Formulation and testing of a novel river nitrification model

Ecological Modelling 220 (2009) 857–866

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Ecological Modelling journal homepage: www.elsevier.com/locate/ecolmodel

Formulation and testing of a novel river nitrification model James J. Pauer a,∗ , Martin T. Auer b a

Z-Tech, an ICF International Company, USEPA Large Lakes Research Station, 9311 Groh Road, Grosse Ile, MI 48138, USA Department of Civil and Environmental Engineering, Michigan Technological University, 863 Dow Environmental Sciences and Engineering Building, Houghton, MI 49931, USA b

a r t i c l e

i n f o

Article history: Received 18 July 2008 Received in revised form 9 December 2008 Accepted 10 December 2008 Available online 29 January 2009 Keywords: Nitrification Water column Benthic River Mathematical modeling

a b s t r a c t The nitrification process in many river water quality models has been approximated by a simple first order dependency on the water column ammonia concentration, while the benthic contribution has routinely been neglected. In this study a mathematical framework was developed for sediment bed nitrification based on mass transfer theory and Monod bacterial growth kinetics. The model describes ammonia transport across the boundary layer and consumption within the biofilm to quantify the overall nitrification flux. Model results suggest that nitrification is usually controlled by the boundary layer thickness, and we estimated a nitrification velocity range between 0.14 and 0.97 m d−1 , assuming typical boundary thicknesses of 0.1–1.0 mm. These ranges compared favorably with reported literature values, including our own measurements. The model was applied to several river systems of different depths where nitrification rates and river depths were available. Assuming that nitrification is exclusively a benthic process, the average velocity of all the rivers evaluated was 0.85 m d−1 (r2 = 0.72). © 2009 Elsevier B.V. All rights reserved.

1. Introduction The ammonia level in lakes and rivers is of water quality concern because of its role in dissolved oxygen depletion (O’Connor, 1967; Brown and Barnwell, 1987), stimulation of algal growth (Welch, 1992; Arhonditsis and Brett, 2005) and toxicity to aquatic life (USEPA, 1985). Nitrification is an important sink in the biogeochemical cycle of ammonia and oxygen and may serve to mediate these levels in aquatic systems. Nitrification kinetics are routinely incorporated in surface water quality models. Most commonly, the process is simulated using first-order kinetics (DiToro and Connolly, 1980; Bowie et al., 1985; Brown and Barnwell, 1987; Chapra, 1997; Pelletier and Chapra, 2005; Kannel et al., 2007) with the rate of nitrification proportional to the water column (bulk liquid) ammonia concentration: V

dS = −Vk1 S dt

(1)

where S is the water column or bulk liquid substrate concentration (g m−3 ); T the time (d); k1 the first order rate constant (d−1 ); V is the water volume (m3 ). However, field studies in rivers and lakes have shown that nitrifier populations are orders of magnitude greater in the sediment than in the water column (Curtis et al., 1975; Hall, 1986), suggesting localization of the process at the sediment–water interface

∗ Corresponding author. Tel.: +1 734 692 7635; fax: +1 734 692 7603. E-mail address: [email protected] (J.J. Pauer). 0304-3800/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2008.12.014

(Kabelkova-Jancarkova, 2006). We have demonstrated in our work on Onondaga Lake and the adjoining Seneca River (a relatively deep system) that nitrifier densities and rates of nitrification are much higher in the sediment than in the overlying water (Pauer, 1996; Pauer and Auer, 2000). It also appears that most scientists are in agreement that nitrification in lakes and rivers occurs in the sediment or associated with suspended particles. (Brion et al., 2000; Féray and Montuelle, 2003; Butturini et al., 2000). A series of papers were published by the International Water Association (IWA) Task Group on River Water Quality Modeling “to create a scientific and technical base from which to formulate standardized, consistent river water quality models and guidelines for their implementation” (Rauch et al., 1998). This effort was intended to lead to the development of river water quality models that are compatible with the existing IWA Activated Sludge Models (e.g. Gujer et al., 1999) and can be readily linked to them. (Rauch et al., 1998; Shanahan et al., 1998, 2001; Reichert et al., 2001; Vanrolleghem et al., 2001). This framework included a general nitrification formulation of nitrifier growth and ammonia oxidation which can be applied to both the water column and sediment bed. They have also applied this model to a shallow stream using only streambed nitrification kinetics (Reichert, 2001). We could also find a few other studies where nitrification was modeled as a benthic process, once again for very shallow streams (Gujer, 1976; Garland, 1978). However, water quality models such as QUAL2E (Brown and Barnwell, 1987) and the updates QUAL2K (Chapra et al., 2005) and QUAL2Kw (Pelletier and Chapra, 2005), WASP (Ambrose et al., 1988; Wool et al., 2006), and CE-QUAL-W2 (Cole and Wells, 2006) which

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are extensively used to model oxygen and eutrophication in rivers, especially in the United States, continue to utilize first order water column nitrification. We believe that the use of first order water column nitrification kinetics is incomplete, mechanistically unsatisfying, and probably will introduce inaccuracy into model predictions. If the nitrification process is localized in the sediment bed, it is more appropriate to visualize the process as an ammonia flux across the sediment–water interface V

dS = −JA dt

(2)

where A is the benthic surface area (m2 ); J is the ammonia flux across the sediment–water interface (g m−2 d−1 ). Dividing Eq. (2) by V yields: dS J =− dt hwc

(3)

where hwc is the thickness of the water column (m). Whether viewed from the perspective of the water column or the sediment bed, the process is seen to be a first-order function of the water column ammonia concentration. The apparent success of this simple approach is somewhat surprising given the complexity of exchange processes at the sediment–water interface and the microbial processes which mediate these transformations. A few researchers have recognized parallels between biofilms in freshwater and fixed film theory as applied in wastewater treatment systems (Williamson and McCarty, 1976a; Rittmann and McCarty, 1978, 1981; Grady and Lim, 1980; Characklis, 1986; Characklis and Marshall, 1990). Application of fixed film theory in freshwater systems has, however, focused largely on sediment oxygen demand (Gantzer et al., 1988; DiToro et al., 1990; Nakamura and Stefan, 1994; Higashino and Stefan, 2005), with less attention devoted to nitrification (Gujer, 1976; Klapwijk and Snodgrass, 1982; Butturini et al., 2000). Here, we seek to identify a mechanistically satisfying and unifying concept of nitrification for application to rivers by (I) developing a benthic-based model derived from traditional fixed film theory; model output is used to propose an explanation for the apparent first-order behavior of nitrification in rivers and to suggest an approach to modeling nitrification, and (II) utilizing the model to reconcile the water-column and benthicbased approaches. 2. Model framework and solution techniques A biofilm is defined as a mixed population of bacteria occupying an extracellular matrix affixed to solid substrate (Breyers, 1993). Biofilms are complex and dynamic biological entities, and not all of their characteristics are amenable to mathematical analysis. Several models have been developed to describe substrate fluxes in biofilms. The concepts underlying these models, termed fixed film theory, have found their primary application in the field of wastewater treatment (Williamson and McCarty, 1976a,b; Rittmann and McCarty, 1978, 1981; Lau, 1990; Characklis and Marshall, 1990). These models form an appropriate framework for exploring the application of fixed film theory to freshwater systems. Benthic nitrification occurs within bacterial biofilms (slimes) attached to hard surfaces such as cobble stream beds or at the sediment–water interface of softer benthic material. These benthic biofilms, with a typical thickness of between a few hundred micrometers to around a millimeter (Zhang and Bishop, 1994; Williamson and McCarty, 1976b; Lau, 1990), can be idealized as having three spatial domains: (1) the bulk liquid (overlying water), (2) the bacterial biofilm (3) a boundary layer (thin water layer at the interface) separating the two (Fig. 1). The bulk liquid is charac-

Fig. 1. Idealized biofilm system showing the substrate concentration in the bulk liquid, boundary layer, and biofilm.

terized by turbulent flow conditions with no gradients in chemical concentration. The boundary layer is characterized by laminar flow with a marked concentration gradient resulting from poor internal mixing and mass transfer into the biofilm. The nitrification process is manifested in the water column by the disappearance of ammonia, usually with the attendant appearance of nitrate. Where the nitrification process is localized in the sediment bed, two phenomena govern the rate of removal of ammonia from the bulk liquid: mass transport across the boundary layer and consumption within the biofilm. Consumption within the biofilm is, in turn, influenced by diffusion within the biofilm and the rate of ammonia oxidation. The flux across the boundary layer can be described using Fick’s first law: Jbl = Dw

dSbl dzbl

(4)

where Jbl is the flux across the boundary layer (g m−2 d−1 ); Dw the diffusion coefficient in boundary layer (m2 d−1 ); Sbl the boundary layer substrate concentration (g m−3 ); zbl is the depth position in the boundary layer (m). If we assume that oxygen is not limiting (well oxygenated system) and there is no reaction (i.e., ammonia oxidation) in the boundary layer, a linear concentration gradient develops and the flux is given by (Williamson and McCarty, 1976a) Jbl =

Dw (S − Sb,0 ) hbl

(5)

where hbl is the depth or thickness of the boundary layer (m) and Sb,0 is the biofilm substrate concentration at the boundary layer interface (g m−3 ). The mass balance describing the rate of ammonia consumption in the sediment bed accommodates the effects of diffusion within the biofilm and of ammonia oxidation, a modeling approach termed diffusion with reaction (Williamson and McCarty, 1976a; Fogler, 1992): ∂2 Sb ∂Sb = Dc −R ∂t ∂z 2

(6)

b

where Dc is the diffusion coefficient within the biofilm (m2 d−1 ); R the rate of ammonia oxidation within the biofilm (g m−3 d−1 ); zb is the depth position in the biofilm (m). Assuming that ammonia is the only limiting substrate (an adequate supply of dissolved oxygen exists) and that the reaction is

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appropriately described by Monod kinetics, Eq. (6) can be written as:

Table 1 Base case model coefficients.

∂Sb Sb ∂2 Sb = Dc −k X Ks + Sb ∂t ∂z 2

Model coefficient

Value

Unit

Biofilm density, X Maximum substrate removal rate, k Half-saturation constant, Ks Boundary layer diffusion coefficient, Dw Biofilm diffusion coefficient, Dc Boundary layer thickness, hbl

35000 3.5 2.1 1.4 × 10−4 1.1 × 10−4 4 × 10−4

gDW m−3 d−1 g m−3 m2 d−1 m2 d−1 m

(7)

b

where k is the maximum substrate removal rate (gS gX−1 d−1 ); X the biofilm density (gDW m−3 ); Ks is the half-saturation constant (gS m−3 ). At steady state the substrate flux in the biofilm (Jb ) may be calculated by: 2

Dc

d Sb dzb2

=k

Sb X Ks + Sb

(8)

At steady state, all of the interfacial fluxes are equal: Jb,0 = Jbl = J and thus Eq. (8) may be solved in concert with Eq. (5) to develop a relationship between the substrate flux at the sediment–water interface (J) and the water column or bulk liquid substrate concentration (S). Eq. (8) is a second order non-linear differential equation with no analytical solution, but it can be solved using an iterative, numerical approach (Williamson and McCarty, 1976a). The second-order differential equation (Eq. (8)) is split into two first-order differential equations and solved using a numerical technique. The assumption that substrate is exhausted at some effective depth within the biofilm (incomplete penetration) permits specification of the two required boundary conditions: dSb = 0 and Sb = ı at zb = zb,e dzb where ı is a small, nonzero substrate concentration and zb,e is the effective depth (m). The numerical integration begins with an initial estimate for the effective depth (z = zb,e and Sb,z = ı) and proceeds upward toward the biofilm surface in small increments of zb . For each increment, initially assumed to represent zb,0 , the calculation yields values for Sb,0 and Jb,0 . The associated flux (Dc × dSb /dz) and a specified bulk liquid substrate concentration are used with Eq. (5) to calculate Sb,0 . The value of Sb,0 determined in this fashion is compared with the value of Sb,0 calculated numerically and the process continues iteratively until the two estimates of Sb,0 agree. The resulting concentration gradient (dSb /dz at the interface) is used to calculate a flux corresponding to each specified value of S. Eq. (8) can also be solved analytically for certain limiting cases (e.g. Ks  S and Ks  S) which are of interest in examining the behavior of the model. The full equation (Eq. (8)) can also be solved for the case of incomplete substrate consumption in the biofilm, a condition termed as thin or shallow biofilm (Pauer, 1996). 3. Model input The benthic nitrification model requires a variety of model coefficients describing mass transport in the boundary layer (Dw and hbl ), in the biofilm (Dc ), and substrate consumption (k, Ks , and X). Values are derived here through a survey of the wastewater treatment literature. Few studies yielding values for these coefficients have been conducted on freshwater systems; however, sources representing natural systems are favored here in selecting model inputs. The wealth of information available for wastewater treatment systems (Sharma and Ahlert, 1977; Mueller et al., 1980; Characklis and Marshall, 1990; Lazarova and Manem, 1995) represents the most common source of model inputs. Best estimates for each coefficient were compiled (Table 1) and collectively termed the base case in model simulations. Considerations addressed in selecting model coefficients are detailed below.

3.1. Diffusion coefficients and boundary layer thickness The diffusion coefficient applied for the non-turbulent boundary layer is set equal to the diffusion coefficient in water (Williamson and McCarty, 1976a). A value of 1.4 × 10−4 m2 d−1 was applied for the base case diffusion coefficient of ammonia (Williamson and McCarty, 1976b; Rittmann and Manem, 1992). The diffusion coefficient in the biofilm (Dc ) is expected to be less than that for molecular diffusion in water (porosity effects). Values for Dc have been determined experimentally (1.3 × 10−4 m2 d−1 : Williamson and McCarty, 1976b; 1.0 × 10−4 m2 d−1 : Rittmann and Manem, 1992); however, estimates are most commonly derived using a Dc /Dw ratio. In biofilms, the Dc /Dw ratio typically varies between 0.6 and 0.95 (Characklis and Marshall, 1990). A value of Dc = 1.1 × 10−4 m2 d−1 (80% of selected Dw value) was applied here for the base case scenario. Although ignored in some applications (Atkinson and Davies, 1974; Christiansen et al., 1995), it is generally accepted that the boundary layer exists and varies in thickness (hbl ) with the degree of turbulence or mixing (Williamson and McCarty, 1976a). The boundary layer is thought to be thinner (enhanced mass transport) in shallow, fast-moving streams and engineered systems (trickling filters) and thicker (reduced mass transport) in deep, slow-moving rivers and lakes. Thus boundary layer thickness has been estimated as a function of fluid velocity through the Reynolds and Schmidt numbers (Williamson and McCarty, 1976a; Grady and Lim, 1980; Gantzer et al., 1988; Zhang and Bishop, 1994). Secondary effects of bed characteristics (surface roughness) on turbulence (Gantzer et al., 1988; Jorgensen and Revsbech, 1985) complicate the calculation in lakes and rivers. De Beer et al. (1991) have measured boundary layers in freshwater cores using micro-probes. They reported values ranging between 0.8 and 1.2 mm. Jorgensen and Revsbech (1985) conducted similar experiments on sea water systems and reported values between 0.25 and 1.1 mm. In situ methods have been developed and applied in sea water systems and boundary layer depths between 0.1 and 1.0 mm have been reported (Santschi et al., 1983). A value as low as 56 ␮m has been reported in well mixed engineered films (Williamson and McCarty, 1976a). Based on the information from engineered and natural systems, an intermediate value of hbl equal to 0.4 mm was applied for the base case scenario. 3.2. Biofilm density and substrate consumption Biofilm density (X) is synonymous with biofilm biomass and in engineered systems is typically expressed as mass dry weight biofilm per unit biofilm volume (gDW m−3 ) (Characklis and Marshall, 1990). In natural systems (sediments, rock slimes, and soils), biomass is often expressed in terms of bacterial density (cells mL wet sediment−1 ) (Alexander and Clark, 1965; Curtis et al., 1975); however, it is not clear that this approach accurately characterizes biofilm biomass. Work with biofilm densities focuses primarily on engineered and synthetic films. A survey of the literature revealed only two estimates of biofilm density developed specifically for nitrifiers (Williamson and McCarty, 1976b; Rittmann and Manem, 1992). The average density from these stud-

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ies (X = 3.5 × 104 gDW m−3 ) was applied for the base case scenario. This value falls in the range of densities measured and reported for a variety of heterotrophic films (Characklis and Marshall, 1990). The rate of ammonia consumption (gS m−3 d−1 ) in the biofilm is calculated as the product of the biofilm density (X) and the maximum substrate removal rate (k, gS gX−1 d−1 ). The coefficient k may also be conceptualized in terms of the specific growth rate and the yield coefficient (/Y), a design convention common to engineered systems. Values for the maximum substrate removal rate (k) as high as 11.9 gS gX−1 d−1 (Castens and Rozich, 1986) and as low as 0.09 gS gX−1 d−1 (Shammas, 1986) have been reported; however, typical values for k range between 1.07 gS gX−1 d−1 (Knowles et al., 1965) and 5.7 gS gX−1 d−1 (Shieh and La Motta, 1979). A maximum substrate removal rate (k = 3.5 gS gX−1 d−1 ), an averaged value from several studies, was applied for the base case scenario. Values for the half-saturation coefficient for nitrification (Ks ) have been widely reported for both engineered (Williamson and McCarty, 1975; Keen and Prosser, 1987; Gee et al., 1990) and freshwater systems (Stratton and McCarty, 1968; Cooper, 1984, 1986). Experimental determination of the half-saturation coefficient has focused on nitrifiers in suspended growth. However, it is generally assumed that coefficient values differ little for the suspended growth and fixed film cases (Williamson and McCarty, 1976b). Half saturation values in natural systems typically range between 0.5 mg L−1 (Cooper, 1984) and 3.7 mg L−1 (Stratton and McCarty, 1968) which are similar to values for wastewater films (Williamson and McCarty, 1975; Keen and Prosser, 1987; Gee et al., 1990). An average value for the half-saturation coefficient (Ks = 2.1 mg L−1 ), calculated using data from natural and engineered systems, was applied for the base case scenario. 4. Modeling Given the uncertainty in model inputs, it is important to examine the sensitivity of the model and attendant interpretation to coefficient selection. Further, sensitivity analysis may be used to identify those mechanisms which drive the nitrification process, i.e. the observed ammonia flux at the sediment–water interface. The model may then be applied to establish which kinetic approach (reaction order) most accurately describes the process, seeking to explain the success of a first-order, water column based approach for simulating nitrification in lakes and rivers. Finally, simplifications of the model framework may be considered, leading to an approach with potential for widespread application to modeling nitrification in freshwater systems. 4.1. Sensitivity analysis Model results suggest that the disappearance of ammonia from the water column (manifestation of nitrification) is governed by mass transport across the boundary layer and by consumption within the biofilm. Assumptions regarding the relative importance of these processes are often applied to simplify the mathematics of modeling fixed films (boundary layer control: Gonenc and Harremoes, 1985; Nakamura and Stefan, 1994; biofilm consumption control: Siegrist and Gujer, 1985; Christiansen et al., 1995). As illustrated in Fig. 2, one may assume: • control by the boundary layer where consumption in the biofilm  than the flux across the boundary layer (i.e., instantaneous consumption at the interface, Fig. 2a); or • control by biofilm kinetic parameters when the flux across the boundary layer  than consumption in the biofilm (i.e., no external mass transfer resistance, Fig. 2b).

Fig. 2. Simplified cases of the idealized biofilm system to describe benthic nitrification velocities for (a) boundary layer control and (b) biofilm control.

The controlling process may be identified by using base case coefficients and calculating flux as a function of the bulk liquid ammonia concentration for these two cases. The case (biofilm or boundary layer control) with the lowest flux at a given ammonia concentration (i.e. the lowest slope) controls the nitrification process. Boundary layer control is simulated by setting the ammonia concentration at the biofilm interface (Sb,0 in Eq. (5)) equal to 0. Biofilm control is simulated by setting the ammonia concentration at the biofilm interface (Sb,0 in Eq. (8)) equal to the bulk liquid ammonia concentration (S). The results of these model calculations using base case coefficients are presented in Fig. 3. It is clear from this analysis that boundary layer parameters (Dw ; hbl ) control. In reality, the flux must be equal to or less than the controlling case, i.e. the unaltered base case (Fig. 3). Traditional sensitivity analysis, variation of model coefficients within specified bounds, provides additional insight into the question of controlling processes. Here, the bulk liquid ammonia concentration was specified (S = 1 mg L−1 ) and each of the biofilm and boundary layer coefficients was varied by ±50%. The resulting model output was then compared with the base case scenario (Table 2). Consistent with the conclusions developed above, boundary layer coefficients (hbl and Dw ) are seen to have the greatest influence on nitrification flux, with a response of 31–77%. Variation in biofilm coefficients (Dc , Ks , k, X) affect the nitrification flux by less than 6%. This further suggests that the base case nitrification

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Fig. 4. Base case benthic flux (solid line) as well as the ranges of fluxes at maximum and minimum values (dashed lines) for the boundary layer coefficients.

biofilm model have a small influence on the resulting nitrification flux (Pauer, 1996). 4.2. Model application

Fig. 3. Model predicted nitrification fluxes versus ammonia concentration for (a) boundary layer control, (b) biofilm control and (c) using the base case parameters.

flux is dominated by conditions in the boundary layer, i.e., external mass transfer resistance. The observation that the calculated flux is sensitive to boundary layer coefficients suggests that the issue of control may rest on selection of values for hbl and Dw . That is, for thinner boundary layers or greater diffusivity in the boundary layer, biofilm coefficients may have a greater impact. This was tested by setting hbl = 0.1 mm and Dw = 1.5 m2 d−1 . These are extremes in the range of reported values which serve to minimize the effects of boundary layer control (Fig. 4). Even here, the observation that the boundary layer controls nitrification flux remains valid. The nitrification flux was also calculated using a thin biofilm model (incomplete penetration within the biofilm) at different biofilm penetration depths. The results demonstrate that changes in the selected penetration depths of the thin

Application of a fixed-film benthic-based approach to modeling nitrification flux in lakes and rivers requires that a mass balance be performed on the biofilm, i.e. the sediment–water interface. Based on the solution for a biofilm at the two extreme cases (Ks  S and Ks  S), we know that the observed nitrification flux can range between zero and first order in the biofilm. However, insights gained through sensitivity analysis provide an opportunity which may markedly simplify application of these concepts. Because the model sensitivity analysis suggests that the boundary layer conditions control the nitrification flux, one would suspect that the process may be approximated using first-order kinetics (see Eq. (5)). Given that the fluxes at the bulk liquid–boundary layer and boundary layer–biofilm interfaces are equal at steady state and that ammonia concentrations at the biofilm interface are much smaller than those in the bulk liquid (Sb,0  S; essentially instantaneous consumption at the interface), Eq. (5) may be simplified to: J=

Dw S hbl

(9)

A plot of J as a function of S calculated for base case conditions yields a linear response (solid line in Fig. 4; R2 ∼ = 1) confirming the firstorder approximation suggested by Eq. (9). The observation that the term (Dw /hbl ) has units of velocity (m d−1 ) suggests an alternative expression: J = vS

(10) (m d−1 ),

Table 2 Model sensitivity to variation in base case model coefficients. Coefficient Biofilm X k Dc Ks

% change in calculated flux for base case coefficient + 50%

% change in calculated flux for base case coefficient − 50%

+4 +4 +4 −3

−6 −6 −6 +4

Boundary layer −31 hbl +40 Dw

+77 −46

estimated as the slope where v is a nitrification velocity of the solid line in Fig. 4, relating flux and the bulk liquid ammonia concentration. The term (Dw /hbl ) is a good approximation of / 0. v, but it yields a slight overestimate of the flux because Sb,0 = Some indication of the anticipated variability in v may be gained by repeating the calculation for values of Dw and hbl representing the range used in the previous sensitivity analysis (dashed lines: Fig. 4). The resulting range in v (0.14–0.97 m d−1 ) represents the expected variability associated with differing boundary layer thicknesses in slow- and fast-moving systems. This analysis offers an explanation for the apparent success of the first-order, water-column (bulk liquid) based approach commonly applied in modeling nitrification in lakes and rivers and

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presented previously as Eq. (3). By comparing Eqs. (3) and (10), note that:

Table 3 Reported river nitrification rates and depths.

v = hwc k

River

(11a)

a

This relationship is analogous to that between the liquid film mass transfer coefficient and the reaeration coefficient used in modeling transport across the air–water interface (Chapra, 1997). This further implies that there may a relatively narrow range in the nitrification velocity, sensitive primarily to boundary layer thickness, that is representative of a wide variety of natural environments and that the great variability in reported values of k1 may rather be a function of system-specific differences in depth rather than differences in nitrification kinetics. In order to confirm these observations, several systems have been evaluated for which both a nitrification rate and a depth are reported. 5. Reconciliation of benthic- and water column-based approaches for well-oxygenated rivers A large number of rivers have been studied for which nitrification rates have been reported (Miller and Jennings, 1979; McCutcheon, 1987); however, relatively little information is available for lakes (Bowie et al., 1985). A strikingly large range exists for the nitrification rate constant from 0.03 d−1 in deep rivers (Bansel, 1976) to 15.8 d−1 for shallow streams (Wezernak and Gannon, 1968). As expected, values for the rate constant were generally lower for lakes (deeper, less turbulence), ranging between 0.025 and 0.2 d−1 (Bowie et al., 1985). Table 3 summarizes rate information and selected environmental conditions for various river-based studies. Values reported here are limited to those for which attendant depth information was available. As stated previously, the mass transport and the associated flux may be quantified through a nitrification velocity, introduced previously as v in Eq. (11a). This equation can be rewritten as k=

v hwc

* a b c d e f g h

(11b)

i j

or expressed as logs: log k = log v − log hwc

Mine Brook Bargeb * Upper Mohawkb * Upper Mohawkb * Upper Mohawkb Middle Mohawkb Lower Mohawkb Seneca Riverc , d Trinitye Ohiob Flintb , f * Shenandoahg , h * Shenandoahg , h Holstoni Grandb , f Chattahoockeee , j Stillk , l Trukeeb , f Willamettem , n Anacostiao Speedp Oostanaulan Sweetwatern Tracen Mudn Orouan Waiotapun Waiohewan Big Blueb South Chickamaugan

k

(12)

where the slope in a plot of k versus 1/hwc (Eq. (11b)) and the intercept in a plot of log k versus log hwc (Eq. (12)) provide estimates of the mass transfer velocity (v). Nitrification rates in rivers are usually determined through observations of in situ changes in nitrogen concentrations. Although the rate is expressed as a water column coefficient (k, d−1 ), the method is in fact measuring the overall rate of nitrification (water column plus sediment bed). If it is true that nitrification in rivers is predominantly a benthic-based process, then Eqs. (11b) and (12) offer an opportunity to isolate depth effects and quantify the mass transfer velocity associated with benthic-based nitrification. Values for the nitrification rate constant (k) are transformed to mass transfer velocities (Eqs. (11b) and (12)), and the relationships between k and hwc are illustrated in Fig. 5a and b. Because the river depth and nitrification rate coefficient data are both log-normally distributed, we believe that the value of 0.85 m d−1 based on Eq. (12) (Fig. 5b) is the better estimate of the mass transfer velocity. The slope (and thus the estimated transfer velocity) of Fig. 5a is to a large extent defined by high nitrification rate constants of three rivers, where their influence is reduced during the log transformation. Fig. 6 shows the 95% confidence intervals (CI) for the log–log plot. The back-transformed 95% CI for v is [0.64, 1.13] (with the central estimated value for v being 0.85). Fig. 7 shows a plot of nitrification rate constant versus depth with back-transformed regression line and 95% CIs (prediction intervals).

l m n o p

Rate coefficient (k; d−1 )

Depth (m)

8.0 0.25 0.25 0.3 0.25 0.30 0.30 0.05 0.51 0.25 1.53 1.25 0.2 0.23 1.9 0.25 0.7 2.4 0.7 0.13 2.3 0.8 0.8 2.2 0.50 6.7 2.8 5.9 0.12 6.6

0.2 3.9 3.66 0.96 2.51 3.81 4.25 6.4 1.53 8.15 0.66 0.6 1.74 1.3 0.58 1.5 0.64 0.51 1.6 4.0 0.43 0.61 0.46 0.46 1.0 0.25 0.61 0.30 1.26 0.84

Reaches of the river. Tuffey et al. (1974). Bansel (1976). Canale et al. (1995). This study. McCutcheon (1987). O’Connor and Di Toro (1970). Deb and Bowers (1983). Deb (1995). Ruane and Krenkel (1977). Miller and Jennings (1979). Curtis (1983). Mauger (1995). Dunnette and Avedovech (1983). Cooper (1986). Sullivan and Brown (1988). Gowda (1983).

Transformation of the water column-based nitrification rate coefficients to benthic-based mass transfer velocities substantially reduces the inter-system variability in estimated rates, suggesting that the wide range observed reflects an artifact of the mode of expression (depth-averaging) rather than intrinsic differences in the rate of nitrification. This point is further illustrated in Fig. 6 where the mass transfer velocity is plotted as a function of depth. The average mass transfer velocity estimated from field data (0.85 m d−1 ; Fig. 5b) is comparable to that determined using the benthic-based model for the base case scenario (0.31 m d−1 ). The field estimates are largely bracketed by simulated velocities representing extremes in boundary layer thickness (0.14 and 0.97 m d−1 ; solid lines in Fig. 8). Nitrification velocities calculated from rate coefficients for very shallow systems (<0.5 m) are notably higher than the maximum value calculated using the benthic model. This is probably because of thinner boundary layers in these usually turbulent shallow rivers. Santschi et al. (1983) proposed a boundary layer of 25 ␮m for systems with “very high turbulence”. Application of this boundary layer thickness to the benthic-based model, yields a nitrification velocity of 1.8 m d−1 (dashed line in Fig. 8). Contrary to the conclusion which might be drawn from a cursory inspection

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Fig. 7. Nitrification rate versus depth (based on Eq. (12)) with the back transformed regression line and 95% confidence intervals (prediction intervals).

Fig. 8. Nitrification velocities versus river depth of a number of rivers. The solid lines represent the minimum and maximum model predictions for “typical” rivers, and the dashed line represents the velocity for very turbulent rivers. Fig. 5. Nitrification coefficient versus river depth for (a) rate versus 1/depth (Eq. (11b)) and (b) log rate versus log depth (Eq. (12)).

of field estimates of volumetric nitrification rate coefficients, this analysis suggests that a comparatively narrow range of mass transfer velocities may satisfactorily represent the nitrification process in natural systems. Even following depth-transformation of water column-based rates, a relationship between depth and the mass transfer velocity appears to persist. Fig. 9 illustrates the relationship (R2 = 0.56)

Fig. 6. Log (nitrification rate) versus log (depth) based on Eq. (12). Dashed lines show the 95% confidence intervals.

between v and hwc which holds for systems <1.5 m in depth. As hypothesized above, this functionality may represent a boundary layer effect where shallow rivers tend to be more turbulent (higher degree of mixing) and therefore have thinner boundary layers and higher velocities.

Fig. 9. Nitrification velocities versus depth for shallow rivers (depth < 3 m).

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Further verification of the mechanistic and empirical models developed here is limited by the availability of field nitrification data that include paired measurements of the rate constant and system depth. In many cases, rate coefficients are measured at one or two sites on the river and an average depth or a range of depths for the entire system are reported (see Table 3). The variety of in situ measurement techniques employed and differences in other environmental conditions such as temperature (Kors et al., 1998), oxygen and suspended solids concentrations (Xia et al., 2004) impart additional uncertainty to the analysis. For these reasons, the success of this analysis in reconciling water column and benthic-based approaches to nitrification (Fig. 5) appears particularly striking. It is known that river velocity and surface roughness also influence turbulence, and it is believed that incorporation of these effects in the model would improve the accuracy of predictions. 6. Discussion Traditionally, an empirical approach has been used to model nitrification in lake and river sediments. Model input parameters are usually obtained from a “best fit line” (regression model) of observed laboratory or field data. The sediment bed model developed here relates benthic nitrification to conventional fixed film theory. Sensitivity analysis demonstrated that the model is most responsive to the boundary layer coefficients (Dw , hbl ) and is thus controlled by external mass transfer resistance. Because mass transport across the boundary layer is a function of mixing and turbulence (Williamson and McCarty, 1976b), it is expected that shallow systems with enhanced velocities and turbulences (rapid flowing rivers) will have higher rates of nitrification than deeper, quiescent systems such as deep lakes. It is therefore important but difficult to mimic in situ conditions in terms of external mass transfer resistance when experimentally measuring (laboratory microcosm experiments) nitrification fluxes. The rate can easily be over-estimated, if the flux across the boundary layer depth is enhanced by stirring a sediment core (which is often done to ensure oxygen saturation). Core experiments probably overestimate the in situ rate for deep lakes, while these experiments likely underestimate the value for fast moving, turbulent streams. Model simulations demonstrated that benthic nitrification can be approximated by a first order bulk water concentration dependency, with an estimated velocity (v) of 0.31 m d−1 for the base case scenario. These values can range between 0.14 and 0.97 m d−1 depending on the variability associated with differing boundary layer thicknesses in slow- and fast-moving systems (Fig. 4). The first order dependency of the benthic nitrification velocity on the bulk water ammonia concentration is consistent with observed first order nitrification kinetics which have frequently been used in lake and river models. This relationship can provide a possible explanation for the apparent successful application of the first order water column approach, in the face of growing evidence that nitrification is a benthic-based, rather than a water column process. Nitrification rates in rivers are usually expressed as a water column process, utilizing first order water column kinetics. It is particularly noticeable in surveying the literature that there is a large range in the reported nitrification rate coefficients (Table 3). It seems that the higher rate coefficients have been associated with shallow streams, and lower values have been reported for deeper systems. These observations were further investigated for case studies where both the nitrification rate and system depth have been reported. A strong relationship was found between the depth of the system and the nitrification rate (Fig. 5a and b). This good correlation (R2 = 0.70; log–log plot) with relatively little scatter was somewhat surprising, because literature values were

obtained under such diverse conditions (temperature, velocities, bed characteristics, etc.) and using a variety of methods. The calculated benthic nitrification velocity (0.85 m d−1 ) compares well with estimates from the benthic model (base case = 0.31 m d−1 , minimum = 0.14 m d−1 , maximum = 0.97 m d−1 ) and the limited number of reported values (0.4 and 2.2 m d−1 : Cooper, 1986). The velocities for very shallow rivers were higher than the benthic model prediction (Figs. 8 and 9), and an additional dependency (R2 = 0.56) on depth has been noted (Fig. 9). It seems therefore that there is a higher order dependency of the reported nitrification rate (k) on depth. We believe that this work should be taken into consideration when formulating nitrification equations for river water quality models. Traditionally nitrification in nitrogen, oxygen and eutrophication models has been expressed as a first order water column ammonia dependency (Kannel et al., 2007; Lindenschmidt, 2006; Wool et al., 2006; Cole and Wells, 2006; Dilks et al., 1992), as follows: Nitrification = f (DO)f (T )knCNH4

(13)

where f(DO) is the low dissolved oxygen concentration correction term; f(T) the temperature correction term; kn the first order rate coefficient (time−1 ); CNH4 is the water column ammonium concentration (mass volume−1 ). In some modeling frameworks, nitrification was formulated as a two-step process (Van Orden and Uchrin, 1993; Summers et al., 1991; Brown and Barnwell, 1987; Yang and Sykes, 1998) with the ammonia first being oxidized to nitrite (first order dependency on the water column ammonia concentration) and the nitrite further oxidized to nitrate (first order dependency on the water column nitrite concentration). However, we propose a nitrification formulation that is dependent on the water column ammonia concentration and river depth and that uses nitrification velocity rather than first order rate coefficient: Nitrification =

v hwc

CNH4

(14)

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