comparison of measured and computed light scattering in the baltic

Tellus (1986), 38B, 4 Comparison of measured and computed light scattering in the Baltic By MIROSLA W JONASZ,* Polish Academy of Sciences, Institute of Oceanology, ul Powstancow Warszawy 55,81-967 Sopot, Poland and HARTMUT PRANDKE, Academy of Sciences of GDR, Institute of Marine Research D DR 253 Rostock- Warnemunde, German Democratic Republic (Manuscript received July I I ; in final form December 30, 1985) ABSTRACT Mie theory was used to calculate the average scattering functions of suspended particles from the surface layer of the Baltic in summer and winter Good agreement with data has been 15" to 165" Corresponding average particle size achieved in the angle range of distributions measured using a Coulter counter in the diameter range of 2.5 to 20 pm were used in the calculations The size distribution of smaller particles and the refractive indices of particles in the entire optically important diameter range were determined using the trial and error method A refractive index of I I was obtained for both summer and winter particles in the diameter range of 0.1 to pm The size distributions of these particles, also determined from light scattering, were hyperbolic with a slope of 4.1 The concentration of particles with diameters between 0.1 and pm in summer was about twice that in winter Refractive indices: 1.050.005i and 1.034.01i were obtained for summer particles with diameters between and 10 pm and over 10 pm respectively A refractive index of 1.1 was obtained for winter particles larger than pm Only particles with diameters in the range of I to 10 pm contributed significantly to the volume scattering function measured Particles smaller than pm dominated light scattering at angles > 10" and larger particles at smaller angles 15" for the summer The calculated volume scattering function at angles smaller than particles agreed with the experimental data Values of the scattering function in this angular range for the winter particles were about half of those measured This is explained as a consequence of an underestimation of the projected areas of particles when using Coulter counter data in the computation of light scattering It can be compensated for in the case of summer particles, with a small refractive index and slope of the size distribution, by selecting a higher than actual refractive index of the particles Such a compensation is not possible in winter for mostly mineral particles whose refractive index and the slope of the size distribution are already high - - - - - Introduction It is generally known that suspended particles dominate the scattering of light in sea water and thus affect the conditions of the transfer of light energy in the sea It is therefore of prime importance in studies of photosynthesis and remote sensing to be able to predict the effect of a Present affiliation: Department of Oceanography, Dalhousie University, Halifax, N.S.B3H 451, Canada - given ensemble of particles on the scattering of light in sea water On the other hand, light scattering can be used to characterize suspended particles Since it can be measured continuously and rapidly in space and time in a water mass, its use to determine physical properties of suspended particles is an attractive alternative to discrete and laborious chemical analyses Both uses of light scattering depend o n the availability of an adequate numerical model In addition, the determination of physical properties of the particles from light scattering depends on Tellus 38B (1986) 145 COMPARISON OF MEASURED AND COMPUTED LIGHT SCAlTERING IN THE BALTIC the existence of a reliable inversion algorithm A numerical model for homogeneous spheres is provided by the Mie theory of light scattering (Mie, 1908; later reviews, e.g., in van de Hulst, 1957; Born and Wolf, 1976) It relates the scattering pattern of a homogeneous sphere to its diameter and refractive index The latter is determined by the chemical composition of a particle Organic particles suspended in sea water have low refractive index relative to water from I 01 (phytoplankton-Carder et al (1972)) to 1.05 (bacteria Ross and Billing (1957)) Minerals are characterized by higher refractive indices from about 1.08 (amorphous silicon) to I 23 (aragonite) An approximate relationship exists between the refractive index and the density of the particles (biological particlesRoss and Billing (1957) and references therein; minerals-Carder et al ( I 974)) Suspended marine particles are nonspherical They exhibit wide variety of shapes and internal structures Their light scattering pattern as an ensemble, however, agrees roughly with patterns computed using Mie theory (Kullenberg, 1970; Kullenberg and Olsen, 1972; Brown and Gordon, 1974; Reuter, 1980; Jonasz, 1980) Thus it appears possible to select an ensemble of spheres that simulates the actual scattering pattern of suspended marine particles The general problem of the determination of physical properties of particles from their light scattering is complex (Rozenberg, 1976) and has not yet been given much attention Limited cases have been considered, e.g., when the refractive index of the particles is known a priori and only the particle size distribution is being sought (Chow and Tiou, 1976) Real situations, with no a priori information about particles, have been approached so far using the trial and error method (Kullenberg, 1970; Kullenberg and Olsen, 1972; Brown and Gordon, 1974; Jonasz, 1980) In this approach, scattering patterns computed for a number of size distributions and refractive indices are matched to experimental data: the size distribution and refractive index providing the best fit are assumed to be closest to the actual characteristics of the particles Physical properties of suspended Baltic particles were determined from light scattering by Kullenberg (1969, 1970) and Kullenberg and Olsen (1972) No independent determinations of Tellus 38B (1986), these properties were made It is thus difficult to assess the validity of their results Measurements of scattering of polarized light (Kadyshevich, 1977) suggest that light scattering by the Baltic particles is more similar to that by spheres than is scattering by oceanic particles Reuter (1980) simulated light scattering of suspended organic particles in the coastal waters of the Baltic using spheres with equal volumes However, he reports that the absolute value of scattering by mineral particles in these waters differs significantly from calculated scattering for spheres with equal volumes Similar conclusions for forward scattering were reached by Jonasz (1980) We postulate that this discrepancy is due to combined effects of underestimation of the projected areas of large particles and the form of the dependency of the scattering efficiency of these particles on their size The aim of this paper is to present a quantitative evidence for that hypothesis Another aim is to determine the size distribution and refractive indices of particles in the size range inaccessible to the Coulter counter The data discussed in the present paper were obtained during two oceanographic expeditions on research vessel “Prof A Penck” of the Academy of Sciences of GDR (Gohs et al., 1978) 59ON Sweden L 57ON 1SOE 18OE 2I0E Fix The sampling stations in the Baltic for particle size distributions and volume scattering function Capital letters denote the period of sampling as follows: M-March 1976, J -June 1977 146 M JONAS2 AND H.PRANDKE in the central Baltic The measurements were made at locations shown in Fig Methods 2.I Sampling and storage of samples Sea water was sampled using a remotely controlled rosette with PTFE samplers of van Dorn type Measurements were usually completed within hours after collection of the samples In order to minimize changes taking place during storage large quantities of sea water ( - 10 1) were sampled and stored in polyethylene containers for particle size analysis Samples for light scattering measurements were stored in 0.5 dark glass bottles 2.2 Particle size distributions A Coulter counter model ZBI with a 100 p m orifice was used to measure cumulative size distributions CD(D) of particles suspended in sea water following the standard procedure (Sheldon and Parsons, 1967; Jonasz and Zalewski, 1978; Jonasz, 1983) The cumulative particle size distribution relates number concentration of particles with diameters larger than D to particle diameter, D This concentration was determined for about 20 values of D in the range of 2.5-20 pm The upper limit was sometimes lowered to keep counts not smaller than particle/cm3 The error of cumulative number of particles, CD(D), is proportional to square root of CD(D) for a single count (Jonasz, 1983) Two or more counts, depending on the number concentration of particles, were made as a rule Errors due to the nonsphericity of particles (Golibersuch, 1973) and the way the particle crosses the orifice (Kachel et al., 1970) are difficult to estimate for the particles we analysed and were not accounted for Cumulative particle size distributions were then converted to frequency particle size distributions, FD(D), related to CD(D) through the equation - CD(D) = j," FD(D) d D (1) using a piecewise numerical differentiation scheme (Jonasz, 1983) The frequency size distribution will be referred to as the particle size distribution (PSD) in the following 2.3 Light scattering The volume scattering functions, P(@, of sea water (for definition, see, e.g., Jerlov (1976)) were measured for 15 to 30 different scattering angles, 0, in the range of 5-165" using a laboratory light scattering meter PSP 75 (Fig 2) The instrument, described in detail by Prandke (1980) has been designed for oceanographic use The light source is a He-Ne mW laser (wavelength 0.633 pm in air) The calibration of the instrument is similar to that of in situ scattering meters (Kullenberg, 1968) and eliminates errors caused by drift of laser power output, sensitivity of the detector, measuring electronics and varying attenuation of the sea water Fluctuations of the scattering intensity caused by variations of the number of scatterers in a relatively small scattering volume (10 mm3 at scattering angle of 90")were smoothed using an electronic integrator The estimated error of the measurement is normally 5%, increasing up to 10% for extremely high fluctuations of the intensity of scattered light The volume scattering functions, P,(O), of suspended particles were computed by subtracting n LI! I A Fig The design of the laboratory scattering meter: ( I ) light source, (2) sample (3) detector (photomultiplier), (4) sample container, (5) glass window, (6) light trap, (7) prism, (8) stop, (9) mixer, (10) axis of rotation of a system of two prisms (7) and two stops (8) Light path is indicated by arrows Tellus 38B (1986), COMPARISON OF MEASURED AND COMPUTED LIGHT SCATTERING IN THE BALTIC the volume scattering function of clear sea water (Jerlov, 1976) p,(e) + = 8.74 x 10-6 ~ - y i 0.835 cosz where e) L is the wavelength of light (pm), from mw 147 existence of well-defined winter mixed layer and summer top layer in the open Baltic waters with distinct sets of particles The winter mixed layer extends from the surface to the permanent halocline at about 60-70 m Increased solar heating of its upper part in spring and summer results in the formation of a summer top layer which extends from the surface to the seasonal picnocline at about 20-30 m 2.4 Mie scattering computations 3.2 Particle size distributions Mie scattering functions, fll(e,x, n), of Particle size distributions characteristic for the individual uniform spheres for scattering angles two layers differ substantially in the particle e=o,o.2,o.~,3,5,1o,2o,~o~1~~1~o,1~o~5~1~o diameter range of 30 pm (Jonasz, 1983) The degrees, where increment is given in parentheses, concentration of particles is higher in the summer and relative particle size x = 0.1 (0.1) (0.2) 10 top layer than in the winter mixed layer, and the (0.5) 50 ( I ) 100 (2) 220 were computed on an shape of the PSD changes also (Fig 8) ELWRO ODRA 1305 computer for 30 complex 21 size distributions from March 1976 were refractive indices, n, with real parts 1.01 (0.02) used to calculate the average PSD typical for the 1.07, 1.10, 1.15, 1.20 and imaginary parts -0.01, winter mixed layer and 12 distributions from -0.005, -0.001, -0.0001 and The relative June 1977 yielded the average PSD typical for the dimension, x, of a sphere of diameter D, is early summer top layer In each case, data from defined as nD/1, where 1, is the wavelength of the top 30 m of the water column were used The light in water Generation of one set of functions early summer PSD varies more within the sumfor a given refractive index took about 12 mer top layer than the winter PSD varies within All computed functions were stored on magnetic the winter mixed layer (Jonasz, 1983) The PSD tape Computations were performed according to typical for the early summer is not representative a modified numerical scheme of Dermendijan for the late summer when the concentration (Dermendijan, 1969; Jonasz, 1980) Numerical increases and the peak at pm disappears problems arising in such computations and opti(Jonasz, 1983) We will nevertheless refer to the mized computer programs in FORTRAN are early summer PSD as summer PSD for brevity described in detail elsewhere (Jonasz, 1980) The least squares approximations for the Scattering functions fl,(6') of suspended parPSDs, using hyperbolic and Gaussian functions ticles characterized by size distribution FD,(x) (Jonasz, 1983), are: = FD(D(x)) and refractive index n ( D ) were obtained by numerical integration of PI(@,.Y, n ) FD(D) weighted by FDJx) over the range of K indicated 3.47 x lo4 D-34' pm < D < 8.6pm previously, using trapezoidal rule of integration 4.06 x lo5 D-456 8.6 pm < D < 33 pm This range of x assures convergence of integrals at all angles B, except 6'= 0" and angles in its (3) vicinity, and corresponds to diameter, D, range of for the winter mixed layer, and 0.015-33 pm for the wavelength of light used in our light scattering measurements FD(D) = 410 exp [ -0.6(D - 6.2)?1 ={ Experimental results 3.1 Oceanographic conditions Depth profiles of light scattering (Prandke, 1978) and particle size distribution (Zalewski, 1977; Jonasz, 1980; Jonasz, 1983) reveal the Tellus 38B (1986), +r ~IO4D-"' 4.45 x lo5 D-4x6 2pm