Development and application of a new sensitivity analysis model for the remote sensing retrieval of heavy metals in water

This work proposes a new sensitivity analysis model, referred to as the D-δ(ε) model, for the remote sensing retrieval of heavy metals in bodies of water. By defining the reflectance ratio function (δ(ε)), we deduce the mathematical relationships between the heavy metal concentration sequences (D_i) that can be effectively used for remote sensing retrievals and the radiometric resolution (ε) of the remote sensing instrument. Then, as a function of wavelength, we obtain the curve of the lower limit of the heavy metal concentrations in water that can be retrieved by remote sensing. To demonstrate the advantages of this model, we take two compounds, copper sulphate (CuSO₄) and cadmium sulphide (CdS), as examples to discuss the remote sensing sensitivity of different wavelengths when retrievals are performed using the Chinese HJ-1A's hyperspectral imager (HSI). The results showed that the lowest detectable concentration of CuSO₄ in the wavelength range of 460.04-496 nm (corresponding to bands 1-17 of the HSI image) can be below 0.15 mg/L, while the concentration of CdS can be lower than 0.001 mg/L in the separate ranges of 460.04-493.59 nm (bands 1-16) and 526.885-594.79 nm (bands 29-51). This model clearly demonstrates the mathematical relationship obeyed by "D-ε". Additionally, this model can not only calculate the retrieval concentration sequences at any observation wavelength but also intuitively provide the curve of the lower concentration limit for heavy metal retrievals. This work provides a theoretical basis for the selection of the most sensitive bands for remote sensing retrieval using hyperspectral images in the future.