地理学报 ›› 2017, Vol. 72 ›› Issue (3): 533-544.doi: 10.11821/dlxb201703013
收稿日期:
2016-09-27
修回日期:
2016-12-13
出版日期:
2017-03-15
发布日期:
2017-05-03
作者简介:
作者简介:江振蓝(1977-), 女, 福建政和人, 博士, 副教授, 主要从事生态环境遥感与信息技术应用研究。E-mail:
基金资助:
Zhenlan JIANG1,2(), Yusheng YANG1, Jinming SHA1(
)
Received:
2016-09-27
Revised:
2016-12-13
Online:
2017-03-15
Published:
2017-05-03
Supported by:
摘要:
目前土壤重金属高光谱反演模型大多忽视了重金属与光谱变量间相关关系的空间异质性,这与实际情况不相吻合,而地理权重回归(GWR)模型能有效地揭示变量间关系的空间异质性。本文以福州市土壤重金属Cd、Cu、Pb、Cr、Zn、Ni为对象,构建土壤重金属预测的GWR高光谱模型,并将预测结果与普通最小二乘法回归(OLS)结果进行比较分析,探讨GWR模型在土壤重金属高光谱预测中的适用性及局限性。结果表明:① GWR模型在土壤重金属高光谱预测中适用与否取决于重金属对光谱变量影响的空间异质性程度:对于Cr、Cu、Zn、Pb等对光谱变量影响空间异质性大的元素,其GWR预测精度较OLS提高明显,表现为GWR模型的调节R2较OLS模型有了明显提高,分别为OLS模型的2.69倍、2.01倍、1.87倍和1.53倍;而AIC值以及残差平方和较OLS模型却明显降低,AIC值减少量均大于3个单位,残差平方和则仅分别为OLS模型的25.33%、30.09%、47.22%和86.84%;对于Cd和Ni等对光谱变量影响空间异质性小的元素,相较于OLS模型,GWR模型的调节R2分别提高了0.015和0.007,残差平方和分别减少了5.97%和4.18%,但AIC值却分别增加了2.737和2.762,GWR预测效果改善不明显;② 光谱变换可以有效增强土壤重金属的光谱特征,其中以光谱的倒数变换效果最好,而且该变换及其微分形式可以很好地提高模型的预测效果;③ GWR模型的应用前提是变量间关系的空间非平稳性,适合在与土壤光谱变量间关系具有显著空间异质性的重金属高光谱预测中推广。
江振蓝, 杨玉盛, 沙晋明. GWR模型在土壤重金属高光谱预测中的应用[J]. 地理学报, 2017, 72(3): 533-544.
Zhenlan JIANG, Yusheng YANG, Jinming SHA. Application of GWR model in hyperspectral prediction of soil heavy metals[J]. Acta Geographica Sinica, 2017, 72(3): 533-544.
表1
福州市土壤重金属描述性统计特征"
重金属 | 最小值 (mg·kg-1) | 最大值 (mg·kg-1) | 平均值 (mg·kg-1) | 标准差 (mg·kg-1) | 偏度 (mg·kg-1) | 峰度 (mg·kg-1) | 变异系数 (%) |
---|---|---|---|---|---|---|---|
Cd | 0.01 | 2.94 | 0.74 | 0.38 | 1.49 | 8.21 | 51.35 |
Cu | 5.68 | 94.60 | 23.54 | 14.89 | 1.93 | 5.32 | 63.25 |
Pb | 8.78 | 155.96 | 44.85 | 24.37 | 1.76 | 3.97 | 54.34 |
Cr | 0.75 | 111.55 | 26.13 | 17.85 | 1.69 | 4.53 | 68.31 |
Zn | 1.15 | 383.13 | 101.19 | 54.73 | 1.63 | 5.54 | 54.09 |
Ni | 0.23 | 50.96 | 12.25 | 8.73 | 1.79 | 4.86 | 71.27 |
表2
福州市土壤重金属含量与光谱变量的最大相关系数"
重金属 | R | FD | SD | RT | RTFD | RTSD | AT | ATFD | ATSD | CR | |
---|---|---|---|---|---|---|---|---|---|---|---|
Cd | 特征波段 相关系数 | 1040 -0.211* | 2420 0.347** | 1990 0.329** | 1040 0.230** | 2420 -0.327** | 1990 -0.352** | 1040 0.220** | 2420 -0.345** | 1250 0.354** | 2170,2190 0.251** |
Cu | 特征波段 相关系数 | 420 -0.478** | 470 -0.426** | 940 0.330** | 380,390,400 0.519** | 510 -0.534** | 450 0.480** | 410 0.511** | 1150 -0.371** | 410 -0.353** | 410 -0.337** |
Pb | 特征波段 相关系数 | 2500 -0.164 | 2490 -0.212* | 1940 -0.240** | 2500 0.182* | 2500 0.234** | 2490 0.237** | 2500 0.171 | 2500 0.222** | 2490 0.218** | 1630 0.190* |
Cr | 特征波段 相关系数 | 520 0.415** | 2230 -0.434** | 1440 0.351** | 360 0.357** | 410 -0.337** | 430 0.319** | 2010 0.411** | 1440 -0.327** | 1440 -0.327** | 2210 0.310** |
Zn | 特征波段 相关系数 | 2240 -0.469** | 390 -0.437** | 440 0.332** | 2150,2160 0.497** | 1050 -0.359** | 2100 0.335** | 2150,2160 0.483** | 2170 -0.313** | 2080 -0.322** | 1480 0.212* |
Ni | 特征波段 相关系数 | 2410 -0.430** | 390 -0.374** | 560 0.300** | 2470 0.438** | 480 -0.399** | 780 0.410** | 2470 0.436** | 600 0.325** | 780 0.294** | 450 -0.293** |
表3
利用光谱变量对福州市土壤重金属进行逐步线性回归的结果"
重金属 | 模型变量 | 调节R2 | 估计误差 | F | 显著性水平 |
---|---|---|---|---|---|
Cd | 常量, SD_1990, RT_1040 | 0.179 | 0.343 | 15.413 | 0.000 |
Cu | 常量, FD_470, RT_380, RTSD_450 | 0.300 | 12.442 | 19.658 | 0.000 |
Pb | 常量, FD_2490, SD_1940, RTSD_2490, CR_1630 | 0.141 | 22.430 | 7.781 | 0.000 |
Cr | 常量, SD_1440, RTSD_430 | 0.226 | 15.685 | 20.170 | 0.000 |
Zn | 常量, RT_2150, RTFD_1050 | 0.312 | 45.235 | 30.706 | 0.000 |
Ni | 常量, RT_2470, RTFD_480 | 0.180 | 7.874 | 15.427 | 0.000 |
表4
福州市土壤重金属OLS及GWR预测模型的精度检验"
重金属 | 建模样本 | 验证样本 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
AIC | 调节R2 | 残差平方和 | 调节R2 | 均方根误差 | |||||||
OLS | GWR | OLS | GWR | OLS | GWR | OLS | GWR | OLS | GWR | ||
Cd | 75.807 | 78.544 | 0.181 | 0.196 | 10.986 | 10.330 | 0.167 | 0.192 | 0.302 | 0.294 | |
Cu | 730.248 | 698.162 | 0.323 | 0.649 | 13758.666 | 4141.423 | 0.217 | 0.613 | 11.658 | 8.192 | |
Pb | 1204.227 | 1199.618 | 0.141 | 0.216 | 64334.784 | 55866.254 | 0.083 | 0.213 | 24.700 | 22.884 | |
Cr | 742.016 | 720.703 | 0.266 | 0.716 | 21484.197 | 5441.275 | 0.090 | 0.396 | 15.487 | 12.463 | |
Zn | 925.785 | 916.964 | 0.281 | 0.525 | 194869.446 | 92018.520 | 0.247 | 0.456 | 39.781 | 31.934 | |
Ni | 602.693 | 605.455 | 0.212 | 0.219 | 5406.102 | 5179.912 | 0.094 | 0.117 | 7.392 | 7.292 |
表5
福州市土壤重金属与变量间关系的空间非平稳性检验"
重金属 | 常量 | 变量1 | 变量2 | 变量3 | 变量4 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
UQ-LQ | SE | UQ-LQ | SE | UQ-LQ | SE | UQ-LQ | SE | UQ-LQ | SE | |||||
Cd | 0.04 | 0.18 | 3286.93 | 2440.54 | 0.03 | 0.09 | ||||||||
Cu | 27.71 | 11.23 | 24251.91 | 10698.67 | 2.51 | 0.82 | 15446.67 | 3914.22 | ||||||
Pb | 252.90 | 287.82 | 1035.71 | 978.55 | 323742.57 | 155253.07 | 1329.4 | 1314.67 | 234.69 | 289.44 | ||||
Cr | 15.78 | 3.60 | 277645.03 | 51064.04 | 6360.06 | 1981.41 | ||||||||
Zn | 153.11 | 31.68 | 80.30 | 17.37 | 17108.15 | 6167.21 | ||||||||
Ni | 6.39 | 5.03 | 2.39 | 2.32 | 61.63 | 70.43 |
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