5.1 Introduction

During the last years spaceborne imaging spectrometers have been providing higher spectral resolution data for ocean colour remote sensing in the visible-near-infrared spectral range (400–1000 nm). To some extent MOS-IRS (Zimmermann 2000), launched in 1996, was a pacemaker in this respect and in-between was followed by several instruments both of experimental and pre-operational status (e.g. CHRIS, MERIS). Where on one hand this new class of instruments allows to access, distinguish and quantify more parameters by remote sensing with increased accuracy, the spectral dimensionality of the data require new retrieval techniques accounting for the multivariate nature of the data (i.e. several parameters may vary independently and influence the spectral signature measured by the instrument) and allowing for regional and/or seasonal optimization of the inversion algorithms. In the last years this led to the development of bio-optical and radiative transfer model based techniques fulfilling these requirements. Examples are Principal Component Inversion PCI (Krawczyk et al. 1993), Neural Network algorithms NN (Doerffer and Schiller 1998; Niang et al. 2003; Zhang et al. 2002) or Spectral Matching techniques SM (Heege et al. 2005; Morel and Bélanger 2006; Van Der Woerd and Pasterkamp 2008). Since these techniques follow a consistent physical model and information theory based approach which is different to “classical” empirical algorithms still often used in remote sensing we will discuss in the following the physical and mathematical basis and how in particular PCI can be used to implement dedicated case-2 inversion algorithms. The algorithms developed were implemented in an operational processing scheme used for water quality monitoring in the Baltic Sea in the frames of the European Global Monitoring for Environment and Security (GMES) programme for German users. Some examples will illustrate this operational application.

5.2 Characteristics of Optically Complex Waters

This paragraph will summarise the main points on this subject, a more extensive discussion can be found in Sathyendranath (2000). Open ocean waters, which are usually characterised by phytoplankton being the main varying water constituent, can be considered as a single-variable system from the remote sensing perspective. Chlorophyll as the dominating optically active substance is determining the “colour” (i.e. reflectance spectrum) of the water body. For satellite measurements, i.e. top of the atmosphere, additional variability in the measurement is caused by atmospheric variability (e.g. aerosols, gaseous absorbers). In most cases for the atmospheric correction the atmosphere is described by Rayleigh scattering, aerosol content and a parameter related to the size distribution of aerosols. Thus, for the inversion of satellite ocean colour measurements in total three main variables seem sufficient for open ocean waters (we neglect here additional variables like absorbing gases assuming a proper positioning of the instrument’s spectral channels to minimise their influence).

Because of the strong light absorption by water at wavelengths above 700 nm and the comparably low phytoplankton concentrations usually the “black water condition” for atmospheric correction firstly introduced by Gordon (1978) can be applied and band ratios using two or three channels in the visible range can be used to retrieve chlorophyll concentrations.

The situation is different in inland and coastal waters or (semi-) closed basins, such as the Baltic Sea or Black Sea, due to one or several of the following reasons:

  • significantly higher phytoplankton concentrations occur, this may result in a non-negligible signal from the water body at wavelengths >700 nm

  • occurrence of several different and statistically independent optically active constituents in the water body will lead to interpretation failures of “one-dimensional” retrieval algorithms

  • large concentrations of inorganic scatterers in the water (in particular suspended sediment) cause a significant signal remitted at wavelengths > 700 nm and violate the “black water condition” for atmospheric correction

  • land influence may cause variations in aerosol composition (i.e. mixtures of maritime and land aerosols) and may require determination of aerosol properties from the measurement to be used in atmospheric corrections.

For the optically active water constituents we find the following situation:

  • the main groups of constituents considered are phytoplankton, dead organic material (Seston), suspended inorganic matter (sediment) and dissolved organic matter (Gelbstoff, DOM)

  • the composition of phytoplankton species, and thus the optical properties and resulting colour characteristics, may vary significantly with region or season

  • due to different origin the colour characteristics of suspended sediments may vary significantly with place and time

  • extremely high concentrations of one or more constituents (e.g. in river plumes or algae blooms) may optically mask other components

  • in general, the different components in the water do not covary due to their different biological or physical nature, different origin and different spread mechanisms.

In result of this all specific requirements become valid for retrieval algorithms to be applied to optically complex (case-2) waters:

  • algorithms are needed capable to account for simultaneous occurrence of several, non-covarying water constituents

  • algorithms and models to be applied need to account for specific optical properties of different water constituents to be able to discriminate between them

  • a retrieval scheme is needed which allows to account for changing, regional specific optical properties of the water body and

  • advanced atmospheric correction algorithms are needed to account for residual water reflectance in the near infrared as well as for varying aerosol properties.

Thus, by dealing with optically complex waters, typically found in coastal and inland waters, we are facing a multivariate mixture of variables in the measurement. This, finally, leads to the demand for more spectral bands and better spectral resolution in the measurement and for adequate, multivariate inversion techniques to retrieve the geo-physical parameters.

5.3 Physics of the Problem

The “Colour” of the water body which is the basis for remote sensing of water constituents is caused by the scattering and absorption properties of pure water and the individual constituents respectively. These properties are described by the corresponding scattering and absorption spectra, or, if normalised to concentrations, the specific spectral scattering and absorption coefficients (inherent optical properties, IOPs). This means, what we “see” by measuring the reflectance spectra, are not the concentrations of water constituents, but the result of several superimposed scattering and absorption processes forming the resulting spectrum.

This understanding is essential for developing retrieval algorithms because it means, from the physical point of view, that primarily we are measuring scattering and absorption properties by remote sensing. These are then implicitly or explicitly linked to concentrations of the single water constituents, implicitly in the case of empirical algorithms correlating reflectances with in situ concentrations, explicitly through the specific IOPs in the case of model-based inversion techniques.

Another important conclusion follows from this physical background: since the scattering and absorption spectra of the single components are smooth, i.e. without strong spectral features (except special effects like Fluorescence which are not considered here) and superimposing in the same spectral range it is almost impossible to retrieve one single parameter without accounting for the occurrence and variation of the others. This, finally, is the reason for the necessity of a larger number of spectral bands, higher spectral resolution and extended spectral range for remote sensing of optically complex case-2 waters.

5.4 Mathematical View

To better understand the function and problems of the retrieval (or inversion) algorithms it is worth to look at the problem from a mathematical and information theory perspective. The spectra measured for case-2 waters remote sensing are a multivariate data set, i.e. variations in the measurement are caused by multiple parameters which are not necessarily co-varying with each other. The spectral measurements in each of the spectral channels of an instrument are statistically not independent due to the smooth and “broadband” optical properties of the individual constituents in the water. It is therefore hardly possible to correlate single bands to the variation of an individual constituent or one optical parameter. In fact, each available channel contains (part of) information on each of the water constituents. Thus, multivariate inversion techniques are the adequate tool to build retrieval algorithms for optically complex waters. This type of inversion technique is capable to use as much as possible spectral information (i.e. use all available spectral bands) to estimate an individual parameter while at the same time accounting for other variables influencing the spectrum.

How this approach translates into concrete algorithms? Figure 5.1 shows the basic scheme for the inversion of a multivariate spectral measurement. In principle what is needed is a multidimensional matrix of weighting coefficients which “maps” (transforms) the spectral reflectance values to the desired geo-physical values. The determination of the coefficients can hardly be done using empirical correlations, since the number of possible parameter combinations would require an unrealistically large set of measured spectra plus corresponding in situ data. Radiative transfer modelling using the specific IOPs of the relevant water constituents and atmospheric parameters provides us with a possible solution. The IOPs, of course, must be known from in situ and laboratory measurements, atmospheric parameters from corresponding measurements or models. The modelling then allows to generate a synthetic data set containing all possible combinations of geo-physical parameters and the corresponding reflectance spectra including observation and sun geometries for a given sensor/satellite. This data set represents the expected variety of measurements of the sensor. This “training” data set may then be used to compute the weighting coefficients for the desired inversion. Numerical techniques have to be applied because a direct (analytical) inversion of the model is not possible.

Fig. 5.1
figure 1

Scheme of a multivariate inversion of spectral (remote sensing) measurements

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There exist a number of mathematical methods to solve the inverse task. Examples are: factor analysis, principal component inversion, neural networks or spectral matching techniques. Due to different mathematical treatment in detail, the resulting inversion schemes or algorithms allow different optimisation strategies and show different behaviour in the case of non-linearities or large variation ranges of the parameters. But the basic approach for this class of algorithms is identical, as described above. Figure 5.2 illustrates the scheme.

Fig. 5.2
figure 2

Scheme of training an inverse algorithm

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5.5 Atmospheric Correction

As outlined above, the classic approach for atmospheric correction fails in the case of high concentrations of scattering constituents in the water (e.g. high sediment load). Atmospheric correction in these cases needs to account for residual signal from the water body also in the near infrared, i.e. above 700 nm. This, as one solution, leads to more complex or iterative atmospheric correction schemes, which in addition to aerosol properties also estimate residual in-water scattering. Following this way to the end, an even more integrated view on the problem can be developed: Applying an atmospheric correction to the data separately, i.e. computing water leaving radiances or reflectances from the top-of-atmosphere (ToA) measurements does not improve the information content in the data with respect to water constituents. It only removes variables related to the atmosphere from the original data set and hence reduces the dimensionality for the inversion. But all variation due to changing water constituents must be resolved in the ToA measurement already, otherwise it may not be seen in atmospherically corrected data. Taking this into account and also reminding that atmospheric correction for case-2 waters must account for residual signal from the water body, it should be possible to couple the retrieval of aerosol parameters and water constituents into an integral inversion or coupled inversion scheme. For this case the training data set for multivariate inversion is simulated for TOA reflectances by including variations of aerosol-related parameters. To derive the inversion schemes the identical mathematical apparatus is used as for water leaving reflectances, but a larger dimensionality has to be accounted for.

Such an approach we tried first for the imaging spectrometer MOS-IRS flying on board of the Indian satellite IRS-P3. The mission was a joint effort of DLR and Indian Space Research Organisation ISRO, where the instrument was developed and built by DLR and ISRO provided the satellite and the launch and operated the satellite. Being planned as a proof-of-concept experiment it was flying successfully for 8 years from 1996 to 2004 (Zimmermann and Neumann 2000). MOS-IRS was the first imaging spectrometer in space for Earth observation and provided measurements in 18 spectral channels between 408 nm and 1.6 μm. Because of very similar instrument characteristics it was used as a precursor for MERIS, allowing for experimental verification of algorithms developed for MERIS on ENVISAT, which was launched in 2003. The Principal Component Inversion technique considered here was firstly developed and tested using MOS-IRS (Krawczyk et al. 1998) data and then extended to be applied to MERIS. Extensive radiative transfer simulations were used to derive and optimise the inversion procedure, the results obtained from MOS-IRS confirmed the simulations and showed very good performance, in particular for case-2 waters. Figure 5.3 shows an impressing example for a very complex and dynamic scene over the Black Sea: where the composite image on the left shows the mixture of all components (water and atmosphere) contributing to the signal measured at the satellite the inversion results illustrate that constituents showing absorption plus scattering (Chlorophyll) are well discriminated from constituents with dominant scattering (inorganic sediment) and the atmospheric component represented by the aerosol. However, at large value of scattering near the coasts saturations and masking effects occur. The methodology is currently tested for MERIS data where the larger variation in viewing geometry due to the large swath of 1500 km makes the problem more complex (MOS-IRS had a 200 km swath). A similar approach using neural networks for inversion has been implemented for MERIS by Schroeder et al. (2007).

Fig. 5.3
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Example for one-step inversion (MOS-IRS, central Black Sea)

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5.6 Principal Component Inversion

Here we can only give a short introduction to Principal Component Inversion, for more details are referred to Krawczyk et al. (1993, 1998). The forward model, which computes the reflectance spectra R from the given set of geo-physical parameters p, is nonlinear and consists of a radiative transfer code and the necessary inherent optical properties of the components, as there are the wavelength-dependent specific absorption and scattering coefficients and the scattering phase functions. The inverse mapping \(R \rightarrow p\) is the desired interpretation algorithm. For PCI the main idea is to estimate the concentration as a linear function of the measured spectral reflectances. But this assumption initially contradicts the nonlinear character of the direct model. Two steps were taken to improve the situation. Firstly instead of the direct parameter p a semi logarithmic representation \(q = p + 0.1 \log(p)\) is used, secondly, the covered variability range for each parameter p is divided into sub-ranges, where the linear assumption is much better justified (quasi-linear approach). The estimator then can be formulated as:

$$q = p + 0.1^{\ast}\log (p) = \sum\limits_{j = 1}^n {k_{ij}^{(r)\ast} R_j + b_j } $$
((5.1))

where k ij and b j are the inversion coefficients to be determined for each sub-range r from the model, n is the number of spectral channels. The estimation shall be optimal in a global sense, i.e. the RMS error of the entire dataset should be minimized. This is a difference to so called direct model inversion methods (e.g. spectral matching), which try to minimize every individual spectrum by finding the optimal concentration set for a given model and single spectrum. Here a local linear regression technique is used to compute the needed coefficients. In this task the inversion of the regression matrix of reflectances is a necessary step. Due to the high spectral correlations this can lead to massive numerical problems. Therefore a regularisation method must be applied, to overcome this ill-posed problem. One also must take into account the radiometric resolution and noise in the measurement. As an optimal information extraction and noise suppression tool, the principal component analysis (PCA) was chosen. Figure 5.4 illustrates the steps to compute the coefficients.

Fig. 5.4
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Steps of the principal component inversion

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The first step is the simulation of a large set of reflectances R or radiances L as explained above. Then a principal component analysis is applied to this data set. The eigenvalues λ determine the intrinsic dimensionality, i.e. the principal components corresponding to the highest eigenvalues contain the main and useful part of information and the lower eigenvalues corresponding components contain the measurement noise. These lower principal components are omitted for further calculations to increase noise stability of the developed inversion algorithm. Next the correlation between geophysical parameters and higher principal components is established (step 4). Since the principle components are orthogonal it can be easily done. But his formula can not yet be used for a general interpretation, because the result of PCA strongly depends on the statistical (covariance) properties of the initial data set. The data set in a natural scene will never be expected the same, as that used for the simulation. Therefore this formula must be generalized. This can be done by back-transforming the principal components to radiances using the eigenvectors. Finally one gets a regression formula between parameters and radiances (steps 5 and 6). Comparing with a Neural Network approach one could asses, both methods are performing a model inversion, minimizing the global interpretation error and differing mainly in the method of “training” the interpretation coefficient sets. Neural nets are often using backpropagation techniques, PCI uses principal component transformation as an optimized error-noise suppressing filter. One advantage of the PCI is the additional information about correlations between the parameters and principal components, which allows a direct estimation of the interpretation potential of the investigated data set. Concerning the piecewise linearization of the data set during interpretation one has to choose the appropriate of the pre-calculated coefficient sets. The problem is solved by trying all sets and testing the sub-range conditions under which they were calculated. In the case of impossibility to find a solution an invalid flag is raised.

Similar basics as described here for the Principal Component Inversion are used in the Minimum Noise Fraction Transformation (MNF, e.g. Chen 2000). However, there it is not the goal to build a physically based inversion to derive geo-physical parameters directly from remote sensing measurements but to find optimal algorithms to reduce dimensionality and noise in the data. Since in the described above Principal Component Inversion we use Eigenvectors normalised to expected measurement noise the optimization effect is similar to the approach of the MNF.

5.7 Monitoring of Water Quality

Monitoring of (coastal) water quality by the use of remotely sensed data has become an important task during the last years (Kratzer et al. 2008). In Europe the Global Monitoring for Environment and Security (GMES, http://www.gmes.info/) programme by ESA and the European Commission has put a significant effort into the development of infrastructure and services providing data and information for coastal environmental management and the monitoring of environmental directives. One project dealing in particular with water quality information and surveillance of critical algal blooms in European waters is the “Marine and Coastal Environmental Services” (MarCoast) funded by ESA (http://gmes-marcoast.com/). At DLR in the frames of this project an operational processing chain for MERIS data has been set up and integrated in the automated environment at the German Remote Sensing Data Center. It serves users in Germany (governmental and public institutions on national and state levels) with information products on a daily basis. The products are available in the form of images as well as scientific data formats, optional GIS-compatible formats are also available. All products are provided as daily maps and 10-day, monthly and seasonal averages.

Water quality:

  • Water constituents (Chlorophyll, suspended sediment, Gelbstoff)

  • RGB colour composites

  • Sea surface temperature

  • Water transparency

Algal bloom monitoring:

  • Bloom strength indicator map

  • Bloom location and extend (text)

The services are running now for three years and will be continued on a regular basis. User access is realised via an ftp-server, in addition all data are archived in DLR’s multimission long term archive system. Figures 5.5 and 5.6 shows examples for the set of information products. The results in terms of geophysical parameters have been validated against in situ measurements from regular monitoring stations operated by state authorities of Mecklenburg-Vorpommern (German state along the Baltic coast). Chlorophyll and sediment show good agreement except very near to the coast where bottom and adjacency effects cause problems. The accuracy of yellow substance, by its physical nature the weakest parameter for retrieval, is currently not satisfactory. One cause for this may be inappropriate bio-optical model, is this is currently investigated.

Fig. 5.5
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Operational water quality products or the Baltic Sea derived from MERIS (top left to bottom right: Chlorophyll, suspended matter, water transparency, sea surface temperature)

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Fig. 5.6
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Products for the monitoring of algal blooms (left: color composite, right: bloom strength indicator)

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5.8 Conclusions

The physical complexity of coastal waters result in a challenge to inversion algorithms applied to data over such waters. Model-based, multivariate inversion techniques provide the adequate tool to solve the task. During the past years this technique using a variety of mathematical methods and implementations has become mature and finds a wide range of applications for environmental monitoring. Hyperspectral instruments which will become more and more available in the upcoming years provide measurements with a dimensionality of an order of magnitude larger than currently operational satellites. Also in this case multivariate algorithms are the tool to cope with this huge information content.