Applicability Comparison of Three Sound Velocity Algorithms in the Mendeleev Ridge Area of the Arctic Ocean ——Based on In Situ Data from the 9th Chinese National Arctic Expedition
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摘要: 声速是海洋声学探测与应用的核心物理参数，其精度直接决定水声通信、海底地形测绘及声层析成像等技术的可靠性。目前声速剖面主要通过温盐深（CTD）数据借助经验公式间接计算获得，其中Chen-Millero（1977）、Del Grosso（1974）和Wilson（1960）公式是全球最常用的三种声速算法。然而，这些公式多基于中低纬度海洋数据构建，在具有低温、强层化、淡水输入显著的北极海域的适用性尚未得到充分验证。本研究基于中国第九次北极科学考察（2018年）在门捷列夫海岭以东172°W经向断面获取的高精度CTD与声速剖面仪（SVP）同步观测数据，系统比较了上述三种算法在北极典型环境下的计算精度。结果表明，在这一断面上，Del Grosso (1974) 经验公式综合性能最优，在整个断面和全水深范围内表现出最高的准确性（平均偏差0.62 m/s）与最佳稳定性（偏差标准差0.23 m/s），是区域声速计算的首选算法。Wilson（1960）公式存在显著深度依赖性系统高估，500 m以深平均偏差达1.17 m/s，不适用于北极深层计算。Chen and Millero（1977）公式表现居中，但对表层极端水文条件敏感，深层也存在系统性高估。算法误差具有明显的空间与垂向异质性，与水文环境复杂程度密切相关，北极特殊的水文过程显著加大了现有经验公式的计算不确定性。Abstract: Sound velocity is a core physical parameter in marine acoustic detection and applications, and its accuracy directly determines the reliability of technologies such as underwater acoustic communication, seabed topographic mapping, and acoustic tomography. Currently, sound velocity profiles are primarily obtained indirectly through empirical formulas using Conductivity-Temperature-Depth (CTD) data, among which the Chen-Millero (1977), Del Grosso (1974), and Wilson (1960) formulas are the three most commonly used algorithms globally. However, these formulas were largely developed based on ocean data from mid and low latitudes, and their applicability in the Arctic Ocean—characterized by low temperatures, strong stratification, and significant freshwater input—has not been fully validated. This study utilizes synchronized high-precision CTD and Sound Velocity Profiler (SVP) data collected along the 172°W meridional section east of the Mendeleev Ridge during the 9th Chinese National Arctic Expedition (2018) to systematically compare the computational accuracy of these three algorithms under typical Arctic environmental conditions. The results indicate that along this section, the Del Grosso (1974) empirical formula exhibits the best overall performance, demonstrating the highest accuracy (mean bias of 0.62 m/s) and optimal stability (standard deviation of bias of 0.23 m/s) across the entire section and full depth range, making it the preferred algorithm for regional sound velocity calculation. The Wilson (1960) formula shows a significant depth-dependent systematic overestimation, with a mean bias of 1.17 m/s below 500 m depth, which renders it unsuitable for deep-layer calculations in the Arctic. The Chen and Millero (1977) formula exhibits intermediate overall performance but is sensitive to extreme surface hydrological conditions, with systematic overestimation also occurring in deep layers. The algorithm errors display distinct spatial and vertical heterogeneity that is closely related to the complexity of the hydrological environment, and the unique hydrological processes of the Arctic Ocean significantly amplify the computational uncertainties of existing empirical formulas.
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图 1 M02（左）、M07（右）站位声速剖面分布
Fig. 1 Distribution of sound velocity profiles at stations M02(left), M07(right)
图 2 M01（左）、M03（右）站位0−200 m声速剖面分布
Fig. 2 Distribution of sound velocity profiles within 0−200 m at stations M01 (left), M03 (right)
表 1 中国第九次北极科学考察M断面海洋声速剖面调查站位信息
Tab. 1 Station Information for sound velocity profile survey at section M during the 9th Chinese Arctic Research Expedition
序号 站位 日期 起始作业时间（UTC） 经度(W) 纬度(N) 当地水深/m 测量深度/m 1 M01 2018.8.3 6:53 172°1.411 ′W 74°48.438′N 316 309 2 M02 2018.8.3 13:10 172°0.127 ′W 75°9.064 ′N 414 403 3 M03 2018.8.3 18:11 172°10.435′W 75°32.752′N 1242 1222 4 M04 2018.8.4 1:19 172°0.497 ′W 76°0.620 ′N 1977 1959 5 M05 2018.8.4 6:27 172°2.824 ′W 76°23.083′N 2253 2230 6 M06 2018.8.4 13:26 171°58.620′W 76°47.974′N 1560 1539 7 M07 2018.8.4 18:30 171°57.300′W 77°11.724′N 2247 2233 
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表 2 加拿大AML公司生产的Minos SVP中传感器XCH-SV-STD技术指标
Tab. 2 Technical specifications of the XCH-SV-STD sensor produced by the Canadian company AML for the Minos SVP.
指标类型 适用最大水深 声速范围 声速精确度 声速准确度 声速分辨率 响应时间 指标值 6000 m1375 ～1625 m/s0.006 m/s 0.025 m/s 0.001 m/s 47 us
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表 3 美国海鸟公司生产的SBE 911plus CTD技术指标
Tab. 3 Technical Specifications of the Sea-Bird SBE 911 CTD sensor produced by Sea-Bird Scientific, USA
传感器 测量范围 测量准确度 稳定度（每月） 分辨率 响应时间 电导率(S/m) 0～7 0.0003 0.0003 0.00004 65 us 温度(℃) −5～+35 0.001 0.0002 0.0002 65 us 压力(dbar) 10000 0.015%FS 0.0015 %FS0.001%FS 15 us
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表 4 M断面上计算声速的最大绝对偏差、平均偏差、偏差标准差统计（单位：m/s）
Tab. 4 Statistics of Maximum Absolute Deviation, Mean Deviation, and Standard Deviation of Deviation for CSV on Section M (in unit m/s)
序号 站位 MAD MD SDD CSV-C CSV-D CSV-W CSV-C CSV-D CSV-W CSV-C CSV-D CSV-W 1 M01 3.66 3.61 3.56 0.60 0.54 0.69 0.57 0.58 0.52 2 M02 2.31 2.22 2.49 0.95 0.84 1.09 0.33 0.32 0.36 3 M03 1.48 1.39 1.65 0.86 0.72 1.03 0.12 0.14 0.15 4 M04 1.29 1.24 1.41 0.86 0.57 1.11 0.11 0.07 0.17 5 M05 1.13 0.90 1.43 0.88 0.55 1.12 0.17 0.06 0.24 6 M06 1.21 0.93 1.45 0.80 0.54 1.02 0.15 0.07 0.21 7 M07 1.12 0.75 1.42 0.88 0.56 1.13 0.18 0.05 0.24 8 最大 3.66 3.61 3.56 0.95 0.84 1.13 0.57 0.58 0.52 9 最小 1.12 0.75 1.41 0.60 0.54 0.69 0.11 0.05 0.15 10 平均 1.74 1.58 1.92 0.83 0.62 1.03 0.28 0.23 0.30
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表 5 M断面上不同深度范围内三种CSVP和MSVP之间MD差异（单位：m/s）
Tab. 5 MD differences among 3 kinds of CSVP and MSVP in different layers on M section (in unit m/s)
序号 站位 0−200 m 200−500 m 500 m以深 CSVP-C CSVP-D CSVP-W CSVP-C CSVP-D CSVP-W CSVP-C CSVP-D CSVP-W 1 M01 0.71 0.69 0.75 0.39 0.26 0.58 —— —— —— 2 M02 0.86 0.82 0.96 1.03 0.87 1.21 —— —— —— 3 M03 0.88 0.82 0.98 0.86 0.69 1.05 0.86 0.64 1.07 4 M04 0.67 0.62 0.78 0.77 0.60 0.96 0.91 0.55 1.18 5 M05 0.56 0.47 0.65 0.69 0.51 0.88 0.95 0.57 1.22 6 M06 0.57 0.51 0.65 0.69 0.52 0.88 0.87 0.55 1.13 7 M07 0.56 0.51 0.64 0.68 0.51 0.87 0.95 0.57 1.23 8 平均 0.69 0.63 0.77 0.73 0.57 0.92 0.91 0.58 1.17
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表 6 M断面上0−200 m范围内不同层面内三种CSVP和MSVP之间MD差异（单位：m/s）
Tab. 6 MD differences among 3 kinds of CSVP and MSVP in different layers within the 0−200 m range on M section (in unit m/s)
序号 站位 0−25 m 25−75 m 75−200 m CSVP-C CSVP-D CSVP-W CSVP-C CSVP-D CSVP-W CSVP-C CSVP-D CSVP-W 1 M01 1.73 1.68 1.58 1.08 1.05 1.15 0.40 0.38 0.46 2 M02 0.67 0.64 0.59 0.81 0.79 0.87 0.92 0.86 1.06 3 M03 0.67 0.64 0.60 0.80 0.77 0.85 0.94 0.87 1.08 4 M04 0.60 0.57 0.51 0.65 0.62 0.69 0.69 0.63 0.85 5 M05 0.53 0.44 0.42 0.51 0.44 0.55 0.59 0.49 0.73 6 M06 0.53 0.50 0.43 0.51 0.47 0.52 0.59 0.53 0.74 7 M07 0.50 0.48 0.41 0.50 0.47 0.51 0.58 0.52 0.72 8 平均 0.75 0.71 0.65 0.69 0.66 0.73 0.67 0.61 0.81 9 M02-M07平均 0.58 0.55 0.49 0.63 0.59 0.67 0.72 0.65 0.86
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