The cumulative crop evapotranspiration during the 29 day experimental period was equal to 65.3 mm, and daily ETC varied from 1.68 to 3.39 mm. Irrigation was initiated on 16 August 2010 and terminated on 13 September, 2010. Irrigation and rainfall were recorded daily and drainage volume was measured 3 times per week throughout the trial period. Daily irrigation was applied in 5 short pulses using an automated irrigation controller, with 2 h breaks between irrigation pulses. The amount of irrigation water applied was slightly higher than ETC for the period. A total of 70 mm of rainfall fell during the experimental period, including a single event of 52 mm on 3 September 2010.The Kcb values for different months were taken from Allen et al. , assuming 70% canopy cover and no ground cover, since the lysimeter was placed in a well-grown citrus orchard, and the lysimeter soil surface was kept free of weeds during the experimental period. Estimated Tp and Ep values during the experimental period varied from 1.5 to 3.2 mm day−1 and from 0.5 to 1.1 mm day−1, respectively. The total Tp and Ep during the experimental period were 59.3 and 21.1 mm, respectively. Note that the potential ETC was larger than the 10-year average,plastic growers pots which was used for irrigation . However, since additional rainfall occurred during the experiment, no shortage of water was expected.
HYDRUS reduces the potential transpiration to the actual transpiration by integrating actual water uptake over the entire root zone, while considering water and salinity stresses. HYDRUS implements a scheme whereby the actual evaporation remains equal to the potential evaporation as long as the pressure head at the boundary is higher than a critical pressure head hCritA, considered to be −10,000 cm in our study. When the pressure head on the soil surface boundary falls below hCritA, the potential evaporation is reduced. The total rainfall was considered to be equal to the effective rainfall for the purpose of modelling, and canopy interception was not considered because through fall and stem flow account for about 90–95% of precipitation in citrus . Runoff was also not considered as the lysimeter was a closed system, which does not allow for surface runoff.The simulation domain was represented by a 110-cm deep and 100-cm wide cylindrical cross section. Drip irrigation was modelled as a circular line source 25 cm from the centre of the lysimeter with a uniform water flux along the drip line. This simplification was made to enable HYDRUS to model this problem in a 2D axi-symmetrical mode , rather than in a full 3D mode, which would be computationally much more demanding. Additionally, since the surface wetted area and input flux densities under drippers were dynamic, an option that we would not be able to model with HYDRUS in a 3D mode, we assumed that the simplification of the problem to axi-symmetrical 2D was adequate. Moreover, the drainage system laid out in the lysimeter also supported the use of an axi-symmetrical domain as the drainage pipes run in a circular fashion to collect and flushdrainage water out of the lysimeter.
The transport domain was discretized into 3294 finite elements, with a very fine grid around the dripper and near the outflow , with gradually increasing element spacing farther from these two locations . Simulations were carried out over a period of 29 days.Since most soils on which citrus is grown in South Australia are coarse textured soils with good drainage, high oxygen levels, low organic matter, and low microbial populations, denitrification and mineralisation was assumed to be negligible in this study. Similarly, the soil adsorption of nitrate was also considered to be negligible since both nitrate and solid surfaces are negatively charged. Plant uptake of non-adsorbing nutrients like nitrate is controlled mainly by mass flow of water uptake . Therefore, it was assumed that nitrate was either passively taken up by the tree with root water uptake or moved downward with soil water. Spatial distribution of nitrate in the transport domain was thus simulated using the convection–dispersion equation for a nonreactive tracer. Molecular diffusion was neglected as it was considered negligible relative to dispersion. The longitudinal dispersivity was considered to be 5 cm, with the transverse dispersivity being one-tenth of this . Similar values of these parameters have been used in other studies .Citrus trees in this region are fertilised from early September till March, and in drip systems fertilizers are mostly applied with the second irrigation pulse for the day. All fertigation scenarios reported here are hypothetical. Fertigation was assumed to be supplied with the same quantity of water as in irrigations without fertigation and to conform to the 2D axi-symmetrical domain. For the initial scenario, 5 fertigation pulses were applied from 30 August 2010 at the rate of one fertigation pulse each day. These were followed by 2 days without fertigation and then another 5 daily fertigation pulses.
The resultant dose of N for the period from 16 August till 13 September was calculated based on recommended fertilizer application practices for 5–6 year old orange tree. The seasonal recommended dose of nitrogen for an orange tree ofthis age is 139 g N applied from September to March . Hence for the seasonal simulation, nitrogen was assumed to be applied in equal monthly doses , in similar pulses as described for the experimental period. The simulation was run for 300 days in order to evaluate the fate of seasonally applied nitrogen fertilizer in citrus. Further scenarios examining the impact of timing of nitrogen application on the efficiency of nitrogen uptake simulated a fertilizer application either at the beginning , middle , or end of the daily irrigation scheme. Since the daily irrigation consisted of 5 pulses, fertigation was applied during the 2, 3 and 4 irrigation pulse in the PF1, PF2 and PF3 scenarios, respectively. It is a common practice that the initial and final irrigation pulses are fertilizer free to ensure a uniform fertilizer application and flushing of the drip lines. In addition to these simulations,blueberry in pot two continuous fertigation scenarios were also performed to compare pulsed and continuous fertigation. The first scenario consisted of applying the same amount of fertilizer spread across all irrigation pulses , except for the last irrigation pulse to enable flushing. The second scenario consisted of continuous irrigation of the same duration and irrigation amount as under pulsed treatments, with fertigation at all times , except for the same period of flushing at the end of irrigation. The fertigation scheme in PF1, PF2, PF3 and continuous scenarios was assumed to start from 17 August 2010. All fertigation simulations were run as for the irrigation experiment, that is for 29 days .To evaluate the impact of the quantity of irrigation water on nitrate leaching, additional simulations were run for all scenarios with 50% , 75% , and 125% of irrigation water applied in the field experiment .The water content distribution in the soil reflects water availability to plants, and plays a crucial role in water movement through and out of the root zone. Volumetric water contents simulated by HYDRUS 2D/3D are compared in Fig. 5 with the measured values obtained using EnviroSCAN probes 15 cm away from the dripper. Simulated values matched measured values well, both spatially and temporally. However, deviations between simulated and measured values were observed at day 19 of simulation, particularly in the upper 50 cm of the soil profifile; at later times this difference was not observed. Simulated and observed daily and cumulative drainage are compared in Figs. 6 and 7, respectively. Both variables showed a close match between simulated and measured values. It can be seen that simulated daily drainage remained slightly below observed values , except for the initial higher leaching on day 1. However,the total drainage observed in the lysimeter was matched closely by the model. The high peak on day 21 represents the effect of high rainfall on that day, which also was very well predicted by the model. However, the cumulative drainage remained slightly over predicted during the initial 15 days, after which the simulated and observed values matched well. Model evaluation was performed using a number of model performance parameters calculated using measured and model generated soil water contents . The mean absolute error varied from 0.006 to 0.22 cm3 cm−3 and the root mean square error ranged between 0.007 and 0.028 cm3 cm−3, which indicated small deviations between measured and simulated values. However,the maximum values of MAE and RMSE were observed at day 19, confirming the deviations shown in Fig. 5 at this time. However, the values of paired t-test between measured and simulated water contents showed insignificant differences at 5%level of significance at all times.Values of the coefficient of determination varied between 0.68 and 0.96, indicating a reliable generation of water contents by the model at all days of simulations.
Similarly, the Nash and Sutcliffe efficiency coefficient values ranged from 0.17 to 0.96, indicating a good performance of the model for the prediction of water contents in this study.However,the relative efficiency value at day 19 reveals unsatisfactory performance of the model at that point according to the criteria suggested by Moriasi et al. . The values of MAE, RMSE, r2, E, and RE for the drainage flux were 2.87, 4.14, 0.97, 0.94, and 0.78 , respectively, which also showed a robust performance of the model for drainage fluxes from the lysimeter. The close match of both water contents and drainage fluxes indicates that the HYDRUS 2D/3D software can be successfully used to predict water movement and drainage fluxes in a lysimeter planted with a citrus tree. Other studies have also reported good performance of this software for various soil, water, and crop conditions under pressurised irrigation systems . Simulated water balance components over the 29 day experimental period are shown in Table 3. It can be seen that simulated drainage, which is similar to the amount measured in the lysimeter, represents 48.9% of the total water balance. A much higher seasonal drainage has been reported for a lysimeter planted with an orange tree in a fine sandy soil . High drainage is bound to occur in highly permeable, coarse textured soils, such as the sand/loamy soil used in this study, where water drains easily and quickly from the root zone because gravity dominates over capillarity . However, Sluggett estimated deep drainage in the range of 6.1–37.2% under citrus trees growing in light textured soils in the Sunraysia region of Australia. A major contributor to the high drainage measured in this experiment was the high amount of water applied, mostly as a result of large rainfall events. Simulated plant water uptake was estimated to be 40% of the water application, indicating low irrigation efficiency of the drip system. The daily plant uptake varied from 1.2 to 3.14 mm . However, plant uptake is a very complex process, and depends on a number of parameters describing the root and canopy development. Since the HYDRUS model does not support a dynamic behaviour of the root system and considers only the static root parameters, root uptake was optimised on the basis of a changing transpiration rate over time. Additionally, since in the present study we dealt with a tree, for which the root distribution development over time is not as fast as observed for seasonal crops like cereals, the root development was considered relatively constant for the modelling purpose. Hence, a static root distribution and variable atmospheric conditions produced a good approximation of plant uptake, as has been revealed in a number of earlier studies that used HYDRUS for modelling purposes .Simulated distribution of nitrate at selected times after commencement of fertigation is shown in Fig. 8. Concentration of NO3-N was maximum at the centre of the plume below the dripper, with a gradual decrease in N concentration towards the outer boundaries of the plume. Subsequent irrigation and fertigation pulses resulted in enlargement of the plume, with a rapid lateral and vertical movement of NO3-N. It is worth noticing that after 15 days of fertigation all nitrate still remained in the lysimeter, reaching a depth of 70 cm. The maximum nitrate concentration at this time was at 20 cm.