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地球信息科学学报 >

2018 , Vol. 20 >Issue 6: 781 - 790

DOI: https://doi.org/10.12082/dqxxkx.2018.170622

2017年中国地理信息科学理论与方法学术年会优秀论文专辑

以坡位为空间配置单元的流域管理措施情景优化方法

  • 高会然 , 1, 2, 3 ,
  • 秦承志 , 1, 2 ,
  • 朱良君 1, 2 ,
  • 朱阿兴 1, 4, 5, 6, 7 ,
  • 刘军志 4, 5, 6 ,
  • 吴辉 8
展开
  • 1. 中国科学院地理科学与资源研究所 资源与环境信息系统国家重点实验室,北京 100101
  • 2. 中国科学院大学,北京100049
  • 3. 中国科学院遥感与数字地球科学研究所 数字地球重点实验室,北京 100094
  • 4. 南京师范大学 虚拟地理环境教育部重点实验室,南京 210023
  • 5. 江苏省地理环境演化国家重点实验室培育建设点,南京 210023
  • 6. 江苏省地理信息资源开发与利用协同创新中心,南京 210023
  • 7. 威斯康星大学（麦迪逊）地理系,威斯康星州 WI 53706,美国
  • 8. 杭州电子科技大学智慧城市研究中心,杭州 310012
*通讯作者：秦承志（1977-）,男,研究员,从事数字地形分析、流域系统模拟和情景分析研究。E-mail:

作者简介：高会然（1992-）,男,博士生,现从事遥感与寒区流域水文过程模拟研究。E-mail:

收稿日期: 2017-12-21

  要求修回日期: 2018-02-02

  网络出版日期: 2018-06-20

基金资助

国家自然科学基金项目（41431177、41422109）

资源与环境信息系统国家重点实验室自主部署项目（O88RA20CYA)

收起

Using Slope Positions as Spatial Units for Optimizing Spatial Configuration of Watershed Management Practices

  • GAO Huiran , 1, 2, 3 ,
  • QIN Chengzhi , 1, 2 ,
  • ZHU Liangjun 1, 2 ,
  • ZHU A-Xing 1, 4, 5, 6, 7 ,
  • LIU Junzhi 4, 5, 6 ,
  • WU Hui 8
Expand
  • 1. State Key Laboratory of Resources and Environmental Information System, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China
  • 2. University of Chinese Academy of Sciences, Beijing 100049, China
  • 3. Key Laboratory of Digital Earth Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100094
  • 4. Key Laboratory of Virtual Geographic Environment (Nanjing Normal University), Ministry of Education, Nanjing 210023, China
  • 5. State Key Laboratory Cultivation Base of Geographical Environment Evolution (Jiangsu Province), Nanjing 210023, China
  • 6. Jiangsu Center for Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing 210023, China
  • 7. Department of Geography, University of Wisconsin-Madison, Madison, WI 53706, USA
  • 8. Smart City Zhejiang, Hangzhou Dianzi University, Hangzhou 310012, China;
*Corresponding author: QIN Chengzhi, E-mail:

Received date: 2017-12-21

  Request revised date: 2018-02-02

  Online published: 2018-06-20

Supported by

National Natural Science Foundation of China, No.41431177,41422109

Innovation Project of LREIS, No.O88RA20CYA

Copyright

《地球信息科学学报》编辑部 所有
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摘要

基于流域过程模型的BMP情景分析是当前流域管理措施评价、非点源污染控制等研究应用中广泛采用的方法,但其通常采用的BMP空间配置单元（地块、农场、水文响应单元或子流域）与坡面上的地形部位关系较弱,难以有效地根据坡面过程特点表达坡面上多种BMP之间的空间配置关系,影响了BMP情景优化效率和结果的合理性。为此,本文提出以坡位单元作为BMP空间配置单元,将各种BMP在不同坡位间合理的空间配置关系显式表达为基于坡位的空间配置规则,通过结合NSGA-II优化算法建立了一套基于坡位单元的BMP空间配置优化方法。应用案例表明,本文构建的基于坡位单元的BMP情景优化方法可有效利用基于坡位的空间配置规则进行BMP情景优化,优化所得的BMP空间配置方案更为合理,优化效率较高。

关键词： 流域过程模拟; 最佳管理措施; 情景分析; 空间配置单元; 坡位; 遗传算法

本文引用格式

高会然 , 秦承志 , 朱良君 , 朱阿兴 , 刘军志 , 吴辉 . 以坡位为空间配置单元的流域管理措施情景优化方法[J]. 地球信息科学学报, 2018 , 20(6) : 781 -790 . DOI: 10.12082/dqxxkx.2018.170622

Abstract

Scenario analysis based on watershed process model is a widely used method for evaluating watershed management practices (BMP) and controlling non-point source pollution. The commonly used spatial configuration units in current scenario analysis include fields, farms, hydrologic response units, and sub-basins. The weak spatial relationships between these spatial units and the topographic positions along hillslope make the use of these spatial units difficult to effectively represent the effect of different BMP on hillslope processes, and thus affect the efficiency and reasonability of optimized scenarios. In this paper, slope positions are used as the spatial configuration units of BMP under the framework of spatially distributed watershed process model and intelligent optimization method for BMP scenarios. Thus, the knowledge of the spatial relationships between BMP and slope positions can be explicitly considered during optimization. A spatially distributed watershed process model (i.e., SEIMS) and an intelligent optimization algorithm (i.e., the genetic algorithm NSGA-II) were combined in this framework in this paper. A small watershed of red soil dominant region in the east of Hetian county, Changting city, Fujian province, was selected as the case study area. The BMP knowledge base including the relationship between five BMP used in this area and slope positions was built for the study area. The experimental results showed that slope position units can well support the description and application of the knowledge on the spatial configuration of different BMP, compared with the BMP configuration units of fields with upslope-downslope relationship. The proposed method can use BMP spatial configuration knowledge to provide optimal BMP scenarios reasonably and effectively, compared with the random optimization method, a typical BMP scenario optimization method of using NSGA-II optimization algorithm with operations of population initialization, crossover, and mutation randomly.

Key words： watershed process modeling; best management practices; scenario analysis; spatial units; slope position; genetic algorithm

1 引言

流域最佳管理措施（Best Management Practices, BMP）是通过对流域径流、泥沙、污染物的产生、输移等过程的控制,防治水土流失、控制和削减非点源污染、保护流域生态环境而采取的一系列管理措施[1],在水土保持及非点源污染治理方面日益得到广泛应用[2,3]。流域治理中往往需要组合应用多种不同功能的BMP,不同的BMP空间配置会得到不同的环境效益[4],例如,蔡强国等[5]根据南方红壤区水土流失特点和我国水土保持综合治理经验,提出流域综合治理模式（图1）,经验性地总结了多种BMP与坡面不同地形部位间有效的空间配置关系,定性地描述有益于流域综合治理的多种BMP空间组合经验。
Fig. 1 Illustration of a comprehensive management scheme for watershed soil and water conservation in southeast China

图1 流域水土保持综合治理模式示意图[5]

基于流域过程模型的BMP情景分析方法（简称流域BMP情景分析）是利用能够精细模拟流域地理过程的流域过程模型[6]（尤其是全分布式流域模型）,对流域内可能的BMP空间配置方案（称为BMP情景）实施后将会产生的效果进行模拟、评价分析,通过与优化算法相结合,可高效自动地进行流域BMP情景优化。该方法由于其灵活性和预测性而逐渐成为流域水土流失治理和农业非点源污染控制等管理工作的重要决策支持手段[7,8,9]。
BMP空间配置单元应能较好地对应坡面地表过程特征单元,合理体现BMP空间配置关系[10,11]。流域BMP情景分析通常采用的BMP空间配置单元包括子流域、水文响应单元（HRU）、地块、农场等。子流域作为BMP空间配置单元时[12],虽然对上下游的空间关系有所体现,但难以有效表达流域内综合管理措施空间组合关系。水文响应单元（HRU）是SWAT等模型所采用的空间单元,指下垫面特征相对单一、均匀、具有相似水文特性的区域[13]。但是以HRU作为BMP空间配置单元的研究中[14,15],BMP配置的空间位置并未被显式体现,难以反映BMP之间的相互作用关系,如上游配置BMP通过控制径流过程影响下游BMP[16]。
为了使BMP情景便于在实施中管理操作,地块[17,18]、农场[2]常被作为BMP配置单元的划分依据。传统的地块单元一般根据土地所有者或土地利用类型划分,易受现有土地利用、土壤类型等边界的影响,农场则更多考虑了权属关系而非自然过程单元。当传统地块单元的划分精细到一定程度时（没有跨坡面分布的情况,甚至精细到单个网 格[19]）,同样可以体现坡面自然过程,但是此时配置单元过于细碎且数量较多,将导致优化等计算负担加重,而且不利于实际的BMP实施。因此,它们用作BMP空间配置单元的通常情况下,难以合理地体现坡面上自然过程的上下游关系,且在情景分析时难以有效表达中国的流域综合治理模式。
针对现有空间单元难以考虑BMP空间配置关系的问题,Wu等[20]根据流向图和土地利用类型划分出具有上下游关系的“地块”,考虑了单一地块的BMP选取规则及相邻地块的BMP配置约束关系,但是其“地块”单元与坡面地形部位[21]（如能够体现坡面自然过程和地形特征的坡位单元）缺乏对应,难以根据坡面过程特点表达流域综合治理模式中对坡面上多种BMP空间配置关系的经验性知识。因此,流域BMP情景分析目前使用的BMP空间配置单元与地形部位关系较弱,难以有效表达坡面上多种BMP的空间配置关系。
针对上述问题,本文提出以坡位单元作为BMP空间配置单元。坡位是对应于坡面地形部位的基本地形元素单元,不同坡位的空间组合形成了完整的坡面形态,是坡面过程的综合体现[22]。流域综合治理模式通常也是在坡面尺度上定性描述多种管理措施间的空间配置关系[4],是按照坡位功能特征对BMP空间配置的指导性知识。以坡位单元为BMP空间配置单元,将BMP在不同坡位间合理的空间配置关系表达为基于坡位的空间配置规则,与智能优化算法相结合,从而可建立一套基于坡位单元的BMP空间配置优化方法。

2 基于坡位单元的流域BMP情景 优化方法

2.1 方法框架

本文提出在现有的空间全分布式流域过程模型结合智能优化算法的BMP情景优化方法框架 下[20,23],以坡位作为流域BMP情景分析的空间配置单元进行流域BMP情景分析（图2）。其方法设计主要包括2个方面：① 坡位单元划分;② 将现有的按照坡位功能特征指导BMP空间配置的经验性知识,显式表达为BMP在不同坡位上的空间配置规则,使得采用坡位单元的智能优化算法可以利用这些知识进行BMP情景优化。
Fig. 2 Framework of BMP scenario optimization using slope positions as spatial configuration units

图2 基于坡位单元的BMP情景优化方法框架

2.2 坡位单元划分

简单但不失一般性,本文暂将坡面自上而下分为3类坡位作为BMP空间配置单元,即山脊、背坡和沟谷[16]。
在实际划分坡位单元时,利用基于各坡位典型位置的坡位空间信息定量化方法[24,25,26],在栅格DEM上计算后“硬化”分类[27]得到确定性坡位。原方法采用山脊、坡肩、背坡、坡脚和沟谷等5类坡位,其中坡肩、坡脚通常范围较窄,主要属于坡位过渡区（对应的隶属度通常并不明显高于这些位置对相邻坡位类型的隶属度）,因此可将坡肩、坡脚两类坡位的位置根据其对相邻坡位的隶属度归并到相近的其它坡位类别（坡肩位置可归类至山脊或背坡,坡脚可归类至背坡或沟谷）。本文对这些位置根据其相似度向量中第二大相似度原则进行归类,例如某个栅格上对山脊、坡肩、背坡、坡脚和沟谷的相似度分别为S1、S2、S3、S4和S5,如果S2>S1>S3>S4>S5,原方法硬化后识别为坡肩位置,本方法根据其第二大相似度对应山脊,将该栅格归类为山脊。
对于坡位分类后细碎分散的栅格,采用K最近邻分类方法[28,29],通过算法自动合并到其邻域内较为集中的坡位类型中,使得坡位单元具有较平滑的边界,以便于BMP实施。除了保留较狭长山脊的完整性之外,对于背坡、沟谷单元,以子流域作为其空间范围约束,跨越子流域边界的背坡、沟谷单元将做分割处理。

2.3 坡位功能指导下的BMP空间配置知识表达与应用方法

基于坡位功能的BMP空间配置知识[20]是指导BMP空间配置和表达其空间关系的依据,主要包括2个方面：① 某类坡位单元上适合配置何种BMP,即在坡位功能的指导下进行BMP空间配置;② 坡位单元之间明确的流向关系,这是显式设置BMP空间配置关系的基础,如上游坡位单元配置某种BMP后,其下游单元则适合配置何种BMP,从而体现BMP之间的空间配置关系。
上述BMP空间配置知识可显式表达为BMP在坡位上的空间配置规则,这些规则在应用于流域BMP情景优化时,与所用的智能优化算法密切关联。本文采用带精英策略的非支配排序遗传算法[30]（Non-dominated Sorting Genetic Algorithms-II,NSGA-II算法）来解决BMP空间配置的多目标优化问题。基于坡位的BMP空间配置知识在优化算法中的应用体现在NSGA-II算法中的种群初始化、交叉/变异算子生成下一代BMP情景等2个过程中：
（1）种群初始化。为应用基于坡位的BMP空间配置规则,对优化算法中传统的种群初始化方式进行改进：① 在不同坡位类型的BMP空间配置单元上按照这些规则配置可能的某种BMP（或无配置）;② 对于已有BMP配置的坡位单元,进行BMP空间配置冲突检查,以确保BMP情景的合理性。
（2）交叉/变异。在生成下一代BMP情景的过程中,进行交叉操作时随机选择一个配置单元为断点,交叉转换存储位置相邻的两个BMP情景（即遗传算法中的染色体）,然后检查交换后的BMP情景是否符合BMP空间配置规则,若发生冲突,则进行更改;进行变异操作时随机选择一个或多个变异位置,根据其上游坡位单元配置的BMP及配置规则产生当前坡位单元适宜的BMP。

3 应用案例

3.1 研究区概况

本文以福建省长汀县河田镇东部的游屋圳小流域作为研究区（图3）,流域面积约5.3 km2,平均坡度15.9°,河流沿岸地势较平坦。游屋圳小流域是长汀地区流域水土流失重点治理区域,流域内水土流失较强烈的区域分布较广,在距离居民地较近以及土层较厚的地区尤其严重。当地水保部门根据小流域特点对其进行综合治理,充分利用该流域雨量丰富、温度适宜等自然特点,对耕作措施、植被措施、工程措施合理配置,取得了较好的水土流失治理效果和良好的社会和经济效益。游屋圳小流域的自然特征、水土流失特点和治理过程在福建红壤区均具有代表性。
Fig. 3 Maps of Youwuzhen watershed

图3 游屋圳小流域空间位置及DEM

空间全分布式流域过程模型在模拟过程中需要能够描述研究区具体情形的土壤、地形、水文等数据,本文收集了研究区DEM、土壤类型、土地利用等空间数据和降水、流量等水文数据,其中土壤类型为长汀县第二次土壤普查1:5万数据,其他空间数据分辨率统一为10 m。

3.2 研究区BMP及空间配置知识

本文主要考虑了研究区中5种典型的BMP：封禁治理、生态林草、经济林果、低效林改造、果园坡改梯（表1）。6种BMP经济成本价格标准按水利部《开发建设项目水土保持工程概（估）算定额》、2010年度《长汀规划》（2010-2017年8年规划）等估算（表2）。根据BMP功能和特点,将生态林草与坡改梯定义为不适合空间相邻的两种BMP,考虑的BMP空间配置知识如表1所示,这些知识用于约束本文方法在智能优化时的种群初始化和交叉/变异时的BMP配置。
Tab. 1 Relationships between BMP and slope positions

表1 5种BMP及其适宜配置的坡位类型

BMP 措施特点 治理效果 适宜配置坡位
封禁治理 适宜在流域边缘、离居民点较远、高山陡坡的轻度水土流失地实施 促进植物的生长,增大冠层截流量;提高蓄水保土能力 山脊、背坡
生态林草 在未达到封育成林强度的水土流失地和园地上方种植生态林草 加快地表植被覆盖;增加地表粗糙度,降低坡面汇流速度 山脊、沟谷
经济林果 在坡地较缓、水肥条件较好的山坡中、下部种植经济林果 加速土壤改良,防止水土流失;促进果树生长 沟谷
低效林改造 适宜在立地条件较差的中度水土流失地与立地条件较好的强度流失坡地实施 促进植物的生长;增加地表粗糙度;降低坡面汇流速度 背坡
果园坡改梯 针对原有埂沟残缺造成水土流失严重之地进行整改 减小山坡的坡度,降低径流速度;减少径流的侵蚀力 背坡
Tab. 2 Economic costs and benefits of different BMP

表2 不同BMP的经济成本及经济效益

BMP 成本/（万元/km2） 年均效益/（万元/km2）
封禁治理 1.80 5.94
生态林草 72.88 20.64
经济林果 113.16 18.75
低效林改造 33.43 11.64
果园坡改梯 78.34 1312.50

3.3 坡位单元划分

研究区坡位单元划分结果如图4所示,共452个坡位单元,其中山脊、背坡和沟谷的单元个数分别为244、118和90。
Fig. 4 Map of slope position units of the study area

图4 研究区坡位单元划分结果

3.4 全分布式流域过程模型建模

流域过程模型需为空间全分布式,才能精细刻画不同空间配置的管理措施对流域过程的影响[30]。本文选取全分布式流域建模框架（Spatially Explicit Integrated Modeling System, SEIMS）[31,32]进行流域过程建模,SEIMS采用模块化的设计,以栅格为空间模拟单元刻画水流空间运动。
根据研究区特点,考虑水文、侵蚀等过程进行建模。其中,土壤侵蚀模块考虑坡面侵蚀和河道侵蚀,坡面侵蚀采用MUSLE模型,河道侵蚀采用简化的Bagnold侵蚀方程,详见表3。
Tab. 3 Sub-process modules used in SEIMS model for the Youwuzhen watershed

表3 游屋圳小流域SEIMS建模子过程模块列表

过程 子过程 模块算法
气候、降水 气象数据进行泰森
多边形空间插值
坡面过程 土壤温度 Finn Plauborg方法
潜在蒸散发 Priestley-Taylor公式
植被冠层截留 Maximum Storage方法
入渗/地表径流 Modified Rational方法
填洼/地表径流 Linsley方法
坡面侵蚀 MUSLE模型
渗漏 Brooks-Corey公式
壤中流 Darcy定律及运动波方程
植物潜在蒸腾及
土壤实际蒸发		 SWAT模拟方法
植物生长 简化的EPIC模型
地下水 线性水库
坡面汇流 瞬时地貌单位线法
侵蚀坡面汇流 瞬时地貌单位线法
河道汇流 河道汇流 Muskingum方法
河道侵蚀 简化的Bagnold公式
模型建模时段设置为2013年1月1日至2014年12月31日,模拟步长为1 d,以2014年作为率定期对模型进行参数率定。图5为2014年流域出口径流率定期结果,Nash效率系数为0.62,R2为0.70,水文模拟效果良好;图6为2014年流域出口泥沙含量率定期结果,Nash效率系数和R2分别为0.23、0.46。泥沙含量率定结果较差,一是由于实测验证数据的质量有待考证,二是由于模型缺乏参数敏感性分析,导致率定结果尚有不足,有待进一步研究。率定结果总体上可刻画研究区水文过程,本文应用案例是在日尺度上的模拟,对不同BMP配置方法间模型模拟的相对结果进行对比分析,因此可接受该率定模型用于BMP情景的模拟评价。
Fig. 5 Result of runoff simulation at the watershed outlet of the study area in 2014

图5 2014年研究区流域出口径流模拟率定结果

Fig. 6 Result of sediment simulation at the watershed outlet of the study area in 2014

图6 2014年研究区流域出口含沙量模拟率定结果

3.5 流域BMP情景优化目标

流域BMP情景优化目标包括环境目标和经济目标2个方面,即实现土壤侵蚀量最小化（等同于减沙效益最大化）和BMP经济成本最小化。
BMP情景的土壤侵蚀量计算公式如下：
F sed X = ∑ 1 m x i （1）
式中：Fsed(X)表示实施BMP后的土壤侵蚀量/kg;SED(xi)表示模型输出每个栅格上的侵蚀量/kg;m表示流域内有效栅格数。
BMP情景的成本计算公式如下：
F cost X = ∑ 1 n C x i × A i （2）
式中：Fcost（X）是BMP情景的经济成本/万元;C(xi)表示单位面积上该种BMP实施费用/万元。Ai表示第 i个配置单元的面积（m2）;n表示配置单元个数。

3.6 评价实验设计

为探讨基于坡位单元的BMP空间配置优化方法的高效性和合理性,本文设计两组对比实验：
（1）采用不同空间配置单元的对比实验。在流域过程模型、BMP模型参数、NSGA-II优化算法参数等条件相同的情况下,将本文方法与目前空间配置单元考虑上下游关系的方法——基于上下游关系“地块”单元的优化方法[20]（简称上下游地块优化方法）进行对比分析;
（2）是否使用基于坡位的BMP空间配置知识的对比实验。将坡位单元作为BMP空间配置单元,在流域过程模型、BMP模型参数、NSGA-II优化算法参数等条件相同的情况下,将本文方法与不使用基于坡位的BMP配置规则、完全随机的BMP情景优化方法[1]（以下简称随机优化方法）进行对比分析。
上述实验中,NSGA-II优化算法的主要参数均设置为：种群规模为60,最大进化代数为50,交叉概率0.75,变异概率0.1。
对实验结果主要根据近似Pareto最优解（即Pareto前沿）进行对比分析,同时结合情景优化结果的BMP空间配置合理性进行讨论。

3.7 结果与讨论

3.7.1 采用不同空间配置单元的对比实验
本文方法和基于上下游地块单元优化方法在不同运行代数（即5、10、25和50代）时的Pareto前沿如图7所示,本文基于坡位单元的BMP情景优化方法在每个进化代数下均具有优势,在同样（甚至更低）的经济成本下可获得较高的减沙效益。
Fig. 7 Comparison of the Pareto fronts derived from the proposed method and the method based on the fields with the upslope-downslope relationship under different generations

图7 本文方法和基于上下游地块单元优化方法在不同运行代数下的Pareto前沿对比

图7显示,由于2种方法均采用一致的BMP空间配置规则,因此投入的经济成本范围较一致。当优化算法进化代数较小时（小于10代）,本文方法与上下游地块优化方法的Pareto前沿有一定的重叠,但前者总体要优于后者。随着优化代数的增加（在25代之后）,本文方法的优势更加明显。上下游地块优化方法虽然考虑了相邻地块单元的BMP上下游约束关系,但由于其地块单元的划分依据为土地利用类型和流向图,与地形部位的对应关系较弱,因此不能有效结合BMP空间配置知识进行优化,导致优化效果不如采用坡位单元的本文方法。
3.7.2 是否使用基于坡位的BMP空间配置知识的 对比实验
基于坡位单元的BMP情景优化中,采用基于坡位的BMP空间配置知识时的本文方法和随机优化方法在不同运行代数（5、10、25和50代）时的Pareto前沿对比如图8所示。结果显示,在同样进化代数下,本文方法较随机优化方法具有明显优势。在同样的减沙效果下,由于本文方法可有效利用基于坡位的BMP空间配置知识,优化结果需要投入的经济成本远低于随机优化方法的结果（如当优化代数为50,产生土壤侵蚀量为45万吨时,本文方法所得到优化结果的经济投入约为100万元,而随机优化方法产生的结果需投入经济成本超过150 万元）。
Fig. 8 Comparison of the Pareto fronts derived from the proposed method and the random optimization method under different generations with a population of 60

图8 本文方法与随机优化方法在种群规模为60时不同运行代数下的Pareto前沿对比

如图8所示,当流域治理投入的经济成本持续增加时（大于150万元,50代时优化结果的最大经济投入达300万元）,随机优化方法所得优化情景的环境效益不断改善,但使用基于坡位的BMP空间配置知识进行优化的本文方法将不再能优化出新的BMP情景。这是由于本文方法使用优化算法时,对种群初始化和交叉、变异操作等过程运用基于坡位的BMP空间配置规则加以限制,避免不合理（即不符合实际BMP实施知识,比如在坡位类型为沟谷的配置单元上配置封禁治理措施）的BMP情景产生,因此难以产生BMP覆盖度较大（所需经济投入更高）的情景。
对于随优化机方法所产生的具有较高经济成本和减沙效益的BMP优化情景,取图9（a）所示的一个情景（经济成本为233.25万元、年侵蚀量为385 225.21 t）分析其合理性。图9(b)中橙色斑块代表评估为BMP配置不合理的单元,比如在沟谷单元上配置封禁治理措施、在山脊单元上配置果园坡改梯措施、以及生态林草与果园坡改梯存在配置上的冲突等,均违反了当地BMP实施时的空间配置经验性知识。该情景下配置不合理单元的面积约占到研究区配置BMP区域面积的50%,虽然模拟评价显示通过大量的成本投入,可获得更好的模拟效果,但是这种BMP情景存在较多不符合BMP空间配置经验性知识之处,难以实施,该BMP情景应是不实际的。
Fig. 9 An selected BMP scenario with high cost generated by the random optimization method

图9 随机优化方法产生的一个高成本BMP优化情景

4 结论

本文以流域最佳管理措施（BMP）情景分析为研究对象,针对当前使用的BMP空间配置单元与地形部位关系较弱,难以体现坡面上BMP空间配置关系的问题,提出了一种基于坡位单元的BMP空间配置优化方法,以有效体现坡面自然过程、表达流域综合治理中的BMP空间组合配置经验。
该方法结合空间全分布式流域过程模型（SEIMS）和智能优化算法（NSGA-II算法）,运用规则化的BMP空间配置知识进行了应用案例实验。分析结果表明,坡位单元可有效支持利用符合坡面过程特点的流域综合治理经验（即体现坡面上多种BMP的空间配置关系）,进行BMP情景优化。相比上下游地块优化方法和随机优化方法,本文方法所得情景优化结果在同样或是较低的经济成本下,可获得更高的减沙效益,且优化配置方案更为合理。

The authors have declared that no competing interests exist.

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[19]
Gaddis E B, Voinov A, Seppelt R, et al.Spatial optimization of best management practices to attain water quality targets[J]. Water Resources Management, 2014,28(6):1485-1499.Diffuse nutrient loads are a common problem in developed and agricultural watersheds. While there has been substantial investment in best management practices (BMPs) to reduce diffuse pollution, there remains a need to better prioritize controls at the watershed scale as reflected in recent US-EPA guidance for watershed planning and Total Maximum Daily Load development. We implemented spatial optimization techniques among four diffuse source pathways in a mixed-use watershed in Northern Vermont to maximize total reduction of phosphorus loading to streams while minimizing associated costs. We found that within a capital cost range of 138 to 32102USD ha -1 a phosphorus reduction of 0.29 to 0.3802kg02ha 611 02year 611 , is attainable. Optimization results are substantially more cost-effective than most scenarios identified by stakeholders. The maximum diffuse phosphorus load reduction equates to 1.2502t02year 611 using the most cost-effective technologies for each diffuse source at a cost of $3,464,260. However, 1.1302t02year 611 could be reduced at a much lower cost of $976,417. This is the practical upper limit of achievable diffuse phosphorus reduction, above which additional spending would not result in substantially more phosphorus reduction. Watershed managers could use solutions along the resulting Pareto optimal curve to select optimal combinations of BMPs based on a water quality target or available funds. The results demonstrate the power of using spatial optimization methods to arrive at a cost-effective selection of BMPs and their distribution across a landscape.

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[20]
Wu H, Zhu A X, Liu J, et al.Best management practices optimization at watershed scale: incorporating spatial topology among fields[J]. Water Resources Management, 2018,32(1):155-177.Abstract Best management practices (BMPs) are widely used to reduce nonpoint source pollutions. In order to obtain cost-effective BMPs configurations, optimization methods are introduced. Recent studies show that knowledge on BMP placement can be used to improve existing algorithms for BMPs optimization. However, some important knowledge has not been fully utilized yet, one of which is about the spatial topology among fields and BMPs interactions. In this paper, a new method for BMPs optimization was proposed, which incorporated knowledge of BMPs interactions into a multi-objective genetic algorithm (i.e., 蔚-NSGAII) based on spatial topology among fields. Then this method was applied to the BMPs optimization in a small agricultural watershed in Southern Manitoba of Canada, and the performance was compared with those of conventional method. In order to make a comprehensive comparison, experiments were conducted under different population sizes (i.e., 60, 100, and 200) and different numbers of fields (i.e., 29, 52, and 79). The results showed that the proposed method was superior to conventional method on the aspect of greater sediment reductions (2% - 17%) at the same cost, and the Pareto curves obtained by the proposed method were more complete. This study demonstrated that incorporating spatial topology among fields into BMPs optimization can lead to better results and this finding could provide valuable references to similar studies.

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[21]
Rathjens H, Bieger K, Chaubey I, et al.Delineating floodplain and upland areas for hydrologic models: A comparison of methods[J]. Hydrological Processes, 2016,30(23),4367-4383.Abstract A spatially distributed representation of basin hydrology and transport processes in hydrologic models facilitates the identification of critical source areas and the placement of management and conservation measures. Floodplains are critical landscape features that differ from neighbouring uplands in terms of their hydrological processes and functions. Accordingly, an important step in watershed modelling is the representation of floodplain and upland areas within a watershed. The aim of this study is (1) to evaluate four floodplain–upland delineation methods that use readily available topographic data (topographic wetness index, slope position, uniform flood stage, and variable flood stage) with regard to their suitability for hydrological models and (2) to introduce an evaluation scheme for the delineated landscape units. The methods are tested in three U.S. watersheds ranging in size from 334 to 62965km2 with different climatic, hydrological, and geomorphological characteristics. Evaluation of the landscape delineation methods includes visual comparisons, error matrices (i.e. cross-tabulations of delineated vs reference data), and geometric accuracy metrics. Reference data were obtained from the Soil Survey Geographic (SSURGO) database and Federal Emergency Management Agency (FEMA) flood maps. Results suggest that the slope position and the variable flood stage method work very well in all three watersheds. Overall percentages of floodplain and upland areas allocated correctly were obtained by comparing delineated and reference data. Values range from 83 to 93% for the slope position and from 80 to 95% for the variable flood stage method. Future studies will incorporate these two floodplain–upland delineation methods into the subwatershed-based hydrologic model Soil and Water Assessment Tool (SWAT) to improve the representation of hydrological processes within floodplain and upland areas. Copyright 08 2016 John Wiley & Sons, Ltd.

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[22]
周启鸣,刘学军.数字地形分析[M].北京:科学出版社,2006.

[ Zhou Q M, Liu X J.Digital terrain analysis[M]. Beijing: Science Press, 2006. ]

[23]
吴辉,刘永波,秦承志,等.流域最佳管理措施情景优化算法的并行化[J].武汉大学学报·信息科学版,2016,41(2):202-207.流域最佳管理措施(beneficial management practices,BMPs)情景优化问题是一个典型的复杂地理计算问题,目前所常用的BMPs情景优化算法需要结合流域模型进行大量的迭代运算,因而花费大量计算时间,难以满足实际应用的要求.本文针对目前代表性的BMPs情景优化算法——ε支配多目标遗传算法(ε-NS-GA-Ⅱ),采用主从式并行策略,利用MPI并行编程库实现了该优化算法的并行化.在江西省赣江上游的梅川江流域(面积为6 366 km2)进行BMPs情景优化的应用案例表明,并行化的优化算法当运行于集群机时,加速比随着核数(8～512核)的增加而递增,当核数为512时,加速比达到最大值(310);并行效率随着核数的增加逐渐下降,最高值0.91,最低值0.61,取得了明显的加速效果.

DOI

[ Wu H, Liu Y B, Qin C Z, et al.Parallelization of an optimization algorithm for beneficial watershed management practices[J]. Geomatics and Information Science of Wuhan University, 2016,41(2):202-207. ]

[24]
秦承志,朱阿兴,施迅,等.坡位渐变信息的模糊推理[J].地理研究,2007,26(6):1165-1174,1307.坡位的空间变化通常是渐变的,定量的坡位空间渐变信息对于精细尺度上的坡面土壤侵蚀、预测性土壤制图等应用具有重要意义。现有基于栅格DEM的坡位模糊识别方法,或是仅在属性域内模糊聚类,忽略了空间信息;或是需要繁琐的规则进行模糊分类,实用性受限。本文建立了一种基于相似度的模糊推理方法,根据各类坡位在空间上的典型位置,计算其他位置与典型位置间的相似度,从而对坡位空间渐变信息进行系统、定量的描述。应用表明本方法能够合理地描述山脊、坡肩、背坡、坡脚、沟谷等重要坡位类型的渐变信息,所获得的坡位渐变信息也能够合理地解释土壤样点的A层土壤含砂量随坡位渐变的变化趋势。

DOI

[ Qin C Z, Zhu A X, Shi X, et al.Fuzzy inference of spatial gradation of slope positions[J]. Geographical Research, 2007,26(6):1165-1174,1307. ]

[25]
Qin C Z, Zhu A X, Shi X, et al.Quantification of spatial gradation of slope positions[J]. Geomorphology, 2009,110(3-4):152-161.Transition between slope positions (e.g., ridge, shoulder slope, back slope, foot slope, and valley) is often gradual. Quantification of spatial transitions or spatial gradations between slope positions can increase the accuracy of terrain parameterization for geographical or ecological modeling, especially for digital soil mapping at a fine scale. Current models for characterizing the spatial gradation of slope positions based on a gridded DEM either focus solely on the parameter space or depend on too many rules defined by topographic attributes, which makes such approaches impractical. The typical locations of a slope position contain the characteristics of the slope position in both parameter space and spatial context. Thus, the spatial gradation of slope positions can be quantified by comparing terrain characteristics (spatial and parametrical) of given locations to those at typical locations. Based on this idea, this paper proposes an approach to quantifying the spatial gradation of slope positions by using typical locations as prototypes. This approach includes two parts: the first is to extract the typical locations of each slope position and treat them as the prototypes of this position; and the second is to compute the similarity between a given location and the prototypes based on both local topographic attributes and spatial context. The new approach characterizes slope position gradation in both the attribute domain (i.e., parameter space) and the spatial domain (i.e., geographic space) in an easy and practicable way. Applications show that the new approach can quantitatively describe spatial gradations among a set of slope positions. Comparison of spatial gradation of A-horizon sand percentages with the quantified spatial gradation of slope positions indicates that the latter reflects slope processes, confirming the effectiveness of the approach. The comparison of a soil subgroup map of the study area with the maximum similarity map derived from the approach also suggests that the quantified spatial gradation of slope position can be used to aid geographical modeling such as digital soil mapping.

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[26]
Zhu L J, Zhu A X, Qin C Z, et al.Automatic approach to deriving fuzzy slope positions[J]. Geomorphology, 2018,304:173-183.Fuzzy characterization of slope positions is important for geographic modeling. Most of the existing fuzzy classification-based methods for fuzzy characterization require extensive user intervention in data preparation and parameter setting, which is tedious and time-consuming. This paper presents an automatic approach to overcoming these limitations in the prototype-based inference method for deriving fuzzy membership value (or similarity) to slope positions. The key contribution is a procedure for finding the typical locations and setting the fuzzy inference parameters for each slope position type. Instead of being determined totally by users in the prototype-based inference method, in the proposed approach the typical locations and fuzzy inference parameters for each slope position type are automatically determined by a rule set based on prior domain knowledge and the frequency distributions of topographic attributes. Furthermore, the preparation of topographic attributes (e.g., slope gradient, curvature, and relative position index) is automated, so the proposed automatic approach has only one necessary input, i.e., the gridded digital elevation model of the study area. All compute-intensive algorithms in the proposed approach were speeded up by parallel computing. Two study cases were provided to demonstrate that this approach can properly, conveniently and quickly derive the fuzzy slope positions.

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[27]
秦承志,朱阿兴,李宝林,等.坡位的分类及其空间分布信息的定量化[J].武汉大学学报·信息科学版,2009,34(3):374-377.

[ Qin C Z, Zhu A X, Li B L, et al.Taxonomy of slope positions and quantification of their spatial distribution information[J]. Geomatics and Information Science of Wuhan University, 2009,34(3):374-377. ]

[28]
Cover T M, Hart P E.Nearest neighbor pattern classification[J]. IEEE Transactions on Information Theory, 1967,13(1):21-27.

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[29]
Tu E, Zhang Y, Zhu L, et al. A graph-based semi-supervised k, nearest-neighbor method for nonlinear manifold distributed data classification[J]. Information Sciences, 2016,367-368(1):673-688.knearest neighbors (kNN) is one of the most widely used supervised learning algorithms to classify Gaussian distributed data, but it does not achieve good results when it is applied to nonlinear manifold distributed data, especially when a very limited amount of labeled samples are available. In this paper, we propose a new graph-basedkNN algorithm which can effectively handle both Gaussian distributed data and nonlinear manifold distributed data. To achieve this goal, we first propose a constrained Tired Random Walk (TRW) by constructing anR-level nearest-neighbor strengthened tree over the graph, and then compute a TRW matrix for similarity measurement purposes. After this, the nearest neighbors are identified according to the TRW matrix and the class label of a query point is determined by the sum of all the TRW weights of its nearest neighbors. To deal with online situations, we also propose a new algorithm to handle sequential samples based a local neighborhood reconstruction. Comparison experiments are conducted on both synthetic data sets and real-world data sets to demonstrate the validity of the proposed newkNN algorithm and its improvements to other version ofkNN algorithms. Given the widespread appearance of manifold structures in real-world problems and the popularity of the traditionalkNN algorithm, the proposed manifold versionkNN shows promising potential for classifying manifold-distributed data.

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[30]
Deb K, Agrawal S, Pratap A.A fast elitist nondominated sorting genetic algorithm for multi-objective optimization: NSGA-II[C]. Proceedings of the Parallel Problem Solving from Nature VI Conference, Paris, 2000,1917:849-858.

[31]
吴辉,刘永波,朱阿兴,等.流域最佳管理措施空间配置优化研究进展[J].地理科学进展,2013,32(4):570-579.最佳管理措施(BMPs)是保护流域水环境免受农业生产活动导致的污染的一系列措施。在进行流域尺度BMPs空间配置时,一方面要考虑BMPs的生态环境效益,另一方面要考虑农业经济效益,因此流域管理决策者需要对这些措施进行空间配置优化。最佳管理措施空间配置优化(简称BMPs空间优化)是基于专家经验或者利用优化算法而得出的方案,并通过流域模型和经济模型评价其环境和经济效益,最后选择效益最优的方案,这也是当前农业非点源污染和水环境保护研究的前沿和热点。本文在介绍BMPs及其评价模型的基础上,对当前BMPs空间优化研究中的两种方法进行了剖析,对当前国内外BMPs空间优化研究现状进行了回顾和总结,最后,指出了BMPs空间优化研究中现存的问题,指出了今后BMPs空间优化研究的方向。

DOI

[ Wu H, Liu Y B, Zhu A X, et al.Review of spatial optimization algorithms in BMPs placement at watershed scale[J]. Progress in Geography, 2013,32(4):570-579. ]

[32]
刘军志,朱阿兴,刘永波,等.基于栅格分层的逐栅格汇流算法并行化研究[J].国防科技大学学报,2013,35(1):123-129.

[ Liu J Z, Zhu A X, Liu Y B, et al.Parallelization of a grid-to-grid routing algorithm based on grids layering[J]. Journal of National University of Defense Technology, 2013,35(1):123-129. ]

[33]
Liu J Z, Zhu A X, Liu Y B, et al.A layered approach to parallel computing for spatially distributed hydrological modeling[J]. Environmental Modeling and Software, 2014,51(51):221-227.61A layered approach to parallel computing for distributed hydrological modeling.61This approach divides simulation units into layers according to flow direction.61In each layer, there are no upstream or downstream relationships among units.61A grid-based model was parallelized to illustrate this approach.61The speedup ratio reached 12.49 under 24 threads.

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