Surface velocity coefficients for discharge monitoring with a surface float method in shallow streams
浅水溪流中采用水面漂浮法进行排放监测的水面速度系数

Natural resource management concerns have brought stream discharge assessment to the forefront of importance for managers worldwide. As water demand for agricultural, industrial, and private uses has increased with population growth, the influence of water extraction on streams and rivers has become evident worldwide (Burt et al., 2002, Kustu et al., 2010, Shi et al., 2022; Zou et al., 2015). For instance, irrigation (Kustu et al., 2010) and industrial uses (Shi et al., 2022) have decreased streamflows, sometimes by as much as $100\mathrm{\%}$$100\mathrm{\%}$100%100 \% (Kraft et al., 2012). Increased impervious surfaces in urban areas have reduced infiltration and limited recharge to streams via shallow groundwater pathways, reducing stream baseflows (Wang et al., 2014). Expanded impervious surfaces have also increased storm runoff intensity and modified runoff timing in streams (Wang et al., 2014). Climate change is also influencing stream discharges (Dey and Mishra, 2017). Such changes in streamflow patterns put aquatic life at risk (Gido et al., 2010), alter food webs (Ledger et al., 2013), and influence food and water availability for human populations (Lambooy, 2011).
对自然资源管理的关注使溪流排放评估成为全球管理者关注的焦点。随着人口的增长，农业、工业和私人用水的需求也随之增加，取水对溪流和河流的影响在全球范围内变得显而易见（Burt 等人，2002 年；Kustu 等人，2010 年；Shi 等人，2022 年；Zou 等人，2015 年）。例如，灌溉（Kustu 等人，2010 年）和工业使用（Shi 等人，2022 年）导致河水流量减少，有时减少幅度高达 $100\mathrm{\%}$$100\mathrm{\%}$100%100 \% （Kraft 等人，2012 年）。城市地区不透水表面的增加减少了渗透，限制了通过浅层地下水途径对溪流的补给，从而减少了溪流基流（Wang 等人，2014 年）。扩大的不透水表面还增加了暴雨径流强度，并改变了溪流的径流时间（Wang 等人，2014 年）。气候变化也影响着溪流的排水量（Dey 和 Mishra，2017 年）。溪流模式的这种变化会危及水生生物（Gido 等人，2010 年），改变食物网（Ledger 等人，2013 年），并影响人类的食物和水供应（Lambooy，2011 年）。

Unfortunately, research budgets can support only a limited number of automated stream discharge monitoring stations (Ettinger et al., 2003; Krabbenhoft et al., 2022). In the United States, about 8,500 automated streamflow gages are supported. These tend to be on larger waterways and not in headwaters as they are strategically positioned to supply critical information to inform public safety (e.g., about floods), environmental conditions, and boundary compacts (United States Geological Survey, 2023). To support continuous data collection, realtime data delivery, quality assurance, and data storage, each gage costs about $22,500 per year to operate (WWALS Watershed Coalition, 2021).
遗憾的是，研究预算只能支持数量有限的自动溪流排放监测站（Ettinger 等人，2003 年；Krabbenhoft 等人，2022 年）。在美国，大约有 8,500 个自动溪流监测站。这些水文站往往位于较大的水道上，而不是在上游，因为它们的战略定位是提供关键信息，为公共安全（如洪水）、环境条件和边界契约提供信息（美国地质调查局，2023 年）。为支持持续的数据收集、实时数据传输、质量保证和数据存储，每个水文站每年的运营成本约为 22,500 美元（WWALS 流域联盟，2021 年）。

In response, natural resource managers partner with members of the public to obtain data needed for decision-making (Au et al., 2000; Conrad and Hilchey, 2011). This is particularly common for water monitoring. Numerous volunteer water-monitoring groups use a surface float method to estimate discharge (e.g., Georgia Department of Natural Resources, 2014; Indiana Department of Environmental Management, 2022; Missouri Department of Natural Resources, 2022; United States Environmental Protection Agency, 1997). The details of the surface float method vary somewhat among protocols, but all involve timing a floating object such as a ball, fishing float, or stick over a measured distance to determine surface velocity, converting surface velocity to mean channel velocity with a ratio, and measuring cross-sectional area of the stream channel. The ratio of the surface velocity to the mean channel velocity (commonly referred to as surface velocity coefficient) is the main area of uncertainty in these methods. Mean channel velocity is lower than surface velocity because friction slows flow near the bottom of the channel. However, wide variation exists in recommended surface velocity coefficients and in how to select an appropriate coefficient for a particular measurement site or flow condition (Table 1). In a laboratory flume, surface velocity coefficients were related to substrate roughness and water depth (Hundt and Blasch, 2019). In practical application on natural streams, the measured surface velocity itself may be biased high by the tendency of floating objects to move toward the area of highest velocity and by impedance of float trials in near-bank areas by vegetation and other obstructions.
为此，自然资源管理者与公众合作，获取决策所需的数据（Au 等人，2000 年；Conrad 和 Hilchey，2011 年）。这在水质监测中尤为常见。许多志愿水质监测团体使用水面漂浮法来估算排放量（例如，佐治亚州自然资源部，2014 年；印第安纳州环境管理部，2022 年；密苏里州自然资源部，2022 年；美国环境保护局，1997 年）。表面漂浮法的细节在不同的规程中略有不同，但都涉及对漂浮物（如球、钓鱼浮子或棍子）在测量距离内的计时，以确定表面速度，将表面速度转换为河道平均速度的比率，并测量河道的横截面积。表层速度与平均河道速度的比值（通常称为表层速度系数）是这些方法的主要不确定因素。河道平均流速低于地表流速是因为摩擦力减慢了河道底部附近的流速。然而，在推荐的表层流速系数以及如何为特定测量地点或水流条件选择合适的系数方面存在很大差异（表 1）。在实验室水槽中，表层流速系数与底质粗糙度和水深有关（Hundt 和 Blasch，2019 年）。在自然溪流的实际应用中，由于漂浮物倾向于向流速最高的区域移动，以及植被和其他障碍物对近岸区域漂浮物试验的阻碍，所测得的表面流速本身可能会偏高。

However, for members of the public to contribute effectively to management decisions, the generated data must be of sufficient quality for intended uses. Volunteer training, methodologies, and data management practices (e.g., development and approval of quality assurance projects plans by state and federal agencies) all contribute to data
然而，要让公众有效地为管理决策做出贡献，所生成的数据必须具有足够的质量，以满足预期用途。志愿者培训、方法和数据管理实践（例如，由州和联邦机构制定和批准质量保证项目计划）都有助于提高数据质量。

Table 1 表 1
Published estimates of the ratio of surface velocity to mean channel velocity in streams, expressed as coefficients by which surface velocity must be multiplied to obtain mean velocity; (NR, not reported). Of all references included in the table, only the United States Environmental Protection Agency (1997) reference is specifically written as a volunteer method.
已公布的溪流地表速度与河道平均速度之比估算值，表示为地表速度乘以系数才能得到平均速度；（NR，未报告）。在表中包含的所有参考文献中，只有美国环境保护局（1997 年）的参考文献是专门作为志愿方法编写的。

Table 1 (continued) 表 1（续）

quality (Freitag et al., 2016). Comparison studies between volunteer and professional methods can also help ensure data quality. A number of such studies related to water monitoring concluded that trained volunteers contributed valuable data, though results depended on parameter monitored, level of precision required, and method used (Au et al., 2000; Bell, 2007). For instance, volunteers produced similar results to professionals when they measured electrical conductivity and pH (Nicholson et al., 2002) and E. coli bacteria (Stepenuck et al., 2011), and when they observed cyanobacteria blooms (Sarnelle et al., 2010). Conversely, volunteers and professionals’ results differed when volunteers had less experience (Bell, 2007) or when volunteer methods or tools had less precision (Nicholson et al., 2002; Loperfido et al., 2010).
质量（Freitag 等人，2016 年）。志愿者方法与专业方法之间的比较研究也有助于确保数据质量。许多与水监测有关的此类研究得出结论，训练有素的志愿者提供了宝贵的数据，尽管结果取决于监测的参数、所需的精度水平以及使用的方法（Au 等人，2000 年；Bell，2007 年）。例如，志愿者在测量电导率和 pH 值（Nicholson 等人，2002 年）、大肠杆菌（Stepenuck 等人，2011 年）以及观察蓝藻藻华（Sarnelle 等人，2010 年）时得出的结果与专业人员相似。相反，当志愿者经验较少（Bell，2007 年）或志愿者的方法或工具精度较低时，志愿者与专业人员的结果也会有所不同（Nicholson 等人，2002 年；Loperfido 等人，2010 年）。

The surface velocity coefficient plays an important role in the accuracy of discharge measurements in the surface float method. Thus, the inconsistent guidance on its estimation is a significant impediment to the credibility of the surface float method in citizen science. In this study, we aimed to improve the accuracy of the surface float method by providing direct, empirical estimates of the surface velocity coefficient for natural streams. To do this, we compared discharge measurements made with a surface float method used by volunteers in Wisconsin, United States (University of Wisconsin, 2010) to measurements made with a velocityarea method (Turnipseed and Sauer, 2010) with an electromagnetic meter commonly used by Wisconsin Department of Natural Resources staff (Wisconsin Department of Natural Resources, 1998). The results provide recommended surface velocity coefficients that are applicable to a wide variety of wadable streams including those with both rocky and smooth beds. We also provided an estimated accuracy of discharge measurements made with the surface float method.
表层流速系数对表层漂浮法测量排水量的准确性起着重要作用。因此，对其估算的指导不一致严重阻碍了表层漂浮法在公民科学中的可信度。在这项研究中，我们的目标是通过对自然溪流的表层速度系数进行直接的经验估算来提高表层漂浮法的准确性。为此，我们比较了美国威斯康星州志愿者使用水面漂浮法（威斯康星大学，2010 年）和威斯康星州自然资源部工作人员使用电磁测量仪（威斯康星州自然资源部，1998 年）使用速度面积法（Turnipseed 和 Sauer，2010 年）进行的排放测量。结果提供了适用于各种可涉水溪流（包括岩石河床和光滑河床）的推荐表面流速系数。我们还提供了采用水面漂浮法测量排水量的估计精度。

Participants in Wisconsin’s Water Action Volunteers stream monitoring program have assessed streamflow with a common methodology since 2003 (University of Wisconsin, 2010). The method was based on Missouri Department of Natural Resources (2000), United States Environmental Protection Agency (1997), and other volunteer monitoring programs’ methods. By June 2011, volunteers had collected 3,476 discharge observations up to $3.5{\mathrm{m}}^3/\mathrm{s}(125\mathrm{cfs})$$3.5{\mathrm{m}}^3/\mathrm{s}(125\mathrm{cfs})$3.5m^(3)//s(125cfs)3.5 \mathrm{~m}^{3} / \mathrm{s}(125 \mathrm{cfs}) at 502 sites across Wisconsin (Board of Regents of the University of Wisconsin System, 2023).
自 2003 年以来，威斯康星州水行动志愿者溪流监测计划的参与者一直在使用一种通用方法评估溪流（威斯康星大学，2010 年）。该方法以密苏里自然资源部（2000 年）、美国环境保护局（1997 年）和其他志愿者监测计划的方法为基础。截至 2011 年 6 月，志愿者们已在威斯康星州的 502 个地点收集了 3476 次排水观测数据（威斯康星大学系统管理委员会，2023 年）。

We selected study sites randomly from the 173 locations where volunteers had monitored streamflow between March 2010 and June 2011 as these were most likely to have active volunteers. The study
我们从 2010 年 3 月至 2011 年 6 月期间有志愿者监测溪流的 173 个地点中随机选择了研究地点，因为这些地点最有可能有活跃的志愿者。研究
originally included 35 sites (Stepenuck, 2013); however, seven sites were dropped from the analysis because of inconsistencies in the types of floating objects used by volunteers in the surface float method. This resulted in 28 study sites widely distributed across Wisconsin (Fig. 1). We selected sites to represent three discharge classes: less than 0.03 cubic meters per second ( ${\mathrm{m}}^3/\mathrm{s};1$${\mathrm{m}}^3/\mathrm{s};1$m^(3)//s;1\mathrm{m}^{3} / \mathrm{s} ; 1 cubic foot per second, cfs), between 0.03 and $0.3{\mathrm{m}}^3/\mathrm{s}$$0.3{\mathrm{m}}^3/\mathrm{s}$0.3m^(3)//s0.3 \mathrm{~m}^{3} / \mathrm{s} ( 1 and 10 cfs ), and greater than $0.3{\mathrm{m}}^3/\mathrm{s}(10\mathrm{cfs}$$0.3{\mathrm{m}}^3/\mathrm{s}(10\mathrm{cfs}$0.3m^(3)//s(10cfs0.3 \mathrm{~m}^{3} / \mathrm{s}(10 \mathrm{cfs} ). Discharge classes were defined by previous volunteer streamflow measurements. These discharge classes were selected because unpublished data from the Missouri Stream Team suggested that accuracy of the volunteer method was highest when streamflow was between 0.03 and $0.3{\mathrm{m}}^3/\mathrm{s}$$0.3{\mathrm{m}}^3/\mathrm{s}$0.3m^(3)//s0.3 \mathrm{~m}^{3} / \mathrm{s} ( 1 to 10 cfs ), but less accurate when outside of that range (personal communciation with Tim Rielly and Chris Riggert, April 2011). For purposes of this paper, the discharge classes provided us with an appropriate range of discharge measurements, but the classes were not important for analyses. Due to variability in streamflow, individual sites sometimes represented multiple size classes. Once a site was selected to represent one size category, it was not selected to represent another size category. After we randomly selected sites, we contacted volunteers to request their participation in the study. When volunteers opted not to participate, we selected different sites in the appropriate size class. When volunteers opted to participate, we included up to three sites they monitored in the study. This process resulted in five sites ( 18 $\mathrm{\%}$$\mathrm{\%}$%\% ) in the smallest size class ( $<0.03{\mathrm{m}}^3/\mathrm{s}$$<0.03{\mathrm{m}}^3/\mathrm{s}$< 0.03m^(3)//s<0.03 \mathrm{~m}^{3} / \mathrm{s} ), 12 sites ( $43\mathrm{\%}$$43\mathrm{\%}$43%43 \% ) in the mid-size class ( $0.03-0.3{\mathrm{m}}^3/\mathrm{s}$$0.03-0.3{\mathrm{m}}^3/\mathrm{s}$0.03-0.3m^(3)//s0.03-0.3 \mathrm{~m}^{3} / \mathrm{s} ), and 11 sites ( $39\mathrm{\%}$$39\mathrm{\%}$39%39 \% ) in the largest size class ( $>0.3$$>0.3$> 0.3>0.3 ${\mathrm{m}}^3/\mathrm{s}$${\mathrm{m}}^3/\mathrm{s}$m^(3)//s\mathrm{m}^{3} / \mathrm{s} ). This representation was similar to the percent of sites monitored in the Water Action Volunteers program within the three size classes. For the 3,476 discharge results collected by volunteers between 2003 and June 2011, $7\mathrm{\%}$$7\mathrm{\%}$7%7 \% of sites were in the smallest size class, $38\mathrm{\%}$$38\mathrm{\%}$38%38 \% of sites were in the middle size class, and $55\mathrm{\%}$$55\mathrm{\%}$55%55 \% of sites were in the largest size class.
最初包括 35 个站点（Stepenuck，2013 年）；但由于志愿者在水面漂浮法中使用的漂浮物类型不一致，有 7 个站点被从分析中剔除。因此，28 个研究地点广泛分布在威斯康星州各地（图 1）。我们选择了代表三个排水量等级的地点：小于 0.03 立方米/秒（ ${\mathrm{m}}^3/\mathrm{s};1$${\mathrm{m}}^3/\mathrm{s};1$m^(3)//s;1\mathrm{m}^{3} / \mathrm{s} ; 1 立方英尺/秒，cfs）、介于 0.03 和 $0.3{\mathrm{m}}^3/\mathrm{s}$$0.3{\mathrm{m}}^3/\mathrm{s}$0.3m^(3)//s0.3 \mathrm{~m}^{3} / \mathrm{s} 之间（1 到 10 cfs）以及大于 $0.3{\mathrm{m}}^3/\mathrm{s}(10\mathrm{cfs}$$0.3{\mathrm{m}}^3/\mathrm{s}(10\mathrm{cfs}$0.3m^(3)//s(10cfs0.3 \mathrm{~m}^{3} / \mathrm{s}(10 \mathrm{cfs} 的地点。）排水量等级是根据以前志愿者测量的溪流流量确定的。之所以选择这些排水量等级，是因为密苏里州溪流小组未发表的数据表明，当溪流流量在 0.03 到 $0.3{\mathrm{m}}^3/\mathrm{s}$$0.3{\mathrm{m}}^3/\mathrm{s}$0.3m^(3)//s0.3 \mathrm{~m}^{3} / \mathrm{s} 之间（1 到 10 立方英尺/秒）时，志愿者方法的准确性最高，但当超出该范围时，准确性则较低（2011 年 4 月与 Tim Rielly 和 Chris Riggert 的个人交流）。就本文而言，排量等级为我们提供了适当的排量测量范围，但等级对分析并不重要。由于溪流的多变性，单个站点有时会代表多个大小级别。一旦某个站点被选中代表一个规模等级，就不会再被选中代表另一个规模等级。随机选取地点后，我们会联系志愿者，要求他们参与研究。如果志愿者选择不参与，我们就会在相应的规模类别中选择不同的站点。当志愿者选择参与时，我们会将他们监测到的最多三个地点纳入研究。 这一过程的结果是，5 个地点（18 个 $\mathrm{\%}$$\mathrm{\%}$%\% 属于最小规模等级（ $<0.03{\mathrm{m}}^3/\mathrm{s}$$<0.03{\mathrm{m}}^3/\mathrm{s}$< 0.03m^(3)//s<0.03 \mathrm{~m}^{3} / \mathrm{s} ），12 个地点（ $43\mathrm{\%}$$43\mathrm{\%}$43%43 \% 属于中等规模等级（ $0.03-0.3{\mathrm{m}}^3/\mathrm{s}$$0.03-0.3{\mathrm{m}}^3/\mathrm{s}$0.03-0.3m^(3)//s0.03-0.3 \mathrm{~m}^{3} / \mathrm{s} ），11 个地点（ $39\mathrm{\%}$$39\mathrm{\%}$39%39 \% 属于最大规模等级（ $>0.3$$>0.3$> 0.3>0.3 ${\mathrm{m}}^3/\mathrm{s}$${\mathrm{m}}^3/\mathrm{s}$m^(3)//s\mathrm{m}^{3} / \mathrm{s} ）。这一比例与水行动志愿者计划监测到的三个大小级别的地点比例相似。在 2003 年至 2011 年 6 月期间由志愿者收集的 3,476 项排放结果中， $7\mathrm{\%}$$7\mathrm{\%}$7%7 \% 个站点属于最小粒度级别， $38\mathrm{\%}$$38\mathrm{\%}$38%38 \% 个站点属于中等粒度级别， $55\mathrm{\%}$$55\mathrm{\%}$55%55 \% 个站点属于最大粒度级别。

Repeated visits were made to each site to assess streamflow at varying discharges. Most sites were visited on four occasions. A few sites were visited less often due to difficulty coordinating with volunteers, volunteer attrition from the program, and drought or flood conditions which made monitoring impossible. In all, 76 site visits were made. This research was approved as exempt by the University of Wisconsin-
对每个地点进行了多次考察，以评估不同排水量下的溪流。大多数地点都考察了四次。由于与志愿者协调困难、志愿者退出计划、干旱或洪水导致无法进行监测等原因，少数站点的访问次数较少。总共访问了 76 个地点。本研究获得了威斯康星大学的豁免批准。

Fig. 1. Location of the 28 sites in Wisconsin, United States, where volunteer and professional streamflow monitoring methods were compared.
图 1.美国威斯康星州 28 个地点的位置，其中对志愿者和专业人员的溪流监测方法进行了比较。

Madison Social and Behavioral Sciences IRB (protocol number SE-2011-0519).
麦迪逊社会与行为科学 IRB（协议编号 SE-2011-0519）。

To learn the Water Action Volunteers streamflow monitoring method (University of Wisconsin, 2010), volunteers attended a hands-on training offered by statewide program staff or a trained local coordinator. At the training, in addition to learning and practicing the streamflow monitoring method, volunteers received written methods and a short training video. Each volunteer was then assigned (by a local program coordinator) or chose a 91.44 m ( 300 ft ) stream monitoring location in a stream in which they could safely wade. Subsequently, each time volunteers visited their stream monitoring location, they followed the prescribed method to measure streamflow (University of Wisconsin, 2010). On their first visit to their stream monitoring location, volunteers identified a straight section of stream at which to monitor streamflow. Volunteers were trained to ensure that section of stream was 6.10 m ( 20 ft ) long and had uniform width and, whenever possible, a depth of at least 0.15 m ( 0.5 ft ; Fig. 2). Once such a stream section was identified, volunteers measured streamflow at this station on each site visit. After marking the up- and down-stream ends of the $6.10\mathrm{m}(20\mathrm{ft})$$6.10\mathrm{m}(20\mathrm{ft})$6.10m(20ft)6.10 \mathrm{~m}(20 \mathrm{ft}) station and its midpoint, volunteers extended a measuring tape from water’s edge to water’s edge at the midpoint of the section to measure stream width. Next, to determine the average water depth across that transect, the volunteers collected up to 20 depth measurements at $0.30\mathrm{m}(1\mathrm{ft})$$0.30\mathrm{m}(1\mathrm{ft})$0.30m(1ft)0.30 \mathrm{~m}(1 \mathrm{ft}) intervals. If stream width was greater than $6.10\mathrm{m}(20\mathrm{ft})$$6.10\mathrm{m}(20\mathrm{ft})$6.10m(20ft)6.10 \mathrm{~m}(20 \mathrm{ft}), volunteers collected the 20 depth measurements at equal intervals across the transect (e.g., if a stream was 12.19 m ( 40 ft ) wide, volunteers collected depth measurements every $0.61\mathrm{m}(2\mathrm{ft})$$0.61\mathrm{m}(2\mathrm{ft})$0.61m(2ft)0.61 \mathrm{~m}(2 \mathrm{ft}). To measure depth, volunteers used a pole marked in tenths of feet. They held the pole on the stream bed without allowing it to sink in (i.e., if the stream had a soft bed). If velocity of the water was fast enough to create a pillow of water on the marked pole (as the water pushed against it), volunteers were trained to be consistent in how they measured the water depth (i.e., they either estimated the mid-point of the water height as it pushed onto the pole or measured the high or low point of the water as it pushed against the pole). Volunteers made the initial depth measurement at $0.30\mathrm{m}(1\mathrm{ft}$$0.30\mathrm{m}(1\mathrm{ft}$0.30m(1ft0.30 \mathrm{~m}(1 \mathrm{ft} ) from the bank or at the set interval for streams wider than $6.10\mathrm{m}(20\mathrm{ft})$$6.10\mathrm{m}(20\mathrm{ft})$6.10m(20ft)6.10 \mathrm{~m}(20 \mathrm{ft}). A zero depth was pre-marked on volunteer data sheets to account for an assumed shallow water area missed by beginning depth measurements away from the water’s edge (Lagler, 1952). To measure velocity, volunteers timed how long it took a float to travel the length of the marked $6.10\mathrm{m}(20\mathrm{ft})$$6.10\mathrm{m}(20\mathrm{ft})$6.10m(20ft)6.10 \mathrm{~m}(20 \mathrm{ft)} section. A tennis ball with a small cut in it served as the float. Volunteers added a little water into the tennis ball to allow it to float approximately neutrally buoyant. If the float was caught on an object in the stream or stopped in an eddy (area of upstream flow or slack water), the float trial was repeated. Volunteers timed three float trials for streams less than $3.05\mathrm{m}(10\mathrm{ft})$$3.05\mathrm{m}(10\mathrm{ft})$3.05m(10ft)3.05 \mathrm{~m}(10 \mathrm{ft}) wide and four float trials for wider streams. The volunteers dropped the float into the water upstream of the upstream marked flag to allow it to reach surface speed by the time it entered the marked streamflow monitoring section. Volunteers began timing the float trial as the tennis ball passed the marked upstream end of the streamflow monitoring section. They stopped timing when the float reached the marked downstream end of the streamflow monitoring section. As the volunteers generally worked in teams, one person would position themselves at the upstream end of the marked section and another at the downstream end of the section. The volunteer at the downstream end caught the ball and delivered it back to the upstream end of the streamflow monitoring station. For each of the three or four float trials, the volunteers positioned the ball in different locations across the width of the stream to account for varied velocities expected due to friction along the stream edges. The volunteers avoided standing in the stream in a manner that would create an eddy or otherwise affect the float path of the tennis ball.
为了学习 "水行动志愿者 "的水流监测方法（威斯康星大学，2010 年），志愿者参加了由全州计划工作人员或经过培训的当地协调员提供的实践培训。在培训中，志愿者除了学习和练习流体监测方法外，还收到了书面方法和培训视频短片。然后，（由当地项目协调员）为每名志愿者分配或选择一个他们可以安全涉水的 91.44 米（300 英尺）长的溪流监测点。随后，志愿者每次前往溪流监测点时，都会按照规定的方法测量溪流流量（威斯康星大学，2010 年）。在第一次前往溪流监测点时，志愿者们会确定一段笔直的溪流，在那里监测溪流。志愿者接受了培训，以确保该段溪流长 6.10 米（20 英尺），宽度一致，水深至少 0.15 米（0.5 英尺；图 2）。一旦确定了这样的溪流断面，志愿者就会在每次实地考察时测量该站的溪流流量。在标记了 $6.10\mathrm{m}(20\mathrm{ft})$$6.10\mathrm{m}(20\mathrm{ft})$6.10m(20ft)6.10 \mathrm{~m}(20 \mathrm{ft}) 站的上下游两端及其中点后，志愿者将卷尺从水边伸到该段中点的水边，以测量溪流宽度。接下来，为了确定该断面的平均水深，志愿者们以 $0.30\mathrm{m}(1\mathrm{ft})$$0.30\mathrm{m}(1\mathrm{ft})$0.30m(1ft)0.30 \mathrm{~m}(1 \mathrm{ft}) 的间隔收集了多达 20 个水深测量值。如果溪流宽度大于 $6.10\mathrm{m}(20\mathrm{ft})$$6.10\mathrm{m}(20\mathrm{ft})$6.10m(20ft)6.10 \mathrm{~m}(20 \mathrm{ft}) ，则志愿者在横断面上以相同的间隔收集 20 个深度测量值（例如，如果溪流宽度为 12.19 米（40 英尺），则志愿者每隔 $0.61\mathrm{m}(2\mathrm{ft})$$0.61\mathrm{m}(2\mathrm{ft})$0.61m(2ft)0.61 \mathrm{~m}(2 \mathrm{ft}) 收集深度测量值）。为了测量深度，志愿者使用了一根以十分之一英尺为单位的杆子。 他们将杆子固定在河床上，不让其下沉（即如果河床较软）。如果水流速度快到足以在标杆上形成水枕（因为水流推动了标杆），则志愿者要接受培训，以确保测量水深的方法一致（即在水流推动标杆时估计水流高度的中点，或在水流推动标杆时测量水流的高点或低点）。志愿者在距离河岸 $0.30\mathrm{m}(1\mathrm{ft}$$0.30\mathrm{m}(1\mathrm{ft}$0.30m(1ft0.30 \mathrm{~m}(1 \mathrm{ft} ）处进行初始深度测量，或者在宽度大于 $6.10\mathrm{m}(20\mathrm{ft})$$6.10\mathrm{m}(20\mathrm{ft})$6.10m(20ft)6.10 \mathrm{~m}(20 \mathrm{ft}) 的河段的设定间隔处进行初始深度测量。志愿者的数据表上预先标注了零深度，以考虑到在远离水边的地方开始深度测量而漏掉的假定浅水区（Lagler，1952 年）。为了测量速度，志愿者们会计算浮标在标记的 $6.10\mathrm{m}(20\mathrm{ft})$$6.10\mathrm{m}(20\mathrm{ft})$6.10m(20ft)6.10 \mathrm{~m}(20 \mathrm{ft)} 区域内移动所需的时间。漂浮物是一个切口很小的网球。志愿者在网球中加入少量水，使其在近似中性浮力的状态下漂浮。如果浮球被溪流中的物体卡住或停在漩涡（上游水流或水流缓慢的区域）中，则重复进行漂浮试验。志愿者在宽度小于 $3.05\mathrm{m}(10\mathrm{ft})$$3.05\mathrm{m}(10\mathrm{ft})$3.05m(10ft)3.05 \mathrm{~m}(10 \mathrm{ft}) 的溪流中进行了三次漂浮试验，在宽度较大的溪流中进行了四次漂浮试验。志愿者将浮标放入上游标记旗帜的上游水中，使其在进入标记的溪流监测段时达到水面速度。当网球通过有标记的上游溪流监测断面时，志愿者开始为浮标试验计时。当浮标到达溪流监测断面下游有标记的一端时，志愿者停止计时。 由于志愿者通常以小组为单位开展工作，因此一个人将自己定位在标记区段的上游端，另一个人则定位在该区段的下游端。下游端的志愿者接住球并将其送回上游端的溪流监测站。在三到四次漂浮试验中，志愿者将球放置在溪流宽度的不同位置，以考虑到由于溪流边缘摩擦而产生的不同速度。志愿者避免站在溪流中，以免造成漩涡或影响网球的漂浮路径。

To calculate streamflow, volunteers first calculated the average
为了计算溪流流量，志愿者们首先计算了平均

Volunteers marked the upstream and downstream ends of the $6.10\mathrm{m}(20\mathrm{ft})$$6.10\mathrm{m}(20\mathrm{ft})$6.10m(20ft)6.10 \mathrm{~m}(20 \mathrm{ft}) long streamflow monitoring station on both sides of stream.
志愿者们在溪流两侧 $6.10\mathrm{m}(20\mathrm{ft})$$6.10\mathrm{m}(20\mathrm{ft})$6.10m(20ft)6.10 \mathrm{~m}(20 \mathrm{ft}) 长的溪流监测站的上下游两端做了标记。
Upstream end of monitoring station
监测站上游端
Downstream end of monitoring station
监测站下游端

Midpoint of streamflow monitoring station. Volunteers used a measuring tape to measure stream width from water’s edge to water’s edge at the midpoint of the marked 6.1 m long station (i.e., at 3.05 m or 10 ft downstream from the marked upstream end of the streamflow monitoring station).
溪流监测站的中点。志愿者用卷尺测量标有 6.1 米长监测站中点的水边到水边的溪流宽度（即在标有溪流监测站上游端的下游 3.05 米或 10 英尺处）。
b) Longitudinal view of float trials
b) 浮筒试验的纵向视图

Volunteers started float trial timing as the float passed the imaginary line between the two upstream flags.
当浮筒通过两面上游旗帜之间的假想线时，志愿者开始为浮筒试验计时。

Volunteers stopped float trial timing when the float passed the imaginary line between the two downstream flags.
当浮标通过两面下游旗帜之间的假想线时，志愿者停止浮标试验计时。

Volunteers placed the tennis ball float in the stream upstream of the upstream flags to allow it to get up to speed before timing began. In each float trial, volunteers started the tennis ball float at a different point across the width of the stream.
志愿者将网球浮标放置在上游旗帜的溪流中，让其在计时开始前达到一定速度。在每次漂浮试验中，志愿者都会在溪流宽度的不同位置启动网球漂浮器。

Fig. 2. Longitudinal (a and b) and transverse © views of a volunteer streamflow monitoring station. Tile a shows station length, marked points at the up and downstream ends of the monitoring station, and distances from upstream to downstream ends of the station and from upstream to the midpoint of the station. Tile b depicts approximate distribution of tennis ball float trials across the stream width, positioning of the tennis ball float upstream of the marked streamflow monitoring station, and the location and process volunteers used to time the float trials. Tile c depicts the process volunteers followed to measure water depth across a transect at the midpoint of the station.
图 2.志愿者溪流监测站的纵向（a 和 b）和横向视图。图 a 显示了监测站的长度、监测站上下游两端的标记点，以及从监测站上游到下游两端的距离和从上游到监测站中点的距离。图块 b 显示了网球浮标在整个河道宽度上的大致分布情况、网球浮标在有标记的水流监测站上游的位置，以及志愿者为浮标试验计时的位置和过程。图示 c 描述了志愿者在监测站中点横断面上测量水深的过程。
depth. Next, volunteers calculated the average surface velocity. They did this by averaging the measured float trial times and dividing that into the distance over which the float trial was timed, which was usually $6.10\mathrm{m}(20\mathrm{ft}$$6.10\mathrm{m}(20\mathrm{ft}$6.10m(20ft6.10 \mathrm{~m}(20 \mathrm{ft} ). Then, volunteers selected a surface velocity coefficient to use to correct measured average surface velocity for the influence of bottom friction. Volunteers had the option to select a surface velocity coefficient of either 0.8 or 0.9 . They selected a coefficient of 0.8 if the stream bottom was comprised of “rough or loose rocks, coarse gravel, or weeds” (University of Wisconsin, 2010). They selected a coefficient of 0.9 if the stream bottom was comprised of “smooth mud, sand or bedrock” (University of Wisconsin, 2010). On any given site visit, volunteers could select either of these two surface velocity coefficients. They had the option to select a different surface velocity coefficient from a previous site visit if the stream bed characteristics had changed. Factors that could influence a change in the selected surface velocity coefficient included such things as presence of weeds that developed on the stream bed during summer months or removal of rocks from the stream bed during low flow periods to allow for less restricted movement of the float during timed trials. Once volunteers selected a coefficient, they calculated streamflow using the following equation:
深度。接下来，志愿者们计算平均水面速度。计算方法是将测得的浮漂试水时间取平均值，再除以浮漂试水的距离（通常为 $6.10\mathrm{m}(20\mathrm{ft}$$6.10\mathrm{m}(20\mathrm{ft}$6.10m(20ft6.10 \mathrm{~m}(20 \mathrm{ft} ）。然后，志愿者选择一个表面速度系数，用来校正测量的平均表面速度，以消除底部摩擦的影响。志愿者可以选择 0.8 或 0.9 的表面速度系数。如果溪流底部由 "粗糙或松散的岩石、粗砾石或杂草 "组成，则选择 0.8（威斯康星大学，2010 年）。如果溪流底部由 "光滑的泥、沙或基岩 "组成，则选择 0.9 的系数（威斯康星大学，2010 年）。在任何特定的实地考察中，志愿者都可以选择这两个表面速度系数中的任何一个。如果河床特征发生了变化，他们还可以选择与之前实地考察时不同的表层流速系数。影响所选表面速度系数变化的因素包括：夏季河床上长满了杂草，或者在低流量期间河床上的石头被移走，以便在定时试验中减少漂浮物移动的限制。一旦志愿者选定了系数，他们就会使用以下公式计算溪流流量：

where $Q$$Q$QQ is discharge ( ${\mathrm{m}}^3/\mathrm{s}$${\mathrm{m}}^3/\mathrm{s}$m^(3)//s\mathrm{m}^{3} / \mathrm{s} or cfs ), $w$$w$ww is the stream width ( m or ft ), $d$$d$dd is the average depth ( m or ft ), $v$$v$vv Is the mean surface velocity ( $\mathrm{m}/\mathrm{s}$$\mathrm{m}/\mathrm{s}$m//s\mathrm{m} / \mathrm{s} or $\mathrm{ft}/\mathrm{s}$$\mathrm{ft}/\mathrm{s}$ft//s\mathrm{ft} / \mathrm{s} ), and $a$$a$aa is the surface velocity coefficient ( 0.8 or 0.9 ).
其中， $Q$$Q$QQ 是排水量（ ${\mathrm{m}}^3/\mathrm{s}$${\mathrm{m}}^3/\mathrm{s}$m^(3)//s\mathrm{m}^{3} / \mathrm{s} 或 cfs）， $w$$w$ww 是流宽（米或英尺）， $d$$d$dd 是平均深度（米或英尺）， $v$$v$vv 是平均表面速度（ $\mathrm{m}/\mathrm{s}$$\mathrm{m}/\mathrm{s}$m//s\mathrm{m} / \mathrm{s} 或 $\mathrm{ft}/\mathrm{s}$$\mathrm{ft}/\mathrm{s}$ft//s\mathrm{ft} / \mathrm{s} ）， $a$$a$aa 是表面速度系数（0.8 或 0.9）。

We (the study researchers) assessed discharge immediately before or after the volunteers within $15.24\mathrm{m}(50\mathrm{ft}$$15.24\mathrm{m}(50\mathrm{ft}$15.24m(50ft15.24 \mathrm{~m}(50 \mathrm{ft} ) of where the volunteers had monitored. All measurements were made during periods of relatively steady discharge based on duration since the last rainfall. We used a Marsh-McBirney Flo-mate Model 2000 m (Marsh-McBirney, Frederick, MD) to determine discharge using standard velocity-area methods described by the United States Geological Survey (Turnipseed and Sauer, 2010) and the Wisconsin Department of Natural Resources (Wisconsin Department of Natural Resources, 1998). The Marsh-McBirney meter was calibrated to zero at the start of each field day (Marsh-McBirney Inc., 1990). At each site, we identified a stream cross section with a reasonably straight channel, a stable streambed free of large rocks, weeds and obstructions that would create eddies, slack water, or turbulence. Whenever possible, we selected areas with depths of approximately $0.15\mathrm{m}(0.5\mathrm{ft})$$0.15\mathrm{m}(0.5\mathrm{ft})$0.15m(0.5ft)0.15 \mathrm{~m}(0.5 \mathrm{ft}) or greater. We measured stream width from water’s edge to water’s edge using a steel engineer’s measuring tape. The tape was fixed in place across the width of the stream using surveyors’ stakes. We measured depth to the nearest $0.003\mathrm{m}(0.01\mathrm{ft})$$0.003\mathrm{m}(0.01\mathrm{ft})$0.003m(0.01ft)0.003 \mathrm{~m}(0.01 \mathrm{ft}) across the stream width at 20 to 30 partials using a top-setting wading rod. No more than $5\mathrm{\%}$$5\mathrm{\%}$5%5 \% to $10\mathrm{\%}$$10\mathrm{\%}$10%10 \% of the discharge was contained in any one partial section. Because all sites had depths of $0.76\mathrm{m}(2.5\mathrm{ft})$$0.76\mathrm{m}(2.5\mathrm{ft})$0.76m(2.5ft)0.76 \mathrm{~m}(2.5 \mathrm{ft}) or less, we made a single velocity reading at each partial at 0.6 depth, as measured from the surface (i.e., $60\mathrm{\%}$$60\mathrm{\%}$60%60 \% depth from surface to stream bottom). The probe was pointed directly into the flow and velocity was recorded after a 15 s averaging period.
我们（研究人员）在志愿者监测地点的 $15.24\mathrm{m}(50\mathrm{ft}$$15.24\mathrm{m}(50\mathrm{ft}$15.24m(50ft15.24 \mathrm{~m}(50 \mathrm{ft} ) 范围内，紧接在志愿者之前或之后对排水量进行了评估。所有测量都是在自上次降雨以来排水量相对稳定的时期进行的。我们使用 Marsh-McBirney Flo-mate 2000 型流量计（Marsh-McBirney，马里兰州弗雷德里克市），采用美国地质调查局（Turnipseed 和 Sauer，2010 年）和威斯康星州自然资源部（威斯康星州自然资源部，1998 年）规定的标准流速-面积法来确定排水量。Marsh-McBirney 测量仪在每个实地考察日开始时校准为零（Marsh-McBirney 公司，1990 年）。在每个地点，我们都要确定一个河道较直、河床稳定、没有大石头、杂草以及会产生漩涡、松弛水流或湍流的障碍物的河流横截面。只要有可能，我们就会选择水深约 $0.15\mathrm{m}(0.5\mathrm{ft})$$0.15\mathrm{m}(0.5\mathrm{ft})$0.15m(0.5ft)0.15 \mathrm{~m}(0.5 \mathrm{ft}) 或更深的区域。我们使用钢制工程师卷尺测量从水边到水边的溪流宽度。使用测量桩将钢卷尺横跨溪流宽度固定到位。我们使用顶置式涉水竿测量溪流宽度上最接近 $0.003\mathrm{m}(0.01\mathrm{ft})$$0.003\mathrm{m}(0.01\mathrm{ft})$0.003m(0.01ft)0.003 \mathrm{~m}(0.01 \mathrm{ft}) 的深度，深度为 20 至 30 分之一。任何一个局部断面的排水量都不会超过 $5\mathrm{\%}$$5\mathrm{\%}$5%5 \% 至 $10\mathrm{\%}$$10\mathrm{\%}$10%10 \% 。由于所有地点的水深都在 $0.76\mathrm{m}(2.5\mathrm{ft})$$0.76\mathrm{m}(2.5\mathrm{ft})$0.76m(2.5ft)0.76 \mathrm{~m}(2.5 \mathrm{ft}) 或以下，因此我们在每个部分的 0.6 水深处（即从水面到溪底的 $60\mathrm{\%}$$60\mathrm{\%}$60%60 \% 水深）读取了一次流速读数。探头直接对准水流，经过 15 秒的平均时间后记录流速。

We calculated discharge by first determining the discharge in each of the partials and then summing them using the equation:
我们在计算放电量时，首先确定每个部分的放电量，然后用公式求和：

where $Q$$Q$QQ is discharge $\left({\mathrm{m}}^3/\mathrm{s}\right)$$\left({\mathrm{m}}^3/\mathrm{s}\right)$(m^(3)//s)\left(\mathrm{m}^{3} / \mathrm{s}\right),
其中 $Q$$Q$QQ 为放电 $\left({\mathrm{m}}^3/\mathrm{s}\right)$$\left({\mathrm{m}}^3/\mathrm{s}\right)$(m^(3)//s)\left(\mathrm{m}^{3} / \mathrm{s}\right) 、
$a_{\mathrm{i}}$$a_{\mathrm{i}}$a_(i)a_{\mathrm{i}} is the cross-sectional area $\left({\mathrm{m}}^2\right)$$\left({\mathrm{m}}^2\right)$(m^(2))\left(\mathrm{m}^{2}\right) for the $i$$i$ii th segment of the $n$$n$nn segments into which the.
$a_{\mathrm{i}}$$a_{\mathrm{i}}$a_(i)a_{\mathrm{i}} 为 $n$$n$nn 段中 $i$$i$ii 第三段的横截面积 $\left({\mathrm{m}}^2\right)$$\left({\mathrm{m}}^2\right)$(m^(2))\left(\mathrm{m}^{2}\right) 。
cross section is divided, and.
横截面的划分，以及
$v_i$$v_i$v_(i)v_{i} Is the mean velocity in the segment ( $\mathrm{m}/\mathrm{s}$$\mathrm{m}/\mathrm{s}$m//s\mathrm{m} / \mathrm{s} ) (Turnipseed and Sauer,
$v_i$$v_i$v_(i)v_{i} 是段内的平均速度（ $\mathrm{m}/\mathrm{s}$$\mathrm{m}/\mathrm{s}$m//s\mathrm{m} / \mathrm{s} ）（Turnipseed 和 Sauer、
2010)

We used mixed effects regression to compare volunteer to professional stream discharge measurements using the lme4 package in $R$$R$RR (Bates et al., 2013; R Core Team, 2013). Substrate type was included in the model as a fixed effect and repeated measures at a stream site were treated as a random effect on the intercept. Discharge was logtransformed prior to analysis to approximate a normal distribution. Measurements obtained with the professional method were considered to be the “true” discharge at each site. The model equation is:
我们使用 $R$$R$RR 中的 lme4 软件包（Bates 等人，2013 年；R 核心小组，2013 年），使用混合效应回归法比较志愿者与专业人员的溪流排放测量结果。基质类型作为固定效应包含在模型中，溪流地点的重复测量作为截距的随机效应处理。分析前对排水量进行对数变换，以接近正态分布。用专业方法获得的测量值被视为每个地点的 "真实 "排水量。模型方程为
$\mathrm{logPro}={\beta }_0+{\beta }_1{}^{\ast }\log \mathrm{Vol}+{\beta }_2{}^{\ast }$$\mathrm{logPro}={\beta }_0+{\beta }_1{}^{\ast }\log \mathrm{Vol}+{\beta }_2{}^{\ast }$logPro=beta_(0)+beta_(1)^(**)log Vol+beta_(2)^(**)\operatorname{logPro}=\beta_{0}+\beta_{1}{ }^{*} \log \operatorname{Vol}+\beta_{2}{ }^{*} substrate $+(1\mid$$+(1\mid$+(1∣+(1 \mid site $)$$)$))
$\mathrm{logPro}={\beta }_0+{\beta }_1{}^{\ast }\log \mathrm{Vol}+{\beta }_2{}^{\ast }$$\mathrm{logPro}={\beta }_0+{\beta }_1{}^{\ast }\log \mathrm{Vol}+{\beta }_2{}^{\ast }$logPro=beta_(0)+beta_(1)^(**)log Vol+beta_(2)^(**)\operatorname{logPro}=\beta_{0}+\beta_{1}{ }^{*} \log \operatorname{Vol}+\beta_{2}{ }^{*} 基质 $+(1\mid$$+(1\mid$+(1∣+(1 \mid 场地 $)$$)$))
where $\log$$\log$log\log Pro is the natural log of discharge measured with the professional method,
其中， $\log$$\log$log\log Pro 是用专业方法测量的排放量的自然对数、
logVol is the natural log of discharge measured with the volunteer method,
logVol 是用志愿者方法测量的排放量的自然对数、
substrate is a categorical substrate term (rocky or smooth),
基质是一个分类基质术语（岩石或光滑）、
${\beta }_0,{\beta }_1$${\beta }_0,{\beta }_1$beta_(0),beta_(1)\beta_{0}, \beta_{1}, and ${\beta }_2$${\beta }_2$beta_(2)\beta_{2} are regression coefficients, and.
${\beta }_0,{\beta }_1$${\beta }_0,{\beta }_1$beta_(0),beta_(1)\beta_{0}, \beta_{1} 和 ${\beta }_2$${\beta }_2$beta_(2)\beta_{2} 是回归系数，并且。
(1|site) denotes the random effect of stream site on the intercept.
(1|site) 表示流经地点对截距的随机影响。
We also tested two other versions of the model with additional variables as fixed effects. The first version included mean water depth based on the findings of Hundt and Blasch (2019). The second version included the number of measurements made by volunteers at the site prior to the study as a surrogate measure of volunteer experience. However, both of these models had less statistical support based on Akaike information criterion (AIC) than Equation (3).
我们还测试了其他两个版本的模型，将其他变量作为固定效应。第一个版本根据 Hundt 和 Blasch（2019 年）的研究结果加入了平均水深。第二个版本包含了志愿者在研究之前在现场进行测量的次数，作为志愿者经验的替代指标。然而，根据阿凯克信息准则（AIC），这两个模型的统计支持度都低于方程 (3)。

In 76 site visits, we measured discharge an average of 2.7 times at each of 28 volunteer stream monitoring sites in 14 Wisconsin counties between August 2011 and November 2012 (Fig. 1). The median stream characteristics, with each site visit included as a single point, at the time of measurement were $4.78\mathrm{m}(15.7\mathrm{ft})$$4.78\mathrm{m}(15.7\mathrm{ft})$4.78m(15.7ft)4.78 \mathrm{~m}(15.7 \mathrm{ft}) wide, $0.21\mathrm{m}(0.69\mathrm{ft})$$0.21\mathrm{m}(0.69\mathrm{ft})$0.21m(0.69ft)0.21 \mathrm{~m}(0.69 \mathrm{ft}) average depth, $0.15\mathrm{m}/\mathrm{s}(0.49\mathrm{ft}/\mathrm{s})$$0.15\mathrm{m}/\mathrm{s}(0.49\mathrm{ft}/\mathrm{s})$0.15m//s(0.49ft//s)0.15 \mathrm{~m} / \mathrm{s}(0.49 \mathrm{ft} / \mathrm{s}) average velocity, and $0.16{\mathrm{m}}^3/\mathrm{s}(5.65\mathrm{cfs})$$0.16{\mathrm{m}}^3/\mathrm{s}(5.65\mathrm{cfs})$0.16m^(3)//s(5.65cfs)0.16 \mathrm{~m}^{3} / \mathrm{s}(5.65 \mathrm{cfs}) discharge (Fig. 3). While volunteers had the option to select between a surface velocity coefficient of 0.8 or 0.9 on each site visit, volunteers only chose an alternate coefficient one time each at six of the 28 sites.
2011 年 8 月至 2012 年 11 月期间，我们对威斯康星州 14 个县的 28 个志愿溪流监测点进行了 76 次实地考察，平均每个监测点测量了 2.7 次排水量（图 1）。测量时的溪流特征中位数为 $4.78\mathrm{m}(15.7\mathrm{ft})$$4.78\mathrm{m}(15.7\mathrm{ft})$4.78m(15.7ft)4.78 \mathrm{~m}(15.7 \mathrm{ft}) 宽、 $0.21\mathrm{m}(0.69\mathrm{ft})$$0.21\mathrm{m}(0.69\mathrm{ft})$0.21m(0.69ft)0.21 \mathrm{~m}(0.69 \mathrm{ft}) 平均深度、 $0.15\mathrm{m}/\mathrm{s}(0.49\mathrm{ft}/\mathrm{s})$$0.15\mathrm{m}/\mathrm{s}(0.49\mathrm{ft}/\mathrm{s})$0.15m//s(0.49ft//s)0.15 \mathrm{~m} / \mathrm{s}(0.49 \mathrm{ft} / \mathrm{s}) 平均流速和 $0.16{\mathrm{m}}^3/\mathrm{s}(5.65\mathrm{cfs})$$0.16{\mathrm{m}}^3/\mathrm{s}(5.65\mathrm{cfs})$0.16m^(3)//s(5.65cfs)0.16 \mathrm{~m}^{3} / \mathrm{s}(5.65 \mathrm{cfs}) 排放量（图 3）。虽然志愿者在每次考察时都可以选择 0.8 或 0.9 的地表速度系数，但在 28 个考察点中，志愿者只在 6 个考察点中选择了一次备用系数。

The mixed effects model indicated a strong linear relationship (slope $=1.00$$=1.00$=1.00=1.00 ) between discharge measurements made with the volunteer and professional methods (Table 2, Fig. 4). The model intercept and substrate estimates can be translated into surface velocity coefficients for
混合效应模型表明，用志愿者方法和专业方法测量的排水量之间存在很强的线性关系（斜率 $=1.00$$=1.00$=1.00=1.00 ）（表 2，图 4）。模型截距和底质估算值可转化为地表速度系数，以用于

Fig. 3. Boxplots of characteristics of the 28 study sites as determined by the researchers.
图 3.研究人员确定的 28 个研究地点的特征方框图。

Table 2 表 2
Fixed and random effects in model relating discharge measurements made with the volunteer and professional methods.
用志愿者方法和专业方法进行排放测量的相关模型中的固定效应和随机效应。

rocky bed streams $(\exp (-0.50)=0.61)$$(\exp (-0.50)=0.61)$(exp(-0.50)=0.61)(\exp (-0.50)=0.61) and smooth bed streams (exp $(-0.50+0.12)=0.69)$$(-0.50+0.12)=0.69)$(-0.50+0.12)=0.69)(-0.50+0.12)=0.69). The standard deviation of the random effects ( 0.02 ) was small, indicating little consistent variation in surface velocity coefficients among streams, though the small number of measurements per stream (1-4) may have limited the power to detect variation.
岩床溪流 $(\exp (-0.50)=0.61)$$(\exp (-0.50)=0.61)$(exp(-0.50)=0.61)(\exp (-0.50)=0.61) 和光滑河床溪流（指数 $(-0.50+0.12)=0.69)$$(-0.50+0.12)=0.69)$(-0.50+0.12)=0.69)(-0.50+0.12)=0.69) 。随机效应的标准偏差（0.02）很小，表明溪流之间的表面速度系数几乎没有一致的变化，尽管每条溪流的测量次数较少（1-4 次），可能限制了检测变化的能力。

We assessed the accuracy of the volunteer method using the newly estimated surface velocity coefficients by the distribution of residuals from the model. The mean absolute percent error was $22\mathrm{\%}$$22\mathrm{\%}$22%22 \%, and $50\mathrm{\%}$$50\mathrm{\%}$50%50 \% and $90\mathrm{\%}$$90\mathrm{\%}$90%90 \% of volunteer measurements were within $15\mathrm{\%}$$15\mathrm{\%}$15%15 \% and $56\mathrm{\%}$$56\mathrm{\%}$56%56 \% of the professional measurement. For comparison, the mean absolute error of measurements that used the original surface velocity coefficients was 37 $\mathrm{\%}$$\mathrm{\%}$%\%. Using the new coefficients, mean absolute errors were $27\mathrm{\%}$$27\mathrm{\%}$27%27 \% for measurements less than $0.03{\mathrm{m}}^3/\mathrm{s},25\mathrm{\%}$$0.03{\mathrm{m}}^3/\mathrm{s},25\mathrm{\%}$0.03m^(3)//s,25%0.03 \mathrm{~m}^{3} / \mathrm{s}, 25 \% for measurements between 0.03 and $0.3{\mathrm{m}}^3/\mathrm{s}$$0.3{\mathrm{m}}^3/\mathrm{s}$0.3m^(3)//s0.3 \mathrm{~m}^{3} / \mathrm{s}, and $18\mathrm{\%}$$18\mathrm{\%}$18%18 \% for measurements greater than $0.3{\mathrm{m}}^3/\mathrm{s}$$0.3{\mathrm{m}}^3/\mathrm{s}$0.3m^(3)//s0.3 \mathrm{~m}^{3} / \mathrm{s}.
我们使用新估算的表面速度系数，通过模型的残差分布来评估志愿者方法的准确性。平均绝对百分误差为 $22\mathrm{\%}$$22\mathrm{\%}$22%22 \% ，志愿者测量的 $50\mathrm{\%}$$50\mathrm{\%}$50%50 \% 和 $90\mathrm{\%}$$90\mathrm{\%}$90%90 \% 与专业测量的 $15\mathrm{\%}$$15\mathrm{\%}$15%15 \% 和 $56\mathrm{\%}$$56\mathrm{\%}$56%56 \% 相差不大。相比之下，使用原始表面速度系数测量的平均绝对误差为 37 $\mathrm{\%}$$\mathrm{\%}$%\% 。使用新系数测量的平均绝对误差为 $27\mathrm{\%}$$27\mathrm{\%}$27%27 \% $0.03{\mathrm{m}}^3/\mathrm{s},25\mathrm{\%}$$0.03{\mathrm{m}}^3/\mathrm{s},25\mathrm{\%}$0.03m^(3)//s,25%0.03 \mathrm{~m}^{3} / \mathrm{s}, 25 \% ，测量值在 0.03 和 $0.3{\mathrm{m}}^3/\mathrm{s}$$0.3{\mathrm{m}}^3/\mathrm{s}$0.3m^(3)//s0.3 \mathrm{~m}^{3} / \mathrm{s} 之间，测量值大于 $0.3{\mathrm{m}}^3/\mathrm{s}$$0.3{\mathrm{m}}^3/\mathrm{s}$0.3m^(3)//s0.3 \mathrm{~m}^{3} / \mathrm{s} ，平均绝对误差为 $18\mathrm{\%}$$18\mathrm{\%}$18%18 \% 。

We compared the original surface velocity coefficients (University of Wisconsin, 2010) to the coefficients derived from the model. For rocky bed streams the ratio between 0.8 and 0.61 translates to a $30\mathrm{\%}$$30\mathrm{\%}$30%30 \% overestimation of discharge when using the original surface velocity coefficients. The ratio between the smooth-bed original surface velocity coefficient ( 0.9 ) and the coefficient derived from the model ( 0.69 ) was nearly identical, indicating that a similar degree of bias has been present in all measurements using this protocol.
我们将原始地表速度系数（威斯康星大学，2010 年）与模型得出的系数进行了比较。对于岩床溪流，使用原始地表速度系数时，0.8 与 0.61 之间的比率意味着 $30\mathrm{\%}$$30\mathrm{\%}$30%30 \% 高估了排水量。光滑河床的原始地表速度系数（0.9）与根据模型得出的系数（0.69）之间的比值几乎相同，这表明使用该方案进行的所有测量都存在类似程度的偏差。

This study compared results of stream discharge measurements made by staff using a standard velocity-area method with an electromagnetic meter to those obtained by trained volunteers using a surface float method. The following discussion focuses on comparison of the empirically derived coefficients to United States national and international standards and common volunteer monitoring protocols, potential utility of revised surface velocity coefficients to improve surface float method discharge estimation, additional opportunities to improve the method, study limitations and future research, and recommendations for use of the empirically derived surface velocity coefficients.
这项研究比较了工作人员使用电磁流量计的标准速度面积法和训练有素的志愿者使用水面漂浮法进行的溪流排放测量结果。以下讨论的重点包括：将根据经验得出的系数与美国国家和国际标准以及常见的志愿者监测协议进行比较；修订后的地表速度系数对改进地表漂浮法排水量估算的潜在作用；改进该方法的其他机会；研究的局限性和未来研究；以及对使用根据经验得出的地表速度系数的建议。

The surface velocity coefficients for rocky ( 0.61 ) and smooth (0.69) bottom streams estimated by this study agree with early coefficient recommendations (British Standards Institution, 1964) for shallow streams ( $<1\mathrm{m}$$<1\mathrm{m}$< 1m<1 \mathrm{~m} ). However, the coefficients are about $25\mathrm{\%}$$25\mathrm{\%}$25%25 \% lower than those currently recommended for use with surface float methods in United States’ national (Turnipseed and Sauer, 2010) and international (ISO, 2021) standards. The higher coefficients (that range from about 0.8 to 0.9 ) are also commonly used by United States-based volunteer stream monitoring groups (e.g., Georgia Department of Natural Resources, 2014; Indiana Department of Environmental Management, 2022; Missouri Department of Natural Resources, 2022; University of Wisconsin, 2010; United States Environmental Protection Agency, 1997). In part, such common use of the higher surface velocity coefficients is due to derivation of coefficients from the same original sources. For instance, United States’ national (Turnipseed and Sauer, 2010) and international (ISO, 2021) standards provide common guidance to use coefficients of 0.84 to 0.9 when a coefficient cannot be measured at the site. Further, volunteer monitoring methods were developed based on one another. By example, United States Environmental Protection Agency (1997) mentioned Missouri Stream Teams as a resource that informed their national volunteer stream monitoring methods manual, and the volunteer protocol used in the present study
本研究估算的岩质河底（0.61）和光滑河底（0.69）的表层流速系数与早期针对浅水溪流（ $<1\mathrm{m}$$<1\mathrm{m}$< 1m<1 \mathrm{~m} ）的系数建议（英国标准协会，1964 年）一致。不过，这些系数比目前美国国家标准（Turnipseed 和 Sauer，2010 年）和国际标准（ISO，2021 年）中建议使用的表层漂浮法的系数 $25\mathrm{\%}$$25\mathrm{\%}$25%25 \% 要低。较高的系数（约为 0.8 至 0.9）也被美国的溪流监测志愿者团体普遍采用（例如，佐治亚州自然资源部，2014 年；印第安纳州环境管理部，2022 年；密苏里州自然资源部，2022 年；威斯康星大学，2010 年；美国环境保护局，1997 年）。之所以普遍使用较高的地表速度系数，部分原因是这些系数来源于相同的原始资料。例如，美国国家标准（Turnipseed 和 Sauer，2010 年）和国际标准（ISO，2021 年）提供了在现场无法测量系数时使用 0.84 至 0.9 系数的通用指导。此外，志愿监测方法也是在相互借鉴的基础上发展起来的。例如，美国环境保护署（1997 年）将密苏里州溪流团队作为其国家志愿者溪流监测方法手册的参考资料，本研究中使用的志愿者协议也是如此。

Fig. 4. Relationship between discharge measurements made with the volunteer and professional methods in Wisconsin, United States, streams with rocky and smooth substrates. Solid lines are mixed effects model estimates of the surface velocity coefficients.
图 4.在美国威斯康星州基质为岩石和光滑基质的溪流中，用志愿者方法和专业方法测量的排水量之间的关系。实线为地表速度系数的混合效应模型估计值。
was based on the United States Environmental Protection Agency (United States Environmental Protection Agency, 1997) and Missouri Stream Team (Missouri Department of Natural Resources, 2000) methods (University of Wisconsin, 2010).
根据美国环境保护局（United States Environmental Protection Agency，1997 年）和密苏里州溪流小组（Missouri Department of Natural Resources，2000 年）的方法（威斯康星大学，2010 年）。

Further inspection of source data in which stream depths were reported (British Standards Institution, 1964) suggests that nuances of those recommendations were lost in guidance documents over the past two decades. This may have been due to confusion in interpretation of that guidance. Namely, there was reference to both “factors” (p. 22 Fig. 1, British Standards Institution, 1964) and “coefficients” (p. 23 Table 1, British Standards Institution, 1964) by which it was recommended to multiply surface velocities to determine mean velocities. Factors - that ranged from about 0.84 for rough beds to 0.88 for smooth beds - were recommended for use in “small channels having an approximately rectangular cross-section” (British Standards Institution, 1964, p. 23). This was described as an open channel in which width was “several times greater than the depth” (British Standards Institution, 1964, p. 22), whereas the coefficients were recommended for use in natural channels with saucer-shaped bed profiles. No information was provided about water depths associated with the factors, however, average depth in the stream reach was reported for each coefficient. These included very shallow ( 0.3 m ) to deep depths ( 6 m and deeper). Recommended coefficients only reached 0.8 when average depths were 6 m and greater. Coefficients for shallower depths ranged from $0.66(0.3$$0.66(0.3$0.66(0.30.66(0.3 $\mathrm{m})$$\mathrm{m})$m)\mathrm{m}) to 0.79 ( 4.5 m depth). Both the table and figure from that 1964 guidance document were reported in later guidance (e.g., Kulin and Compton, 1975; United States Bureau of Reclamation, 2001). However, reference to the table of coefficients and associated depths was not included in guidance documents in later years. Instead, only brief mention of an average coefficient of 0.85 (Rantz et al., 1982) or the range of coefficients from 0.84 to 0.90 (Turnipseed and Sauer, 2010; ISO, 2021) were provided. We believe these were derived empirically (Hulsing et al., 1966), but the data that informed the coefficients were collected in small streams ( $0.03{\mathrm{m}}^3/\mathrm{s})$$\left.0.03{\mathrm{m}}^3/\mathrm{s}\right)${: 0.03m^(3)//s)\left.0.03 \mathrm{~m}^{3} / \mathrm{s}\right) to very large rivers $(18,009{\mathrm{m}}^3/\mathrm{s})$$\left(18,009{\mathrm{m}}^3/\mathrm{s}\right)$(18,009m^(3)//s)\left(18,009 \mathrm{~m}^{3} / \mathrm{s}\right) and may have been influenced by observations made in larger waterways. Thus, the nuanced use of the smaller coefficients for shallower average water depths in natural channels was lost over time.
对报告溪流深度的原始数据（英国标准协会，1964 年）的进一步检查表明，过去二十年来，这些建议的细微差别已在指导文件中消失。这可能是由于对该指南的解释混乱所致。也就是说，指导文件中提到了 "系数"（第 22 页图 1，英国标准学会，1964 年）和 "系 数"（第 23 页表 1，英国标准学会，1964 年），建议用它们乘以表面流速来确定平均流速。系数范围从粗糙河床的 0.84 到光滑河床的 0.88，建议用于 "横截面近似矩形的小水道"（英国标准协会，1964 年，第 23 页）。这被描述为宽度 "比深度大几倍 "的明渠（英国标准协会，1964 年，第 22 页），而这些系数被推荐用于具有碟形河床剖面的天然河道。没有提供与系数相关的水深信息，但报告了每个系数在河段中的平均水深。其中包括很浅（0.3 米）到很深（6 米及以上）的水深。只有当平均水深达到或超过 6 米时，推荐系数才会达到 0.8。较浅深度的系数从 $0.66(0.3$$0.66(0.3$0.66(0.30.66(0.3 $\mathrm{m})$$\mathrm{m})$m)\mathrm{m}) 到 0.79（4.5 米深度）不等。1964 年指导文件中的表格和图表在后来的指导文件中都有报道（如 Kulin 和 Compton，1975 年；美国垦务局，2001 年）。不过，后来的指导文件中并未提及系数表和相关深度。取而代之的是，仅简要提及平均系数为 0.85（Rantz et al.我们认为这些系数是根据经验得出的（Hulsing 等人，1966 年），但这些系数的数据是在小溪（ $0.03{\mathrm{m}}^3/\mathrm{s})$$\left.0.03{\mathrm{m}}^3/\mathrm{s}\right)${: 0.03m^(3)//s)\left.0.03 \mathrm{~m}^{3} / \mathrm{s}\right) ）到大河（ $0.03{\mathrm{m}}^3/\mathrm{s})$$\left.0.03{\mathrm{m}}^3/\mathrm{s}\right)${: 0.03m^(3)//s)\left.0.03 \mathrm{~m}^{3} / \mathrm{s}\right) ）收集的。我们认为这些系数都是根据经验得出的（Hulsing 等人，1966 年），但这些系数的数据都是在小溪（ $0.03{\mathrm{m}}^3/\mathrm{s})$$\left.0.03{\mathrm{m}}^3/\mathrm{s}\right)${: 0.03m^(3)//s)\left.0.03 \mathrm{~m}^{3} / \mathrm{s}\right) 到大河 $(18,009{\mathrm{m}}^3/\mathrm{s})$$\left(18,009{\mathrm{m}}^3/\mathrm{s}\right)$(18,009m^(3)//s)\left(18,009 \mathrm{~m}^{3} / \mathrm{s}\right) ）中收集的，可能受到了在较大水道中观测结果的影响。因此，自然河道中平均水深较浅时使用较小系数的细微差别随着时间的推移而消失了。