使用线性回归方法构建水体叶绿素a浓度高光谱估算模型的一个逻辑问题

在当前利用实测光谱数据通过线性回归方法构建水体叶绿素a浓度反演模型的过程中,通常的数据处理流程是首先通过相关分析确定与水体叶绿素a浓度具有最大相关系数的波段组合,然后通过回归方法建立该波段组合与水体叶绿素a浓度的关系模型.在逻辑上,这个流程首先假定了线性关系的存在,然而,实际上测量数据里的波段组合与水体叶绿素a浓度之间的关系经常是非线性关系.针对这个逻辑不一致的问题,提出了一个新的数据处理流程,即数据分组-散点图绘制-数据变换-相关分析-模型构建.利用关系已知的模拟数据和关系未知的太湖夏季实测数据,经过对比分析两个流程,结果表明,原有的数据处理流程会导致分析结果出现偏差,表现为不恰当的波段组合选择、较低的模型拟合度、具有异方差性的散点分布、较差的模型可解释性,建立的所谓"最佳"模型并不是最佳的,由此会影响不同研究成果之间的可比性.提出的数据处理流程可较好的弥补原有数据处理流程的不足,在遥感反演中可用来帮助构建合适的回归模型.

A Logical Problem in the Building Linear Regression Model on Estimating Chlorophyll-a Concentration in Lake Based on the Measured Spectrum Data

In the building of regression model on estimating chlorophyll-a concentration(Chla) based on the measured spectrum on the water surface,the data processing procedure most used is as follows:first,determining the band combination of spectrum based on the maximum linear correlation with Chla,and then,building the regression model.The default of this procedure is that relationship between band combination and Chla is linear,but in fact,the relationship may be nonlinear.The nonlinear relationship used as linear relationship will result in a logical disagreement.To resolve this problem,this paper proposes a new data processing procedure,i.e.,data grouping-scatter plotting-data transformation-correlation analysis-model building,and compares this procedure with the previous by simulation data with given relationship and measured data in Taihu lake with unknown relationship.The result showed that the previous procedure lead to bias,such as the inappropriate band combination selection,a lower model goodness of fit,unhomogeneous scatter point distribution,poor model's explanation. The model built by previous procedure is not the best in fact,and model's inappropriate band combination has a great influence on the comparison application among different studies. The new procedure proposed in this paper compensates for the previous deficiency and can be used to build an appropriate regression model in remote sensing inversion study.