Diel variation of in-stream nitrification

War. Res. Vol. 20, No. 10, pp. 1325-1332, 1986 Printed in Great Britain

0043-1354/86 $3.00+ 0.00 Pergamon Journals Ltd

TECHNICAL NOTE DIEL VARIATION OF IN-STREAM NITRIFICATION JOHN J. WARWICK Graduate Program in Environmental Sciences, The University of Texas at Dallas, Richardson, TX 75080, U.S.A.

(Received October 1985) Abstract--The diel variation of in-stream nitrification is explained as a function of observed fluctuations in temperature and pH. A simultaneous nitrogen and dissolved oxygen mass balance model was used to calculate hourly nitrification rate coefficient values. These calculated rate coefficients were based upon observed spatial and temporal changes in nitrogen species and dissolved oxygen concentrations. A non-linear regression analysis was performed to determine the functional relationship between calculated in-stream nitrification variation and observed changes in bulk fluid temperature and pH.

Key words--nitrification, stream, model, kinetics, water quality

NOMENCLATURE

Eo = reaction activation energy (kgm s-I) KN(pH ) ffi nitrification rate coefficient at specified pH value K~o.0) = nitrification rate coefficientat pH value of 7.0 /~T, pH) = nitrification rate coefficient at specified temperature and pH values K(Tf20,pH.7 ) nitrification rate coefficient at temperature value of 20°C and pH value of 7.0 Kr= reaction rate coefficient at specified temperature value K20= reaction rate coefficient at 20°C R = universal gas constant (kg m s - l K ) T = reaction temperature (°C) Tl, T2= upper and lower bounds* on reaction temperature, respectively (K) fl =dimensionless nitrification pH correction coefficient ~ = dimensionless, temperature dependent, nitrification pH correction coefficient 0 •dimensionless temperature correction coefficient 0n = dimensionless nitrification temperature correction coefficient. =

INTRODUCTION Most state-of-the-art water quality models incorporate some type of temperature correction for instream nitrification kinetics. Many researchers (Wild et al., 1971; Huang and Hopson, 1974; Kholdebarin and Oertli, 1977; Stratta, 1981) have also reported the additional impact of pH on nitrification rates. This impact appears to be quite significant in the pH range from 6.0 to 8.5. The noted pH range encompasses most flowing freshwater systems; with many individual, highly productive, systems exhibiting diel pH variation within the stated boundaries. Unfortunately, current water quality models do not, as a rule, adjust in-stream nitrification rates as a function of bulk fluid pH. It is hoped that this paper will serve two basic purposes. The first is to present a simple mathe-

matical function which relates observed bulk fluid temperature and pH values to in-stream nitrification rates. The second purpose is to promote the establishment and subsequent utilization of a baseline nitrification rate which is referenced to both temperature and pH. Traditionally, nitrification rates are reported at a standard temperature of 20°C to facilitate comparison. It will be argued that the inclusion of a reference pH value (pH = 7.0) is needed in the definition of a baseline nitrification rate. MASS BALANCING METHODOLOGY

A simultaneous nitrogen and dissolved oxygen mass balancing technique was utilized to calculate hourly in-stream nitrification rate coefficients. These rate coefficients were principally based upon observed spatial and temporal changes in nitrogen species and dissolved oxygen concentrations. The simultaneous nitrogen and oxygen analysis program (SNOAP) is a one-dimensional, pseudo unsteady-state, water quality model which was developed to simultaneously solve both a nitrogen and dissolved oxygen mass balance. The SNOAP model diverges from more traditional modeling approaches by requiring water quality input data at each station and calculating nitrogen reaction rates for all reaches. The model data requirements for each station include: diel variation of flow, temperature, pH, dissolved oxygen, and nitrogen species concentration. In addition, rates of carbonaceous biochemical oxygen demand removal, atmospheric reaeration, and benthal oxygen demand must be specified for each reach. The nitrogen mass balancing component calculates hourly reaction rate coefficients associated with ammonification, nitrification, bacterial and aquatic plant nitrogen assimilation, ammonia exsolution, and denitrifieation. A zero-order kinetic formulation is used to describe both aquatic plant and bacterial

1325

1326

Technical Note

nitrogen assimilation. A m m o n i a - N exsolution (stripping) is modeled with first-order kinetics. The remaining nitrogen transformation pathways (ammonification, nitrification, and denitrification) can be optionally simulated using either first- or zero-order kinetics. The dissolved oxygen mass balancing component calculates hourly reaction rates associated with gross photosynthetic oxygen production, aquatic plant respiration, and nitrification. In-stream nitrification rate coefficients are typically expressed in terms of the impact nitrification has on dissolved oxygen concentrations. The SNOAP model calculates in-stream nitrification rate coefficients based upon the sequential oxidation of ammonia-N to nitrite--N and nitrite--N to nitrate-N. The stoichiometric equivalents reported by Haug and McCarty (1972) for NH +--*NO~- (3.22 mg O2/mg N H + - N ) and NO2 -~NO3 (1. l 1 mg O2/mg N O 2 - N ) were used to relate observed temporal and spatial changes in nitrogen species concentrations to dissolved oxygen. In most natural systems, changes in nitrite-N concentration are minimal which results in an overall stoichiometric conversion factor of 4.33 mg O2/mg NH+-N. The general solution technique utilized within the SNOAP model is iterative in nature, with convergence occurring when a value of nitrification rate is found which simultaneously satisfies both mass balances. The computed in-stream nitrification rate coefficients are therefore determined solely from observed temporal and spatial changes in dissolved oxygen and nitrogen species concentrations, without the direct use of measured temperature and pH values. These SNOAP model calculated rates are assumed to accurately represent the actual variation of in-stream nitrification. Details regarding the development and initial application of this modeling methodology has been presented elsewhere (Warwick and McDonnell, 1985a,b). FACTORS AFFECTING NITRIFICATION

Several environmental factors have been shown to influence the rate of nitrification, including: pH, temperature, dissolved oxygen concentration, and suspended solids concentration. This review will focus on previous work concerning only the effects due to temperature and pH. Typically, the impact of temperature on biochemical reaction rates has been modeled using a simplified form of the Arrhenius equation:

K r = K2oO~r 20,

(1)

in which K r , K20 = reaction rate coefficients at temperature T and 20°C, respectively; 0 = dimensionless temperature correction coefficient and T = temperature (°C). It should be noted that the 0 value in equation (1) is not truly independent of temperature. The original Arrenhius formulation shows that 0 should be defined as follows: 0 = exp[E,/(R*T*T2)]

(2)

where E, = activation energy ( k g m s ~); R = universal gas constant (kg m s -~ K); and T~, 7"2 = upper and lower temperature values respectively (K). For situations in which the range of temperature variation is < 10°C the 0 value remains reasonably constant which results in the simplified expression already presented. The performance of equation (1) may therefore prove questionable for temperatures < 10°C and >30°C. Researchers (e.g. Friedman and Schroeder, 1972; Sayigh and Malina, 1978; Thornton and Lessem, 1978) have found equation (1) to increasingly overestimate reaction rate coefficients as the temperature deviates away from the 20°C reference value. Thornton and Lessem (1978) developed a more complex formulation based upon the premise that a biological process should reach a maximum rate at some optimum temperature. Schneiter and Grenney (1983) subsequently improved upon this work by allowing for the assignment of an arbitrary reference temperature. While these recent advances appear to improve reaction rate coefficient estimates, the more complex formulations do require additional parameter assignments that may prove difficult to accurately ascertain for mixed aquatic communities. Due to these difficulties, the more simplistic Arrhenius formulation was used as the basis for nitrification rate coefficient temperature correction. Table 1 summarizes a range of reported temperature correction coefficients for nitrification (0,). Many researchers have reported the significant effect of pH on observed nitrification rates, with an optimum pH range of 8.4-8.6 being cited most often. The results reported by Wild e t al. (1971), Huang and Hopson (1974) and Stratta (1981) were combined by this author and plotted in Fig. 1 to indicate the overall variation of nitrification rate as a function of pH. The data indicates that an 80% reduction in nitrification rate can be expected when the pH is

Table 1. Temperaturecorrectioncoefficientsfor nitrification Temperature correction References Environment coefficient(0,) (1) Buswellet al. (1954) Lab Nitrosomonas culture 1.0757 (2) Knowleset al. (1965) Lab mixedculture 1.0997 (3) Stratton (1966) Streams 1,0876 (4) Wild et al. (1971) Suspended growth reactor 1.0548

Technical Note

1327

5.0

100

4.5

4.o

80

315

o=

0

LL 3.0

60 []

C

~ 4o E

Z

E ~ 20

I

2.0 6

12

I 18 Time

I

24

I 30

i 36

of d a y

O

Fig. 2. Measured volumetric flow rate variation.

0 6

I 7

I El

I 9

I 10

I 11

I 12

pH

Fig. 1. Effect of pH on nitrification rate. ©, Wild; A, Huang and Hopson; I-q, Stratta; - - , cubic spline; - - . - - , linear regression.

lowered from 8.5 to 6.0. This result is quite significant since m a n y productive aquatic systems fluctuate within this range o f pH. The solid curve in Fig. 1 is a cubic regression function which is presented to accentuate the overall trend in nitrification rate variation. The relationship appears linear within the p H range from 6.0 to 8.5 and can therefore be represented by the following expression: KN{pm = Ks(7.0)[1.0 + fl*(pH - 7.0)1

(3)

where K,v(ps), Kt~(7.0)=nit rification reaction rate coefficients at some specified p H value and at a p H o f 7.0 respectively and fl = dimensionless p H correction coefficient. The dashed line in Fig. 1 represents a least squares linear regression of all data in the p H range from 6.0 to 8.6, with a resulting value for fl o f 0.642.

observed fluctuation of stream flow for Survey 3 is shown in Fig. 2. The measured flow data points were fit by a cubic spline function to accentuate the observed variation. The measured diel variation of in-stream flow rate was a direct result of the wastewater treatment plant cyclic discharge pattern. Similar diel variations were also observed in the concentrations of all the measured nitrogen species. Flow times were only measured once per survey using the fluorescent dye, uranine. Flow time measurements were conducted during periods of average stream flow so as to approximate average travel times between stations. A more complete description of the measurement techniques used and resulting data is presented in Warwick and McDonnell (1985b). SNOAP MODEL RESULTS The S N O A P model calculates hourly values o f in-stream nitrification which satisfy both the observed variation in all nitrogen species and dissolved oxygen. The model was successfully calibrated and verified for all three o f the aforementioned water quality surveys. Figure 3 summarizes results from Reach 3, Survey 3. The calculated hourly values of in-stream nitrification rate were fit with a cubic spline function to assist in visualizing the diel variation. The values presented in Fig. 3 are expressed using zeroorder kinetics and mass units. Analysis of N B O D removal and nitrogen species spatial variation indi-

FIELD INVESTIGATIONS Three separate, data intensive, water quality surveys were conducted on Marsh Creek during the summer of 1981. Marsh Creek is located in the Pine Creek watershed on the Appalachian Plateau in north-central Pennsylvania. The lithology of the area is characterized by sandstones, shales, conglomerates and coal from the Carboniferous and Devonian Periods and till deposits from the Pleistocene Epoch. Four monitoring stations were established on a 1.29 mile segment of Marsh Creek which was immediately downstream from a wastewater treatment plant effluent discharge. Water quality samples were collected at hourly intervals for a period of at least 24 h at all monitoring sites. Water quality measurements included dissolved oxygen, total Kjedhal nitrogen, ammonia-N, nitrite-N, nitrate-N, ternperature and pH. In addition, ultimate carbonaceous and nitrogen biochemical oxygen demand was measured for a composite sample taken at each station. Stream volumetric flow rates were also measured on an hourly basis at a separate station located in the middle of the study area. The

j%

*~: 60 7>, ~ 50 c~ i 4o -

ao 20

~: lo ~ ~

o 6

I 12

I 18

I 24

I 30

I 36

T i m e of d o y

Fig. 3. Diel variation of calculated in-stream nitrification rate coefficients.

1328

Technical Note rection factor. The temperature dependence of HI c a n be defined with the following expression.

25

fll ~-" fl0(nT-20)' 20

(6)

Combination of equations (5) and (6) yields the final formulation for Model B.

o) o c0

Kjv(r,prl)= KN(T=20,pH=7)0~T-2°'

~0

× [1.0 + fl*(pH - 7.0)]. 10 6

J 12

I 18 Time

I 24 of

J 30

Fig. 4. Measured bulk fluid temperature variation.

cated the appropriateness of using a zero-order reaction for this particular situation in which the ammonia-N concentration averaged well above 3.0mgNH~-NI-I. The use of mass units (flow.concentration) was necessitated by the substantial fluctuation in stream flow rate. Figures 4 and 5 present measured variations in temperature and pH for Reach 3, Survey 3. Again, cubic spline functions were fit through the data points to accentuate trends. Concurrent timing of maximum temperature and maximum in-stream nitrification rate was observed for all three reaches in Surveys 1 through 3. However, there was an apparent 1-2 h delay or lag period between the time of maximum bulk fluid pH and the occurrence of maximum instream nitrification. This lag period was found to occur in all reaches used in this study, with most reaches exhibiting a 2 h lag time.

PROPOSED

MODELS

Two models were originally proposed to explain the diel variation in calculated in-stream nitrification rate coefficients as a function of measured changes in temperature and pH. The first model (Model A) assumes that the effects of temperature and pH on in-stream nitrification rate are independent and additive. Model A can be formulated as follows: KN= KNtr:2o.pu:7)[O~r-2°) + fl*(pH - 7.0)1 (4) where K~ccr,om, K~(r=2o,pn=7)= in-stream nitrification rate coefficients at specified temperature and pH values and at reference conditions of 20°C and pH = 7.0 respectively. Equation (4) states that the linear pH effect (fl) will be the same regardless of the temperature. A second model (Model B) was proposed that incorporated a temperature dependent linear pH correction factor: KN(T, pH ) =

I-£1(T- 20)

Ku{r=20,pn=7)tt,,

+ f l l * ( P n - 7.0)1

DATA ANALYSIS

J 36

doy

(5)

where fll = temperature dependent linear pH cor-

(7)

The two proposed, hypothetical, models [Model A represented by equation (4) and Model B represented by equation (7)] were evaluated to determine their ability to explain the variation of calculated in-stream nitrification as a function of observed changes in bulk fluid temperature and pH. Calculated nitrification rate coefficients were substantially different from reach to reach and survey to survey. Combination of results from all surveys was deemed desirable so as to increase the statistical significance of the analysis. Non-dimensional nitrification rate coefficients were calculated by dividing each value by the maximum rate that occurred in the reach. Calculated in-stream nitrification rate coefficients were therefore converted into dimensionless values representing the percent of the maximum rate for that reach. Combination of results from all three surveys yielded 152 data sets, with each containing a SNOAP calculated value of percent maximum in-stream nitrification rate paired with measured temperature and pH values. A non-linear regression package (Statistical Analysis System, SAS Institute Inc., Cary, North Carolina) was used to determine the best values of K~c
~5

7".3 Z2

7.1 7.01

6

I

f

J

I

12

18

24

30

Time

of d o y

Fig. 5. Measured bulk fluid pH variation.

? 36

Technical Note

1329

Table 2. Statisticalanalysisof Models A and B Parameter estimates(95% confidenceintervals) Residual sum

Model

KS(T- 2o,pn = 7)

(I) Model A (full) (2) Model B (full) (3) ModelsA and B (reduced)

0.476 (0.413-0.534) 0.502 (0.445-0.559) 0.602 (0.580-0.625)

0.

fl

1.081 (1.067-1.095) 1.067 (1.053-1.080) 1.081 (1.069-1.093)

unexplained, sum of error squared), Three dimensional plots have been constructed to elucidate the differences between the two proposed models. Figures 6 and 7 present the variation of in-stream nitrification as predicted by Models A and B, respectively. Parameter estimates shown in Table 2 were used in generating Figs 6 and 7. A temperature value of 4°C was assumed to define the lower limit for biological activity. In addition, an upper bound nitrification rate of 100% was imposed. The shaded zone in each figure represents the region occupied by the data base. The models behave quite similarly within this region which explains the closeness in the residual sum of squares values reported in Table 2. But, the behavior of Models A and B is significantly different outside the shaded zones. Figure 6 (Model A) projects a nitrification rate value equal to 80% of the maximum rate at a pH of 8.5 and temperature of 4°C. The results for Model B (Fig. 7) show a nitrification rate value of only 36% for the

0.961 (0.388-1.534) 0.705 (0.255--1.155) 0.000

of squares 2.371 2.418 2.652

same temperature and pH conditions. In addition, Model A predicts zero nitrification occurring at a temperature of 20°C and pH equal to 5.7, while Model B estimates a value equal to 18% of the maximum. The graphical projections of Models A and B show the functional superiority of Model B. Predictions of Model A become progressively unrealistic as the environmental parameters of temperature and pH are pushed further away from the range of measured values (shaded zones). Specifically, the behavior of Model A is unacceptable at low temperatures and low pH values. Therefore, Model B will be proposed as the most reasonable relationship between in-stream nitrification and the factors of temperature and pH. Substitution of the parameters estimates found in Table 2 into equation (7) yields the final expression.

Model

KN(T.pH) = KA,(T=20,pH=7)*1.067 (r-2°) X [1.0 + 0.705*(pH -- 7.0)].

A

100.00

I00.00

66.67 0)

==

66.67

J~ 0

E 333 3

E 0

E

33.33

8.5

0.00

ternperoture ( oC )

0

Fig. 6. Extrapolation of Model A,

(8)

1330

Technical Note Model B

I00.00 ~00.00

66.67 6K67 o E

o E

"6

33.33 33.33

85

0.00

•

~'"peroture (*C)

0

Fig. 7. Extrapolation of Model B.

The value of fl (0.705) used in equation (8) agrees most favorably with the value of 0.642 previously determined from laboratory data presented in Fig. 1. Model B [equation (8)], while being functionally superior to Model A, has some of the same behavioral difficulties at conditions of low temperature and low pH. Model B appears to be overestimating in-stream nitrification rate values at low temperatures. This overestimation is probably due to the use of the simplified Arrhenius formulation [equation (1)] for reaction rate temperature correction. In addition, the linear relationship used to describe the effect of pH on in-stream nitrification rates is only valid up to a maximum pH of 8.5 and may be invalid for pH levels below 6.0. Therefore, equation 8 should only be applied with the following constraints: (a) 10°C ~< T ~< 30°C and (b) 6.0 ~< pH ~< 8.5. Figure 8 shows the application of equation (8) to the data originally presented in Figs 3, 4 and 5. The values plotted in Fig. 8 are baseline in-stream nitrification rate coefficients which have been corrected to a reference temperature of 20°C and pH equal to 7.0. The mean value of KN(T=20,pH=7)is 26.0 kg 02 day -l h -1. The uncertainty of the calculated mean (standard error of the mean, a/x/n) is only 0.97 kg 02 day-J h-~ or 3.8% of the mean. This zero-order in-stream nitrification rate coefficient should remain constant with respect to time, but Fig. 8 shows that a certain degree of variability still persists. There are many sources of probable error which

could account for the degree of remaining variation in corrected nitrification rates plotted in Fig, 8. The most likely sources of error include: (a) field measurement error (flow, flow time, DO, pH and temperature) (b) laboratory measurement error (nitrogen species) (c) model error. The amount of random error associated with field and laboratory measurement will result in a certain degree of uncertainty for each value of calculated in-stream nitrification rate shown in Figs 3 and 8. Model error can be defined as the failure of the applied mathematical construct to simulate true system behavior. Classic sources of modeling error include assumptions regarding the lack of temporal (steady state) and spatial (uniform) variations. A simple sensitivity analysis was conducted to estimate the effect of field and laboratory measurement error on in-stream nitrification calculation. Computed nitrification rate coefficients were found to be most sensitive to variation in ammonia-N concentration. An error scenario was constructed by assigning a _ 5% error in ammonia-N measurement which resulted in a + 3 9 % error in calculated in-stream nitrification rate coefficients. The error bars shown in Fig. 8 correspond to this error scenario, with only one bar not intersecting the mean value. The relatively large degree of nitrification rate sensitivity is a result of three contributing factors. First, ammonia-N con-

Technical Note

1331

60

7TI II

7,, 50 ~ 4o

!

I

30

Ill

o

c 0

20

o u 'r"

10

.

.

.

.

.

li

i 12

.

.

.

.

.

i

.

.

.

.

.

18

i

.

.

.

.

.

24

i

.

30

.

.

.

. 36

Time of day

Fig. 8. Baseline in-stream nitrification rate variation.

centrations in this reach (Reach 3, Survey 3) were quite high, with an average of 4 . 2 8 m g N 1 -t. Secondly, the nitrite-N concentration was held constant which resulted in the rate o f a m m o n i a - N change being multiplied by 4.33 mg O2/mg N H ~ - N to obtain the reported nitrification values. Finally, the small travel time (1.37 h) accentuated the impact of nitrogen species measurement error on nitrification rate computation. Model error will result in erroneous patterns or trends in the computed values. Figure 8 shows a lingering sinusoidal variation which implies the existence of model error. Two possible sources of modeling error are: (1) assumption of time invariant (steady state) travel times and (2) assumption of steady state zero-order reaction kinetics. A constant travel time for each reach was assumed to apply over the entire duration of each survey. Figure 2 indicates a strong sinusoidal variation of stream volumetric flow rate which will affect the travel time for all reaches. Unfortunately, there was an insufficient quantity of data to allow for the development of a rigorous functional relationship between flow regime and travel time. A time invariant, zero-order reaction rate coefficient was utilized to describe the in-stream removal of carbonaceous biochemical oxygen demand (CBOD). This assumption is appropriate for situations characterized by a steady population of microorganisms under high substrate concentrations. The aforementioned fluctuation of the wastewater treatment plant effluent discharge caused a definite degree of fluctuation in the bulk fluid CBOD concentration. In addition, it may have resulted in a cyclical variation of the bulk fluid heterotrophic microbial population. Neglecting the impact of this possible CBOD variation on the measured dissolved oxygen

concentrations would result in the calculation of an erroneous cyclical pattern for in-stream nitrification. The identified sources of modeling error could have both contributed to the small degree of lingering sinusoidal variation in computed nitrification rates. The amount of unexplained variation presented in Fig. 8 is rather small and mostly contained within the expected uncertainty due to field and laboratory measurement error. The development and subsequent utilization of equation (8) is therefore assumed to be valid within the constraints of unavoidable model and measurement error. A "complete validation" of Model B was not possible due to the limited fluctuation of stream temperature and pH. The shaded regions in Figs 6 and 7 show the range of observed temperature variation to be from 13.5 to 27.5°C with pH changes from 6.75 to 7.65. This limitation of system variation resulted in the inability to statistically differentiate Models A and B. A more extensive validation of the predictive capabilities of equation (8) will require the collection and analysis of data from stream systems operating beyond the range of conditions reported in this paper. SUMMARY

AND

CONCLUSIONS

Two models were proposed to explain the diel variation of in-stream nitrification as a function of temperature and pH. Statistical analysis of a rather extensive data base showed the significant impact of pH on calculated in-stream nitrification rates. Results of the statistical analysis proved inconclusive when trying to evaluate the functional superiority of Model A [equation (4)] vs Model B [equation (7)]. Three dimensional graphical extrapolations of each model indicated that the behavior of Model A was un-

1332

Technical Note

acceptable in regions of low temperature and low pH. Equation (8) (Model B with associated parameter estimates) was finally proposed as a reasonable relationship between in-stream nitrification and the environmental parameters of temperature and pH. Nitrification rate coefficients have traditionally been reported at a reference temperature of 20°C. The results of this study have reinforced the significant impact of pH on in-stream nitrification. It is therefore important to consider both temperature and pH when calculating a baseline nitrification rate. A reference temperature of 20°C and pH value of 7.0 have been utilized to define the environmental conditions for determination of a baseline in-stream nitrification rate. It is hoped that the use of expressions like equation (8), which incorporate both temperature and pH, will result in improved estimation and application of in-stream nitrification rates.

REFERENCES

Friedman A. A. and Schroeder E. D. (1972) Temperature effects on growth and yield of activated sludge. J. Wat. Pollut. Control Fed. 44, 1433-1442. Haug R. T. and McCarty P. L. (1972) Nitrification with

submerged filters. J. Wat. Pollut Control Fed. 44, 2086-2102. Huang C. S. and Hopson N. E. (1974) Nitrification rate in biological processes. J. envir. Engng Div. Am. Soc. cir. Engrs 100, 409--422. Kholdebarin B. and Oertli J. J. (1977) Effect of pH and ammonia on the rate of nitrification of surface water. J. War. Pollut. Control Fed. 49, 1688-1692. Sayigh B. A. and Malina J. F. Jr (1978) Temperature effects on the activated sludge process. J. Wat. Pollut. Control Fed. 50, 678~87. Schneiter R. W. and Grenney W. J. (1983) Temperature corrections to rate coefficients. J. envir. Engng Div. Am. Soc: cir. Engrs 109, 661--667. Stratta J. (1981) Nitrification Enhancement Through pH Control with RBCs. Thesis, presented to the Pennsylvania State University, at University Park, Pa, in partial fulfillment of the requirements for the degree of Doctor of Philosophy. Thornton K. W. and Lessem A. S. (1978) A temperature algorithm of modifying biological rates. Trans. Am. Fish. Soc. 107, 284--287. Warwick J. J. and McDonnell A. J. (1985a) Simultaneous in-stream nitrogen and D.O. balancing. J. envir. Engng Div. Am. Soc. cir. Engrs 111, 401-416. Warwick J. J. and McDonnell A. J. (1985b) Nitrogen accountability for fertile streams. J. envir. Engng Div. Am. Soc. cir. Engrs 111, 417-430. Wild H. E., Sawyer C. N. and McMahon T. C. (1971) Factors affecting nitrification kinetics. J. Wat. Pollut. Control Fed. 43, 1845-1854.