青藏高原纳木错湖冰物候变化遥感监测与模拟

青藏高原纳木错湖冰物候变化遥感监测与模拟 Lake ice phenology of the Nam Co at Tibetan Plateau： Remote sensing and modelling 1 2 first-author 吴艳红，1979年生，女，副研究员，研究方向为遥感水文。E-mail：wuyh@aircas.ac.cn 吴艳红，1979年生，女，副研究员，研究方向为遥感水文。E-mail：wuyh@aircas.ac.cn wuyh@aircas.ac.cn 1 2 1 2 1 1 2 1 2 corresp 张兵，1969年生，男，研究员，研究方向为高光谱遥感。E-mail：zb@aircas.ac.cn 张兵，1969年生，男，研究员，研究方向为高光谱遥感。E-mail：zb@aircas.ac.cn zb@aircas.ac.cn 中国科学院空天信息创新研究院 数字地球重点实验室, 北京 100094 中国科学院空天信息创新研究院 数字地球重点实验室, 北京 100094 Key Laboratory of Digital Earth Science, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China Key Laboratory of Digital Earth Science, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China 中国科学院大学, 北京 100049 中国科学院大学, 北京 100049 College of Resources and Environment, University of Chinese Academy of Sciences, Beijing 100049, China College of Resources and Environment, University of Chinese Academy of Sciences, Beijing 100049, China 湖冰物候是反映区域气候变化的直观指标。由于青藏高原湖冰物候的地面观测不足，遥感与模拟成为动态监测湖冰物候变化并揭示其变化机理的重要途径。本文以纳木错为例，通过不同遥感方法获取了纳木错2000年—2015年湖冰物候的动态变化。在此基础上，将遥感与物理基础清晰的湖泊过程模型相结合，重建了纳木错1963年—2018年的湖冰物候序列，并分析了近60 a来纳木错湖冰物候的变化规律。研究结果表明，气候变暖影响下，湖冰融化日期显著提前，纳木错湖泊的冰期以6.4 d/（10 a）的速率显著缩短。未来气温升高2 ℃的情景下，湖冰融化日期平均可提前12.4 d。 Lake ice phenology refers to the dates of lake freeze-up and break-up and period of ice cover; it is considered a valuable indicator of regional climate change. The shifts of lake ice phenology in association with a warming climate is widely interesting because it not only serves as evidence of the changes in climate but could show substantial impacts on regional hydrological processes and the aquatic ecosystem. Ground-based records of lake ice phenology over the Tibetan Plateau are limited because of the harsh geographical conditions and the high observation costs. Satellite-based observation and modeling are expected to be effective in investigating the long-term changes in lake ice phenology for regions with poor ground observations. We aim to reconstruct the lake ice phenology time series and to identify the long-term changes of lake ice phenology in responding to the climate of Nam Co Lake at the Tibetan Plateau and for the past 60 years based on a process-based model, where remotely sensed lake surface water temperature is used to calibrated the process-based model. The research framework includes retrieving lake surface water temperature and lake ice phenology information from remotely sensed data, calibrating the process-based model against the remotely sensed lake surface water temperature, determining lake ice phenology according to the simulated water temperature, validating the simulated lake ice phenology by comparing against that derived from the remotely sensed data, detecting the long-term trends in the reconstructed lake ice phenology, and modeling the response of lake ice phenology to changes in air temperature. Four different remotely sensed datasets and the corresponding approaches are used to retrieve lake ice phenology of the Nam Co for the period 2000—2015. The process-based model (LAKE 2.3) is a 1D lake surface energy balance model. It is used to reconstruct lake ice phenology of Nam Co for the period 1963 to 2018 and investigate the sensitivity of lake ice phenology to climate change. The Mann–Kendall nonparametric statistical test approach is used in detecting the trend of lake ice phenology. Lake ice phenology derived using different remotely sensed data and approaches with consistency in the trend but with considerable uncertainties due to the temporal and spatial resolution of the sensors. The reconstructed lake ice breaking-up date based on the model is more comparable to that remotely sensed data than the other lake ice phenology indicators. The reconstructed time series of lake ice phenology shows that, during the previous 57 years, the freezing-up date was significantly delayed whereas the breaking-up date was earlier, thereby resulting in a shortened ice cover duration. The ice cover duration is shortened at a rate of 6.4 days/10a during the period 1963 to 2018. Sensitivity analysis shows that the breaking-up date would be significantly earlier in a warm climate. Under the 2 °C warmer scenario, the breaking-up date would be 12.4 days earlier on the average, and the ice cover duration would be shortened by 19.7 days, on the average. This study combines the strengths of remote sensing and numerical modeling in forming a novel research framework to reconstruct lake ice phenology of regions with poor ground-observation, such as the Tibetan Plateau. The results show that the framework is reliable and valuable to explore the long-term changes in lake ice phenology and its response to climate change. However, uncertainties exist in the remotely sensed lake ice phenology and the numerical modeling, which needs to be improved and further validated where or when ground-based observations are available. 湖冰物候 遥感监测 湖泊模型 纳木错 青藏高原 lake ice phenology multi-source remote sensing lake model Nam Co Tibetan Plateau 1　引 言 1 湖冰物候（湖泊的冻结和消融时间）直接受湖泊能量平衡变化的影响，对区域气候变化有很好的指示作用（ Kouraev等，2007 Kouraev等，2007 ； Marszelewski和Skowron，2006 Marszelewski和Skowron，2006 ）。湖冰物候在反映气候变化方面某种程度上可能比气温更可靠（ Livingstone，1997 Livingstone，1997 ）。湖冰物候的变化影响着湖泊生态系统中生物的繁殖以及渔业、运输业等人类生产活动。因此，近年来中高纬度湖冰物候对全球变暖的响应越来越为研究人员所关注（ Salonen等，2009 Salonen等，2009 ； Bengtsson，2011 Bengtsson，2011 ； Fu和Yao，2015 Fu和Yao，2015 ； Gou等，2017 Gou等，2017 ； Latifovic和Pouliot，2007 Latifovic和Pouliot，2007 ； Magnuson等，2000 Magnuson等，2000 ）。比如， Magnuson等（2000） Magnuson等（2000） 利用实测数据分析了150年间北半球39个湖泊的湖冰物候变化趋势，发现北半球湖冰物候表现出结冰日延后和融冰日提前的趋势，并为后续的研究所证实（ Bernhardt等，2012 Bernhardt等，2012 ； Brown和Duguay，2010 Brown和Duguay，2010 ； Ghanbari等，2009 Ghanbari等，2009 ）。 基于AVHRR、MODIS等光学传感器（如： Latifovic和Pouliot，2007 Latifovic和Pouliot，2007 ； Kropáček等，2013 Kropáček等，2013 ； Duguay等，2015 Duguay等，2015 ）和微波遥感器（如：QuickSCAT，SSM/I，SMMR，AMSR-E）等对湖冰物候进行动态监测已成为当前湖冰物候研究的重要手段。其中，光学遥感湖冰物候监测常用的方法包括阈值法、指数法、反射率光谱曲线法等（ 庞毓雯 等，2020 庞毓雯 等，2020 ； Guo等，2018 Guo等，2018 ） 。在微波遥感方面， 邱玉宝等（2017） 邱玉宝等（2017） 利用微波亮温数据分析了青藏高原湖冰的冻融变化。 遥感是获取湖冰物候信息的有效途径。然而，由于遥感平台的服务年限相对较短，难以揭示湖冰物候的长期变化规律。另外，遥感信息反映了湖冰物候变化的事实而无法解释其变化的物理机制。认识湖泊冻融过程的物理机制，进而量化湖冰物候对气候的响应，通常则需借助数值模拟的方法来实现（ 任晓倩 等，2014 任晓倩 等，2014 ）。数理模型考虑了多种气候强迫项和湖泊形态特征对湖冰冻融过程的作用，有助于从机理的层面揭示和预测湖冰的生消过程。现有湖泊过程模式如MIMLAKE96（ Fang和Stefan，1996 Fang和Stefan，1996 ）、LAKEoneD（ Joehnk和Umlauf，2001 Joehnk和Umlauf，2001 ）、LAKE模式（ Stepanenko等，2016 Stepanenko等，2016 ）、SIMSTRAT（ Goudsmit等，2002 Goudsmit等，2002 ）CLIM（ Duguay等，2003 Duguay等，2003 ）、LIMNOS（ Vavrus等，1996 Vavrus等，1996 ）、HIGHTSI（ Launiainen和Cheng，1998 Launiainen和Cheng，1998 ）等。这些模型在世界各地区已经得到了应用和验证。中国湖泊研究起步较晚，现有模型多为外国学者针对当地环境开发，在青藏高原的适用性仍然有待验证（ 宋兴宇等，2020 宋兴宇等，2020 ）。 方楠等（2017） 方楠等（2017） 改进并评估了WRF模型在纳木错的适用性； 苏东生等（2018） 苏东生等（2018） 利用“中国区域高时空分辨率地表气象驱动数据集（CMFD）”驱动Flake模型模拟青海湖热力状况对气候变化的响应； Huang等（2019） Huang等（2019） 评价了3个一维湖泊模式在纳木错湖泊的适用性并通过敏感性试验对模型进行率定。 青藏高原地区受人类活动影响较小，其气温升温速率大于同期全球陆表气温的变化速率（ Huang等，2017 Huang等，2017 ），是全球变化的敏感区域（ 杜娟 等，2020 杜娟 等，2020 ）。由于历史观测数据的缺乏，青藏高原湖冰物候的变化研究还不够充分。本文利用过程模型（LAKE 2.3）重建青藏高原纳木错湖泊长时序（1962年—2018年）的湖面温度和湖冰物候，并将模拟结果与遥感监测结果进行对比验证。在此基础上，分析近60 a来纳木错湖冰物候的变化趋势。本文所用的LAKE 2.3模型（ Stepanenko等，2016 Stepanenko等，2016 ）是综合性的一维湖泊模型，涉及湖泊的热力学过程以及生物地球化学过程。该模型已有许多应用，但在青藏高原湖泊研究中的应用还较少。 2　研究区与数据 1 2.1　研究区概况 2 纳木错位于30°30′N—30°55′N，90°16′E—91°03′E（ 图1 图1 ），海拔4718 m，湖泊面积1981 km 2 。纳木错是西藏自治区第二大湖，也是世界上海拔最高的湖泊之一。湖泊集水面积10610 km 2 ，2005年测得的最大深度超过90 m（ Wang等，2009 Wang等，2009 ）。纳木错所处流域内冰川占比约1.5%（ Wu等，2014 Wu等，2014 ）。近几十年来，随着青藏高原气温的升高，纳木错湖泊的面积、水位、水温、冰期以及生物化学过程也发生着深刻的变化（ Guo等，2020 Guo等，2020 ； Huang等，2017 Huang等，2017 ； Zhang等，2011 Zhang等，2011 ）。纳木错属于高原亚寒带季风半干旱气候带，辐射强烈，年日照时数达2900—3200 h，年均温1.9 ℃，年降水量约500 mm，湖面年蒸发量约1200 mm。 2.2　遥感数据 2 本文首先基于多源遥感信息应用不同方法提取纳木错的湖冰物候信息。主要的遥感数据源包括：ARC-Lake（V3），MODIS以及基于微波辐射计（AMSR-E、AMSR2和FY-3 MWRI）的湖泊亮温信息。 ARC-Lake（V3）是基于沿轨道扫描辐射计（ATSR2/AATSR）获取的湖泊表面温度日尺度数据集（ http：//www. http://www. ‍laketemp.‍net/home_ARCLake/［2021-04-30］），包括日间和夜间的湖面温度。本研究以日间温度和夜间温度的均值作为纳木错湖面温度日值，以此获取的湖面温度序列作为模拟湖面温度的验证数据之一，时间范围1995-06-01—2012-04-05。 中分辨率成像光谱仪MODIS（moderate resolution imaging spectroradiometer）搭载于两颗极轨卫星Terra和Aqua上。Terra上午自北向南穿过赤道，Aqua下午穿过赤道。双星系统1—2 d就可以覆盖全球一次。MODIS传感器包含36个波段，已经拥有应用于各个领域的多种产品。本文应用的是其L3级日尺度陆面温度产品（MOD11A1），空间分辨率为1 km。数据集包含日间和夜间的陆表温度及发射率。为计算湖泊面上的平均温度，本文首先将纳木错湖泊矢量边界图向内缩进1 km以避免湖岸混合像元的影响。然后，以日间温度和夜间温度的均值作为湖表的日均温度，从而获取湖表日均温度序列。为保证数据集之间的可比性，本文选择的MODIS产品的时间跨度与ARC-Lake一致。 此外，本文还采用了 邱玉宝等（2017） 邱玉宝等（2017） 生产的“2002年—2016年高亚洲地区中大型湖泊微波亮温和冻融数据集”（ http：//www.csdata.org/p/49/ http://www.csdata.org/p/49/ ［2021-04-30］）。该数据集依据微波辐射计（AMSR-E、AMSR2和FY-3 MWRI）观测像元内湖泊和陆表的面积比例，并应用混合像元分解方法获取像元（亚像元级）的湖泊亮温信息，是通过被动微波遥感对像元级湖冰冻融进行监测的一种方法。 2.3　LAKE模型驱动数据 2 LAKE模型需要的输入包括气温、比湿、气压、风速、短波辐射、长波辐射和降水等气象要素。短波辐射和向下的长波辐射根据纬度、实际日照时数、气温和水汽压以计算而得。其他气象变量以距纳木错最近的当雄站（30°29′N，91°06′E，海拔4200 m）的气象数据为依据。基础气象数据来自中国气象数据网，包括1963年—2019年近60 a的气温、降水、风速、气压、相对湿度和日照时数。 考虑到气温随高程的变化，本文首先以0.65℃/100 m的气温大气直减率（ 胡芩 等，2014 胡芩 等，2014 ）对气象站气温 T station 进行高程校正得到湖泊气温 T lake ，即 <math display="block" id="M1"><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">e</mi></mrow></msub><mo>=</mo><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>+</mo><mfenced separators="|"><mrow><msub><mrow><mi>H</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi 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mathvariant="normal">n</mi></mrow></msub><mo stretchy="false">)</mo><mo>/</mo><mn mathvariant="normal">2</mn></mrow><mrow><mn mathvariant="normal">273</mn></mrow></mfrac></mrow></mfenced></mrow></mfrac></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653378&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653376&type= 75.52266693 15.15533447 式中，比湿 q 的计算公式为 <math display="block" id="M7"><mi>q</mi><mo>=</mo><mfrac><mrow><mi>ε</mi><mo>·</mo><mi>e</mi></mrow><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">e</mi></mrow></msub><mo>-</mo><mo stretchy="false">(</mo><mn mathvariant="normal">1</mn><mo>-</mo><mi>ε</mi><mo stretchy="false">)</mo><mi>e</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653384&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653369&type= 29.37933159 8.63599968 式中， <math id="M8"><mi>ε</mi><mo>=</mo><mn mathvariant="normal">0.622</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653408&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653403&type= 14.81666565 2.70933342 ， e 为水汽压，是相对湿度RH与饱和水汽压 <math id="M9"><msub><mrow><mi>e</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653413&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653410&type= 2.87866688 3.72533321 的乘积，而饱和水汽压可用Bolton公式（ Bolton，1980 Bolton，1980 ）计算： <math display="block" id="M10"><msub><mrow><mi>e</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">6.112</mn><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mtext> </mtext><mfenced separators="|"><mrow><mfrac><mrow><mn mathvariant="normal">17.67</mn><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">e</mi></mrow></msub></mrow><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">e</mi></mrow></msub><mo>+</mo><mn mathvariant="normal">243.5</mn></mrow></mfrac></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653418&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653414&type= 44.45000076 9.90600014 3　方法 1 3.1　湖冰物候指标 2 本文基于遥感与模拟提取的湖冰物候指标包括：开始结冰日FUS（湖面由完全是水到开始有像元变为冰对应的日期）、完全融化日BUE（湖面由存在冰到所有像元为水对应的日期），以及湖泊结冰期（ID），即BUE与FUS二者之间的天数。这3个指标与湖气界面的水热交换过程密切相关。 3.2　湖冰物候遥感监测 2 本文参照 Guo等（2018） Guo等（2018） 的方法，基于不同的遥感信息源提取纳木错2000年—2015年的湖冰物候，并分析其变化规律。湖冰物候的遥感监测方法具体包括：（1）利用MOD09GA产品生成全湖平均的反射率时间序列，通过阈值法在反射率时间序列上提取湖冰物候（M1）；（2）利用MOD10A1冰雪产品，计算湖面水体占湖泊面积的比，以水占比10%为物候提取阈值（M2）；（3）利用MOD11A1产品生成全湖平均湖面温度时间序列，通过阈值法提取湖冰物候（M3）。上述3种方法的详细过程可参考 Guo等（2018） Guo等（2018） 。此外，本文从“2002年—2016年高亚洲地区中大型湖泊微波亮温和冻融数据集”中获取纳木错2002年—2016年的湖冰物候作为对比数据（M4）。 3.3　基于LAKE模型的湖冰物候模拟 2 本文采用的LAKE模型（ Stepanenko等，2016 Stepanenko等，2016 ）其热力学过程表述为 <math display="block" id="M11"><msub><mrow><mi>c</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub><mi>ρ</mi><mfrac><mrow><mo>∂</mo><mi>T</mi></mrow><mrow><mo>∂</mo><mi>t</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>c</mi></mrow><mrow><msup><mrow><mi>h</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msup></mrow></mfrac><mfrac><mrow><mo>∂</mo></mrow><mrow><mo>∂</mo><mi>ξ</mi></mrow></mfrac><mfenced separators="|"><mrow><mi>λ</mi><mfrac><mrow><mo>∂</mo><mi>T</mi></mrow><mrow><mo>∂</mo><mi>ξ</mi></mrow></mfrac></mrow></mfenced><mo>+</mo><msub><mrow><mi>c</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub><mi>ρ</mi><mfrac><mrow><mi mathvariant="normal">d</mi><mi>h</mi></mrow><mrow><mi mathvariant="normal">d</mi><mi>t</mi></mrow></mfrac><mfrac><mrow><mi>ξ</mi></mrow><mrow><mi>h</mi></mrow></mfrac><mfrac><mrow><mo>∂</mo><mi>T</mi></mrow><mrow><mo>∂</mo><mi>ξ</mi></mrow></mfrac><mo>-</mo><msub><mrow><mi>c</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub><mi>ρ</mi><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>h</mi></mrow></mfrac><mfrac><mrow><mi mathvariant="normal">d</mi><msub><mrow><mi>h</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">d</mi><mi>t</mi></mrow></mfrac><mfrac><mrow><mo>∂</mo><mi>T</mi></mrow><mrow><mo>∂</mo><mi>ξ</mi></mrow></mfrac><mo>-</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>h</mi></mrow></mfrac><mfrac><mrow><mo>∂</mo><mi>S</mi></mrow><mrow><mo>∂</mo><mi>ξ</mi></mrow></mfrac><mo>+</mo><mi>M</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653422&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653402&type= 102.53133392 9.05933285 式中， T 为水温，垂直坐标 z 以湖面为 z =0，垂直向下为正， h 为湖泊深度，并定义为 ξ = z / h 为坐标。 <math id="M12"><msub><mrow><mi>c</mi></mrow><mrow><mi mathvariant="normal">w</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653427&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653426&type= 2.87866688 3.72533321 是水的比热容， <math id="M13"><mi>ρ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653445&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653429&type= 1.69333339 3.38666677 是水的密度， <math id="M14"><mi>λ</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653464&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653447&type= 2.28600001 2.62466669 涡流扩散率， <math id="M15"><mfrac><mrow><mi mathvariant="normal">d</mi><msub><mrow><mi>h</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></mrow><mrow><mi mathvariant="normal">d</mi><mi>t</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653467&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653466&type= 5.67266655 7.61999989 是湖泊表面水量平衡， S 是太阳辐射通量，穿透到深度 z ， M 是浮力混合（对流）。穿透到深度 z 的太阳辐射计算： <math display="block" id="M16"><mi>S</mi><mfenced separators="|"><mrow><mi>ξ</mi></mrow></mfenced><mo>=</mo><mtext> </mtext><mi>S</mi><mfenced separators="|"><mrow><mn mathvariant="normal">0</mn></mrow></mfenced><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi><mi mathvariant="normal">p</mi><mtext> </mtext><mfenced separators="|"><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub><mi>h</mi><mi>ξ</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653453&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653469&type= 35.72933197 5.24933338 式中， <math id="M17"><msub><mrow><mi>α</mi></mrow><mrow><mi mathvariant="normal">e</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653457&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653472&type= 3.21733332 3.72533321 是消光系数。 湖泊水温的上边界条件是湖泊表面能量平衡： <math display="block" id="M18"><mi>S</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>α</mi></mrow></mfenced><mo>+</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>a</mi></mrow></msub><mo>-</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>-</mo><mi>H</mi><mo>-</mo><mi>L</mi><mi>E</mi><mo>=</mo><mo>-</mo><mfrac><mrow><mi>λ</mi></mrow><mrow><mi>h</mi></mrow></mfrac><mfrac><mrow><mo>∂</mo><mi>T</mi></mrow><mrow><mo>∂</mo><mi>ξ</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653480&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653459&type= 59.68999863 8.04333401 式中， S 是太阳辐射， E a 向下的大气辐射， E s 向上的长波辐射， H 和 LE 分别是显热和潜热通量， <math id="M19"><mi>α</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653486&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=28653493&type= 2.20133328 2.62466669 是表面反照率。 本研究中用到的是LAKE 2.3模型。LAKE模型包含的参数较多，但参数大多具有明确的物理意义。模拟过程中，除了湖泊基本形态参数（湖泊经纬度、湖泊面积、湖泊深度等），本文参考2005年—2007年实地考察的纳木错湖盆形态估算出各个深度的水平截面面积，作为湖泊形态参数输入模型。在模拟中，本文取纳木错的平均深度为40 m，水体的消光系数为0.1，冰的消光系数为100。主要的模型参数设定如 表1 表1 。这些参数取值与 Huang等（2019） Huang等（2019） 的研究中对纳木错消光系数设置相一致。 模型参数 参数化方案 湖泊深度/m 40 湖水分层/层 160 表面冰的分层/层 20 模型预热时长/a 20 水的消光系数/m 0.1 冰的消光系数/m 100 边界条件 自由对流的Neuman边界条件 本文设定LAKE模型时预热时间为20 a，并以模型最终输出的表层温度（skin temperature）的年内变化特征获取湖泊结冰和融化的日期。 4　结果分析与讨论 1 4.1　基于遥感的湖冰物候 2 图2 图2 给出了纳木错2003年—2014年基于不同遥感监测方法的湖冰物候。纵轴是年积日（DOY）（从当年01-01起开始计算的天数），大于365 d的表明物候日期发生在第2年。由 图2 图2 中可以看出，纳木错湖泊结冰日多始于12月底至次年1月，次年4—5月湖冰则完全融化。多年平均情况下，开始结冰日（FUS）为01-07，完全化冻日（BUS）为03-10。年均湖泊结冰期（ID）的长度大致为124 d，标准差为10 d。研究时段内，湖冰物候的变化总体趋势并不显著。 不同方法之间的比较可以看出，基于微波亮温数据（M4）获取的冰期通常比其他方法监测所得的冰期短，而其他3种遥感方法在湖冰物候监测上的差异没有明显的规律。这一结果表明，受遥感数据时空分辨率的影响（如：数据缺失），湖冰物候的遥感监测还存在较大的不确定性。 4.2　湖冰物候模拟 2 由于遥感的数据序列相对较短，难以反映纳木错湖冰物候近几十年来的变化规律，因此本文借助LAKE模型以重建纳木错的湖冰物候序列，并揭示湖冰物候的长期变化规律及其对气候变化的响应。 图3 图3 首先给出了LAKE模型湖面温度的模拟结果。由 图3 图3 中可以看出，湖泊表面温度的模拟值与遥感监测的湖面温度一致性较高，模拟结果与ARC-Lake水温数据的纳什效率系数（Nash-Sutcliffe efficiency coefficient）达0.82，均方根误差为1.75℃。基于LAKE模型的湖冰物候模拟结果如 图4 图4 所示。由 图4 图4 可以看出，模拟所得的3个物候指标中，融化日期BUE与遥感监测的结果一致性最高，均方根误差为8.5 d。模拟的开始结冰日FUS普遍早于遥感监测的结果，模拟的结冰期总体上大于遥感监测的结冰期。 LAKE模拟结果与遥感监测结果之间的差异，一方面受模型的不确定性的影响（包括模型结果、参数以及输入的不确定性）；另一方面也受遥感监测的不确定性的影响。特别是遥感监测的湖面温度通常为卫星过境的瞬时值（或日间夜间瞬时值的均值），而不能真正代表一天内的平均温度，且MODIS监测的表面温度受云等影响波动较大。此外，确定湖冰物候时相关阈值的设定也会影响湖冰物候的判别。因此，虽然遥感和模拟都可以获取湖冰物候信息，但湖冰物候监测与模拟的准确性还需要进一步的地面观测加以验证。 4.3　近60年来湖冰物候变化趋势 2 LAKE等有物理基础的数值模型刻画了气候因子与湖冰物候之间的定量关系，有助于揭示湖冰物候对气候变化的响应。基于LAKE模型，本文重建了近60 a来纳木错的湖冰物候如 图5 图5 所示。 基于Mann-Kendall（MK）非参数检验法（ Kendall，1955 Kendall，1955 ； Mann，1945 Mann，1945 ）的湖冰物候变化趋势分析表明，近60 a来纳木错湖泊结冰推迟、融化提前、冰期缩短，且所有物候指标的变化趋势均达到95%的显著性水平。结冰日期（FUS）平均每10 a延后3.3 d，融化日期（BUE）每10 a提前3.0 d。冰期（ID）的变化速率最快，以6.4 d/（10 a）的速率缩短。 4.4　湖冰物候对气候变化的敏感性 2 已有研究表明，至21世纪末，青藏高原气温相对于1980年—1999年将升高2℃（ Chen和Frauenfeld，2014 Chen和Frauenfeld，2014 ）。为了定量分析湖冰物候对气候变化的响应特征，本文基于LAKE模型开展了湖冰物候对气候变化的敏感性分析。在敏感性分析中，假设纳木错气温以0.1℃的间隔持续升高至2℃，而后基于LAKE模型的模拟结果，计算分析湖冰物候随气温升高相较于历史时期（1963年—2018年）的可能变化，结果见 图6 图6 。 模拟结果表明，当气温升高达0.7℃时，开始结冰日（FUS）显著推迟。如果气温升高2℃，结冰日期平均推迟7.3 d。湖冰融化过程对气温的响应比结冰过程更显著。当气温升高2℃，融化日期平均提前12.4 d。因此，冰期随着温度升高将显著缩短，平均缩短19.7 d。湖冰物候的变化会影响湖泊水量平衡、能量平衡过程、湖泊及周围的生态系统和人类活动。因此，在气候变暖的背景下，需要对湖冰物候变化情况进行持续的监测和预测。 5　结论 1 本研究以纳木错湖泊为研究区，基于4种不同的遥感监测方式获取了2002年—2015年纳木错的湖冰物候指标，结果表明各方法之间的年际变化情况比较一致，但基于微波亮温数据获取的冰期通常比其他方法监测的时间短。 在遥感监测的基础上，利用一维湖泊模型（LAKE）重建了1962年—2018年纳木错湖冰物候序列，揭示了近60 a来纳木错湖冰物候的变化趋势及其对气候变化的响应特征。研究结果表明，近60 a来，纳木错结冰推迟、融化提前、冰期缩短（6.7 d/（10 a））。湖冰物候（特别是融冰日期）对气候变化十分敏感。在气温升高2℃的气候变化情景下，未来纳木错冰期将缩短19.7 d。 本研究将遥感与数值模拟相结合，发挥两种手段的优势，为湖冰物候研究提供了新的思路和方法。但是，在青藏高原湖冰物候的研究中，现有的遥感方法和数值模拟方法都存在不同程度的不确定性。在未来的研究中，除了需要进一步提高遥感信息的精度和分辨率，完善模型的结构和参数化方案外，在条件适宜的地方开展持续的湖冰物候地面观测，将有助于提高青藏高原湖冰物候监测与模拟水平。 参考文献（References） Bengtsson L . 2011 . Ice-covered lakes: environment and climate—required research . Hydrological Processes , 25 ( 17 ): 2767 - 2769 [ DOI: 10.1002/hyp.8098 http://dx.doi.org/10.1002/hyp.8098 ] Ice-covered lakes: environment and climate—required research Bernhardt J , Engelhardt C , Kirillin G and Matschullat J . 2012 . Lake ice phenology in Berlin-Brandenburg from 1947-2007: observations and model hindcasts . Climatic Change , 112 ( 3/4 ): 791 - 817 [ DOI: 10.1007/s10584-011-0248-9 http://dx.doi.org/10.1007/s10584-011-0248-9 ] Lake ice phenology in Berlin-Brandenburg from 1947-2007: observations and model hindcasts Bolton D . 1980 . The computation of equivalent potential temperature . Monthly Weather Review , 108 ( 7 ): 1046 - 1053 [ DOI: 10.1175/1520-0493(1980)108<1046:TCOEPT>2.0.CO;2 http://dx.doi.org/10.1175/1520-0493(1980)108<1046:TCOEPT>2.0.CO;2 ] The computation of equivalent potential temperature Brown L C and Duguay C R . 2010 . The response and role of ice cover in lake-climate interactions . Progress in Physical Geography: Earth and Environment , 34 ( 5 ): 671 - 704 [ DOI: 10.1177/0309133310375653 http://dx.doi.org/10.1177/0309133310375653 ] The response and role of ice cover in lake-climate interactions Chen L and Frauenfeld O W . 2014 . Surface air temperature changes over the twentieth and twenty-first centuries in China simulated by 20 CMIP5 models . Journal of Climate , 27 ( 11 ): 3920 - 3937 [ DOI: 10.1175/JCLI-D-13-00465.1 http://dx.doi.org/10.1175/JCLI-D-13-00465.1 ] Surface air temperature changes over the twentieth and twenty-first centuries in China simulated by 20 CMIP5 models Du J , Wen L J and Su D S . 2020 . Analysis of simulated temperature difference between lake surface and air and energy balance of three alpine lakes with different depths on the Qinghai-Xizang Plateau during the ice-free period . Plateau Meteorology , 39 ( 6 ): 1181 - 1194 Analysis of simulated temperature difference between lake surface and air and energy balance of three alpine lakes with different depths on the Qinghai-Xizang Plateau during the ice-free period 杜娟 , 文莉娟 , 苏东生 . 2020 . 青藏高原不同深度湖泊无冰期湖气温差及湖表辐射与能量平衡特征模拟分析 . 高原气象 , 39 ( 6 ): 1181- 1194 [ DOI: 10.7522/j.issn.1000-0534.2019.00133 http://dx.doi.org/10.7522/j.issn.1000-0534.2019.00133 ] 青藏高原不同深度湖泊无冰期湖气温差及湖表辐射与能量平衡特征模拟分析 Duguay C R , Bernier M , Gauthier Y and Kouraev A . 2015 . Remote sensing of lake and river ice //Tedesco M, ed. Remote Sensing of the Cryosphere . New York : John Wiley and Sons, Ltd.: 273 - 306 Remote sensing of lake and river ice Duguay C R , Flato G M , Jeffries M O , Ménard P , Morris K and Rouse W R . 2003 . Ice-cover variability on shallow lakes at high latitudes: model simulations and observations . Hydrological Processes , 17 ( 17 ): 3465 - 3483 [ DOI: 10.1002/HYP.1394 http://dx.doi.org/10.1002/HYP.1394 ] Ice-cover variability on shallow lakes at high latitudes: model simulations and observations Fang N , Yang K , La Z , Chen Y Y , Wang J B and Zhu L P . 2017 . Research on the application of WRF-lake Modeling at Nam Co Lake on the Qinghai-Tibetan Plateau . Plateau Meteorology , 36 ( 3 ): 610 - 618 Research on the application of WRF-lake Modeling at Nam Co Lake on the Qinghai-Tibetan Plateau 方楠 , 阳坤 , 拉珠 , 陈莹莹 , 王君波 , 朱立平 . 2017 . WRF湖泊模型对青藏高原纳木错湖的适用性研究 . 高原气象 , 36 ( 3 ): 610- 618 [ DOI: 10.7522/j.issn.1000-0534.2016.00038 http://dx.doi.org/10.7522/j.issn.1000-0534.2016.00038 ] WRF湖泊模型对青藏高原纳木错湖的适用性研究 Fang X and Stefan H G . 1996 . Long-term lake water temperature and ice cover simulations/measurements . Cold Regions Science and Technology , 24 ( 3 ): 289 - 304 [ DOI: 10.1016/0165-232X(95)00019-8 http://dx.doi.org/10.1016/0165-232X(95)00019-8 ] Long-term lake water temperature and ice cover simulations/measurements Fu C S and Yao H X . 2015 . Trends of ice breakup date in south-central Ontario . Journal of Geophysical Research: Atmospheres , 120 ( 18 ): 9220 - 9236 [ DOI: 10.1002/2015JD023370 http://dx.doi.org/10.1002/2015JD023370 ] Trends of ice breakup date in south-central Ontario Ghanbari R N , Bravo H R , Magnuson J J , Hyzer W G and Benson B J . 2009 . Coherence between lake ice cover, local climate and teleconnections (Lake Mendota, Wisconsin) . Journal of Hydrology , 374 ( 3/4 ): 282 - 293 [ DOI: 10.1016/j.jhydrol.2009.06.024 http://dx.doi.org/10.1016/j.jhydrol.2009.06.024 ] Coherence between lake ice cover, local climate and teleconnections (Lake Mendota, Wisconsin) Gou P , Ye Q H , Che T , Feng Q , Ding B H , Lin C G and Zong J B . 2017 . Lake ice phenology of Nam Co, Central Tibetan Plateau, China, derived from multiple MODIS data products . Journal of Great Lakes Research , 43 ( 6 ): 989 - 998 [ DOI: 10.1016/j.jglr.2017.08.011 http://dx.doi.org/10.1016/j.jglr.2017.08.011 ] Lake ice phenology of Nam Co, Central Tibetan Plateau, China, derived from multiple MODIS data products Goudsmit G H , Burchard H , Peeters F and Wüest A . 2002 . Application of k-ϵ turbulence models to enclosed basins: the role of internal seiches . Journal of Geophysical Research: Oceans , 107 ( C12 ): 3230 [ DOI: 10.1029/2001JC000954 http://dx.doi.org/10.1029/2001JC000954 ] Application of k-ϵ turbulence models to enclosed basins: the role of internal seiches Guo L , Zheng H X , Wu Y H , Zhang T Q , Wen M X , Fan L X and Zhang B . 2020 . Responses of lake ice phenology to climate change at Tibetan Plateau . IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , 13 : 3856 - 3861 [ DOI: 10.1109/JSTARS.2020.3006270 http://dx.doi.org/10.1109/JSTARS.2020.3006270 ] Responses of lake ice phenology to climate change at Tibetan Plateau Guo L N , Wu Y H , Zheng H X , Zhang B , Li J S , Zhang F F and Shen Q . 2018 . Uncertainty and variation of remotely sensed lake ice phenology across the Tibetan Plateau . Remote Sensing , 10 ( 10 ): 1534 [ DOI: 10.3390/rs10101534 http://dx.doi.org/10.3390/rs10101534 ] Uncertainty and variation of remotely sensed lake ice phenology across the Tibetan Plateau Hu Q , Jiang D B and Fan G Z . 2014 . Evaluation of CMIP5 models over the Qinghai–Tibetan Plateau . Chinese Journal of Atmospheric Sciences , 38 ( 5 ): 924 - 938 Evaluation of CMIP5 models over the Qinghai–Tibetan Plateau 胡芩 , 姜大膀 , 范广洲 . 2014 . CMIP5全球气候模式对青藏高原地区气候模拟能力评估 . 大气科学 , 38 ( 5 ): 924- 938 [ DOI: 10.3878/j.issn.1006-9895.2013.13197 http://dx.doi.org/10.3878/j.issn.1006-9895.2013.13197 ] CMIP5全球气候模式对青藏高原地区气候模拟能力评估 Huang A N , Lazhu , Wang J B , Dai Y J , Yang K , Wei N , Wen L J , Wu Y , Zhu X Y , Zhang X D and Cai S X . 2019 . Evaluating and improving the performance of three 1-D lake models in a large deep lake of the central Tibetan Plateau . Journal of Geophysical Research: Atmospheres , 124 ( 6 ): 3143 - 3167 [ DOI: 10.1029/2018JD029610 http://dx.doi.org/10.1029/2018JD029610 ] Evaluating and improving the performance of three 1-D lake models in a large deep lake of the central Tibetan Plateau Huang L , Wang J B , Zhu L P , Ju J T and Daut G . 2017 . The warming of large lakes on the Tibetan Plateau: evidence from a lake model simulation of Nam Co, China, during 1979-2012 . Journal of Geophysical Research: Atmospheres , 122 ( 24 ): 13095 - 13107 [ DOI: 10.1002/2017JD027379 http://dx.doi.org/10.1002/2017JD027379 ] The warming of large lakes on the Tibetan Plateau: evidence from a lake model simulation of Nam Co, China, during 1979-2012 Joehnk K D and Umlauf L . 2001 . Modelling the metalimnetic oxygen minimum in a medium sized alpine lake . Ecological Modelling , 136 ( 1 ): 67 - 80 [ DOI: 10.1016/S0304-3800(00)00381-1 http://dx.doi.org/10.1016/S0304-3800(00)00381-1 ] Modelling the metalimnetic oxygen minimum in a medium sized alpine lake Kendall M G . 1955 . Rank Correlation Methods. 2nd ed. New York, NY: Hafner Publishing Rank Correlation Methods. 2nd ed. New York, NY: Hafner Publishing Kouraev A V , Semovski S V , Shimaraev M N , Mognard N M , Légresy B and Remy F . 2007 . Observations of Lake Baikal ice from satellite altimetry and radiometry . Remote Sensing of Environment , 108 ( 3 ): 240 - 253 [ DOI: 10.1016/j.rse.2006.11.010 http://dx.doi.org/10.1016/j.rse.2006.11.010 ] Observations of Lake Baikal ice from satellite altimetry and radiometry Kropáček J , Maussion F , Chen F , Hoerz S and Hochschild V . 2013 . Analysis of ice phenology of lakes on the Tibetan Plateau from MODIS data . The Cryosphere , 7 ( 1 ): 287 - 301 [ DOI: 10.5194/TC-7-287-2013 http://dx.doi.org/10.5194/TC-7-287-2013 ] Analysis of ice phenology of lakes on the Tibetan Plateau from MODIS data Latifovic R and Pouliot D . 2007 . Analysis of climate change impacts on lake ice phenology in Canada using the historical satellite data record . Remote Sensing of Environment , 106 ( 4 ): 492 - 507 Analysis of climate change impacts on lake ice phenology in Canada using the historical satellite data record Launiainen J and Cheng B . 1998 . Modelling of ice thermodynamics in natural water bodies . Cold Regions Science and Technology , 27 ( 3 ): 153 - 178 [ DOI: 10.1016/S0165-232X(98)00009-3 http://dx.doi.org/10.1016/S0165-232X(98)00009-3 ] Modelling of ice thermodynamics in natural water bodies Livingstone D M . 1997 . Break-up dates of Alpine lakes as proxy data for local and regional mean surface air temperatures . Climatic Change , 37 ( 2 ): 407 - 439 [ DOI: 10.1023/A:1005371925924 http://dx.doi.org/10.1023/A:1005371925924 ] Break-up dates of Alpine lakes as proxy data for local and regional mean surface air temperatures Magnuson J J , Robertson D M , Benson B J , Wynne R H , Livingstone D M , Arai T , Assel R A , Barry R G , Card V , Kuusisto E , Granin N G , Prowse T D , Stewart K M and Vuglinski V S . 2000 . Historical trends in lake and river ice cover in the Northern Hemisphere . Science , 289 ( 5485 ): 1743 - 1746 [ DOI: 10.1126/science.289.5485.1743 http://dx.doi.org/10.1126/science.289.5485.1743 ] Historical trends in lake and river ice cover in the Northern Hemisphere Mann H B . 1945 . Nonparametric tests against trend . Econometrica , 13 ( 3 ): 245 - 259 [ DOI: 10.2307/1907187 http://dx.doi.org/10.2307/1907187 ] Nonparametric tests against trend Marszelewski W and Skowron R . 2006 . Ice cover as an indicator of winter air temperature changes: case study of the Polish Lowland lakes . Hydrological Sciences Journal , 51 ( 2 ): 336 - 349 [ DOI: 10.1623/hysj.51.2.336 http://dx.doi.org/10.1623/hysj.51.2.336 ] Ice cover as an indicator of winter air temperature changes: case study of the Polish Lowland lakes Pang Y W , Huang Y X , Gong Z , Wen J Y and Xu J F . 2020 . Advances in Phenological Monitoring of Lake Ice based on Multi-spectral remote Sensing . Transactions of Oceanology and Limnology , ( 2 ): 90 - 99 Advances in Phenological Monitoring of Lake Ice based on Multi-spectral remote Sensing 庞毓雯 , 黄雨馨 , 巩志 , 问静怡 , 徐俊锋 . 2020 . 基于多光谱遥感的湖冰物候监测方法研究进展. 海洋湖沼通报, (2): 90 - 99 基于多光谱遥感的湖冰物候监测方法研究进展. 海洋湖沼通报, (2): Qiu Y B , Guo H D , Ruan Y J , Fu X R , Shi L J and Tian B S . 2017 . A dataset of microwave brightness temperature and freeze-thaw for medium-to-large lakes over the High Asia region ( 2002 ‒ 2016 ). Science Data Bank , 2 ( 2 ): 30 - 41 A dataset of microwave brightness temperature and freeze-thaw for medium-to-large lakes over the High Asia region 邱玉宝 , 郭华东 , 阮永俭 , 付心如 , 石利娟 , 田邦森 . 2017 . 2002～2016年高亚洲地区中大型湖泊微波亮温和冻融数据集 . 中国科学数据(中英文网络版) , 2 ( 2 ): 30- 41 [ DOI: 10.11922/csdata.170.2017.0117 http://dx.doi.org/10.11922/csdata.170.2017.0117 ] 2002～2016年高亚洲地区中大型湖泊微波亮温和冻融数据集 Ren X Q , Li Q , Chen W and Liu H Z . 2014 . A new lake model for air-lake heat exchange process and evaluation of its simulation ability . Chinese Journal of Atmospheric Sciences , 38 ( 5 ): 994 - 1004 A new lake model for air-lake heat exchange process and evaluation of its simulation ability 任晓倩 , 李倩 , 陈文 , 刘辉志 . 2014 . 一个新的湖——气热传输模型及其模拟能力评估 . 大气科学 , 38 ( 5 ): 994 - 1004 一个新的湖——气热传输模型及其模拟能力评估 Salonen K , Leppäranta M , Viljanen M and Gulati R D . 2009 . Perspectives in winter limnology: closing the annual cycle of freezing lakes . Aquatic Ecology , 43 ( 3 ): 609 - 616 [ DOI: 10.1007/s10452-009-9278-z http://dx.doi.org/10.1007/s10452-009-9278-z ] Perspectives in winter limnology: closing the annual cycle of freezing lakes Song X Y , Wen L J , Li M S , Du J , Su D S , Yin S C and Lü Z . 2020 . Comparative study on applicability of different lake models to typical lakes in Qinghai-Tibetan Plateau . Plateau Meteorology , 39 ( 2 ): 213 - 225 Comparative study on applicability of different lake models to typical lakes in Qinghai-Tibetan Plateau 宋兴宇 , 文莉娟 , 李茂善 , 杜娟 , 苏东生 , 阴蜀城 , 吕钊 . 2020 . 不同湖泊模式对青藏高原典型湖泊适用性对比研究 . 高原气象 , 39 ( 2 ): 213- 225 [ DOI: 10.7522/j.issn.1000-0534.2019.00102 http://dx.doi.org/10.7522/j.issn.1000-0534.2019.00102 ] 不同湖泊模式对青藏高原典型湖泊适用性对比研究 Stepanenko V , Mammarella I , Ojala A , Miettinen H , Lykosov V and Vesala T . 2016 . LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes . Geoscientific Model Development , 9 : 1977 - 2006 [ DOI: 10.5194/gmd-9-1977-2016 http://dx.doi.org/10.5194/gmd-9-1977-2016 ] LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes Su D S , Hu X Q , Wen L J , Zhao L and Li Z G . 2018 . Simulation of the response of Qinghai Lake thermal conditions to climate change . Plateau Meteorology , 37 ( 2 ): 394 - 405 Simulation of the response of Qinghai Lake thermal conditions to climate change 苏东生 , 胡秀清 , 文莉娟 , 赵林 , 李照国 . 2018 . 青海湖热力状况对气候变化响应的数值研究 . 高原气象 , 37 ( 2 ): 394- 405 [ DOI: 10.7522/j.issn.1000-0534.2017.00069 http://dx.doi.org/10.7522/j.issn.1000-0534.2017.00069 ] 青海湖热力状况对气候变化响应的数值研究 Vavrus S J , Wynne R H and Foley J A . 1996 . Measuring the sensitivity of southern Wisconsin lake ice to climate variations and lake depth using a numerical model . Limnology and Oceanography , 41 ( 5 ): 822 - 831 [ DOI: 10.4319/lo.1996.41.5.0822 http://dx.doi.org/10.4319/lo.1996.41.5.0822 ] Measuring the sensitivity of southern Wisconsin lake ice to climate variations and lake depth using a numerical model Wang J B , Zhu L P , Daut G , Ju J T , Lin X , Wang Y and Zhen X L . 2009 . Investigation of bathymetry and water quality of Lake Nam Co, the largest lake on the central Tibetan Plateau, China . Limnology , 10 ( 2 ): 149 - 158 [ DOI: 10.1007/s10201-009-0266-8 http://dx.doi.org/10.1007/s10201-009-0266-8 ] Investigation of bathymetry and water quality of Lake Nam Co, the largest lake on the central Tibetan Plateau, China Wu Y H , Zheng H X , Zhang B , Chen D M and Lei L P . 2014 . Long-term changes of lake level and water budget in the Nam Co Lake Basin, Central Tibetan Plateau . Journal of Hydrometeorology , 15 ( 3 ): 1312 - 1322 [ DOI: 10.1175/JHM-D-13-093.1 http://dx.doi.org/10.1175/JHM-D-13-093.1 ] Long-term changes of lake level and water budget in the Nam Co Lake Basin, Central Tibetan Plateau Zhang B , Wu Y H , Zhu L P , Wang J B , Li J S and Chen D M . 2011 . Estimation and trend detection of water storage at Nam Co Lake, central Tibetan Plateau . Journal of Hydrology , 405 ( 1/2 ): 161 - 170 [ DOI: 10.1016/j.jhydrol.2011.05.018 http://dx.doi.org/10.1016/j.jhydrol.2011.05.018 ] Estimation and trend detection of water storage at Nam Co Lake, central Tibetan Plateau 10.11834/jrs.20221288 1007-4619（2022）01-0193-08 吴艳红，郭立男，范兰馨，文梦宣，迟皓婧，张兵.2022.青藏高原纳木错湖冰物候变化遥感监测与模拟.遥感学报，26（1）： 193-200 吴艳红，郭立男，范兰馨，文梦宣，迟皓婧，张兵.2022.青藏高原纳木错湖冰物候变化遥感监测与模拟.遥感学报，26（1）： 193-200 Wu Y H，Guo L N，Fan L X，Wen M X，Chi H J and Zhang B. 2022. Lake ice phenology of the Nam Co at Tibetan Plateau： Remote sensing and modelling. National Remote Sensing Bulletin， 26（1）‍：193-200 Wu Y H，Guo L N，Fan L X，Wen M X，Chi H J and Zhang B. 2022. Lake ice phenology of the Nam Co at Tibetan Plateau： Remote sensing and modelling. National Remote Sensing Bulletin， 26（1）‍：193-200 第二次青藏高原综合科学考察研究资助（编号：2019QZKK0202）；国家自然科学基金（编号：41671203） Supported by Second Tibetan Plateau Scientific Expedition and Research Program (STEP) (No. 2019QZKK0202); National Natural Science Foundation of China (No. 41671203) 2021-04-30 2022-01-07 2022-05-31 2021-08-03 遥感学报 1 26