economic development, ecological protection, and sustainable management of regional landscapes. However, most existing frameworks focus primarily on land use area allocation while neglecting spatial pattern metrics, leading to fragmented landscapes and reduced ecological benefits. In this study, we propose a new multi-objective optimization framework that incorporates land use patch number as an explicit objective, providing a more direct way to make a trade-off between economic development, ecological protection, and landscape sustainability. Using Jinan’s Xiaoqing River Basin as a case study, we compare four scenarios, natural development, economic priority, ecological priority, and sustainable development, under both the traditional optimization framework (multi-objective allocation based on area and post-evaluation of spatial pattern based on land use simulation) and the proposed optimization framework. The results show that while the two frameworks yield similar levels of overall economic and ecological benefits, the traditional framework produces highly fragmented ecological land and overly aggregated construction land. In contrast, the new framework effectively reduces cropland and grassland fragmentation and enhances ecological land cohesion, generating more natural and sustainable landscape configurations. These findings highlight the importance of integrating spatial pattern objectives into land use optimization, providing a more comprehensive and spatially explicit approach to land use optimization, offering scientific support for rational land allocation and sustainable development within the urban river basin.