Algorithm Theoretical Basis Document Chlorophyll

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Algorithm Theoretical Basis Document Chlorophyll

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Algorithm Theoretical Basis Document
Chlorophyll Fluorescence (MODIS Product Number 20)
Mark R. Abbott Ricardo M. Letelier College of Oceanic and Atmospheric Sciences Oregon State University
1. Introduction The chlorophyll fluorescence product group (MODIS Product 20) includes several parameters. Two of these parameters will be described in the document: fluorescence line height (parameter 2575) and chlorophyll fluorescence efficiency (parameter 3211). We will discuss Version 3.0 of the algorithms associated with these two parameters. Chlorophyll fluorescence line curvature (parameter 2573) will be produced by Hoge and will be described in a separate ATBD. We have accelerated plans to develop a primary productivity research product that will utilize the fluorescence data. We emphasize that this is a research product only and will not be part of the DAAC standard product suite. However, in the interest of completeness, we include a preliminary overview of the theoretical basis of this product in the ATBD. It will eventually be produced in our Science Compute Facility (SCF) and be available to any interested user. The fluorescence line height algorithm is a relative measure of the amount of radiance leaving the sea surface, which is presumably a result of chlorophyll fluorescence. By constructing a baseline using bands on either side of the fluorescence band, we can estimate the deviation from the amount of radiance expected for pure water that results from chlorophyll fluorescence. This increase in radiance (centered at 683 nm for chlorophyll) has been noted for decades in measurements of the light field in the ocean. This signal is generally weak, even in regions of high chlorophyll concentrations. To measure fluorescence, the signal to noise ratio (SNR) was increased for the fluorescence band and the adjacent “baseline”bands at 665.1 nm (band 13) and 746.3 nm (band 15). The fluorescence measurement itself is made at 676.7 nm (band 14) as a compromise between measuring the fluorescence peak (683 nm) and the presence of an oxygen absorption band at 687 nm. The chlorophyll fluorescence efficiency algorithm is also straightforward. ARP (number of photons absorbed by phytoplankton) will be calculated as part of MOD22 by K. Carder. This product will be converted into radiance units. Fluorescence line height will be normalized by this modified ARP product. The resulting ratio will provide an estimate of the efficiency of the conversion of absorbed solar radiation into fluorescence by phytoplankton. This document will describe fluorescence and its relationship to photosynthesis by phytoplankton. We will cover the main points of fluorescence physiology, in particular

its relationship to photoadaptation. The fluorescence algorithm will be described, as well as how information on fluorescence will be used in oceanographic research. Although fluorescence has been used for decades to estimate phytoplankton chlorophyll concentrations, our eventual focus will be on its use in estimating primary productivity. Other ATBD’s of interest include upwelling radiance by H. Gordon (MOD18), absorbed photons by phytoplankton by K. Carder (MOD22), and primary productivity by W. Esaias (MOD27). 2. Overview and Background Fluorescence by the light-harvesting pigments of phytoplankton is one of the main pathways for the deactivation of photosystem II (responsible for over 95% of chlorophyll fluorescence). This portion of the photosynthetic cycle (PS II) is responsible for the splitting of water molecules and the formation of oxygen. NADP reduction takes place in photosystem I (PS I), and this photosystem is only weakly fluorescent. Together, PS I and PS II are known as the “light”reactions as they require light energy to proceed. The amount of fluorescence is a complicated function of light capture by chlorophyll and the rate of electron flow between PS II and PS I. Thus much attention has been focused on the use of fluorescence to estimate chlorophyll concentrations and primary productivity. In the following sections, we will describe how such measurements are used, the historical basis for the algorithm, and how the algorithm is related to specific characteristics of the MODIS sensor.
2.1. Experimental Objectives Fluorescence line height (hereinafter referred to as FLH) will form the basis of chlorophyll fluorescence efficiency (hereinafter referred to as CFE) as well as for daily primary productivity (MOD27, parameter 2602) which will be a post-launch product. As fluorescence is an indicator both the amount of chlorophyll and the rate of photosynthesis, higher order products will be based on FLH. Similar applications of fluorescence have been made in oceanographic and limnological studies using variants of the fluorometer. The basic fluorometric measurement was described by Holm-Hansen et al. (1965) and Lorenzen (1966); standard instruments were soon available, notably those made by Turner Associates, which was soon followed by Turner Designs. The basic measurement has been unchanged for nearly 30 years. A water sample is illuminated, usually by a blue light source, and the fluorescence emission is measured at 683 nm. Numerous improvements have been made in the electronics and optics of the sensors, resulting in a system that can work in turbid waters with either high sediment loading or high chlorophyll concentrations and can detect extremely low chlorophyll concentrations as well. An excellent summary of fluorescence can be found in Kiefer and Reynolds (1992). The basic fluorometer has seen a wide range of modifications over the last decade. Spectrofluorometers (with varying excitation and emission wavelengths) have been used to study taxonomic composition Low-power fluorometers have been deployed on

moorings and drifters. Light sources ranging from strobes to lasers have also been employed. The primary use of fluorescence has been the estimation of chlorophyll concentration. With the development of flow-through sampling systems, it became possible to measure small-scale horizontal and vertical patchiness of phytoplankton abundance. Although data collection was fairly straightforward, the estimation of chlorophyll via in vivo fluorescence remained controversial. Most fluorescence studies collect occasional calibration samples where the pigment would be extracted from the phytoplankton, and chlorophyll would be measured using spectrophotometric methods. Using these calibration samples, the ratio of chlorophyll to in vivo fluorescence was assumed to be constant. However, the literature is filled with studies that document the numerous processes that can change the relationship between chlorophyll and in vivo fluorescence on a wide range of time and space scales. These processes included species changes, nutrient concentrations, incident radiation, etc. In essence, these processes are related to the physiological state of the phytoplankton. Several modifications to the basic fluorescence method have been employed in an attempt to quantify the physiological state of the phytoplankton. This is based on the recognition that fluorescence instantly responds to all of the competing photosynthetic processes. A brief description of the process will help clarify matters. Within the phytoplankton cell, light is absorbed by chlorophyll molecules within the thylakoid membrane. Excitation energy is delivered to the reaction centers (where absorbed light energy is used in the photochemical process) by the proximal and distal antenna systems. When the reaction centers are “open”, excitation energy can be trapped by passing electrons through an intermediate phaeophytin (a pigment related to chlorophyll) to a quinone acceptor (QA) and then used to oxidize water (PS II). If QA is already reduced by a previous excitation, then the reaction center is said to be “closed.” The probability that the excitation energy will be fluoresced increases significantly when the reaction center is closed. Thus the intensity of fluorescence will depend on how much light is absorbed, how efficiently it can be delivered to the reaction centers, and how fast the absorbed (excitation) energy can be passed through the photosynthetic system. One can view the entire process as “the controlled production and dissipation of an electrochemical gradient where oxidation of water provides a source of free electrons and the initial driving energy is free energy released by the de-excitation of an excited pigment molecule”(Falkowski and Kiefer 1985). This coupling between fluorescence and the rate of photosynthesis has intrigued researchers for many years. Samuelsson and Öquist (1977) suggested that the addition of a photosynthetic inhibitor (DCMU, a common herbicide) could be used to separate the effects of light absorption (as an indicator of chlorophyll concentration) from light utilization (photosynthesis). Although DCMU does block electron flow and thus stimulates fluorescence, there are numerous other processes that affect fluorescence yield. Again, DCMU-induced fluorescence, as with the basic fluorescence method, can be used as an indicator of various physiological processes within the cell, but the relationship is complex (Prézelin 1981).

Recent research has focused on the use of sun-stimulated fluorescence to estimate primary productivity (e.g., Chamberlin et al. 1990, 1992; Kiefer et al. 1989; Kiefer and Reynolds 1992; Stegmann et al. 1992; Abbott et al. 1995). Although there is a link between the rate of productivity and the rate of fluorescence, it is not straightforward. As noted by Falkowski and Kolber (1995), the quantum efficiency of photosynthesis varies inversely to the quantum efficiency of fluorescence. However, there is no simple predictor of photosynthetic quantum efficiency. Although Falkowski and Kolber (1995) suggest that sun-stimulated fluorescence may not work over the wide range of oceanic conditions, MODIS will only be able to make useful estimates of FLH in regions of moderate to high chlorophyll concentration. The development of a post-launch primary productivity algorithm based on FLH will focus on such research. Of interest here is the role of the xanthophyll cycle in non-photochemical quenching (Demmig-Adams, et al., 1996; Frank et al., 1994; Horton et al., 1994). This process involves carotenoid pigments which can deactivate absorbed light energy and protect cells from photodestruction. This is especially important for phytoplankton that are growing under high light conditions near the ocean surface. For satellite measurements of sun-stimulated fluorescence, it must be borne in mind that the FLH signal will be derived from these high-light phytoplankton populations. The relatively simple model of productivity based on sun-stimulated fluorescence developed by Kiefer and co-workers is unlikely to work with MODIS data in large part because of non-photochemical quenching. The xanthophyll cycle varies among different species groups as well as over time depending on light and nutrient histories.
2.2. Historical Perspective Early measurements of upwelled radiance in natural waters showed the presence of a distinct peak in the spectrum centered at 683 nm. As the height of this peak was related to the chlorophyll concentration, it was easily recognized as the fluorescence emission peak. Papers by Smith and Baker (1978; 1981) clearly show this phenomenon using high quality, narrow bandwidth radiance measurements. This effect has been studied by numerous researchers, including Gordon (1979), Topliss (1985), Topliss and Platt (1986), and Kishino et al. (1984). Gower and co-workers were among the first researchers to suggest using this signal to estimate chlorophyll concentrations from aircraft and satellites. The principle was identical to the basic fluorometer; a light source (in this case, the sun) would stimulate the fluorescence reactions which would then be measured by a narrow band detector. Known as solar or sun-stimulated fluorescence and occasionally as passive or “natural” fluorescence, this technique would complement the more traditional method of ocean color remote sensing based on radiance ratios in the blue/green portion of the spectrum. Neville and Gower (1977) described the first measurements of sun-stimulated fluorescence from aircraft. Gower’s program continued through the late 1970’s and early 1980’s with more sophisticated sensors with more bands and narrower bandwidth, culminating with the FLI (Fluorescence Line Imager) instrument that was optimized for

fluorescence measurements (Gower 1980; Gower and Borstad 1981; Gower and Borstad 1990). Similar sun-stimulated fluorescence measurements were made in Germany by Fischer and co-workers (Fischer and Kronfeld, 1990; Fischer and Schlüssel, 1990). The Airborne Oceanographic Lidar (AOL) operated by Hoge can also be run in passive mode. The fluorescence peak at 683 nm is approximately Gaussian with a half-power bandwidth of 25 nm. The fluorescence intensity can vary by a factor of eight based on laboratory studies and field measurements. This variation can be caused by changes in light intensity and nutrient stress (Kiefer 1973 a and b; Abbott et al. 1982), and the response can occur on time scales of a few seconds to several hours. Borstad et al. (1987) compiled FLH observations from several years and noted that the relationship between FLH and chlorophyll could vary by a factor of eight. They also noted that the relationship within a particular study region was quite good and that the variability occurred when comparing different studies. In general, FLH varies from 0.01 to 0.08 W/m2/sr/mm per mg Chl. Radiance leaving the ocean undergoes several modifications before it reaches the sensor. There is the addition of reflected sun and sky light from the sea surface and scattered light from the intervening atmosphere. There is also absorption by gases in the atmosphere. Scattering effects are most pronounced at shorter wavelengths, but the fluorescence line is located in region of the spectrum where there are several narrow absorption features. In particular, there is an oxygen absorption band at 687 and 760 nm as well as water vapor absorption band at 730 nm. This means the fluorescence band will no longer have a simple Gaussian shape. There are several approaches to atmospheric correction. The first is to rely on reflectance (radiance:irradiance ratios) but this is not feasible for remote sensing. A second approach is to model the atmosphere as was done for the Coastal Zone Color Scanner. Third, we could use a linear or curved baseline through wavelengths that are less affected by atmospheric absorption and scattering. Finally, we could use a high spectral resolution sensor to avoid known absorption features, such as oxygen. This algorithm will follow a combination of the second, third, and fourth approaches, building on the work pioneered by Gower and co-workers. Gower used aircraft-based sensors to test various channels as a baseline to calculate FLH. Bandwidth and position were varied, and eventually they developed a simple linear model using three bands (Borstad et al. 1987). Although a linear baseline was used, Gower and Borstad (1987) suggested that a curved baseline might perform better. Gower used an algorithm that is quite similar to that proposed for MODIS using bands 13 (667 nm), 14 (678 nm), and 15 (748 nm). Although there was some dependence of FLH on altitude (implying that there were some atmospheric effects present in the measurements), it tended to be smaller than the natural variability of the fluorescence measurement itself. Gower and co-workers (reported in Borstad et al. 1987) compared FLH with chlorophyll concentrations from several locations. First, recall that the fluorescence signal is reduced by oxygen and water vapor which erodes the long wavelength portion of the fluorescence peak. Second, we expect that there will be considerable variability in

fluorescence yield which will further complicate the estimation of chlorophyll concentrations. Despite these challenges, the FLH method worked reasonably well, even in turbid coastal waters with a high inorganic sediment load. As suggested by Borstad et al. (1987), combining the FLH measurement with an independent estimate of chlorophyll concentration (using the blue/green ratio approach) will provide a powerful tool to assess the physiological state of the phytoplankton. The input radiances will be the normalized water-leaving radiances from MOD18 by Gordon. These radiances are corrected for sun-sensor geometry as well as for atmospheric scattering and absorption. However, the latter part of this correction (atmospheric effects) will be relatively simple compared with the more complex Rayleigh and aerosol corrections used in the blue and blue-green portion of the spectrum. Rayleigh scattering will be small at these fluorescence baseline wavelengths, and aerosol scattering should not vary much across this wavelength span (H. Gordon, pers. comm.) Thus we will compute only a simple atmospheric correction as well as correct for changes in view angle and solar geometry.
2.3. Instrument Characteristics The three primary bands for FLH are bands 13 (665.1 nm), 14 (676.7 nm), and 15 (746.3 nm). Because of the low signal associated with fluorescence, these bands must have a high SNR to detect variations in the signal. The bands must be relatively narrow to avoid absorption features in the atmosphere. They must also be stable in terms of both bandwidth and position because of the spectral proximity of these absorption features. The present design for MODIS meets these requirements. 3. Algorithm Description In this section, we will describe the fundamentals of the FLH and CFE algorithms. The FLH algorithm will be based on the calibrated, normalized water-leaving radiances as described under MOD18 (see ATBD by H. Gordon). Thus the bulk of the calculations will occur within the procedures necessary to transform the sensor data into Level 2 radiances. CFE will rely on a combination of FLH and the number of photons absorbed by phytoplankton (ARP) which is described by K. Carder in the ATBD for MOD22.
3.1 Theoretical Description 3.1.1 Physics of the Problem
The initial step in the algorithm will be the estimation of calibrated, normalized waterleaving radiances for each of the MODIS ocean bands. This will include registration of the bands (so that each band corresponds to the same pixel on the Earth’s surface), calibration, and atmospheric correction. The details of this processing may be found in the ATBD’s developed by Gordon and Evans. Because of the low levels of water-leaving radiance in the fluorescence wavelengths and because the bulk of the atmospheric effects take place in the blue wavelengths, we do not anticipate that an especially sophisticated procedure for atmospheric correction will be required. However, one potential difficulty may be the effects of sea foam (Frouin et al. 1996). Gordon is investigating these processes as part of his research on atmospheric correction; as we

shall show later, our analyses indicate that even a fairly crude estimate of atmospheric effects is sufficient. The dominant source of uncertainty in fluorescence-based measurements is in the physiological processes of the phytoplankton themselves (Letelier and Abbott, 1996). Chlorophyll fluorescence will increase the amount of water-leaving radiance at 683 nm (Gordon 1979; Topliss 1985; Topliss and Platt 1986) than would be expected for chlorophyll-free water. The amount of this increase will depend on several factors including the specific absorption of chlorophyll, fluorescence quantum efficiency, the amount of incident sunlight, and various atmospheric effects. However, judicious choice of wavelengths should tend to minimize the effects of the atmosphere. Thus the main component of the algorithm is the estimation of the increased radiance caused by fluorescence. By defining a baseline underneath the expected fluorescence peak, one can estimate the relative contribution to the upwelled radiance field by chlorophyll fluorescence. This baseline will be linear, based on MODIS channels places on either side of the fluorescence peak. FLH will then simply be the intensity of upwelled radiance in MODIS band 14 (676.7 nm) above the baseline created from bands 13 (665.1 nm) and 15 (746.3 nm). The figure below shows a schematic of the FLH algorithm.

Exitance, W m-2 µm-1 Exitance (W/m2/um) FLH Normalized Transmitance and Ocean Surface
Exitance (W/m2/um)

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1
0 650

MODIS normalized filter spectra of bands #13, 14 and 15 and Ocean Surface Exitance for 0.01 and 10 mg Chl/m3

0.01 mg (right axis)

10 mg/m3 (1st axis) #13 (2d axis) #14 (2d axis) #15 (2d axis) 0.01 mg/m3 (2d axis)

1.40E-01 1.20E-01


10 mg (left axis)



L13 Lbaseline




10 mg C hl/m3 bas eline



Wavelength (nm)
Wavelength, nm


0.00E+00 775

Figure 1. A schematic of the FLH algorithm, with dash/dot lines representing the normalized transmittance of MODIS bands 13, 14, and 15. The solid lines show the spectral distribution of upwelling radiance above the surface of the ocean for chlorophyll concentrations of 0.01 and 10 mg/m3. The fluorescence per unit chlorophyll is assumed to be 0.05 W/m2/µm/sr per mg chlorophyll. Chlorophyll fluorescence efficiency refers to the conversion of incident sunlight into chlorophyll fluorescence. CFE requires an estimate of the amount of incoming solar radiation that is absorbed by phytoplankton in the near-surface waters since the

fluorescence signal measured by MODIS will originate here. This estimate will be provided by MOD22 and is based on estimates of chlorophyll concentration, instantaneous photosynthetically available radiation, and the specific absorption of chlorophyll. Details can be found in the ATBD by Carder. The ARP product will be converted into radiance units as the original product will be expressed in terms of photons absorbed. Because the fluorescence peak can sometimes be below the baseline, we will add a constant radiance to all of the FLH values. This constant (0.05 W/m2/µm/sr) corresponds to the minimum amount of fluorescence expected based on historical measurements. This modified FLH will then be normalized by the converted ARP to estimate CFE.

For both the FLH and CFE products, the input data sets will be level 2 data. For areas of chlorophyll greater than 1.5 mg/m3, we will calculate FLH and CFE on a per pixel basis. For areas with chlorophyll less than 1.5 mg/m3, we will examine 5 by 5 pixel regions to improve SNR in regions where the fluorescence signal will be small. We will average the appropriate input products (normalized water-leaving radiances, ARP) to decrease the noise level. We assume that noise will decrease as roughly 1/ n , where n is the number of clear pixels.

3.1.2. Mathematical Description

The mathematics of both the FLH and the CFE algorithms are straightforward. After correcting for scan geometry, calibration, illumination, and the atmosphere, we take the normalized upwelled radiances as follows:

FG b g IJ FLH = L − L13 − L15 * λ − λ + L


H K 14 λ13 − λ15




where the subscript refers to the MODIS band number. The formalism of (1) establishes a baseline between bands 13 and 15 and measure the peak height (band 14) above this baseline. A graphical representation of the algorithm is shown below:









In this representation, LA is the short wavelength band, LF is the long wavelength band, and LC is the center or fluorescence wavelength. The distance between points B and E is denoted as x and the distance between point E and F is denoted as y. Using a simple like-triangles calculation, we may calculate FLH as:


FLH = CD = LC − (LF + DE)


This can be simplified as:

FLH = LC − (LF + ((LA − LF ) * y / (x + y)))


In this case, we have simply rearranged (2) and expressed FLH as a linear function of the two baseline wavelengths and the fluorescence band.

Other researchers have suggested using a curvilinear baseline, but our analysis (Sec. 3.2) suggests that this not warranted. We also note that a band closer to 700nm, rather than 750 nm, would have improved the FLH response. The GLI sensor has such a band.

CFE will be estimated by adding a constant radiance (FLHmin) to the FLH value and then normalizing by the radiance absorbed by phytoplankton in the upper ocean (ARPradiance).

CFE = FLH + FLHmin



These algorithms have been embedded in the MODIS Oceans Team products processing system developed at the University of Miami.

3.2 Performance and Uncertainty Estimates

A complete sensitivity analysis of the FLH algorithm was published in Remote Sensing of the Environment (Letelier and Abbott, 1996). We present a summary of this paper here. As CFE is largely dependent on FLH, we expect that uncertainty in CFE will follow uncertainty in FLH.

There are three processes that will affect measurements of FLH. The first will be changes in the absorption and scattering properties of the atmosphere. Scattering will dominate at shorter wavelengths, but the presence of specific absorption features can be important in the fluorescence wavelengths. In particular, the oxygen absorption bands at 687 and 760 nm and the water vapor band at 730 nm will significantly influence the shape of the fluorescence peak such that it deviates from a pure Gaussian curve. By designing MODIS such that these absorption features are avoided, these problems are generally reduced. The second process involves the performance of the MODIS instrument itself. This is the only component that we can control (at least before launch). The final process is physiological change in the phytoplankton which will result in variability in FLH. As discussed earlier, this can be troublesome if we try to estimate chlorophyll concentrations from FLH as the amount of fluorescence per unit chlorophyll is not constant. The amount of fluorescence will vary as a function of the amount of light absorbed as well as the quantum efficiency of fluorescence. These quantities can vary according to the species and physiological state of the algae.

Specifications of the filter spectrum and signal to noise ratio (SNR) for each band are presented in Table 1. Based on Eq. 1 and assuming that noise is independent between bands, the SNR of the baseline may be calculated as


( ) ( ) 1

1 1




* λ15 − λ14 / λ15 − λ13

SNRbaseline SNR15 SNR13 SNR15 

The SNR of the FLH is calculated as:

1 =1+ 1 SNRFLH SNR14 SNRbaseline

Given the specifications of Table 1, the SNR of FLH is 752.

MODIS Band #

Center Wavelength Tolerance

Bandwidth Tolerance






(nm) (nm)




















lower (nm) 6.1 5.4 5.3

Band SNR
1368 1683 1290

Table 1. Specifications for the fluorescence-related bands on MODIS (W. Barnes, pers. comm.) A realistic range of upwelling radiance at the top of the atmosphere (TOA) for λ = 685 nm and a solar zenith angle of 50.7° is 8-20 W m-2 sr-1 µm-1 (Fischer and Schlüssel 1990). The lower end of this range corresponds to an atmospheric turbidity factor of 0.5 (visibility = 88 km), and the upper value corresponds to a turbidity factor of 10 (visibility = 6 km). A similar value is obtained when the radiance spectrum at the TOA is calculated using a marine atmosphere model with a visibility of 50 km, a solar zenith angle of 60°, and the ocean spectrum without chlorophyll as input datasets for LOWTRAN 4.2 (Kneizys et al., 1988). The upwelling radiance at the TOA for λ = 685 nm obtained through this method is 8.65 W m-2 sr-1 µm-1. However, given the characteristics of MODIS band 14, a more accurate estimate of the sensitivity is obtained by using the calculated TOA upwelling radiance at λ = 676.7 nm. In this case, the upwelling radiance at TOA calculated using LOWTRAN is 9.05 W m-2 sr-1 µm-1. The TOA spectra are shown in the figure below.