A simple model of stream nitrate concentrations in forested and deforested catchments in Mid-Wales

Journal of

Hydrology ELSEVIER

Journal of Hydrology 158 (1994) 61-78

[31

A simple model of stream nitrate concentrations in forested and deforested catchments in Mid-Wales William T. Sloan*, Alan Jenkins, Andrew Eathera11 Institute of Hydrology, Wallingford, OXIO 8BB, UK

(Received 14 November 1992; revision accepted 18 December 1993)

Abstract A model is developed specifically for simulating the nitrate concentrations in a stream at approximately weekly intervals in an upland forested and a moorland catchment. It is constructed on the basis of observed nitrate concentrations in rain water and in two streams, the Hafren and the Hore, at Plynlimon, Mid-Wales, where long data records exist. The Hore catchment has recently undergone extensive deforestation. A simple regression model relating temperature to stream nitrate concentrations was capable of simulating the seasonal fluctuations in nitrate concentration observed in the Hafren. However, this ignores the influx of nitrate through wet deposition and is incapable of simulating land-use change. The regression model was developed into a simple dynamic model which includes a deposition term and a biomass indicator. The extended Kalman filter algorithm was used to estimate the optimum values of the parameters and to assess the model structure. The model was applied to both catchments, and the fit between observed and simulated nitrate concentrations at the Hafren was good. At the Hore, the model was able to capture the major changes in nitrate concentration through the deforestation and replanting phases although detailed short-term dynamics were not well represented. Finally, the model is related, speculatively, to processes which are known to occur in most catchments. This simple model is intended as a step towards the development of similar but more comprehensive catchment models of stream nitrogen dynamics.

1. Introduction It has long been a s s u m e d t h a t n i t r o g e n in u p l a n d c a t c h m e n t s is tightly cycled a n d essentially s u p p l y - l i m i t e d . T h a t is, u p l a n d v e g e t a t i o n c o m m u n i t i e s w o u l d readily c o n s u m e all a d d i t i o n a l n i t r o g e n which m i g h t be supplied f r o m the a t m o s p h e r e . * Corresponding author. 0022-1694/94/$,07.00 © 1994 - Elsevier Science B.V. All rights reserved SSD1 0022-1694(94)0245 I-G

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W.T. Sloan et al. / Journal o f Hydrology 158 (1994) 61-78

This assumption stemmed largely from observations of surface water chemistry which showed little or no nitrate and ammonia content. In these upland areas there is little nitrogen addition to the terrestrial catchment as fertiliser, except perhaps where plantation forestry has been introduced, and certainly no point source effluents high in nitrogen. More recently, however, extensive surface water and rainfall surveys have identified areas where both high nitrogen deposition (Warren Springs Laboratory, 1990), in the form of nitrate and ammonia, and relatively enhanced nitrogen runoff (Battarbee et al., 1992), in the form of nitrate, occur. It is clear, therefore, that the deposition of nitrogen oxides as an acidifying agent must be considered within the framework of political negotiation on reductions of atmospheric emissions. To this end, the concept of critical loads (Nilsson and Grennfelt, 1988) has been proposed as the basis for future negotiation (Bull, 1992), but whilst empirical and dynamic models exist for calculating critical loads of sulphur (Henriksen et al., 1992), methods for calculating nitrogen critical loads are crude applications of the principles of long-term equilibrium (Kamari et al., 1992). Estimating the impacts of nitrogen deposition on catchment ecosystems is complicated by the wide variety of forms of nitrogen in the environment and the pathways these nitrogen compounds take as they travel from catchment surface to outlet. The leaching of nitrate to surface waters is dependent on the relative rates of biologically mediated processes of transformation and uptake and on the input flux (Aber et al., 1989). The biological processes are driven largely by temperature, producing large seasonal fluctuations in nitrate fluxes from catchments, but they are also mediated by soil wetness. The hydrological response of a catchment is also important in so far as water provides the transport mechanism and so largely determines the short-time or storm-period variability of nitrate concentration at the catchment outflow. Shortterm pulses of nitrate have been observed at many locations, particularly in association with snowmelt (Tranter et al., 1986; Jenkins et al., 1993) and drought (Burt et al., 1988; Reynolds et al., 1992). Attempts at modelling this system have been made on a variety of scales ranging from within-forest stand or plot scale (Addiscott and Whitmore, 1987; Johnsson et al., 1987) to catchment scale (Jury, 1982; Rastetter et al., 1991). Most plot-scale models have been developed for the purpose of agricultural management. The heterogeneous nature of the soil, temperature and moisture are conventionally handled using a distributed representation of the catchment, and the physics and chemistry of the nitrogen processes are explicitly incorporated as a set of rate equations tied together within the boundary conditions of an overall mass and charge balance. As a result, such models tend to rely on a large number of variables which must be measured in the field or derived from laboratory experiments. In theory these 'heavily' parameterised models could be applied on a catchment scale. However, in the absence of good field observations of the variables and underlying theories, a simpler representation would seem both appropriate and timely. The approach taken here does not attempt to separate the various processes within the terrestrial nitrogen cycle. Knowledge of how the concentration of nitrate in a stream varies seasonally along with how it reacts to a change in land use are used to develop the model structure.

W.T. Sloan et al. / Journal of Hydrology 158 (1994) 61-78

63

In order to justify this approach, it is worth considering how some of the processes which add and subtract nitrate have been treated by previous modellers. Most models (Addiscott and Whitmore, 1987; Baraclough and Smith, 1987; Johnsson et al., 1987; Vereecken et al., 1990) are defined, either for a series of steady states or continuously, by contributions from the various nitrogen processes. The magnitude of the contribution to the leachate from each process is determined by parameters pertaining to the rate at which they occur. Mineralization of organic nitrogen and nitrification of reduced nitrogen forms (particularly ammonium) add nitrate to the system. They are dependent, inter alia, on the size of various organic stores, microbial population, temperature and the organic carbon cycle. A comprehensive model should involve approximations to all of these although this has not been achieved, even on a plot scale. Laboratory experiments (Stanford and Smith, 1972; Tabatabai and A1-Khafaji, 1980; Addiscott, 1983) have resulted in simple empirical relationships for mineralization and nitrification. In general, the amount of nitrogen produced in time t, Nt, can be expressed by a simple zero-order relationship N t = kt. Addiscott (1983) showed that rate constants for several soil types were well related to the absolute temperature by the Arrhenuis equation. Addiscott and Whitmore (1987) use this type of relationship in their leaching model. Hence nitrification and mineralization are continuously adding nitrate to the system at a temperature-dependent rate. More nitrate is added in the summer than in the winter, when the temperature is lower. Uptake by the biomass continually removes nitrate from the system. The rate at which this occurs has been quantified and various models have been proposed. Most of these require extensive knowledge of vegetation type, availability of nutrients, Forest

J

Felled Area

mplingpoints I Rain River Severn Catchment

C) Stream

LowerHafren

/

LowerHore Fig. 1. The studycatchmentsin the Plynlimonresearcharea, Mid-Wales.

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W.T. Sloan et al. / Journal of Hydrology 158 (1994) 61-78

temperature and solar radiation. Underlying all of these models, however, is the principle that uptake is proportional to the rate of transpiration (Feddes and van Wijk, 1990).

2. Study sites and data

collection

The Afon Hore and Afon Hafren streams drain two adjacent upland catchments at Plynlimon, Mid-Wales (Fig. 1). A p r o g r a m m e of afforestation began in both catchments in 1937. Between 1937 and 1964 conifers, predominantly Sitka spruce (Picea sitchensis), were planted on the lower slopes of both catchments, covering approxi-

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Year Fig. 2. Temporal variation in stream temperature at the Afon Hafren (a), and observed and simulated stream nitrate concentrations. Simulated concentrations are derived from the model run with parameter values held constant at the optimal EKF estimate (b).

65

W.T. Sloan et al./JournalofHydrology158 (1994) 61-78

(a)~lS! o) o O

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mately 50% of the Hafren catchment and 77% of the Hore catchment. Clear felling of the lower half o f the Hore catchment began in 1985, resulting in the removal of approximately 50% of the forest within 4 years. Soon after harvesting, the slopes were replanted with juvenile Sitka spruce. Stream water and rainfall have been sampled for chemical analysis at weekly intervals since May 1983 (Neal et al., 1992a). Rainfall and flow volumes have also been monitored continuously during this period and annual rainfall averages approximately 2500 mm, with evapotranspirational losses of 500 mm year -I for the Hafren and 6 5 0 m m y e a r i for the Hore. The hydrological and hydrochemical responses of both streams were similar prior to deforestation of the Hore catchment (Newson, 1976; Kirkby et al., 1991). Observed stream nitrate concentrations and stream temperatures for both sites are given in Figs. 2 and 3. Rainfall and nitrate concentrations are shown in Fig. 4. In both streams the nitrate concentrations are always greater than zero, indicating nitrogen saturation (Abet et al., 1989), and there is a distinct seasonal variation in the nitrate concentration whereby more nitrate is leached in the winter when the soil and stream temperatures and transpiration rates are low than in the summer when they are higher. This seasonal variation can be

W.T. Sloan et al. / Journal o f Hydrology 158 (1994) 61-78

66

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W.T. Sloan et al. / Journal of Hydrology 158 (1994) 61 78

67

related to stream temperature by a simple linear regression (Fig. 5): Stream nitrate (mg-NO31 -I) = -0.119 x Temp ( ° C ) + 2.18 The root mean square error between this regression line and the observed stream concentrations is 0.5 mg-NO31-1. Mean nitrate concentration in the Afon Hafren is 1.3 mg-NO31 -l and the amplitude of the fluctuation is approximately 0.5 mg-NO31-1 . In the Afon Hore prior to deforestation, mean nitrate concentration and amplitude of fluctuation are similar at 1.5 and 0.5 mg-NO31-1 , respectively. During the period of deforestation, mean annual concentrations increased to a maximum of 4.6mgNO31 I and subsequently decreased to 4.0 mg-NO31-1 by 1989. The amplitude of seasonal fluctuation post-deforestation is approximately double that prior to deforestation. There is no significant correlation between short-term variations in concentrations of either nitrate or total inorganic nitrogen (NO3 + NH4) in rain and stream water even when the seasonal fluctuation in stream water concentration is removed, and the weekly influx and efflux are rarely in balance. However, the annual influx and efflux of nitrate were approximately in balance pre-felling (Neal et al., 1992b). This was anticipated, as variations in the stream concentration of stable isotopes and chloride, which are chemically conserved, is damped compared with rainfall. This suggests that only a minor portion of the water which enters the catchment during a storm event travels directly to the stream (Neal and Rosier, 1990).

3. The model

The model is continuously defined by the first-order differential equation, dN dt

= k I ( Q R N R -- Q N ) + d ( - k 2 T

+ I(k3 T - k4) )

(1)

where N = n i t r a t e concentration in the stream (mg-NO31-1); QR =rainfall (mm day-l); NR = nitrate concentration in the rainfall (mg-NO3 l-l); Q = stream flow (mmday l); T = stream temperature (°C); I = a positive index indicating changes in the biomass; k 1 = c o n s t a n t mm l; k2 = c o n s t a n t mg-NO3(l°C)-l; k 3 = constant mg-NO 3 (I°C)-I; k 4 = constant mg-NO 31-1. Changes in the biomass index, L are assumed to be proportional to changes in the biomass. So if there was no significant vegetation change in the catchment during the period of the simulation, the value of I would remain constant. If, however, the biomass doubled, the magnitude of I would double. The first part of Eq. (1) describes the contribution of nitrate to the system by atmospheric deposition and its removal by leaching. The form of this expression is typically used in mass balance models assuming a completely mixed tank; its inclusion is prompted by the fact that annual fluxes pre-felling are in balance. The second part of Eq. (1) describes the combined effects of the biologically mediated processes operating within the terrestrial parts of the catchment. It is dependent on temperature and biomass change index. The structure is derived

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W.T. Sloan et al. / Journal of Hydrology 158 (1994) 61-78

from three observed phenomena in upland forested and moorland catchments (Likens et al., 1978; Stevens and Hornung, 1987; Adamson and Hornung, 1990; Neal et al., 1992a): first, a seasonal oscillation in the concentration of nitrate in the stream which appears to be inversely proportional to temperature; second, an increase in the amount of nitrate leached during and after a period of deforestation; third, after such an event the amplitude of the oscillation increases. These are certainly evident in the data from the Afon Hafren and Afon Hore. If I is held constant for the period of the simulation, indicating no disruption in the biomass, then (-k2 + Ik3) remains constant. Hence the contribution to nitrate concentration by this part of the equation is proportional to the temperature. If I is reduced, indicating a reduction in the biomass, (-k2 + Ik3) becomes more negative and -Ik4 becomes less negative. Hence the amplitude of the seasonal oscillation increases and there is an overall increase in the mean nitrate concentration in the stream. Clearly, this model structure cannot be used to separate the processes of uptake and mineralisation so that quantitative estimates can be made and compared. Empirical estimates of the rates at which the processes of uptake, mineralization and nitrification occur can be determined at plot-scale by experimentation. Unfortunately, this is impractical on a catchment scale because of spatial factors and the inherent variability of the physical and chemical characteristics of soils and vegetation. Any attempt to separate these processes on the evidence of the concentration of nitrate in the stream would be purely speculative, since soil temperature and the rate of transpiration tend to be well correlated. Rather, the second half of Eq. (1) incorporates a net assimilation term which effectively represents uptake minus mineralisation. The final discussion speculates on the relative importance of these processes to this term. Ammonium transformations are not explicitly identified in the model, mainly because deposition of ammonium in this area is lower relative to nitrate, and concentrations of ammonium in stream waters are very low (Table 1) (Neal et al., 1992b). Implicit in the model, however, are the assumptions that ammonium input to the catchment is rapidly transformed by nitrification processes to nitrate and/or ammonium is very strongly utilised by plants and effectively removed from the system (Fiebig et al., 1990). It is clear that this representation of the ammonium dynamics Table 1 Mean and range in concentration of NO 3 and NH4 for rainfall and stream water

Rain water Hafren Hore pre-felling Hore post-felling

NO3 (mg I-I)

NH4 (mg 1-1)

0.8 (0.0-75.0) 1.5 (0.0-6.0) 1.6 (0.4-3.3) 2.7 (0.3-4.7)

0.3 (0.0-5.0) 0.02 (0.0-0.1) 0.04 (0.0-0.8) 0.02 (0.0-0.2)

W.T. Sloan et al. / Journal of Hydrology 158 (1994) 61-78

69

is inadequate for predicting effects within the terrestrial part of the catchment system, but for the purposes of this work, where the objective is to model surface water nitrate concentrations, these assumptions are adequate. In any case, a lack of model fit may result from inadequate representation of ammonium dynamics, indicating that it is not possible to utilise these lumped catchment processes for modelling stream nitrate concentration.

4. Model cafibrafion and appficafion The model described by Eq. (1) is dependent on four parameters which cannot be attributed to the rate at which any single process occurs; hence they must be estimated using observed data. For both the Afon Hore and Afon Hafren, parameter estimations were carried out using the extended Kalman filter (EKF) algorithm. This estimates the parameters of a system of first-order differential equations by attempting to minimise the error between the simulated and observed states. The algorithm is recursive; hence it updates the parameter estimates while working serially through the data. It has the advantage over non-recursive estimation techniques in two respects. First, it explicitly takes account of random disturbances and measurement error in the driving variables. Second, variation in parameter estimates throughout the period of simulation can highlight any inadequacies in the model structure. A full description of the algorithm is given in Jazwinski (1970). It has previously been used to identify model structure and estimate the parameters of several models of environmental systems (Beck and Young, 1976; Whitehead et al., 1979). To use the E K F algorithm, the differential Eq. (1) was incorporated into a continuous dynamic system which predicts the stream nitrate concentration and the temporal variation in parameters and includes stochastic components in the model specification, parameter estimates and the observed nitrate concentration. Since the parameters kl, k2, k 3 and k 4 are considered to be time-invariant, the system is described by dN = kI(QRNR - QN) + (-k2 +

+ (Tk3 + k4)-d-~ + ~

da --= = 0 + ( dt

(2a)

and the observed nitrate concentration is given by N(ti) = N(ti) q- ~l(ti)

(2b)

where a__= [kl, k2, k3, k4] T, superscript T denotes the transpose of a vector, ~ is the system noise, _( is a vector of parameter disturbances, N is the observed nitrate concentration and rl(ti) is a random additive measurement error at a discrete instant in time. The system noise, ~, is a series of unmeasured, possibly random, errors which are related to uncertainties in the internal description of the model. It is a combination of the errors associated with the assumptions and simplifications made in the model, such as spatial, temporal and ecological aggregation. The better the model describes

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W.T. Sloan et al. / Journal of Hydrology 158 (1994) 61-78

reality, the smaller the system noise. The parameter disturbances, _(, are random processes representing the expected variation in the parameters. If it is believed that the parameters of the model are constant through time, then ( is zero. However, Beck 0987) points out that this does not imply that the recursive estimates in the parameters will be invariant with time; this is a point of fundamental significance in assessing whether the model structure is adequate. It is beyond the scope of this paper to repeat the derivation or describe the E K F algorithm. It is sufficient to detail the additional information required when using it to solve the system described in Eqs. (2a) and (2b). The initial value of the nitrate concentration and initial estimates of the parameter values have to be stipulated, and a measure of confidence in these initial conditions is required. This is achieved by specifying their expected error, or variance. The system is ill-defined until the stochastic processes (, ( and ~ are described, and again this is achieved by specifying their expected variance, d I / d t and d T / d t are estimated using finite difference approximations. The E K F algorithm predicts the nitrate concentration and the parameter estimates while simultaneously propagating their variance and covariances through time. The system was solved under the hypothesis that its structure is correct and hence the parameters are constant in time. Thus, the vector of parameter disturbances, _(, and the system noise, ~, are identically zero and hence their associated variances are zero. If this hypothesis is correct, then the predicted and observed nitrate concentrations should be in close agreement and the parameter estimates should converge to constant values. If, however, the parameter estimates exhibit a significant and persistent adaptation, then the hypothesis is incorrect and, hence, the model structure is inadequate. This approach to estimating the parameters and assessing the structure of a model has been advocated by Beck and Young (1976). Initially the system of differential equations was solved using the Afon Hafren data with the value of the biomass change index, I, set to 1 for the entire period of

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W.T. Sloan et al. / Journal of Hydrology 158 (1994) 61-78

71

simulation, representing no significant change in catchment biomass. This results in Eq. (1) reducing to dT dN = k I ( Q R N R -- Q N ) + (-k2 + k3) ~ t dt

(3)

and, hence, k4 becomes redundant and k2 and k 3 are not unique. The expected variance in kl, k2 and k 3 was set at 5% of their initial value. The recursive estimates of kl, k2 and k 3 for the Hafren are given in Fig. 6(a), and the uncertainties in these, characterised by their variances, are shown in Fig. 6(b). These parameters are stable through the period of simulation. Since I is kept constant, k2 and k 3 are not unique. However, ( - k 2 + k3) is approximately equal to -0.12. The final parameter values predicted by the E K F were substituted into the model and held constant for the period of the simulation. In this case, a simple R u n g e - K u t t a algorithm was used to solve Eq. (3). The resulting simulated nitrate concentration is displayed in Fig. 2. The root mean square error between the observed and simulated values is 0.4 mg-NO31-1 . The system of differential equations was then solved using the Afon Hore data and a simple shape for the biomass change index function, I. This was assumed to be constant with a value of 1 until deforestation began, and then to decrease linearly for 3 years to a value of 0.5 and remain constant at this value until the end of the simulation (Fig. 7). This is taken to represent the reduction in biomass due to clear felling of the forest. The recursive estimates of the parameters are given in Fig. 8. kl, k2 and k 3 remain fairly constant, although k4 tends to drift towards a larger value after the start of the deforestation in late 1985. The E K F algorithm is adjusting k 4 in

Initial Approximation ---

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Year Fig. 7. The biomass change index is utilised at each time step in the model to represent major vegetation changes in the catchment.The initial approximationused was replacedby the optimisedcurvefor the model simulation shown in Fig. 3(b) followingapplication of the EKF algorithm.

72

W.T. Sloan et al. / Journal o f Hydrology 158 (1994) 61-78

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Fig. 8. EKF recursive parameter estimates for k I (a), k2 (b), k 3 (c) and k4 (d) for the model applied at the Afon Hore. The solid line shows the parameter estimates obtained using the initial biomass function approximation, and the broken line shows the estimates using the optimised biomass function. an attempt to compensate for some inadequacy in the model specification. Either the model structure or the shape o f the biomass change function, L is inadequate. The initial shape o f the biomass change function, L remained constant after the completion o f deforestation, and this neglects the replanting o f y o u n g sitka spruce trees. Hence, rather than alter the model structure, the index function was changed. A process o f trial and error was used to identify the shape o f the biomass change

W.T. Sloan et al. / Journal of Hydrology 158 (1994) 61-78

73

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function, L which would yield a stable estimate of the k4 parameter, and the final optimised shape of the function is shown in Fig. 7. The resulting, recursive, parameter estimates are given in Fig. 8, the uncertainty in these are displayed in Fig. 9, and the model simulation run using the final parameter values from the EKF-held constant is displayed in Fig. 3. In general terms, the model fit captures trends observed in the data; the increase in nitrate concentration immediately following felling rose to a peak

74

W.T. Sloan et al. / Journal of Hydrology 158 (1994) 61-78

(d) 06

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some 2 years later and then decreased gradually. Short-term dynamics, however, are poorly simulated and the root mean square error is 1.1 mg-NO31-1. The model consistently fails to reproduce observed winter peaks and summer troughs in nitrate concentration post-felling. This cannot be explained by an inadequate representation of any of the processes associated with the terrestrial nitrogen cycle since these are not explicitly specified in the model. Implicit in the model is the assumption that net assimilation encompasses components of processes such as mineralization of organic nitrogen and plant uptake which are highly correlated with temperature and the size of the biomass. The lack of model fit post-felling implies that there are effects of clear felling on net assimilation which are not implicit in the model. It is possible to speculate on the nature of these without estimating their relative contribution. After clear felling, there is likely to be an increase in the organic detritus on the surface of the catchment which might increase the amount of organic nitrogen mineralised and subsequently nitrified into nitrate (Likens et al., 1978). Vegetation type and temporal variation in uptake change after felling, as does the hydrological response of the catchment (Neal et al., 1992b), all of which could affect short-term stream nitrate dynamics.

5. Discussion

A simple linear regression relationship was capable of simulating the seasonal variation in the stream nitrate concentrations of the Hafren. However, this ignores the influx of nitrate through wet deposition and is incapable of simulating land-use change. It was developed into a simple dynamic model which includes a deposition term and a biomass-indicating function. The fit of simulated to observed nitrate concentrations was better than for the simple regression model at the Hafren. This must be due to the inclusion of the deposition term, since the biomass-indicating

W.T. Sloan et al. / Journal of Hydrology 158 (1994) 61-78 _

75

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function remained constant for the period of simulation. The influence of the deposition term is dictated by the magnitude of the parameter k] in Eq. (1). In this case it was small. However, the E K F analysis showed that when it was allowed to be timedependent it remained fairly constant. If the influence of the deposition term were negligible, the value of k] would have drifted towards zero. It is anticipated that a simple model of this type could be used to predict changes in leaching from nitrogensaturated catchments, such as the Hafren, as a result of changes in anthropogenic deposition. This is demonstrated by doubling (notionally) the concentration of nitrate in the rain water for the period between 1984 and 1991. The simulated increase in stream nitrate concentration is compared to the observed concentration in Fig. 10. At the Hore catchment, the ability of the model to capture the major changes in nitrate concentrations through the deforestation and subsequent re-planting phases is encouraging, although detailed short-term dynamics are not well reproduced. In the simpler case of the Hafren catchment where no land-use change occurs, it is possible to make a speculative split of the model into two of the nitrogen processes

W.T. Sloan et al. / Journal of Hydrology 158 (1994) 61-78

76

which are known to occur. As described in the introduction, the net effect of mineralization and nitrification have previously been described by a first-order, temperature-dependent, rate equation which could be approximated by d N / d t = cT, where c is a constant (mg per (1 day °C)) and T is temperature (°C). However, in late summer and autumn the rate of mineralization is likely to be greater than for spring and early summer at a similar temperature due to the increased availability of organic nitrogen from litterfall. This can be accounted for by subtracting a term which is dependent on the rate of change of temperature, dN dT = cl T - c2 dt dt

(4)

where el is a constant (mg-NO3 per (1 day °C)) and c2 is a constant (mg-NO3 per (I°C)). d T/d t > 0 in the spring and d T/d t < 0 in the autumn. Therefore, the rate of change of nitrate concentrations due to mineralization and nitrification is greater in autumn than in spring for the same temperature. Similarly, for uptake the rate of transpiration is greater in the spring than in the autumn for the same temperature and hence the rate at which nitrogen is taken up by vegetation is greater. This can be described in an analogous manner. dN dt

-

c3 T + ¢4

dT dt

(5)

where c3 is a constant (mg-NO3 per (1 day °C)) and c4 is a constant (mg-NO3 per (I°C)). Combining these representations of mineralization and uptake with the deposition and leaching terms results in

dNdt = kI(NRQR -- NQ) + (c I

dT

-

-

c3)T + (c 2 + c4) - ~

(6)

where kl, NR, QR and Q are the same as in Eq. (1). IfCl = c2, then annual uptake and mineralization are in balance and Eq. (6) reduces to the simplified form of Eq. (1), which was applied to the Hafren. This is a speculative split which cannot be validated on the basis of the stream nitrate concentrations alone. If it is correct, it suggests that the winter leaching of nitrate can be explained by the difference between mineralization and uptake during the autumn and spring months. In the Hore catchment, where land-use change occured, there is no neat way of splitting the model into uptake and mineralization terms. This suggests that although the biomass index function is highly correlated with the number of trees in the catchment, its influence extends further than uptake by trees alone. The most important conclusion from this work is that a rather simple model structure, numerically representing three broad catchment processes and driven by temperature and atmospheric nitrogen deposition, is capable of simulating the dynamics of stream nitrate concentrations at the catchment outflow. The use of such lumped models in catchment hydrochemistry has already proved particularly effective in simulating the long-term impacts of sulphur deposition, as described by the M A G I C model (Cosby et al., 1985). Clearly, the results presented here offer a first step towards similar catchment models for predicting nitrogen dynamics in the long

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term and, consequently, a useful tool for the assessment of critical loads for nitrogen in upland waters.

6. Acknowledgements We thank Colin Neal for providing hydrochemical data for the study sites, and Paul Whitehead and Hans Stigter for their helpful comments. This research was carried out under funding from NRA, DOE, EC and NERC.

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