Analysis of environmental factors affecting Timothy yields

Agricultural Meteorology, 22 (1980) 319--339

319

Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

ANALYSIS OF ENVIRONMENTAL FACTORS AFFECTING TIMOTHY YIELDS* W. BAIER 1 , J.C. ST-PIERRE 2 and J.H. LOVERING 3

1 Agrometeorology Section, Land Resource Research Institute, Research Branch, Agriculture Canada, Ottawa, Ontario, K I A 0C6, (Canada) 2 Forage Crops Physiology, Ste-Foy Research Station, 2560 Boul. Hochelaga, Ste-Foy, Quebec, G I V 2J3 (Canada) 3 Head, Crop-Livestock Systems Section, Charlottetown Research Station, P.O. Box 1210 Charlottetown, Prince Edward Island, CIA 7M8 (Canada) (Received December 4, 1978 ; accepted after revision December 5, 1979 )

ABSTRACT Baier, W., St-Pierre, J.C. and Lovering, J.H., 1980. Analysis of environmental factors affecting timothy yields. Agric. Meteorol., 22 : 319--339. An earlier-developed wheat--weather analysis model was modified to provide estimates of first-cut and second-cut timothy dry matter yield as a function of nitrogen application rate, last yield and weather as reflected in the daily observed maximum and minimu m air temperatures and estimated soil moisture. Data used in the development of the new timothy--weather analysis model were collected at eight locations in eastern Canada from 1960 to 1973, consisting of 78 station-years for the first-cut and 73 station-years for the second-cut. Modifications include (1) standardization of weather variables selected as input to the model, (2) reduction of the regression coefficients from 12 to 6 in each iteration of the analysis, (3) elimination of negative daily contributions in two out of the three factorial terms in the model, (4) inclusion of an equation accounting for the effect of nitrogen application rate on scaled timothy yield, and (5) weighting of effect~ of scaled yield due to nitrogen application and last yield together with seasonal weather (maximum temperature, minimum temperature and soil moisture) on observed yield. The first evaluation criterion was the coefficient of determination (100 CD). Nitrogen application rate alone accounted for 32% of first-cut timothy yield variations among station-years. The 100 CD increased to 52% when last yield was included and to 60% when both last yield and weather were included in the multiple variable regression. Respective values for second-cut yields were 27, 47 and 60%. Other criteria were: scatter of individual station-year yield estimates, mean station bias, and an inspection of the overthe-season accumulated daily growth response curves for selected stations, years and Nrates for first- and second-cut timothy yields. The approach is promising but further research is required to validate the accuracy of yield estimates for operational assessment of timothy-yield prospects and to improve the non-linear regression technique used in the model.

INTRODUCTION

Several Agriculture Canada, Research Branch establishments have collaborated in a joint project to provide consistent and coordinated information * L R R I Contribution No. 10, Ste-Foy Contribution No. 149, Charlottetown Contribution No. 420.

0002-1571/80/0000--0000/$02.25

© 1980 Elsevier Scientific Publishing Company

320

{from several disciplines) useful in the management of on-farm feed--livestock systems in Eastern Canada. Initial efforts have been restricted to the consideration of a timothy silage--dairy cow system. Various approaches including systems analysis and design, computer simulation and optimization techniques, and other existing models relevant to the purpose of this study, were considered. Russell et al. (1975) reported on a computer simulation model to study the effects of varying the level of machinery input to the forage harvesting task on costs, yield and crop quality, given various harvesting strategies and acreages of four varieties of timothy (Phleum pratense L.) harvested at Charlottetown, P.E.I. Since their data were sparse and appropriate sub-models were not available at the time of their report (Russel et al., 1975), simulation input functions for yield of dry matter were specified on the basis of the number of days since the start of growth or regrowth of various t i m o t h y varieties. The same potential yield level was assumed for the four varieties (Clair, Champ, Climax and Bounty), namely approx. 5,000 kgha -1 for the first cut, 3,500 kgha -1 for the second cut, 1,400 kgha -1 for the third cut, and 900 kgha -1 for the fourth cut. Obviously, these growth functions had several shortcomings, e.g. they did n o t reflect the effect of weather on growth or regrowth in any particular year. In order to improve the day-to-day dry matter input to the initial model of the t i m o t h y silage--dairy cow system, consideration was given to the development of suitable sub-models which would provide daily timothy dry matter production as a function of weather, soil characteristics and fertilizer applications. A sub-model was required to evaluate at any time during the crop growing period the influence of past and current weather on potential yield. A so-called timothy--weather analysis model was developed on the basis of an earlier published crop--weather analysis model for wheat grain yields (Baier, 1973). This technique evaluates simple and interacting daffy contributions of up to three observed or derived variables (such as air temperatures or soil moisture) to "yield" (e.g. grain yield or dry matter yield) obtained at harvest time. Robertson (1974) described the use of such a factorial yield--weather model for analyzing trends of wheat yields at Swift Current, Saskatchewan. This paper describes the development of the timothy--weather analysis model using field experimental data collected at eight locations in eastern Canada for 1960--1973. Several analytical approaches are used to evaluate the performance of this technique as a research tool. EXPERIMENTAL DETAILS

Agronomic data Yield and related agronomic data were acquired through variety trials at eight locations in eastern Canada: St-Augustin, Fredericton, L'Assomption,

321 TABLE I Data source for timothy--weather analysis model development No.

1 2 3 4 5 6 7 8

Station

St. Augustin Fredericton L'Assomption Macdonald College Ottawa La Pocati~re Normandin Lennoxville

First cut

Second cut

Years

Total

Years

Total

1969--1973 1960--1969 * 1965--1969 1967--1973 1965--1968 1968--1971,1973 1966--1973 1969--1973

5 40 5 6 4 5 8 5

1969--1973 1960--1969 1965--1969 1967--1969,1971 1965--1968 1968--1971,1973 1966--1968,1970,1973 1969--1973

5 40 5 4 4 5 5 5

78(n 1 )

73(n2)

* Four N levels.

Macdonald College, Ottawa, La Pocati~re, Normandin and Lennoxville. A summary of the data source is given in Table I. Data included timothy dry matter yield (kg ha -1 ), date of cutting and, various nitrogen application rates (kgha -1 ), separately for first and second cuts over 5--8 years within the period 1960--1973. The Fredericton data, however, were homogeneous, viz four nitrogen application rates (0, 90, 180 and 270 k g h a -1 y-1 ), two cutting dates, and complete for each of the years 1960--1969. The Fredericton experiments for four nitrogen levels over the 10-year period were considered as a data set of 40 "station-years". Altogether, data from 78 station-years (nl) for first cut and data from 73 station-years (n2) for second cut were used in the model development.

Timothy growth data Observed dates of first and second cuts together with respective dry matter yields (kgha -1 ) and nitrogen rates (kgha -1 ) were taken from experimental records. The starting date of timothy growth was estimated as the last day of the 5-day period when smoothed mean air temperature was >~4.4°C (40 ° F). The growing period from start of growth to cutting date was divided into five equal sub-periods (t) denoted as 0--1, 1--2, 2--3, 3--4 and 4--5, similar to the biometeorological time scale suggested by Robertson (1968). This change from calendar time to standard t-periods was necessary to compare growth rates in different years or at different locations; it also facilitated the use of existing computer programs for the purpose of this study. Table II gives averages of the estimated start of growth (t -- 0), the observed cutting dates (t = 5), and the computed dates for t = 1, 2, 3 and 4.

322 TABLE II Station-averages of observed cutting dates (t = 5), estimated start-of-growth dates (t -- 0) and computed dates for t = 2, t = 3 and t = 4 Location

t=0 (start of growth)

t= 1

t= 2

t=3

t--4

t=5 (cutting date)

St. Augustin Fredericton L'Assomption Macdonald College Ottawa La Pocati~re Normandin Lennoxville

28 23 17 18 11 25 6 23

11 7 30 1 27 9 20 9

May May Apr. May Apr. May May May

24 May 21 May 13 May 14 May 12 May 23 May 3 June 24 May

6 4 25 26 27 5 16 8

19 17 6 7 11 18 29 23

2 30 18 19 26 1 12 8

All stations

23 Apr.

7 May

20 May

3 July 1 July 19 June 20 June 27 June 2 July 13 July 9 July

18 July 13 July 3 July 4 July 14 July 14 July 24 July 29 July

2 25 16 18 31 26 4 14

1 July

14 July

28 July

First cut

Apr. Apr. Apr. Apr. Apr. Apr. May Apr.

June June May May May June June June

3 June

June June June June June June June June

July June June June June July July July

16 June

30 June

30 16 11 14 2 18 25 17

13 27 24 27 18 27 4 4

Second c u t

St. Augustin Fredericton L'Assomption Macdonald College Ottawa La Pocati~re Normandin Lennoxville All stations

Aug. July July July July July Aug. Aug.

16 5 29 1 17 7 15 31

Aug. Aug. July Aug. Aug. Aug. Aug. Aug.

11 Aug.

Aug. Aug. Aug. Aug. Sept. Aug. Aug. Sept.

24 Aug.

Sept. Aug. Aug. Aug. Sept. Aug. Sept. Oct.

6 Sept.

Environmental data source As in the case of the wheat--weather analysis model, only standard climatological data (maximum temperature, minimum temperature and precipitation) were used as basic input to the model. Daily climatological No. 4 format data, originally provided by the Atmospheric Environment Service, Environment Canada. were available in computer~ompatible form in the Agrometeorological Data Bank of Agriculture Canada. Daffy climatological data were used as input to the Versatile Soil Moisture Budget (Baler and Robertson, 1966; Baler et al., 1979) for estimating daily values of potential evapotranspiration (PE), actual evapotranspiration (AE) and soil moisture (SM) in six budget zones or depths within the rooting zone of a timothy sod. The timothy k-coefficients used in the Versatile Budget computations of this study are given in Table III. Table IV presents basic information on the soils and soil water characteristics as used in this study for estimating soil moisture at the eight experimental locations. In Table IV,

323 TABLE III Timothy k-coefficients per zone and t-period used in soil moisture estimations of this study* Budget zone

Percent of capacity

t-period 0--1

1--2

2--3

3--4

4--5

1 2 3 4 5 6

5.0 7.5 12.5 25.0 25.0 25.0

0.50 0.20 0.10 0.05 0.03 0.02

0.53 0.22 0.10 0.05 0.03 0.02

0.55 0.25 0.10 0.05 0.03 0.02

0.60 0.30 0.15 0.08 0.04 0.03

0.60 0.30 0.15 0.08 0.04 0.03

* F o r definition of t-periods see text. For technique of soil moisture estimation by Versatile Budget, see Baler et al. (1979).

TABLE IV Soil water characteristics of timothy plots at experimental locations Location

Soil type

Plant-available .1 water capacity (cm)

Soil moisture drying curve .2

St. Augustin Fredericton L 'Aasomption Macdonald College Ottawa La Pocati~re Normandin Lennoxville Charlottetown

Silty loam Sandy loam Soulanges sandy loam Clay loam Uplands sandy loam Kamouraska clay Normandin clay loam Sheldon sandy loam Sandy loam

10.9 16.4 9.6 15.5 9.1 5.5 10.2 12.0 15.1

G H H G G D G H G

• 1 Capacity (cm) for plant-available water in 60-cm rooting zone of timothy sod. • 2 Soil moisture drying curves as used in the Versatile Soil Moisture Budget represent different relationships between AE:PE and soil moisture content (Baler et al., 1979). For explanation see text. t h e i n f o r m a t i o n u n d e r " s o i l m o i s t u r e d r y i n g c u r v e " r e f e r s t o t h e t y p e o f selected relationship between A E : P E ratio and plant available soil moisture c o n t e n t ( p e r c e n t ) u s e d in t h e V e r s a t i l e S o i l M o i s t u r e B u d g e t ( B a l e r e t al., 1979). Type D -- 100--70%, no reduction; 70--0%, exponential decay form reduction. Type G -- 100--70%, no reduction; 70--0% reduction. Type H -- 100--50%, no reduction; 50-0%, linear reduction.

324 For the selection of input variables to the model, literature on temperature and moisture requirements of timothy was consulted. From that literature review and experimental results by Mack and Finn (1970), it was concluded that day and night temperatures are important for optimum growth and that the rate of regrowth also depends on the soil moisture regime. Therefore, the following input variables as defined earlier (Baler, 1973) were selected: daily minimum air temperature, daily maximum air temperature, and daily soil moisture, i.e., the ratio of the estimated plant available soil moisture to soil moisture capacity within the timothy crop rooting zone. Notation

The following is a list of all environmental, phenological and derived variables and other parameters mentioned in the text. MIN Daily minimum air temperature (°C) MAX Daily maximum air temperature (°C) Daily ratio of plant-available soil moisture to soil moisture capSM acity within the timothy crop rooting zone (0--1) AE Actual evapotranspiration (mm) PE Potential evapotranspiration (mm) Scaled daffy input data XTrans Actual input variable (observed or derived) XAct Lowest value in entire data set ZLo w Highest value in entire data set XH~h Estimated crop yield (kg ha-1 ) YEST YEST1 First approximation of estimated crop yield (kg ha-' ) YEST2 Second approximation of estimated crop yield (kg ha- 1 ) YEST3 Third approximation of estimated crop yield (kg ha-1 ) YLST Last or preceding yield for same station-year (kg ha- 1 ) t Biometeorological time: timothy growing period from estimated start of growth (t = 0) to observed cutting date (t = 5) subdivided into five equal sub-periods. Regression coefficients U 1 • . . 12 6 Functions of the selected independent variables (X) used in V 1 ,V: ,V3 basic timothy--weather analysis equation (1), e.g., V M A X or VMIN or VSM. Nitrogen application rate (kg ha-1 ) N YN Scaled yield due to nitrogen application (kg ha-1 ) YMIN Lowest observed yield (kgha- 1 ) YMAX Highest observed yield (kg ha- 1 ) YOBS Observed yield in any station-year (kg ha-l ) CD Coefficient of determination CV Coefficient of variation SEE Standard error of estimate

Mean S.D. Highest Lowest

SM ( 0 - - 1 )

Mean S.D. Highest Lowest

Mean S.D. Highest Lowest

MIN(°C)

SM ( 0 - - 1 )

S.D. Highest Lowest

Second cut (n 2 ----73) M A X (°C) Mean

Mean S.D. Highest Lowest

Mean S.D. Highest Lowest

MIN (°C)

First cut (n 1 ----78) M A X (°C)

Variables

1 July

0.47 0.25 1.00 0.05

12.4 3.9 23.3 1.7

24.7 3.8 35.0 11.7

0.80 0.17 1.00 0.36

0.9 3.9 15.6 --11.1

12.8 5.3 32.8 1.1

Quantity t: 0 D a t e : 23 A p r . Period : 0--1

14 J u l y

1 7 May

0.50 0.24 1.00 0.09

13.3 3.8 23.9 2.2

25.2 3.8 33.9 13.3

0.73 0.20 1.00 0.31

3.5 4.1 16.7 - - 7.2

15.9 5.5 31.7 4.4

1--2

28 J u l y

2 20 M a y

0.50 0.23 1.00 0.06

13.2 3.8 23.3 1.1

24.9 3.6 33.9 12.8

0.62 0.21 1.00 0.23

6.1 4.0 18.3 - - 4.4

19.2 5.3 32.8 5.6

2--3

11 Aug.

3 3 June

0.43 0.25 1.00 0.07

12.2 4.2 24.4 - - 0.6

24.0 3.9 32.2 12.2

0.48 0.20 1.00 0.13

9.0 4.2 20.1 - - 2.2

22.0 4.5 32.2 10.0

3--4

23.4 4.3 33.9 10.6

4--5

22.1 4.8 33.9 4.4

0.49 0.29 1.00 0.05

10.8 4.6 21.7 - - 4.4

24 Aug.

0.42 0.21 0.99 0.07

11.0 3.8 22.2 - - 0.6

4 16 J u n e

6 Sept.

5 30 J u n e

Means, s t a n d a r d d e v i a t i o n s (S.D.) a n d e x t r e m e s b y g r o w t h stage p e r i o d s o f a g r o m e t e o r o l o g i c a l d a t a u s e d in t h e m o d e l d e v e l o p m e n t

TABLE V

t~ ¢9a

326

Scaling o f input data

A summary of the " r a w " climatological and agrometeorological data used as input to the timothy--weather analysis model by t-periods for first and second cuts is given in Table V. However, experience with the wheat-weather model had shown that the use of " r a w " data in the model development sometimes resulted in unrealistic estimates, especially when the coefficients were applied to climatic data sets different from those used in the development of the model. To overcome this problem, which appeared to be most serious over the range of extreme weather data, a transformation of the temperature input data was developed for the timothy--weather analysis model. The daily input data were scaled as follows X T r a n s ~- ( X A c t - - X L o w ) / ( X H i g h - - X L o w )

As a result of this temperature scaling, which is optional in the c o m p u t e r program, and since SM is a ratio, all daily input data varied from 0 to 1. DETAILS OF THE MODEL Basic equation

The timothy--weather analysis model developed in this study is a modification of the earlier presented crop--weather analysis model for wheat grain yields (Baier, 1973). Modifications as described below were necessary partly because of different management practices in the wheat and t i m o t h y experiments. The basic timothy--weather analysis equation is as follows Y = ~ V 1 It(I), M I N (I)] × Y 2 It(I), MAX(I)] × V 3 It(I), SM(I) ]

(1)

I

where Y is the dependent variable such as the observed timothy yield, I = 1, 2 . . . . , ICUT, t(I) = 5I/ICUT, t(I} is the stage of development at day I, ICUT is the number of days from initiation of growth to cutting date, and (I) denotes any parameter on the Ith day. Thus, the contribution to yield on day I is Yl [t(I), MIN(I)] × Y 2 [t(/), M A X ( D ] × Y 3 [t(/), SM(I)]

(2)

The final yield is the sum of the daily contributions from initiation of growth to cutting, as in eq. 1. Modification of daily weighting procedure

In the timothy--weather analysis equation (1) it is assumed that for a specific day the crop response to a weather variable can adequately be de-

327 scribed by a parabola, e.g., it would model the response to SM where there is an optimum range but levels below or above are detrimental. The shape and magnitude of such a response curve is, however, assumed to depend on the phenological stage. Therefore, a daily weighting procedure had to be developed in which the coefficients of the response parabola were made to be functions of the phenological stage expressed as biometeorological time (t). For wheat, the specific effect of soil water supply on grain yields at various crop developing stages is well documented (Bauer, 1972). Thus, it was shown in the wheat--weather analysis model (Baler, 1973) that a fourth-degree polynomial was required to follow the changes in the response parabola coefficients with phenological stage. In the case of vegetative growth of t i m o t h y , which is also cut at an early development stage, a second-degree polynomial was found adequate for proper daily weighting, i.e., to follow changes in response functions of t i m o t h y growth with biometeorological time. Through this simplification of each V-function, it was possible to reduce the number of coefficients from 12 to 6 in each estimation of u-coefficients in the multiple-variable regression analysis (7). The justification for this simplification was based on an inspection of t i m o t h y growth curves such as those presented by Calder and MacLeod (1968) and subsequently confirmed in various computer runs as part of this study. It should be emphasized that a reason for selecting polynomials rather than some other functional form for the parabolic-type response curve and the daily weighting coefficients was so that each V-function would have linear coefficients which could be evaluated using linear least-squares estimation on final yield. The major feature of this procedure is that the coefficients of two of the three V's are assumed known and the remaining coefficients of the third V are evaluated using a standard multiple regression of the summation in eq. 1 against final yield. The process is repeated with a new V at each iteration until it converges. An advantage of this procedure over other non-linear least-square techniques is that no previous knowledge of initial estimates of coefficients is required.

Elimination o f negative daily contributions Contrary to grain production, it was considered unlikely that adverse weather can reduce the already accumulated t i m o t h y dry matter yield. Therefore an a t t e m p t was made in this study to set negative contributions equal to zero from the two V-functions of which the coefficients are assumed known. When the summatiori in eq. 1 is performed, all negative contributions are set to zero, but when the regression is performed, the coefficients are selected to give the best fit to the final yield. This estimation procedure by computer was used in the model because no dry matter data at different development stages were available for fitting a response curve over the t i m o t h y growing season extending from t = 0 to t = 5.

328 Robertson (1968) discussed this problem of negative contributions and during the iterative solution omitted all negative daffy values of the temperature and photoperiod terms in the biometeorological time scale model. He reasoned that crop development towards maturity is an irreversible process, thus daffy values of the environmental factors below the lower critical limit or above the upper critical limit cannot reverse the progress towards maturity. Elimination of daily input data that produce a negative contribution and their re-introduction in the regression analysis at a later iteration when the contribution turned positive was not adopted in either the wheat-weather or the timothy--weather analysis model. Such a procedure results in the use of a different data set in the iterative regression analyses and causes instability of the coefficients and other regression statistics from one iteration to the next. E v a l u a t i o n o f n i t r o g e n c o n t r i b u t i o n to y i e l d

No allowance for fertilizer effects on yields was made in the wheat-weather model since, in that experiment, plots were fertilized for optimum production for the soil type at each experimental site (Baier and Robertson, 1968). In the t i m o t h y experiments, however, nitrogen application rates varied from 0 to 135 kg ha-' per cut. Since this fertilizer effect is not a daily contribution to yield, as in the case of climatological or derived agrometeorological data, special procedures had to be developed to account for seasonal rates of nitrogen application (N). Again, the available literature was consulted and results from a field experiment at Fredericton, N.B., on the effects of various N application rates on timothy yields were found to be applicable to the data used in the present study. Grant and McLean (1966) presented the relationship between levels of applied N and timothy" yield in fig. 2 of their paper. In their experiment, N-rates varied from 0 to 134 kgha- 1 and yields from 1122 to 2912 kgha-' for the first cut and from 280 to 1904 kgha- 1 for the second cut. From these logarithmic-type curves, the relationship between scaled yield (YN) and N rate was assumed as follows YN

= 1 - - e cN

YN

= ( Y O B S -- Y M I N / Y M A X

(3) -- Y M I N )

(4)

Regression was used to estimat.e the coefficient in (3) YN

= 1-

e -0"02sOsN

(5)

W e i g h t i n g o f YN a n d YLST

The next step involved the proper weighting of the scaled yield (YN) due to nitrogen application rate (N) to obtain yield estimates (YEST1) comparable to the observed t i m o t h y yields for first and second cuts of the present experiment. Weighting of Y N was then performed together with the weight-

329 ing of the effect of the last yield (YLST) on estimated yield (YEST2). Preliminary regression-type analysis had indicated a rather strong dependence of the yields from the second cuts on yields from the first cut. Similarly, yields of the first c u t were dependent on yields from the second cut of the preceding year. This dependency may be due to the effects of a number of crop and soil factors on t i m o t h y yields, in addition to the weather effects as accounted for in the model. The " c r o p " factors probably account indirectly for the age of the stand, the physiological responses of the plants to cutting and/or winter conditions, and a more or less active root system. The "soil" factors include the general fertility level, physical and chemical characteristics of the soil, and topographical features of the experimental sites. Weighting of both Y N and Y L S T in relation to the observed yields was accomplished by multiple regression analysis. Results for the first and second cuts are given in Table VI.

New timothy--weather analysis model Considering the modifications as described above, the new t i m o t h y - weather analysis model takes the form Y/YEST2 = ~ V1 × V2 x V3

(6)

where each V = (Uxt + u2t 2) + (u3t + u 4 t 2 ) X + (ust + u 6 t 2 ) X 2

(7)

(For definitions see Notations section and eq. 1). The left-hand side of eq. 6 becomes the dependent variable (YEST3) in the multiple regression analysis and represents the observed t i m o t h y dry matter yield (YOBS) adjusted for nitrogen application rate (YN) and last yield (YLST). The right-hand side represents the weather effect due to the interaction of the three selected input variables. When the coefficients have been established, the product V1 × V2 × V3 (weather effect) is multiplied by YEST2 (nitrogen and last yield effects) to obtain a yield estimate (YEST3) comparable with the corresponding observed yield (YOBS). Since there is no unique solution for eq. 6 the earlier-developed iterative, multiple-variable regression analysis was used here. The regression analysis is based on the S004 B program version prepared by B. Thompson and K. Price of the Engineering and Statistical Research Institute, Agriculture Canada. The regression is through the origin and the six variables in each V-function are introduced simultaneously. The selection of the iteration from which the coefficients are to be used for the yield estimates is based on the stability of the coefficients and other regression statistics, b u t also on the minimum number of daily negative contributions. Usually between 19 and 24 iterations were required to develop a suitable set of coefficients.

330 TABLE VI Summary of statistical results of timothy--weather model development YOBS

Variable(s)

(kgha -1 )

SEE

CV

(kgha -1 )

(%)

100 C D (%)

1335 1127 1023

30 26 23

32 52 60

1051 902 775

52 45 38

27 47 60

F i r s t c u t ( n l -~ 78 station-years)

4408

YEST1 YEST2 YEST3

~ 2441 4-2956 Y N ~ 1858 -}- 1511 Y N q- 0.7817 Y L S T = YEST2 × (VMIN × VMAX × VSM)

S e c o n d c u t (n 2 ~- 73 station-years)

2016

YEST1 YEST2 YEST3

~ 929 q-1805 Y N ~ 234 + 1053 Y N q- 0.3671 Y L S T ---- Y E S T 2 × ( V M I N × V M A X × V S M )

RESULTS AND DISCUSSIONS

From preliminary studies including standard regression analysis and initial runs of the timothy--weather analysis model, variables to be included in the model were selected from available climatological records (MIN, M A X Mean, Range) and from derived agrometeorological data (AE, PE, PE -- AE, AE/PE, SM). On the basis of these pre-study results, experience with the wheat--weather model and known growth responses of t i m o t h y to weather, results are here presented only for the analysis of timothy yields from 78 first cuts and 73 second cuts in relation to maximum temperature (VMAX), minimum temperature (VMIN) and soil moisture (VSM), the effect of each variable on the observed yield (YOBS) weighted by YLST and YN. The decision on the set of coefficients to be used in the final model was based n o t only on the regression statistics, but also on the distribution of the daily and seasonal dry matter yield estimates as compared with the observed yield data. Statistical results of the timothy--weather analysis model develo p m e n t are summarized in Table VI. The first evaluation criterion is the coefficient of determination (100 CD). Nitrogen rate (YN) alo.ne accounted for 32%, and YN together with last yield (YLST) for 52% of first-cut yield variations. Y N together with YLST and the three weather variables (VMIN × VMAX x VSM) accounted for 60%. The increase due to weather (8%) appeared to be small, b u t much of the yield variation was probably already accounted for through the variations in YN and YLST. Second-cut yields were somewhat less dependent on YN (27%), but more on weather variables (13%), than first-cut yields. Y N and YLST, together with weather variables, accounted for 60% of second-cut yield variations, although the SEE and CV values were higher than in the case of first-cut yields.

331

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•

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[ '#%sM n I,!IHI

•

L, IIt,L)~ ~111,

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1000

2O0(}

3{]00

4000

5000

f~(J0[ I

7f)l]0

5~q

gll('[)

~ ( hi

Fig. 1. S c a t t e r d i a g r a m o f o b s e r v e d (YOBS) a n d e s t i m a t e d (YEST) t i m o t h y y i e l d s f r o m first c u t a r o u n d 1 : 1 r e g r e s s i o n line. F r e d e r i c t o n N : b = 0, c = 4 5 , d = 9 0 , e = 1 3 5 kg ha - I .

YOBS

Second cut

D

5000

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4000 •

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• ~. 0 × x AA / ~ O~ i / x

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•

Macdonald C<)lleqe

•

Fredencton c Frederlcton d

• •

Ottawa La Pocatlere

,3

Frederlcton e L'Assomption

•

Normandm Lennoxvllle

O z~

•

s Aog. i 1000

i 2000

i 3000

i 4000

i 5000

I 6000

i 7000

.

.

, 8000

G

.

.

.

YEST kq, ha

Fig. 2. S c a t t e r d i a g r a m o f o b s e r v e d ( Y O B S ) a n d e s t i m a t e d (YEST) t i m o t h y y i e l d s f r o m s e c o n d c u t a r o u n d 1 : 1 r e g r e s s i o n line. F r e d e r i c t o n N : b = 0, c = 4 5 , d = 9 0 , e = 1 3 5 k g ha -1 .

The second criterion for the validity of the model development is the scatter of the station-year yield estimates around the 1:1 regression line as compared with the observed yields (Figs. 1 and 2). The slopes (0.88 and 0.85) of the regression lines, and the correlation coefficients (0.77 and 0.78) between observed and estimated yields, are similar for first and second cuts.

332 T A B L E VII M e a n o b s e r v e d a n d e s t i m a t e d t i m o t h y yields p e r s t a t i o n - y e a r Station

n

Mean N (kg h a - l )

Observed yield (kg h a -1 )

Estimated yield (kg h a -1 )

Difference from o b s e r v e d yield kg h a-1 %

5 10 10 10 10 5 6 4 5 8 5 78

84 0 45 90 135 35 60 59 70 40 44 --

5779 1526 3871 3974 4962 5780 5677 5125 4722 4368 5918 4408

5639 1997 3972 4481 5092 4441 4161 4870 4265 4031 6762 4329

- - 140 + 471 + 101 + 507 + 130 --1339 --1516 - - 255 - - 457 - - 337 + 844 -79

-- 2 +31 + 3 +13 + 3 --23 --27 -- 5 --10 -- 8 +14 -- 2

5 10 10 10 10 5 4 4 5 5 5 73

45 0 45 90 135 31 19 9 80 27 82 --

3257 316 1591 1882 2607 2941 1998 2020 2483 1452 3294 2016

3528 294 1830 2054 2437 2382 2937 2159 2260 1300 3680 2086

--+ + --+ + --+ +

--8 -- 7 +15 + 9 -- 7 --19 +47 -- 7 ---9 --11 +12 + 3

First cut St. A u g u s t i n Fredericton

L 'Assomption M a c d o n a l d College Ottawa La Pocati6re Normandin Lennoxville All s t a t i o n s

Second cut St. A u g u s t i n Fredericton

L 'Assomption M a c d o n a l d College Ottawa La P o c a t i ~ r e Normandin Lennoxville All s t a t i o n s

271 22 239 172 170 559 939 139 223 152 386 70

The points scatter around the expected 1:1 regression line but the residuals tend to increase with higher yields especially for the second cut estimates. There is no consistent difference between stations, except for the Macdonald College estimates which are mostly above the 1:1 line for the first cut and below the 1:1 line for the second cut. The third criterion is therefore an analysis of the estimated mean yields for individual stations in terms of their station bias. Table VII indicates that there was a negative bias in the estimated first-cut means for L'Assomption and Macdonald College (23 and 27% of the station mean), and a positive bias of 31% for the 0 k g h a -1 N-rate yields at Fredericton; the remaining 8 station-years had a positive or negative bias of 14% or less. The statistics of s e c o n d ~ u t yields show a positive bias of" 47% at Macdonald College and a

333 TIMOTHY kg/ha

YIELD

8000--

A L L STATION YEARS MEAN

I 6000-

4ooo2j O8S

EST

Q

I

......

FIRST CUT SECOND CUT

78 STATION YEARS 73 STATION YEARS

2000 7

O~

i

1

i

1

2

3

J - - - - q

4

5

TIME

Fig. 3. Observed and estimated timothy yields for first and second cuts: Means of all station-years. positive or negative bias of 19% or less at all other station-years. Analysis of variance using years as replicates indicated that the station-year bias was significant for the first-cut (F = 4.6; Fo.05 = 1.98) but not for the secondcut (F = 1.2; Fo.05 = 1.99). The discrepancies, especially at Macdonald College, imply that the model did not properly reflect certain local influences and t h a t different models may be required for different stations. Finally, a critical inspection of the curves showing accumulated daily yield estimates also provides important information on the day-to-day response of t i m o t h y dry matter production to weather and soil moisture conditions. Such curves for the first and second cuts, together with the corresponding observed yields (Table VII}, are shown as means over all stations and years (Fig. 3) and for selected station-years (Figs. 4--8). The selection was made to include a variety of (1) locations representing different soil water characteristics and (2) years representing different weather conditions. For a conversion of time (t-values) to calendar dates, see Table II. Even though a quantitative comparison between estimates and observations is only possible for the yield estimates at t = 5 with the yields as reported for the first and second cuts, a qualitative comparison between the average curves for the first and second cuts is informative. For example, a noticeable increase in the average yield curves occurred at t = 2 for the first

334

TIMOTHY YIELD kg/ha 8000]

FREDERICTON 1964 FIRST CUT

i 6000

EST

I 4000~

I I

OBS

o ..... 45 kg/ha N . . . . .

:

135 kq/ha N . . . . . . . .

.."'" O

O

,*/" /;/..,

*f J"

O •

:,'/'f/ ,,(//

l

..f /

2000

0

i

i

TIME

Fig. 4. Observed and estimated timothy yields for four nitrogen application rates. Fredericton 1964, first cut.

cut and at t = 1 for the second cut (Fig. 3). The first cut curve is still on the increase at the average cutting date (30 June), whereas the second-cut curve already levelled out at the average cutting date (6 September). Inspection of the curves for individual years and cuts is also useful in comparing years, stations and effects of N-rates on yields. The curves for Fredericton are particularly interesting since they provide information on the performance of the model in response to weather and fertilizer applications. The accuracy of the annual estimates probably varies as a result of unexplained weather effects. For example, the 1964 first and second cut yield estimates for the four nitrogen application rates are all close to the observed data (Figs. 4 and 5 respectively), whereas in 1969 (Figs. 6 and 7) there are considerable discrepancies between observations and estimates. However, the yield curves, together with the data in Table VII for Fredericton, indicate t h a t there is no significant bias in the estimates due to nitrogen rates. These results imply that the response of t i m o t h y to nitrogen was realistically modelled and that the contribution of the nitrogen variable to yields was properly weighted. Figure 8 presents for another station (Normandin, 1966) an example of a smooth growth curve for the first-cut growing period resulting in a moderate yield estimate of 4478 k g h a-1 as compared with the observed yield of

335

TIMOTHY YIELD kg/ha 8000-

FREDERICTON 1964 SECOND CUT

EST 6000-

OkqhaN 45 kg~haN . . . . . 90 kg,'ha N . . . . . . 135 kq/ha N . . . . . . . .

OBS

q m

4000

I 2000 t

. . . . .

D

............

-

. .,;~.~-~:L~

I

,.,..,..,.,..~..~.,~/~"

>"

/ -

°1 ,:o

~

~

~

4

TIME

Fig. 5. As Fig. 4. Fredericton 1964, second cut.

4645 k g h a -1 ; both yields are slightly above the average value for this station (Table VII). CONCLUSIONS

The modifications which were made to the crop--weather analysis model, earlier developed for grain yields, resulted in a reduction of the coefficients from 12 to 6 in each of the iterative regression analyses. Other improvements included partial elimination of negative yield contributions, modelling the relationship between nitrogen application rate and timothy yields, and weighting of this nitrogen contribution together with the last yield effect on current t i m o t h y yields. Because of this interaction between weather, nitrogen and last yield effects, the contribution in statistical terms of the weather variables per se to t i m o t h y yields was apparently small, b u t all effects together accounted for 60% of the variation of first observed yields. Modelling of the nitrogen effect on yields was successful as there is no significant bias in the mean estimates of the yields for the four application rates at Fredericton. There is, however, a bias in the mean estimates for some of the stations especially Macdonald College. The model provided

336 TIMOTHY YIELD kg/ha

8000-

FREDERICTON 1969 FIRST CUT

6000-

/ EST 4000-

0 kg, ha N 45 kg/ha N 90 kg/ha N 135 kq/ha N

. . . . ..... ........

OBS

,'

• • O D

," f .. • /" J// / / / j "

.~ /.--L

2000 j. Y

2

;

4

6

TIME

Fig. 6. As Fig. 4. Fredericton 1969, first cut.

daily timothy yield estimates which {when accumulated over the growing season) reflect the total effect of nitrogen, last year and seasonal weather on the so-far accumulated yield. This information is useful for analyzing the growing conditions of past years and for comparing yields for different locations or from the first and second cuts. Additional work is necessary to determine whether the accumulatecl dally estimates at any time are sufficiently accurate for operational assessments of current timothy yield prospects. The concept of a factorial yield--weather model for analyzing daily crop responses to the interacting effects of selected environmental variables is promising b u t requires further research. In preparing the final version of this paper, the authors realized that the timothy--weather analysis model as here described has severe limitations which should be considered in future research and development of models: (1) The use of daffy observed temperature data and estimated soil moisture stress or deficiency indices as compared to monthly values is recommended in crop--weather analysis. However, further statistical studies should be undertaken to clarify whether or not these input data should be transformed to a 0--1 scale in view of potential model applications with a data range different from that used in the model development. (2) The currently used method for driving the timothy--weather model,

337

TIMOTHY

YIELD

kg/ha 8000-

F R E D E R I C T O N 1969 SECOND C U T

EST

60000 45 90 135

kg 'ha kg'ha kg'ha kq,ha

N N N N

OBS •

. . . . . . . . . ........

© o

4000-

..,"

_ _ - C.~ ~ "

2000

.

~,~"

,_~

.....

I

t:

0

4

1

5

TIME

Fig. 7. As Fig. 4. Fredericton 1969, second cut.

i.e. for identifying the crop growth stage in terms of biometeorological time (t), should be replaced by another weather-based variable or index such as accumulated degree-days possibly adjusted for soil moisture stress or another meaningful expression. (3) The so,ailed "daily weighting procedure", which at present is a second-degree polynominal based on biometeorological time (t), is purely statistical and could be replaced by a weighting procedure to be developed from known crop requirements for temperature and soil moisture at different growth stages. (4) Together with the comments under (1) and (2), an improved regression-type technique for evaluating the coefficients in the model should be investigated. In the Agrometeorology Section of the Land Resource Research Institute, research is in progress on the use of other non-linear regression techniques which would permit a wide range of functions for analyzing yield data. Thus, the application of the timothy--weather analysis model as presented here is not recommended, but the data source together with the preliminary results and the critical comments should be useful in the development of improved crop--weather analysis techniques.

338 TIMOTHY kg/ha

YIELD

NORMANDIN 1966

8000

6000

-

OBS EST ......

FqRST CUT SECOND CUT

30 kg,ha N 30 kg,'ha N

4000-

2000 -

i

2

~

i

4

i

6

TIME

Fig. 8. Observed and estimated timothy yields for first and second cuts. Normandin, 1966

ACKNOWLEDGEMENTS

Our most sincere thanks are extended to Drs. E.A. Grant of the Fredericton Research Station and W.R. Childers of the Ottawa Research Station, and to the Conseil des Productions V~g~tales du Quebec for providing the basic agronomic data essential in the development of the model. The authors are also grateful to t h e staff members of the LRRI (formerly CBRI) Agrometeorology Section for their helpful comments at various stages of the study. In particular, Dr. H.N. Hayhoe contributed to this study through developing the new mathematical equations in the timothy model and providing advice on the final presentation of the manuscript. Thanks are also due to the Agrometeorology Data Processing Group, especially D. Chaput for programming and data analysis.

REFERENCES Baier, W., 1973. Crop--weather analysis model: review and model development. J. Appl. Meteorol., 12: 937--947. Baier, W. and Robertson, G.W., 1966. A new versatile soil moisture budget. Can. J. Plant Sci., 46: 299--315.

339 Baier, W. and Robertson, G.W., 1968. The performance of soil moisture estimates as compared with the direct use of climatological data for estimating crop yields. Agric. Meteorol., 5 : 17--31. Baler, W., Dyer, J.A. and Sharp, W.R., 1979. The Versatile Soil Moisture Budget. Tech. Bull. No. 87, Agzometeorology Section, Land Resource Research Institute Research Branch, Agriculture Canada, Ottawa, 52 pp. Bauer, A., 1972. Effect of Water Supply and Seasonal Distribution on Spring Wheat Yields. Bulletin 490, Agricultural Experiment Station, North Dakota State University, Fargo, ND, 21 pp. Calder, F.W. and MacLeod, L.B., 1968. In vitro digestibilityof forage species as affected by fertilizerapplication, stage of development and harvest dates. Can. J. Plant Sci.,48 : 17--24. Grant, E.A. and MacLean, A.A., 1966. Effect of nitrogen, phosphorus, and potassium on yield, persistence, and nutrient content of timothy. Can. J. Plant Sci., 46: 577--582. Mack, A.R. and Finn, B.J., 1970. Differential response of timothy clonal lines and cultivars to soil temperature, moisture and fertility. Can. J. Plant Sci., 50: 295--305. Robertson, G.W., 1968. A biometeorological time scale for a cereal crop involving day and night temperatures and photoperiod. Int. J. Biometeorol., 12: 191--223. Robertson, G.W., 1974. Wheat yields for 50 years at Swift Current, Saskatchewan, in relation to weather. Can. J. Plant Sci., 54: 625--650. Russell, D.G., Lievers, K.W. and Lovering, J., 1975. The Economic Interaction of Machinery System Size, Harvest Strategy, and Differentially Maturing Variety Usage in Timothy Silage Production at Charlottetown. Paper No. 75-302. Presented to the 1975 Annual Meeting, Can. Soc. Agric. Eng., 22--26 June, Brandon, Manitoba.