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PAGE 1 1 EFFICIENCY OF PLANT RESPONSE TO APPLIED NITROGEN FOR CROPS By J. COLLEEN HOWARD A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2010 PAGE 2 2 2010 J. Colleen Howard PAGE 3 3 To my mother, Patricia Howard who has encouraged me throughout my academic career PAGE 4 4 ACKNOWLEDGMENTS First and f oremost, I would like to express my sincere gratitude to my advisor Dr. Allen Overman for the continuous support of my graduate work, for his patience, motivation, enthusiasm, and immense knowledge. His guidance helped me in the research and writing of th is thesis. I could not have imagined having a better advisor and mentor for my graduate research. It is a pleasure for me to thank Dr. Richard Scholtz, who is an excellent teacher, mentor and friend. Dr. Scholtz played a key role in my decision to contin ue my education and enter into my area of research. I would also like to express my appreciation to my thesis committee: Dr. Ray Bucklin, Dr. Paul Chadik, and Dr. George Hochmuth, for contributing their time, encouragement and insights. The financial support of the University of Florida is gratefully acknowledged. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 6 LIST OF FIGURES ................................ ................................ ................................ ......................... 7 ABSTRACT ................................ ................................ ................................ ................................ ..... 8 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................... 9 Common Crop Models ................................ ................................ ................................ ........ 10 Background ................................ ................................ ................................ ......................... 11 2 MODEL DESCRIPTION ................................ ................................ ................................ ....... 12 Extended Logistic Model ................................ ................................ ................................ .... 12 Efficie ncy Measure Development ................................ ................................ ....................... 14 3 DATA ANALYSIS ................................ ................................ ................................ ................ 16 Coastal Burmadagrass Response to Applied Nitrogen ................................ ....................... 16 Efficiency Calculations ................................ ................................ ................................ ....... 19 4 CONCLUSION ................................ ................................ ................................ ....................... 26 Discussion of Model Parameters ................................ ................................ ......................... 26 Summary of Logistic Model ................................ ................................ ............................... 27 LIST OF REFERENCES ................................ ................................ ................................ ............... 29 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ......... 31 PAGE 6 6 LIST OF TABLES Table page 3 1 Prine and Burton field data 1953 54, gives applied nitrogen rate, harvest interval, yield and N uptake for both years. ................................ ................................ ..................... 21 4 1 Model parameters and efficiency results for 1953 and 1954. ................................ ............ 28 PAGE 7 7 LIST OF FIGURES Figure page 3 1 Response of biomass yield ( Y ), plant N uptake ( N u ) and plant N concentration ( N c ) to applied nitrogen ( N ) for harvest interval of 4 weeks and two years (1953 and 1954) for coastal bermudagrass grown at Tifton, GA. Data adapted from Prine and Burton (1956). ................................ ................................ ................................ ................................ 22 3 2 Phase plots of biomass yield ( Y ) and plant N concentration ( N c ) vs. plant N uptake ( N u ) for harvest interval at 4 weeks and two years (1953 and 1954) for coastal bermudagrass grown at Tifton, GA. Data adap ted from Prine and Burton (1956). .......... 23 3 3 Response of plant N uptake ( N u ) to applied nitrogen ( N ) for harvest interval of 4 weeks and two years (1953 and 1954) for coastal bermudagrass grown at Tifton, GA .... 24 3 4 Dependence of efficiency of plant N uptake on appl ied nitrogen ( N ) for harvest interval of 4 weeks and two years (1953 and 1954) for coastal bermudagrass grown at Tifton, GA. ................................ ................................ ................................ ..................... 25 PAGE 8 8 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Master of Engineering EFFICIENCY OF PLANT RESPONSE TO APPLIED NITROGEN FOR CROPS By J. Colleen Howard December 2010 Chair: Allen Overman Major: Agricultural and Biological Engineering Many factors contribute to crop production. These include applied nutrients, water availability (such as rainfall and irrigation), and frequency of harvest (for perennial grasses). An important factor in resource management is to optimize crop utilization of applied nitrogen ( N ). In this article the logistic equation is used for this purpose. This work links three model parameters to water availability, background nitrogen levels and plant response to applied nitrogen. Two measures of optimum efficiency are derived from this model: a differential measure and an integral measure. The two measures are shown to be closely related. The d ata used for this analysis are from a field study at Tif ton, Georgia on response to applied N with the warm season perennial coastal bermudagrass grown on Tifton loamy sand. The study was conducted over a two year period which included 1953 (normal rainfall) and 1954 (severe drought). Optimum efficiency of plant N utilization was approximately 100% for 1953 and approximately 50% for 1954. This shows the interaction between plant N uptake and water availability. This general theory is believed to apply to other crop species (perennials and annuals), soi l types, and the three major nutrients (nitrogen, phosphorus, and potassium). PAGE 9 9 CHAPTER 1 INTRODUCTION From 1959 t o 1999, the world population doubled from three billion to six billion people. ion s imply the population will increase again by an additional three billion people by 2044 reaching nine billion people (U.S. Census Bureau 2010 ). Predictions for food supply, demand, and prices rely heavily on the projections of population growth and agri cultural productivity (Islam 1995 ). Given the likely population trends, it is necessary to anticipate potential food supply requirements and prepare to meet those requirements Determining an efficient resource management m odel is imperative for increase d crop yield s and a sustainable future for agriculture (FAO 1991). An accurate model of plant response to applied nutrient allows for better understanding of plant nutrient use as well as overall increased understanding of plant physiology. A greater per spective of plant nutrient use facilitates more accurately prescribed fertilizer recommendations. Improved f ertilizer recommendations optimize crop yield and decrease loss of nutrients to the environment, thus increasing profit (Bhumbla 2010) Currently, s everal philosophies are used with soil test results for fertilizer recommendations The most common are basic cation saturation ratios, percent sufficiency ranges (crop nutrient requirement) and build up and maintenance. Each of these philosophies is bas ed on different assumptions about crop needs and how crops respond at different soil test levels and different amounts and ratios of nutrients (Hochmuth and Hanlon 2010). Excess n utrients have the potential to pollute surface and groundwater in the surrou nding environment. Numerous works have identified agricultu ral nonpoint source pollution (n utrient losses ) as the leading cause of water quality impacts. Nitrate is the number one cause of public water supplies being closed in violation of drinking water PAGE 10 10 standards; expensive water treatment is required to return the water quality to drinking water standards (Bhumbla 2010). Common Crop Models There are several commonly used m ethod s for crop modeling : the polynomial equation the quadratic equation (a second order polynomial) Mitscherlich model and the extended logistic model. A polynomial equation is often used for crop modeling due to the ease of its use; it can be determined by a number of common graphing programs. The polynomial model fits the d ata exactly; however, it cannot be used to predict trends in the overall system. In addition since each data point is fit exactly to the equation there are no degrees of fr eedom for statistical analysis. Furthermore, the polynomial model will produce a hi gh number of parameters making it difficult to draw inference as to their meaning. The most commonly used method for crop modeling is the quadratic model. The quadratic model is a simplified form of the polynomial model; it has only three parameters to b e interpreted. The downfall of the quadratic model is that it depicts a peak (and subsequently a decline), which is not true of the data and can lead to unrealistically high fertilizer recommendations (Overman and Scholtz 2002). It has been shown that the typical plot of yield vs. applied nutrient is a sigmoid or S shaped curve (Russell 1937) The Mitscherlich model depicts the upper portion of the sigmoid curve and has few parameters for interpretation. Conversely the Mitscherlich model allows for nega tive yields with a decrease in soil nutrients, which has no physical meaning The extended logistic equation like the quadratic and Mitscherlich models, has few parameters for analysis. In addition, the extended logistic model depicts a sigmoid curve ; moreover the extended logistic model does not allow for negative yields with decreasing soil nutrients. The disadvantage of the extended logistic model is that it requires nonlinear regression to determine the model parameters, which can be laborious (Ov erman and Scholtz 2002). PAGE 11 11 Background In 1990, the logistic model was used to relate dry matter yield to applied nitrogen and provided a sensitivity analysis of the parameters by Overman et al. (1990a). Continued research by Overman et al. (1990b) used the logistic model to link equation parameters for bermudagrass and bahiagrass to water availability and harvest interval. The logistic model has been used to relate c oastal bermudagrass to applied nitrogen phosphorus, and potassium (N, P, and K respect ively) (Overman et al. 1991). In 1994 the extended logistic model coupled dry matter yield and nitrogen uptake to applied nitrogen; it accu rately described the relationship of nitrogen concentration data as the ratio of nitrogen uptake to yield (Overman e t al. 1994). The 1994 work by Overman was also first to identify the common response coefficients for the two logistic equations. The logistic model has been rigorously defended and compared to other regression models such as the exponential model and th e Mitscherlich model ( Overman 1995). Since the development of the model it has been successfully applied to numerous crops, soils and nutrients (Overman et al. 2003). The research described herein applied the ex tended logistic model to biomass yield and nitrogen uptake in response to applied nitrogen. The efficiency of nitrogen uptake was analyzed with the differential measure of efficiency and the integral measure of efficiency PAGE 12 12 CHAPTER 2 MODEL DESCRIPTION Extended Logistic Model Through data analysis of field experiments on nitrogen uptake, a two part postulate can be formed showing that the extended logistic model describes crop response to applied nutrients. The first part, plant nitrogen uptake ( N u ) is related to applied nitro gen ( N ) by the extended logistic equation. Secondly, biomass yield ( Y ) follows a hyperbolic relationship with N u The logistic equation for plant nitrogen uptake corresponding to applied nitrogen is written as (1) for which, N is applied nitrogen, kg ha 1 ; A n is the maximum nitrogen uptake, kg ha 1 ; b n is the intercept parameter for nitrogen uptake, and c n is the response coefficient to applied nitrogen, ha kg 1 The units of c n are the reciprocal for those of N allo wing N u units of kg ha 1 The hyperbolic relationship of biomass yield ( Y ) to nitrogen uptake is given by (2) where Y m is the maximum potential yield, Mg ha 1 ; and K n is the response parameter for N uptake, kg ha 1 Substituting the logistic equation for nitrogen uptake (Eq. 1) into the hyperbolic equation for yield (Eq. 2) leads to a second logistic equation relating yield to applied nitrogen, given in Eq. ( 3 ) (3) where A y is the max imum yield, Mg ha 1 ; and b y is the intercept parameter for yield. Substitution of Eq (1) into Eq (2) defines a new parameter A y as PAGE 13 13 (4) From these definitions it can also be shown that (5) From Eq s. (4) and (5) it can be shown that the hyperbolic and logistic parameters are related by Eq. (6) and (7) (6) (7) wit h the hyperbolic parameters on the left hand side and logistic param eters are on the right hand side The definition of is given by Eq. (8). (8) B y definition A n and A y must be greater than zero and Y m and K n must also be greater than zero; therefore, from Eqs. ( 5 ) and ( 6 ) must also be greater than zero. To determine maximum and minimum plant nitrogen concentration N c can be written as the ratio of the two logistic equations of N u and Y (9) where N cm = A n / A y is maximum plant N concentration, g kg 1 If N cm is the maximum plant N concentration then the lower limit of N c is N cl found by taking the limit of Eq. (9) for reduced N levels. Using the definition of N cl is defined by Eq. (10). PAGE 14 14 (10) Since N cl < N cm it follows from Eq. (10) that must be positive and b n > b y Equation (10) also demonstrates that since N cm and N cl are characteristic of the plant then must also be characteristic of the plant. These parameters were found to be strong functions o f the crop, invariant to location, soil type and water availability for corn and ryegrass (Scholtz, 2002). As defined, plant nitrogen concentration ( N c ) is the ratio of nitrogen uptake over biomass yield, N c = N u / Y From Eq (2) the nitrogen concentration, N c can be linearized as follows (11) The intercept of this linear equation, K n / Y m is the lower limit on nitrogen concentration, N cl This lower N limit occurs at highly depleted soil nitrogen levels. Efficiency Measure Development One of the goals of modeling crop response to applied nutrient is to determine the point of maximum efficiency of applied nutrient to yield or nutrient uptake. The most commonly used is yield efficiency, which is not discussed herein and does not follow the usual confines of an efficiency definition. There are two other competing theories of how to determine peak efficiency; which are the differential measure of effi ciency and the integral measure of efficiency (commonly used by agronomists). These measures of efficiency both refer to a unit of nitrogen uptake per unit of nitrogen applied. The differential measure of efficiency gives the maximum differential or the greatest rate of nitrogen uptake per applied nitrogen. This is s hown graphicall y at the point which N u vs. N has the greatest slope, known as N 1/2 This point, N 1/2 can be determined by Eq. (12) PAGE 15 15 (12) and from Eq. (1) at b n c n N = 0 N u = A n /2 Substituting b n c n N = 0 into the first derivative results in the slope at N 1/2 From this Eq. (13) was derived. (13) The integral me asure provides the greatest amount of nitrogen uptake per applied nitrogen. The definition of the integral measure of efficiency is given in Eq. (14) (14) where N uo is the nitrogen uptake at N equals zero. Data gathered in previous research established that the peak efficiency, E p occurs at 1.5* N 1/2 which will be referred to as N p (Overman, 2006). S ubstituting Eq. (1) into Eq. (14 ) the peak efficiency is written as Eq. (15). (15) PAGE 16 16 CHAPTER 3 DATA ANALYSIS Coastal Burmadagrass Response to Applied Nitrogen In this work data was employed from field research performed at Tifton, GA by G.M. Prine and G.W. Burton in 1953 and 1954. The study was on coastal bermudagrass ( Cynodon dactylon L.) grown on Tifton loamy sand (fine loamy, kaolinitic, thermic Plinthic Kandiudult) investigating the effect of applied nitrogen rate and harvest interval on yield (Prine and Burton, 1956). The study used applied nitrogen rates of 0, 112, 336, 672 and 1 008 kg ha 1 and harvest intervals of 2, 3, 4, 6 and 8 weeks. Plant biomass and nitrogen uptake were reported as listed in Table 3 1 The two year study generated unexpected results when 1953 had average rainfal l and 1954 had a severe drought. For this e xperiment, all non treatment agronomic practices were held constant. These circumstances made it possible to detect the effect of weather, and namely water availability, on plant response. Figure 3 1 illustrates the relationship of biomass yield, nitroge n uptake and nitrogen concentration to applied N and is useful for explaining the development of the logistic model. For simplification only the analysis from the four week harvest interval of both years will be shown. The plot of N u vs. N shown in Figure 3 1 can be used to visually estimate maximum N uptake ( A n ) required for determining c n and b n parameters. By inspection A n is approximately 740 kg ha 1 for 1953 (wet year) and 350 kg ha 1 for 1954 (dry year) The c n and b n parameters could be de termined several ways; a simple method would be linear regression on both years on the four week harvest interval. Another approach would be to average all five harvest intervals then perform a linear regression ; however for this complex set of data, th e most accurate method is a nonlinear regression ( pe rformed by Overman et al. (1990 b) ) Overman found that A n of 650 PAGE 17 17 kg ha 1 for 1953 and 340 kg ha 1 for 1954 are more accurate fit. Using the A n c n and b n parameters in Eq. (1), plant nitrogen uptake can be estimated using Eqs. (16a) and (16b) 1953: (16a) 1954: (16b) The curves for N u vs. N in Figure 3 1 are governed by Eqs. (16a) and (16b). Figure 3 2 shows the phase plots of Y and N c vs. N u produced by performing regression analysis on Eq. (11) yielding Eqs. (17a) and (17b). 1953: (17a) 1954: (17b) This leads to the hyperbolic relationship from Eq. (2) of Y to N u to Eq. (18). 1953: (18a) 1954: (18b) The hyperbolic curves of Y vs. N u are governed by Eqs. (18a) and (18b). Having determined the parameters A n and K n allows for b y and A y to be determined and ultimately be used to evaluate the logistic equation for Y To determine b y Eq. (6) was rearranged for and used in Eq. (7) as demonstrated in Eqs. (19a) and (19b). 1953: (19a) PAGE 18 18 1954: (19b) The final parameter required to write the logistic equation of yield response to applied N is A y determined by rearranging Eq. (5) yields Eq. (20). 1953: Mg ha 1 (20a) 1954: Mg ha 1 (20b) The curve for yield response to applied N in Figure 3 1 is governed by Eqs. (21a) and (21b) 1953: (21a) 1954: (21b) Using Eq. (1) for N u and Eqs. (21a) and (21b) for Y N c is the written as 1953: (22a) 1954: (22b) Equations (22a) and (22b) are used to plot the curve for N c vs. N in Figure 3 1. Comparing the fit of the curves with data points it appears the model is reasonably accurate. From Eq. (12) the range of nitrogen concentration is found to be 13.20 to 27.23 g kg 1 for 1953 and 13.70 to 28.23 g kg 1 for 1954. It should be noted that N c commonly referred to as plant nitrogen concentration, is the specific nitrogen content or mass of plant N per unit of biomass. PAGE 19 19 Efficiency Calculations For the Prine and Burton data, both measures of efficiency calculation, the differential method a nd the integral method, were used and the resulting graphs are shown in Figures 3 3 and 3 4, respectively. The applied N axis ranges from negative to positive, negative N represents depleted soil nitrogen; this is shown to illustrate that the model is continuous and well behav ed. The differential method is presented in the graph of N u vs. N (Figure 3 3) showing the corresponding point ( N 1/2 A n /2) which defines the inflection point of the curve representing the greatest rate of nitrogen response. From Eq. (13) N 1/2 is calculated for both years, shown in Eq. (23). kg ha 1 (23) From Eq. (1) at N = N 1/2 N u = A n /2, calculated in Eqs. (24a) and (24b). 1953: kg ha 1 (24a) 1954: kg ha 1 (24b) Employing the differential method for efficiency, applying 273 kg ha 1 nitrogen will produce the peak nitrogen uptake of 325 kg ha 1 in 1953 and 170 kg ha 1 1954. The slope of the curve at N 1/2 is determined from Eq. (13 ) 1953: (25a) 1954: (25b) Where ever the slope exceeds one the rate nitrogen uptake will be greater than the amount of nitrogen applied. For 1953, the slope at and near to N = N 1/2 is greater than one. For 1954, the PAGE 20 20 slope at N = N 1/2 is less than one and since N 1/2 represents the peak slope, the rate of nitrogen uptake was less than applied N at all levels of applied N The integral method for maximum efficiency is illustrated in Figure 3 4 from Eq. (15 ) where N p is 1.5* N 1/2 or 409 kg ha 1 The peak of the graph is the maximum efficiency of N u to applied N The peak efficiency as measured by the integral method is given in Eqs. (26a) and (26b). 1953: (26a) 1954: (26b) From Figure 3 4 and the calculations of Eq. (26) it is shown that N u reaches maximum efficiency at applied N of 409 kg ha 1 for both years. In 1953 the peak efficiency possible is reached due to sufficient available water. In 1954, the maximum efficiency is half that of 1953, which illustrates the effect of available water on nitrogen uptake. The A n is the only parameter that changes between the Eq. (26a) and (26b), showing the effect of rainfall on N u efficiency. PAGE 21 21 Table 3 1. Prine and Burton field data 1953 54, gives applied nitrogen rate, harvest interval, yield and N uptake for both years. The four week harvest interval was used in this analysis. 1953 Applied N kg ha 1 0 112 336 672 1008 Y Mg ha 1 2 2.3 6.0 11.8 17.4 19.7 3 3.3 8.9 13.6 19.2 20.5 4 2.7 9.9 17.7 21.7 23.6 6 4.4 12.8 21.8 28.1 30.1 8 5.6 13.7 22.9 27.9 29.3 N u kg ha 1 2 37 130 327 582 721 3 51 184 363 579 682 4 40 176 431 590 739 6 53 158 392 621 738 8 62 184 372 545 624 1954 Applied N kg ha 1 0 112 336 672 1008 Y Mg ha 1 2 0.76 2.7 6.8 7.8 8.6 3 0.94 3.7 7.4 9.9 10.0 4 1.08 4.6 9.5 11.1 11.5 6 1.30 6.2 11.6 13.6 14.1 8 1.93 6.5 12.2 15.9 16.2 N u kg ha 1 2 17 70 224 299 320 3 15 75 208 294 364 4 19 80 233 323 344 6 21 92 261 293 390 8 26 100 223 325 417 Adapted from Overman and Scholtz (2002, Tables 3.5 and 3.6). PAGE 22 22 Figure 3 1. Response of biomass yield (Y), plant N uptake (Nu) and plant N concentration (Nc) to applied nitrogen (N) for harvest interval of 4 weeks and two years (1953 and 1954) for coastal bermudagrass grown at Tifton, GA. Data adapted from Prine and Burton (1956). PAGE 23 23 Figure 3 2. Phase plots of biomass yield ( Y ) and plant N concentration ( N c ) vs. plant N uptake ( N u ) for harvest interval at 4 weeks and two years (1953 and 1954) for coastal bermudagrass grown at Tifton, GA. Data adapted from Prine and Burton (1956). PAGE 24 24 Figure 3 3. Calculated r esponse of plant N uptake ( N u ) to applied nitrogen ( N ) for harvest interval of 4 weeks and two years (1953 and 1954) for coastal bermudagrass grown at Tifton, GA PAGE 25 25 Figure 3 4. D ependence of calculated efficiency of plant N uptake on applied nitrogen ( N ) for harvest interval of 4 weeks and two years (1953 and 1954) for coastal bermudagrass grown at Tifton, GA. Points are calculated. PAGE 26 26 CHAPTER 4 CONCLUSION Discussion of Model Parameters Figures 3 1 through 3 3 illustrate the accuracy of the extended logistic model in describing plant response to applied nitrogen. This wor k confirms what previous research efforts have determined in c being common for both years and therefore independent of available water and likely related to plant species. Also b n is shown to be the intercept of N u and N and is the background level of N in the system; b n is independent of plan t type but related to soil conditions. The effect of b n on efficiency should be noted; a decrease in b n is an i ncrease in the background soil nitrogen Decreasing b n causes the integral efficiency curve, figure 3 4, to shift to the left, where the peak integral efficiency will improve until b n = 0. The differential efficiency does not change with either an increase or decrease in b n the differential efficiency is on ly dependent on A n or c n Large positive values of b n represent a deficiency in soil nitrogen and require large quantities of N for the soil plant system to become efficient. When b n is a positive value near zero it indicate s that little N is required in order for the system to become efficient. Negative values of b n efficiency has already been exceeded by the excess levels of background N in the soil This work shows that for the extended l ogistic model, A n describes the effect of available water on plant nitrogen utilization. It is shown by comparing the equations for peak efficiency (Eq. 26a and 26b) that A n is the only parameter to change for the two years For the Prine and Burton stu dy all non treatment agronomic practices where held constant (i.e. all but N application rate and harvest interval) ; therefore the variation in A n must be attributable to the weather change between the two years, the substantive difference coming from rainfall. This is also evident from E qs. (25a) and (25b) where c n is invariant between the years, leaving A n a s the PAGE 27 27 key parameter in optimizing the efficiencies amplitude. Since the only uncontrolled input was the weather (namely rainfall) and the only par ameter that varied from one year to the next was A n there exists a relationship between the two Previous work studying corn response to water and applied nutrients supports the link of A n to available water (Reck and Overman 1996). Given the difference in the efficiency of nitrogen utilization in the two years, (1953 having greater yields) it is clear optimum water availability will result in optimum nutrient uptake efficiency. T able 4 1 of mo del parameters is provided for compariso n Summary of Logistic Model Further work can be done to determine the dependence of A n on harvest interval. The 1953 54 Prine and Burton study used five harvest intervals and it was determined that the same trend is present for A n for all harvest in tervals for both years. However in a study by Beaty et al. (1963), longer harvest intervals wer e used and A n does not follow the same trend. The A n parameter was found to be a linear exponential function of harvest interval. This model can be extended to compare other plant species and to model the effects of nutrients other than nitrogen su ch as phosphorus and potassium. The extended logistic model performs well for both mobile and non mobile nutrients (Overman et al. 1991) While t he model has been u sed extensively on warm season perennials with various fixed harvest intervals, it has also been proven to apply to warm season annuals with dormant cycles (Overman and Scholtz 2002). The extended logistic model has yet to be applied to slow growing peren nial woody plants Further work can also be preformed to assess the application of the integral measure of efficiency for estimating depletion rates of soil nutrients. PAGE 28 28 T able 4 1. Model parameters and efficiency results for 1953 and 1954. Model Parame ter 1953 1954 Units 4 4 wk A y 23 12 kg ha 1 A n 650 340 kg ha 1 b y 1.4 1.4 b n 2.10 2.10 c n 0.0077 0.0077 ha kg 1 N cm 28 29 g kg 1 N 1/2 273 273 g kg 1 A n c n /4 1.25 0.66 N p 409 409 g kg 1 E p 1.0 0.53 Adapted from Overman and Scholtz (2002, Table 3.8). PAGE 29 29 LIST OF REFERENCES Beaty, E.R., J.D. Powell, R.H. Brown, and W.J. Etheredge. 1963. Effect of nitrogen rate and clipping frequency on yield of Pensacola bahiagrass. Agron. J ., 55, 3 4. Bhumbla, D.K. 2010. Agriculture Practices and Nitrate Pollution of Water [Fact Sheet]. Web. 1 Nov 2010. < http://www.caf.wvu.edu/~forage/nitratepollution/nitrate.htm > Food and Agriculture Organization of the United Nation http://www.fao.org/docrep/u3550t/u3550t02.htm > Web. 1 Nov. 2010. PAGE 30 30 Reck, W.R. and A.R. Overman. 1996. Estimation of corn response to water and applied nitrogen. J. Plant Nutr 19, 201 214. Russell, E.J. Soil Conditions and Plant Growth, 7 th ed. London: Longmans, Green & Co ., 1937. Print. Scholtz, R. V. 2002. Mathematical Modeling of Agronomic Crops: Analysis of Nutrient Removal and Dry Matter Accumulation Doctor of Philosophy Dissertation. University of Florida. Gainesville, Florida. 139 pgs. United States. Census Bureau. International Data Base. 2010. Web. 1 Nov. 2010 PAGE 31 31 BIOGRAPHICAL SKETCH J. Colleen Howard, a Texas native, moved to Gainesville, Florida in 2002 where she co mpleted her high school education while taking college courses at Santa Fe Community College While at Sa nta Fe Community College Colleen realized she wanted to study to become an agricultural engineer. By s pring 2006, she had obtained her Associate of Science degree. In fall of 2006, Colleen transferred to The University of Florida and entered into their engineering program. While attending The University of Florida Colleen was an active member of the American Society of Agricultural and Biological En gineers (ASABE) Colleen represente d ASABE on the Agricultural Committee (2007) and as captain of T he University of G.B. Gunlogson Fountain Wars Design Competition (2007 and 2008). In August of 2009, Colleen graduated with her Bachelor of Science degree in engineering, focusing on land and water resources and she Colleen focused on mathematical models for crop nutrient uptake Upon fulfilling all requirements for the Master of Engineering degree, Colleen will pursue a career in the agricultural engineering field. 