植冠下土壤类型差异对遥感估算冬小麦叶面积指数的影响

doi:10.17521/cjpe.2017.0231

摘要/Abstract

摘要：

遥感是从田块到区域乃至全球范围无损探测叶面积指数(LAI)的有效方法。土壤背景是LAI遥感研究的重要制约因素之一, 而土壤类型是组成土壤背景的主要部分, 对植被冠层-土壤的光学性质有重要影响, 但目前植冠下土壤类型背景对遥感LAI估算的影响尚不明确。该文通过分析归一化差异植被指数、修正型土壤调节植被指数、修正的叶绿素吸收比率指数、红边拐点、红边振幅、红边面积、红边对数指数和归一化差异光谱指数在不同土壤类型下对LAI的敏感性, 挖掘最不敏感的光谱参数; 通过比较两种回归模型(偏最小二乘回归和随机森林回归)在单一土壤类型和多种土壤类型区对LAI的预测精度, 探究将单一土壤类型下发展的LAI估算模型应用到复杂土壤类型地区时可能出现的问题。结果表明: (1)虽然8种光谱指数对LAI的敏感性因土壤类型不同而差异明显, 但红边拐点受植冠下土壤类型影响最小; “lambda-by-lambda”波段优选算法不仅可以提供对LAI最敏感的光谱区间, 而且可在一定程度上为抵抗植冠下土壤类型差异影响的光谱指数构建提供可行思路; (2)回归模型的LAI预测精度因是否考虑土壤类型而不同, 但在小区域尤其是田块尺度研究时, 对变量的解释能力是选择模型的第一考虑, 而偏最小二乘回归在此方面优于随机森林回归; 在未知地表先验知识的前提下, 随机森林回归对大区域LAI估算比偏最小二乘回归适合, 但地表先验知识的获取对LAI遥感估算仍然十分必要。

关键词: 遥感, 土壤类型, 冬小麦叶面积指数, 光谱指数, 偏最小二乘回归, 随机森林回归

Abstract: Aims Remote sensing is an effective and nondestructive way to retrieve leaf area index (LAI) from plot, regional and global range. Soil background is one of the confounding factors limiting remotely estimating LAI. And soil type contains a large proportion of soil background information, which can influence the optical properties of vegetation canopy and soil. However, our knowledge on the effects stemmed from soil types underneath the canopy on LAI remote estimating have been in shortage. Thus, this study aims to explore the influences of soil types underneath the canopy on winter wheat LAI remote estimating. Methods We analyzed the sensitivity variation of eight spectral indices, named normalized difference vegetation index (NDVI), modified soil-adjusted vegetation index (MSAVI), modified chlorophyll absorption ratio index 2 (MCARI₂), red edge inflection point (REIP), red edge amplitude (Dr), red edge area (SDr), red edge symmetry (RES), normalized difference spectral index (NDSI), to LAI in different soil types, and then we identified some spectral intervals or parameters that were insensitive to soil type variations underneath the canopy. We also compared the accuracy of two commonly used regression models, partial least squares regression (PLSR) and random forest regression (RFR), in estimating LAI for different soil types. We also explored the problems arising from applying the regression model developed in single soil type area to complex soil types area in retrieving LAI. Important findings This paper demonstrates the effects of soil types underneath the canopy on LAI retrieving. 1) The sensitivity of spectral indices to LAI is significantly different due to the soil type variation, but REIP has the least effects from soil type variation among the eight spectral indices. Meanwhile, the band selection algorithm of lambda-by-lambda not only chooses the most sensitive spectral interval for LAI, but also provides a feasible way to construct the spectral index that exhibits strong resistances to the effects of soil types underneath the canopy. 2) The accuracy of LAI estimation by regression models differs under soil type considered or not. So we suggest that in small scale researches, especially in a field scale, the ability of regression models in explaining variables is the priority consideration, while the PLSR is superior to RFR in this respect. Under the premise of unknown priori knowledge of land surfaces, the RFR is more suitable for retrieving LAI than PLSR, but land surface priori knowledge is still necessary. These findings provide the theoretical basis and methods for developing remotely sensing estimating LAI models adapted to various land surfaces. Further analysis is needed in applying the findings in more crop types, cultivars and growth stages.

Key words: remote sensing, soil type, winter wheat leaf area index, spectral indices, partial least squares regression, random forest regression

高林, 王晓菲, 顾行发, 田庆久, 焦俊男, 王培燕, 李丹. 植冠下土壤类型差异对遥感估算冬小麦叶面积指数的影响. 植物生态学报, 2017, 41(12): 1273-1288. DOI: 10.17521/cjpe.2017.0231

GAO Lin, WANG Xiao-Fei, GU Xing-Fa, TIAN Qing-Jiu, JIAO Jun-Nan, WANG Pei-Yan, LI Dan. Exploring the influence of soil types underneath the canopy in winter wheat leaf area index remote estimating. Chinese Journal of Plant Ecology, 2017, 41(12): 1273-1288. DOI: 10.17521/cjpe.2017.0231

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图/表 15

参考文献 56

1	Abdi H (2003). Partial least square regression (PLS regression). In: Salkind N ed. Encyclopedia of Measurement and Statistics. Thousand Oaks, Sage, USA.
2	Allen WA, Gausman HW, Richardson AJ (1973). Willst?tter- Stoll theory of leaf reflectance evaluated by ray tracing.Applied Optics, 12, 2448-2453. DOI URL
3	Atzberger C, Guérif M, Baret F, Werner W (2010). Comparative analysis of three chemometric techniques for the spectroradiometric assessment of canopy chlorophyll content in winter wheat. Computers and Electronics in Agriculture, 73, 165-173. DOI URL
4	Baret F, Guyot G (1991). Potentials and limits of vegetation indices for LAI and APAR assessment.Remote Sensing of Environment, 35, 161-173. DOI URL
5	Bausch WC (1993). Soil background effects on reflectance- based crop coefficients for corn.Remote Sensing of Environment, 46, 213-222. DOI URL
6	Bolton DK, Friedl MA (2013). Forecasting crop yield using remotely sensed vegetation indices and crop phenology metrics.Agricultural and Forest Meteorology, 173, 74-84. DOI URL
7	Breiman L (2001). Random forests.Machine Learning, 45, 5-32. DOI URL
8	Broge NH, Leblanc E (2001). Comparing prediction power and stability of broadband and hyperspectral vegetation indices for estimation of green leaf area index and canopy chlorophyll density.Remote Sensing of Environment, 76, 156-172. DOI URL
9	Chen JM, Black TA (1992). Defining leaf area index for non-flat leaves. Plant, Cell & Environment, 15, 421-429. DOI URL
10	Cho MA, Skidmore A, Corsi F, van Wieren SE, Sobhan I (2007). Estimation of green grass/herb biomass from airborne hyperspectral imagery using spectral indices and partial least squares regression.International Journal of Applied Earth Observation and Geoinformation, 9, 414-424. DOI URL
11	Danson FM, Plummer SE (1995). Red-edge response to forest leaf area index.Remote Sensing, 16, 183-188. DOI URL
12	Delegido J, Verrelst J, Meza CM, Rivera JP, Alonso L, Moreno J (2013). A red-edge spectral index for remote sensing estimation of green LAI over agroecosystems.European Journal of Agronomy, 46, 42-52. DOI URL
13	Darmawan A, Nadirah, Wibowo A, Evri M, Mulyono S, Nugroho AS, Sadly M, Hendiarti N, Kashimura O, Kobayashi C, Uchida A, Uraguchi A, Sekine H (2009). Quantitative analysis from unifying field and airborne hyperspectral in prediction biophysical parameters by using partial least square (PLSR) and Normalized Difference Spectral Index (NDSI). . Cited: 2017-9-1.
14	Elsayed S, Elhoweity M, Schmidhalter U (2015). Normalized difference spectral indices and partial least squares regression to assess the yield and yield components of peanut.Australian Journal of Crop Science, 9, 976.
15	Fang HL, Liang SL, Hoogenboom G (2011). Integration of MODIS LAI and vegetation index products with the CSM-CERES-Maize model for corn yield estimation.International Journal of Remote Sensing, 32, 1039-1065. DOI URL
16	Farrar TJ, Nicholson SE, Lare AR (1994). The influence of soil type on the relationships between NDVI, rainfall, and soil moisture in semiarid Botswana. II. NDVI response to soil moisture.Remote Sensing of Environment, 50, 121-133. DOI URL
17	Feng W, Zhu Y, Yao X, Tian YC, Guo TC, Cao WX (2009). Monitoring nitrogen accumulation in wheat leaf with red edge characteristics parameters.Transaction of the Chinese Society of Agricultural Engineering, 25, 194-201.(in Chinese with English abstract) [冯伟, 朱艳, 姚霞, 田永超, 郭天财, 曹卫星 (2009). 利用红边特征参数监测小麦叶片氮素积累状况 . 农业工程学报,25, 194-201.] DOI URL
18	Filella I, Penuelas J (1994). The red edge position and shape as indicators of plant chlorophyll content, biomass and hydric status.International Journal of Remote Sensing, 15, 1459-1470. DOI URL
19	Gao L, Yang GJ, Li CC, Feng HK, Xu B, Wang L, Dong JH, Fu K (2017). Application of an improved method in retrieving leaf area index combined spectral index with PLSR in hyperspectral data generated by unmanned aerial vehicle snapshot camera.Acta Agronomica Sinica, 43, 549-557.(in Chinese with English abstract) [高林, 杨贵军, 李长春, 冯海宽, 徐波, 王磊, 董锦绘, 付奎 (2017). 基于光谱特征与PLSR结合的叶面积指数拟合方法的无人机画幅高光谱遥感应用. 作物学报, 43, 549-557.]
20	Gausman HW, Allen WA, Myers V, Cardenas R (1969). Reflectance and internal structure of cotton leaves,Gossypium hirsutum L. Agronomy Journal, 61, 374-376.
21	Haboudane D, Miller JR, Pattey E, Zarco-Tejada PJ, Strachan IB (2004). Hyperspectral vegetation indices and novel algorithms for predicting green LAI of crop canopies: Modeling and validation in the context of precision agriculture.Remote Sensing of Environment, 90, 337-352. DOI URL
22	Hansen PM, Schjoerring JK (2003). Reflectance measurement of canopy biomass and nitrogen status in wheat crops using normalized difference vegetation indices and partial least squares regression.Remote Sensing of Environment, 86, 542-553. DOI URL
23	Herrmann I, Pimstein A, Karnieli A, Cohen Y, Alchanatis V, Bonfil DJ (2011). LAI assessment of wheat and potato crops by VENμS and Sentinel-2 bands.Remote Sensing of Environment, 115, 2141-2151. DOI URL
24	Horler DNH, Dockray M, Barber J (1983). The red edge of plant leaf reflectance.International Journal of Remote Sensing, 4, 273-288. DOI URL
25	Huete AR (1988). A soil-adjusted vegetation index (SAVI).Remote Sensing of Environment, 25, 295-309. DOI URL
26	Huete AR, Jackson RD, Post DF (1985). Spectral response of a plant canopy with different soil backgrounds.Remote Sensing of Environment, 17, 37-53. DOI URL
27	Jasinski MF, Eagleson PS (1989). The structure of red-infrared scattergrams of semivegetated landscapes.IEEE Transactions on Geoscience and Remote Sensing, 27, 441-451. DOI URL
28	Ju CH, Tian YC, Yao X, Cao WX, Zhu Y, Hannaway D (2010). Estimating leaf chlorophyll content using red edge parameters.Pedosphere, 20, 633-644. DOI URL
29	Lee KS, Cohen WB, Kennedy RE, Maiersperger TK, Gower ST (2004). Hyperspectral versus multispectral data for estimating leaf area index in four different biomes.Remote Sensing of Environment, 91, 508-520. DOI URL
30	Li F, Mistele B, Hu Y, Chen X, Schmidhalter U (2013). Comparing hyperspectral index optimization algorithms to estimate aerial N uptake using multi-temporal winter wheat datasets from contrasting climatic and geographic zones in China and Germany.Agricultural and Forest Meteorology, 180, 44–57. DOI URL
31	Li H, Chen ZX, Jiang ZW, Wu WB, Ren JQ, Liu B, Tuya H (2017). Comparative analysis of GF-1, HJ-1, and Landsat-8 data for estimating the leaf area index of winter wheat.Journal of Integrative Agriculture, 16, 266-285. DOI URL
32	Li XC, Zhang YJ, Bao YS, Luo JH, Jin XL, Xu XG, Song XY, Yang GJ (2014). Exploring the best hyperspectral features for LAI estimation using partial least squares regression.Remote Sensing, 6, 6221-6241. DOI URL
33	Liu L, Zhang R, Zuo Z (2016). The relationship between soil moisture and LAI in different types of soil in central eastern China.Journal of Hydrometeorology, 17, 2733-2742. DOI URL
34	McLachlan G (2004). Discriminant Analysis and Statistical Pattern Recognition. John Wiley & Sons, Hoboken.
35	Myneni RB, Hall FB, Sellers PJ, Marshak AL (1995). The interpretation of spectral vegetation indices.IEEE Transactions on Geoscience and Remote Sensing, 33, 481-486. DOI URL
36	Nolet C, Poortinga A, Roosjen P, Bartholomeus H, Ruessink G (2014). Measuring and modeling the effect of surface moisture on the spectral reflectance of coastal beach sand.PLOS ONE, , 9, e112151. doi: 10.1371/journal.pone.0112151. DOI URL
37	Qi J, Chehbouni A, Huete AR, Kerr YH, Sorooshian S (1994). A modified soil adjusted vegetation index.Remote Sensing of Environment, 48, 119-126. DOI URL
38	Rondeaux G, Steven M, Baret F (1996). Optimization of soil-adjusted vegetation indices.Remote Sensing of Environment, 55, 95-107. DOI URL
39	Rossel RA, Webster R (2012). Predicting soil properties from the Australian soil visible-near infrared spectroscopic database.European Journal of Soil Science, 63, 848-860. DOI URL
40	Rouse JW, Haas RH, Schell JA, Deering DW, Harlan JC (1974). Monitoring the vernal advancements and retrogradation of natural vegetation, NASA/GSFC, Type III, Final Report. . Cited: 2017-9-1.
41	Sadeghi M, Jones SB, Philpot WD (2015). A linear physically- based model for remote sensing of soil moisture using short wave infrared bands.Remote Sensing of Environment, 164, 66-76. DOI URL
42	Schlemmer M, Gitelson A, Schepers J, Ferguson R, Peng Y, Shanahan J, Rundquist D (2013). Remote estimation of nitrogen and chlorophyll contents in maize at leaf and canopy levels.International Journal of Applied Earth Observation and Geoinformation, 25, 47-54. DOI URL
43	Siegmann B, Jarmer T (2015). Comparison of different regression models and validation techniques for the assessment of wheat leaf area index from hyperspectral data.International Journal of Remote Sensing, 36, 4519-4534. DOI URL
44	Thenkabail PS, Lyon JG, Huete A (2012). Hyperspectral Remote Sensing of Vegetation. CRC Press, New York.
45	Todd SW, Hoffer RM (1998). Responses of spectral indices to variations in vegetation cover and soil background.Photogrammetric Engineering and Remote Sensing, 64, 915-922.
46	Vi?a A, Gitelson AA, Nguy-Robertson AL, Peng Y (2011). Comparison of different vegetation indices for the remote assessment of green leaf area index of crops.Remote Sensing of Environment, 115, 3468-3478. DOI URL
47	Vogelmann JE, Rock BN, Moss DM (1993). Red edge spectral measurements from sugar maple leaves.International Journal of Remote Sensing, 14, 1563-1575. DOI URL
48	Wang FM, Huang JF, Lou ZH (2011). A comparison of three methods for estimating leaf area index of paddy rice from optimal hyperspectral bands.Precision Agriculture, 12, 439-447. DOI URL
49	Wang HW, Wu ZB, Meng J (2006). Partial Least Squares Regression-Linear and Nonlinear Methods. National Defense Industry Press, Beijing.(in Chinese) [王惠文, 吴载斌, 孟洁 (2006). 偏最小二乘回归的线性与非线性方法. 国防工业出版社, 北京.]
50	Wold S, Sj?str?m M, Eriksson L (2001). PLS-regression: A basic tool of chemometrics.Chemometrics and Intelligent Laboratory Systems, 58, 109-130. DOI URL
51	Woolley JT (1971). Reflectance and transmittance of light by leaves.Plant Physiology, 47, 656-662. DOI URL PMID
52	Xu XR (2005). Physics of Remote Sensing. Peking University Press, Beijing.(in Chinese) [徐希孺 (2005). 遥感物理. 北京大学出版社, 北京.]
53	Yeniay O, Goktas A (2002). A comparison of partial least squares regression with other prediction methods.Hacettepe Journal of Mathematics and Statistics, 31, 99-101.
54	Yuan HH, Yang GJ, Li CC, Wang YJ, Liu JG, Yu HY, Feng HK, Xu B, Zhao XQ, Yang XD (2017). Retrieving soybean leaf area index from unmanned aerial vehicle hyperspectral remote sensing: Analysis of RF, ANN, and SVM regression models.Remote Sensing, 9, 309. doi: 10.3390/rs9040309. DOI URL
55	Yu K, Lenz-Wiedemann V, Chen X, Bareth G (2014). Estimating leaf chlorophyll of barley at different growth stages using spectral indices to reduce soil background and canopy structure effects.ISPRS Journal of Photogrammetry and Remote Sensing, 97, 58-77. DOI URL
56	Zhao CJ, Wang ZJ, Wang JH, Huang WJ (2012). Relationships of leaf nitrogen concentration and canopy nitrogen density with spectral features parameters and narrow-band spectral indices calculated from field winter wheat (Triticum aestivum L.) spectra. International Journal of Remote Sensing, 33, 3472-3491. DOI

土壤类型 Soil type	LAI					p
土壤类型 Soil type	最小值 Min	最大值 Max	平均值 Mean	标准差 SD	变异系数 CV (%)	p
潮土 Fluvo-aquic soil	1.970	5.870	3.650	1.031	28.24	0.105
水稻土 Paddy soil	2.240	5.880	4.114	0.962	23.39	0.593
棕壤 Brown soil	1.100	6.710	3.482	1.557	44.71	0.610
砂姜黑土 Lime concretion black soil	1.700	5.500	3.463	1.018	29.39	0.536
褐土 Cinnamon soil	1.320	5.860	4.483	1.235	27.54	< 0.005
5种土壤 Five type soils	1.100	6.710	3.838	1.232	32.09	0.242

土壤类型 Soil type	LAI					p
土壤类型 Soil type	最小值 Min	最大值 Max	平均值 Mean	标准差 SD	变异系数 CV (%)	p
潮土 Fluvo-aquic soil	1.970	5.870	3.650	1.031	28.24	0.105
水稻土 Paddy soil	2.240	5.880	4.114	0.962	23.39	0.593
棕壤 Brown soil	1.100	6.710	3.482	1.557	44.71	0.610
砂姜黑土 Lime concretion black soil	1.700	5.500	3.463	1.018	29.39	0.536
褐土 Cinnamon soil	1.320	5.860	4.483	1.235	27.54	< 0.005
5种土壤 Five type soils	1.100	6.710	3.838	1.232	32.09	0.242

光谱指数 Spectral indices	公式 Equation	来源 Reference
归一化差异植被指数 Normalized difference vegetation index (NDVI)	$NDVI=\frac{{{R}_{800}}-{{R}_{680}}}{{{R}_{800}}+{{R}_{680}}}$	Rouse et al., 1974
修正型土壤调节植被指数 Modified soil-adjusted vegetation index (MSAVI)	$MSAVI=\frac{1}{2}\times \left[ 2\times {{R}_{800}}+1-\sqrt{{{\left( 2\times {{R}_{800}}+1 \right)}^{2}}-8\times \left( {{R}_{800}}-{{R}_{670}} \right)} \right]$	Qi et al., 1994
修正的叶绿素吸收比率指数 Modified chlorophyll absorption ratio index 2 (MCARI₂)	$MCAR{{I}_{2}}=\frac{1.5\times \left[ 2.5\times \left( {{R}_{800}}-{{R}_{670}} \right)-1.3\times \left( {{R}_{800}}-{{R}_{550}} \right) \right]}{\sqrt{{{\left( 2\times {{R}_{800}}+1 \right)}^{2}}-\left( 6\times {{R}_{800}}-5\times \sqrt{{{R}_{670}}} \right)-0.5}}$	Haboudane et al., 2004
红边拐点 Red edge inflection point (REIP)	$REIP=700+40\times \frac{\left( {{R}_{670}}+{{R}_{780}} \right)\text{/2}-{{R}_{700}}}{{{R}_{\text{740}}}-{{R}_{\text{700}}}}$	Danson & Plummer, 1995
红边振幅 Red edge amplitude (Dr)	$d{{\lambda }_{\text{red-edge}}}$	Feng et al., 2009
红边面积 Red edge area (SDr)	$\sum{d{{\lambda }_{\left( 680\text{-}750 \right)}}}$	Filella & Penuelas, 1994
红边对称指数 Red edge symmetry (RES)	$RES=\frac{{{R}_{718}}-{{R}_{675}}}{{{R}_{755}}-{{R}_{675}}}$	Ju et al., 2010
归一化差异光谱指数 Normalized difference spectral index (NDSI)	$NDS{{I}_{(i,j)}}=\frac{{{R}_{i}}-{{R}_{j}}}{{{R}_{\text{i}}}+{{R}_{j}}}$	Li et al., 2013

光谱指数 Spectral indices	公式 Equation	来源 Reference
归一化差异植被指数 Normalized difference vegetation index (NDVI)	$NDVI=\frac{{{R}_{800}}-{{R}_{680}}}{{{R}_{800}}+{{R}_{680}}}$	Rouse et al., 1974
修正型土壤调节植被指数 Modified soil-adjusted vegetation index (MSAVI)	$MSAVI=\frac{1}{2}\times \left[ 2\times {{R}_{800}}+1-\sqrt{{{\left( 2\times {{R}_{800}}+1 \right)}^{2}}-8\times \left( {{R}_{800}}-{{R}_{670}} \right)} \right]$	Qi et al., 1994
修正的叶绿素吸收比率指数 Modified chlorophyll absorption ratio index 2 (MCARI₂)	$MCAR{{I}_{2}}=\frac{1.5\times \left[ 2.5\times \left( {{R}_{800}}-{{R}_{670}} \right)-1.3\times \left( {{R}_{800}}-{{R}_{550}} \right) \right]}{\sqrt{{{\left( 2\times {{R}_{800}}+1 \right)}^{2}}-\left( 6\times {{R}_{800}}-5\times \sqrt{{{R}_{670}}} \right)-0.5}}$	Haboudane et al., 2004
红边拐点 Red edge inflection point (REIP)	$REIP=700+40\times \frac{\left( {{R}_{670}}+{{R}_{780}} \right)\text{/2}-{{R}_{700}}}{{{R}_{\text{740}}}-{{R}_{\text{700}}}}$	Danson & Plummer, 1995
红边振幅 Red edge amplitude (Dr)	$d{{\lambda }_{\text{red-edge}}}$	Feng et al., 2009
红边面积 Red edge area (SDr)	$\sum{d{{\lambda }_{\left( 680\text{-}750 \right)}}}$	Filella & Penuelas, 1994
红边对称指数 Red edge symmetry (RES)	$RES=\frac{{{R}_{718}}-{{R}_{675}}}{{{R}_{755}}-{{R}_{675}}}$	Ju et al., 2010
归一化差异光谱指数 Normalized difference spectral index (NDSI)	$NDS{{I}_{(i,j)}}=\frac{{{R}_{i}}-{{R}_{j}}}{{{R}_{\text{i}}}+{{R}_{j}}}$	Li et al., 2013

光谱指数 Spectral indices	LAI
光谱指数 Spectral indices	1-1.5	1.5-2	2-2.5	2.5-3	3-3.5	3.5-4	4-4.5	4.5-5	>5
NDVI	6.32	10.91	7.18	7.94	4.37	1.95	1.9	2.01	1.44
MSAVI	13.86	24.48	18.57	24.42	12.77	8.72	10.01	8.02	4.25
MCARI₂	15.72	25.98	20.51	26.03	13.95	8.94	9.97	8.28	4.84
RES	20.54	25.8	24.06	18.15	16.26	8.36	8.49	11.69	7.8
REIP	0.44	0.45	0.53	0.39	0.41	0.23	0.25	0.29	0.24
NDSI	100.97	206.38	187.41	139.56	154.61	155.92	114.89	158.33	150.22
Dr	19.51	28.93	20.25	31.48	15.98	15.68	12.38	13.61	7.38
SDr	17.01	23.61	14.44	27.18	12.2	16.32	11.07	11.35	6.68