Materials and methods Directory UMM :Data Elmu:jurnal:E:European Journal of Agronomy:Vol14.Issue1.Jan2001:

duce complexity and to adapt the simulation to an intended use in decision support.

2. Materials and methods

2 . 1 . Experiments The effects of interspecific radiation competi- tion between common lambsquarters aka. fat hen, Chenopodium album L., Conrad Appel, Darmstadt, Germany and cauliflower Brassica oleracea L. convar. botrytis var. botrytis L. cv. Fremont, Royal Sluis, Neustadt, Germany were examined in field trials in 1994 and 1995. The trial in the second year was carried out as a spring ‘experiment 1’ and a summer planting ‘experi- ment 2’ with identical layouts Table 1. The experiments were made on a silty loam at the experimental station in Ruthe near Hanover, Ger- many. To achieve different degrees of competi- tion, planting density of C. album was varied at two levels. In addition to mixed stands, plots with C. album in monoculture were planted on both densities. The experiments were set up in com- pletely randomised blocks with four replications. Within each plot, separate subplots were used for four successive samplings throughout the growing period. 2 . 1 . 1 . Culti6ation Cauliflower seedlings were cultivated in a green- house until the transplants had an average fresh weight of c. 5 g and had four to five leaves. At least 1 week prior to planting the transplants were hardened off in a cold frame. In the field, the plants were arranged in a rectangular pattern in 1994 and in an isometric pattern in 1995. Nitro- Table 1 Cultivation and sampling data of field experiments Cauliflower 1994 1995 experiment 1 1995 experiment 2 18 February Sowing date 24 February 8 June 18 April 24 April 18 July Date of transplanting Harvest dates 24 May 16 May 9 August 31 May 9 June 23 August 13 September 28 June 20 June 10 July 9 October 1 July a Planting pattern m 0.45×0.52 0.5×0.6 0.45×0.52 3.33 Plants m − 2 4.27 4.27 Plot area m 2 7.28×2.0 8.4×4.0 7.28×2.0 Plants per harvest 4 4 10 Chenopodium album Sowing date 19 April 3 April 27 June 20 July – Date of 3 May transplanting Plants m − 2 Target: 25, emerged: 24 Low density Mixed: 12.8, pure: 17.1 Mixed: 12.8, pure: 17.1 Target: 50, emerged: 41 High density Mixed: 38.5, pure: 42.7 Mixed: 38.5, pure: 42.7 Five or three early or late Plants per harvest Five or three early or late Five or three early or late growth stages, respectively growth stages, respectively growth stages, respectively a No dry matter data available. gen fertilisation was given shortly before and 4 weeks after transplanting: after soil sampling, the mineral N supply was replenished to 130 kg N ha − 1 at the first and to 270 kg N ha − 1 at the second application Lorenz et al., 1989. In 1994, C. album was sown by hand directly into the field. After a germination test, a quantity of seeds ap- propriate to obtain target densities was mixed with quartz sand and spread out uniformly over the plot. In low density plots, the target density was achieved, but it fell short in high density plots Table 1. Still, a considerable variation between the treatments could be expected. Due to a long juvenile phase, the onset of competition with cauliflower was notably delayed. To achieve early competition, C. album plants were raised and transplanted to the field for the 1995 experiments. Four to five seeds were laid into peat-filled cone- trays and singled after emergence. After raising the seedlings in a greenhouse, they were trans- planted when having about three nodes and an average height of 3 cm. The weed densities were achieved by placing one or three C. album be- tween two cauliflower plants for low and high density plots, respectively. In pure weed stands, the same pattern was used, except that the posi- tion of the cauliflower plant was filled by another weed. This resulted in slightly higher planting densities in pure than in mixed stands. All plots were well irrigated to avoid water limitations and weeds emerging spontaneously were removed by hand. Pests and insects were controlled chemically for both crops and weeds. 2 . 1 . 2 . Data collection At four successive sampling dates, a number of cauliflower and C. album plants were taken from the designated sub-plots. Plants were dug out to a depth of c. 20 cm; the roots were washed and separated from the shoot just above the first lateral root branching off. Measurements of shoot length from base to top and its greatest width gave the plant height and diameter, respectively, both with an accuracy of c. 5 mm. The shoots were divided into stems including petioles, green leaves, senescent leaves and reproductive organs only cauliflower. All plant parts were dried for at least 3 days at 100°C and weighted. The area of green leaves was measured with a LI-COR 3100 Area Meter LI-COR Inc., Lincoln, NE, USA. From these data the green leaf area index LAI was calculated. Hourly data of air temperature, global incoming radiation and relative humidity were supplied by an on-site automatic weather station Campbell Scientific, UK. For further details see Ro¨hrig et al. 1999 and Ro¨hrig 1999. 2 . 2 . Model description The model presented here was derived from a crop growth simulation for faba beans Stu¨tzel, 1995a,b, which calculates plant growth based on the insolation. The profile of absorbed radiation in the canopy is computed assuming a leaf area distribution in three dimensions. From the ab- sorbed radiation and the efficiency of its use, the total growth rate of the competing species is estimated. The biomass produced is partitioned into the various plant organs. From the leaf dry weight and the specific leaf area, the LAI is calculated, which is distributed in the canopy according to plant positions and dimensions. De- velopmental processes such as vernalisation and ontogeny are modelled as a function of ambient temperature Kage and Stu¨tzel, 1999. 2 . 2 . 1 . Calculations Fifty percent of the incoming global radiation 400 – 3000 nm is assumed photosynthetically ac- tive radiation PAR, 400 – 700 nm. The thermal time scale is defined in the model as the tempera- ture sum TS °C day: TS = T av with T av = T min + T max 2 1 where T av , T min and T max are the daily average, minimum and maximum temperatures in °C, re- spectively. A base temperature of 0°C for both cauliflower Wurr et al., 1990; Grevesen and Olesen, 1994 and C. album Angus et al., 1981 was used. 2 . 2 . 2 . Growth processes The radiation absorption submodel is described in detail by Ro¨hrig et al. 1999. In brief, the complete canopy volume is divided into cubic subunits, which are either empty or filled with leaf area. Leaf area of each plant of a species is distributed in a geometric foliage envelope, which is defined in the model domain by plant height, diameter and position. Foliage envelopes may overlap resulting in a multiple occupation of a cube by one or more species. Radiation transmis- sion is then calculated by following the path of a solar ray through the canopy volume until ground level is reached. The absorption of diffuse radia- tion is calculated by selection and integration of solar rays from 15 directions according to the Gaussian integration algorithm Goudriaan, 1986. This routine is also used to integrate the diurnal course, yielding a daily total of absorbed radiation, I a MJ m − 2 , Eq. 19 in Ro¨hrig et al., 1999, for each species. The increase of total plant biomass, W T g m − 2 , is calculated as a function of I a and the radiation-use efficiency, RUE g MJ − 1 : dW T dt = I a RUE 2 In 1995 it was found that a RUE of cauliflower showed a seasonal variation between the experi- ments and b crop dry matter decreased due to profound shading by C. album. The seasonal vari- ation of RUE can be attributed to a differing insolation that was also found in potatoes Man- rique et al., 1991. A log – normal function was used to describe both findings: RUE = e 1 + e 2 e − 0.5lnI 0, c e 3 e 4 2 3 where e 1 to e 4 are calibration constants and I 0, c MJ m − 2 is the daily radiation incident on a horizontal plane above the cauliflower plants. The constant e 1 is the minimum of the function and e 3 denotes the maximum, i.e. the irradiance at which RUE is maximum. If I MJ m − 2 is the insola- tion and I a,t MJ m − 2 denotes the radiation absorbed by the entire canopy, then the irradiance above species S, I 0, S , amounts to: I 0, S = I − I a, t − I a, H S 4 where I a, H S MJ m − 2 is the radiation absorbed by the canopy from the height of species S, H S , down to ground level. In the case of monospecific stands I 0, S equals I ; in mixtures the term in parentheses represents the radiation absorbed by species with leaf area between the top of the canopy and the top of the species under consider- ation. Newly produced biomass is allocated to root, W R g m − 2 , and shoot dry matter, W Sh g m − 2 , using an allometric growth equation Per- sall, 1927. As shown by Kage and Stu¨tzel 1999, Eq. 18, the growth rates of plant organs growing allometrically are obtained by: dW Sh dt = dW T dt 1 1 + e a bW Sh b − 1 and dW R dt = dW T dt − dW Sh dt 5 Considering roots and shoots, the term e a is the ratio between the initial weights Persall, 1927 and the allometric growth coefficient b denotes the fixed ratio between the relative growth rates Thornley and Johnson, 1990. For cauliflower, the shoot dry matter is allo- cated to vegetative, W V g m − 2 , and reproductive organs, W G g m − 2 , but only after curd initiation Kage and Stu¨tzel, 1999. They proposed that during the reproductive phase the ratio of curd growth rate to shoot growth rate increases logisti- cally in time. On the transition from the exponen- tial to the linear phase of the logistic function, the sink strength of the curd becomes substantial. At this point, it is assumed that a fraction of the vegetative shoot dry weight is reallocated to the curd. The reproductive growth rate is then: dW G dt = Á Ã Í Ã Ä f dW Sh dt if f 5 0.1 f dW Sh dt + r t T av W 6 if f \ 0.1 6 where f is a logistic growth function of thermal time after curd initiation see Eq. 21 in Kage and Stu¨tzel, 1999 and r t °C − 1 day − 1 is the translocation rate. For the distribution of vegeta- tive shoot dry matter into stems, W S g m − 2 , and leaves, W L g m − 2 , the approach of Stu¨tzel et al. 1988 and Stu¨tzel and Aufhammer 1991 is used, which mainly assumes allometric growth. Thus, in analogy to Eq. 5 the growth rates of leaves and stem are obtained by: dW L dt = dW V dt 1 1 + e h gW L g − 1 and dW S dt = dW V dt − dW L dt 7 where h and g are constants. In case of low irradiance Eq. 3 may become negative. Since stems and roots are less physiologically active, these losses are solely attributed to leaf dry weight and all other growth rates are set to zero. It is furthermore assumed that the leaf area in- dex, L m 2 m − 2 , is directly linked to leaf dry weight by: dL dt = Á Ã Í Ã Ä dW L dt SLA if dW L dt \ dW L dt 0.5 L W L if dW L dt 5 8 where SLA m 2 g − 1 is the specific leaf area of newly formed leaves. Eq. 8 also implies that per unit dry weight loss, leaf area is decreasing only by half the actual leaf area ratio. SLA is a con- stant input parameter for C. album, but in cauliflower it is made a function of the radiation environment quantified by Alt 1999 personal communication: SLA = 0.059I 0, c, av − 0.85 9 where I 0, c, av is I 0, c MJ m − 2 as a running aver- age of 5 days. This relationship takes into ac- count leaves becoming thinner when growing under low radiation. Dry matter production and distribution of C. album are quantified in Ro¨hrig 1999. The radiation-use efficiency and the co- efficients of the allometric growth equation are estimated and the effects of competitive stress on the growth processes are discussed. All data from the 1995 experiments were used for calibration. 2 . 2 . 3 . De6elopmental processes Vernalisation and flower initiation in cauliflower are modelled by the temperature sum approach of Wiebe 1979 as modified by Kage and Stu¨tzel 1999. The spatial expansion of cauliflower plants is calculated as a hyperbolic function of stem dry weight for plant height, H m, and vegetative shoot dry weight for plant diameter, D m. Plant dimensions, however, are not allowed to be less than the initial values H and D at transplanting, thus: H = max H max W S w S,h + W S , H and D = max D max W V w V,d + W V , D 10 where H max and D max m denote the maximum height and diameter, respectively. The calibration constants w S, h g m − 2 and w V, d g m − 2 are the stem and vegetative shoot dry weights at which half of the maximum stem heights and plant diameters are achieved. Canopy development of C. album is modelled explicitly in response to the competitive environment Ro¨hrig, 1999. In brief, C. album as a shade avoiding weed species adapts its morphology to the degree of crowding. The leaf area around the extending internodes of C. album ‘effective’ LAI is assumed mainly respon- sible for plant height modulation. In the ap- proach, stem extension is related to the thermal time and an estimate of the ‘effective’ LAI result- ing in a different plant height of C. album for each treatment. The relationships were calibrated using data from all treatments in the 1995 trial. All plants in the model were assumed to have an ellipsoidal foliage envelope and the cube edge length was set to 0.01 m Ro¨hrig et al., 1999. The latitude of the experimental site 52°15 N was input in the model as well as the north – south alignment of the field. Crop canopies usually have a specific planting pattern and are thus defined by a repeating basic unit. This basic unit is specific for each treatment and is modelled accordingly by a its boundaries in a west – east x-axis and south – north y-axis direction and b the number and position of each species under consideration Fig. 1. In the 1994 experiment, C. album was sown by hand. In the model, the position of C. album plants was thus distributed at random and the number of plants corresponds with the observed planting density Table 1. In 1995 C. album was trans- planted in a defined pattern and this was re- peated in the simulation. Fig. 1. Distribution of cauliflower and C. album plants in the field experiments as repeated in the model. The top and the middle row represent the mixed stands of the cauliflower experiments in 1994 A – C and 1995 D – F, re- spectively. The bottom row shows the pure weed plots in the 1995 experiments G – H. The columns from left to right represent weed free, low and high weed planting densities. calculated per layer. Within a layer, a homoge- nous leaf area distribution is assumed, whereas in the vertical dimension a parabolic density func- tion is used. Summation over all layers yields the total radiation absorbed by each species. The modification used here applies to the ex- tinction coefficient for diffuse radiation. Instead of using a constant value, the absorption of solar rays from selected elevation angles in a layer is calculated to be integrated over the hemisphere according to the Gaussian integration procedure Goudriaan, 1986. Five points, p, are selected at defined distances, d 5p , from the central point of the integration range of the solar elevation angle b . The absorption of radiation originating at these solar heights b p is calculated and weighted, w 5p . For the distances and weights for the Gaus- sian integration see Ro¨hrig et al. 1999, Table 1. The solar elevation angles are determined by: b p = p 2 0.5 + d 5p for 0 B b 5 p 2 with p = [1…5] 11 The radiation extinction coefficient to be used for integrating the absorption of diffuse radiation is Goudriaan, 1977, Eq. 2.41: K a = O av sin b p 1−s 12 where O av is the average projection of leaves, which is 0.5 for a spherical leaf angle distribution and s is the scattering coefficient, which amounts to 0.2 for visible radiation. According to the Gaussian integration the relative absorption of diffuse radiation, F a,f , is then the weighted sum of all rays considered: F a, f = p 2 5 p = 1 I p 1 − e − K a L LY sin b p cos b p w 5p 13 where I p is the relative irradiance of the selected solar ray, which amounts to 1p for each solid angle above the canopy and L LY is the total leaf area in layer LY. Multiplication by sin b p consid- ers the fraction of radiation effective on a hori- zontal plane and the factor cos b p is needed when integrating the solid angles over the hemisphere. Since the radiation absorption of canopy with a 2 . 2 . 4 . Run control The model runs start at the date of cauliflower transplanting. C. album is initiated at the three- node stage, i.e. at about 300°C days after sowing in the 1994 experiment and at the date of trans- planting in the 1995 experiments. The simulation is terminated when the crop has reached harvest time, which is determined by a specified curd diameter in cauliflower. For those treatments where curds did not reach a marketable size, the model is stopped at the day of the final harvest. 2 . 2 . 5 . Model simplification To reduce complexity, the detailed model was compared to a modified version of the radiation interception module XASSNM of SUCROS87 Spitters, 1989, which stratifies the canopy into a number of horizontal leaf layers, amounting to one layer per 0.01 m canopy height. For each competing species, the absorption of diffuse and direct radiation by sunlit and shaded leaves is horizontally homogeneous leaf area distribution is insensitive to changes of the solar azimuth angle, the weighted sum has finally to be multiplied by the integration range of both solar angles 2pp 2 = p 2 . Calculating the absorption of diffuse radiation in a layer with the above procedure yields a value that is dependent on the leaf area Goudriaan, 1977 and on the depth in the canopy. Subsequently, the ‘effective’ diffuse radia- tion extinction coefficient, K f , is calculated, which is needed to realise the relative absorption of diffuse radiation given by Eq. 13, thus: F a,f = 1 − e − K f L LY 14 which can be rewritten as K f = − ln1 − F a, f L LY 15 Eq. 13 estimates the fraction of absorbed diffuse radiation in relation to the irradiance above the canopy. If the absorption is calculated from the irradiance above a layer I 0, LY , Eq. 15 is modified to give K f, LY = − ln1 − F a, f I 0, LY L LY 16 yielding the ‘effective’ diffuse radiation extinction coefficient in a layer K f, LY , which is used in the routines of XASSMN.

3. Results and discussion