TSIT-PatchTST model: a missing value interpolation method for net ecosystem exchange (NEE)
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摘要:目的
净生态系统交换量（NEE）是评估陆地生态系统在全球碳循环中作用的重要指标，NEE原始观测数据缺失值的插补精度会直接影响生态系统关键参数的可靠性和精确性。为提高不同植被NEE在长时间连续性数据缺失情景下的插补精度，提出一种融合时间序列表征向量的TSIT-PatchTST深度学习模型。
方法以全球长期通量观测网络站点的碳通量因子数据为研究对象，通过构造短缺失（1 d）、中缺失（7 d）、长缺失（30 d）3种随机连续数据缺失场景，评估边际分布采样法（MDS）、PatchTST模型、TS2Vec-PatchTST模型和TSIT-PatchTST模型在8种不同植被类型下NEE的插补结果。
结果在短缺失场景下，4种插补方法都表现出最优的性能。随着连续缺失天数的增多，MDS的插补精度逐渐下降，该方法在长缺失场景下已不能对NEE进行有效插补，而其他3种深度学习模型能够有效地插补NEE缺失数据。综合3种缺失场景，TSIT-PatchTST模型表现出最优的插补性能，尤其在长缺失场景下该模型具有较高的插补精度。长缺失场景下，TSIT-PatchTST模型对31个站点插补结果的平均均方误差（MSE）为0.942 μmol/(m2·s)，平均绝对误差（MAE）为0.628 μmol/(m2·s)，平均R2为0.457。与PatchTST模型的插补结果相比，TSIT-PatchTST模型平均MSE下降了53.3%， 平均MAE下降了39.7%，平均R2相持平。
结论综合8种植被类型和3种缺失场景的应用结果，得出TSIT-PatchTST模型的插补效果最佳，并具有适应性。TSIT-PatchTST模型可应用于时间序列数据缺失场景以提高数据插补精度。
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关键词:
- 深度学习 /
- 模型开发 /
- 数据插补 /
- TSIT-PatchTST模型 /
- 碳循环 /
- 植被类型 /
- 净生态系统交换量（NEE）
Abstract:ObjectiveNet ecosystem exchange (NEE) is an important indicator for evaluating the role of terrestrial ecosystems in the global carbon cycle. The accuracy of imputation of missing values in NEE raw observation data directly affects the reliability and precision of key ecosystem parameters. To enhance the imputation accuracy of NEE in scenarios of continuous long-term data gaps across different vegetation types, a TSIT-PatchTST model was proposed based on deep learning.
MethodUsing carbon flux factor data from sites within the global long-term flux observation network as the research object, three types of random continuous data gap scenarios were constructed, including short missing (1 d), medium missing (7 d), and long missing (30 d). The imputation results of marginal distribution sampling (MDS) method, PatchTST model, TS2Vec-PatchTST model, and TSIT-PatchTST model under eight different vegetation types were evaluated.
ResultIn the scenario of short missing, all imputation methods demonstrated optimal performance. As the number of consecutive missing days increased, the imputation accuracy of MDS method gradually declined, and it was no longer effective for imputing NEE in the long missing scenario. In contrast, the three deep learning models were capable of effectively imputing missing NEE data. Considering all three missing scenarios, the TSIT-PatchTST model exhibited the best imputation performance, particularly with a high accuracy in long missing scenarios. In the long missing scenario, the TSIT-PatchTST model achieved an average mean squared error (MSE) of 0.942 μmol/(m2·s), an average mean absolute error (MAE) of 0.628 μmol/(m2·s), and an average R2 of 0.457 across 31 sites. Compared with PatchTST model, the TSIT-PatchTST model reduced the average MSE by 53.3%, average MAE by 39.7% and the average R2 remained unchanged.
ConclusionIntegrating the performance across eight vegetation types and three missing scenarios, the TSIT-PatchTST model demonstrates the best imputation effect and adaptability. It can be applied to the problem of missing data in time series to improve the accuracy of data imputation.
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图 5 TSIT-PatchTST模型插补效果折线图
稀树草原以AU-Cpr站点为例，落叶阔叶林以DE-Lnf站点为例，常绿针叶林以US-GLE站点为例，草地以US-SRG站点为例，开放灌木地以US-Whs站点为例，农田以DE-Geb站点为例，混合林以US-Syv站点为例，木本灌草丛以US-Ton站点为例。
Figure 5. Effect line chart of TSIT-PatchTST model interpolation
表 1 站点数据集植被分类
Table 1 Vegetation classification of site dataset
站点 纬度 经度 时间区间（年月日时刻） 数据量/条 植被类型 罗林斯 US-GLE 41°21′59″N 106°14′24″W 201205241430 − 201406221530 36 435 常绿针叶林 梅托利乌斯 US-Me2 44°27′08″N 121°33′27″W 200401181300 − 200601041530 34 422 常绿针叶林 尼沃特岭 US-NR1 40°01′58″N 105°32′47″W 201009281530 − 201208101900 32 744 常绿针叶林 内华达 US-Var 38°24′48″N 120°57′03″W 201303280000 − 201407070030 22 370 草地 埃尔福特 DE-Geb 51°05′59″N 10°54′53″E 201202171030 − 201303141130 18 771 农田 波特科尔伯恩 CA-TP3 42°42′25″N 80°20′54″W 200512160530 − 200612260930 18 009 常绿针叶林 科奇斯 US-SRG 31°47′22″N 110°49′40″W 201101270030 − 201201160300 16 998 草地 坦普斯通 US-Whs 31°44′38″N 110°03′08″W 201007281300 − 201106081130 15 118 开放灌木地 埃森纳赫 DE-Hai 51°04′45″N 10°27′08″E 200602280300 − 200612240230 14 352 落叶阔叶林 默里桥 AU-Lox 34°28′14″S 140°39′18″E 200808191630 − 200906091000 14 100 落叶阔叶林 诺福克 CA-TP1 42°39′39″N 80°33′34″W 200512311330 − 200610131230 13 727 常绿针叶林 库特韦克 NL-Loo 52°09′59″N 5°44′37″E 200205220830 − 200303031230 13 689 常绿针叶林 内珀维尔 US-IB2 41°50′26″N 88°14′28″W 200508221300 − 200605310200 13 515 草地 韦兰德 CA-TP4 42°42′37″N 80°21′27″W 200207201400 − 200304271900 13 499 常绿针叶林 斯普林斯 AU-TTE 22°17′13″S 133°38′24″E 201305220130 − 201401180230 11 571 草地 先锋市 US-Ton 38°25′51″N 120°57′58″W 201305081200 − 201312312200 11 397 木本灌草丛 沙欣尼 US-LWW 34°57′38″N 97°58′44″W 199802181030 − 199810040000 10 924 草地 罗尔斯顿 AU-Emr 23°51′31″S 148°28′29″E 201202062100 − 201209191500 10 837 草地 巴梅拉 AU-Cpr 34°00′08″S 140°35′21″E 201206020930 − 201301041100 10 372 稀树草原 鲍威 US-Wkg 31°44′12″N 109°56′31″W 200506171000 − 200601170230 10 258 草地 科菲维尔 US-Goo 34°15′17″N 89°52′25″W 200510170000 − 200605161030 10 150 草地 埃尔奥拜德 SD-Dem 13°16′58″N 30°28′42″E 200810141400 − 200905031400 9 649 稀树草原 拉龙日 CA-SF1 54°29′06″N 105°49′04″W 200603130130 − 200609202100 9 208 常绿针叶林 诺德豪森 DE-Lnf 51°19′42″N 10°22′04″E 200302221030 − 200308311030 9 121 落叶阔叶林 凯瑟琳 AU-DaS 14°09′34″S 131°23′17″E 201104081600 − 201110142230 9 086 稀树草原 西姆科 CA-TP2 42°46′28″N 80°27′32″W 200505171330 − 200511190730 8 917 常绿针叶林 西斯特斯 US-Me4 44°29′57″N 121°37′21″W 200006081300 − 200012070630 8 724 常绿针叶林 伍德拉夫 US-Syv 46°14′31″N 89°20′52″W 200305310000 − 200311241930 8 536 混合林 塞拉维斯塔 US-SRM 31°49′17″N 110°51′58″W 200910211530 − 201004131300 8 348 木本灌草丛 纽伦比 AU-DaP 14°03′48″S 131°19′05″E 200905081630 − 200910272100 8 266 草地 比格里弗 CA-SF3 54°05′30″N 106°00′20″W 200405051330 − 200410230830 8 199 开放灌木地 注：混合林由树木主导，覆盖百分比超过60%，高度超过2 m。包括交错混合或其他4种森林类型的树木，且任何一种植被类型都不超过60%。 
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表 2 NEE响应因子字段
Table 2 NEE response factor field
字段名称 中文名称 单位 SW_IN_F 短波辐射 W/m2 VPD_F_MDS 饱和水汽压差 hPa TA_F_MDS 空气温度 ℃ NETRAD 净辐射能量 W/m2 WS 风速 m/s WD 风向 G_F_MDS 土壤热通量 TS_F_MDS 土壤温度 ℃ RH 相对湿度 % SWC_F_MDS 土壤含水量 %
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表 3 模型主要超参数设置
Table 3 Primary hyper-parameter setting of models
超参数 含义 设定值 top_k 准确率 5 layers 层 2 dmin, dmax 深度范围 （64, 128） batch_size 批量大小 1500 learning_rate 学习率 0.001 epoch 迭代次数 10 注：因长缺失场景需要制造连续1 440条数据缺失，故模型批量大小设置为1 500；上述超参数设置可以满足模型对NEE缺失数据插补的需要。
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表 4 数据插补结果
Table 4 Data imputation results
缺失情况 植被类型 PatchTST TS2Vec-PatchTST TSIT-PatchTST 边际分布采样法 MDS MSE/
(μmol·m−2·s−1)MAE/
(μmol·m−2·s−1)R2 MSE/
(μmol·m−2·s−1)MAE/
(μmol·m−2·s−1)R2 MSE/
(μmol·m−2·s−1)MAE/
(μmol·m−2·s−1)R2 MSE/
(μmol·m−2·s−1)MAE/
(μmol·m−2·s−1)R2 短缺失 农田 1.547 0.950 0.886 0.736 0.570 0.641 0.191 0.230 0.879 0.233 0.293 0.002 落叶阔叶林 1.550 0.936 0.611 0.824 0.657 0.450 0.457 0.465 0.596 2.201 0.813 0.014 常绿针叶林 1.208 0.865 0.448 0.913 0.690 0.323 0.617 0.518 0.439 4.792 1.014 0.045 草地 2.057 1.046 0.329 1.804 0.935 0.247 1.428 0.798 0.309 17.340 1.542 0.039 混合林 2.596 1.223 0.834 1.176 0.771 0.591 0.377 0.392 0.847 2.307 0.677 0.064 开放灌木地 1.116 0.856 0.423 1.007 0.745 0.304 0.750 0.592 0.439 1.114 0.521 0.025 稀树草原 2.232 1.175 0.388 2.043 1.085 0.284 1.534 0.895 0.409 3.551 0.864 0.032 木本灌草丛 3.853 1.289 0.531 2.141 1.026 0.391 1.149 0.726 0.536 18.586 1.816 0.023 中缺失 农田 1.501 0.939 0.875 0.903 0.607 0.633 0.237 0.224 0.874 0.810 0.529 0.026 落叶阔叶林 1.577 0.942 0.647 0.738 0.621 0.476 0.403 0.426 0.652 5.777 1.308 0.034 常绿针叶林 1.198 0.862 0.475 0.910 0.683 0.351 0.588 0.502 0.475 14.790 1.574 0.119 草地 2.046 1.044 0.313 1.888 0.954 0.218 1.452 0.796 0.316 16.691 1.547 0.102 混合林 2.610 1.223 0.850 1.178 0.757 0.604 0.371 0.355 0.844 2.370 0.684 0.087 开放灌木地 1.084 0.844 0.612 0.967 0.718 0.399 0.590 0.486 0.601 1.027 0.516 0.045 稀树草原 2.159 1.160 0.403 2.277 1.136 0.293 1.615 0.914 0.394 2.804 0.755 0.091 木本灌草丛 3.927 1.290 0.529 2.078 1.026 0.372 1.141 0.732 0.528 14.882 2.472 0.055 长缺失 农田 1.538 0.948 0.901 0.835 0.598 0.648 0.177 0.209 0.903 1.248 0.733 0.008 落叶阔叶林 1.559 0.939 0.603 0.695 0.607 0.447 0.398 0.436 0.607 6.709 1.539 0.013 常绿针叶林 1.206 0.864 0.442 0.912 0.690 0.323 0.610 0.518 0.439 20.316 2.492 0.047 草地 2.052 1.046 0.292 1.877 0.954 0.204 1.458 0.801 0.297 38.533 2.238 0.041 混合林 2.603 1.223 0.851 1.136 0.778 0.615 0.354 0.401 0.850 4.565 1.006 0.065 开放灌木地 1.106 0.852 0.589 1.028 0.745 0.389 0.640 0.506 0.579 2.098 0.699 0.021 稀树草原 2.205 1.170 0.423 2.290 1.138 0.310 1.593 0.907 0.422 8.449 1.237 0.031 木本灌草丛 3.878 1.290 0.548 2.006 1.014 0.385 1.092 0.714 0.544 37.945 2.534 0.013 注：加粗字体表示在同一植被类型下插补效果最佳方法。下同。
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表 5 长缺失下数据插补结果的平均R2对比
Table 5 Comparison of average R2 of data imputation results under long missing
插补方法 农田 落叶阔叶林 常绿针叶林 草地 混合林 开放灌木地 稀树草原 木本灌草丛 TSIT-PatchTST 0.903 0.607 0.439 0.297 0.850 0.579 0.422 0.544 RFR10[20] 0.700 0.623 0.547 0.638 0.689 0.397 0.784 0.437
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表 6 US-GLE站点日间与夜间NEE插补结果
Table 6 Daytime and nighttime NEE imputation results of US-GLE station
时间段 评价指标 短缺失 中缺失 长缺失 日间 MSE 0.509 0.635 0.709 MAE 0.429 0.514 0.502 R2 0.479 0.285 0.321 夜间 MSE 0.448 0.537 0.498 MAE 0.387 0.418 0.404 R2 0.439 0.386 0.429 注：日间时间段为上午10点至下午16点，夜间时间段为下午16点至次日上午10点。
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表 7 US-GLE站点生长季与非生长季NEE插补结果
Table 7 NEE imputation results during growing and non-growing seasons of US-GLE station
时期 评价指标 短缺失 中缺失 长缺失 生长季 MSE 0.424 0.429 0.451 MAE 0.402 0.411 0.416 R2 0.486 0.398 0.392 非生长季 MSE 1.005 0.913 0.647 MAE 0.552 0.578 0.480 R2 0.191 0.105 0.204 注：生长季为4月到10月，非生长季为10月到次年4月。
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