The efforts to management agricultural non-point source pollution from the field to watershed scale is an ongoing challenge that needs to take into account trade-offs between environmental and economic objectives. Best management measures (BMPs) are considered as an effective means to achieve this balance in the management of agricultural non-point source pollution. Many studies have focused on a single spatial scale for placement of the BMPs, however, the effectiveness in improving water quality at different scale will affect by many factors such as the land use, soil type and the river network and so on. In order to demonstrating the relationship or impact of spatial scale changes on the allocation and effectiveness of BMPs. The present study attempts to development a novel multi-scale model framework and indices as a decision support platform for solve the impact of spatial scale change on the optimization of best management measures in the Chaohe River Watershed in Beijing and Hebei province. And used it in a drinking water source area which was affected by the agricultural nonpoint source pollution in recent decades in Beijing, China. A series of the utility functional between the utility of the water quality improvement and the number of watersheds, watershed size, the unit cost of BMPs and integrated these three functional relations by Generalized Reduced Gradient Algorithm. We found that the nonlinear threshold response function can play a key role in the configuration of BMPs from field to watershed scale. The results show that 1) the utility functions for pollution load reduction and the number of watersheds can be described by the log-sigmoid curve, and the optimal number of watershed for total nitrogen (TN) and total phosphorus (TP) control are 25 and 23 respectively, 2) the most utility function for the pollution load reduction and the mean sub-watershed area is exponential function curves, and the optimal mean sub-watershed areas are168 km2 and 214 km2 for TN and TP, respectively, 3) the relationship between pollution load reduction and cost of per unit after BMPs implemented can be drawing by the logistic curves, and the optimal average unit cost are 4622 and 7692 CNY$ha
۱ for TN and TP, respectively, 4) the comprehensive optimal of these above functions shown that the total cost of BMP plans is 2.01 107 and 4.7 107 CNY for TN and TP, respectively at the trad-offs scenario. This study will provide a systematic approach to determine more reasonable and feasible management practices system on more reasonable spatial scale for the protection of water quality and safety in watershed.

Introduction

In recent years, agricultural nonpoint source (ANPS) pollution has become the main source of eutrophication in most lakes and rivers. The wicked nature of this problem poses substantial challenges to the design and implementation of effective and efficient management policies in the worldwide(Shortle and Horan, 2017). Agricultural activities, such as livestock and poultry breeding and rural activities, were found to be the major sources of ANPS, with more than 50% of N and P loadings in many watersheds in China (Qu and Fan, 2010). Increased nutrients loading accelerates eutrophication of surface waters (Conley et al., 2009). Total nitrogen and total phosphorus from agricultural nonpoint source pollution can be successfully controlled by implementing the structural or non-structural BMPs of the right type, in the right place, in the right combinations, and right level of adoption within different spatial scale watershed (Cherry et al., 2008; McDowell et al., 2014; Xu et al., 2017). However, hydrologic, meteorological, and geomorphologic factors at field, farm, sub-watershed and watershed scales, are important factors that confound response to ANPS pollution (Dai et al., 2016; Panagopoulos et al., 2011; PetitBoix et al., 2017). Their effectiveness for water quality improvement through pollution load reduction must be quantified before BMPs are adopted at various spatial and temporal scales. Although the effectiveness of individual BMPs has been usually assessed by field plots (generally less than 1.0 ha), it is necessary to find out the trade-offs of BMPs from the field to watershed scale to ensure that practices taken will be adequate to achieve the water quality goals (Smets et al., 2008; Wu et al., 2018; Yang and Best, 2015).