Model Analysis of an Overland Flow Waste Treatment System. I. Accumulation of Dry Matter and Plant Nutrients with Time #

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1 COMMUNICATIONS IN SOIL SCIENCE AND PLANT ANALYSIS Vol. 34, Nos. 13 & 14, pp , 2003 Model Analysis of an Overland Flow Waste Treatment System. I. Accumulation of Dry Matter and Plant Nutrients with Time # A. R. Overman* and R. V. Scholtz III Agricultural and Biological Engineering Department, University of Florida, Gainesville, Florida, USA ABSTRACT Land application is widely used for treatment of animal waste. One of the methods is overland flow treatment where soil properties favor surface runoff over infiltration. In these systems the land is graded to a uniform slope on which a grass cover is established. The grass is then harvested periodically. In this article an empirical model is used to describe accumulation of dry matter and plant nutrients with time. Data from a field study are used to illustrate the procedures for model parameter evaluation. Treatments of the study included a control, inorganic fertilizer, and three loading rates with effluent from a swine lagoon. The empirical model of crop growth provides a relatively simple means of # Florida Agricultural Experiment Station Journal Series No. R *Correspondence: A. R. Overman, Agricultural and Biological Engineering Department, University of Florida, Gainesville, FL , USA; aoverman@agen.ufl.edu DOI: /CSS Copyright q 2003 by Marcel Dekker, Inc (Print); (Online)

2 1944 Overman and Scholtz accounting for accumulation of plant biomass and nutrients over the season. INTRODUCTION Land treatment of waste is predicated on the principle of beneficial reuse of water and nutrients. Methods of land treatment include infiltration basins for groundwater recharge, slow rate irrigation, and overland flow. Overland flow treatment is suitable for soils which contain a layer that restricts infiltration and favors flow across the land surface. It requires a graded slope and a vegetative cover to stabilize the soil surface and to provide a medium for biological activity. Design and application of this method has been discussed previously. [1] Detailed procedures of process analysis have been given. [2] One of the components of the overland flow system is accumulation of biomass and plant nutrients with time by the vegetative cover on the slope. An empirical model has been developed to describe this accumulation. [3,4] It uses the probability equation which contains three parameters for dry matter accumulation. While a more comprehensive model based on an intrinsic growth function has been developed, [5] the empirical model will prove adequate for our purpose here. MODEL DESCRIPTION The empirical model for accumulation of dry matter by a forage grass which is harvested on a fixed interval during the season is given by Y n ¼ Y t 2 1 þ erf t 2 m p ffiffi 2 s ð1þ where t ¼ calendar time since Jan. 1, wk; Y n ¼ cumulative dry matter for n harvests, Mg ha 21 ; Y t ¼ seasonal total dry matter, Mg ha 21 ; m ¼ time to the mean of the dry matter distribution, wk; s ¼ standard deviation of the dry matter distribution, wk; and where the error function is defined by erf x ¼ p 2 ffiffiffi p Z x 0 expð2u 2 Þdu ð2þ

3 Overland Flow Waste Treatment System. I 1945 Normalized dry matter distribution, F y, is defined by F y ¼ Y n ¼ 1 Y t 2 1 þ erf t 2 m p ffiffiffi 2 s A plot of F y vs. t yields a straight line on probability paper. The empirical model contains the three parameters Y t, m, and s which must be evaluated from data. Equation 3 can be converted to the linearized form z ¼ erf 21 ð2f 2 1Þ ¼ 2 pffiffiffi m þ p 1 ffiffi t 2 s 2 s where erf 21 designates the inverse error function. This form can be used to estimate parameters m and s by linear regression of z vs. t. Values for the error function can be obtained from mathematical tables. [6] ð3þ ð4þ DATA ANALYSIS Data for this analysis are taken from a field study by Liu et al. [7] A mixture of Russell bermudagrass [Cynodon dactylon (L.) Pers.] and annual ryegrass (Lolium multiflorum Lam.) was grown on Marvyn loamy sand (fine loamy, kaolinitic, thermic Typic Kanhapludult) graded to a slope of 10%. Average harvest interval in 1993 was 5.8 wk. Plots were replicated four times. Treatments included a control ðn ¼ 0; P ¼ 0Þ; fertilizer ðn ¼ 560 kg ha 21 ; P ¼ 0Þ; effluent 1x ðn ¼ 560 kg ha 21 ; P ¼ 71 kg ha 21 Þ; effluent 2x ðn ¼ 1120 kg ha 21 ; P ¼ 142 kg ha 21 Þ; and effluent 4x ðn ¼ 2240 kg ha 21 ; P ¼ 284 kg ha 21 Þ: Effluent was derived from a second stage lagoon at the Auburn University Swine Unit. Crop data are listed in Tables 1 through 5, where DY; DN u ; and DP u are quantities of dry matter, plant N, and plant P contained in each harvest, respectively. Normalized fractions F y, F n, and F p are computed at each harvest time by dividing the cumulative quantity by the seasonal total for dry matter, plant N, and plant P, respectively. Equation 4 is used to linearize dry matter distribution for each treatment as shown in Table 6. Linear regression of z vs. t is then used to estimate the time parameters m and s. As an example, for the control treatment we obtain z ¼ 2 pffiffiffi m þ 2 s p 1 ffiffi t ¼ 21:67 þ 0:0621t r ¼ 0:9947 ð5þ 2 s with a correlation coefficient of r ¼ 0:9947; which leads to m ¼ 26:9 wk and

4 Table 1. Plant accumulation of dry matter, plant N, and plant P with time for the control treatment of the overland flow study at Auburn, AL (1993). a t wk DY Mg ha 21 Y Mg ha 21 F y DN u kg ha 21 N u kg ha 21 F n DP u kg ha 21 P u kg ha 21 F p a Harvest data adapted from Liu et al. (Ref. [7], Table 3) Overman and Scholtz MARCEL DEKKER, INC. 270 MADISON AVENUE NEW YORK, NY 10016

5 Overland Flow Waste Treatment System. I 1947 Table 2. Plant accumulation of dry matter, plant N, and plant P with time for the fertilizer treatment of the overland flow study at Auburn, AL (1993). a t wk DY Mg ha 21 Y Mg ha 21 F y DN u kg ha 21 N u kg ha 21 F n DP u kg ha 21 P u kg ha 21 F p a Harvest data adapted from Liu et al. (Ref. [7], Table 3).

6 Table 3. Plant accumulation of dry matter, plant N, and plant P with time for the effluent treatment (1x) of the overland flow study at Auburn, AL (1993). a t wk DY Mg ha 21 Y Mg ha 21 F y DN u kg ha 21 N u kg ha 21 F n DP u kg ha 21 P u kg ha 21 F p a Harvest data adapted from Liu et al. (Ref. [7], Table 3) Overman and Scholtz MARCEL DEKKER, INC. 270 MADISON AVENUE NEW YORK, NY 10016

7 Table 4. Plant accumulation of dry matter, plant N, and plant P with time for the effluent treatment (2x) of the overland flow study at Auburn, AL (1993). a t wk DY Mg ha 21 Y Mg ha 21 F y DN u kg ha 21 N u kg ha 21 F n DP u kg ha 21 P u kg ha 21 F p a Harvest data adapted from Liu et al. (Ref. [7], Table 3). Overland Flow Waste Treatment System. I 1949 MARCEL DEKKER, INC. 270 MADISON AVENUE NEW YORK, NY 10016

8 Table 5. Plant accumulation of dry matter, plant N, and plant P with time for the effluent treatment (4x) of the overland flow study at Auburn, AL (1993). a t wk DY Mg ha 21 Y Mg ha 21 F y DN u kg ha 21 N u kg ha 21 F n DP u kg ha 21 P u kg ha 21 F p a Harvest data adapted from Liu et al. (Ref. [7], Table 3) Overman and Scholtz MARCEL DEKKER, INC. 270 MADISON AVENUE NEW YORK, NY 10016

9 Overland Flow Waste Treatment System. I 1951 Table 6. Linearized form of dry matter distributions. Fy z Fy z Fy z Fy z Fy z t wk Control Fertilizer Effluent 1x Effluent 2x Effluent 4x

10 1952 MARCEL DEKKER, INC. 270 MADISON AVENUE NEW YORK, NY Overman and Scholtz Table 7. Summary of system response. Treatment N kg ha 21 P kg ha 21 m wk s wk Yt Mg ha 21 Nut kg ha 21 Put kg ha 21 Nct gkg 21 Pct gkg 21 Control Fertilizer Effluent 1x x x

11 Overland Flow Waste Treatment System. I 1953 Table 8. Estimates from the empirical model. t wk x erf x F x ¼ p t2m ffiffi 2 s ¼ t225:5 17:5 : F ¼ 1 t225:5 2 1 þ erf 17:5 : s ¼ 11:4 wk. System parameters are summarized in Table 7. From this analysis we obtain an overall average of m ¼ 25:5 wk and s ¼ 12:4 wk. These values can be used in Equation 3 to write F ¼ þ erf t 2 m p ffiffi 2 s ¼ þ erf t 2 25:5 17:5 ð6þ Calculations for F vs. t are listed in Table 8. Distributions for dry matter, plant N, and plant P are shown in Figure 1 for the fertilizer treatment, where the curves are drawn from Equation 6. Normalized plant N vs. normalized dry matter is shown in Figure 2, while the equivalent plot for plant P is shown in Figure 3 for all treatments.

12 1954 Overman and Scholtz Figure 1. Simulation of accumulation of dry matter, plant N, and plant P with time for the fertilizer treatment by the overland flow system at Auburn, AL. Data are taken from Table 2. Curves are drawn from Equation 6. DISCUSSION The empirical model provides a reasonable description of dry matter and plant nutrient accumulation over the growing season (Fig. 1). While there is slight dependence of parameters m and s on level of applied nutrients (Table 7), it appears adequate to assign constant values to both for all treatments.

13 Overland Flow Waste Treatment System. I 1955 Figure 2. Normalized plant N vs. normalized plant dry matter for all treatments by the overland flow system at Auburn, AL. Data are taken from Tables 1 through 5. Figure 3. Normalized plant P vs. normalized plant dry matter for all treatments by the overland flow system at Auburn, AL. Data are taken from Tables 1 through 5.

14 1956 Overman and Scholtz Dependence on applied nutrients can be assigned to seasonal total dry matter, plant N uptake, and plant P uptake. In fact the empirical model can be used to describe accumulation of dry matter with time, and then couple plant N and P accumulation by simple linkage to dry matter (Figs. 2 and 3). This applies for a fixed harvest interval of the grass. Estimates of cumulative plant N uptake, N un, and plant P uptake, P un, can be made from N un ¼ N ct Y n ð7þ P un ¼ P ct Y n ð8þ where values for seasonal plant N and plant P concentrations, N ct and P ct, are taken from Table 7. Seasonal yield and nutrient uptake are known to depend on harvest interval, water availability, and applied nutrients. [8] Dependence of production on nutrient input is discussed in part 2 of this series. REFERENCES 1. Overman, A.R.; Wolfe, D.W. Overland flow treatment of wastewater at Florida state prison. J. Water Pollut. Control Fed. 1986, 58, Overman, A.R.; Angley, E.A.; Schanze, T.; Wolfe, D.W. Process analysis of overland flow treatment of wastewater. Trans. Am. Soc. Agric. Eng. 1988, 31, Overman, A.R. Estimating crop growth rate with land treatment. J. Environ. Eng. Div. ASCE 1984, 110, Overman, A.R.; Angley, E.A.; Wilkinson, S.R. Empirical model of coastal bermudagrass production. Trans. Am. Soc. Agric. Eng. 1988, 31, Overman, A.R. An expanded growth model for grasses. Commun. Soil Sci. Plant Anal. 1988, 29, Abramowitz, M.; Stegun, I.A. Handbook of Mathematical Functions; Dover Publications: New York, Liu, F.; Mitchell, C.C.; Odom, J.W.; Hill, D.T.; Rochester, E.W. Swine lagoon effluent disposal by overland flow: effects on forage production and uptake of nitrogen and phosphorus. Agron. J. 1997, 89, Overman, A.R.; Neff, C.R.; Wilkinson, S.R.; Martin, F.G. Water, harvest interval, and applied nitrogen effects on forage yield of bermudagrass and bahiagrass. Agron. J. 1990, 82,