Model Analysis for Response of Dwarf Elephantgrass to Applied Nitrogen and Rainfall

Transcription

1 COMMUNICTIONS IN SOIL SCIENCE ND PLNT NLYSIS Vol. 35, Nos. 17 & 18, pp , 2004 Model nalysis for Response of Dwarf Elephantgrass to pplied Nitrogen and Rainfall. R. Overman* and R. V. Scholtz III gricultural and Biological Engineering Department, University of Florida, Gainesville, Florida, US BSTRCT In numerous articles, the extended logistic model has been used to describe response of annual and perennial crops to applied nutrients [such as nitrogen (N), phosphorus, and potassium]. The model accounts for coupling between dry matter and plant nutrient accumulation by way of phase relationships. Factors such as water availability and harvest interval (for perennials) can be easily incorporated. The model is well behaved and is simple to use for estimation purposes. In this article, response of a bunchgrass to applied nitrogen and rainfall is discussed. Field studies in Florida lead to similar parameter values as those in Texas. Linkage of lower and upper limits on plant N concentration is explained. *Correspondence:. R. Overman, gricultural and Biological Engineering Department, University of Florida, P.O. Box , Gainesville, FL , US; Fax: ; aoverman@agen.ufl.edu DOI: /LCSS Copyright & 2004 by Marcel Dekker, Inc (Print); (Online)

2 2486 Overman and Scholtz Key Words: Model; Nitrogen uptake; Elephantgrass. INTRODUCTION The extended logistic model was developed to describe crop response to applied nitrogen (N). [1] It was shown to apply to the annual crop corn (Zea mays L.) by Overman et al. [2] In the present analysis, the focus was on response of the bunchgrass dwarf elephantgrass (Pennisetum purpureum L. Schum.) to applied nitrogen and seasonal rainfall. Details of parameter evaluation are discussed. This analysis was part of an ongoing effort to generalize application of the model to a large variety of crops, soils, and environmental conditions. MODEL DESCRIPTION The extended logistic model of forage production is given by Y ¼ 1 þ expðb cnþ ð1þ n N u ¼ ð2þ 1 þ expðb n cnþ N c ¼ N u Y ¼ N 1 þ expðb cnþ cm ð3þ 1 þ expðb n cnþ where N ¼ applied nitrogen, kg ha 1 ; Y ¼ seasonal dry matter yield, Mg ha 1 ;N u ¼ seasonal plant N uptake, kg ha 1 ;N c ¼ plant N concentration, g kg 1 ; ¼ maximum yield at high N, Mg ha 1 ; n ¼ maximum plant N uptake at high N, kg ha 1 ; b ¼ intercept parameter for yield; b n ¼ intercept parameter for plant N uptake; c ¼ nitrogen response coefficient, ha kg 1 ;N cm ¼ n / ¼ maximum plant N concentration at high N, g kg 1. Equations (1) and (2) can be combined to give the phase relations between Y and N u. Y ¼ N u K n þ N u N c ¼ N u Y ¼ K n þ 1 N u ð4þ ð5þ

3 Response of Dwarf Elephantgrass to pplied Nitrogen and Rainfall 2487 where the phase and logistic parameters are related by ¼ K n ¼ 1 expð bþ n expðbþ 1 with the definition b ¼ b n b ð6þ ð7þ ð8þ DT NLYSIS Data for response of dwarf elephantgrass to applied N is adapted from Valentim et al. [3] Experiments were conducted in Gainesville, Florida, on rredondo loamy fine sand (loamy, siliceous, hyperthermic Grossarenic Paleudult). No irrigation was provided during the period Plots were harvested in early June, late July, late ugust, and late October. Results for seasonal dry matter yield, plant N uptake, and plant N concentration are given in Table 1. Table 1. Response of seasonal dry matter yield (Y), plant N uptake (N u ), and plant N concentration (N c ) to applied nitrogen (N) for dwarf elephantgrass at Gainesville, Florida ( ). a Year N Y (Mg ha 1 ) N u N c (g kg 1 ) =Y 1 n =N u avg b c r a Data adapted from Valentim et al. [3]

4 2488 Overman and Scholtz Since yields and plant N uptake were consistently lower in 1987 than in 1986 for all applied N levels (due to difference in rainfall), results were first averaged for the two years, as shown in Table 1. The model is rearranged to linear form and linear regression performed to obtain the equations ln 12:50 Y 1 ¼ b cn ¼ 0:98 0:0129N r ¼ 1:0000 ð9þ ln ¼ b n cn ¼ 1:30 0:0127N r ¼ 0:9970 ð10þ N u For application purposes, we will write the logistic equations as Y ¼ 1 þ expð1:00 0:0125NÞ n N u ¼ 1 þ expð1:30 0:0125NÞ 1 þ expð1:00 0:0125NÞ N c ¼ N cm 1 þ expð1:30 0:0125NÞ ð11þ ð12þ ð13þ trial-and-error approach is then used to obtain parameter estimates for 1986 and 1987 of (1986) ¼ 15.0 Mg ha 1, (1987) ¼ 11.0 Mg ha 1 ; n (1986) ¼ 320 kg ha 1, n ¼ 235 kg ha 1 ; N cm (1986) ¼ 21.3 g kg 1,N cm (1987) ¼ 21.4 g kg 1. summary of these parameters is given in Table 2, which are used in Eqs. (11) (13) to draw the curves shown in Fig. 1. The next step is to construct the phase relations (Y and N c vs. N u ). Equations (6) and (7) are used to estimate the phase parameters and K n for each year, which leads to the equations 1986: Y ¼ N u K n þ N u ¼ 57:9N u 915 þ N u ð14þ Table 2. Summary of model parameters for dwarf elephantgrass. Year (Mg ha 1 ) n N cm c (g kg 1 ) b b n (ha kg 1 ) N 1/2 0 N 1/

5 Response of Dwarf Elephantgrass to pplied Nitrogen and Rainfall 2489 Figure 1. Response of seasonal dry matter yield (Y), plant N uptake (N u ), and plant N concentration (N c ) to applied nitrogen (N) for dwarf elephantsgrass grown at Gainesville, Florida ( ). Data adapted from Valentim et al. [3] Curves drawn from Eqs. (11) (13), with parameters listed in Table 2. N c ¼ K n Y M þ 1 N u ¼ 15:8 þ 0:0173N u ð15þ 1987: Y ¼ N u ¼ 42:4N u ð16þ K n þ N u 670 þ N u

6 2490 Overman and Scholtz Figure 2. Phase plots of seasonal yield (Y) and plant N concentration (N c ) vs. plant N uptake (N u ) for dwarf elephantgrass grown at Gainesville, Florida. Data adapted from Valentim et al. [3] Curves drawn from Eqs. (14) and (16); lines drawn from Eqs. (15) and (17). N c ¼ K n Y M þ 1 N u ¼ 15:8 þ 0:0236N u The phase plots are shown in Fig. 2. ð17þ DISCUSSION The extended logistic model appears to describe response of dry matter yield and plant N uptake for dwarf elephantgrass to applied

7 Response of Dwarf Elephantgrass to pplied Nitrogen and Rainfall 2491 N rather well (Figs. 1 and 2). Plant N concentration appears to be independent of year and simply a function of the grass. From Eq. (5) and Fig. 2, it follows that the lower limit of plant N concentration, N cl,is given by N cl ¼ K n ¼ 15:8 gkg 1 ð18þ and is the same for both years. From Fig. 1 and Table 2, maximum plant N concentration, N cm, is 21.4 g kg 1. Now it can be shown that N cl N cm ¼ expð bþ ð19þ from which it follows that b ¼ This value is consistent with that listed in Table 2. Since N cl and N cm are characteristic of the plant species, we conclude that b is also characteristic of the plant. Equations 1 and 2 can be written in the alternative forms Y ¼ ð20þ 1 þ exp ðn N 1=2 Þ=N 0 n N u ¼ h i ð21þ 1 þ exp ðn N1=2 0 Þ=N0 where N 0 ¼ 1/c ¼ characteristic N, kgha 1 ; N 1/2 ¼ b/c ¼ applied N required to reach Y ¼ /2, kg ha 1 ; N 0 1/2 ¼ b n /c ¼ applied N to reach N u ¼ n /2, kg ha 1. It may be noted from Table 2 that these values are independent of year. In other words, variation between years is accounted for in parameters and n. Results obtained from this study are consistent with model analysis of bunchgrasses lovegrass (Eragrostis curvula Schrad.), kleingrass (Panicum coloratum L.), and buffelgrass (Cenchrus ciliaris L.) grown at Stephenville, Texas. [4] Finally, we examine dependence of parameters and n on seasonal rainfall, R, (pril through September), which amounted to 65.1 and 52.4 cm for 1986 and 1987, respectively. ssume the procedure of Overman and Scholtz [5] with the exponential relationship ¼ m 1 exp R R 0 R 0 ð22þ where m ¼ maximum value of at high rainfall, Mg ha 1 ; R 0 ¼ intercept parameter for ¼ 0, cm; R 0 ¼ characteristic rainfall, cm. It appears

8 2492 Overman and Scholtz reasonable to assume m ¼ 23.0 Mg ha 1, which leads to R 32 ¼ 23:0 1 exp 31 Dependence of parameter n on R is given by R 32 n ¼ 21:3 ¼ exp 31 ð23þ ð24þ Results are shown in Fig. 3, where the curves are drawn from Eqs. (23) and (24). It should be noted that for R ¼ 100 cm, the parameters reach 89% of maximum. For the 26-wk growing season, this represents Figure 3. Dependence of yield parameter () and plant N uptake parameter ( n ) on seasonal rainfall (R) for dwarf elephantgrass grown at Gainesville, Florida. Data from Table 2. Curves drawn from Eqs. (23) and (24).

9 Response of Dwarf Elephantgrass to pplied Nitrogen and Rainfall cm d 1 (0.22 inch d 1 ), which appears to be a reasonable estimate of evapotranspiration for a high level of water availability. The reader may object that this part of the analysis is based on only two data points. We readily concede the point and suggest further study to investigate water consumption by the plants. The interested reader can find extensive application of the extended logistic model and growth models for a variety of crops and soils in the text by the authors. [6] REFERENCES 1. Overman,.R.; Wilkinson, S.R.; Wilson, D.M. n extended model for forage grass response to applied nitrogen. gron. J. 1994, 86, Overman,.R.; Wilson, D.M.; Kamprath, E.J. Estimation of yield and nitrogen removal by corn. gron. J. 1994, 86, Valentim, J.F.; Ruelke, O.C.; Prine, G.M. Evaluation of forage yield, quality, and botanical composition of a dwarf elephantgrass-rhizoma peanut association as affected by nitrogen fertilization. Soil Crop Sci. Soc. Fla. Proc. 1988, 47, Overman,.R.; Sanderson, M..; Jones, R.M. Logistic response of bermudagrass and bunchgrass cultivars to applied nitrogen. gron. J. 1993, 85, Overman,.R.; Scholtz, R.V. Corn response to irrigation and applied nitrogen. Commun. Soil Sci. Plant nal. 2002, 33, Overman,.R.; Scholtz, R.V. Mathematical Models of Crop Growth and Yield; Marcel Dekker, Inc.: New York, 2002.