Thorough validation and characterisation of some of these remote sensing models has been performed, and have an error of 0. Our understanding of how the photo-physiological parameters vary within size-classes or taxa over basin scales remains poor and is still limited by the availability of in situ observations. There are few direct measurements of size-fractionated PE parameters e. Since different phytoplankton taxa contain different diagnostic pigments, information on pigment composition can be used to estimate the taxonomic composition of a sample Everitt et al.
Two methods have been developed methods to derive PE parameters of different size classes from pigment markers. These are either based on empirical approaches between size class marker pigments, the associated photo-physiological parameters and its dependence on irradiance in the water column Uitz et al. These methods have not yet been compared to evaluate any potential differences between them. The objectives of this paper are therefore to: 1 Compare two different pigment-based methods at estimating size class specific PE parameters, and then 2 Analyse the relationship between environmental variables and photosynthetic rates in different size-classes using these methods.
The resulting relationships are discussed in the context of choosing appropriate models to estimate phytoplankton size-class primary production using remotely-sensed data. None of the LOV samples were dominated by micro- or pico-phytoplankton so a direct comparison with this laboratory was not possible.
Water samples were collected from 3 to 8 depths in the upper m of the water column Figure 1. Mixed-layer depth zm was calculated using climatological data from the World Ocean Atlas Levitus et al. Temperature, salinity and potential density data were estimated using the algorithms given in Jackett et al. The mean mixed-layer PAR was also calculated using estimates of light attenuation coefficients from Chl a concentrations, zm and surface PAR following the methods of Platt et al.
Location of stations where simultaneous measurements of phytoplankton pigments and photosynthesis-irradiance curves were made showing stations dominated by micro- A , nano- B , and pico-phytoplankton C using the method of Uitz et al.
Colour scale is the relative fraction of each size class normalised to 1. For the analysis of nutrients, seawater samples were collected directly from the CTD rosette, stored frozen until analysis and then equilibrated to room temperature prior to analysis. LOV measured nitrate, nitrite and phosphate using a Technicon Autoanalyzer using the methods of Wood et al. Dissolved nitrate and nitrite were determined by the spectrophotometric methods described by Brewer and Riley The analysis of soluble reactive phosphorus SRP concentration was based on the method described by Zhang and Chi Dissolved silicate DSi was determined using standard colorimetric methods Kirkwood, Phytoplankton Pigments Chl a was measured using a Turner Designs fluorometer before and after acidification.
BIO used the method of Holm-Hansen et al. Bidigare Claustre and Marty, ; Stuart et al. Summary of HPLC methods. In brief, seawater samples were collected from 3 to 8 depths based on the vertical structure in the in vivo fluorescence profile. During the 14C incubations the temperature of the photosynthetron was closely matched with ambient in situ temperature.
For surface samples, the ships surface underway seawater supply was used to maintain the incubations at sea surface temperature. For deeper samples, each photosynthetron was connected to a temperature control unit which was used to maintain the incubations at ambient temperature.
Ambient PAR was monitored over a 2—3 hr period prior to collecting the water samples for 14C incorporation and the photosynthetron irradiance was matched to the average PAR over this period. Thus, using this simple methodology, the parameters of the Weibull distribution can be estimated. Determining the X and Y Position of the Plot Points The points on the plot represent our data or, more specifically, our times-to-failure data. If, for example, we tested four units that failed at 10, 20, 30 and 40 hours, then we would use these times as our x values or time values.
Determining the appropriate y plotting positions, or the unreliability values, is a little more complex. To determine the y plotting positions, we must first determine a value indicating the corresponding unreliability for that failure.
In other words, we need to obtain the cumulative percent failed for each time-to-failure. This is a simple method illustrating the idea. The most widely used method of determining this value is the method of obtaining the median rank for each failure, as discussed next. Median Ranks The Median Ranks method is used to obtain an estimate of the unreliability for each failure.
The rank can be found for any percentage point, , greater than zero and less than one, by solving the cumulative binomial equation for. This represents the rank, or unreliability estimate, for the failure in the following equation for the cumulative binomial: where is the sample size and the order number.
The median rank is obtained by solving this equation for at : For example, if and we have four failures, we would solve the median rank equation for the value of four times; once for each failure with. This result can then be used as the unreliability estimate for each failure or the plotting position. The solution of cumulative binomial equation for requires the use of numerical methods. Beta and F Distributions Approach A more straightforward and easier method of estimating median ranks is by applying two transformations to the cumulative binomial equation, first to the beta distribution and then to the F distribution, resulting in [12, 13] : where distribution at the 0.
Kaplan-Meier The Kaplan-Meier estimator also known as the product limit estimator is used as an alternative to the median ranks method for calculating the estimates of the unreliability for probability plotting purposes. The equation of the estimator is given by: where: Probability Plotting Example This same methodology can be applied to other distributions with cdf equations that can be linearized.
Different probability papers exist for each distribution, because different distributions have different cdf equations. ReliaSoft's software tools automatically create these plots for you. Special scales on these plots allow you to derive the parameter estimates directly from the plots, similar to the way and were obtained from the Weibull probability plot.
The following example demonstrates the method again, this time using the 1-parameter exponential distribution. Let's assume six identical units are reliability tested at the same application and operation stress levels.
All of these units fail during the test after operating for the following times in hours : 96, , , , and The steps for using the probability plotting method to determine the parameters of the exponential pdf representing the data are as follows: Rank the times-to-failure in ascending order as shown next.
Obtain their median rank plotting positions.
Optical weighting of these measurement were considered, however given the variability of the water types sampled and associated mixed layer depths, and the necessary assumptions to apply an optical model for this purpose, it was decided not to introduce additional sources of uncertainty for these data points. However, the users consulted within the OC-CCI project expressed a preference for uncertainties based on comparison with in situ data Sathyendranath et al. The theoretical work of Stramski and Kiefer , assuming spherical and homogenous particles, indicated that small particles can make an important contribution to the backscattering signal in the oceans. The maximum number of pieces that could exist in the sample zone is Further data were included from the Atlantic Meridional Transect AMT including data derived from both CTD and the ship's clean water supply and other cruises in the Southern Ocean see a description of the Good Hope line and associated data collection in Thomalla et al.
This paper compares five different algorithms for estimating POC concentrations, selected as being representative of varied approaches that are prevalent for POC retrieval from ocean-color data. Platt et al. Phytoplankton Pigments Chl a was measured using a Turner Designs fluorometer before and after acidification. To determine the scale parameter, also called the characteristic life , one reads the time from the x-axis corresponding to. Weibull distribution says to expect no failures up to time To obtain the value from the plot, draw a vertical line from the abscissa, at hours, to the fitted line.
Our understanding of how the photo-physiological parameters vary within size-classes or taxa over basin scales remains poor and is still limited by the availability of in situ observations. Need at least 21 failures in the data set.
This is shown in Figure Chapter 3 of The New Weibull Handbook describes four criteria that should always be met before using a 3-parameter Weibull: 1. Phytoplankton Size from Space Recently, there have been an increasing number of studies that have retrieved the size structure of phytoplankton from remote-sensing Brewin et al. Here we use a common set of satellite data OC-CCI to compute POC using the different algorithms and compare the products against a common set of in situ data. Bidigare Claustre and Marty, ; Stuart et al. Phytoplankton Cell Size, Turbulence, and Nutrient Assimilation Cell size has important implications for resource acquisition, such as nutrient uptake Sournia, and light harvesting Duysens, ; Morel and Bricaud,
For example, two of the algorithms algorithms A and B presented below were derived solely from coincidentally collected in situ data, whereas Algorithm D G06—described below combined in situ measurements of POC and beam attenuation, with satellite-derived measurements of diffuse attenuation coefficient. However these overpass times are generally around 12 p. Once the line has been drawn, the slope of the line can be obtained some probability papers include a slope indicator to simplify this calculation. The satellite ocean-color signal is influenced by particle composition, size, and concentration and provides a way to observe variability in the POC pool at a range of temporal and spatial scales.
This represents the rank, or unreliability estimate, for the failure in the following equation for the cumulative binomial: where is the sample size and the order number. Other methods exist: e. They tend to thrive in regions rich in nitrate. These are either based on empirical approaches between size class marker pigments, the associated photo-physiological parameters and its dependence on irradiance in the water column Uitz et al.