Based on first order kinetics and assuming completely mixed conditions, Marais and Shaw⁹ proposed a model for the die - off of indicator bacteria in WSP. Because

temperature was found to affect the bacterial removal efficiency substantially, Marais⁶ altered the model and derived a first-order equation in which the first-order rate constant was assumed to be temperature dependent. Other coliform decay models in WSP, developed by Klock,¹⁰ Bowles et al.,¹¹ and Ferrara and Harleman,¹² were of the first-order reactions in which the decay rate is temperature dependent.

In fact, the WSP should be considered as a complex system encompassing the existence of several living species, especially the interrelationship of algae and bacteria, which bring about an ecological pattern different from pure culture behavior. Numerous authors^11,13 have pointed to a need to improve existing models of coliform decay. The comprehensive model should include the relationship of coliform die-off to other major parameters: algal biomass concentration (C_s), temperature(T), organic loading (OL), sunlight intensity (I), sunlight duration (L), hydraulic detention time (0), substrate degradation rate (K_s), and pond dispersion (d). A research program was undertaken to develop mathematical relationships of the bacterial die-off in WSP¹⁴ incorporating two proposed models, one for the bacterial die-off rate coefficient, k, and the other for the algal concentration, C_s. Verification of the results obtained was made with experimental data from the full-scale WSP and some published data for existing ponds in northeast Brazil.^15,16 The portion of the work pertaining to mathematical relationships of bacterial die-off (the k model) and data verifications is reported herein.

Ne = No
(1 + k_T0)ⁿ

where N_e and N_o are effluent and influent fecal coliform numbers per 100 ml wastewater, respectively; q is in days; and kT, the first-order rate constant for fecal coliform removal at T°C, in days-1, has an approximate value in the temperature range 2 to 212°C, or:

k_T = 2.6(1.19)^T-20 (2)

A later study by Mara et al.¹⁶ found the above equations valid for temperatures up to 30°C. Although q might appear to affect the bacterial die-off directly, it actually induces changes in the pond environment, such as the variation of d, C_s, pH, and nutrients that consequently influence the bacterial die-off process. To improve existing models, Thirumurthi¹⁷ considered the non-ideal flow in WSP for the model developed for BOD reduction, which included the dispersion number (d) to evaluate the liquid flow and mixing characteristics. The value of d incorporates physical flow characteristics, such as the pond shape, presence of inert zones, flow velocity, and mixing conditions such as wind curretns, thermal stratification, and turbulence.

For ideal plug flow conditions, d is zero, whereas for ideal completely mixed conditions, d reaches infinity. As the value of d becomes greater, the flow deviates from the plug flow towards the completely mixed conditions.

In view of the above mentioned factors, the bacterial die-off in WSP could be related as follows:

Die-off = f(k,d,0) (3)

where

k = bacterial die-off rate coefficient, day^-1.

Since the movement of bacteria with seepage water to the outside pond environment could be regarded as minimal when compared to the amount present in the pond,¹⁸ the downward diffusion of coliform bacteria was disregarded in the model development. Under steady state conditions, Levenspiel’s¹⁹ flow model for chemical reaction and dispersion was modified in this study to account for the bacterial die-off and dispersion. A steady flow WSP of length L₀ through which fluid is flowing with a constant velocity, and in which bacteria is mixed axially with a dispersion coefficient, d was considered as shown in Figure 1. By referring to the elementary section of the pond, the bacterial density mass balance was written as:

input = output + disappearance by pond action
+ accumulation (4)

Equation 4 was modified as in Equation 5:

(output – input)_{bulk flow} + (output – input)_{axial dispersion}
+ disappearance by pond action
+ accumulation = 0 (5)

in which the final elementary equation is shown in Equation 6.

d . d ²N - d N - k0N = 0 (6)
d Z² d Z

Wehner and Wilhelm²⁰ solved this type of equation for any kind of entrance and exist conditions. The solution of Equation 6 is given below:

Ne = 4ae(1/2d) (7)
No (1 + a)²e^(a/2d) – (1 – a)²e^(-a/2d)

where          

a = V 1 + 4k0d;

and N_e, N_o, k, and d are as defined previously.
Equation 7 can be valid for WSP in which reactions are occurring uniformly throughout the pond depth at a rate coefficient k. However, in field conditions, owing to uneven light penetration and possible stratification, the k value can be slightly different at various depths. In this study the evaluation of the k value was made for the overall pond depth to compensate for uneven bacterial die-off rates.

The proposed k model. Although k is dependent on tmeperature (Equation 2), other investigators observed k to vary with pH, dissolved oxygen (DO), and nutrient content in the pond.^2,4,8 Because pH and DO vary as the algal concentration changes² and mixed algal species enhance greater bacterial die-off rates,⁵ the dependence of k on the external factors can be related as:

k = f(T,Cs,OL) (8)

Because the influence of T, OL, and C_s on k are complex, the k model was postulated to be non-linear as follows:

ek = R₁w₁Tw₂^CsW₃OL (9)

in which R1, w1, w2, and w3 are constants . In order to test the potential lethal effect of sunlight on bacterial die-off in WSP, as reported by Moeller and Calkins,²¹ the k model could be presented in an alternative form as in Equations 10 and 11.

k = f(T, C_s, OL, UVI) (10)

ek = R_a1w_a1^Tw_a2^Csw_a2w_a3^OLw_a4^UVI (11)

where UVI = ultraviolet rays index, dimensionaless, ad R_a1, w_a1, w_a2, w_a3, and w_a4 are constants. The UVI index was weighed in accordance with the sunlight intensity (I, cal/day/cm²).

UVI = 1 + I (12)
100

In the absence of sunlight, UVI was considered to be unity. The constants in Equations 9 and 11 were deter-mined by entering a series of experimental values obtained from laboratory and pilot scale WSP for different combinations of T, OL, C_s, and UVI into the multiple regression equations. The accuracy of these parameters depends upon arriving at a low standard error, a high multiple correlation, and a high F-value. The total coliform species was chosen in the experiments as the indicator bacteria for the k-model, but it can be extended to predict the k-values of other enteric bacterial species.
To accommodate for any species of bacteria, a species constant, l , was included in the model (Equation 9).

EkF = R_1l w₁Tw₂^Csw₃^OL (13)

Because total coliforms were chosen as the indicator bacteria in this model, the species constant, l , is unity. A series of kF values for fecal coliforms were obtained experimentally for a combination of T, OL, and Cs values. By entering these values into Equation 13, the average R1 value for fecal coliforms (Rf) could be determined, in

                           Parameter                                                                       Range

       Temperature, °C                                                                           20.0 – 33.0
       Light intensity, cal/cm²• d                                                               80.0 – 3 30.0
       Light duration, h/d                                                                            8.0 – 14.0
       Influent COD, mg/l                                                                      150.0 – 170.0
       Dispersion number (d)                                                                      0.100 – 0.200
       Detention time, days                                                                        3.0 – 10.0
______________________________________________________________________________

which:

R_F = l ₁R₁ (14)

where

R_F = R value for fecal coliforms,
R₁ = R value for total coliforms, and
l ₁ = Species constant for fecal coliforms.

Figure 4 -- Layout of AIT waste stabilization ponds (FWSP).

Pilot-scale WSP (PWSP). The PWSP exeperiments were carried out under ambient conditions, with three ponds connected in series (Figure 3). A constant head tank was used to feed wastewater to PWSP at a constant rate, but a pump with a timer was used for sewage feeding periodically to avoid pipe blockage. The ranges of operating conditions of the PWSP experiments are shown in Table 2. The same measurements taken for the LWSP, plus the diurnal variations of pH and DO, were taken for each PWSP.

Full-scale WSP (FWSP). The wastewater treatment facility (Figure 4) at AIT comprises two parallel sets of ponds in series (FWSP). The FWSP1 serves a facultative function, while the FWSP2 is a maturation pond. The final effluent is discharged into a nearby canal. The EWSP operation is under the control of the AIT physical plant, but cooperation was provided in the measurements of flows and other important parameters similar to the LWSP and PWSP.

Tracer study. To determine the dispersion characteristics of the LWSP2, PWSP, and FWSP, tracer studies were carried out for different q of each pond. Sodium chloride (NaCl) was the impulse tracer material for all the experiments, as in the experiments of Thirumurthi¹⁷. According to Levenspiel¹⁹, the response tracer concentration should be monitored at the exit stream at fixed time intervals. The amount of input impulse tracer concentration varied from 30 g in the LWSP to about 700 kg in the FWSP. The base amount of NaCl present in the wastewater was taken into consideration when the exit responses were monitored. The calculation of the d values was made with theroposed by Levenspiel and Smith, which is described below:

Mean detention time (actual), q = S q i Ci (15)
S Ci
Standard deviation, s ² = S Ciq i - (q )² (16)
S Ci
if Æ = q i
q
then s ² = 2d – 2d² (1-e-1/d) (17)

The term, d, can be calculated by trial and error from Equation 17 in which.

q i = time after impulse injection, days; and
Ci = tracer response concentration at the exist stream,  mg/l.

Though tracer studies require careful attention and much time, they are one of the most reliable techniques for evaluating the actual flow pattern in a WSP. Previous investigators, such as Thirumurthi¹⁷, Bowles et al., and Uhlmann, based their mathematical formulations of WSP performance on partial mixing conditions and flow pattern.
Analytical methods. All analyses were undertaken according to the methods described in "Standard Methods"²⁴. DO measurements were conducted with a DO meter. PH of the water samples was measured with a fluent flows of the LWSP. Intensity of artificial light and sunlight was measured with a bimetallic actinograph instrument. The samples for algal analysis were initially filtered through a 150-m m mesh to separate out zooplanktons, measured for the percent absorbance with a spectrophotometer at a wavelength of 650 mm, and weighed for dry algal concentration with the specimen curve prepared in advance.

The total coliform counts were enumerated by the standard MPN method using the five-tube dilution technique. Appropriate dilutions, prepared in buffered dilution water, were inoculated into lactose broth, presumptively tested by incubation at 35°C for 24 hours. All the positive tubes were the confirmatively tested by subculturing into brilliant green lactose bile broth at 35°C for 48 hours. The fecal coliform MPN counts were determined by subculturing all the positive presumptive tubes into an EC medium at 44.5°C for 24 hours.

COD, mg/l (filtered)                100-440                               180                                            50                                              30
BOD, mg/l (filtered)                 60-150                                120                                           35                                              15
SS, mg/l                                     20-120                                110                                            80                                            115
VSS, mg/l                                   10-90                                    45                                             --                                               --
Org-N, mg/l                                  2-5                                       --                                             --                                               --
NH₃-N, mg/l                                 4-10                                    5.5                                          3.0                                          Trace
P04-3, mg/l                                0.5-1.5                                     --                                           0.4                                             0.3
PH                                              6.2-7.5                                    7.3                                          7.5                                             8.0
Temperature, °C                       28-33                                       _                                        28-33                                        2 8-33
Total coliforms, MPN/100 ml 22 x 10⁵-16 x 10⁶               11x10 ⁶                               15 X 10⁵                                   24 X 10³
Fecal coliforms, MPN/100 ml 16 x 10³-92 x 10⁴                46 x 10 ³                            93 X 10²                                   11 X 10²
Detention time (0), days                                                                                       &a mp;a mp;n bsp;                 8                                              20
Dimension, I X w X d, m3                                                                                       &a mp;a mp;n bsp;       50 X 23 X 2.4                 120 X 43 X1.3
____________________________________________________________________________

______________________________________________________________________________________________________________

74.71              79.41                 0.160                      3.0              215.0             118.0                  22.5                14.0              326.1
87.71              89.54                 0.110                      3.0              140.2             105.6                  30.0                14.0                81.7
86.14              88.00                 0.160                      3.0              129.4             101.7                  30.0                14.0                81.7
77.72              81.76                 0.170                      3.0                31.8             113.4                  30.0                14.0                81.7
76.17              80.00                 0.190                      3.0                31.8             106.8                  30.0                14.0                81.7
77.44              80.00                 0.200                      3.0                28.0               52.7                  30.0                14.0                81.7
73.00              79.41                 0.165                      4.0              182.0               89.1                  22.5                14.0              326.1
82.60              96.07                 0.120                      6.0                89.5               54.7                  22.5                14.0              326.1
93.51              97.39                 0.120                      6.0              158.6               58.9                  33.0                14.0              326.1
96.16              97.39                 0.120                      6.0              136.0               57.6                  33.0                16.0              372.7
77.50              80.93                 0.120                      6.0              260.0               57.0                  22.5                12.0              279.5
77.50              78.12                 0.120                      6.0                50.0               57.0                  22.5                10.0              232.9
78.80              80.00                 0.120                      6.0              150.0               55.9                  22.5                14.0              326.1
73.71              79.41                 0.120                      6.0                62.0               55.9                  22.5                  8.0              186.3
83.07              90.00                 0.110                      8.0              177.0               42.5                  22.5                12.0              279.5
86.15              91.53                 0.100                    10.0              148.0               34.0                  22.5                14.0              326.1
____________________________________________________________________________________________________________________________

level), and C_s in the pond water. In this study, the DO at dawn did not reach zero because the applied loadings of the PWSP were les than 280 kg COD/ha • d, the level considered as facultative.^3,29 The decrease of C_s in the later period of a day could be caused by light and nutrient limitations, competition for food, algal cell sedimen-tation, and unfavourable conditions existing at high pH conditions.
Performanceof FWSP. The data in Table 3 indicated a considerable reduction of COD and BOD int the FWSP operated in series as their concentrations in the FWSP2 effluent were only about 30 and 15 mg/l, respectively. However, the SS concentration of 155 mg/l was con-sidered high, which was caused by algal cell suspension in the effluent. There were decreases in the total and fecal coliform densities of about 80% in the FWSP1 (0 = 8 days), and about 90 to 98% in the FWSP2 (0 = 20 DAYS). The removal of organics and bacteria in the FWSP are comparable with other ponds reported in the literature.²⁹

It seems that another polishing pond, connected in series to the FWSP2, should be provided to achieve the stringent standards of SS and bacteria required by some regulatory agencies.²⁶

It can be seen from the results of the LWSP, PWSP, and FWSP that bacterial die-off is a complex phenomenon involving various factors and interactions in the WSP. Because in actuality, the WSP are not in either completely mixed or plug-flow conditions, and not just a single parameter, such as T, controls the bacterial die-off rate, the proposed Equations 7 and 9 or 11, as models for bacterial die-off, would better represent the pond performance.
The k model. The experimental k values were determined by entering each data ser of PAT, d, and q in Tables 4 and 5 as input variables into Equation 7. Then, together with the respective values of T, OL, Cs, and UVI, the experimental values as determined were entered into the multiple regression equations (Equations 9 and 11) to evaluate the regresion coefficients (or constants) using a computer program form a scientific subroutine package. The multiple regression results including the multiple correlation coefficients, standard errors of estimate, and F-statistic values obtained for Equations9 and 11 were, respectively, 0.695 and 0.719, 0.152 and 0.294, and 19.039 and 16.109. Although Equation 9 had a slightly lower multiple correlation coefficient, its standard error of estimate and F-statistic value were lower and higher, respectively, than Equation 11, indicating that both equations represented a certain degree of correlation withing the same range btween k and the parameters T, C_s, O_L, and I. In a WSP, k would depend on factors other than just those above mentioned parameters. But for practical reasons, Equation 9 was chosen to represent the k model, which can be written as in Equation 18:

e^k = 0.6351(1.0281)^T(1.0016)^Cs(0.9994)^OL (18)

The empirical relationship obtained for k in Equation 18 is essentially an extension of Equation 2, which quantifies the dependence of k on temperature only, and it eliminates the necessity for a temperature correction. However, a comparison of the k values based on Equations 18 and 2 is not relevant because the equations governing bacterial die-off (Equations 7 and 1, respectively) are of different order. Although Equation 18 does not include the parameter I or UVI, the direct relationship between I and C_s has been substantially reported,² thus the term C_s indirectly represents the influence of I on k.

The regression coefficients represent the factor by which each parameter (T, Cs, and OL) contributes to the independent parameter determining whether the contribution is negative or positive. For Equation 18, an increment in either T or Cs results in an increase in the k vaue while the opposite is true for OL, these phenomena could be explained as follws. Although Marais⁶ observed that beyond a temperature of 21°C, k decreased as temperature increased, a later study by Mara and Silva¹⁶ showed that k increased with temperature up to at least 30°C. At a temperature range of 21 to 30°C, bacterial activity is stimulated and results in a higher probability of bacterial survival, but other factors, such as increased algal activity and pH, cause higher die-off rates by offsetting the stimulated bacterial activity. The algal concentration in the pond was found to increase with the onset of the light period. With the consequent increae in pH (Oswald and Gotaas³⁰ and Figures 5 and 7), the pH variation from about 8 to 10 canyield a hostile environment for bacterial survival⁴. The regression coefficient for OL indicates that an increase in organic loading causes a slight decrease in k because of more nutrient availability for the bacterial activity.²⁸ Therefore, the regression coefficients and their signs, as shown in Equation 18, are considered to be in accordance with actual pond performance and the literature, when operated within the ranges employed for the LWSP and PWSP in this study.
Species coefficient for fecal coliforms (l ₁). The fecal coliform die-off coefficients (k_F) were calculated by entering the respective values of PAF, d, and 0 in Tables 4 and 5 into Equation 7. The values of R_{1l 1} or R_F could be determined by entering the values of the calculated k_F, T, Cs, and OL into Equation 13, in which the values of w₁, w₂, and w₃ were the same as in Equations 9 or 18. By entering the mean RF value into Equation 14, the species constant, l ₁ was found to be 1.1274, and the k_F is given as follows:

e^kF = 1.1274(0.6351)(1,0281)^T(1.0016)^Cs(0.994)^OL (19)

Thoug the k to kF ratio is constant, the resulting PAT to PAF ratio is variable because Equations 18 and 19 have to be used with Equation 7, which has a higher order to predict the bacterial survival ratio in WSP. From Equations 18 and 19, the value of k_F is marginally higher than k, which is in accordance with the results of Fransmathes, who reported better survival of the total coliforms than the fecal coliforms in WSP.

Comparing the 22 experimental data observed PAT in the FWSP with those predicted by Equations 7 and 18 gave the correlation coefficient of 0.986, indicating that the models developed in this study performed with a high degree of accuracy in the prediction of the total coliform die-off. The mean and standard deviation of percentage errors (MPR and SDPR, respectively) as resulted form the PAT prediction by Equation 7, were lower than that of Equation 7 yielded a correlation coefficient of 0.988, and there were lower mean and standard deviation of percentage errors in Equation 7 than that of Equation 1. By assuming the values of I, L, and d to be 390 cal/cm² • d, 11.5 h/d, and 0.150, respectively, for the pond data in northeast Brazil, the comparison between the fecal coliform percentage reduction and those predicted by Equations 7 and 1 could be made. The observed PAF and those predicted by Equation 7 had a correlation coefficient of 0.994, further asserting te accuracy of the proposed models. There were lower mean and standard deviation of percentage errors of the predicted PAF by Equation 7 than those by Equation 1. The main reasons for this difference are probably because Equation 1 assumes complete-mixing conditions in the pond and it includes only T and 0, whereas the proposed models cater for actual dispersion characteristics of the pond and encompass other important parameters, such as C_s and OL.

Because the values of the multiple regression coefficients in Equation 18 appear to be close to unity, it could be interpreted that the model was not sensitive. An attempt was made to observe the effects that variation of the T, Cs, and OL have upon the value of k. It was found that as T increases from 10 to 30°C, k changes by as much as 0.55; as C_s increases from 25 to 300 mg/l/k changes by as much as 0.44; and when OL increases from 50 to 300 kg. COD/ha•d, k decreases by as much as 0.15. For the parameter ranges mentioned above, k changes from a minimun value of –0.17 to a maximum of 0.68. Equation 7 was tested to observe the effects that variation in k and d have on the coliform survival ratio. By assuming the following: T = 25°C, OL = 100 kg COD/ha • d, C_s = 250 mg/l, 0 = 10 days, and d = 0.4; it was found that if k changes from 0.5 to 1.0, the Ne/No ratio decreases from 0.061 to 0.012, a decrease in coliform density of about 80%. However, with the same values of T, OL, Cs, 0, and the k value of 0.5, it was observed that as d changes from 0.4 to 0.8, the Ne/No ratio increases from 0.061 to 0.089, an increase in coliform density of about 46%. Hence it is apparent that the changes in the values of T, Cs, and OL can cause significant changes in the k value, which in turn, together with the d value, can cause significant variations in effluent coliform quality.

The Wehner and Wilhelm equation (Equation 8) may seem complicated, but charts may be prepared similar to that of Thirumuthi¹⁷ (for BOD reduction) to read off directly the coliform survival ratio as a function of the pond mixing pattern (d) and the value of k0. Because the second term in the denominator in Equation 7 is small, it may be neglected, in which case the equation can be simplified as:

Ne = 4ae^(1-a/2d) (20)
No (1 + a)²

The error of Equation 20 may be significant when the value of d exceeds 2.0. However, based on the data in Tables 4 and 5 of this study and of Nashashibi,³² d seldom exceeds 1.0 because of low hydraulic loads. In practice, the values of T, OL, C_s, and d need to be known if the coliform survival ratio in WSP is to be predicted from Equations 7 and 18 or 19. T can be measured onsite directly and OL can be calculated or taken from the literature,^25,29 thus only Cs and d need to be determined. Oswald and Gotaas,³⁰ reported the rate of algal yield to vary from 2.5 tons/ha • moth in the winter to 12.5 tons/ha • month in the summer. From continuous cultures, they found the dry weight algal cell material to be a logarithmic function of the substrate (BOD), up to approximately 400 mg/l (for the wastewater BOD ranging from 75 to 375 mg/l). The corresponding algal cell concentrations were from 125 to 325 mg/l, respectively. A model was recently developed¹⁴ that relates the Cs in WSP to the substrate degradation rate, hydraulic detention time, and other factors, such as T, L¸and I. It was found to be satisfactory in predicting the algal concentration. The value of d can be obtained by conducting tracer studies in existing, similarly shaped ponds. It should be noted that the proposed equations

(Equations 7, 18, and 19) are applicable to the types of single-cell ponds experimented with (facultative and maturation), and the ranges of operating conditions conducted in this study. Additional research is required to modify these equations so that they can be used to predict bacterial die-off in a series of WSP.
Design example. Determine the hydraulic detention time, 0, of WSP treating domestic wastewater so that the final effluent will contain less than 100 fecal coliforms/100 ml, which is the standard for reuse in restricted irrigation. The initial COD and fecal coliform concentrations are 300 mg/l and 10/100 ml, respectively. The expected monthly temperature in the pond in tropical areas is about 20°C in winter. Tracer studies and water analyses in the existing, similarly shaped pond indicate that the values of d and Cs are approximately 0.200 and 200 mg/l, respectively.
Solution 1. Select the OL value to be 200 kg. COD/ha • d. The value of kF can be determined according to Equation 19:

e^kF = 1,1274(0.6435)(1.0281)²⁰(1.0016)²⁰⁰(0.9994)²⁰⁰

in which k_F was found to be equal to 0.433 day ^-1. Take a = Ö 1+4k_F0 d and put it into Equation 20. By trial and error, the WSP hydraulic detention time (0) is found to be 34 days to produce effluent with fecal coliform concentration less than 100/100 ml.
Solution 2. If Equations 1 and 2 are to be used in the design, take from Equation 2, k_T = 2.6(1.19)^20-20 = 2.6 day –1.
From Equation 1, the hydraulic detention time, 0, can be determined as follows:

if n = 1, 0 = 384 days,
n = 2, 0 = 12 days, and
n = 3, 0 = 3.5 days.

It is difficult to say, based on the above results, which method is superior in terms of WSP design for bacterial reduction. Although Solution 2 gave the anomalous value of 0 for the case n = 1, for the case n = 1, for the case n = 2, the total 0 is 12 x 2 = 24 dys, which is less than the Solution 1 result. At this stage, it could be generally stated that the proposed equations (Equations 7, 18, and 19) should be used in the design of single-cell facultative or maturation ponds, and that bacterial die-off in the ponds can be predicted by these equations with high accuracy. Equations 1 and 2 should be used in the design of WSP in series, as they gave more choices in selecting the n-series of ponds.

Cs = algal concentration, mg/l
d = dispersion number, dimensionaless
I = light intensity, calories/cm² • d
k = bacterial die-off rate coefficient, day^{-1
Kf = fecal coliform die-off rate coefficient,} day ^-1
kT = first-order rate constant for bacterial die- off, day ^-1
L = light duration, h/d
n = number of waste stabilization ponds in series
Ne,No = effluent and influent bacterial densities, respectively, MPN/100 ml
OL = influent COD loading rate, kg COD / ha • d
PAF = percentage fecal coliform reduction
PAT = percentage total coliform reduction
R₁,w₁ = multiple regression coefficients for
w₂,w₃ the k-model
R_ai,w_a1, = multiple regression coefficient for the
w_a2, w_a3 k-model with UVI as a parameter
w_a4
R_F = a multiple regression coefficient for the k-model of fecal coliforms
T = pond wter temperature, °C
UVI = ultra-violet ray index, dimensionaless
0 = pond hydraulic detention time, days
l = bacterial species constant, dimensionaless
l ₁ = species constant for fecal coliforms, dimensionaless