Evapotranspiration Partition and Crop Coefficients of Tifton 85 Bermudagrass as Affected by the Frequency of Cuttings. Application of the FAO56 Dual K c Model

: This study aims to model the impacts of the frequency of cuttings of Tifton 85 bermudagrass on the dynamics of evapotranspiration (ET c ) and to derive crop coefﬁcients appropriate for grass water management. Two seasons of experimentation were used with four different cutting treatments which provided ﬁeld data for calibration and validation of the soil


Introduction
The landscape of southern Brazil is characterized by the Pampa biome, which occupies 63% of the State of Rio Grande do Sul. Grassland is the dominant vegetation and livestock production is a main economic activity in the area, but large areas have been converted into cropland, mainly for soybean production, thus suppressing the native grass vegetation [1]. Therefore, the sustainability of this biome for livestock production requires the planting of new and highly productive grasses such as the Tifton 85 bermudagrass [2,3], recently introduced in the region. Assessing grass evapotranspiration and water requirements as influenced by the frequency of cuttings is required to support an upgraded management of those grasslands. An innovative approach used is to relate the frequency of cuttings with the density coefficient (K d ) and then estimate the basal crop coefficient from K d following the Allen and Pereira approach [4].
Studies on evapotranspiration (ET) of grasslands are numerous. Research has commonly been devoted to assessing the dynamics and abiotic driving factors of ET, mainly relative to climate influences on the processes of energy partition into latent and sensible heat. Such studies often use eddy covariance and/or Bowen ratio energy balance (BREB) observations, data which are commonly used in analysis performed with the Penman-Monteith (PM) combination equation [5] and/or the Priestley-Taylor (PT) equation [6], thus using the canopy resistance or the PT parameter α as behavioral indicators [7][8][9]. As an alternative to those measurement techniques, scintillometer measurements [10] and satellite images [11][12][13] were also used. Adopting similar research approaches, other studies compared the ET of grasslands with ET of forests or shrublands [14][15][16]. In addition to the available energy for evaporation, soil water availability and crop ground cover or the leaf area index (LAI) were often identified as main driving factors influencing grass ET [14][15][16][17].
Studies such as those referred to above are likely of great importance for understanding the variability of grass ET when focusing on the Pampa biome but different, operational research approaches are required when aiming at knowing grassland water requirements and/or grassland water management issues. Related operational studies are also numerous and refer to various climates, grass species and diverse herbage uses for hay or for grazing with different frequency of cuttings. However, such ET studies are lacking in southern Brazil and for Tifton 85 bermudagrass. ET research aiming at improved farm water management generally uses the grass reference ET (ET o ) proposed in the Food and Agriculture Organization guidelines for computing crop water requirements (FAO56) [17]; nevertheless, recent studies [3,18] relative to irrigated bermudagrass yields used the climatic potential ET equation of Thornthwaite [19], developed in 1948.
The reference ET o was defined after parameterizing the PM combination equation [5] for a cool season grass, thus resulting that ET o is defined as the rate of evapotranspiration from a hypothetical reference crop with an assumed crop height h = 0.12 m, a fixed daily canopy resistance r s = 70 s m −1 , and an albedo of 0.23, closely resembling the evapotranspiration from an extensive surface of green grass of uniform height, actively growing, completely shading the ground and not short of water [17]. This definition is described by the daily PM-ET o equation [17], which represents the climatic demand of the atmosphere. Thus, following FAO56 [17], the ET o is to be used with a crop coefficient (K c ) when estimating or predicting the ET of a given surface, that is, the K c -ET o approach. K c is the ratio between the crop ET and ET o and varies with the crop surface characteristics and the crop growth stage, and is influenced by the climate and management. Single and dual K c may be used [17]. The dual K c consists of the sum K e + K cb of the soil evaporation coefficient (K e ) and the basal crop coefficient (K cb ), and thus with consideration of both processes included in evapotranspiration. The K c values are standard or potential when the crop is not stressed, while actual K c values (K c act or K cb act ) are often smaller than the standard K c or K cb when water, salt, disease or management stresses affect crop transpiration. These effects may be considered using a stress coefficient applied to K c or K cb . Tabulated values of standard K c and K cb are provided by Allen et al. [17] for a variety of crops, including grasses and pastures. The standard K c and K cb values are transferable to other sites considering adjustments for climate described by Allen et al. [17]. The time variation of the K c and K cb values are described by K c curves [17] that describe in a simplified way the dynamics of LAI and vegetation ET. The form of these curves varies from one crop to another; for grasses with cuttings, several successive K c curves should be considered, each representing the dynamics of ET during each crop growth cycle between cuttings [17].
The operational use of the ET o equation implies, therefore, the use of crop coefficients and the build-up of K c curves to describe the respective time variation. It could be observed that several papers reporting on the use of the grass reference ET o did not follow the concepts described above. A few authors directly compared ET obtained with eddy covariance, BREB, or a soil water balance with ET o but not searching for a K c value [20], or even assumed equality between grass ET and ET o [21]. Other authors just computed daily K c act values (often using different designations for that parameter) but did not search for a K c curve that would describe their seasonal variation [22,23], or just identified a mean seasonal K c act [24]. The lack of search for a K c curve led some authors to consider the K c -ET o approach as non-useful [25]. By contrast, Pronger et al. [26] did not clearly assume the concepts behind actual vs. potential K c and, in addition to K s , adopted a correction factor to ET o for highly stressed grass. This is theoretically not appropriate because it contradicts the concepts of reference ET, which depends solely upon the climate and not the crop under study, and of the K c act that has to be derived from the standard K c when adapting to the management and environmental conditions [17]. The approaches referred to above, like other research quoted before, may support an improved understanding of the dynamic behaviour of grass ET but are likely not appropriate for operational use in irrigation water management.
The FAO56 K c -ET o method [17] was first applied by Cancela et al. [27] to grass using the single K c act with successive four-stage curves relative to four cuttings using the ISAREG soil water balance model [28]. Single K c act four stage curves were defined for remote-sensed grazed grasslands [29,30]. By contrast, other authors preferred replacing the typical four stages curve by average monthly K c act values [31]. The FAO dual K c approach [32] was successfully used by Greenwood et al. [33], who reported on a large number of K cb act curves to represent numerous grass cuttings using the FAO56 spreadsheet [17]. The FAO dual K c approach was adopted by Wu et al. [34] to represent a natural groundwater dependent grassland, then using a seasonal four-growth stages K cb act curve using the SIMDualKc model [35]. Krauß et al. [36] also used the dual K c method to estimate the footprint of milk production but did not report about the K c curves used.
The dual K c approach has the advantage of partitioning ET into crop transpiration (T c ) and soil evaporation (E s ). Knowing T c and E s provides for a more detailed water balance and a better approach to understanding the functioning of the ecosystems. In addition, partitioning ET allows estimating T c and therefore better calculating yields [37] since it directly relates to biomass production. Moreover, good results were obtained with the soil water balance SIMDualKc model [35] for the partition of ET using the FAO dual Kc approach, namely when applied to crops that nearly fully cover the ground, such as wheat, barley and soybean [38][39][40] whose E s estimated values compared well with E s observations using microlysimeters. T c simulated also compared well with sap flow observations in tree crops [41,42], thus confirming the goodness of ET partitioning.
The application of various ET partition methods to grass is often reported, namely using the two source Shuttelworth and Wallace [43] model (SW). It is very precise when an appropriate parameterization is achieved, which is a quite demanding task that limits the operational use of SW in agricultural water management practice; various examples of the application of SW to grass are reported in the literature [44,45]. Other double source models were applied to grass, such as the one reported by Huang et al. [46], which is based upon the estimation of gross ecosystem productivity using CO 2 fluxes observed with the eddy covariance method, and that proposed by Wang and Yamanaka [47], which consists of a modification of the SW model. Empirical ET partitioning approaches include the use of time series of soil surface temperature [15], and the adoption of a radiation extinction coefficient (k rad ) combined with a ground cover index [20] or with LAI when using the PT equation [48]. These approaches using k rad are comparable with the FAO dual K c approach [17,32]. Partitioning ET fluxes using stable isotopes is another proved alternative [49,50].
The dual K c approach has been shown to be appropriate to partitioning grass ET, as reported above [33,34], and has shown to be less demanding in terms of parameterization and field and laboratory instrumentation than other ET partition methods. In addition, it is easily implemented using the referred SIMDualKc model, which has been extensively tested as reported above. Therefore, the objectives of this study consist of (a) assessing and partitioning evapotranspiration of Tyfton 85 bermudagrass in southern Brazil as influenced by the frequency of cuttings using the model SIMDualKc applied to two years of field data; and (b) deriving crop coefficient curves adapted to grass cuttings of various frequencies. Moreover, the study aims to contribute to the sustainability of grass uses in the Pampa biome, and to create the knowledge required to cope further with climate change in the region. The climate of the region, according to the Köppen climatic classification, is a "Cfa", that is, humid subtropical without a defined dry season and with hot summers [51]. The meteorological conditions during the experimentation are given in Figure 1 and were observed in an automatic weather station located at 300 m from the experimental area which is in the charge of the National Institute of Meteorology. The reference evapotranspiration (ET o ) was computed with the PM-ET o equation [17]. using the PT equation [48]. These approaches using krad are comparable with the FAO dual Kc approach [17,32]. Partitioning ET fluxes using stable isotopes is another proved alternative [49,50]. The dual Kc approach has been shown to be appropriate to partitioning grass ET, as reported above [33,34], and has shown to be less demanding in terms of parameterization and field and laboratory instrumentation than other ET partition methods. In addition, it is easily implemented using the referred SIMDualKc model, which has been extensively tested as reported above. Therefore, the objectives of this study consist of (a) assessing and partitioning evapotranspiration of Tyfton 85 bermudagrass in southern Brazil as influenced by the frequency of cuttings using the model SIMDualKc applied to two years of field data; and (b) deriving crop coefficient curves adapted to grass cuttings of various frequencies. Moreover, the study aims to contribute to the sustainability of grass uses in the Pampa biome, and to create the knowledge required to cope further with climate change in the region. The climate of the region, according to the Köppen climatic classification, is a "Cfa", that is, humid subtropical without a defined dry season and with hot summers [51]. The meteorological conditions during the experimentation are given in Figure 1 and were observed in an automatic weather station located at 300 m from the experimental area which is in the charge of the National Institute of Meteorology. The reference evapotranspiration (ETo) was computed with the PM-ETo equation [17].  The textural and hydraulic properties of the soil of the experimental site are given in Table 1. Disturbed and undisturbed soil samples were collected at the initiation of the experimentation. The particle size distribution was obtained using an ASTM 151H soil hydrometer (Chase Instruments Co., Swedesboro, NJ, USA). Soil water retention at matric potentials between −10 and −5000 cm were determined with a pressure plate apparatus (Soil Moisture Equipment Corp., S. Barbara, CA, USA) and at potentials of −5000 and −15,000 cm were determined with a WP4 dewpoint potentiometer (Decagon Devices, Pullman, WA, USA). The soil water content at field capacity (FC) and at wilting point (WP) were measured for the matric potentials at −10 kPa and −15,000 kPa, respectively.

Grass and Field Observations
Three treatments of grass cuttings were used in the current study and three replications were adopted; the area of each experimental unit was 16 m 2 . In agreement with information relative to cuttings of Tifton 85 [2,3], the stubble height (SH) of 0.15 m was adopted for all cuttings. The latter were executed with an electric lawnmower with adjusted cutting height, which provided for a precise SH. The cuttings were performed when the cumulative growing degree days (CGDD) attained 124, 248 and 372 • C after the start of each cutting cycle. The base and cut-off temperatures were 10 • C and 30 • C, respectively. The cuttings dates are given in Table 2. It can be observed that defining the intervals between cuttings for selected CGDD results in time intervals that are different within each treatment and among treatments, varying from a minimum near the summer solstice to a maximum by the winter solstice (Table 3).  The K c curves adopted for each cutting cycle considered only three growth stages: initial, from initiation after a cutting until rapid growth starts; rapid growth, from then on until growth slows down; and before cutting, from then on until a cutting is performed. Curves are described by three K c or K cb values corresponding to the three growth stages identified, respectively K cb ini , K cb gro and K cb cut . Cutting cycles were, therefore, described with the following observations: (a) The time duration (days) of the three phases of the cutting cycles: initial, rapid growth and before cutting, whose time durations are respectively t ini , t gro and t cut , with their sum equalling the time interval between cuttings, t int . Their values varied among treatments and with air temperature, that is with climate. (b) The grass height at the end of the periods referred to above, thus h ini , h gro and h cut in the day of cutting, with h ini = SH. Values varied among treatments but not within each treatment due to the great dependence of crop growth relative to temperature. (c) The fraction of ground cover at the same days referred for h, thus f c ini , f c gro and f c cut .
Alternatively, LAI could be observed by the same days. As for h, values of f c varied among treatments but very little within each treatment.
The canopy height was measured with a millimeter graduated ruler. The fraction of ground cover was observed visually using frames with an area of 0.625 m 2 . Photos taken vertically were used to count the percent of ground covered. Errors of observations of h and f c did not exceed 10%.
Average h and f c values are presented in Table 4. The effective root depth (Z r , m) was observed using nine soil samples taken at each 0.10 m layer, down to the depth of 0.6 m, which were washed, sieved and observed for the root material. Results have shown that 90% of the roots were above the 0.3 m depth and only a very small fraction was below the 0.5 m depth. Thus, in agreement with literature [9,13,14,46], Z r = 0.5 m was adopted for the simulations. Table 4. Average of observed canopy height (h, m) and fraction of ground cover (fc, dimensionless) relative to treatments with various intervals between cuttings defined by observed CGDD. All treatments used sprinkler irrigation to supplement rainfall and assure that the crop was not water stressed, so allowing for potential ET and crop coefficients to be determined. Full circle sprinklers Pingo ® (Fabrimar Ltda., Joinville, SC, Brazil), spaced 6 m and operating at the pressure of 180 kPa were used. The coefficient of uniformity averaged 82% and the applied net irrigation depths varied from 12-22 mm in 2015-2016 and from 7.5-12.5 mm in 2016-2017. Irrigations were performed whenever the soil moisture in the 0.50 m layer reached less than 85% of the FC. The soil water content (SWC, cm 3 cm −3 ) was daily monitored with Frequency Domain Reflectometry (FDR) sensors installed in the center of each unit in the 0.00-0.20 m and 0.20-0.50 m depth layers. The CS616 sensors were connected to a CR10X data logger with the AM16/32 channel relay multiplexer (all from Campbell Scientific, Logan, UT, USA). The FDR system was calibrated for soil water contents ranging from near the wilting point up to saturation.

The SIMDualKc Model
The soil water balance SIMDualKc model [35] uses a daily time step to compute the grass crop evapotranspiration (ET c ) using the dual crop coefficient approach [17,32]. This model has previously been applied to a variety of crops as referred to in the "Introduction", in particular to a Leymus chinensis (Trin.) Tzvel. grassland [34], however not submitted to cuttings.
The SIMDualKc model computes the daily soil water balance in the crop root zone as: where D r,i and D r,i−1 are the root zone depletion [mm] at the end of day i and i − 1, respectively, P i is precipitation, RO i is runoff, I i is net irrigation depth, CR i is capillary rise from the groundwater table, ET c,i is crop evapotranspiration, and DP i is deep percolation, all referring to day i and expressed in mm. In the present application, the water table is quire deep and CR is null. The soil water balance refers to a soil in which total available water (TAW, mm) is: In the current application, with Z r = 0.50 m, FC = 0.336 m 3 m −3 and WP = 0.088 m 3 m −3 , this results in TAW = 124 mm. The readily available soil water (RAW, mm) is the fraction of TAW that may be depleted without causing any water stress, and thus RAW = (1 − p) TAW. A constant value p = 0.55 was used for all cycles, thus resulting in RAW = 56 mm.
ET c act is computed as a function of the available soil water in the root zone (ASW, mm). If the depletion exceeds the depletion fraction for no stress (p), i.e., ASW < RAW, then the stress coefficient becomes K s < 1.0, otherwise K s = 1.0 [17]. Thus, in general, we have: where K e is the soil evaporation coefficient and K cb is the basal crop coefficient. As referred to before, K cb act = K s K cb . The actual daily grass transpiration is, therefore, T act = K cb act ET o and the soil evaporation is E s = K e ET o . K e are daily computed through a daily water balance of the soil evaporative layer, whose thickness is (m), when knowing the total and readily evaporable water, respectively TEW (mm) and REW (mm). Considering the two-stage evaporation process, the first is energy limiting and the corresponding evaporable amount is REW; the second stage is water limiting and evaporation is linearly decreasing until TEW is depleted [17,32,52]. The thickness Z e = 0.15 m was adopted for the evaporation layer as commonly occurs for medium to heavy textured soils. TEW and REW are optimized during the process of model calibration. The water balance of the evaporation layer, that considers the referred evaporative characteristics of the soil, takes into consideration the fraction f c of ground shaded by the crop, which determines the fraction of the soil that is both exposed to solar radiation and wetted by rain or irrigation, and from where most of the soil evaporation originates, as well as effects of mulching in reducing the energy available at the soil surface [35].
The deep percolation DP is computed by the model using the respective parametric function proposed by Liu et al. [53], which is a time decay function that relates the soil water storage near saturation after the occurrence of a heavy rain or irrigation with the draining time until FC is attained. The values of the parameters (a D , b D ) are optimized during model calibration. Runoff was estimated using the curve number approach following the USDA-ARS Hydrology Handbook [54].
The initial K cb ini , K cb gro and K cb cut were estimated from the f c and h values observed using the equation proposed by Allen and Pereira [4]: where K d is the density coefficient, K cb full is the estimated K cb during peak plant growth for conditions having nearly full ground cover (or LAI > 3), and K c min is the minimum basal K c for bare soil, with K cb min = 0.15 under typical agricultural conditions and for native vegetation when rainfall frequency is high. K d can be estimated as a function of measured or estimated leaf area index LAI: or as a function of the fraction of ground covered by vegetation, as in the present study, where f c eff is the effective fraction of ground covered or shaded by vegetation [0.01-1] near solar noon, ML is a multiplier on f c eff describing the effect of canopy density on shading and on maximum relative ET per fraction of ground shaded [1.5-2.0], and h is the mean height of the vegetation in m. For low and dense crops such as grass, it may be assumed that f c eff = f c . The ML multiplier on f c eff in Equation (6) imposes an upper limit on the relative magnitude of transpiration per unit of ground area as represented by f c eff and is expected to range from 1.5 to 2.0, depending on the canopy density and thickness [4]. The value for ML can be adjusted to fit the specific vegetation.
The input data required by the SIMDualKc model consist of: (i) daily meteorological data of rainfall (mm), ET o (mm), minimum relative humidity (RH min , %) and wind speed at 2 m height (u 2 , m s −1 ); (ii) the soil water content at FC and WP for all root zone soil layers; (iii) the soil water evaporation parameters Z e (m), TEW and REW (mm); (iv) the deep percolation parameters; (v) crop heights (h, m); (vi) the effective rooting depth Z r ; (vi) the fraction of ground cover f c ini , f c gro , and f c cut ; (vii) the water depletion fraction for no stress, p; (viii) the irrigation dates and net irrigation depths applied; (ix) the soil wetted fraction by irrigation (f w ); and (x) the runoff curve number (CN).
In this application, because the ground is covered by plant litter, the importance of which in Tifton 85 bermudagrass fields is well known [55], the effect of plant litter on E s was considered in modelling [35]. Litter, like organic mulches, reduces the energy available at the soil surface and, consequently, soil evaporation. The respective model inputs consisted of: the fraction of mulched soil of 1, low thickness of the mulch, and 3% reduction in E s for each 10% of soil surface covered. In former applications of SIMDualKc to soils with organic mulch or crop residuals [56,57] a larger reduction of E s was considered.
The standard K cb values should refer to the minimum relative humidity RH min = 45% and the average wind speed at 2 m height u 2 = 2 m s −1 [17]. They were obtained from the calibrated ones by adjusting them for climate using the climate adjustment equation [17] inversely: where the K cb are the standard values, K cb calib are those values obtained from calibration, u 2 and RH min are the average values observed during the calibration, and h are the observed crop heights. The current adjustment refers to K cb ini , K cb gro and K cb cut , as well as to K c .

Model Calibration and Validation and Goodness of Fitting Indicators
Model calibration and validation for the Tifton 85 bermudagrass were performed using independent data sets of the referred two years of observations. The calibration of the model was performed with data collected in the summer and autumn seasons of 2016. The calibration of SIMDualKc aimed at optimizing the basal crop coefficients (K cb ini , K cb gro and K cb cut ), which was performed independently for the three cutting treatments because respective growth characteristics are different, the soil evaporation parameters (TEW, REW), the deep percolation parameters (a D and b D ) and the runoff CN value. An iterative trial-and-error procedure was applied in order to minimize the deviations between the available soil water data observed and simulated by the model. The procedure described by Pereira et al. [39] was adopted. The trial and error was first applied to the K cb ini , K cb gro and K cb cut relative to the treatment of CGDD 248 • C, and then interactively applied to the K cb values, the soil evaporation TEW and REW, the deep percolation parameters and CN. Using the DP, soil evaporation and runoff parameters already calibrated for the treatment of CGDD 248 • C, which are common to all treatments, the trial and error procedure was in the following applied independently to the other cutting treatments for calibration of the respective K cb values. The model validation consisted in applying the calibrated K cb ini , K cb gro and K cb cut , TEW and REW, DP parameters and CN to the remaining observed data relative to the spring seasons of 2015 and 2016 and the summer and autumn seasons of 2017.
The initial parameter values were estimated as follows: (1) the K cb values were computed for each treatment with Equation (4) assuming K c min = 0.15, K cb full = 0.95, and with the density coefficient K d computed with Equation (6) using the observed data given in Table 4; (2) the depletion fraction for no stress p was estimated from the values tabulated in FAO56 [17]; (3) TEW was computed from the difference (FC-0.5 WP) relative to the top soil layer of depth Z e (0.15 m), and REW was estimated from the textural characteristics (Table 1) of that same layer [17,32]; (4) the DP parameters a D and b D were estimated from those proposed by Liu et al. [53] for moderately permeable soils; and (5) CN was obtained from tabulated values for grasses in moderately permeable soils [54].
A set of goodness of fit indicators were used to assess model fitting during calibration and to evaluate the results of validation. As analyzed previously in various SIMDualKc applications, these indicators [39,58,59] which should be as small as possible and has the same units of the variable under analysis. (iv) the normalized RMSE (NRMSE, %), ratio of RMSE to the mean value of the variable observations, which expresses the relative size of the estimation errors and which target is a small value, at least smaller than 10%.
(v) The average relative error (ARE, %), which express the relative size of estimated errors in alternative to NRMSE: (9) and which target is a value as small as possible, generally smaller than 10%. (vi) The percent bias of estimation, PBIAS (%), is an indicator that measures the average tendency of the simulated data to be larger or smaller than the correspondent observations and is given by: Its optimal value is 0.0; thus, values near 0.0 indicate that model simulation is accurate, while positive or negative values indicate under-or over-estimation bias. (vii) The modelling efficiency (EF, dimensionless), that indicates the relative magnitude of the variance of residuals of estimation compared to the measured data variance: the target value of which is 1.0 when the variance of residuals is negligible relative to the variance of observations; EF values close to 0 or negative indicate that the observations mean is as good or better predictor than the model. Therefore, achieving a positive EF is a must.

Model Calibration and Validation
The initial values of parameters used with the SIMDualKc model to simulate the three treatments of frequency of cuttings of Tifton 85 bermudagrass are presented in Table 5. The calibration of the SIMDualKc model through minimizing the differences between simulated and observed available soil water (Figure 2) enabled the calibrated parameters also listed in Table 5 to be obtained for the three cutting treatments considered. These parameters were later used for validation of the model for other observation periods, whose results are shown in Figure 3.
The goodness of fit indicators relative to the calibration and the validation are presented in Table 6. It can be observed that the regression coefficient b 0 is close to 1.0 for all sets of data used both in the calibration and validation for all treatments, thus indicating a trend for equality of simulated and observed values, thus no trend to over-or underestimation of the ASW. Consequently, the PBIAS are quite small, thus confirming no trends for over-or underestimation. The determination coefficients are above 0.80 for the calibration, indicating that there is a dispersion of pairs P i -O i around the 1:1 line, i.e., a fraction of less than 20% of cases cannot be explained by the model. An explanatory hypothesis is that the FDR sensors used, which were previously tested for conditions where wettings consisted of controlled irrigation applications and not intense rainfall events [56], have not been shown to be adequate to record quick changes in ASW when heavy rains occur. This can be observed in Figures 2 and 3 in cases when peak increases of ASW occurred. However, R 2 values are generally high and, in combination with high b 0 values, confirm the adequacy of model simulations. Errors of estimation are small (Table 6). On the one hand, the RMSE range from 4.2-5.2 mm at calibration and 5.0-7.2 mm at validation, corresponding to NRMSE in the range of 4.0-6.7% of observed ASW, as well as ARE also ranging from 3.2-5.2%, thus indicating good accuracy of model simulations. On the other hand, EF values were quite high for the calibration cases (0.76-0.86) and reasonably good for the validation simulations, which ranged from 0.42-0.79, therefore indicating Errors of estimation are small (Table 6). On the one hand, the RMSE range from 4.2-5.2 mm at calibration and 5.0-7.2 mm at validation, corresponding to NRMSE in the range of 4.0-6.7% of observed ASW, as well as ARE also ranging from 3.2-5.2%, thus indicating good accuracy of model simulations. On the other hand, EF values were quite high for the calibration cases (0.76-0.86) and reasonably good for the validation simulations, which ranged from 0.42-0.79, therefore indicating that the variances of the residuals of estimation were much smaller than the variance of observations. Errors of estimation are small (Table 6). On the one hand, the RMSE range from 4.2-5.2 mm at calibration and 5.0-7.2 mm at validation, corresponding to NRMSE in the range of 4.0-6.7% of observed ASW, as well as ARE also ranging from 3.2-5.2%, thus indicating good accuracy of model simulations. On the other hand, EF values were quite high for the calibration cases (0.76-0.86) and reasonably good for the validation simulations, which ranged from 0.42-0.79, therefore indicating that the variances of the residuals of estimation were much smaller than the variance of observations. Overall, the goodness of fit indicators point to the appropriateness of using SIMDualKc to simulate the soil water balance of Tifton 85 bermudagrass adopting the obtained calibrated parameters and, in particular, the adequacy of adopting a K cb curve consisting of successive individual cutting K cb lines designed with the respective K cb ini , K cb gro and K cb cut . Table 6. Goodness-of-fit indicators relative to both the calibration and validation of all treatments. The proximity of initial and calibrated K cb values result from the goodness of Equation (4), which computes K cb from the fraction of ground cover and crop height, as well as from K cb full . In this application h and f c were observed while values for K cb full were estimated from the K cb values tabulated in FAO56 [17]. These results demonstrate that the Allen and Pereira equation 4 [4] is highly valuable to estimate K cb from simple field observations. An alternative K cb curve with a non-variable K cb was also assessed for the treatment with CGDD of 124 • C, i.e., with highly frequent cuttings. Results for crop height and fraction of cover of this treatment (Table 4) indicate small variation of both h and f c for each cutting cycle, which do not imply quite distinctive K cb values. Assuming this single K cb sing = K cb gro (0.80), this results in goodness of fit indicators (Table 7) similar to those discussed above (Table 6). It may therefore be assumed that when h and f c of bermudagrass vary little, a simple solution with a single K cb value may be used. However, to better represent the dynamics of evapotranspiration and crop transpiration [17], the best solution is to use a 3-value K cb curve for each cutting cycle. Table 7. Goodness-of-fit indicators for the treatment relative to frequent cuttings with CGDD of 124 • C when adopting a single K cb = 0.80.

Crop Coefficients
The K cb , K e and K c (=K cb + K e ) curves relative to all three treatments and the simulations of the Summer-Autumn periods of both years are shown in Figure 4. Also included is information on the frequency of cuttings. The K cb curves show a regular variation for every cutting cycle, increasing from a minimum after each cutting up to a maximum just before it occurs. Apparently, a three-segments curve adapted well to each cutting cycle.  The maximum Kcb values represented in Figure 4 are slightly smaller than those tabulated for bermudagrass in FAO56 [17]. This is likely due to the humid climate conditions prevailing at time of experiments, that were likely influenced by the El Niño Southern Oscillation (ENSO) in both years, when very abundant rainfall occurred, together with reduced air temperature and solar radiation, and high air humidity (Figure 1). These humid climatic conditions were less favorable to crop transpiration, thus lowering the Kcb. The standard Kcb summarized in Table 8 were computed by adjusting the calibrated values to climate with Equation (7). This adjustment was mainly due to the high RHmin observed during both years, consequently resulting in standard Kcb higher than the calibrated Kcb values of Figure 4. Therefore, it may be observed that the standard Kcb curves obtained in this study are comparable to those tabulated in FAO56 [17], which allows us to conclude that the standard Kcb values obtained in the present study (Table 8)  The maximum K cb values represented in Figure 4 are slightly smaller than those tabulated for bermudagrass in FAO56 [17]. This is likely due to the humid climate conditions prevailing at time of experiments, that were likely influenced by the El Niño Southern Oscillation (ENSO) in both years, when very abundant rainfall occurred, together with reduced air temperature and solar radiation, and high air humidity (Figure 1). These humid climatic conditions were less favorable to crop transpiration, thus lowering the K cb . The standard K cb summarized in Table 8 were computed by adjusting the calibrated values to climate with Equation (7). This adjustment was mainly due to the high RH min observed during both years, consequently resulting in standard K cb higher than the calibrated K cb values of Figure 4. Therefore, it may be observed that the standard K cb curves obtained in this study are comparable to those tabulated in FAO56 [17], which allows us to conclude that the standard K cb values obtained in the present study (Table 8) may be transferable to other locations when adjusted to the local climate and considering the locally adopted frequency of cuttings. This assumption may be confirmed by observing that K cb from this study are similar to those reported by Greenwood et al. [33] for a ryegrass/clover pasture and are larger than those computed by Wu et al. [34] for a groundwater-dependent grassland where Leymus chinensis (Trin.) Tzvel. is the dominant grass. The K e curves show a strong dependency upon the wetting events, well apparent in Figure 4. K e are higher for the treatment with more frequent cuttings (CGDD of 124 • C) because the ground cover was smaller than for other treatments (Table 4), thus affecting less the energy available at the ground for soil evaporation. The K c curves, representing the daily combination of K cb and K e , are more flat and irregular than the K cb curves (Figure 4). This is likely due to the nearly constant values of K e resulting from the abundant and frequent rains that kept the soil evaporation layer wet most of time for all three cutting treatments. The standard K c values reported in Table 8 for this study with Tifton 85 bermudagrass are larger than those reported by Wherley et al. [23] for bermudagrass and by Graham et al. [48] for ryegrass, and slightly larger than those reported by Neal et al. [24] for ryegrass. These authors also adopted a single averaged K c . Considering the behavior of K c in this study (Figure 4), it may be appropriate to adopt a single K c value for Tifton 85 bermudagrass when a dual K c approach is not used.

Soil Water Balance and Transpiration and Soil Evaporation Ratios
The results of the soil water balance relative to all simulations performed during calibration and validation of the model are summarized in Table 9. Note first the unusual fact that the sum of runoff and deep percolation exceeds ET c in the Spring of 2015 and during the Summer-Autumn of 2017 because rainfall was likely impacted by ENSO as previously stated. RO was particularly high in 2017 as well as DP. The latter was larger than irrigation in all the periods considered which leads us to realize that using irrigation was likely a wrong option, but the exceptional rainfall observed was not predicted at time of planning and starting the experiment. Differences in RO and DP among treatments are not notable. However, as expected from the differences in terms of f c and K cb , crop evapotranspiration increases when the frequency of cuttings is smaller, and the same happens with T c . By contrast, soil evaporation is higher when the cutting frequency is also greater.
When analysing the evaporation and transpiration ratios (Table 10) it is evident that the E s /ET c ratio is much smaller than the T c /ET c ratio, particularly for the treatments with CGDD of 248 and 372 • C. Low values of the evaporation ratio relate to the high ground cover fraction f c and to the effects of plant litter, which limit the energy available at the soil surface. This effect was reported by Wang and Yamanaka [47]. High f c also indicates favorable conditions for plant transpiration. Low values for the E s /ET c ratio were reported by Greenwood et al. [33] and Wu et al. [34], while much higher values were reported for various meadows in northern China [28,44]. A small E s /ET c ratio of 13% was also referred to for native grasslands, however for arid conditions [49]. High transpiration ratios, but smaller than those observed in this study, were reported by various authors [15,46,50], namely influenced by soil texture [45]. Transpiration ratios for tropical and temperate grasslands of 62 ± 19% and 57 ± 19%, respectively, were reported by Schlesinger and Jasechko [60], therefore values with upper limits that are smaller than those observed in this study. This behaviour may indicate that Tifton 85 grasslands are efficient in terms of beneficial water use [61] since results show a very high transpiration ratio of 90% when cuttings are not very frequent.

Conclusions
The current study is a first application of the FAO dual crop coefficient approach to assess evapotranspiration and water use of a bermudagrass, more precisely the Tifton 85. It was performed using two years of field data relative to three cutting treatments where intervals between cuttings were defined by CGDD of 124 • C, 248 • C and 372 • C. These independent data sets were used to calibrate and validate the water balance model SIMDualKc, which allowed the K cb and K e curves for Tifton 85 to be obtained when managed with those three cutting intervals. Data of Summer and Autumn of 2016 were used for calibration and data for Spring 2015 and 2016, and Summer and Autumn of 2017 were used for validation. The procedure used led to quite small errors of estimation of the available soil water throughout both years, which allowed us to assume that the calibrated K cb values were accurately estimated and may be considered as standard for the three cutting frequencies studied after adjustments with Equation (7). It is important to note that the estimation of the initial K cb values from the crop cover and height has shown quite small differences to the calibrated values. Moreover, the Allen and Pereira [4] Equation (4) was revealed to be very accurate in estimating K cb from h and f c provided that K cb full is well estimated. The operational use of this Equation (4) is therefore recommended.
The K cb curves consist of a series of K cb curves relative to each cutting cycle, each one constructed with three linear segments. This approach follows the one proposed by the FAO56 guidelines [17] and differs from the commonly used single K c curve. It was revealed to be accurate in describing crop transpiration and providing for the accuracy of soil water dynamics computed through the calibration and validation processes. However, for the case of very frequent cuttings (CGDD of 124 • C) there was no advantage over a single, averaged K cb .
The K e curve reflects the abundant and stormy rains that occurred in both years of field experiments, which made the soil evaporation layer wet most of the time. Thus, the K e curve varied little throughout the periods under analysis. However, the soil water evaporation was mitigated due the organic mulch effect of the plant litter covering the ground, which reduced the energy available at the soil surface, thus reducing K e and E s . Comparing K e for the three cutting treatments, this resulted in a larger value for that with very frequent cuttings (CGDD of 124 • C) because the ground cover was smaller than for cuttings with large intervals, thus giving more time for the crop to grow and crop density to increase during each cutting cycle. Due to the nearly flat form of the K e curve, the K c curve and the sum of the K e and K cb curves do not reflect the aggregation of individual K c curves relative to each cycle of cutting. Therefore, by contrast with the K cb curves, a single K c value is appropriate, however specific for each cutting treatment.
Results for the soil water balance are marked by the enormous amount of rain observed during these two years, likely due to the impacts of ENSO. Thus, the amount of runoff and, mainly, deep percolation exceeded crop ET. Thus, the option of irrigating to avoid any water stress was shown to be inappropriate despite not being prejudicial to the experiments. However, the large number of rainy days and the large amount of rain were likely associated with reduced solar radiation and temperature, which could have contributed to reduce transpiration and the K cb values. However, the latter, as well as the K c values, are larger than most of K cb and K c values reported in literature, which support the assumption that K cb values may be considered standard and transferable to other locations after appropriate adjustments.
The soil evaporation fraction (E s /ET c ) for all cases was small, near 13% in the case of frequent cuttings and about 9% when cuttings were less frequent. These values could slightly decrease if soil wettings were less frequent. These results indicate that beneficial consumptive water use by the crop is high, with the transpiration ratio near 90%. These results agree well with those reported in literature relative to well-managed grasslands, particularly tropical ones. This may indicate that the Tifton 85 bermudagrass has the potential to contribute to the sustainability of the Pampa biome in southern Brazil. Adopting a median cuttings frequency (CGDD of 248 • C) is likely the most favorable. However, more studies are required, mainly relative to herbage production and water productivity, which are expected to be undertaken based upon the field data used in the current study.