Performance of SMAC model on crop evapotranspiration estimation

Many simulation models found in the literature integrates data on climate and crop characteristics to provide great information on the season for different crops. The objectives of this study were: a) to measure soil water balance components of a wheat crop to determine its evapotranspiration (ETc) and crop coefficients (Kc) during the growing season; b) to use experimental data to evaluate the performance of SMA-C in estimating evapotranspiration for a wheat in Paraná State, Brazil; and c) to make adjustments to improve model estimates. Two weighing lysimeters cultivated with a wheat crop were used to measure soil water storage and ETc during the growing season of a wheat crop. Reference evapotranspiration (ETo) was determined by FAO 56 method using data from a local weather station. Wheat crop coefficients were calculated by the ratio ETc/ETo, were 0.7, 1.5 and 0.6, for initial, mid and late season, respectively. The comparison of SMA-C simulations with the observed data showed inaccuracies in estimation of soil water storage due to model underestimation for ETc. Estimates were improved by adjusting the model to consider Kc measured in the field.


INTRODUCTION
The economic viability of an agricultural business is associated with high quality and quantity of data collection during all seasons of a crop production.Utilizing information such as local climate variable and crop characteristics is very important to improve the decisionmaking by farmers.
Many simulation models found in the literature integrates data on climate and crop characteristics to provide great information during the season for different crops.Examples such as DSSAT (Jones et al., 2003), APSIM (Holzworth et al., 2014), AquaCrop (Steduto et al., 2009), CERES (Ritchie et al., 1998), STICS (Brisson et al., 2003), VegSyst (Giménez et al., 2013) and CropSyst (Stöckle et al., 2003) use mainly data on climate and crop characteristics to estimate crop development in different conditions, with the aim of improving decisionmaking by the user.In Brazil, MCID (Borges et al., 2008) provides data to help develop irrigation and drainage *Corresponding author.E-mail: rogeriofaria@fcav.unesp.br.
Author(s) agree that this article remain permanently open access under the terms of the Creative Commons Attribution License 4.0 International License projects.The Agroclimatic Monitoring System (SMA-C) (Caramori and Faria, 2002) uses meteorological data from weather station across Paraná State, crop development and soil water characteristics to provide input information and evaluate the crop water demand.
Despite the fact that many models have the ability to provide good information on crop water demand during the season, it is important to verify their reliability.Thus, the test of models such as SMA-C is needed by comparing simulation with measured data.Since crop water balance is the main component in SMA-C, comparing crop evapotranspiration (ET c ) measured in the field with estimated ET c is the right approach to test the model performance.
ET c is a biophysical process to transfer liquid water to vapor through soil evaporation and plant leaf transpiration (Allen et al., 1998).It represents the crop consumptive use in a cultivated area.Besides ET c , the reference evapotranspiration (ET o ) is a meteorological variable defined as the water demand of a reference surface (grass or alfalfa), which is used in many studies worldwide (Allen, 1998).
Although there are several methods to determine ETo, the standardized Penman-Monteith by FAO (Allen et al., 1998) is the most used so far.This method uses as input solar radiation, air temperature, wind speed and relative humidity.
In the past, it was difficult to measure ET c in the field because of complex and expensive required equipment.Nowadays, with the advance of technology, it is possible to determine ET c using different methodologies with low cost and easy maintenance equipment.The use of a high precision weighing lysimeter is one of the most suitable method to determine ET c (Howell et al., 1985;Faria et al., 2006;Jia et al., 2006;Payero and Irmak, 2008;Mariano et al., 2015).
The objectives of this study were to: a) measure soil water balance components of a wheat crop to determine its evapotranspiration and crop coefficients during the growing season; b) use experimental data to evaluate the performance of SMA-C in estimating evapotranspiration for a wheat in Paraná State, Brazil; and c) make adjustments to improve model estimates.

MATERIALS AND METHODS
This study was conducted in an experimental area of Instituto Agronômico do Paraná (IAPAR), in Londrina, Paraná State, Brazil (23° 18′ S and 51° 9′ W, 585 m).The soil is classified as a Red Latosol and the climate is subtropical humid (Cfa), acording to Köppen-Geiger climate classification (Kottek el al., 2006), characterized by humid and hot summers and mild winter, with mean annual temperature of 21.5°C and annual precipitation of 1584 mm (IAPAR, 1994).
Wheat cultivar IPR-130 (IAPAR, 2016) was sown in two weighing lysimeters and also in a buffer area of about 0.5 ha, in May 2 nd , 2009, with 0.17 m spacing between rows.The experimental area was divided into irrigated (T1) and rainfed (T2) treatments.Figure 1 shows the weather station, the buffer area and the two treatments, one with lysimeter installed in the irrigated area and the other in the rainfed area.Figure 2 shows the cross section of the lysimeter system, with internal and external tanks, concrete pillars, steel frames and load cells.The lysimeter tank was made of fiber glass in a square format of 0.95 x 0.95 m and 1.3 m depth.An external fiber glass tank of 1 x 1 m surface and 1.5 m depth was installed to isolate the smaller lysimeter tank from the surrounding soil.Four load cells were placed between the concrete pillar and the steel frame.
Lysimeter mass was measured every 3 s by four load cells Model-I, ALFA Instruments (ALFA, 2016).The electric signals measured by each load cell were averaged every 10 min (200 readings) and then storage in a datalogger model CR10x (Campbel Scientific) was powered by a 12 V battery.The measured data by each load cell was sent to a union box through a coaxial cable and then to the datalogger.The data, in mV, were input in the calibration equation to calculate mass, in kg, using the procedure described by Faria et al. (2006) and Mariano et al. (2015).Soil water storage, in mm equivalent, was then calculated from lysimeter mass, in kg, by dividing by mass by lysimeter area (0.9 m 2 ).
Irrigation management of treatment T1 was preconized to maintain soil water storage higher than 70% of the soil available water, by application of water to replace the soil at field capacity twice a week.Soil available water, as given by difference between field capacity and permanent wilting point for the experimental area, was determined by Faria and Caramori (1986) as 10% in a volumetric basis.Thus, the soil available water in 1.3 m depth in the lysimeter profile varied from zero, at permanent wilting point, to 130 mm, at field capacity.To represent graphically lysimeter mass variation in the range of soil available water (Figure 3), the lysimeter mass (converted to mm equivalent) at field capacity was assigned to 130 mm and the remaining measurements were calculated proportionally.The lysimeter was considered to be at field capacity at 4 days of drainage after occurrence of a precipitation sufficient to reach soil saturation (Faria and Caramori, 1986).Crop evapotranspiration and soil water storage in each lysimeter were determined according to the following equation: (1) where ETc is crop evapotranspiration, P is precipitation, I is (2) Where Kc is crop coefficient (dimensionless), ETc is crop evapotranspiration and ETo is grass reference evapotranspiration, both in mm d -1 .Daily ETo was computed by CLIMA software (Faria et al., 2002), using the standardized Penman-Monteith equation (Allen et al., 1998) with daily data from an automatic weather station installed in the IAPAR Experimental Station, at 150 m from the lysimeter (Figure 1).
SMA-C uses a soil moisture module described in detail by Faria and Madramootoo (1996).The inputs are plant characteristics such as rooting depth and leaf area index (LAI), soil water retention data and meteorological data to calculate soil water balance components of a specific crop.In this study, wheat LAI data was determined five times during the experimental period by a leaf area integrator (LI-COR, 1996), and soil water retention characteristics for the experimental area were taken from data collected by Faria and Madramootoo (1996).Wheat phenological stages were evaluated every week to characterize crop development.Daily simulated ETc and water storage data were compared with measured data, using linear regression and the t-test (p = 1%).

RESULTS AND DISCUSSION
This research reported on two treatments of water management, irrigated and rainfed.However, due to the high precipitation during the growing season (Figure 3), it was not necessary to irrigate and, thus, soil water storage was similar in both treatments.Instead of the two treatments, the measurements of the two lysimeters were averaged to perform the test of the model.The results show that precipitation was sufficient to supply crop requirements and soil water storage was close to the field capacity during the whole growing season (Figure 3).
Daily ET c varied from 1 to 5 mm d -1 during the growing season.It was higher during milk stage and lower from emergence to the end of flowering and during ripening (Figure 4a).In addition, ET c was low during some periods (45, 70 DAP and 100 DAP) due to decrease in ET o , caused by low temperature, as a result of rainy periods.Average seasonal ETo was equal to 2.4 mm d -1 , which was about 10 and 20% less than seasonal ET c .K c  increased from emergence to reach higher values during the mid-crop stages, and then decreased during the later stages (Figure 4b).Variations in K c were mostly related to LAI variation during the growing season (Figure 5).LAI was higher than 5 during flowering (60 DAP).At that time, transpiration was the main component of ET c because of full soil cover by the canopy.After the reproductive period, the plant initiated the senesce, decreasing the LAI and also ETc.
The comparison between simulated and observed soil water storage showed that model followed the same trend with the observed data, decreasing when ET c was high and increasing during precipitation events (Figure 6).Simulations agreed with the observed data from emergence to 55 DAP.After that, simulated soil water storage was always higher than observed data.The analysis by t-test showed significant difference (p = 1%) between the two data sets.Therefore, SMA-C overestimates soil water retention, indicating that the model needs corrections in its calculation method.
Simulated ET c overestimated observed data, as given by statistical difference at 1% probability by t-test using data for the whole growing season (Figure 7).While observed ET c was 270 mm, the model simulated 220 mm during the growing season, was an underestimation of 18.5%.The difference between model estimates and field data was more evident for the period from 60 to 128 DAP.This finding confirms the need to correct the method  of calculating ET c in SMA-C.In that model, K c is equal to 1 by assuming ET c equal to ET o in conditions of no water stress.However, this was not correct because the values of K c estimated using field data measured in this study varied according to crop development, as given in Figure 4b.
In order to improve SMA-C estimates, the model was modified to consider K c measured in the field.That coefficient was used into the model to multiply ET o and then to calculate ET c , following the approach described by Allen et al. (1998).Therefore, the crop season was divided into three phases in which K c was assumed to be 0.7, 1.5 and 0.6 for initial, mid and late seasons, respectively.The results in Figure 8 show that simulations are in close agreement with observed data.
In addition, to demonstrate the improvement in model estimates, a regression analysis was performed on daily and accumulated ET c estimated by the original and adjusted model against observed data (Figure 9).The scatter of data around 1:1 curve decreased considerably for both, daily and accumulated ET c data using the adjusted model.The linear regression for simulated vs. observed data gave a slope coefficient significantly different from 1 for the original SMA-C and not different t 2 (p = 0.01)

Figure 1 .
Figure 1.Field layout of the experimental area.

Figure 2 .
Figure 2. Cross section view of a lysimeter and its components.

Figure 3 .
Figure 3. Soil water storage and precipitation during the growing season.FC is field capacity and PWP is permanent wilting point.

Figure 5 .
Figure 5. Leaf area index during the growing season.

Figure 6 .
Figure 6.Precipitation and observed and simulated soil water storage during the growing season.

Figure 7 .
Figure 7. Observed and simulated accumulated crop evapotranspiration for the growing season.

Figure 8 .
Figure 8. Accumulated crop evapotranspiration for the growing season, observed and simulated by adjusted SMA-C.

Figure 9 .
Figure 9. Regression of observed and simulated daily (a) and accumulated (b) crop evapotranspiration (ETc) for the original and adjusted SMA-C.