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CHAPTER 3 MODELLING
Evaluation of the SWB model
The SWB model was tested according to the guidelines provided by CAMASE (1995). The verification of the model, i.e.:
i) inspection of the internal consistency of the model;
ii) software implementation;
iii) checking units used in the computer program;
iv) detection of violation of natural ranges of parameters and variables;
v) inspection of qualitative behaviour of the model and its implementation by checking whether the response of model output to changing values of a single parameter conforms to theoretical insights;
vi) on-line checks on mass conservation; was reported in Annandale et al. (2002).
In this Chapter, comparison of model output with independent data sets of real world observations and sensitivity analysis are presented. An example of calibration of the simple quasi-2D FAO-based cascading model is presented for peaches (Section 3.2). This was done by adjusting some FAO crop factors such that the model prediction of soil water deficit was consistent with field measurements. The most important observations gathered in the field trials at Hatfield and Syferkuil, and relevant to the development of the SWB model, are also presented.
The two-dimensional energy interception sub-model was evaluated using independent data sets (Sections 3.3). The two-dimensional soil evaporation model evaluation was presented in Annandale et al. (2002) and is not included in this thesis. The two-dimensional soil water balance model integrates the interactions of the various components, as it uses the 2D energy interception and 2D soil evaporation sub-models to split evaporation and transpiration. The functionality of the entire model was then evaluated by comparing the output obtained with the two-dimensional soil water balance model to independent field measurement data (Section 3.4).
Scenario simulations were carried out to perform sensitivity analyses (Section 3.5). Scenarios were simulated by varying one input parameter and retaining the same values for the other inputs. Logical sensitivity analyses were performed to establish by inspection of output results whether the model is sensitive at all to changes in an input (factor screening).
This could indicate which input parameters need to be accurately measured or estimated. The sensitivity analyses also provided estimates of scenario effects in order to recommend the most suitable practices for improved water use efficiency under different environmental conditions. One should, however, be aware that the sensitivity to an input may depend on the particular set of values used for other inputs.
Calibration of the FAO-type model and field observations
The simple, quasi two-dimensional, cascading soil water balance model was calibrated using data from the peach trial at the Hatfield experimental station. In the process, FAO basal crop coefficients (Kcb) were determined for first and second leaf peach trees.
FAO basal crop coefficients were determined by plotting daily Kc values over time for the first two growing seasons of peach trees (Figures 4.1 and 4.2). The daily Kc value was calculated using evapotranspiration measurements from the lysimeters and the grass reference evapotranspiration calculated from weather data. The Kcb values for the various growth stages were determined by fitting an appropriate line through the lower values of Kcb, which are taken to reflect the conditions where the soil surface is dry (negligible evaporation from soil surface) and there is sufficient water not to restrict transpiration. The longer development period during the first season can be expected since it is necessary to develop the tree structure. The drop in actual evapotranspiration measured with lysimeters during the late stage of the first season was caused by water stress (Figure 3.1). The Kcb line during this late stage was estimated.
Simulations of soil water deficit (SWD) with the SWB model were then carried out and compared to measurements obtained with the neutron water meter (Figures 3.3a and 3.3b). The Kcb factors in Figures 3.1 and 3.2 were refined by fitting the simulations of soil water deficit to measured data points (Figures 3.3a and 3.3b).
The initial period of the first season was not well evaluated as too few measurements with the NWM were taken (Figure 3.3) while the experimental procedures were being developed. Thereafter, more measurements were available, which enabled a better evaluation of model predictions. Generally, there was good agreement between predicted and measured soil water balance. This should be expected since the calibration data came from the trial. A section of trees (20 m row length) was stressed in the period from 10 January 1997 to 20 February 1997 in order to check the reliability of SWB under limited water supply. Each of these sections included neutron water meter (NWM) measurement site facilities to monitor soil water status. Comparing the results from the NWM measurements and the SWB.
predictions it is seen that the model adequately predicted soil water deficit (SWD) for the stressed (Figure 3.3a) and non-stressed treatments (Figure 3.3b).
The accuracy of the predictions of SWD was evaluated by comparison with SWD determined from NWM measurements. When measured SWD for the whole area (tree row and inter- row) is used, the agreement between predicted and measured SWD is good (r2 = 0.79) (Figure 3.5a). However, if measured SWD is taken only at the tree row centre (0 m from tree, Figure 3.5c) the agreement decreases (R2 = 0.53). When one considers SWD measured at the inter-row centre (2 m from tree, Figure 3.5b) there is little agreement (r2 = 0.33). The reduction in agreement between SWB predictions and actual values is due to the fact that irrigation is applied only under the tree canopy (i.e. near tree trunk) as well as a differing energy balance occurring in the inter-row region. It is thus vitally important to realise that in hedgerow plantings the whole area must be borne in mind when assessing soil water content. The practice of using single or restricted locality measurements, as utilised in agronomic crops, can be misleading in orchards. Orchardists that use single point measurements (e.g. only one tensiometer or NWM access tube arbitrarily placed under tree canopy) could be making large errors in their assessment of the water status of the hedgerow.
The reason for this is obviously the effect of the irrigation distribution, particularly when it is applied only under the tree canopy as illustrated in Figure 3.6. Soil water distribution is also effected by interception of rain by the canopy. Figure 3.7 shows how the percentage rainfall penetration differed for 5 separate rain events. For two of the five events the soil surface between – 1 and 0 m on the southern side of the hedgerow received ~140% of the rain while the corresponding distances on the northern side received only 80 % of the rainfall; a difference of 60 %!, In addition, with changes in canopy characteristics as the season progresses, there are changes in radiation interception by the canopy and the irradiance reaching the soil surface. Figures 3.8 and 3.9 highlight the variation in canopy radiation interception across the row as the season progresses. It is seen that in winter (4 July; DOY 185), when there is no tree canopy, the irradiance across the tree row is around 10 MJ m-2.d– Two months later (4 September; DOY 247), with the onset of spring, the daily irradiance has increased to around 17 MJ m-2.d-1 on the northern side of the hedge-row, whilst on the southern side, due to canopy development, soil irradiance has increased to only about 15 MJ m-2.d-1. In mid-summer (28 December, DOY 362), the irradiance in the inter-row region reaches 22.5 MJ m-2.d-1, whilst under the canopy the irradiance has decreased to about 2.5 MJ m-2.d-1. Figures 3.8 and 3.9 also show how the position of the shadow moves from ~ 1.3 m (Figure 3.8; DOY 185) to virtually under the tree on DOY 362 (Figure 3.9) as the sun elevation increases into summer.
A common assumption with tree crops is that rooting volume is of a similar magnitude to canopy volume. It was therefore interesting to investigate root length densities of peaches at Hatfield and of clementines at Syferkuil. As can be expected, the root length density decreased with depth both in the case of peaches and clementines (Figures 3.10 and 3.11). It was interesting to note the root length density across the tree row (Figures 3.10 and 3.11). There are at least as many, if not more roots in the inter-row region (i.e. in the 1 to 2 m distance from the tree trunk) than in the canopy drip area (0 to 1 m from tree trunk), in particular for peaches. It is common practice in hedgerow plantings to irrigate only under the tree canopy and not irrigate in the inter-row region at all. It must be noted that there are significant amounts of roots in the inter-row region, at least in areas receiving rainfall during the growing season, and thus this portion of the rooting volume must not be disregarded when assessing the contribution of rain to the water balance.
The resultant effect of the root length densities on the profile SWD across the hedgerow into the inter-row is depicted in Figure 3.12 for peaches with grass sod and bare soil in the inter- row area. This Figure depicts the change in SWD through one drying cycle during the development period. It is apparent that, during the 36 h after irrigation, most water was used from the wetted area. The presence or absence of a grass sod also had minimal influence on profile SWD which is to be expected since no irrigation water was applied in the inter-row.
The same effect was observed by analysing data of soil matric potential obtained with heat dissipation sensors. For example, in Figure 3.13, matric potential values decreased (became more negative) at two depths in the soil profile of peaches during a drying cycle after rain. This occurred both for grass sod and bare soil in the inter-row area. It is interesting to note that the top soil (6 cm depth) was wetter than the deeper layer (26 cm depth), as the rain was light and the wetting front did not reach 26 cm soil depth.
Figure 3.14. shows the volumetric soil water content across the row for different depths during a drying cycle of clementines at Syferkuil. The drying cycle started after the soil was wetted by heavy rain. It is evident that root water uptake occurred both from the wetted and non-wetted portion of the soil, due to an evenly distributed root system across the row (Figure 3.11). It is also interesting to note that even though the 56cm depth the matric potential is decreasing much slower than the upper layers, the matric potential is decreasing throughout the entire profile, not just the top layers.
The effect of the canopy absorbing solar energy is highlighted in the diurnal variation of soil temperature at a depth of 6 cm during summer is depicted in Figure 3.15 for peaches. It is seen that under the tree, soil temperature is around 19 to 20 oC at 06h00 and increases to 22 oC at 14h00. However, in the inter-row region, the 06h00 temperature is 24 oC and increases to 31 oC (grass-sod inter-row) and 33 oC (bare soil inter-row) at 14h00.
The above features, i.e. differing water use under differing water regimes and drastically differing soil temperatures, is a very clear indication in the vastly differing energy balances that occur in hedgerow plantings and the necessity to apply a 2-dimensional approach when analysing the energy and water balance for hedgerow plantings.
Evaluation of the two-dimensional energy interception model
Overview of the field trials
area densities, shapes and row orientations. Data collected in the peach and Leucaena orchards were used to evaluate the two-dimensional energy interception model for deciduous fruit trees, whilst data obtained from citrus orchards in Syferkuil and Brits were used to evaluate the model for evergreen fruit trees. For the benefit of the reader of this thesis, locality and orchard planting specifications are summarised in Table 3.1.
There are 11 horizontal surface nodes simulated in the model, one at the centre line of the canopy and five on either side of the row, but only seven tube solarimeters were available. Solar radiation interception by the canopy was therefore determined with the use of seven tube solarimeters positioned under the canopy and in the inter-row region. Soil irradiance measurements were taken next to the trunk and on each side of the centre of the row. This arrangement created a symmetrical and equidistant pattern of soil surface irradiance assessment. The solarimeter positions for each canopy are presented in Table 3.2. In the case of the tramline Valencia orchard in Brits (Table 3.1), the position midway between two adjacent tree rows was taken as the centre of the canopy for the simulation (Table 3.2, tube solarimeter No 4). The dimensions of the set-up is presented in Figure 3.11.
The solarimeters were coupled to a CR10 data-logger through an AM416 multiplexer. Milli- volt readings were taken every 10 s for each solarimeter, converted to solar radiation values (W m-2) with the appropriate calibration, and these values were averaged over one hour intervals. Above canopy radiation was measured at automatic weather stations erected in a nearby open area. The AWS was equipped with a CR10X data-logger coupled to a LI 200X pyranometer to measure solar radiation. The data-logger was programmed to take readings every 10 s and automatically calculate and record hourly averages. The logged data was regularly downloaded using a laptop computer.
Radiation data were collected from the various sites during the second half of 1999 and collection details are summarised in Table 3.3. In the case of the Leuceaena hedgerows, leaves were stripped from the canopy in a uniform manner to give a range of leaf area densities. The peach hedgerow was measured at the beginning of the season when the canopy was in the initial period, approximately a month later during the development period and then when the canopy was fully developed at fruit harvest.
The required parameter values are also presented in Table 3.3. These, as well as the respective values in Tables 3.1 and 3.2, were used as the defining parameters for the hedgerow canopies used in simulating the radiant transmittance. As can be seen in the Tables, a considerable range was covered. Not only were the measurements done from the end of May to early December (i.e. including a good sample of different solar elevations and direct flux densities), the LAI ranged from negligible (0.45) to substantial (5.5). These differences contributed to a range in LAD from 0.3 to 2.16 m2 leaves m-3 canopy. It must also be pointed out that there were also differences in canopy structure; viz. a typical “lollipop” (dense ball stuck on a stem) structure as typified by the clementine orchard to the multiple stem scraggy hedge growth found in the Leuceaena. There were also differences in leaf type in that the citrus and peach had simple leaves while the Leuceaena has compound leaves. The orchard canopies also varied tremendously in that the Empress mandarin orchard was a relatively dense planting which approximated a one-dimensional system since little direct radiation penetrated to the soil. On the other extreme were the peach trees during the initial stage (i.e. soon after bud-break) when the foliage was sparse. The single row Leuceaena site was also very open. The clementine, Valencia and mature peach hedgerows formed distinct two-dimensional systems with a dense high hedgerow canopy and a distinct inter- row region. Leaf absorptivity and the canopy extinction coefficient were assumed to be 0.5 for all simulations of total solar radiation transmission (see Section 1.1).
Acknowledgement
List of tables
List of figures
List of acronyms and symbols
Abstract
INTRODUCTION
1 MODEL DESCRIPTION
1.1. Two-dimensional water balance and energy interception model for hedgerow fruit trees (SWB -2D)
1.1.1. Two dimensional energy interception model
1.1.2. Spatial distribution of soil evaporation
1.1.3. Two-dimensional finite difference soil water balance model .
1.1.3.1. The soil profile
1.1.3.2. Two-dimensional water flow
1.1.3.3. Upper boundary condition
1.1.3.4. Lower boundary condition
1.1.3.5. Model stability
1.1.4. Link between the two-dimensional radiation and soil water balance model
1.1.5. Required inputs
1.2. FAO-based crop factor model
1.2.1. FAO-type crop factor modification
1.2.2. Soil water balance with localised irrigation
1.2.2.1. Water redistribution
1.2.2.2. Evaporation
1.2.2.3. Transpiration
1.2.3. Yield predictions with the FAO model
2 MATERIALS AND METHODS
2.1. Experimental set-up at the University of Pretoria
2.1.1. Location and environmental characteristics
2.1.2. Orchard lay-out, irrigation and cultivation practices
2.1.3. Lysimeter characteristics
2.1.4. Calculation of evapotranspiration and crop coefficient from lysimeter data
2.1.5. Weather monitoring
2.1.6. Soil measurements
2.1.6.1. Soil physical properties
2.1.6.2. Soil matric potential
2.1.6.3. Soil water content
2.1.7. Plant measurements
2.1.7.1. Root distribution
2.1.7.2. Canopy radiation interception
2.1.7.3. Leaf area index and density
2.1.7.4. Canopy size and row orientation
2.1.8. Leucaena trial
2.2. Experimental set-up at the University of the North
2.2.1. Location and environmental characteristics
2.2.2. Orchard lay-out, irrigation and cultivation practices
2.2.3. Weather monitoring
2.2.4. Soil measurements.
2.2.5. Plant measurements .
2.3. Field trial at Brits
3 MODELLING
3.1. Evaluation of the SWB model
3.2. Calibration of the FAO-type model and field observations
3.3. Evaluation of the two-dimensional energy interception model
3.3.1. Overview of the field trials
3.3.2. Peach trial (Hatfield)
3.3.3. Leucaena trial (Hatfield)
3.3.4. Citrus trial (Syferkuil)
3.3.5. Citrus trial (Brits)
3.4. Evaluation of the two-dimensional water balance model
3.5. Scenario modelling and sensitivity analysis
3.5.1 Row orientation
3.5.2 Wetted diameter and canopy width.
3,5,3 Root density
3,5,4 Interpretation of results
4 CONCLUSIONS AND RECOMMENDATIONS
5 REFERENCES..
Appendix A
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