Abstract. 1 Introduction

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An experiment in modelling vertical P-transport in the unsaturated zone of a former sewage farm with a simple compartment model S. Pudenz, G. Nutzmann, J.

1 An experiment in modelling vertical P-transport in the unsaturated zone of a former sewage farm with a simple compartment model S. Pudenz, G. Nutzmann, J. Gelbrecht Institute of Freshwater and Fish Ecology, D Berlin, Germany Abstract A modelling concept is evaluated to predict the vertical transport of phosphate in the unsaturated zone corresponding to experimental data from a wastewater irrigation field test site. In contrast to deterministic models, compartment models are subject to several simplifying assumptions requiring a small data set. So the assumption of a time constant soil moisture profile is proved in calculating the water balance with a deterministic model. Based on measured phosphate distribution, different combinations of the K<j coefficient and a sink term are used to describe the retention and leaching process of phosphate in the unsaturated zone. Deviations from measured data, especially in the upper soil layers, and investigations into the sorption behavior indicate that a Langmuir isotherm may describe the process sufficiently. 1 Introduction Wastewater irrigation during the last years in the north-east of Berlin (Hobrechtsfelde) has led to increasing concentrations of nutrients (P, N) and other pollutants in surface as well as in subsurface waters and in the soil, Nutzmann et al. [1]. Now, the stoppage of wastewater application in 1987 has caused an intrinsic reduction of soil and water pollution, but under the influence of acid rain, phosphate compounds and heavy metals, sorbed on inorganic matter, are being mobilized and leached into the near-surface groundwater. To examine and to control this leaching an artificial groundwater recharge experiment with purificated wastewater irrigation was started and a field test site was installed. Because of ourfieldobservations we obtainedfirstand foremost more detailed information about water balance (atmospheric conditions, soil water,

382 Water Pollution groimdwater) than about the geochemical behavior of phosphate in the vadose zone. Therefore, a model is selected which requires only a small data set.

2 382 Water Pollution groimdwater) than about the geochemical behavior of phosphate in the vadose zone. Therefore, a model is selected which requires only a small data set. Compartment models are often used to predict exposure of contaminants in the environment over long-time periods and due to several simplifying assumptions only a small data set is required. In contrast to spatial- and timediscrete models they calculate intramedium transport of contaminants taking into account a mass-balance concept. The EXSOL model, Matthies et al. [2], is an one-dimensional vertical multi-layer model considering the processes of advection with pore water flow, hydrodynamic dispersion, sorption (IQ-concept), decay, root uptake, and others. It is obvious that modelling transport of phosphate compounds in soil demands information about some transport parameters (e.g. dispersivity), sorption and precipitation behavior and the geochemical conditions. Considering these processes in a more or less operational sense, a combination of a geochemical model and a transport model allows satisfactory prediction of phosphate mobility in a laboratory scale, Isenbeck-Schroter et al. [3]. But a transfer of these results to different hydrological and geochemical conditions at field scale seems to be complicated and another conceptual model is developed here. To find out if the assumption of a time-constant soil moisture profile is sufficient for modelling vertical transport of phosphate with a compartment model over a long-time period the dynamic water balance in the unsaturated zone of the irrigation test site is calculated with a deterministic flow model based on measured hydrologic boundary conditions and soil moisture data. Furthermore, the purpose of the paper is to show how well predictions for environmental exposure of phosphate can be made if only a limited set of experimental data is available. 2 Modelling of unsaturated water balance The SUNSOL model [4], based on the Richards-equation, demands besides the input of boundary conditions information about the hydraulic properties. On the field test site in Berlin-Hobrechtsfelde several measuring devices were installed to observe the hydrologic components like irrigation, rainfall, meteorological data for estimating the potential evapotranspiration and groundwater level movement in a continuous manner (for more details see Ginzel et al.)^. Furthermore, soil moisture and pressure head in three soil horizons at 50 cm, 160 cm and 215 cm depth are also measured continuously. The potential evapotranspiration rate, calculated with the Penman-Monteith model*', is estimated to 2.78 mm/d. To get a complete description of the upper boundary the ratio between infiltration and evapotranspiration versus time has to be computed. In the following Table 1 the irrigation quantities (m^) and the rainfall (mm) from April 1993 to April 1994 are given as monthly sums. Considering the irrigated area of max nf, it is obvious that the artificial infiltration rate is one order of magnitude greater than the rainfall and both

3 Water Pollution 383 components (irrigation + rain) influence the soil water flux more than the evapotranspiration. Table 1: Irrigation and rainfall from april 1993 to april t 4/93 5/93 6/93 7/93 8/93 9/93 10/3 11/93 12/93 1/94 2/94 3/94 Q(nv>) N(mm) Modelling the artificial irrigation regime on the test site two different phases are considered here: the infiltration of purificated waste water continues during three hours per day, and a following redistribution phase of 21 hours is assumed. The subsurface water flow at the test site was simulated in a time-period of one week. During five days an intermittent irrigation took place. That means, after irrigation (3 hours) the soil moisture is redistributed (21 hours) in the entire profile and a groundwater recharge is observed. From the mass balance, calculated at all time-steps, different partitions like infiltration, evapotranspiration, mass change in the profile and groundwater recharge are separated and the cumulative daily results are given in Table 2. Table 2: Mass balance of unsaturated flow simulation: all quantities in (cm/d). AQ: mass change in the profile; I-E: infiltr. - pot. evapotr.; GWr: groundwater recharge. AQ day I-E GWr A zero trend of the the mass change in the profile after five days of intermittent irrigation indicates that infiltration effects directly the groundwater recharge. The daily recharge rate after one week is in the same range as at the beginning of the simulation. Furthermore it is shown, that infiltration and redistribution processes are approximately in balance, and for predicting the transport of contaminants in a long-time-scale a stationary-state water regime can be considered here. 3 Compartment modelling of phosphate transport The EXSOL model was originally developed to describe the transport and transformation of organics in soif. It assumes a time constant vertical water flow in a one-dimensional soil column and an instantaneous equilibrium partitioning of the chemical between adsorbed, dissolved and gaseous phases. The soil column of

4 384 Water Pollution one unit area consists of up to ten layers and in which each layer is divided into sub-layers. Transport between the layers and the compartments soil water, soil air and soil matrix is described using capacity coefficients for the vapor, solid and liquid phases. The model is based on the one-dimensional convection-dispersion equation: where C, is the total concentration in soil, D is the diffusion-dispersion coefficient, V is the fluid velocity and A represents an additional removal term which is specified as a (pseudo-) first-order degradation kinetic. At the soil surface a steady state input flux type boundary condition is imposed for the chemical input. At the bottom of the soil column a zero concentration gradient is assumed. The equation is solved by a Crank-Nicolson finite difference approximation scheme. To simulate transport, each soil layer requires the input of values for the porosity n, bulk density p, dispersion coefficient D, distribution coefficient K& degradation constant X (if requested as sink term), water content 0 and the Darcy water flux q. Measured and estimated data for EXSOL simulations are listed in Table 3. Phosphate concentrations were determined as total phosphorus TP. The volumetric water content was calculated by SUNSOL (see below). Dispersion was neglected. Porosity and volumetric water content were averaged on a layer thickness of each 20 cm, the rock density over the entire profile. Table 3: Soil parameters depth (cm) p (kg/of) n(-) (vol.%) First, phosphate transport was modelled over a period of 275 d (May Nov. 1993). The mean net infiltration rate (vertical boundary water flux) for this period was calculated to mm/d and the TP input, with the irrigation water, was capt constant as a surface boundary condition with a value of g/m^*d. The soil compartment with a thickness of 1.2 m was subdivided into 6 equidistant layers with depths of 0.2 m. Different Kd - values, constant over the entire column and variable for each layer and in combination with a sink or degradation rate (e.g. as a precipitation term) are used. All parameters are fitted according to the measurement of Nov. 93. The best fits are given in Table 4.

5 Table 4: Fitted Kd - values and degradation rates Water Pollution 385 depth (m) variable K<j I (cm%) II X( ly y) 1.5 * jo-' 1.0* 10-' 1.0* io-= 1.0* 10 s 1.0* 10-' constant K^ I 33.5 (cmvg) II *10^ Both, the fitted distribution coefficients and degradation rates are used to model over a second period of 62 d (Dec Jan. 94) under a minor deviation of boundary conditions. Thus, the mean net infiltration rate is calculated to rnm/d and the steady state input flux to g/nf*d P-concentration (g/kg) 2.0 Q_ CD ID variable Kd variable K^ and decay Kd=10 - decay=0.0001/d 1.50 I/ t\y JJ.3 77 C measured concentration Figure 1: Comparison of calculated (fitted) with measured concentrations for the period of 275d. Under the condition of a variable Kd, especially without decay, the fitting result for the simulation period of 275 d seems to be sufficient. However, regarding the simulation period over 62 d (see Figure 2) it is emphasized that the differences between calculated and measured concentrations in the upper soil layers are serious; after all, the variable Kd - concept (case I and II) provides better results than a constant Kd. Considering only the fitted K<j - values and degradation rates, and neglecting the chemical background both may be sensitive to a minor deviation of boundary conditions (net infiltration and TP input rate). But instead of investigating this assumption we have to look at the sorption behavior.

6 386 Water Pollution P-concentration (g/kg) CL CD "D variable K<j variable Ky and decay Kd=10 - decay=0.0001/d I/ l\jj OvJ.O ~Z "Z C measured concentration 2.00^ Figure 2: Comparison of calculated with measured concentrations for the period of 62 d i measured (0-30 cm) measured (60-90 cm) Langmuir (0-30 cm) Langmuir (60-90cm) Equilibrium concentration c (mg P/l) Figure 3: Measured concentrations compared with a derived Langmuir isotherm. Sorption capacity 0-30cm=0.237 mg P/g, 60-90cm = mg P/g.

7 Water Pollution Experimental sorption behavior Here, the result of an investigation into the sorption behavior of phosphate with a comparable soil is presented. Soil samples of two different depths have been used, mainly because of the high concentration in th eupper soil, as shown in Figure 2. The Langmuir isotherms (see Figure 3) result form a comparsion with a 'two-site' Langmuir isotherm and a Freundlich isotherm. The relatively high sorption capacity of the sample 0-30 cm may result from the high part of humic substances. Regarding in this case the additional phosphate input during modelling transport, the sorption capacity of the derived isotherm emphasizes that an adequate description of the phosphate enrichment in the upper soil can be achieved. 5 Conclusions It is obvious that a combination of precipitation and sorption leads to phosphorus retention. Commonly these processes are described utilizing a two-site Langmuir isotherm (sometimes kinetic), a combination of a Langmuir isotherm and a precipitation term or just one Langmuir isotherm (see e.g. Isenbeck-Schroter et al., 1993; van der Zee a. Bolt, 1991; Sposito, 1982)^'^ whereas investigations on the application of the K<j - value to phosphorus transport seems not to exist. Nevertheless, a fit of variable K<j - values into measured data is possible. Again, an application of these values to modified boundary conditions is not feasible. The difference between the two derived Langmuir isotherms indicates that even in this case both isotherms are appropriate to represent enrichment and migration of phosphate. Further investigations involving the Langmuir isotherm will be accomplished. Acknowledgement We are greatfull to B. Mekiffer and our colleague H.J. Exner, who provided the chemical analysis of soil samples and the sorption data. References 1. Nlitzmann, G., Ginzel, G., Handke, H., Scholz, H., Siegert, G. & Schwamm, D. Hydrologisch-hydrogeologische Untersuchung der ehemaligen Rie self elder Berlin-Buck (Abschlufibericht), Inst. Gewasserokologie u. Binnenfischerei, Berlin, Matthies, M., Behrendt, H. & Munzer, B. EXSOL - Modellfur den Transport und Verbleib von Stoffen in Boden, GSF-Bericht 23/87, Munchen-Neuherberg, 1987.

8 388 Water Pollution 3. Isenbeck-Schroter, M., Doring, U., Moller, A., Schroter, J. & MattheB, G. (1993): Experimental approach and simulation of the retention processes limiting orthophosphate transport in groundwater, /. Contam. Hydro!., 1993, 14, Niitzmann, G. A simple finite element method for modeling one-dimensional water and solute transport in variably saturated soils, Acta Hydrophys., 1991, 35, Ginzel, G., Handke, H. & Nutzmann, G. Untersuchungen zur Wiedervernassung ehemaliger Rieselfeldstandorte im Nordosten Berlins, Z. dt. geol Ges. (submitted), Beven, K. A sensitivity analysis of the Penman-Monteith actual evapotranspiration estimates, /. HydroL, 1979,44, Matthies, M., Bruggemann, R., Miinzer, B., Schernewski, G. & Trapp, S. Exposure and ecotoxicity for environmental chemicals (e4chem): application of fate models for surface water and soil, Ecol Modelling, 1989,47, Sposito, G. On the use of the Langmuir equation in the interpretation of "adsorption" phenomena. H The "two-surface" Langmuir equation, Soil Sci. Soc. Am. /., 1982, 46, Van der Zee, S.E.A.T.M.& Bolt, G.H. Deterministic and stochastic modelling of reactive solute transport, J. Contam. Hydrol., 1991, 7,

12 SWAT USER S MANUAL, VERSION 98.1

12 SWAT USER S MANUAL, VERSION 98.1 CANOPY STORAGE. Canopy storage is the water intercepted by vegetative surfaces (the canopy) where it is held and made available for evaporation. When using the curve