A convenient model and program for the assessment of abiotic degradation of chemicals in natural waters

ECOTOXICOLOGY AND ENVIRONMENTAL SAFETY 17,323-332 (1989)

A Convenient Model and Program for the Assessment of Abiotic Degradation of Chemicals in Natural Waters

*Universitiit Hohenheim, D-7000 Stuttgart 70, Federal Republic of Germany, and tBattelle-Institut e. V. Am Riimerhof 35, D-6000 Frankfurt 90, Federal Republic of Germany

Received June 30.1988

A convenient model for the estimation and comparison of rates of various degradation processes of chemicals in natural waters is described. The estimates are determined by combining physicochemical properties of the chemicals with properties of natural waters and solar photon irradiancies. 0 1989 Academic press, IKE.

INTRODUCTION

After their use in the technosphere many man-made chemicals reach the air, water, and soil of the environment. Chemicals which are not volatile are often released with wastewater streams and can reach natural waters if they are not readily removed in wastewater treatment plants. Fortunately, various abiotic degradation processes may occur in natural waters, e.g., photodegradation, reactions with radicals or similarily reactive species, and hydrolysis. Photodegradation may be divided into direct processes, photoreactions of chemicals which are caused by light absorption by the chemicals themselves and indirect processes, e.g., reactions which are caused by energy or electron transfer to chemicals from a sensitizing molecule, which is excited by light absorption. The reactive species (photo oxidants) which most frequently occur in natural waters are singlet oxygen, hydroxyl radicals, and probably organic oxy and peroxy radicals which cannot be exactly specified (Faust, 1987). These species also originate from photochemical processes. Humic and fulvic acids as well as nitrate and nitrite (especially for OH radicals) can act as sensitizers or precursors of the reactive radicals.

Therefore, the rate of most abiotic degradation processes is governed by solar photon ii-radiance upon natural waters, the light transmission of these waters, and the absorption spectrum of the reacting chemicals or the sensitizers. As many chemicals absorb the UV part of the spectrum only, the spectral solar photon irradiance is of special importance. Data for photon irradiancies at the earth’s surface have been recently published (Kok, 1972; Kommission der Europaischen Gemeinschaften, 1979; Zepp, 1977; Frank, 1988).

In this paper a convenient model for estimating the rate of various abiotic degradation processes of chemicals and their distribution in natural waters is described. The estimates are obtained by combining spectral solar photon irradiancies, relevant properties of natural waters, and physicochemical characteristics of the pollutants. The model is similar to the approach used in the GC-SOLAR program of the U.S. Environmental Protection Agency, but the solar photon irradiancies used especially

323 0147-6513/89$3.00 Copyright 0 1989 by Academic Press, Inc. All rights of reproduction in any form reserved.

324 FRANK AND KLijPFFER

reflect the situation in Central Europe. Contrary to GC-SOLAR this program allows not only the photochemical processes but also other transformation processes.

SPECTRAL PHOTON IRRADIANCE IN NATURAL WATERS

Spectral Solar Photon Irradiance at the Earth’s Surface

Detailed information on solar radiation intensity and its attenuation in the atmosphere is given by Iqbal (Iqbal, 1983). Data for solar photon irradiancies at the earth’s surface which are especially suited to the treatment of photoreactions have been published by two groups (Zepp, 1977; Frank, 1988). The model (and computer program) described in this paper uses the data of Frank and Klijpffer (Frank, 1988) but it is suitable for other data as well. These data are average values for the 15th of every month and correspond to the photon ii-radiance in Central Europe.

Entrance of Light into Natural Water

A part of the solar radiation which strikes the surface of natural waters is reflected, but a larger amount reaches the body of water and is absorbed there. According to measurements the amount reflected varies from 3 to 15% in Central Europe (Munroe, 1981; Kopf, 1983).

Within the body of water the light is attenuated by absorption and scattering. Due to scattering, an upward-directed light stream E,, in addition to the initial, downward- directed stream Ed arises. The ratio EJE, converges to a constant value (approximately 0.25 for various waters) with increasing water depth (Spigel, 1984). In the surface layer of the water this ratio is less than 0.02; in extremely turbid waters it may reach 0.1 (Kopf, 1983; Leckner, 1978; Neckel, 1984; Calkins, 1982; Roof, 1982; Spigel, 1984; Howard-Williams, 1984). Therefore, the amount of light released from the water back into the atmosphere is less than 2% for practically all waters.

In the model it is assumed that 90% of the solar photon irradiance reaching the earth’s surface can activate photochemical degradation processes in natural waters, the residual 10% being reflected and scattered back from below the surface (Zepp, 1977; Neely, 1985; Kopf, 1983; Kishino, 1984; Davis-Colley, 1983). For the performance of calculations the spectral solar photon irradiancies at the earth’s surface, therefore, are simply multiplied by 0.9 in order to obtain approximate photon irradiancies for the surface layer of natural waters.

Photodegradation, however, takes place not only at the surface but also in deeper water layers as long as light is available. The next step, therefore, is to calculate the depth of water wherein most of the light is absorbed. This depth is a function of the absorbancies of the waters and of the chemicals. The total absorbance Ek at wavelength X per centimeter can be calculated by

Eh = Ehw + CiiCi, (1)

where E,, is the decadic absorbance per centimeter of the natural water, tiA the decadic absorption coefficient (M-l cm-‘) of the dissolved substance i at wavelength X, and ci (M) the concentration of this substance. As the concentrations of (anthropo- genie) chemicals in natural waters are normally very low, in most cases the second term in Eq. (1) will be small compared to the first. In this case, the depth of water S,

ABIOTIC DEGRADATION OF CHEMICALS IN WATER 325

(in cm) wherein 99% of the incoming light is absorbed can be calculated according to Iambert-Beer’s law by

S, = 2/E,. (2)

As the absorbance is a function of wavelength an appropriate Ek must be used in the calculation. The most convenient way to obtain an average value which is indepen- dent of wavelength is to calculate S by

S = 4/(E,,, + G.md (3)

where E,,,, is the maximum and Ehmin the minimum absorbance in the spectral solar wavelength interval of 290 to 800 nm. Equation (3) takes into account that in most cases the absorbance of the natural water itself is somewhat higher than that due to the dissolved chemical i and that the absorbance of natural waters often decreases approximately linearly at wavelengths greater than 290 nm.

Equations ( 1) to (3) are exactly valid only if sunlight encounters the water surface at normal incidence. This is normally not true for direct irradiation, but the intensity distribution of (indirect) sky radiation shows a maximum at normal incidence. The fraction of sky radiation is higher than that of direct radiation in the UV part of the solar spectrum at the earth’s surface. Since most of the photoreactions occurring in natural waters are initialized by UV radiation, the use of Eq. (3) seems appropriate.

Dilution and Mixing of Chemicals in Natural Waters: Number of Compartments in the Model

Dilution and mixing of wastewater streams released into natural waters is a compli- cated process governed by convection and diffusion. Various methods have been developed to describe such processes, but for most natural waters values for the parameters used in these methods will be unknown or hard to attain. The model described in this work uses only one compartment. Therefore, it is valid only as long as mixing of chemicals in natural water is fast compared to transformation processes. The results obtained with the model should be tested to determine whether they correspond with the assumption of rapid mixing. For rivers, the following test equation can be used,

L = 0.17B2/1, (4)

where B is the width and 1 the depth of a river, and L is the distance wherein in most cases complete mixing of a wastewater stream (released in the middle of the river) and the river water occurs (Neely, 1985). Due to the complexity of mixing, Eq. (4) can yield only approximations.

When chemicals are released into lakes reasonably fast mixing occurs only within the mixing layer, that is, within the top 2 to 10 m. For an estimate of the fate of chemicals in lakes, the depth of water should be restricted to this top layer.

Calculation of Transformation, Dilution, and Transfer to Other Compartments

The model described in this work is mainly dedicated to the estimation of the rate of abiotic processes. Biotic and other processes can be treated by the program as far as they can be approximately described by differential equations which are equivalent to those used for the treatment of mono- or bimolecular chemical reactions.

Further, it is assumed that all chemicals are dissolved in the water. In natural waters, chemicals can be either dissolved or adsorbed on suspended material. Adsorbed


chemicals may have different transformation rates. Within the program the fraction of initially adsorbed chemicals can be calculated if the adsorption coefficients of the chemicals to organic carbon Koc, the amount of suspended material in the water, and its content of organic carbon are available. This figure can be used to test whether there is a chance that the rate of transformation may be altered due to adsorption of the chemicals. In order to obtain an easy-to-use model, no algorithms were developed for more detailed and quantitative treatment of these phenomena.

MONOMOLECULAR AND EQUIVALENT PROCESSES

These processes are treated by differential equations of the form

= -kjci,

where subscriptj refers to the transformation process, kj is the rate coefficient of pro- cessj (s-l), and Ci is the concentration of substance i in molarity. Within the program, the actual corresponding half-lives are calculated taking actual parameters like pH of the natural water and temperature into account. Furthermore, the distance within which the initial concentration cjo becomes cio/2, assuming a point source, is calculated. Within the program four essential (described below) and six further processes can be included.

Hydrolysis

The concentrations of some anthropogenic chemicals can be lowered by hydrolysis. Within the program the rate coefficient of hydrolysis for a chemical can be introduced at three different pH values. During performance of the calculation the actual rate coefficient-depending on the pH of the actual natural water-is determined from these three values by linear interpolation. In order to avoid larger errors due to linear interpolation, the rate coefficients of the chemicals should be introduced at appropriate pH values in the range of approximately 4 to 8.5. These values should correspond to 20°C. As the temperature of natural waters varies throughout the year, rate coefficients of thermal reactions are corrected during the performance of calculations. The best way to perform such corrections would be to use the corresponding Arrhenius parameters. As these parameters often are not available,

kjkorr = kj5/(25 - T) (6)

is used instead, where T is the temperature of the natural water in degrees Celsius. Equation (6) reflects the simple rule that an increase in temperature of 10 K speeds up the rate of reaction by a factor of 2 to 3. In the program, Eq. (6) is used to correct all thermal rate coefficients. Values for T must be chosen for the same month as that for which the photon irradiancies have been selected. In the computer program, appropriate temperature values are part of the files which contain the photon irradiancies.

Dilution

After complete mixing of a wastewater stream within a river, further dilution occurs slowly by diffusion processes. A larger decrease in concentration of the chemical


is possible only if additional unpolluted water reaches the river. This decrease can be taken into account within the model if the mass flow of the river at two different locations is known. As the mass flow of rivers is a function of season these data should correspond to the month for which the photon irradiancies have been selected.

Volatilization of Chemicals

The concentration of a chemical in a natural body of water may decrease by volatilization. Rate coefficients, which are used to describe this process, normally are tabu- lated for a water depth of 1 m. When this rate coefficient is known, the actual rate of volatilization is calculated according to the depth of the selected body of water.

Sensitized Photodegradation

The rate of these processes is a function of the concentrations of the various substances in the natural water which can act as sensitizers. At the moment, there exists no method to estimate the rate of sensitized processes from the concentrations of selected substances (e.g., hum&). It is also not yet clear which kinds of chemical reactions contribute to these processes. The overall loss of a substance due to these reactions can be described by a single monomolecular rate coefficient. For a given substance, it must be determined for every natural body of water. In the program described here this coefficient is treated like a substance-specific value. During a run of the program, this value therefore can be corrected by the user.

BIMOLECULAR PROCESSES

Reactions between water pollutants and reactive species in natural waters are bimolecular reactions. Fixed reactive species in the program are OH radicals, singlet oxygen, organic oxy- and peroxyradicals, and triplet carbonyls. Another five bimolecular processes can be optionally taken into account. In practice, the reactions are treated as pseudomonomolecular reactions. The user must introduce the substance- specific bimolecular rate coefficient and the steady-state concentrations of the reactive species in the natural water. The reactive species mentioned above are produced by photochemically initiated processes, which can occur only as long as light is available. The user must introduce the steady-state concentrations valid for the top layers of a water body. If the depth of the water exceeds the depth within which most of the sunlight is absorbed, the bimolecular rate coefficients are corrected using

kbicom = kbis/A (7)

where kbi is the rate coefficient of the ith bimolecular reaction, S is the depth within which 99% of the incoming sunlight is absorbed, and I is the depth of the water. Typical values for the concentrations of reactive species in natural waters have been published by Hoigne (Faust, 1987; Scully, 1987; Haag, 1985).

DIRECT PHOTODEGRADATION

Water pollutants with a measurable optical absorption coefficient at wavelengths greater than 290 nm can be excited by solar radiation. The excited molecules can relax by thermal deactivation, photophysical, or photochemical processes. The rate of photochemical transformation is determined by their quantum yield. The rate of

328 FRANK AND KLGPFFER

the photochemical transformation is not proportional to the concentration of the water pollutant, but to the number of photons absorbed by the chemical. Therefore, the rate becomes a more complex function of the concentration of the chemical and the light absorption of the natural water, which can be described by (Mauser, 1967, 1974)

1 - lo-f,hl-‘Xc~ t WA

l+c cl A

with

where c is the concentration of the chemical in A& Ix is the mean photon it-radiance in the wavelength interval X in mol photons s-i cme2 nm-‘, 6X is the width of the wavelength interval in nm, 4x is the quantum yield of the chemical at wavelength X, ex is the decadic absorption coefficient of the chemical at wavelength X in M-r cm-‘, cWx is the decadic absorption coefficient of the natural water at wavelength h in cm-‘, and I is the depth of the natural water in cm. The summation must be done over those wavelength intervals within which the product Ixtx is greater than 0, starting at 290 nm. Equation (8) has no analytical solution and therefore can be solved only numerically. For the performance of this calculation, a Runge-Kutta-Merson algo- rithm is used in the program. But, if the absorbance of the natural water E,~I is large compared to the absorbance of the chemical txcl in every wavelength interval, Eq. (8) simplifies to (8a). This is a simple differential equation and in this case the reaction can be treated like a monomolecular reaction. In the program, this approximation is applied if(i) the direct photoreaction contributes less than 10% to the total amount of transformation, (ii) the absorbance of the water pollutant is less than 10% of the absorbance of the natural water itself, or (iii) the total absorbance is less than 0.001.

The rate of photoreactions calculated with these equations and spectral solar photon irradiancies is an average value. It is valid only as long as mixing within the water body is fast compared to the photoreaction itself. Otherwise, it would be necessary to calculate local rates for various water layers.

The rate of mixing in most rivers, which in Central Europe frequently are more polluted than lakes, is much higher than that of the photoreaction. Consequently, if the transformation rate in lakes is to be calculated, the depth of water should be restricted to the depth of the mixing layer.

As various processes can contribute to the transformation rate for a more detailed treatment, the local rates of all these processes should be available. Up to now the authors do not know a simple method to obtain this information. In order to obtain a convenient model and short calculation times, rapid mixing of the chemical in the body of water is assumed.

Photoreactions and reactions with photochemically produced reactive species can take place only during the daytime. The rate coefficients k of these processes, therefore, are corrected by

km = k(dW), (9 where dl is the day length in hours. The transformation times and rates estimated with the program, therefore, are mean values averaged over 24 hr.


DESCRIPTION OF THE PROGRAM

The program was designed on an IBM PC. It contains five subprograms: STEU, SEIN, GEIN, RECH, and KORR. The first four programs can be used by starting subprogram STEU. The program language is Basic; a compiled version is available. The program was designed on a PC containing only two floppy-disk drives, but it is possible to run it on other PCs as well. Part of the program is twelve data files containing the solar photon irradiancies for Central Europe separated into 52 wavelength intervals. The width of these intervals is relatively small in the UV (2.5 nm) but increases to larger values in the visible (25 nm at wavelength greater than 600 nm). These files also contain the day length of the respective month, values for the water temperature, and the deviations of the photon irradiancies from their average values. Detailed information on solar photon u-radiance is given elsewhere (Frank, 1988). The separate program KORR can be used to alter the contents of these files.

Additional data files contain the properties of the natural bodies of waters and of the chemicals. These files must be created by the user. Subprogram GEIN is used for the input of properties of natural bodies of waters and SEIN for the chemicals. These files contain the name of the natural body of water, the pH, the content of suspended material and its content of organic carbon, and the decadic absorbance of the natural water (in cm-‘) at the same wavelength intervals as the 52 solar photon irradiancies. The data files for the chemicals contain the names of the chemical, the absorption coefficients and the quantum yield at 52 wavelengths, the rate coefficient of hydrolysis at three pH values, the adsorption coefficient for organic carbon &, and the rate coefficients for the various mono- and bimolecular processes. For the performance of calculations, subprogram RECH is used. Calculations are performed only as far as data are available. The results of the calculations are stored in a file and can be printed out after the calculation.

Example

In order to illustrate some of the capabilities of the model and program, the results of a calculation of the photochemical transformation of 2,4,6-trichlorophenol are given as an example. The results of the calculation can be compared with experimental results given by Parlar et al. (Parlar, 1986).

For the performance of the calculations, the following input data have been used:

Starting concentration, 1 X 1 Ow6 A4

Solar u-radiance, data of April

Waters, (a) dest. water (depth: 5 cm); (b) German river Neckar. (depth: 200 cm)

Flow rate, 0.5 m s-’

Dilution, none.

Further data are given in Table 1. Parlar et al. irradiated 2,4,6-trichlorophenol in pure water in sunlight in April.

They observed an experimental half-life of 58 hr. The depth of the water layer during the experiment was approximately 5 cm. Using the absorption coefficient and quantum yield of Parlar et al. (Table l), the absorption of pure water, and a water depth of 5 cm, the mean half-life calculated with the program is 50 hr. The calculated minimum half-life can be 27 and the maximum half-life can be 200 hr. This result shows

330 PRANK AND tiPFFER

TABLE 1

INPUT DATA FOR THE EXAMPLE CALCULATION

2,4,6-Trichlorophenol Center of Natural water

wavelength absorption Absorption interval Solar irradiance coefficient coefficient Quantum

(nm) (mol photons cmm2 s-’ nm-‘) (cm-‘) (fw cm-‘) yield

292.5 295 297.5

E.5 305 307.5 310 312.5 315 317.5 320 322.5 325 327.5 330 333.3 340 350 360 370 380 390 400 410 420 430

2 460 470 480 490 500 510 520 530

22 560 570 580 590

Et 650 675 700 725 750 775 800

0.495E08 0.99OEO8 0.195Ell 0.389Ell 0.505E12 0.972E12 0.243E13 pm;: 0: 107E 14 0.135Ei4 0.165814 0.199E14 0.233E14 0.293E14 0.354El4 0.354E14 0.399El4 0.439E14 0.467El4 0.622El4 0.689El4 0.727E14 0.109El5 0.116E15 0.124El5 O.lllE15 0.137E15 0.170E15 0.171E15 0.173E15 0.185E15 0.178E15 0.177E15 0.190E15 0.180E15 0.198E15 0.193815 0.202E 15 0.198E15 0.198E15 0.205E15 0.199E15 0.2OOE 15 0.209E15 0.213E15 0.210E15 0.21 lE15 0.194El5 0.207E15 0.194E15 0.199El5

0.068 0.066 0.065 0.064 0.063

EC2 0.057 0.056 0.055 0.052 0.050 0.048 0.047 0.046 0.045 0.043 0.042 0.038 0.036 0.034 0.032 0.030 0.028 0.027 0.026 0.025 0.024 0.022 0.021 0.02 1 0.020 0.020 0.020 0.020 0.019 0.019 0.018 0.018 0.018 0.017 0.017

0.016 0.017

%E 0:020 0.023

2210 1860 1610 1030

E 603 459 435 411 388 364 302 240 177 115 96

5i

ii

:

i

i

:

i

i 0

i 0

i

i 0

:

: 0 0

:

:

0.0077

Es% o&77 0.0077 0.0077 0.0077 0.0077 0.0077 0.0077 0.0077 0.0077 0.0077 0.0077 0.0077 0.0077 0.0077 0.0077

E

E

E

::Ei

E

E

i::

::z

i::

it: 0:o

i::

Eli 0:o

2:

i-z 0:o

E 0:o


good agreement between calculated and experimental half-lives. Using the absorption of a natural body of water (Table 1) instead of pure water, but the same water depth of 5 cm, the mean calculated half-life increases to 59 hr. Increasing the water depth to 200 cm, the mean calculated half-life increases to 400 hr. (minimum 220, maximum 1600). Within this half-life, 2,4,6-trichlorophenol would be transported over a mean distance of 730 km.

CONCLUSIONS

In this work, a convenient model for the assessment of degradation processes of chemicals in natural waters is developed. This model is the basis of a computer program, which is especially suited to calculate the transformation of chemicals by various abiotic processes. The program system supplies the user with a set of spectral solar irradiancies and allows him to build up database files which contain the necessary properties of the natural waters and the chemicals. From this information, the rates of the various degradation processes and the half-lives of the chemicals in natural waters can be calculated.

The results of such calculations should be treated with care. As a first possibility to judge the results not only are mean values calculated but also the variations in the half-lives which are caused by the variation in the solar irradiancies. From these calculations the user forms an impression about the variations in the half-lives which can at least occur in the environment. Therefore, and because of other simplifications within the model, calculated half-lives should be taken only as estimates of the real- world transformation, although, it has been possible to achieve good agreement between calculated and experimental values (Parlar et al., 1986).

The main advantage of the program is that it allows the quick calculation of half- lives of chemicals at various times of the year and in various natural waters. These results can reveal which degradation processes (if any) are active at a certain time and in which natural waters. With this information, the user can gain more precise insight into the possible degradation processes of a chemical. The assessment of the environmental fate of this chemical can be improved and a comparison with the fate of other chemicals becomes possible.

Remark. The program including some data files is available from the author. Ifyou are interested in the program please send a formatted disk (5.25 in., MS-DOS) to the author (R.F.).

ACKNOWLEDGMENT

This work has been sponsored by Umweltbundesamt Berlin (German Environmental Protection &ew).

REFERENCES

CALKINS, J. (Ed.) (1982). The Role ofSolar Ultraviolet Radiation in Marine Ecosystems. Plenum, New York.

DAVIES-C• LLEY, R. J. (1983). Optical properties and reflectance spectra of three shallow Iakes obtained from a spectrophotometric study. New Zealand J. Mar. Freshwater Rex 17,445.

FAUST, B. C., AND HOIGNJ?, 1. (1987). Sensitized photooxidation of phenols by fulvic acids and in natural waters. Environ. Sci. Technol. 21,957.

FRANK, R., AND KL~PFFER, W. (1988). Spectral solar photon irradiance in Central Europe and the adja- cent North !%a. Chemosphere 10,985.


HAAG, W. R., AND HOIGNI?, J. (1985). Photo-sensitized oxidation in natural water via OH radicals. Che- mosphere 14, 1659.

HOWARDWILLIAMS, C., AND VINCENT, W. F. (1984). Optical properties of New Zealand lakes. Arch. Hydrobiol. 99,3 18.

IQBAL, M. (1983). An Introduction to Solar Radiation. Academic Press, London. KISHINO, M., AND OKAMI, N. (1984). Underwater radiant energy absorbed by phytoplankton, detritus,

dissolved organic matter, and pure water. Limnol. Oceanogr. 29,340. KOK, C. J. ( 1972). Spectral irradiance of daylight for air mass, Part 2. J. Phys. D 5,85. Kommission der Europa&hen Gemeinschaften (1979). Atlas iiber die Sonnenstrahlung Europas, Vol. 1,

W. Griischen Verlag, Dortmund. KOPF, W. (1983). Some aspects of the underwater light climate of regulated rivers. Z. Wasser Abwasser

Forsch. 16, 168. LECKNER, B. (1978). The spectral distribution of solar radiation at the earth’s surface. Sol. Energy 20, 143. MAUSER, HEINZ (1974). Z. Naturforsch. b 22,367; (1974) Formale Kinetik. Bertelsmann Universmitsver-

lag, Diisseldorf. MUNROE, M., AND SHEPERD, W. ( 198 1). An assessment of solar energy availability in different regions of

the solar spectrum. Sol. Energy 26,4 1. NECKEL, H., AND LABS, D. (1984). The solar radiation between 3,300 and 12,500 A. Sol. Phys. 90,205. NEELY, W. B., AND LUTZ, R. W. (1985). Estimating exposure from a chemical spilled into a river. J.

Hazard. Mater. 10,33. PARLAR, H., BANDLOW, M., HERRMANN, M., HUSTERT, K., KOTZIAS, D., AND ZOLNAY, A. (1986). GSF-

Endbericht an das Umweltbundesamt. Ausarbeitung eines abgestujien Priifungssystems fir die abiot- ische Abbaubarkeit in wixriger Liisung.

ROOF, A. A. M. (1982). Aquatic photochemistry. In Handbook OfEnvironmental Chemistry (0. Hutzinger, ed.) Vol. 2B.

SCULLY, JR., F. E., AND HOIGN~, J. (1987). Rate constants for reactions of singlet oxygen with phenols and other compounds in water. Chemosphere 16,68 1.

SPIGEL, R. H., AND HOWARD-WILLIAMS, C. (1984). A method for comparing scalar irradiance measurements with upward and downward irradiance in lakes. Water Resour. Res. 20,507.

ZEPP, R. E., AND CLINE, D. M. (1977). Rates of direct photolysis in aquatic environment. Environ. Sci. Technol. 11,353.

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A convenient model and program for the assessment of abiotic degradation of chemicals in natural waters