June 1991
Iolf)
Central Sc:ence
Buli~iin813 (Technical)
JUL 2 4 19S1
University of Florida
Estimation of Dry Matter Production and Nitrogen
Removal by Coastal Bermudagrass in Florida
Allen R. Overman, Fred M. Rhoads,
Robert L. Stanley, Jr., O. Charles Ruelke
Agricultural Experiment Station
Institute of Food and Agricultural Sciences
University of Florida
J.M. Davidson, dean
Estimation of Dry Matter Production and Nitrogen Removal
by Coastal Bermudagrass in Florida
Allen R. Overman
Fred M. Rhoads
Robert L. Stanley, Jr.
O. Charles Ruelke
The authors are: Professor of Agricultural Engineering, Professor of Soil Science, Professor of Agronomy, and Pro
fessor Emeritus of Agronomy, University of Florida, Gainesville, Florida 32611.
Table of Contents
List of Tables ......................................................... iii
List of Figures ......................................................... iv
Preface .............................................. ............... v
Introduction ................................................ .......... 1
Yield Response to Applied N .............................................. 2
Quincy, Florida (19871988)
Gainesville, Florida (19691970)
Jay, Florida (19541955)
Forage N Concentration ................................................. 4
Estimation Equation
Quincy, Florida (1987)
Gainesville, Florida (1969)
Summary of Estimation Procedures ......................................... 4
Estimation of Yield
Estimation of Forage N Concentration
Estimation of Forage N Removal
Example Calculations
C conclusions .......................................................... 6
References ............... ............................................ 7
Tables ................................ .............................. 8
Figures .......................................... .................. 19
List of Tables
1. Coastal bermudagrass studies included in analysis ................... 8
2. Yield distributions for Coastal bermudagrass at Quincy, Florida for 1987
3. Yield distributions for Coastal bermudagrass at Quincy, Florida for 1988 ..... 9
4. Parmeters for empirical model for Coastal bermudagrass at Quincy, Florida
5. Normalized yield versus normalized time for Coastal bermudagrass at
Q uincy, Florida for 1987 ........................................ 10
6. Normalized yield versus normalized time for Coastal bermudagrass at
Quincy, Florida for 1988
7. Summary of N response parameters for Coastal bermudagrass at
Q uincy, Florida ................................... ........ ... 11
8. Analysis of variance for Coastal bermudagrass at Quincy, Florida
9. Normalized total yield versus nomalized N for Coastal bermudagrass
at Quincy, Florida ................................. ......... 12
10. Yield distributions for Coastal bermudagrass at
Gainesville,\Florida for 19691970
11. Parameters for empirical model for Coastal bermudagrass at
Gainesville, Florida ........................................... 13
12. Normalized yield versus normalized time for Coastal bermudagrass
at Gainesville, Florida
13. Summary of N response parameters for Coastal
bermudagrass at Gainesville, Florida ................................... 14
14. Normalized total yield versus normalized N
for Coastal bermudagrass at Gainesville, Florida
15. Total yields for Coastal bermudagrass at
Jay, Florida for 19541955
16. Summary of N response parameters for Coastal
bermudagrass at Jay, Florida .................................... 15
17. Analysis of variance for Coastal bermudagrass
at Jay, Florida
18. Normalized total yield versus normalized N for
Coastal bermudagrass at Jay, Florida
19. Forage N concentration and removal by Coastal
bermudagrass at Quincy, Florida for 1987 .......................... 16
20. Comparison of estimated and measured forage N concentration for Coastal
bermudagrass at Quincy, Florida for 1987
21. Forage N concentration for Coastal bermudagrass at
Gainesville, Florida for 1969 ..................................... 17
22. Summary of N response parameters for Equation (4)
for bermudagrass
23. Summary of yield response parameters in Equations (4) and
(7) for berm udagrass .......................................... 18
List of Figures
1. Normalized yield versus normalized time for Coastal bermudagrass
at Quincy, Florida .................. ................... ....... 19
2. Cumulative yield versus time for Coastal bermudagrass
at Quincy, Florida
3. Dependence of mean time (t) and time spread (a) on applied N
for Coastal bermudagrass at Quincy, Florida
4. Dependence of total yield on applied N for Coastal bermudagrass
at Q uincy, Florida ............................................ 20
5. Normalized total yield versus normalized N
for Coastal bermudagrass at Quincy, Florida
6. Normalized yield versus normalized time for Coastal bermudagrass
at Gainesville, Florida .......................................... 21
7. Cumulative yield versus time for Coastal bermuda
grass at Gainesville, Florida
8. Dependence of mean time (t) and time spread (a) on applied N
for Coastal bermudagrass at Gainesville, Florida
9. Dependence of total yield on applied N for Coastal bermudagrass
at Gainesville, Florida (Data from Ruelke and Prine, 1971) ............... 22
10. Normalized total yield versus normalized N for Coastal bermudagrass
at Gainesville, Florida
11. Dependence of total yield on applied N for Coastal bermudagrass
at Jay, Florida (Data from Jeffers, 1955) ............................ 23
12. Normalized total yield versus normalized N
for Coastal bermudagrass at Jay, Florida
13. Estimated dependence of mean time (t) and time spread (a) on applied N
for Coastal bermudagrass in Florida ............................... 24
14. Estimated dependence of total yield (YT) on applied N and harvest
interval (At) for Coastal bermudagrass in Florida
15. Sensitivity of total yield response of Coastal bermudagrass
on model parameters in Equation (4) .............................. 25
16. Effect of residual soil N on response of total yield of Coastal
bermudagrass to applied N
17. Estimated dependence of forage N concentration on applied N
and harvest interval (At) ........................................ 26
18. Estimated dependence of forage N removal on applied N, harvest interval,
and water availability
Preface
The purpose of this report is to provide documentation of procedures for estimation of dry matter
production and N removal by Coastal bermudagrass under Florida conditions. Such documentation is
needed by professionals (engineers, advisors, managers, and regulators) in an age of increased account
ability and liability. The research community can serve a vital role in this responsibility. In essence,
this report was developed to ultimately serve practitioners in the field. Additional articles, based on
this material are planned for technical journals and in an extension format.
The equations used in this analysis may be viewed as regression models. While the models are not
the ultimate in sophistication (biological and mathematical), they do provide a useful tool to aid in
management decisions. Furthermore, they are easy to implement on a pocket calculator.
Introduction
Coastal bermudagrass (Cynodon dactylon, (L)
Pers.) is grown extensively in the United States for
hay and pasture. Numerous field studies have been
conducted in Florida. Jeffers (1955) compared re
sponse of Coastal bermudagrass and Pensacola ba
hiagrass [Paspalum notatum Flugge] to applied N
and water availability. Ruelke and Prine (1971)
compared response of several warm season grasses,
including Coastal bermudagrass, to applied N. More
recently Rhoads and Stanley (1989) evaluated re
sponse to applied N and S.
Overman and Blue (1990) have summarized the
response of Pensacola bahiagrass to applied N, har
vest interval, and water availability, with a focus on
Florida conditions. This bulletin is written as a
companion for Coastal bermudagrass.
Overman et al. (1988a,b; 1990b) have developed an
empirical model of Coastal bermudagrass produc
tion. The model relates dry matter distribution over
the season and total dry matter for the season to
applied N, harvest interval, and water availability.
Cumulative yield is given by
Y. = YT 1 + erf (to i (1)
2 J2 oa
where
t, = time to nth harvest (since Jan. 1), wk
= time to mean of dry matter yield distri
bution, wk
a = time spread of dry matter yield distribu
tion, wk
Y. = cumulative dry matter yield through nth
harvest, t/ha
n
= M Ayi
i=1
Ay, = dry matter yield of ith harvest, t/ha
Y, = total dry matter yield for season, t/ha
2 if exp (u2) du
Fractional yield is given by
F, =1 I1+ erf it __
2 [2 a
where
F, = Y,/YT
A plot of F. vs t, yields a straight line on probability
paper (Overman et al., 1988 a,b). It has been shown
(Overman et al., 1988b) that the parameters (YT, t,
a) in Equation (1) all depend upon applied N. Total
yield is related to applied N by the logistic equation
YT= A
1 + exp (bcN)
where
Y, = total annual dry matter yield, t/ha
N = applied N, kg/ha
A = maximum total dry matter yield, t/ha
b = intercept
c = N response coefficient, ha/kg
The parameters (A, b, c) in Equation (3) are esti
mated by nonlinear regression (Overman et al.,
1990 a,b). Equation (3) can be written in the equiv
alent form
Y, =
1 + exp (NN,,2/N')
where
N' = 1/c
= characteristic N, kg/ha
N1/2 = b/c
erf = error function
= N application required for half response
(YT = A/2), kg/ha
Parameters in Equations (2) and (3) are estimated
by nonlinear regression to minimize the error sum
of squares, E, according to
E = ( Zj Z)2 (5)
j
where
Zj = measured value of F. or YT
Z = estimated value of F. or YT [Equation 2 or 3]
j = observation number
The correlation coefficient, R, for nonlinear regres
sion is calculated from (Cornell & Berger, 1987)
R = [1 E (Z Zj )2/y (Zj Z)2112
where Z is the mean of Zj.
Overman et al. (1990b) have shown that the effect
of harvest interval may be included in the model,
Equation (3), by the equation
A = Ao (1 + 0.267 At) (7)
where Ao is the intercept, and depends upon water
availability. Equation (7) holds for At 2 6 wk.
Yield response to applied nitrogen
A list of studies included in this analysis is given
in Table 1. Data for individual harvests were not
available for the study conducted at Jay; thus only
total yields were included. Experimental details are
given in the references. Brief descriptions are given
here for completeness.
Equations listed in the previous section are used to
describe dry matter distribution over the season and
total yield for the season as related to applied N,
water availability, and harvest interval.
Quincy, Florida (19871988)
Rhoads & Stanley (1989) reported a threeyear
study with Coastal bermudagrass on Dothan loamy
sand. Data from 1986 were not used here due to
stabilization of the plots. Ammonium nitrate was
applied at rates of 0, 224, 448, 672, and 896 kg
N/ha each year in split applications, with onehalf
in early spring and onehalf following the second
harvest. Annual applications of 112 kg P/ha and
390 kg K/ha were made to all plots in early March
of each year. All treatments were replicated four
times. Clipping height was 2.5 cm.
Yield data are listed in Table 2 (1987) and Table 3
(1988). Dry matter yield (Ay), for individual har
vests are the average for four replications. Harvest
dates and times (t), referenced to January 1, are
given. Cumulative yields (Z Ay) and fractional yields
(F) are also listed. The last cumulative yield value
on each line accounts for estimated growth after the
last harvest.
Yield data were analyzed by nonlinear regression
to optimize parameters for Equation (2). Values of
time to mean (t) and time spread (a), along with
estimated total yield (YT) and correlation coefficient
(R), are summarized in Table 4. The correlation
coefficient was calculated by Equation (6).
According to Equation (2), a probability graph of
F versus (t 1)/o should reduce all data to a single
straight line, where appropriate i, and a for each
applied N are used. Calculated values are given in
Table 5 (1987) and Table 6 (1988), and are shown
in Figure 1. The lines are drawn from Equation (2).
These results indicate that dry matter production is
normally distributed over the season.
Dry matter production may also be presented in
the more conventional format of Figure 2, where
the curves are drawn from Equation (1) with appro
priate (YT, I, a) from Table 4.
Dependence of t and a on applied N is shown in
Figure 3. The curves are drawn from
I = 26.0 + 3.0 exp( N/200)
a = 9.0 2.0 exp( N/200)
Equations (8) and (9) follow the format used previ
ously by Overman et al. (1988a) and Overman and
Blue (1990). The effect of increased N is to provide
earlier growth (reduced 1) and spread out the
growth (increased a). The effect was most sensitive
at very low N levels.
Response of total dry matter yield to applied N is
shown in Figure 4. The curves are drawn from
Equation (3) with the coefficients shown in Table 7.
The overall correlation coefficient (R) for nonlinear
regression is 0.9984. Error estimates in Table 7 are
small for A and c and large (0.68) for b. The latter
occurs because b has a very low value (0.040) for
these data. Analysis of variance is given in Table 8
for this study, and follows procedures discussed by
Overman et al. (1990a,b). In mode (1) nonlinear
regression is performed for Equation (3) for 1987
and 1988 combined (2 yrs x 5 N levels). In mode (2)
the equation was fitted to each year separately.
Comparison of the two shows highly significant
difference, since the critical variance ratio was F (3,
4, 99) = 16.7. Mode (3) accounts for the variation
between years with individual A values in Equation
(3), since F (2, 4, 95) = 6.94.
According to Equation (4), a semilog graph of
(A/YT 1) versus (NN1/2)/N' should reduce all data
to a single straight line. Calculated values are given
in Table 9 and shown in Figure 5. The data follow
the logistic function rather closely.
The effect of harvest interval (At) can be account
ed for by Equation (7). In this study average harvest
interval was 4.4 wk (1987) and 5.2 wk (1988). In
serting appropriate At and A (Table 7) into Equa
tion (7) and solving for Ao yields 11.58 t/ha (1987)
and 9.61 t/ha (1988). Overman et al. (1990b) ana
lyzed data of Prine & Burton (1956) for Tifton,
Georgia and obtained A, of 11.40 t/ha (1953, wet
year) and 5.44 t/ha (1954, severely dry year). Thus,
Ao accounts for water availability. Results for
Quincy are consistent with this since 1988 was a
dry season with irrigation below optimum due to
limited water supply.
Gainesville, Florida (19691970)
Ruelke & Prine (1971) reported a three year study
on Scranton loamy sand. Data for 1968 are not used
due to lower P and K applications. Application rates
were 134, 269 and 538 kg N/ha annually. Onethird
was applied prior to first harvest, onethird prior to
third harvest and onethird prior to the fifth har
vest. A 413 ratio of NPgO,K20 was applied dur
ing 1969 and 1970. Treatments were replicated five
times. Clipping height was 5.0 cm.
Yield data are listed in Table 10. Model parame
ters are summarized in Table 11. High correlations
may be noted. These values were used to calculate
reduced time (tt)/a, (Table 12). Correlation of
relative yield with reduced time is shown in Figure
6 where the lines are drawn from Equation (2). Cu
mulative yields are shown in Figure 7, where curves
are drawn from Equation (1) with appropriate pa
rameters from Table 11.
Dependence of t and a upon applied N is shown
in Figure 8, where the curves are given by
S= 25.5 + 5.0 exp(N/200)
Id
a = 9.5 3.0 exp(N/200)
(10)
Response of total yield to applied N is shown in
Figure 9, where the curves are drawn from Equa
tion (3) with parameters listed in Table 13. Individ
ual A with common b and c were assumed. Analysis
of variance is not possible, since the model contains
three parameters and there are three treatments.
Reduced yields versus reduced N are listed in Table
14 and graphed in Figure 10. High correlation is
apparent.
The effect of harvest interval was estimated from
Equation (7). With appropriate A from Table 14 and
harvest interval of 5.2 wk for both years, we obtain
Ao of 5.11 t/ha (1969) and 5.53 t/ha (1970). As poi
nted out by Ruelke & Prine (1971), this soil tended
to be saturated during the rainy season and exces
sively dry during the dry season. Irrigation was not
included in the study.
Jay, Florida (1954 1955)
Jeffers (1955) conducted a twoyear study with
Coastal bermudagrass on Red Bay sandy loam.
Ammonium nitrate was applied in four applications
at approximately 45 day intervals beginning the
first week of March. In March, 1954 95 kg/ha of
P205 and of KO0 were applied. In 1955 an NP20,
K20 ratio of 211 was used. Plots were replicated
four times. Clipping height was not stated.
Total yields are listed in Table 15 and are plotted
in Figure 11. Curves are drawn from Equation (3)
with parameters listed in Table 16. Yields were
lower for 1954 (severely dry season) compared to
1955 (normal season). Analysis of variance (Table
17) showed significant difference between years,
since F (3, 4, 95) = 6.59. This difference was accou
nted for by individual A, since F (2, 4, 95) = 6.94.
Reduced yields versus reduced N are listed in Ta
ble 18 and graphed in Figure 12. Values follow Equ
ation (4) reasonably well.
Equation (7) is again used to account for harvest
interval. With appropriate A from Table 16 and At
of 5.9 wk (1954) and 7.8 wk (1955), it follows that
Ao is 5.74 t/ha (1954) and 6.15 t/ha (1955). The
value for 1954 compares to 5.44 t/ha for 1954 (se
vere drought) estimated for Tifton, Georgia by Ove
rman et al. (1990b). The value for 1955 (At = 7.8
wk) is questionable since Equation (7) has only
been shown valid for At < 6 wk.
Forage nitrogen concentration
Estimation equation
Overman and Wilkinson (1990) developed an equa
tion to relate forage N concentration for bermuda
grass to applied N and harvest interval. The equa
tion is given by
Nc = 4.50 (10.075 At) [1exp(N+200/350)] (12)
where
Nc = forage N concentration, %
At = harvest interval, wk
N = applied N, kg/ha
It was calibrated from six field studies and validated
for five additional data sets. Estimates from Equa
tion (12) are compared to experimental results in
the following section.
Quincy, Florida (1987)
Rhoads and Stanley (1989) reported forage N con
centration at two N rates for 1987 (Table 19). Indi
vidual cutting yields (Ay) and N removal (AN) are
also listed in Table 19. Weighted average Nc values
are
N = 0 kg/ha:
N = 224 kg/ha:
No = 169/11,280 = 1.50%
Nc = 346/17,760 = 1.95%
These are given in Table 20, along with estimated
values from Equation (12) for harvest interval of 4.4
weeks. The equation underestimates Nc by 13% at
N = 0. This effect was also observed by Overman
and Wilkinson (1990), where the procedure overes
timated by 9% at N = 0.
Gainesville, Florida (1969)
Ruelke and Prine (1971) reported forage N con
centration for (1969) averaged over three N rates.
Estimated values of Nc, calculated by Equation (12),
are listed in Table 21. Average estimated Nc of
2.04% compares to average measured value of 1.97
%, for a difference of 3.6%. Agreement is rather
close.
Summary of estimation procedures
Results from previous sections are now used to
develop estimation equations for dry matter yield,
forage N concentration, and forage N removal in
relation to applied N, harvest interval, and water
availability.
Estimation of yield
From results above for Quincy and Gainesville,
Florida it is concluded that 1 and a may be
estimated from
i = 26.0 + 3.0exp(N/200)
nd
a = 9.0 2.0exp(N/200)
These are shown in Figure 13. Estimates from
Equations (13) and (14) can then be used in
Equation (2) to calculate yield distribution over the
season.
Estimates are needed for the parameters in
Equation (4). Results from several studies are given
in Table 22 for N1,2 and N'. Average values of 150
kg/ha are assumed for both. More detailed analysis
would be required to relate variability of the
(14)
parameters to soil or climatic differences among
sites.
Values of the yield response parameter A in
Equation (4) are given in Table 23. Harvest interval
was incorporated through Equation (7).
Corresponding values of Ao are listed in Table 23.
The pattern stands out by comparison of values for
Tifton, Georgia for 1953 (wet year) and 1954
(severely dry year).
The general yield response equation is thus
written as
(15)
YT = A, (1+0.25 At)/1 +exp(N150/150)
where
Ao = 10 t/ha (optimum moisture)
Ao = 5 t/ha (severe water stress)
Equation (15) relates total annual dry matter yield
(YT) to applied N and harvest interval (At).
Application should be restricted to At 6 weeks.
Yield response curves are shown in Figure 14 for
harvest intervals of 2, 4, and 6weeks.
Cumulative dry matter production may be
calculated by combining Equations (13) (15) with
Equation (1).
Figure 35 provides an indication of sensitivity of
Equation (4) to each parameter (A, N1/2, N').
Parameter A simply serves as a multiplier, and is
influenced by harvest interval and water availability
(Figure 15a). The second parameter, N1/2, indicates
applied N where yield reaches onehalf maximum
(Figure 15b). Finally, N' controls incremental yield
response at N= N1I2 (Figure 15c).
The special case where N1/2= 0 (essentially the
same as for Quincy, Florida) is shown in Figure 16.
This indicates a high base level of soil N. In other
words, the plant "sees" the combination of applied N
and high soil N as the effective available N. For this
particular case, available N, N,, might be related to
soil N, N,, by
N, = N, + N (16)
300 + N
At Quincy, Florida bermudagrass followed highly
fertilized and irrigated corn of several years
duration, which provided a large pool of soil N. This
effect should appear in soil tests, and should receive
further attention.
Estimation of forage N concentration
Equation (12) appears to provide adequate
estimation of forage N concentration in terms of
applied N and harvest interval. Curves are shown in
Figure 17 for harvest intervals of 2, 4, and 6
weeks. Crude protein (CP) can be calculated from
CP = 6.25 Nc
Estimation of forage N removal
Forage N removal was calculated as the product
of dry matter yield and forage N concentration.
Cumulative N removal through the nth harvest is
given by
N, = 10Y, Nc
where
N, = cumulative N removal through nth harvest,
kg/ha
Y, = cumulative yield through nth harvest, t/ha
Nc = forage N concentration, %
The factor of 10 simply converts units to the proper
form. Annual total N removal is given by
(18)
NT = 10 YT Nc
where
NT = total annual N removal, kg/ha
YT = total annual yield, t/ha
Figure 18 shows forage N removal for harvest
intervals of 2 and 6weeks, and A, of 5 t/ha and 10
t/ha.
Example calculations
Application of the estimation procedure is now
illustrated by way of an example. Estimation can be
done from either equations or graphs; both are
referenced in this example. Choices must be made
for applied N, harvest interval (At), and water
availability (A,). for the present case we assume
N = 150 kg/ha
At = 6 wk
Ao = 5 t/ha (limited water)
It follows that
t = 27.4 wk (Equation (13) or Figure 13)
a = 8.1 wk (Equation (14) or Figure 13)
YT = 6.3 t/ha (Equation (15) or Figure 14)
Nc = 1.56% (Equation (12) or Figure 17)
NT = 98 kg/ha (Equation (17) or Figure 18)
It should be apparent from Figure 18 that forage
N removal was sensitive to applied N and water
availability, but insensitive to harvest interval (At).
This last effect occurs because dry matter
production increases with harvest interval, while
forage N concentration decreases, and the two
approximately offset each other.
Conclusions
An empirical model was used to analyze data for
Coastal bermudagrass from three separate field
studies. Inputs consisted of applied N, harvest
interval, and water availability. Output included dry
matter yield and distribution, forage N
concentration, and forage N removal. Estimation
equations included:
Equations (1), (13),
(14), and (15)
Forage N concentration Equation (12)
Forage N removal
Equations (17) and (18)
Example calculations for 150 kg/ha applied N, 6
wk harvest interval, and limited water availability
lead to 6.3 t/ha total annual yield, 1.56% forage N
concentration, and 98 kg/ha forage N removal.
Under these conditions, N recovery was 98/150 =
65%. Under ideal soil conditions, total yield and
forage N removal would be twice these values for
the same applied N and At.
Procedures discussed in this report are useful for
estimating agricultural production and
environmental impact. They also relate to
sustainable agriculture in terms of efficient
utilization of resources (such as nutrients and
water). It was noted that forage N removal was
sensitive to applied N and water availability, but
relatively insensitive to harvest interval (Figure 18).
Maximum incremental yield and N removal
occurred at applied N of 150 kg/ha (Figures 14 and
18). Further attention should be given to the effect
of soil N reserves on yield response to applied N
(Figure 16), which relates to antecedent
cropping/fertilizer conditions.
Dry matter yield
References
1. Cornell, J.A., and R.D. Berger. 1987. Factors that in
fluence the value of the coefficient of determination in
simple linear and nonlinear regression models. Amer.
Phytopath. Soc. 77: 6370.
2. Evans, E.M., L.E. Ensminger, B.D. Doss, and O.L.
Bennett. 1961. Nitrogen and moisture requirements of
Coastal bermuda and Pensacola bahia. Bulletin 337.
Alabama Agricultural Experiment Station, Auburn, AL.
19p.
3. Huneycutt, H.J., C.P. West, and J.M. Phillips. 1988.
Responses of bermudagrass, tall fescue and tallfescue
clover to broiler litter and commercial fertilizer. Bulle
tin 913. Arkansas Agricultural Experiment Sta tion,
University of Arkansas, Fayetteville, AK. 20 p.
4. Jeffers, R.L. 1955. Response of warmseason perma
nent pasture grasses to high levels of nitrogen. Soil and
Crop Sci. Soc. Fla. Proc. 15: 231239.
5. Overman, A.R., and W.G. Blue. 1990. Dry matter pro
duction and nitrogen uptake by Pensacola bahiagrass in
Florida. Florida Agr. Exp. Sta. Res. Bul. 880. University
of Florida, Gainesville, Fl. 80 p.
6. Overman, A.R., and S.R. Wilkinson. 1990. Estimation
of nitrogen concentration in bcrmudagrass. Fert. Res.
21:171177.
7. Overman, A.R., E.A. Angley, and S.R. Wilkinson.
1988a. Empirical model of Coastal bermudagrass pro
duction. Trans. Amer. Soc. Agr. Engr. 31: 466470.
8. Overman, A.R., E.A. Angley, and S.R. Wilkinson.
1988b. Evaluation of an empirical model of Coastal
bermudagrass production. Agr. Sys. 28: 5766.
9. Overman, A.R., F.G. Martin, and S.R. Wilkinson.
1990a. Alogistic equation for yield response of forage
grass to nitrogen. Commun. Soil Sci. Plant Anal. 21:
595609.
10. Overman, A.R., C.R. Neff, S.R. Wilkinson, and F.G.
Martin.1990b. Effect of water, harvest interval and ap
plied N on forage yield of bermudagrass and bahia
grass. Agron. J. 82: 10111016.
11. Prine, G.M., and G.W. Burton. 1956. The effect of
nitrogen rate and clipping frequency upon the yield,
protein content and certain morphological characteris
tics of Coastal bermudagrass (Cynodon dactylon, (L)
Pers.). Agron. J. 48: 296301.
12. Rhoads, F.M., and R.L. Stanley, Jr. 1989. Coastal
bermudagrass yield, soil pH, and ammonium sulfate 
nitrate rates. NFREC, Quincy Research Report 899.
University of Florida, Gainesville. 11 pp.
Table 1. Coastal bermudagrass studies included in analysis.
Location Years Soil Type Reference
Quincy, Florida 1987 Dothan loamy Rhoads & Stanley
1988 sand (1989)
Gainesville, Florida 1969 Scranton loamy Ruelke & Prine
1970 sand (1971)
Jay, Florida 1954 Red Bay Jeffers
1955 sandy loam (1955)
Table 2. Yield distributions for Coastal bermudagrass at Quincy, Florida for 1987.'
N Date 4/28 5/27 6/29 7/27 8/27 10/1 2
kg/ha t, wk 16.9 21.0 25.7 29.7 34.1 39.1
0 Ay, t/ha 1.24 1.58 2.23 2.36 2.49 1.38
SAy, t/ha 1.24 2.82 5.05 7.41 9.90 11.28 12.28
F 0.101 0.230 0.411 0.603 0.806 0.919 1
224 Ay, t/ha 2.94 3.60 3.58 3.70 2.55 1.39 
SAy, t/ha 2.94 6.54 10.12 13.82 16.37 17.76 18.30
F 0.161 0.357 0.563 0.755 0.895 0.970 1
448 Ay, t/ha 3.65 4.95 3.30 4.66 3.51 1.98 
SAy, t/ha 3.65 8.60 11.90 16.56 20.07 22.05 23.00
F 0.159 0.374 0.517 0.720 0.873 0.959 1
672 Ay, t/ha 3.38 5.46 3.31 5.31 3.54 2.05 
SAy, t/ha 3.38 8.84 12.15 17.46 21.00 23.05 24.00
F 0.141 0.368 0.506 0.728 0.875 0.960 1
896 Ay, t/ha 3.16 5.44 3.36 4.92 4.20 2.47 
S Ay, t/ha 3.16 8.60 11.96 16.88 21.08 23.55 24.80
F 0.127 0.347 0.482 0.681 0.850 0.950 1
'N = Applied N
t = time since January 1 to harvest
Ay = dry matter of harvest
~ Ay = cumulative dry matter
F = cumulative yield fraction
2 Last column gives estimated total dry matter.
Table 3. Yield distributions for Coastal bermudagrass at Quincy, Florida for 1988.1
N Date 5/17 6/20 7/18 8/25 10/10 2
kg/ha t, wk 19.6 24.4 28.4 33.9 40.4
0 Ay, t/ha 1.37 0.78 2.22 3.94 2.39
SAy, t/ha 1.37 2.15 4.37 8.31 10.70 11.50
F 0.119 0.181 0.380 0.723 0.930 1
224 Ay, t/ha 4.41 1.02 3.99 3.85 2.38 
SAy, t/ha 4.41 5.43 9.42 13.27 15.65 16.75
F 0.263 0.324 0.562 0.792 0.934 1
448 Ay, t/ha 5.77 2.44 4.05 3.61 3.31 
SAy, t/ha 5.77 8.21 12.26 15.87 19.18 20.50
F 0.282 0.400 0.598 0.774 0.936 1
672 Ay, t/ha 5.72 2.80 4.23 4.27 3.87 
SAy, t/ha 5.72 8.52 12.75 17.02 20.89 22.30
F 0.256 0.382 0.572 0.763 0.937 1
896 Ay, t/ha 5.85 2.94 3.92 4.26 3.94 
SAy, t/ha 5.85 8.79 12.71 16.97 20.91 22.40
F 0.261 0.392 0.567 0.758 0.934 1
1N = Applied N
t = time since January 1 to harvest
Ay = dry matter of harvest
SAy = cumulative dry matter
F = cumulative yield fraction
2 Last column gives estimated total dry matter.
Table 4. Parameters for empirical model for Coastal bermudagrass at Quincy, Florida.'
Year N YT I a R
kg/ha t/ha wk wk
1987 0 12.28 27.4 8.2 0.9996
224 18.30 24.3 7.9 0.9992
448 23.00 24.7 8.5 0.9966
672 24.00 24.8 8.2 0.9957
896 24.80 25.5 8.6 0.9958
1988 0 11.50 30.2 7.0 0.9959
224 16.75 27.0 9.2 0.9891
448 20.50 26.2 10.1 0.9967
672 22.30 26.7 9.8 0.9976
896 22.40 26.7 10.0 0.9980
Avg. 0  28.8 7.6 
224  25.6 8.6
448  25.5 9.3
672  25.8 9.0
896  26.1 9.3 
'Parameters are for Equation 1.
Table 5. Normalized yield versus normalized time for Coastal bermudagrass at Quincy, Florida for 1987.'
N
kg/ha t, wk 16.9 21.0 25.7 29.7 34.1 39.1
0 t t 1.28 0.78 0.21 0.28 0.81 1.42
o
F 0.101 0.230 0.411 0.603 0.806 0.919
224 t T 0.94 0.42 0.18 0.68 1.24 1.88
o
F 0.161 0.357 0.553 0.755 0.895 0.970
448 t T 0.92 0.44 0.12 0.59 1.11 1.69
F 0.159 0.374 0.517 0.720 0.873 0.959
672 t 0.95 0.46 0.11 0.59 1.12 1.72
o
F 0.141 0.368 0.506 0.728 0.875 0.960
896 t 1.01 0.53 0.02 0.49 1.01 1.60
o
F 0.127 0.347 0.482 0.681 0.850 0.950
t = time since January 1
t = time to mean of yield distribution
o = time spread of yield distribution
F = cumulative yield fraction
Table 6. Normalized yield versus normalized time for Coastal bermudagrass at Quincy, Florida for 1988.1
N
kg/ha t, wk 19.6 24.4 28.4 33.9 40.4
0 tT 1.50 0.81 0.24 0.54 1.47
o
F 0.119 0.181 0.380 0.723 0.930
284 t 0.81 0.28 0.15 0.75 1.46
F 0.263 0.324 0.562 0.792 0.934
448 t 0.65 0.18 0.22 0.76 1.41
F 0.282 0.400 0.598 0.774 0.936
Table 6. (Continued)
672 t t 0.72 0.23 0.17 0.74 1.40
F 0.256 0.382 0.572 0.763 0.937
896 t T 0.71 0.23 0.17 0.72 1.36
a
F 0.261 0.392 0.567 0.758 0.934
t = time since January 1
S= time to mean of yield distribution
a = time spread of yield distribution
F = cumulative yield fraction
Table 7. Summary of N response parameters for Coastal bermudagrass at Quincy, Florida.'
Parameter Year Parameter Standard Relative
Estimate Error Error
A, t/ha 1987 25.18 0.20 0.008
1988 22.95 0.19 0.008
b both 0.040 0.027 0.68
c, ha/kg both 0.0048 0.0002 0.04
'Parameters are for Equation 3.
Table 8. Analysis of variance for Coastal bermudagrass at Quincy, Florida.1
Mode Parameters Degrees Residual Mean F
Estimated Freedom Sum Sum
Squares Squares
(1) Common 3 7 9.28 1.33
A,b,c
(2) Individual 6 4 0.558 0.140
A,b,c
(1) (2) 3 8.72 2.91 20.8
(3) Individual A 4 6 0.629 0.105
Common b,c
(3) (2) 2 0.071 0.036 0.25
'Parameters are Equation 3.
Table 9. Normalized total yield versus normalized N for Coastal bermudagrass at Quincy, Florida.'
Year N N8 Y, A 1
kg/ha 208 t/ha YT
1987 0 0.04 12.28 1.05
224 1.04 18.30 0.376
448 2.12 23.00 0.0948
896 4.27 24.80 0.0153
1988 0 0.04 11.50 0.996
224 1.04 16.75 0.370
448 2.12 20.50 0.120
672 3.19 22.30 0.0292
896 4.27 22.40 0.0246
1 1987: A = 25.18 t/ha
1988: A = 22.95 t/ha
N = applied N
YT = total dry matter yield
A = yield parameter in Equation 4.
Table 10. Yield distributions for Coastal bermudagrass at Gainesville, Florida for 19691970.1
1969 N Date 5/14 6/16 7/14 8/11 9/16 11/11 2
kg/ha t, wk 19.1 23.9 27.9 31.9 37.0 45.0
134 Ay, t/ha 0.87 0.92 1.43 1.01 1.34 0.88 
E A, t/ha 0.87 1.79 3.22 4.23 5.57 6.45 6.60
F 0.135 0.278 0.489 0.641 0.844 0.978 1
269 Ay, t/ha 1.50 1.35 1.77 1.34 1.72 0.78 
S Ay, t/ha 1.50 2.85 4.62 5.96 7.68 8.46 8.56
F 0.175 0.333 0.540 0.697 0.897 0.988 1
538 Ay, t/ha 2.97 2.00 1.74 1.55 1.68 0.85 
2Ay, t/ha 2.97 4.97 6.71 8.26 9.94 10.79 11.00
F 0.270 0.451 0.610 0.751 0.903 0.981 1
1970 N Date 5/7 6/15 7/15 8/17 9/15 11/4
kg/ha t, wk 18.1 23.7 28.0 32.7 36.9 44.0
134 Ay, t/ha 1.22 0.57 1.63 1.39 1.46 0.49 
EAy, t/ha 1.22 1.79 3.42 4.81 6.27 6.76 6.85
F 0.178 0.261 0.499 0.701 0.914 0.986 1
269 Ay, t/ha 1.65 0.72 2.44 1.64 1.82 0.62 
SAy, t/ha 1.65 2.37 4.81 6.45 8.27 8.89 9.10
F 0.181 0.260 0.528 0.709 0.909 0.977 1
538 Ay, t/ha 2.73 0.89 2.83 1.96 2.10 1.18 
SAy, t/ha 2.73 3.62 6.45 8.41 10.51 11.69 12.00
F 0.227 0.302 0.538 0.701 0.876 0.974 1
1 N = Applied N
t
Ay =
FAy =
F =
time since January 1 to harvest
dry matter of harvest
cumulative dry matter
cumulative yield fraction
2 Last column gives estimated total dry matter.
Table 11. Parameters for empirical model for Coastal bermudagrass at Gainesville, Florida.'
Year N Y, t a R
kg/ha t/ha wk wk
1969 134 6.60 28.6 8.4 0.9992
269 8.56 27.2 8.3 0.9991
538 11.00 25.1 9.6 0.9997
1970 134 6.85 27.9 8.1 0.9922
269 9.10 27.7 8.2 0.9921
538 12.00 27.2 9.5 0.9916
Avg. 134  28.2 8.2
269  27.5 8.3
538  26.2 9.5
'Parameters are for Equation 1.
Table 12. Normalized yield versus normalized time for Coastal bermudagrass at Gainesville, Florida.'
1969 N t, wk 19.1 23.9 27.9 31.9 37.0 45.0
kg/ha
134 (tt)/o 1.14 0.56 0.08 0.39 1.00 1.96
F 0.132 0.272 0.489 0.641 0.844 0.978
269 (tI)/o 0.97 0.40 0.08 0.57 1.18 2.15
F 0.175 0.333 0.540 0.697 0.897 0.988
538 (ti)/o 0.62 0.12 0.29 0.70 1.23 2.06
F 0.270 0.451 0.610 0.751 0.903 0.981
1970 N t, wk 18.1 23.7 28.0 32.7 36.9 44.0
kg/ha
134 (ti)/o 1.21 0.52 0.01 0.59 1.11 1.99
F 0.178 0.261 0.499 0.701 0.914 0.986
269 (tt)/o 1.18 0.49 0.04 0.61 1.13 2.00
F 0.181 0.260 0.528 0.709 0.909 0.9777
538 (ti)/o 0.95 0.37 0.08 0.58 1.02 1.76
F 0.227 0.302 0.538 0.701 0.876 0.974
't = time since January 1
t = time to mean of yield distribution
a = time spread of yield distribution
F = cumulative yield fraction
Table 13. Summary of N response parameters for Coastal bermudagrass at Gainesville, Florida.'
Parameter Year Parameter
Estimate
A, t/ha 1969 12.20
1970 13.20
b both 0.594
c, ha/kg both 0.0053
'Parameters are for Equation (3).
Table 14. Normalized total yield versus normalized N for Coastal bermudagrass at Gainesville, Florida.'
Year N N114 YT A1
kg/ha 189 t/ha Y,
1969 134 0.116 6.60 0.848
269 0.831 8.56 0.425
538 2.25 11.00 0.109
1970 134 0.116 6.85 0.927
269 0.831 9.10 0.451
538 2.25 12.00 0.100
1969: A
1970: A
N
YT
A
= 12.20 t/ha
= 13.20 t/ha
= applied N
= total dry matter yield
= yield parameter in Equation 4.
Table 15. Total yields for Coastal bermudagrass at Jay, Florida for 19541955.1
Year N Y,
kg/ha t/ha
1954 38 1.90
76 2.84
140 5.60
280 8.80
560 12.68
1955 56 3.79
112 5.22
224 8.96
448 14.16
896 19.20
SData from Jeffers (1955).
N = applied N
YT = total dry matter yield
Table 16. Summary of N response parameters for Coastal Bermudagrass at Jay, Florida.1
Parameter Year Parameter Standard Relative
Estimate Error Error
A, t/ha 1954 14.78 0.76 0.051
1955 18.97 0.66 0.035
b both 1.70 0.10 0.059
c, ha/kg both 0.0067 0.0006 0.090
'Parameters are for Equation 3.
Table 17. Analysis of variance for Coastal bermudagrass at Jay, Florida.1
Mode Parameters Degrees Residual Mean F
Estimated Freedom Sum Sum
Squares Squares
(1) Common 3 7 15.64 2.23
A,b,c
(2) Individual 6 4 1.60 0.40
A,b,c
(1) (2)  3 14.04 4.68 11.7
(3) Individual A 4 6 3.78 0.63
Common b,c
(3) (2)  2 2.19 1.09 2.72
1 Parameters are for Equation 3.
Table 18. Normalized total yield versus normalized N for Coastal bermudagrass at Jay, Florida.1
Year N N250 YT A 1
kg/ha 150 t/ha Y,
1954 38 1.41 1.90 6.78
76 1.16 2.84 4.20
140 0.73 5.60 1.64
280 0.20 8.80 0.680
560 2.07 12.68 0.166
1955 56 1.29 3.79 4.00
112 0.92 5.22 2.63
224 0.17 8.96 1.12
448 1.32 14.16 0.340
896 4.31 19.20 
'1954: A
1955: A
N
YT
14.78 t/ha
18.97 t/ha
applied N
total dry matter yield
Table 19. Forage N concentration and removal by Coastal bermudagrass at Quincy, Florida for 1987.1
N Cutting Ay No AN
kg/ha t/ha % kg/ha
0 1 1.24 1.99 25
2 1.58 1.60 25
3 2.23 1.72 38
4 2.36 1.33 31
5 2.49 1.24 31
6 1.38 1.37 19
Total 11.28 169
224 1 2.94 2.73 80
2 3.60 1.87 67
3 3.58 2.32 83
4 3.70 1.64 61
5 2.55 1.42 36
6 1.39 1.40 19
Total 17.76 346
' Ay = dry matter yield for cutting
Nr = forage N concentration
AN = forage N removal for cutting
Table 20. Comparison of estimated and measured forage N concentration for Coastal bermudagrass at Quincy,
Florida for 1987.1
N At N, No Diff.
kg/ha wk % % %
0 4.4 1.31 1.50 13
224 4.4 2.12 1.95 9
'N = applied N
At = harvest interval
No = estimated from Equation 12.
No = forage N concentration
Table 21. Forage N concentration for Coastal bermudagrass at Gainesville, Florida for 1969.1
A
N At Nc Nc Diff.
kg/ha wk % % %
134 5.2 1.69  
269 5.2 2.03  
538 5.2 2.41  
Avg. 5.2 2.04 1.97 3.6
'N = applied N
At = harvest interval
N, = estimated from Equation 12.
N = forage N concentration
Table 22. Summary of N response parameters for Equation 4 for bermudagrass.
Site Reference N2 N'
kg/ha kg/ha
Quincy, This report 8 250
Florida
Gainesville, This report 110 190
Florida
Jay, This report 250 150
Florida
Fayetteville, Overman et al. 170 120
Arkansas' (1990b)
Thorsby, Overman et al. 180 120
Alabama2 (1990b)
Tifton, Overman et al. 180 130
Georgia3 (1990b)
Avg. 150 160
Std. Dev. + 80 + 50
'Yield data from Huneycutt et al. (1988)
2 Yield data from Evans et al. (1961)
3 Yield data from Prine and Burton (1956)
N,/2 and N' are N response parameters for Equation 4.
Table 23. Summary of yield response parameters in Equations 4 and 7 for bermudagrass.1
Site Year At A Ao
wk t/ha t/ha
Quincy, 1987 4.4 25.18 11.58
Florida 1988 5.2 22.95 9.61
Gainesville, 1969 5.2 12.20 5.11
Florida 1970 5.2 13.20 5.53
Jay, 1954 5.9 14.78 5.74
Florida 1955 7.8 18.97 6.15
Tifton, 1953   11.40
Georgia2 1954  5.44
'At = harvest interval
A = yield parameter for Equation 4.
Ao = intercept for Equation 7.
2 Values from Overman et al. (1990b) for field data of Prine and Burton (1956).
99
98
95
90
so
80
70
60
50
40
30
20
10
5
! 2
1
LC 98
95
90
80
70
60
50
40
30
20
10
5
2
1
t t Time, calendar weeks
o"
Figure 1. Normalized yield versus normalized time for Coast Figure 2. Cumulative yield versus time for Coastal bermuda
al bermudagrass at Quincy, Florida. grass at Quincy, Florida.
b
68
6
28
I,
Applied N, kg/ha
Figure 3. Dependence of mean time (T) and time spread (o)
on applied N for Coastal bermudagrass at Quincy, Florida.
30 1 1 
25 Symbol N. kg/ha 1988
a 0
20 x 224
# 448
15 @ 672
c 1+ 896
0 10
S 5 x
0
8> 1987
25 
20 
U 15 
10 
5
0
0 10 20 30 40 50
x x
x # #
# 00
00
Symbol Year
a 1987
x 1988
# Avg.
x x
# # # 0
o o
200 400 600 800 1000
4
I I 1
0 200 400 600 800 1000
Applied N, kg/ha
Figure 4. Dependence of total yield on applied N for Coastal bermuda
grass at Quincy, Florida.
0.01
N N1/2
N'
Figure 5. Normalized total yield versus normalized N for Coastal bermuda
grass at Quincy, Floirda.
Symbol Year A. t/ha N1/2, kg/ha N'. kg/ho
o 1987 25.18 8 208
x 1988 22.95 8 208
x
0 2 3 4
0 1 2 3 4
0. 1 F
99
98
95
90
80
70
60
50
40
30
20
10
5
Pt 2
1
: 98
95
90
80
70
60
50
40
30
20
10
5
2
1
0 10 20 30 40 50
t t Time, weeks
aT
Figure 6. Normalized yield versus normalized time for Coast Figure 7. Cumulative yield versus time for Coastal bermuda
al bermudagrass at Gainesville, Florida. grass at Gainesville, Florida.
10 i1
b
6 I  l 
Symbol Year
a 1969
30 x 1970
28 
\x
I, x
26
24
0 200 400 600 800 1000
Applied N, kg/ha
Figure 8. Dependence of mean time (1) and time spread (a)
on applied N for Coastal bermudagrass at Gainesville, Flori
da.
0'
0 200 400 600 800 1000
Applied N, kg/ha
Figure 9. Dependence of total yield on applied N for Coastal bermuda
grass at Gainesville, Florida (Data from Ruelke and Prine, 1971).
N N1/2
N'
Figure 10. Normalized total yield
mudagrass at Gainesville, Florida.
versus normalized N for Coastal ber
0 i 11 i 1
0 200 400 600 800 1000
Applied N, kg/ha
Figure 11. Dependence of total yield on applied N for Coastal bermuda
grass at Jay, Florida (Data from Jeffers, 1955).
10 i I I I I
z >.
N NI/2
N'
Figure 12. Normalized total yield versus normalized N for Coastal ber
mudagrass at Jay, Florida.
8
29
27
25
0 100 200 300 400 500
Applied N, kg/ha
Figure 13. Estimated dependence of mean time () and time
spread (a) on applied N for Coastal bermudagrass in Florida.
Applied N, kg/ha
Figure 14. Estimated dependence of total yield (YT) on applied N and
harvest interval (At) for Coastal bermudagrass in Florida.
o 0 i I l I
(b) A = 20 t/ho
20 N'= 150 kg/ha
CV NI/2 100 k9/ha
0 N1 N] 200 100 k/h
S 0 N 200 kg/ho
0 0
(a) N1/2 = 150 kg/ho
20 N' = 150 kg/ho
A = 20 t/ha
10 
A 10 t/ha
0 3
0 100 200 300 400 500
Applied N. kg/ha
Figure 15. Sensitivity of total yield response of Coastal
bermudagrass on model parameters in Equation 4.
10
300 200 100 0
100 200 300 400
Applied N, kg/ho
Figure 16. Effect of residual soil N on response of total yield of Coastal
bermudagrass to applied N.
I I I I
A = 20 t/ha
NI/2 = 0 kg/ho
N' = 150 kg/ha
I I
0 L
0'
0 100 200 300 400 500
Applied N, kg/ho
Figure 17. Estimated dependence of forage N concentration on applied
N and harvest interval (At).
500
Applied N, kg/ha
Figure 18. Estimated dependence of forage N removal on applied N,
harvest interval, and water availability.
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