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Simulation of the Responses of Dry Beans (Phaseolus vulgaris L.) to Irrigation

M. Espadafor, L. Couto, M. Resende, D. W. Henderson, M. García-Vila, E. Fereres


Published in Transactions of the ASABE 60(6): 1983-1994 (doi: 10.13031/trans.12386). Copyright 2017 American Society of Agricultural and Biological Engineers.


Submitted for review in April 2017 as manuscript number NRES 12386; approved for publication as part of the “Crop Modeling and Decision Support for Optimizing Use of Limited Water” collection by the Natural Resources & Environmental Systems Community of ASABE in September 2017.

The authors are Mónica Espadafor, Postdoctoral Researcher, Department of Agronomy, University of Córdoba, Spain; Lairson Couto, Professor, Centro Universitário Sete Lagoas, Minas Gerais, Brazil; Morethson Resende, Researcher, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico, Lago Sul, Brasília, Brazil; Delbert W. Henderson, Professor (deceased), Department of Land, Air, and Water Resources, University California, Davis, California; Margarita García-Vila, Postdoctoral Researcher, andElías Fereres, Professor, Department of Agronomy, University of Córdoba, Spain. Corresponding author: Elías Fereres, University of Córdoba, Apartado 4084, E-14080 Córdoba, Spain; phone: +34-957499264; e-mail: ag1fecae@uco.es.

Abstract AquaCrop is a crop simulation model developed by the FAO aimed at assessing the yield response to water supply. Once the model is calibrated and validated, it is a useful tool to simulate crop yields under different management options or climatic and soil conditions. Until now, AquaCrop has not been parameterized for dry beans ( L.), and thus our objective was to calibrate and validate the model for this crop using experiments performed 40 years ago at Davis, California. A set of parameters derived from the calibration with one irrigation experiment was used to validate the model using five experiments carried out in 1977 and 1978 that had treatments vastly differing in irrigation depth and frequency. Yield predictions over a wide range of values (<1 to 3.5 t ha-1) were very good, with RMSE of 0.16 t ha-1 and Willmott’s d of 0.978. Seasonal ET was also accurately predicted by the model (RMSE = 40 mm, d = 0.930), as also evidenced by comparing the lysimeter measured ET of 489 mm against the lysimeter simulated ET of 501 mm. Canopy cover and the time course of biomass were adequately simulated as well. Even though total soil water extraction was well simulated, the simulated soil water distribution with depth differed from measured values in the dryland treatment. We conclude that AquaCrop can now be used for the simulation of dry beans in different environments, and we emphasize the value of carefully conducted field experiments for the validation of crop simulation models.

Keywords.AquaCrop, Calibration and validation, Dry beans (Phaseolus vulgaris L.), Irrigation, Simulation model, Water stress.

Dry beans (Phaseolus vulgaris L.) are an important source of high-quality protein, vitamins, and mineral nutrients in the human diet (Graham and Ranalli, 1997) and are the most important grain legume for direct human consumption (Beebe et al., 2013). World production is about 17 million tons from a cropped area of 23 million ha (FAOSTAT). Latin America is the region of greatest production, representing about 50% of global production, with Brazil being the main producing country, followed by Africa (25%). The crop is usually grown by smallholder farmers who are often exposed to unfavorable conditions and have a minimum use of inputs (Beebe et al., 2013).

The water requirements of a 60-day to 120-day dry bean crop vary between 300 and 500 mm depending on climate (Allen et al., 1998). Under full irrigation experimental conditions, dry bean yield can be 4 t ha-1 or more (Beebe et al., 2013). Even though irrigation is generally needed for maximum production, it is estimated that up to 73% of the total Latin American bean production and 40% of the total African bean production occur under moderate to severe water deficits, and less than 10% of the bean growing area is well watered (Broughton et al., 2003). Even in Brazil, where large-scale agriculture has been widely promoted, only about 4% of the area and 15% of the bean production uses high-input irrigated systems (Broughton et al., 2003). Beans are sensitive to water deficits, particularly during the flowering and pod development stages (Graham and Ranalli, 1997), thus the need to supply sufficient water for economic production.

Understanding crop responses to different irrigation scenarios is essential to support farmers’ decisions aimed at obtaining maximum net profits when irrigation water is limited. Given the complexity of plant responses to water deficits, field experiments have been conducted for many years in an attempt to characterize the relationships between yield and water supply. However, the paucity, empiricism, and costs of field experiments limit the capacity to predict crop responses to irrigation. Simulation models have long been proposed (Loomis et al., 1979) as an alternative tool to test hypotheses, to synthesize knowledge, to describe and understand complex systems, and to compare different scenarios (Marcelis et al., 1998). A recent example of the use of a simulation model to characterize maize responses to full and deficit irrigation illustrates how it is possible to enhance the understanding of the crop-environment interactions underlying the overall yield response to water (Qi et al., 2016). In the case of dry beans, the DSSAT model has been calibrated for this crop (Hoogenboom et al., 1994), and more recently, several crop models have been developed to simulate aspects of bean growth and yields (Marrou et al., 2014; Wagner et al., 2016; Seidel et al. 2016).

AquaCrop is a crop simulation model developed by the FAO (Steduto et al., 2009) that aims at reaching a balance among simplicity, accuracy, and robustness. AquaCrop has a relatively limited number of input parameters and has a strong appeal due to its simplicity of use. Parameters for the major field crops to use in conjunction with AquaCrop are provided on the FAO website, although there are none for dry beans. Because the AquaCrop model is water-driven, many of its applications have been related to irrigation management, including the evaluation of responses to deficit irrigation. A number of reports have been published recently on that subject for maize (Ahmadi et al., 2015), sorghum (Araya et al., 2016), winter wheat (Xiangxiang et al., 2013), potato (Montoya et al., 2016), and soybean (Adeboye et al., 2017). Beyond the plot scale, AquaCrop has been used for economic optimization at the farm scale (García-Vila and Fereres, 2012), for yield gap analyses (Nyakudya and Stroosnijder, 2014; Angella et al., 2016), and for yield prediction in climate change scenarios (Vanuytrecht et al., 2016; Yang et al., 2017).

Periodically, reports have been published on AquaCrop model parameterization for different crops; the first was on maize (Hsiao et al., 2009) and more recently on bambara groundnut (Mabhaudhi et al., 2014), sweet potato (Rankine et al., 2015), pearl millet (Bello and Walker, 2016), and vining pea (Paredes and Torres, 2017). There is wide variation in the amount and quality of the data used in parameterization exercises. Oliveral et al. (2016) attempted to test AquaCrop with dry beans using the results of just a single experiment without differential water treatments. The availability of detailed, high-quality experimental data is essential for successful calibration and credible validation of simulation models (Trout and DeJonge, 2017). Two previously unpublished dissertations that reported the results of field experiments conducted in Davis, California, on dry bean responses to a variety of irrigation regimes (Couto, 1978; Resende, 1979) offered a wealth of information that could be used to parameterize the AquaCrop model for dry beans. Thus, the objectives of this work were to calibrate and validate the AquaCrop model for dry beans grown under different irrigation treatments.

Table 1. Experimental data sets used for calibration and validation of the AquaCrop model with the experimental information reported in Couto (1978) and Resende (1979).
Field
Experiments
n[a]CultivarPlant
Density
(plants m-2)
Sowing
Date
Emergence
(DAP)[b]
Flowering
(DAP)
Maturity
(DAP)
Maximum
Rooting
Depth
CalibrationCO764Light red kidney13.211 June540-4596-120170 cm
ValidationCO774Light red kidney13.216 June540-45102-109170 cm
RE7710Dark red kidney13.223 June-45--
RE7810Dark red kidney21.930 June-45--

    [a] Number of experimental treatments.

    [b] DAP = days after planting.

Material and Methods

Two experimental datasets reported in two doctoral dissertations (Couto, 1978; Resende, 1979) addressing the response of dry beans (Phaseolus vulgaris L.) to different irrigation treatments were used to parameterize and validate the AquaCrop model. The experiments reported by Couto (1978) took place in 1976 (CO76) and 1977 (CO77), whereas the experiments reported by Resende (1979) were carried out during 1977 (RE77) and 1978 (RE78).

All the experiments were performed on the university farm at Davis, California (38° 32' N, 121° 45' W). The soil of the experimental area is a very deep alluvial Yolo clay loam (order Entisol, subgroup Typic Xerothents) with uniform texture in the upper 1.8 m and with relatively high water-holding capacity. The soil has a good structure and is readily penetrable by roots. The experiments were conducted in the same general area as the maize experiments of Acevedo (1975) that were used to calibrate AquaCrop by Hsiao et al (2009). In that area, field capacity (FC) was determined by Acevedo (1975) to be 33% and permanent wilting point (PWP) was 13.8%, all on a volume basis.

The climate is Mediterranean, with rainfall confined mostly to the period from late October to early May. Rainfall (October to September) in 1976, 1977, and 1978 was 172, 194, and 685 mm, respectively. Daily weather data, required as input for the simulations, were measured at a weather station of the university farm nearby and downloaded from the IPM website (http://ipm.ucanr.edu/WEATHER/wxactstnames.html). AquaCrop uses daily maximum and minimum air temperature to calculate growing degree days (GDD). The daily reference evapotranspiration (ETo) was calculated with the procedure recommended in AquaCrop using the FAO Penman-Monteith equation, as described by Allen et al. (1998).

Crop and Management Practices and Irrigation Treatments

    The bean cultivars involved in the experiments were light red kidney and dark red kidney. According to the information reported in the dissertations, the phenology and responses to water stress were similar, while the two cultivars differed in harvest index (HI). Therefore, the phenology and stress functions used in the simulations were the same for both cultivars. A summary of the experimental data used in the simulations is presented in table 1.

Planting density was 13.2 plants m-2 in all experiments, except for the RE78 experiment in which the density was 21.9 plants m-2, all in 76 cm row spacing. Plots in CO76 received nitrogen fertilizer in the amount of 220 kg N ha-1 as ammonium sulfate, while plots in RE77 and RE78 received 112 kg N ha-1 as ammonium nitrate. No nitrogen fertilizer was applied in CO77. In order to enable germination, the soil was irrigated before planting in all cases. The method of irrigation differed in the two dissertations; CO76 and CO77 were surface irrigated, while RE77 and RE78 were irrigated by sprinkling.

Table 2. Timing and amount of irrigation events in the experiments reported by Couto (1978) used for calibration and validation
1976FISympPod
DAP[a]mmDAPmmDAPmm
211002910051100
291004415063100
391007210083100
45100
5650
70100
1977FIFlowPod
DAPmmDAPmmDAPmm
321004510059100
3950537566100
45506610081100
537581100
66100
81100

    [a] DAP = days after planting.

Figure 1. Applied irrigation in the (a) Resende 1977 experiment and (b) Resende 1978 experiment. Only the maximum (A) and minimum (E) treatments are shown. NF and HF indicate normal and high frequency irrigation, respectively.

All four experiments had a control treatment (FI) that was irrigated at regular intervals to fully meet the crop water requirements. In CO76 and CO77, there were three water deficit treatments: the first treatment was not irrigated at all after planting (Dry), the second treatment was irrigated only after the appearance of visible stress symptoms (Symp) in CO76 or after the flowering stage (Flow) in CO77, and the third treatment received irrigation after the start of the pod development stage (Pod). The CO experiments had a randomized complete block design with plots of 180 m2 in 1976 and 216 m2 in 1977 and four replications. The RE77 and RE78 experiments used a sprinkler line source design (Hanks et al., 1976) to develop variable irrigation amounts about 100%, 74%, 52%, 35%, and 16% of the applied irrigation water, all at the same frequency. In both years, two line source systems were installed and run at different irrigation intervals (normal and high frequency). The high frequency (HF) line source was operated every other day in both years, while normal frequency (NF) had a seven-day irrigation interval in RE77 and 12 days in RE78. Table 2 shows the timing and amount of irrigation in the Couto (1978) experiments, and figure 1 shows the seasonal irrigation patterns in the Resende (1979) experiments.

Field Measurements

Soil water content (SWC) was monitored in all the experiments at 30 cm intervals down to a depth of 2.1 m using a neutron moisture meter (Troxler Electronic Laboratories, Inc.). Gravimetric determinations were made in CO76 and CO77 to check the calibration of the neutron meter. SWC measurements were made every seven to ten days. Detailed SWC records are provided by Couto (1978) and Resende (1979). Seasonal crop evapotranspiration (ETc) was estimated by Couto (1978) and Resende (1979) as:

ETc = ?SW + IR + ETci (1)

where ?SW is the change in SWC from the first SWC measurement to the last measurement at end of the season, IR is the total amount of irrigation plus rainfall during the same period, and ETci refers to the ET of the initial time period, i.e., from pre-irrigation to the date of the first SWC measurement. Drainage below the root zone was assumed to be negligible (Couto, 1978; Resende, 1979). The initial ETci was estimated by assuming that the ETc measured in a 6.1 m diameter weighing lysimeter planted to dry beans in 1976 and 1977 in a field nearby by W. O. Pruitt was equivalent to the ETci of all treatments in the CO76, CO77, and RE77 experiments. In RE78, the ratio of lysimeter ETci to Epan was calculated for 1977 and used to multiply the Epan of 1978 to estimate the ETci of RE78. The measured ETc values, estimated as described above (eq. 1), were compared against the E+T values simulated with AquaCrop in the different treatments.

Crop observations varied in intensity and included measurements of ground cover, leaf area index (LAI), dry matter accumulation, and partitioning into leaves, stems, and pods, taken at intervals that varied among experiments. The CO77 experiment was intensively monitored throughout the season, while CO76 had much fewer observations. The RE experiments were monitored with about the same level of detail in both years. Substantial additional work on plant-water relationships in the different stressed treatments was conducted but is not used in this work. At harvest, total aboveground biomass and seed yield were measured in representative areas inside the experimental plots. In CO76, yield was determined by harvesting 27 m2 per replicate plot, whereas 30 m2 were harvested in CO77. In the RE experiments, two rows, each 10 m (15.2 m2) long, were harvested per individual plot. Further details are provided by Couto (1978) and Resende (1979).

Model Calibration and Validation

Calibration was performed with the four irrigation treatments of the CO76 experiment. The procedure recommended by Hsiao et al. (2012) starts by first matching the performance of the canopy ground cover (CC) evolution and then comparing the simulated versus observed biomass (B) and yield (Y). The CO76 experiment did not report CC data; thus, we focused on comparing B and Y. Calibration and validation were performed with a new version of AquaCrop (v.6.0) about to be publicly released. AquaCrop calculates crop yield in four steps operating on a daily basis: (1) calculation of CC, (2) calculation of transpiration (T) proportional to CC, (3) conversion of T into biomass (B) through a normalized water productivity (WP) factor, and (4) calculation of yield (Y) as the product of B and harvest index (HI). Water stress affects the results by reducing the increments in CC, inducing stomatal closure and early canopy senescence, and reducing HI.

Considering the four steps, a first set of parameters was chosen to match the results of the CO76 experiment based on the general knowledge of the crop. This initial set of parameters was repeatedly adjusted by comparing the simulation results with the observed B and Y data until a satisfactory set of values (table 3) was obtained that matched the CO76 results as closely as possible.

Couto (1978) reported that emergence was observed at five days after planting (DAP) and flowering started between 40 and 45 DAP, while maximum CC was achieved around 57 DAP. This information was used for parameterizing the model in calendar time mode; subsequently, the model was switched to growing degree days (GDD) mode.

AquaCrop uses CC as a canopy parameter instead of LAI, which is often used in crop physiology and in other simulation models to characterize canopy size. From the reported data in the two dissertations on CC (ground cover measured with a tape) and LAI, the following empirical relationship related CC (%) to LAI for dry beans:

CC = -6.1168(LAI)2 + 49.325(LAI) + 5.0367 (2)

The only consistent difference found between the two cultivars was in their harvest indices. Based on the data reported by Couto (1978) and Resende (1979), the maximum HI values were set at 40% and 44% for the light red kidney and dark red kidney cultivars, respectively.

Table 3. Calibrated parameters of the dry bean data file in AquaCrop.
DescriptionValue
Temperature
Base temperature9°C
Cut-off temperature30°C
Canopy development
Canopy cover per seedling at 90% emergence (CCo)10 cm2 plant-1
Canopy growth coefficient (CGC)11.8% d-1
Maximum canopy cover (CCx)99%
Crop coefficient for transpiration1.05
Canopy decline coefficient (CDC) at senescence0.881% GDD-1
GDD from DAP to emergence[a]59 GDD
GDD from DAP to maximum canopy752 GDD
GDD from DAP to senescence903 GDD
GDD from DAP to maturity1298 GDD
Flowering
Duration of flowering233 GDD
GDD from DAP to flowering556 GDD
Length building up harvest index (HI)668 GDD
Root development
Maximum rooting depth1.7 m
GDD from DAP to maximum rooting depth888 GDD
Water stress response
Canopy expansion p(upper)0.15% TAW[b]
Canopy expansion p(lower)0.65% TAW
Canopy expansion shape factor2.5
Stomatal closure p(upper)0.6% TAW
Stomatal closure shape factor2.5
Early canopy senescence p(upper)0.7% TAW
Early canopy senescence shape factor2.5
Maximum positive effect on HI10%
Before flowering (+)Small
During flowering (-)Moderate
During yield formation (+)None
During yield formation (-)Very strong
Production
Reference harvest index (HI)40%
Normalized water productivity (WP*)15 g m-2
Adjustment for yield formation90%

    [a] GDD = growing degree days; DAP = day after planting.

    [b] TAW = total available soil water (between field capacity and permanent wilting point) in the root zone.

AquaCrop Inputs and User-Specific Parameters

AquaCrop needs a set of input files to describe the soil-atmosphere environment in which the crop develops, as well as information on out-of-season field practices. The input data files are for climate, soil, crop, irrigation, management, and initial SWC (Raes et al., 2009). All simulations started at the date of pre-irrigation and ended at maturity. The first SWC measurement reported in each experimental treatment took place two or three weeks after emergence. To determine the initial SWC on the pre-irrigation day for the simulations, AquaCrop was used to calculate the cumulative ET for the period that spanned the pre-irrigation date up to the day of SWC measurement. This amount was added to the measured SWC profile to set the initial SWC for the simulations in such a way that the simulated SWC closely matched the first SWC measurement.

Figure 2. Simulated versus observed values of (a) seed yield and (b) biomass at harvest for the CO76 experiment used for model calibration.

Data Analysis

To evaluate AquaCrop performance, a regression analysis was carried out to compare the observed and simulated values of Y, B, HI, and seasonal ETc, and the slope, intercept, and coefficient of determination (r2) were determined. Two statistical measures of model performance were calculated: the root mean square error (RMSE, eq. 3) and the index of agreement (d) of Willmott (1982) (eq. 4):

(3)

(4)

where Si and Mi are the simulated and measured values respectively, and n is the number of observations. The model fit improves as RMSE approaches zero and d approaches unity.

Results

Figure 2 presents the Y and B experimental results against the simulated results for CO76, the experiment that was used for calibration of the model. There was generally good fit, although the simulated extreme values (full irrigation and dryland) better fit the measured observations than the intermediate irrigation treatments (fig. 2). The calibrated values for the different parameters are presented in table 3 and were used in the validation exercises described below.

Validation of AquaCrop

The second-year experiment of Couto (1978), i.e., CO77, used the same irrigation treatments as in the previous year except that the Symp treatment was replaced with the Flow treatment, but CO77 reported a wealth of information on different plant parameters that was collected at frequent intervals during the growing season. Figure 3 presents a comparison between measured and simulated canopy cover (derived from LAI measurements; Couto, 1978) for the four irrigation treatments. The simulated patterns closely matched both the maximum observed CC values and the measurements throughout the season, although there was a tendency of the model to predict a slightly faster early canopy development than what was measured (fig. 3).

The line source experiments of Resende (1979) did not have many plant-related measurements during the season, as the focus was on the comparison of two irrigation frequencies. Nevertheless, in 1978, there were some observations of canopy cover and LAI, although only two replications were measured. Figure 4 presents a comparison of the simulated canopy cover with all the observed values reported by Resende (1979) for the RE78 experiment. While the maximum observed CC values were matched by the simulations, it appears that the observations in all four treatments showed a slower canopy development rate than what was simulated (fig. 4).

Biomass Production

Figure 5 depicts the comparison between simulated and measured values of biomass production at various times during the CO77 season. AquaCrop simulated well the accumulation of biomass in the FI and Flow treatments, which had better water supply than the Pod and Dry treatments, where the model overpredicted B accumulation, particularly in the Pod treatment (fig. 5).

Soil Water Content and Evapotranspiration

The total amount of soil water depletion from the profile was well simulated by AquaCrop, as evidenced in figures 6a and 6b for data from the CO76 and CO77 Dry experiments. However, the model did not simulate well the depth of water extraction by plant roots (fig. 6c). The experimental evi-

dence indicates that there was more extraction at deeper depths in the Dry treatment than the model simulated. Thus, even though the average SWC throughout the profile was similar in the simulated and observed soil profiles, the model extracted more water from the upper soil layers and less from the deeper layers than was observed (fig. 6c).

Figure 3. Observed and simulated seasonal course of canopy cover (CC, %) for the FI, Flow, Pod, and Dry irrigation treatments of the CO77 experiment used for model validation.
Figure 4. Observed and simulated seasonal course of canopy cover (CC) for normal frequency (NF) and high frequency (HI) irrigation observed at 100% (FI) and 17% (E) irrigation treatments of the RE78 experiment used for model validation.

Figure 7 shows a comparison of simulated and measured seasonal ETc for all the experiments. There is excellent agreement between the simulated and measured ETc for the water deficit treatments. However, as the water supply and ETc increased, measured ETc exceeded simulated ETc in all cases where treatments received the highest irrigation amounts (fig. 7).

The agricultural engineer W. O. Pruitt (Department of Water Science and Engineering, University of California, Davis), who was in charge of the lysimeter facility at UC Davis at that time, planted dry beans in a weighing lysimeter within days of the 1977 plantings by Couto (1978). The daily lysimeter ETc records of Pruitt are reported in an addendum by Couto (1978) and were used to test the validity of AquaCrop to simulate seasonal ETc. Table 4 presents the lysimeter measured ETc, which was 489 mm, while the simulated ETc for the FI treatment was 443 mm. To test the hypothesis that the ET differences were due to differences in E, we identified the irrigation dates in the lysimeter from the daily ETc peaks and thus simulated the lysimeter growth and ETc with AquaCrop. The simulated ETc of 501 mm is only 2.5% higher than the lysimeter measured ETc (table 4). AquaCrop has a routine to calculate the net irrigation requirements (NIR) under high frequency irrigation that yielded an ETc of 566 mm and had the highest simulated E of the three cases (table 4).

Biomass and Yield

All the available B and Y data collected in the CO77, RE77, and RE78 experiments (a total of five experiments, as each of the RE experiments had two line-source experiments) were used for the final validation of AquaCrop performance after calibration. The results are shown in figure 8 with 14 data points for B and 24 data points for Y, more than for B, as RE77 did not report B information at harvest. The Y predictions in the range of 1 to 3.5 t ha-1 are very good, as shown in table 5, where the pertinent statistics for goodness-of-fit are presented. Only HI had somewhat less goodness-of-fit due to one value of the simulated HI being less sensitive than the observed value to the most severe water stress treatment.

The fits were very good in general, with r2 = 0.85, except for ETc, where the relationship did not appear linear (fig. 7), and for HI, where there was a very small range of values. The RMSE values were small, always representing less than 15% of the observed mean value. For Y, the RMSE was 0.28 and 0.16 t ha-1 for the calibration and validation data, respectively, representing 15% and 6% of the observed mean values. Willmott’s d statistic was close to unity for all the variables except HI, which had a lower value.

Discussion

Calibration of the AquaCrop model for dry beans was performed using data from one field experiment (CO76) that had four treatments, from fully irrigated to dryland. During the calibration process, a set of conservative parameters was produced, as reported in table 3. Using these parameters and the pertinent climate, soil, and irrigation data, AquaCrop accurately simulated the SWC (fig. 6), ETc (fig. 7), as well as the final biomass and seed yield. The parameters in table 3 were used in a more extensive validation test in which five experiments were used. The predictions of yield and biomass for a wide range of irrigation treatments were very good in all cases (fig. 8), even though two different irrigation meth-ods and large differences in irrigation frequency were used. We attribute the greater dispersion in Y predictions in RE77 (fig. 8) to uncertainty in defining the initial SWC in those two experiments, as Resende (1979) only reported the initial SWC profiles of two extreme treatments (100% and 17% of applied water) that were different from each other. The high sensitivity of AquaCrop to the initial SWC conditions could explain why the yield predictions did not match the measured values in RE77. Table 5 also indicates that HI predictions were not as good in the case of the severely stressed treatments. This was probably due to the difficulty in determining the onset of senescence in the dry treatment for simulation.

Figure 6. Soil water content (SWC) integrated from 0.3 to 1.8 m, measured over the season (circles) against simulated values (solid lines) in the Dry treatments of the (a) CO76 and (b) CO77 experiments, and (c) observed and simulated SWC profiles early and late in the season for the Dry treatment of CO77.

There was a general tendency of AquaCrop to predict a slightly faster early canopy development than was observed (figs. 3 and 4). This may have been due to CC being more sensitive to water deficits than was simulated, as the fit was better in the well-watered treatments. Nevertheless, the CC expansion stress parameters had reasonable values as compared to other crops (Steduto et al., 2012). There were also differences in the observed versus simulated CC decline that could be attributed to the difficulties in determining the start of senescence, both in the field and in the model. However, the differences in CC did not impact much on the simulation of yield. For instance, in the case of treatments NF-E and HF-E in figure 4, where discrepancies between measured and simulated CC are clear, small differences between observed and simulated yields were obtained (2.1 vs. 1.9 t ha-1 for NF-E, and 1.7 vs. 1.6 t ha-1 for HF-E). Heng et al. (2009) reported similar behavior in their calibration of irrigated and water-deficient maize.

The model predicted very well the seasonal time course of SWC in CO76 and CO77 (fig. 6), although the model slightly overestimated SWC in CO76. By contrast, the changes in SWC with depth were not well simulated by AquaCrop, as the model predicted more water extraction from the upper layers and less from the deeper layers than was observed in the Dry treatment of CO77 (fig. 6c). A possible cause is the preference for extraction from the upper layers built into the model, and the unusually low mechanical resistance of the subsoil at the university farm, where water extraction down to 3 m has been documented for dryland maize and sorghum (Hsiao et al., 1976). In the bean experiments, it is possible that the rate of root system expansion exceeded the root growth patterns in AquaCrop, particularly in the dry treatment. More refined root growth and soil water extraction models are needed to simulate SW depletion patterns in dryland situations.

Figure 8. Simulated versus observed values of (a) biomass and (b) seed yield at harvest for the CO77, RE77, and RE78 experiments used for model validation.
Figure 7. Simulated versus observed values of dry bean evapotranspiration (ETc) for the CO76 experiment used for calibration, and for the CO77, RE77, and RE78 experiments used for model validation.

Despite the differences between observed and simulated soil water extraction, the seasonal ETc predictions were good (fig. 7), indicating that the overall computation of E and T by the model was accurate for a range of ETc values. Given that Couto (1978) reported ETc plus percolation, drainage losses may have increased as irrigation increased, as indicated by the curvature of the data in figure 7 in which the deviation from the 1:1 increased for the wettest treatments. If we assume that the simulated ETc values are correct, the model could be used to estimate the drainage losses in every treatment. The fact that the weighing lysimeter provided an independent, accurate measure of ETc in 1977 (table 4) gives us an opportunity to test the validity of ET calculations by AquaCrop. The simulated ETc of 501 mm compares very well with the measured ETc of 489 mm. The simulated ETc of the FI treatment was less (443 mm), due to differences in E caused by fewer irrigation applications, as shown by the differences in the E component simulated by AquaCrop (table 4).

Once the model has been validated, it is possible to use it for the simulation of some features that were not measured in the original experiments. We simulated the performance of the D treatment (35% of applied water) of NF and HF in RE77, where only the yield and the estimated ETc values were reported by Resende (1979). Table 6 compares the measured and simulated values of Y and ET, as well as the simulated values of B and HI, which were not measured. The low irrigation frequency of NF had much higher measured and simulated yields than HF, presumably because the direct E losses must have been much higher, given the high frequency of irrigation. Figure 9 shows the seasonal course of simulated E, T, CC, and B for NF and HF, showing that there was greater E with HF, and quantifies the irrigation differences to explain the differences reported in table 6.

The hypothesis that high frequency irrigation would enhance plant growth and yield as compared to a normal irri-gation frequency, a popular hypothesis promoted by the recent development of drip irrigation at the time the research was conducted (Rawlins, 1973; Rawlins and Raats, 1975), was not confirmed under the environmental conditions of the experiments, and the model now provides evidence of the magnitude of the enhanced E losses due to HF irrigation, a limitation that was magnified in treatments that did not meet the crop water requirements, such as the one in figure 9. The large magnitude of E due to the use of sprinkler irrigation would decrease substantially if other irrigation methods, such as drip, were used.

Table 5. Statistics for the comparisons between observed and simulated values of seed yield, final biomass, crop evapotranspiration (ETc), and harvest index (HI) for the calibration and validation of the AquaCrop model. Slope, intercept, and r2 are for the linear regression of observed against simulated values.
VariableNo. of Treatments
(n)
MeanRMSESlopeInterceptr2Willmott’s
d
ObservedSimulated
CalibrationYield (t ha-1)41.841.700.280.8060.220.9400.969
Biomass (t ha-1)44.984.400.700.9330.250.9580.966
HI435.437.64.00.40423.320.8480.741
ValidationYield (t ha-1)242.642.600.160.8870.250.8930.978
Biomass (t ha-1)146.136.540.610.7791.770.9370.959
HI1443.241.13.590.7508.680.2040.448
ETc1442438940.00.643116.900.8270.930
Table 6. Comparisons of observed and simulated yield (Y), biomass (B), harvest index (HI), evapotranspiration (ET), transpiration (T), and evaporation (E) for a normal treatment (NF-D) and a high frequency treatment (HF-D) in the RE77 line source experiments when both treatments received 35% of the maximum applied water.
YBHIETTE
NF-35%
Observed2.8--377--
Simulated2.15.538347237110
HF-35%YBHIETTE
Observed0.99--318--
Simulated1.032.738321120201
Figure 9. Time course of simulated (a) evaporation, (b) transpiration), (c) canopy cover, and (d) biomass in the NF (solid line) and HF (dashed line) line source experiments (RE77) of a deficit irrigation treatment that received 35% of the maximum applied water in both cases.

Given that we have used data only from one location, there is a need to test the parameters in table 3 in areas of diverse climates and soils where dry beans are grown. As dry beans are sensitive to salinity and respond strongly to N application (Sameni et al., 1980; Saberali et al., 2016), it would be interesting to validate AquaCrop with data sets from field experiments that capture the response of dry beans to different N and salinity levels.

Conclusion

Experiments performed about 40 years ago in Davis, Cal-ifornia, were used to calibrate and validate AquaCrop for dry beans. Calibration was carried out with the results of one experiment, and validation with data from five experiments differing in irrigation depths and frequency gave very good seed yield predictions within a range spanning from <1 to ~3.5 t ha-1. Seasonal ET was accurately simulated by AquaCrop, as verified with independent data from the UC Davis weighing lysimeter facility. However, simulation of the dynamics of soil extraction did not match the measured soil water profiles in the dryland treatment, suggesting that the soil water extraction module of AquaCrop would benefit from more detailed treatment of root growth and soil water extraction. Given the wide range of varieties, management practices, and climates where dry beans are grown, it would be advisable to locally validate AquaCrop if accurate yield predictions are sought.

Acknowledgements

M. Espadafor acknowledges the support of the EC program FACCE-JPI-SustainFARM, and E. Fereres thanks the Junta de Andalucía, Spain (P12-AGR2521). L. Couto and M. Resende deeply thank their major professor D. W. Henderson, and the Government of Brazil for funding their doctoral studies.

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