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Implementing Standardized Reference Evapotranspiration and Dual Crop Coefficient Approach in the DSSAT Cropping System Model

K. C. DeJonge, K. R. Thorp


Published in Transactions of the ASABE 60(6): 1965-1981 (doi: 10.13031/trans.12321). 2017 American Society of Agricultural and Biological Engineers.


The authors have paid for open access for this article. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License https://crea tivecommons.org/licenses/by-nc-nd/4.0/

Submitted for review in March 2017 as manuscript number NRES 12321; 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.

Mention of company or trade names is for description only and does not imply endorsement by the USDA. The USDA is an equal opportunity provider and employer.

The authors are Kendall C. DeJonge, ASABE Member, Agricultural Engineer, USDA-ARS Water Management and Systems Research Unit, Fort Collins, Colorado; Kelly R. Thorp, ASABE Member, Agricultural Engineer, USDA-ARS Water Management and Conservation Research Unit, Maricopa, Arizona. Corresponding author: Kendall C. DeJonge, 2150 Centre Ave., Building D, Suite 320, Fort Collins, CO 80526; phone: 970-492-7417; e-mail: kendall.dejonge@ars.usda.gov.

Abstract.  While methods for estimating reference evapotranspiration (ETo or ETr) and subsequent crop ET (ETc) via crop coefficient (Kc) and dual crop coefficient (Kcb, Ke) methods have been standardized since 2005 and 1998, respectively, the current version of the DSSAT cropping system model (CSM) has not been updated to fully implement these methods. In this study, two major enhancements to the model’s ET routines were evaluated: (1) addition of the ASCE Standardized Reference Evapotranspiration Equation so that both grass and alfalfa reference ET were properly calculated using the most recent reference ET standard and (2) addition of the FAO-56 dual crop coefficient approach to determine potential ET, which combined an evaporative coefficient (Ke) for potential evaporation with a dynamic basal crop coefficient (Kcb) for potential transpiration as a function of simulated leaf area index. Previously published data sets for maize in Colorado (five years) and cotton in Arizona (seven years) were used to parameterize the model. Simulations of ETo were compared to outputs from Ref-ET software, and simulated crop coefficients were contrasted among three crop coefficient methods: the current approach (Kcs), a previously published adjustment to the model’s Kc equation (Kcd), and a new dual Kc approach that follows FAO-56 explicitly (Kcb). Results showed that crop coefficient simulations with the new ETo-Kcb method better mimicked theoretical behavior, including spikes in the soil evaporation coefficient (Ke) due to irrigation and rainfall events and basal crop coefficient response as associated with simulated crop growth. Simulated ETc and yield with the new ETo-Kcb method were up to 4% higher and 28% lower for cotton and up to 13% higher and 26% lower for maize, respectively, than that with the current ETo-Kcs method, indicating that the seasonal ETc effects were minimal while yield effects were more substantial. Use of FAO-56 concepts and current ET standards in DSSAT-CSM demonstrated a well-accepted ET benchmark to guide assessment of other ET methods in the model and made the model much more conceptually relevant to irrigation and ET specialists.

Keywords.Cotton, DSSAT, Evaporation, Evapotranspiration, FAO-56, Maize, Reference crop ET, Standardization, Transpiration.

Evapotranspiration (ET), the combined result of soil surface evaporation and plant transpiration, is an important component of agricultural water management and landscape hydrology, particularly in the field of irrigation management. Adequate quantification of ET is imperative as demand for freshwater resources increases. Several U.S. states such as Colorado use quantification of ET as a “consumptive use” in water rights transfer legal cases. Many past studies have shown a direct physiological relationship between crop yield and ET (Doorenbos and Kassam, 1979; Hunsaker et al., 2015; Trout and DeJonge, 2017) and particularly yield and transpiration (Paredes et al., 2014; Steduto et al., 2012). Furthermore, accurate estimation of ET partitioning into evaporation (E) and transpiration (T) is paramount in irrigated and water-limited systems (Jensen and Allen, 2016; Kool et al., 2014; Pereira et al., 2015; Phogat et al., 2016). Ideally, these subcomponents of ET (i.e., E and T) should be evaluated independently rather than as a residual of each other (Kool et al., 2014). The Appendix reviews recent institutionally supported efforts to standardize procedures for ET quantification on several scales, which should be well known material for ET experts but is made available for readers who are unfamiliar with the subject. Full details of the FAO-56 dual crop coefficient methodology are available in FAO Irrigation and Drainage Paper No. 56 (Allen et al., 1998) and ASCE Manual 70 (Jensen and Allen, 2016) and have recently been summarized by Pereira et al. (2015). According to ASCE Manual 70, these standards were developed to establish benchmark ET equations, which represent the current state of the art in estimating ET.

Over many decades, researchers have also developed complex cropping system models, which aim to comprehensively simulate the hydraulic processes, nutrient transformation and transport processes, and crop growth and development processes that occur in a cropping system. Such models have wide applicability for crop management, yield gap analysis, crop improvement, yield forecasting, synthesis of agronomic research, and assessment of policy (Boote et al., 1996). Because ET is often a large component of the water balance, simulation of the ET process is central to the calculations of these models, and accurate calculations of crop growth and yield depend on accurate ET calculations. However, the ET methods implemented among different models are often variable, and many do not incorporate the published ET standards as a simulation option. Generally, programming updates to the ET algorithms in the models have not kept pace with the development of new ET standards. Furthermore, preliminary results from a recent crop model intercomparison study demonstrated large variability in ET simulation results from 29 maize models parameterized for Iowa conditions (Kimball et al., 2016), which highlights the divergent nature of existing ET methods in crop models.

Inclusion of current ET standards as a simulation option in crop models offers several advantages for improvement of model functionality, interpretation of simulation results, and assessment of alternative ET simulation methods. Fundamentally, the standard ET methods should be considered a “benchmark” ET method in crop models, because the theory and equations are explicitly defined in the literature, well-accepted in the irrigation and ET community, and, most importantly, standardized by organizations with broad interest in ET and water management issues. Efforts to incorporate the ET standards into crop models should therefore proceed with minimal deviation from the accepted standardized equations and algorithms, thereby providing a benchmark ET method within the crop model to which other ET simulation options can be compared. Note that “benchmark” ET method does not necessarily imply “preferred” ET method but simply a benchmark standard that sets the performance baseline for any other ET method. As demonstrated herein, one advantage of incorporating standardized ET methods is to assist the identification of coding or behavioral errors in other ET simulation options. Comparatively, it is easier to program an algorithm from existing standardized equations than to (1) program a completely novel ET algorithm without error or (2) debug an existing ET algorithm that is misbehaving due to syntactical or conceptual errors. In each of these cases, coding improvements can be facilitated by comparisons to the benchmark ET standard.

The motivation for the present study arose from the authors’ independent work to use the Decision Support System for Agrotechnology Transfer (DSSAT) cropping system model (CSM) for irrigation management applications in semi-arid to arid environments of the western U.S.: maize in Colorado (DeJonge et al., 2011, 2012a) and wheat and cotton in Arizona (Thorp et al., 2010, 2014). Those studies highlighted issues with the ET methods of DSSAT-CSM, which the authors sought to remedy by bringing the model code into agreement with accepted standardized ET methods. The efforts have led to a new ET simulation option in DSSAT-CSM that implements the ASCE Standardized Reference Evapotranspiration Equation (Allen et al., 2005) with an FAO-56 dual crop coefficient (Kcb) approach (Allen et al., 1998) that calculates basal crop coefficients from simulated leaf area index (LAI). The main objective of the present study was to fully document the development of this new ET approach in DSSAT-CSM. Specific objectives were to use data from five maize growing seasons in Colorado and seven cotton growing seasons in Arizona to:

Background

DSSAT-CSM (ver. 4.6.0.040) programmatically synthesizes current knowledge of cropping system processes and uses mass balance principles to simulate the carbon, nitrogen, and hydrologic processes and transformations that occur within a cropping system (Jones et al., 2003). Simulations of crop development and growth for over 28 crops are possible, including the CERES family of models for maize and sorghum and the CROPGRO family of models for soybean and cotton. Simulated plant growth responds to management practices, cultivar selection, soil properties, and meteorological conditions. Minimum data requirements for FAO-56 ETpm (eq. A1) simulations include daily meteorological values for minimum and maximum air temperature, solar irradiance, dew point temperature, and wind speed.

The DSSAT-CSM soil water balance uses a one-dimensional “tipping bucket” approach, which simulates soil water flow and root water uptake for individual user-defined soil layers. Each soil layer requires information on initial soil water and nutrient content, wilting point, field capacity, and saturated water content (Ritchie, 1985). Potential ET (i.e., not reference ET) is calculated by DSSAT-CSM and can be defined here as ETc based on environmental evaporative demand, under conditions of no crop water stress and a wet soil surface to supply soil water evaporation. Potential ET in DSSAT-CSM can be calculated with several reference ET methods, including Priestley-Taylor (Priestley and Taylor, 1972), and since DSSAT v4.0 (Hoogenboom et al., 2004) the Penman-Monteith combination equation for a short reference crop (eq. A1, denoted “FAO56” in DSSAT), but ASCE standardized procedures (eq. A2; Allen et al., 2005) are not explicitly followed. For Arizona conditions, a preliminary comparison of (1) ETo calculated by DSSAT-CSM, (2) ETo calculated by an Arizona Meteorological Network (AZMET) station, and (3) ETo from a custom Python script that followed the ASCE reference ET guidelines (Allen et al., 2005) demonstrated that the DSSAT-CSM ETo was on average 1.5 mm d-1 lower than standard ETo calculations. Furthermore, simulation of a tall reference crop ET (ETr) is not currently available as an option in DSSAT-CSM. Based on these preliminary assessments, updates to the DSSAT-CSM reference ET calculations were deemed warranted and necessary.

Crop coefficients (Kcs) are calculated for the current Penman-Monteith ET approach in DSSAT-CSM as:

(1)

where LAI is the simulated leaf area index, EORATIO is defined as the maximum Kcs at LAI = 6.0 (Sau et al., 2004; Thorp et al., 2010), and Kcs is the DSSAT-CSM crop coefficient. This formula ensures that Kcs varies daily between 1.0 and EORATIO. Values of EORATIO less than 1.0 should not be used, as this would actually decrease the ET with increases in LAI. Typical values of EORATIO are between 1.0 and 1.4. Currently, EORATIO is implemented only for the CROPGRO-based crop models (e.g., soybean and cotton); for the remaining crops (e.g., maize) the parameter is hard coded to EORATIO = 1.0. This fixes Kcs at 1.0 for the entire simulation, making it thus static and limiting mid-season crop coefficient options for crops such as maize, which have recommended mid-season Kc values of 1.2 and above (Allen et al., 1998). DSSAT-CSM employs the following formula for calculation of E0 (potential crop ET):

E0 = KcsETpm (2)

As noted by DeJonge et al. (2012a), Kcs is not necessarily the same as crop coefficients described in FAO-56 (i.e., Kc in eq. A4). While it is true that the DSSAT-CSM crop coefficient Kcs is multiplied by a reference ET, the resulting value (E0) denotes ET potential, therefore demand, and not necessarily actual ET.

E0 is then partitioned into potential plant transpiration (EPo) and potential soil water evaporation (ESo):

EPo = E0(1 - exp[-KEP(LAI)]) (3)

ESo = E0exp[-KEP(LAI)] = E0 - EPo (4)

where KEP (typically ranging from 0.5 to 0.8) is defined as an energy extinction coefficient of the canopy for total solar irradiance, used for partitioning E0 to EPo and ESo (Ritchie, 1998). The model calculates ET partitioning in the following order: (1) ESo via equation 4, (2) actual E from one of two algorithms (Ritchie, 1972; Ritchie et al., 2009), (3) EPo as the minimum of equation 3 and E0 minus actual E, and (4) actual T as the minimum of EPo and available water supplied by the soil through the simulated root profile. The ESo calculation in equation 4 is implemented for the CSM-CERES-Maize model and several other crop models. However, the ESo calculation is different for the CROPGRO models, including CSM-CROPGRO-Cotton, as discussed later.

Actual soil water evaporation is calculated as the minimum of ESo and results from one of two soil water evaporation algorithms. The Ritchie (1972) algorithm evaporates water using a two-stage drying process based on the water content of the upper soil layer only, commonly specified with a depth of 5 cm. The Ritchie et al. (2009) method adds an upward flux calculation for all soil layers based on diffusion theory, and actual evaporation is the minimum of the surface soil layer upflux and ESo. Soil-limited plant (root) water uptake (EPr) is calculated based on simulated root growth and available water supply in each user-defined soil layer (Ritchie, 1998). The actual plant water uptake is calculated as the minimum of EPr and EPo. If the potential plant transpiration can be supplied by the soil water, then this demand is fully met. Otherwise, transpiration is limited to the supply, and water deficit stress factors are calculated based on the ratio of plant-available water supply (EPr) and potential transpiration demand (EPo). Because the stress factors are used primarily for limiting simulated crop growth in response to water deficits and other stresses, accurate calculation of potential transpiration demand is an essential aspect of crop growth simulations in DSSAT-CSM.

Recent Studies of DSSAT ET Module

In a recent CERES-Maize study in semi-arid Colorado, the DSSAT-CSM ETpm-Kcs method consistently predicted higher ETc than observed (DeJonge et al., 2011). These researchers later performed a sensitivity analysis of EORATIO (eq. 1) between values of 1.0 and 1.3 for both fully irrigated (non-stressed) and limited irrigation treatments (DeJonge et al., 2012a). They found that by increasing EORATIO above 1.0, the ETc under no stress increased, but under limited irrigation there was no change. Additionally, they found that changing the energy extinction coefficient (KEP, eqs. 3 and 4) had no effect on cumulative ETc for either treatment. In other words, adjustments of neither EORATIO nor KEP were able to bring ET closer to observed values.

Because the results using existing ETc methods in DSSAT-CSM were unsatisfactory, an alternative approach was created that used a dynamic approach to Kc as a direct function of simulated LAI. The primary factor causing an increase in the crop coefficient is an increase in plant cover or leaf area (Jensen and Allen, 2016); thus, Kc is correlated with LAI. Using Kc and LAI comparisons from the literature, DeJonge et al. (2012a) created a dynamic crop coefficient for DSSAT-CSM to replace Kcs in equation 1:

Kcd = Kcdmin + (KcdmaxKcdmin)(1 – exp[-SKc(LAI)]) (5)

where Kcdmin is the minimum crop coefficient or Kcd at LAI = 0, Kcdmax is the maximum crop coefficient at high LAI, and SKc is a shaping parameter that determines the shape of the Kcd versus LAI curve. Similar to equation 2, E0 is calculated as the product of Kcd and ETpm. Recommended values for Kcdmin and Kcdmax can be found in FAO-56, and DeJonge et al. (2012a) recommended 0.5 < SKc < 1.0 as a typical shape to match past literature on the subject. Note that Kcdmax in equation 5 is different from Kcmax in equation A6. By running CERES-Maize with the dynamic crop coefficient Kcd (eq. 5) using a five-year maize data set from field experiments that tested full and limited irrigation, there was reduced error in limited irrigation ET (RMSD from 80.9 to 49.9 mm) and water use efficiency (yield divided by ET; RMSD from 5.97 to 2.86 kg ha-1 mm-1), while error in limited irrigation yield increased slightly (RMSD from 1229 to 1451 kg ha-1). Model output under full irrigation was essentially unchanged. These results were found by changing only the crop coefficient equation, without any recalibration of the model. The Kcd technique of equation 5 was implemented by Thorp et al. (2014) using the CSM-CROPGRO-Cotton model, and they also added the ASCE Standardized Reference ETo Equation (eq. A2) in DSSAT-CSM and verified ETo simulations with ETo from a local meteorological network station at their field site in Arizona. This study also found improved ETc simulations using these methods.

While the incorporation of equation 5 into DSSAT-CSM improved results of ET and water use efficiency (WUE) under limited irrigation (DeJonge et al., 2012a), some researchers expressed concern that the method was redundant with the partitioning of potential ET into potential evaporation and transpiration (eqs. 3 and 4). Equation 5 uses an exponential function of LAI to scale reference ET to potential ET through Kcd, while equations 3 and 4 use a similar expression for partitioning E and T, leading to the claim of redundancy. Further investigation has shown that the original approach (eq. 1) and the DeJonge et al. (2012a) approach (eq. 5) both have advantages and disadvantages, and the strengths of the two approaches must be combined for DSSAT-CSM simulations of Kc to mimic theoretical patterns, as described in FAO-56 and observed through various techniques (e.g., lysimetry). To accomplish this goal, a dual crop coefficient approach was added to DSSAT-CSM.

Methods and Materials

The locations used in this study were chosen to evaluate ET in arid (Arizona) and semi-arid (Colorado) areas with high evaporative demand where irrigation is required, water use is closely monitored, and ET decision support is common. The crops used in this study were the prevalent high water commodity crops in these areas: maize in eastern Colorado and cotton in central Arizona. The selected crops also cover both the CERES (maize) and CROPGRO (cotton) families of models in DSSAT, each of which has its own nuances of ET simulation, as demonstrated below.

In a prior study, the CSM-CERES-Maize model was evaluated using data from a multi-replicate field research experiment near Fort Collins, Colorado (40° 39' 19? N, 104° 59' 52? W) from 2006-2008. Complete experimental details can be found in DeJonge et al. (2011, 2012a). Two irrigation treatments were applied to continuous maize during the 2006-2010 growing seasons: full irrigation (ET requirement met by irrigation throughout the season) and limited irrigation (no irrigation before the V12 growth stage unless necessary for emergence, and then full irrigation afterwards). Irrigations were applied with a linear-move sprinkler system, generally at a weekly interval. Irrigation amounts were determined by crop need (using a daily checkbook method and soil water content measurements via neutron scattering probe) and supported by potential ET estimates from on-site meteorological measurements. Typical soils at the site were loam. An on-site weather station (station FTC03; 40° 39' 9? N, 105° 0' 0? W; elevation 1557.5 m) within the Colorado Agricultural Meteorological Network (CoAgMet; http://ccc.atmos.colostate.edu/~coagmet/) continually recorded daily precipitation, solar radiation, minimum and maximum temperature, vapor pressure (which was converted to dew point temperature), and wind run. This dataset was also used in a global sensitivity and uncertainty analysis of CERES-Maize yield, ET, and growth responses to input variability (DeJonge et al., 2012b).

Thorp et al. (2014, 2017) described the evaluation of CSM-CROPGRO-Cotton using data sets from seven cotton experiments conducted near Maricopa, Arizona (33.068° N, 111.971° W) in 1990, 1991, 1999, 2002, 2003, 2014, and 2015. The objectives of the field experiments were variable but tested cotton responses to full and limited irrigation and fertilizer management, planting density, and free-air carbon dioxide enrichment (FACE). The irrigation method differed among the experiments, and subsurface drip, overhead sprinkler, and furrow irrigation methods were all represented. Soil water balance methods based on twice-weekly measurements of soil water content with neutron scattering probes were used to quantify crop water use during each experiment. Typical soil types at the field site included sandy loam and sandy clay loam. The central Arizona cotton growing season is hot and dry, with daily maximum temperatures regularly exceeding 38°C during July and August and seasonal precipitation often amounting to less than 10% of ETo. Meteorological data were collected from an Arizona Meteorological Network (AZMET; http://ag.arizona.edu/azmet/) station within 1 km of each experimental site.

Updates to DSSAT-CSM ET Module

Due to unsatisfactory performance of the DSSAT-CSM ET routines for Arizona conditions (Thorp et al., 2010), Thorp et al. (2014) added an algorithm based strictly on the ASCE Standardized Reference ET procedures (Allen et al., 1998, 2005) and evaluated CSM-CROPGRO-Cotton using the DeJonge et al. (2012a) crop coefficient method (eq. 5). By explicitly following ASCE Standardized Reference ET procedures, both short (ETo) and tall (ETr) reference ET could be calculated in this algorithm according to equation A2. The model’s original code for calculation of ETpm via equation A1 remained unmodified as an independent algorithm from the equation A2 updates. Because ETo is the most widely used ET reference worldwide and because DSSAT versions 4.0 and above approximated ETo (eq. A2) via ETpm (eq. A1), results in this study focus on the short reference crop (ETo). However, changes made to the model are also applicable to users of the tall (ETr) reference, with specification of proper crop coefficients. Although Thorp et al. (2014) first described the addition of ASCE Standardized Reference ET to the model, they did not report comparisons of their algorithm with other ETo software or with other DSSAT-CSM ET methods.

Novel in the present study, a dual crop coefficient approach was incorporated into DSSAT-CSM to determine potential soil evaporation and plant transpiration separately by independently determining Ke and Kcb, respectively (eq. A4). Evaporative coefficients (Ke) were determined by following the methods described in equations A5 through A9 (Allen et al., 1998). Transpiration or basal crop coefficients (Kcb) were calculated using an exponential extinction function similar to current partitioning in DSSAT-CSM (eq. 3) and more closely resembling the Kcd dynamic crop coefficient (eq. 5) (DeJonge et al., 2012a):

Kcb = Kcbmin + (KcbmaxKcbmin)(1 – exp[-SKc(LAI)]) (6)

Table 1. Standardized, current DSSAT-CSM, and proposed DSSAT-CSM ET methodologies.
OperationStandardCurrent DSSAT-CSMModel IssuesProposed Model Improvement
Reference ET:
ETo = short “grass”
reference, and
ETr = tall “alfalfa”
reference
ASCE ETo and ETr,
which assume
well-watered,
non-stressed
vegetation.
“FAO-56 P-M”
ETpm (eq. A1)
Methodology varies slightly
from ASCE ETo, meaning it
is not in full agreement with
current standards.
ASCE ETo and ETr added as
options, methodology explicitly
follows the ASCE standard
(Allen et al., 2005) (eq. A2)
Crop coefficient
for potential
ET
Kc = KsKcb + Ke
(eq. A4)
Kcs = 1.0 + (EORATIO - 1.0)
× (LAI/6.0)
(eq. 1)
Mathematically, Kcs = 1
always, which does not
follow FAO-56 methods.
Kc = KsKcb + Ke = 1.0(Kcb) + Ke
used for calculation of potential
ET, so Ks = 1 (potential ET
assumes no stress)
Potential crop
ET
ETc = EToKc
(eq. A3)
E0 = KcsETpm
(eq. 2)
Because Kcs = 1, E0 = ETpm
always (i.e., even in fallow)
ETc = ETo(Kcb + Ke)
(eqs. A3 and A4)
Potential plant
transpiration
Kcb from FAO-56,
a trapezoidal
function of days
after planting.
Partitioned from potential ET (E0):
EPo = E0(1 - exp[-KEP(LAI)])
(eq. 11)
The model first calculates
“potential ET” and then
partitions E and T based
on LAI. FAO-56 calculates
E and T separately based
on explicit crop coefficient
calculations.
EPo = EToKcb
Kcb = Kcmax(1 - exp[-SKcLAI])
(eqs. 6 and 7)
Dynamic Kcb = f(LAI), mimics
FAO-56 trapezoidal function
Potential soil
evaporation
Ke from FAO-56,
which allows high-E
events with wet soil
surface and low
canopy cover.
Partitioned from potential ET (E0):
ESo = E0(exp[-KEP(LAI)])
ESo = E0 - EPo
(eqs. 3 and 4)
ESo = EToKe
Ke = min[KcmaxKcb, fewKcmax]
where Kcmax = f(u2, RHmin, h, Kcb)
and few = min(1 – fc, fw)
(eqs. 8 and A5-A8)

where Kcbmin is the minimum basal crop coefficient representing a dry, bare, or nearly bare soil surface. Kcbmax is user-defined and obtained from recommended crop-specific coefficients in FAO-56. Both equation 5 and equation 6 are similar in form to equation 97 in FAO-56, as well as equations 10-25a and 10-28 in ASCE Manual 70 (Jensen and Allen, 2016). The approach uses model-simulated LAI to calculate the Kcb, which means Kcb is more dynamic and responsive to cultivar, weather, and soil variability, as simulated by the model (Thorp et al., 2017). This is in contrast to the fixed trapezoidal crop coefficient curves recommended by FAO-56. Similar to equations 3 and 4, daily potential plant transpiration (EPo) and soil evaporation (ESo) were then determined from Kcb and Ke, respectively, in the following equations:

EPo = KcbETo (7)

ESo = KeETo (8)

Because the aim of equation 8 is potential soil evaporation, Ke is obtained from equation A5 with Kr = 1.0.

Similar to the current Kcs method (eqs. 1 through 4), actual T is less than EPo if soil water available to the plant root system is too low, essentially T = KcbKsETo from FAO-56. However, rather than implementing the FAO-56 Ks method, the native DSSAT-CSM routines for calculating water stress effects on crop growth (discussed above) were used. Table 1 summarizes the enhancements to calculations of reference ET and dual crop coefficients for plant transpiration (Kcb) and soil water evaporation (Ke) in DSSAT-CSM. Similar to equation 5 for the Kcd method, the minimum Kcb value (Kcbmin) is defined and here assumed as 0. Understanding that this deviates slightly from true FAO-56 recommendations, there are several important reasons for considering a null Kcbmin in crop model simulations. First, within the FAO-56 water balance approach, Kcbmin is used to account for upflow from deep soil layers (Richard Allen, personal communication). However, the evaporation routine in DSSAT-CSM already accounts for this (Ritchie et al., 2009). Second, DSSAT-CSM is often used for sequential simulations of crop rotations, including fallow periods when transpiration simulations should be zero. Finally, specifying Kcbmin > 0 leads to a discontinuity in simulated Kcb on the day of emergence if the simulation is initiated prior to emergence.

Other assumptions were required to merge the FAO-56 and DSSAT-CSM methods. In FAO-56, Kr (eq. A5) is calculated as a function of soil moisture depletion in the FAO-56 soil surface profile and is used for direct calculation of reduced evaporation as the soil surface profile dries. On the other hand, the soil water evaporation routines in DSSAT-CSM are specific to its layered soil profile and therefore deviate, with good reason, from the FAO-56 approach. Thus, the Kr term in the DSSAT-CSM implementation of FAO-56 was fixed at 1.0 in the calculation of Ke (eq. A5), and the native DSSAT-CSM soil evaporation routines, e.g., the Suleiman-Ritchie (Ritchie et al., 2009) approach for maize and the Ritchie (1972) approach for cotton, were used to reduce actual evaporation from potential evaporation as the soil profile dried. Similarly, FAO-56 uses Ks (eq. A4) to directly reduce transpiration under water limitation, and Ks is calculated from soil moisture depletion in the simple FAO-56 soil profile. However, DSSAT-CSM considers soil moisture simulations in a layered profile and capacity for root growth to extract water from the soil layers. Thus, Ks in DSSAT-CSM was not explicitly simulated, and native DSSAT-CSM routines were instead used to account for effects of water limitation by calculating water stress coefficients (discussed above), which are conceptually similar to Ks but with different formulation. With these assumptions, Ke and Kcb in DSSAT-CSM were used only to calculate potential E and T, respectively (eqs. 7 and 8), while the native DSSAT-CSM algorithms were used to calculated actual E and T from potential. In addition, fw (eq. A8) was assigned as 1.0, assuming that water applications (both precipitation and irrigation) were distributed over the entire ground surface.

The reference ET and ET partitioning methods used in this study were tested in various combinations, and for clarity are hereafter specified using the symbols in table 2 (e.g., ETpm-Kcs for the existing DSSAT-CSM v4.6 method and ETo-Kcb for the new method).

Table 2. Reference ET methods and ET partitioning methods with corresponding abbreviations.
MethodsSymbol
Reference ET
DSSAT-CSM v4.6 FAO-56 P-METpm
ASCE ETo short reference (Allen et al., 2005)ETo
ASCE ETr tall reference (Allen et al., 2005)ETr
ET partitioning
DSSAT-CSM v4.6 (eqs. 1-4)Kcs
DeJonge et al. (2012a) (eqs. 2-5)Kcd
FAO-56 (Allen et al., 1998) (eqs. A4-A9 and 6-8)Kcb

Simulations

Maize simulations used the Colorado data set described earlier, including five years (2006-2010) and two treatments each year (full and limited irrigation). Cotton simulations used the Arizona data sets described earlier, including seven cotton seasons (1990-1991, 1999, 2002-2003, 2014-2015). Simulations were conducted using weather files and calibration results from several prior studies for the maize data set (DeJonge et al., 2011, 2012a, 2012b) and cotton data sets (Thorp et al., 2014, 2015, 2017).

Model simulations of daily reference ET were compared for five growing seasons in both Colorado and Arizona. Specifically, calculations of ETpm from DSSAT-CSM (ver. 4.5.1.005), ETpm from DSSAT-CSM (ver. 4.6.0.040), and FAO-56 based ETo from a custom algorithm added to the DSSAT-CSM code were compared to FAO-56 ETo calculations from Ref-ET software (Allen, 2011), which is designed to calculate standardized reference ET for comparison with other computer programs such as DSSAT-CSM. Simulations from the older DSSAT-CSM version 4.5 were included to highlight a major issue with the wind height transfer function, which led to deeper investigation of the DSSAT-CSM ET methods (Thorp et al., 2010, 2014) and development of new methods presented herein.

Qualitative graphical comparisons between the ETo-Kcs, ETo-Kcd, and ETo-Kcb methods were conducted to demonstrate differences in simulated daily crop coefficients. The reference ET method was ETo for all three cases to focus comparisons on the crop coefficient method alone. The 2008 maize growing season and the 2015 cotton growing season were used for graphical representation of crop coefficient time series. Simulated crop yield and seasonal ET among the ET partitioning methods were also compared for both crops in all five growing seasons. Simulations with the ETo-Kcb method used values of Kcbmax = 1.15 and SKc = 0.5 for maize, and Kcbmax = 1.15 and SKc = 0.6 for cotton (eq. 6; table 3). Kcbmax values were determined from tabular values of mid-season Kcb found in FAO-56 (Allen et al., 1998). Values for SKc were determined from the recommended range (generally 0.5 to 1.0) for shaping the relationship of Kcd (eq. 5) and by prior testing to create a reasonable relationship between ETc and yield. Simulations with the ETo-Kcs and ETo-Kcd methods were parameterized as described by DeJonge et al. (2011) and Thorp et al (2014); EORATIO for maize simula-tions was hard-coded to 1.0 within DSSAT-CSM. Because the objective was to compare simulation results among different ET methods, the only adjustments to model parameterization were the choice of ET simulation method and associated ET parameters. This strategy ensured that the simulation results demonstrated differences due to ET method alone. Future efforts with the new ET method will likely require recalibration of non-ET parameters to improve agreement between measured and simulated data; however, this was beyond the focus of the present study.

A sensitivity analysis of yield, ETc, E, and T responses to parameters in equation 6 was conducted using the new ETo-Kcb approach. The analysis was conducted using all five maize seasons (2006-2010) but only two cotton seasons (2014-2015) because cotton responses to full and limited irrigation were not available for every growing season and were best quantified in 2014 and 2015. The value of Kcbmax was varied between 0.9 and 1.4 with a base level of Kcbmax = 1.15, which is the tabular value from FAO-56 (Allen et al., 1998) for both crops. The value of SKc was varied between 0.4 and 0.9 with a base level of 0.5 for maize and 0.6 for cotton from prior calibration efforts (DeJonge et al., 2011; Thorp et al., 2014). With an assumption of Kcbmin = 0 as described before, the values of Kcbmax and SKc were varied to understand the influence of these variables on simulated yield and ETc for maize and cotton.

Table 3. Parameter values used to simulate three DSSAT-CSM ET partitioning methods (Kcs, Kcd, and Kcb) for maize and cotton.
CropPartitioning
Method
KEPSKcKcmin[a]
Kcbmin[b]
Kcmax[a]
Kcbmax[b]
EORATIO[c]
MaizeKcs0.5--1.0
Kcd0.50.50.31.2
Kcb-0.501.15
CottonKcs0.7--1.1
Kcd0.70.60.351.2
Kcb-0.601.15

    [a] For Kcd method only.

    [b] For Kcb method only.

    [c] For Kcs method only.

Results

Any crop model or other program used to calculate ETo should produce very similar results as obtained by specifically following the standardized methods, justifying why Ref-ET software was developed (Allen, 2011). As compared to older ETpm simulations with DSSAT-CSM, simulations of ETo using the new algorithm based explicitly on the ASCE standard (Allen et al., 2005) were in closest agreement with ETo calculated by Ref-ET software (fig. 1). The root mean squared errors (RMSE) between Ref-ET ETo and DSSAT-CSM ETo were less than 1.0% for both Arizona and Colorado conditions, while the RMSE values between Ref-ET ETo and DSSAT-CSM ETpm were greater than 2.0%. The results demonstrate that the new DSSAT-CSM ETo algorithm better aligned with published ET standards (Allen et al., 2005) and accepted software for standardized ET calculations (Allen, 2011). Errors between the Ref-ET ETo and DSSAT-CSM ETo results are likely due to minor numerical errors arising from differences in the formulation of the two algorithms.

Figure 1. Daily reference evapotranspiration outputs for DSSAT-CSM versus Ref-ET software: (a) CSM v4.5 ETpm method for Arizona (AZ) data (n = 872 days over five cotton growing seasons), (b) CSM v4.6 ETpm method for AZ data, (c) new CSM standardized ETo method for AZ data, (d) CSM v4.5 ETpm method for Colorado (CO) data (n = 626 days over five maize growing seasons), (e) CSM v4.6 ETpm method for CO data, and (f) new CSM standardized ETo method for CO data. MAE = mean average error, and RMSE = root mean squared error.

With an RMSE of 22.8%, drastic discrepancies were found in the comparison of Ref-ET ETo and ETpm from DSSAT-CSM version 4.5 for Arizona conditions (fig. 1a). In 2014, the authors linked the problem to a misspecification of the equation used to adjust wind speed measurements to a standard height of 2.0 m. In DSSAT-CSM, this calculation is accomplished with the following equation:

(9)

where u2 is the calculated wind speed at a standard height of 2.0 m, uz is the measured wind speed at a height of zw, and a is an empirically derived coefficient that is hard-coded but varies based on the stability of the atmosphere. In DSSAT-CSM v4.5, the model erroneously used a = 2.0, which was corrected to a = 0.2 in DSSAT-CSM v4.6. This coding error in DSSAT-CSM version 4.5 (and likely prior versions) greatly affects ETpm calculations for weather networks with anemometers at heights other than 2.0 m, such as AZMET in Arizona, but has no effect on networks with anemometers at 2.0 m, such as CoAgMet in Colorado. The use of independent standardized software such as Ref-ET is highly recommended in crop model development efforts to verify ET algorithms and ensure quality of simulated ET data.

Although the wind speed adjustment coefficient (a in eq. 9) has been corrected in DSSAT-CSM version 4.6, the update does not match the ASCE standard equation (Allen et al., 2005) for adjusting wind speed measurements to a standard height of 2.0 m:

(10)

Thus, differences between ETpm (figs. 1b and 1e) and ETo (figs. 1c and 1f) calculations in DSSAT-CSM version 4.6 are partially attributed to different wind speed adjustment equations for each method (eqs. 9 versus 10, respectively). Incorporation of current reference ET standards (Allen et al., 2005) in DSSAT-CSM not only helped identify coding errors in the model’s existing ET methods but also established the appropriate reference ET calculations (ETo or ETr) as intended for use with FAO-56 crop coefficient approaches.

Crop Coefficient Methods

To visually illustrate the crop coefficients simulated by DSSAT-CSM, figure 2 shows the behavior of crop coefficients for Colorado maize under full and limited irrigation in 2008 using the ETo-Kcs method, the ETo-Kcd method, and the new ETo-Kcb method, and figure 3 shows similar results for Arizona cotton in 2015. These figures show simulated values for crop coefficients Ke (= E/ETo), KcbKs (= T/ETo), and Kc (= ETc/ETo). As described in equations A3 and A4, these coefficients represent the ratio of E, T, or ETc to the reference evapotranspiration (ETo), which was calculated from the daily DSSAT-CSM outputs for each ET method. As discussed above, Ks and Kr were not explicitly calculated in DSSAT-CSM because the model used alternative algorithms to calculate the effects of water limitation. However, by calculating Ke, KcbKs, and Kc from the model output of E, T, ETc, and ETo, the resulting crop coefficient plots are conceptually similar to the description of these terms in FAO-56. In particular, the KcbKs terms in figures 2 and 3 represent the basal crop coefficient adjusted for water stress effects. If high transpiration demand is calculated by equation 1, 5, or 6 for Kcs, Kcd, or Kcb, respectively, but soil water is not available to meet that demand, then the simulated transpiration would be a lesser value and is represented in figures 2 and 3 as KcbKs. By calculating FAO-56 crop coefficients from model-simulated ET, different ET methods can be evaluated and contrasted for adherence to theoretical crop coefficient responses (Allen et al., 1998). Gross deviations from accepted theory highlight issues with the implementation of a particular ET method and suggest that further coding modifications are needed.

Early in the growing season, there was little canopy cover, and ET was mostly surface soil water evaporation (maize in fig. 2 and cotton in fig. 3). As canopy cover increased with vegetative growth, the transpiration portion exceeded the evaporation portion of ET, beginning around DOY 165 for maize and DOY 175 for cotton. When the crop reached full canopy (around DOY 185 for maize and DOY 200 for cotton), transpiration was the majority of ET. As the crop began to senesce (around DOY 265 for maize and DOY 270 for full-irrigation cotton), the transpiration demand decreased until maturity, and very abruptly for cotton. During early crop development (e.g., DOY 120 to 165 for maize), there was very little vegetation, leading to low transpiration, so evaporation was very important at this time. According to FAO-56, plots of daily Ke and overall Kc should demonstrate periodic sharp increases or spikes due to irrigation events and particularly rainfall (e.g., figs. 2c and 3c), which wets the entire soil surface. While the ETo-Kcs method was responsive to these evaporative spikes, the ETo-Kcd method was much less responsive with less surface evaporation for both full and limited irrigation. The ETo-Kcb method was more similar to the ETo-Kcs method, although evaporation was slightly higher in this period.

As mentioned earlier and in table 1, the ETo-Kcs method fixes Kcs at 1.0 for maize (eq. 1), which limits overall Kc to a maximum of 1.0, as was found in three instances of high precipitation during the early season (figs. 2a and 2d). During these same periods in the ETo-Kcb method, both Ke and overall Kc exceeded the value of 1.0 because Ke is limited instead by evaporative demand, as computed according to FAO-56 methods in equations A5 and A6. Likewise, early season evaporative spikes in cotton (fig. 3) are limited to values very close to 1.0 because low LAI forced Kcs close to 1.0 (eq. 1). The new revision of ASCE Manual 70 (Jensen and Allen, 2016) states that for an ETo reference, these early-

season spikes in Kc and Ke should typically approach maximum values of 1.0 to 1.2, which is here achieved only by the new ETo-Kcb method in DSSAT-CSM (figs. 2c, 2f, 3c, and 3f). It is important to note that during the early season, the ETo-Kcb method was otherwise very similar to ETo-Kcs overall.

In the mid-season, ETc as shown by Kc was lower for the ETo-Kcs method than for both the ETo-Kcd and ETo-Kcb methods and for both irrigation treatments, especially compared to ETo-Kcb under full irrigation. In maize, from DOY 190 to 260, Kc for ETo-Kcs was unrealistically limited to 1.0 due to the hard-coded EORATIO = 1.0 in the CERES-Maize model (eq. 1). For cotton, EORATIO was parameterized to 1.1 (table 3), and while this allowed Kc from ETo-Kcs to be more dynamic with cotton than with maize (e.g., comparing figs. 2 and 3), the upper values for Kc were still minimally responsive, especially when compared with the new ETo-Kcb method. Because cotton Kc was generally higher in the mid-season for the ETo-Kcb method than for the ETo-Kcs method, the model simulated more crop water use and some stress events, even under full irrigation (fig. 3c).

During late-season senescence, the crop coefficient plots showed that both E and T generally declined. Cotton ET declined rapidly after irrigation was terminated on DOY 247, but crop coefficients increased prior to DOY 280 due to two rainfall events at that time. The ETo-Kcd method was very similar in shape to the ETo-Kcs method, especially under limited irrigation. The ETo-Kcb method was very different from the ETo-Kcs method under full irrigation but was fairly similar under limited irrigation.

A notable difference between the crop coefficient behav-ior in figures 2 and 3 is that the cotton crop had more daily variation in the magnitude of Kc, especially under limited irrigation. This was because the Arizona climate had much higher ET demand during the growing season (fig. 1) and less frequent and productive rainfall. The cotton experiment was also conducted on a sandy clay loam soil, which may have limited water availability to the crop. As evidenced by Kc for the limited irrigation cotton treatment in 2015 (fig. 3f), the simulated crop experienced water stress for short intervals on a weekly basis as a result of the suboptimal irrigation schedule. Additional irrigation applications would be necessary to fully alleviate this issue and eliminate drops in mid-season Kc.

The cotton simulations for ETo-Kcs and ETo-Kcd revealed unrealistic patterns of sharply increasing KcbKs, most clearly visible on DOY 181 and DOY 259 (figs. 3a and 3b). There is no practical reason why T should sharply increase on these dates, particularly because they correspond to the latter days of a drying cycle when soil water is less available. The KcbKs results for ETo-Kcb did not reveal these unrealistic patterns (fig. 3c), and none of the ET methods for the maize simulations demonstrated this behavior (fig. 2). With deeper inspection of the model code, the calculation of ESo for the CROPGRO model was found to deviate from the rest of the crop models. Instead of using equation 4 for ESo, the CROPGRO model currently uses the following expression:

(11)

Thus, CROPGRO bypassed the use of KEP for ESo calculations but used KEP for EPo calculations. Comparing the results of equation 4 (with KEP = 0.7 from table 3) and equation 11 for identical E0 and LAI, the latter approach consistently calculated higher ESo for the 2015 cotton season (not shown). As a result, ESo and EPo no longer summed to E0 (eq. 4). The major problem arose when EPo was calculated as the minimum of equation 3 and E0 minus actual E. Because equation 11 permitted higher ESo than equation 4, E0 minus actual E was often lower than the result of equation 3, particularly following wetting events, which led to a drop in EPo. As the soil dried, equation 3 eventually determined EPo again, because little water was available for actual E. The result was several unrealistic discontinuities in the temporal EPo calculations for the ETo-Kcs and ETo-Kcd methods (fig. 3), which subsequently affected actual T and KcbKs calculations (figs. 3a and 3b). Because the ETo-Kcb method used Ke, Kcb, and ETo to calculate ESo and EPo (eqs. 7 and 8) independently, this problem was averted for ETo-Kcb, and the EPo curve was more realistic (fig. 4). Similar to the identification of problems for reference ET calculations (fig. 1), this problem with ET partitioning was revealed only after incorporating existing ET standards into DSSAT-CSM and using FAO-56 theory to scrutinize the model’s ET output.

Overall, the results demonstrate how crop coefficient calculations from daily crop model outputs of E, T, ET, and ETo can be used to assess the adherence of different ET methods to expected crop coefficient patterns, as reported in FAO-56. Deviations from the expected patterns can help diagnose issues with an ET method, while inclusion of the ETo-Kcb method establishes the benchmark standard to which any other approach can be compared.

Figure 4. Ratio of potential transpiration (EPo) and grass reference ET (ETo) for three ET methods (ETo-Kcs, ETo-Kcd, and ETo-Kcb) as simulated by CSM-CROPGRO-Cotton for the 2015 well-watered Arizona cotton treatment.

Yield and ETc Sensitivity to ET Method

When adjusting only the ET method and associated input parameters (table 3), simulated patterns in yield and seasonal ETc were similar among the two crops for the three ET methods (fig. 5). Similar to the results of DeJonge et al. (2012a), maize yield and seasonal ETc values for ETo-Kcd were minimally changed as compared to the ETo-Kcs module. While seasonal ETc simulations were sometimes similar, simulated Kc (figs. 2 and 3) demonstrated that the daily ETc simulations were not at all similar among the methods. Thus, if the ET methods compute relatively similar seasonal ETc amounts, it is through fundamentally different daily ETc simulations. For the ETo-Kcb method with both crops, simulated yield was up to 28% lower for both full and limited irrigation. This result is likely related to higher EPo for the ETo-Kcb approach (fig. 4). Additionally, the ETo-Kcb method with both crop models resulted in up to 13% higher ETc for full irrigation, while differences among the ET methods were small for limited irrigation. These results indicate the need for the new module to be more fully evaluated using measured data from multiple locations, as the updates obviously influenced the main outputs of yield and ETc. High-quality daily ETc data, such as the data obtained from lysimetry (Evett et al., 2016), would be best for such evaluations, but none of the field experiments for the present study included crop water use data from lysimeters. While this study does not specifically compare simulation results to measured values, it has shown that there were fundamental differences in daily ET calculations (figs. 2 and 3) that led to impacts on simulated yield (fig. 5). Additionally, the findings demonstrate how some methods follow existing ET standards more closely than others. Presumably, this should correspond to improved ET simulations when compared to field measurements. However, because the goal was to develop the new ETo-Kcb module and compare it to existing ET modules, only the ET parameters were adjusted (table 3), while the soil and cultivar parameters remained consistent among the ET methods. In reality, soil and cultivar parameters could be adjusted to different values for each ET method to improve agreement between measured and simulated yield and ETc. Future studies will address this issue through model calibration efforts against high-quality daily ETc data.

Figure 5. Mean yield and ETc for (a) maize and (b) cotton under full and limited irrigation, comparing the ETo-Kcs method, ETo-Kcd method (DeJonge et al., 2012a), and new ETo-Kcb method. Error bars for maize indicate standard deviations over five years; error bars for cotton are omitted due to only having two years in sample (2014 and 2015).

Yield and ET Sensitivity to ETo -Kcb Parameters

Under full irrigation, Kcbmax with the ETo-Kcb method had little influence on maize and cotton yield for 0.9 < Kcbmax < 1.15, but simulated yield decreased rapidly for Kcbmax > 1.15 (fig. 6a). However, under limited irrigation, yield increased with decreasing Kcbmax, likely due to the reduced transpiration demand via equation 6 and therefore less simulated water stress.

Simulated ET was not sensitive to changes in Kcbmax for values above 1.15 due to conservation of mass, but as Kcbmax decreased there was some additional ETc loss under full irrigation for maize (fig. 6c).

Amounts of E and T were very sensitive to Kcbmax changes with the new ETo-Kcb module (figs. 6e and 6g). Generally, as Kcbmax increased, seasonal soil evaporation decreased and transpiration increased. This was mostly due to the effect of Kcbmax on partitioning of E and T; however, overall ETc changed very little (fig. 6c). This result has drastic implications for model calibration using measured separate E and T data, rather than ETc data alone, because Kcbmax adjustments affect simulated E and T much more than ETc. Ideally, high-quality data on E and T independent from ETc are needed to adjust the parameterization of Kcbmax. Otherwise, it is recommended to obtain values from the Kcb tables in FAO-56.

The shaping parameter SKc is very interesting because it influenced yield more than seasonal ETc (figs. 6b and 6d). Similar to Kcbmax, this is likely due to the effects of the

Figure 6. Sensitivity analysis of (a-b) yield, (c-d) ETc, (e-f) E, and (g-h) T from changes in Kcbmax and SKc using the ETo-Kcb method (eq. 6). Both maize and cotton models used Kcbmax = 1.15 from the FAO-56 tables as the base value (i.e., no change), while maize used SKc = 0.5 and cotton used SKc = 0.6 as base values from previous calibration efforts.

parameter on simulated potential T demand with subsequent impacts on water stress factors (eqs. 6 and 7). SKc also influenced changes in E and T in an inversely proportional manner (figs. 6f and 6h), but it had much less impact on the overall ETc (fig. 6d). Similar to Kcbmax, this result has major implications for the adjustment of SKc to calibrate the

DSSAT-CSM ETc simulation, particularly when separate E and T data are not available, because SKc adjustments affects ETc to a much lesser degree than E and T simulations individually. While SKc provides a parameter to adjust the portions of ETc attributed to E and T, calibrating SKc to ETc alone does not guarantee accurate simulations of E and T individ-ually. If E and T data are unavailable, values of SKc from 0.5 to 0.7 are recommended. While total ETc data are much easier to obtain than partitioned E and T, the results highlighted the robustness gained by using dual crop coefficient procedures to partition E and T as compared to single crop coefficient approaches (figs. 2 and 3). Therefore, dual crop coefficient procedures combined with crop growth simulation is advantageous for in-depth analyses of crop water use efficiency and water production functions.

Discussion

Current potential ET methods in DSSAT-CSM include the Priestley-Taylor (Priestley and Taylor, 1972) and ETpm-Kcs approaches. The Priestley-Taylor method (which was not tested herein) is advantageous for simulations requiring long-term weather data in areas with limited meteorological stations because it requires only minimum and maximum air temperature and solar radiation and does not require humidity and wind speed data. However, the Priestley-Taylor method is subject to substantial underestimation under advective conditions often experienced in the western U.S. (Jensen and Allen, 2016). Furthermore, most modern meteorological stations in developed countries include all of the required inputs for the ASCE Standardized Reference ET Equation (Allen et al., 2005), i.e., air temperature, humidity, solar radiation, and wind speed. The capabilities of modern cropping system models should reflect the capabilities of meteorological data collection systems. The inclusion of both grass and alfalfa reference ET calculations based explicitly on the ASCE standard (Allen et al., 2005) is a strong step forward for ET simulation in DSSAT-CSM.

The current ETpm-Kcs approach in DSSAT-CSM does not follow established ET standards in two main ways. First, it approximately calculates ETo (fig. 1), but it uses older Penman-Monteith equation settings (eq. A1), explicitly calculates resistance terms from grass reference crop characteristics, uses a non-standard wind speed adjustment equation (eq. 9) with known errors in DSSAT v4.5, and does not incorporate an alfalfa reference ET calculation. All of these problems were updated and resolved by adding the ASCE Standardized Reference ET algorithm (eq. A2; Allen et al., 2005) to DSSAT-CSM. Second, the crop coefficient approach in the ETpm-Kcs method does not truly follow FAO-56 protocol, even though the method has historically been named “FAO-56” in the model. As described herein, an FAO-56 dual crop coefficient (Kcb) approach was implemented to scale reference ET to potential ET and to partition potential E and T, while native DSSAT-CSM algorithms were used to calculate actual E and T based on available soil water and root system growth. According to ASCE Manual 70 (Jensen and Allen, 2016), this reference ET and crop coefficient method (i.e., ETo-Kcb, ETr-Kcb) has more consistent and standardized procedures than the direct resistance-based Penman-Monteith equation (eq. A1) and is more appropriately applicable under water-stressed conditions.

Both the ETo-Kcs and the ETo-Kcd methods have issues in model behavior with respect to the FAO-56 conceptualization of ET. The former has limitations on its maximum Kc value and is not responsive to mid-season evaporation spikes, while the latter has more dynamic mid-season transpiration behavior but is unresponsive to evaporation spikes throughout the season. The new ETo-Kcb method is a valuable addition that not only follows standardized procedures but also solves the behavioral issues of the prior approaches. The mid-season growth stage, with full canopy, the highest crop coefficients, longer length, and typically the highest evaporative demand (i.e., ETo), may be considered the most significant growth stage in terms of seasonal ETc, so the accuracy of this stage is most important. For the mid-season transpiration portion, the ETo-Kcs method for maize had the limitation of Kcs = 1.0 (fig. 2a) and for cotton was defined very close to 1.0 (fig. 3a). Because the transpiration demand is partitioned from the maximum value, the Ke had a defined concave shape. The ETo-Kcd method had a dynamic overall Kc shape that was not limited to a maximum value like the ETo-Kcs method, yet the Ke during midseason has a very similar shape and nearly identical evaporative portion. The similarities between these methods exist because they use the same partitioning algorithm that first calculates potential ETc and then separates it into E and T components. However, one major issue with this method is that the mid-season crop coefficients are not responsive to evaporative spikes during full or nearly full canopy growth, from DOY 190 to DOY 260 for both crops (figs. 2 and 3). While these evaporative spikes for ETo-Kcb are small during this growth stage, they have been verified through studies using water balance methods (da Silva et al., 2012), lysimetry (López-Urrea et al., 2012), energy balance (Anderson et al., 2017), and isotope tracing (Nay-Htoon, 2016); thus, they should be properly simulated by cropping system models. The new ETo-Kcb method is very responsive to frequent irrigations, with both the evaporation and resulting ET being highly dynamic (figs. 2c and 3c) and more similar to theoretical representations in FAO-56.

Sensitivity of yield, ETc, E, and T to Kcbmax and SKc (fig. 6) is now available for users and will provide guidance for parameterization. Future studies should use reliable E and T measurements to fully evaluate the ETo-Kcb method and further compare it to other DSSAT-CSM ET methods. Such a study would provide further guidance on recommended parameterization for Kcbmax and SKc. However, the new method facilitates use of the tabular values in FAO-56 and other subsequent references (Allen et al., 1998, 2007; Jensen and Allen, 2016) for initial parameterization of Kcbmax.

Criticisms of the new ETo-Kcb method have largely focused on the empiricisms inherent to the FAO-56 dual Kc approach, which prevent dynamic calculations of aerodynamic and bulk resistance terms in the Penman-Monteith equation as well as calculations of more complex biophysical relationships between crop growth and water use. However, the most commonly used ET methods in DSSAT-CSM, including Priestley-Taylor and ETpm-Kcs, also suffer from these limitations. Other ET methods that have a stronger biophysical basis are available in DSSAT-CSM, but they are rarely used due to languished development and lack of resources for thorough testing. By adding the new ETo-Kcb option based on accepted ET standards, a benchmark ET routine was established in DSSAT-CSM that can be used as a baseline to evaluate and develop any other ET method. As demonstrated herein, the ETo-Kcb standard method was useful for diagnosis of deficiencies in other DSSAT-CSM ET methods. When unexpected model behavior was encountered in both present and past studies (DeJonge et al., 2012a; Thorp et al., 2014), the issues were more thoroughly understood and resolved by incorporating standardized ET equations into the model and comparing model outputs from existing ET methods to the standard methods. By establishing a performance benchmark, the standard methods highlighted aspects of other ET methods that were not sensible (e.g., figs. 1 and 4). Thus, although the ET standards are somewhat less mechanistic than an ideal ET method that dynamically calculates resistance terms, stomatal conductance effects, and other biophysical intricacies, they are valuable for setting a baseline performance benchmark that any other ET method should at least meet, if not exceed. Likewise, the standard ET methods could similarly be useful in the development of novel ET approaches that aim to establish better mechanistic linkages among simulations of crop biology, soil water conditions, and ET. In this case, the standard ET methods again set the performance benchmark that the new method should aim to improve upon; otherwise, they offer little above what is embodied in the current ET standards. Essentially, the ET standards provide an unbiased, well-accepted protocol for calculating ET, which can shield crop model development from modeler bias and opinion. Statements on the appropriateness of an ET method for use in a crop model have greater scientific foundation when the ET method of question is shown to match or exceed the behavior and performance of the existing ET standard, for example, via daily crop coefficient plots (figs. 2 and 3) or by direct comparison to measured ET data. While the present study did not include comparisons to measurements, future studies are planned to further compare DSSAT-CSM ET methods using high-quality ET data sets.

Summary

The evapotranspiration module in DSSAT-CSM was revised to incorporate standardized ET procedures. This included explicitly following the ASCE Standardized Reference Evapotranspiration Equation (Allen et al., 2005) for tall and short reference ET (ETr and ETo, respectively) and explicitly following FAO-56 guidelines for the dual crop coefficient method. With these changes, the reference ET results matched almost exactly with another software package for standardized ET calculations. The new module resulted in more responsive crop coefficients, where the basal transpiration portion was directly linked to canopy cover via LAI, and the evaporation component was responsive to irrigation and rainfall events throughout the season. Newly added parameters need not be extensively calibrated, as they have referenced values and ranges, but a sensitivity analysis showed how they affect simulated yield and both E and T components of ETc. These new methods are an essential step forward for irrigation and ET modelers who use DSSAT-CSM for ET quantification and irrigation management under limited water conditions. In addition, this research demonstrates the use of FAO-56 concepts and existing ET standards to compare and contrast the ET outputs of different ET methods in crop models. The approach has great potential for applicability not only to DSSAT-CSM but also to other crop models, and it can provide a basis for intercomparison of ET methods both within and among crop models for model improvement purposes.

Acknowledgements

The authors thank the DSSAT Foundation and Dr. Gerrit Hoogenboom for sponsoring their attendance at a 2014 DSSAT Development Sprint, where the ideas for this study were born. Cotton Incorporated is acknowledged for partial support of cotton simulation modeling activities in Arizona. The authors also thank Dr. Rick Allen for his feedback, clarification, and suggestions on basal crop coefficient theory and behavior, and Dr. Kenneth Boote for his feedback and suggestions on implementation of ET methods in the DSSAT-CSM. Both of the authors contributed equally to this work.

Appendix

As documented in FAO Irrigation and Drainage Paper No. 56 (Allen et al., 1998), the Penman-Monteith combination equation was adopted as a basis to standardize calculations of crop ET:

(A1)

where latent heat flux (?ET), net radiation (Rn) and soil heat flux (G) are in W m-2, air density (?a) is in kg m-3, specific heat of dry air (cp) is 1,010 J kg-1 °C-1, saturation vapor pressure (es) and actual vapor pressure (ea) are in kPa, ra is aerodynamic resistance in s m-2, rs is the bulk surface resistance in s m-1, and the slope of the saturation vapor pressure versus temperature curve (?) and the psychrometric constant (?) are in kPa °C-1. The Penman-Monteith combination equation incorporates parameters that can be measured or calculated from weather data, and FAO-56 provided equations for calculations of ra and rs from wind measurement characteristics, canopy height, and leaf area index (LAI). Furthermore, FAO-56 demonstrated the simplification of terms in equation A1 as required for ET calculations from a hypothetical grass reference crop (ETo) with height of 0.12 m, surface resistance of 70 s m-1, and albedo of 0.23.

In May 1999, the Irrigation Association (IA) requested that the Evapotranspiration in Irrigation and Hydrology Committee of the ASCE Environmental and Water Resources Institute establish and define a benchmark reference ET equation. The purpose of this equation was to standardize the calculation of reference evapotranspiration and to improve transferability of crop coefficients across regions. Standardized versions of the Penman-Monteith equation were created by the ASCE-EWRI (Allen et al., 2005) to calculate reference ET for both a short crop (ETo) and a tall crop (ETr) following the format adopted by FAO-56. When the supporting parameter equations for ra, ?a, and ? from the Penman-Monteith combination equation (eq. A1) are reduced and combined, the daily time step, FAO-styled, and reduced equation of ASCE-EWRI results:

(A2)

where ETref applies to both clipped grass and alfalfa reference surfaces. ETref has units of mm d-1 for 24 h time steps, net radiation (Rn) and soil heat flux (G) are in MJ m-2 d-1, mean daily air temperature (T) is in °C, mean daily wind speed at 2 m height (u2) is in m s-1, saturation vapor pressure (es) and actual vapor pressure (ea) are in kPa, the slope of the saturation vapor pressure versus temperature curve (?) and the psychrometric constant (?) are in kPa °C-1, and Cn and Cd are coefficients that change with reference type (grass ETo or alfalfa ETr). For a short reference crop, Cn = 900 and C= 0.34; for a tall reference crop, Cn = 1600 and Cd = 0.38. Further details on these coefficients are available in Allen et al. (2005). This form of the equation, at a minimum, requires meteorological inputs of daily minimum and maximum air temperature, minimum and maximum relative humidity or vapor pressure deficit, solar irradiance, and average wind speed. These measurements are common on most modern micrometeorological stations for microclimate monitoring and ET prediction, and Allen et al. (2005) gave recommendations for estimating missing climatic data when necessary. Both short and tall reference surfaces are adopted worldwide as ET standards, and the preference of short or tall reference surfaces often varies by country or state.

The single crop coefficient approach was introduced in FAO-24 (Doorenbos and Pruitt, 1977) and explained further in FAO-56 and ASCE Manual 70 (Jensen and Allen, 2016), which describes the calculation of crop evapotranspiration (ETc, the sum of soil evaporation E and plant transpiration T) under well-watered optimal agronomic conditions (i.e., no limitations due to water stress, salinity stress, pest and disease, weeds, fertility, etc.). In other words, the approach calculates potential ET for a given crop at a particular stage of growth by scaling reference ET (ETr, or ETo in this case) with a single crop coefficient (Kc):

ETc = E + T = KcETo (A3)

FAO-56 characterizes seasonal daily crop coefficient (Kc) curves using a trapezoidal shape that resembles crop canopy growth over time, often based on days after planting or growing degree days. Recommended Kc varies by crop and by region; for most agronomic crops, Kc has an initial or minimum value between 0.3 and 0.5 and a maximum value between 1.0 and 1.2 (see fig. 34 in FAO-56; Allen et al., 1998). FAO-56 also describes a basal crop coefficient approach in which Kc is divided into evaporation (Ke) and transpiration (Kcb) components, and Ks is the water stress coefficient:

(A4)

where Ks = 1 indicates no stress and Ks = 0 indicates maximum stress and complete transpiration shutdown.

This method has the distinct advantage of separating plant water use from surface (soil) water evaporation losses, as well as reducing ET when the canopy experiences water stress or other stressors (see fig. 10-1 in Jensen and Allen, 2016). This dual approach improves the accuracy of the overall ET estimate by separating E and T and improving the accuracy of the E estimate (Pereira et al., 2015). Proper partitioning of E and T is important not only for water management purposes (Kool et al., 2014) but also for yield estimation, as yield is physiologically linked more closely to T than to the combination of E and T (Paredes et al., 2014; Steduto et al., 2012). Kcb typically has a trapezoidal shape similar to Kc and is described for non-stressed crops in FAO-56. Kcb also can be related to reduced canopy cover due to prior stresses, a potential indirect and delayed result of limited soil water (fig. 10-1 in Jensen and Allen, 2016). The evaporation component (Ke) is calculated through several steps:

Ke = min[Kr(KcmaxKcb), fewKcmax] (A5)

where Ke is the soil evaporation coefficient, Kcb is the basal crop coefficient, Kcmax is the maximum value of Kc following rain or irrigation, Kr is a dimensionless evaporation reduction coefficient dependent on the cumulative depth of water evaporated from the topsoil, and few is the fraction of the soil surface that is both exposed and wetted (i.e., the fraction of soil surface from which most evaporation occurs). Following rain or irrigation Kr is 1, and evaporation is only determined by the energy available for evaporation. As the soil surface dries, Kr becomes less than 1, and evaporation is reduced. Kr becomes 0 when no water is left for evaporation from the upper soil layer. Complete details for calculating Kr are in FAO-56 and ASCE Manual 70. The upper limit (Kcmax) is determined for grass reference (ETo) and alfalfa reference (ETr) by equations A6 and A7, respectively:

Kcmaxo =

(A6)

Kcmaxr = max(1.0, Kcb + 0.05) (A7)

where h is the mean maximum plant height during the period of calculation (m), and all other terms are previously defined. The fraction of evaporable water (few) is calculated as:

few = min(1 - fc, fw) (A8)

where 1 - fc is the average exposed soil fraction not covered (or shaded) by vegetation (0.01 to 1), and fw is the average fraction of soil surface wetted by irrigation or precipitation (0.01 to 1). Values for fw are 1.0 for precipitation and certain types of irrigation (i.e., sprinkler and flood irrigation) but are lower for other types of irrigation (i.e., furrow or drip irrigation). Values for fc can be determined by methods used to estimate canopy cover or can be estimated using the relationship described in FAO-56:

(A9)

where Kcb is the basal crop coefficient for the particular day, Kcmin is the minimum Kc for dry bare soil with no ground cover, and Kcmax is the maximum Kc immediately following wetting (eq. A6).

References

Allen, R. G. (2011). Ref-ET: Reference evapotranspiration calculation software for FAO and ASCE standardized equations. Moscow, ID: University of Idaho.

Allen, R. G., Pereira, L. S., Raes, D., & Smith, M. (1998). Crop evapotranspiration: Guidelines for computing crop water requirements FAO Irrigation and Drainage Paper No. 56. Rome, Italy: United Nations FAO.

Allen, R. G., Walter, I. A., Elliott, R., Howell, T., Itenfisu, D., & Jensen, M. (Eds.) (2005). The ASCE standardized reference evapotranspiration equation. Final report. Reston, VA: ASCE Environmental and Water Resources Institute.

Allen, R. G., Wright, J. L., Pruitt, W. O., Pereira, L. S., & Jensen, M. E. (2007). Chapter 8: Water requirements. In G. J. Hoffman, R. G. Evans, M. E. Jensen, D. L. Martin, & R. L. Elliot (Eds.), Design and operation of farm irrigation systems (2nd ed.) (pp. 208-288). St. Joseph, MI: ASABE. https://doi.org/10.13031/2013.23691

Anderson, R. G., Alfieri, J. G., Tirado-Corbala, R., Gartung, J., McKee, L. G., Prueger, J. H., ... Kustas, W. P. (2017). Assessing FAO-56 dual crop coefficients using eddy covariance flux partitioning. Agric. Water Mgmt., 179, 92-102. https://doi.org/10.1016/j.agwat.2016.07.027

Boote, K. J., Jones, J. W., & Pickering, N. B. (1996). Potential uses and limitations of crop models. Agron. J.,88(5), 704-716

da Silva, V. D., Borges, C. J., Farias, C. H., Singh, V. P., Albuquerque, W. G., & da Silva, B. B. (2012). Water requirements and single and dual crop coefficients of sugarcane grown in a tropical region, Brazil. Agric. Sci., 3(2), 13. https://doi.org/10.4236/as.2012.32032

DeJonge, K. C., Andales, A. A., Ascough, J. C., & Hansen, N. (2011). Modeling of full and limited irrigation scenarios for corn in a semiarid environment. Trans. ASABE, 54(2), 481-492. https://doi.org/10.13031/2013.36451

DeJonge, K. C., Ascough, J. C., Ahmadi, M., Andales, A. A., & Arabi, M. (2012b). Global sensitivity and uncertainty analysis of a dynamic agroecosystem model under different irrigation treatments. Ecol. Model., 231, 113-125. https://doi.org/10.1016/j.ecolmodel.2012.01.024

DeJonge, K. C., Ascough, J. C., Andales, A. A., Hansen, N. C., Garcia, L. A., & Arabi, M. (2012a). Improving evapotranspiration simulations in the CERES-Maize model under limited irrigation. Agric. Water Mgmt., 115, 92-103. https://doi.org/10.1016/j.agwat.2012.08.013

Doorenbos, J., & Kassam, A. K. (1979). Yield response to water. Irrigation and Drainage Paper No. 33. Rome, Italy: United Nations FAO.

Doorenbos, J., & Pruitt, W. O. (1977). Crop water requirements. Irrigation and Drainage Paper No. 24. Rome, Italy: United Nations FAO.

Evett, S. R., Howell, T. A., Schneider, A. D., Copeland, K. S., Dusek, D. A., Brauer, D. K., ... Gowda, P. H. (2016). The Bushland weighing lysimeters: A quarter century of crop ET investigations to advance sustainable irrigation. Trans. ASABE, 59(1), 163-179. https://doi.org/10.13031/trans.59.11159

Hoogenboom, G., Jones, J. W., Wilkens, P. W., Porter, C. H., Batchelor, W. D., Hunt, L. A., ... Bowen, W. T. (2004). Decision Support System for Agrotechnology Transfer. Ver. 4.0. Honolulu, HI: University of Hawaii.

Hunsaker, D. J., French, A. N., Waller, P. M., Bautista, E., Thorp, K. R., Bronson, K. F., & Andrade-Sanchez, P. (2015). Comparison of traditional and ET-based irrigation scheduling of surface-irrigated cotton in the arid southwestern USA. Agric. Water Mgmt., 159, 209-224. https://doi.org/10.1016/j.agwat.2015.06.016

Jensen, M. E., & Allen, R. G. (2016). Evaporation, evapotranspiration, and irrigation water requirements. Manual 70. Reston, VA: ASCE.

Jones, J. W., Hoogenboom, G., Porter, C. H., Boote, K. J., Batchelor, W. D., Hunt, L. A., ... Ritchie, J. T. (2003). The DSSAT cropping system model. European J. Agron., 18(3-4), 235-265. https://doi.org/10.1016/S1161-0301(02)00107-7

Kimball, B. A., Boote, K. J., Hatfield, J. L., Ahuja, L. R., Stockle, C. O., Archontoulis, S. V., & Twine, T. (2016). Prediction of evapotranspiration and yields in maize: An intercomparison among 29 maize models. Proc. ASA-CSSA-SSSA Intl. Annual Meeting. Madison, WI: ASA-CSSA-SSSA.

Kool, D., Agam, N., Lazarovitch, N., Heitman, J. L., Sauer, T. J., & Ben-Gal, A. (2014). A review of approaches for evapotranspiration partitioning. Agric. Forest Meteorol., 184, 56-70. https://doi.org/10.1016/j.agrformet.2013.09.003

Lopez-Urrea, R., Montoro, A., Manas, F., Lopez-Fuster, P., & Fereres, E. (2012). Evapotranspiration and crop coefficients from lysimeter measurements of mature Tempranillo wine grapes. Agric. Water Mgmt., 112, 13-20. https://doi.org/10.1016/j.agwat.2012.05.009

Nay-Htoon, B. (2016). Water use efficiency of rainfed and paddy rice ecosystem: Disentangling agronomic and ecosystem water use of rice. PhD diss. Bayreuth, Germany: University of Bayreuth.

Paredes, P., Rodrigues, G. C., Alves, I., & Pereira, L. S. (2014). Partitioning evapotranspiration, yield prediction, and economic returns of maize under various irrigation management strategies. Agric. Water Mgmt., 135, 27-39. https://doi.org/10.1016/j.agwat.2013.12.010

Pereira, L. S., Allen, R. G., Smith, M., & Raes, D. (2015). Crop evapotranspiration estimation with FAO-56: Past and future. Agric. Water Mgmt., 147, 4-20. https://doi.org/10.1016/j.agwat.2014.07.031

Phogat, V., Simunek, J., Skewes, M. A., Cox, J. W., & McCarthy, M. G. (2016). Improving the estimation of evaporation by the FAO-56 dual crop coefficient approach under subsurface drip irrigation. Agric. Water Mgmt., 178, 189-200. https://doi.org/10.1016/j.agwat.2016.09.022

Priestley, C. H., & Taylor, R. J. (1972). On the assessment of surface heat flux and evaporation using large-scale parameters. Monthly Weather Rev., 100(2), 81-92. https://doi.org/10.1175/1520-0493(1972)100<0081:otaosh>2.3.co;2

Ritchie, J. T. (1972). Model for predicting evaporation from a row crop with incomplete cover. Water Resour. Res., 8(5), 1204-1213. https://doi.org/10.1029/WR008i005p01204

Ritchie, J. T. (1985). A user-orientated model of the soil water balance in wheat. In W. Day, & R. K. Atkin (Eds.), Wheat growth and modelling (pp. 293-305). New York, NY: Plenum Press. https://doi.org/10.1007/978-1-4899-3665-3_27

Ritchie, J. T. (1998). Soil water balance and plant water stress. In G. Y. Tsuji, G. Hoogenboom, & P. K. Thornton (Eds.), Understanding options for agricultural production (pp. 41-54). Dordrecht, The Netherlands: Kluwer Academic. https://doi.org/10.1007/978-94-017-3624-4_3

Ritchie, J. T., Porter, C. H., Judge, J., Jones, J. W., & Suleiman, A. A. (2009). Extension of an existing model for soil water evaporation and redistribution under high water content conditions. SSSA J., 73(3), 792-801. https://doi.org/10.2136/sssaj2007.0325

Sau, F., Boote, K. J., Bostick, W. M., Jones, J. W., & Minguez, M. I. (2004). Testing and improving evapotranspiration and soil water balance of the DSSAT crop models. Agron. J., 96(5), 1243-1257.

Steduto, P., Hsiao, T. C., Fereres, E., & Raes, D. (2012). Crop yield response to water. FAO Irrigation and Drainage Paper No. 66. Rome, Italy: United Nationa FAO.

Thorp, K. R., Barnes, E. M., Hunsaker, D. J., Kimball, B. A., White, J. W., Nazareth, V. J., & Hoogenboom, G. (2014). Evaluation of CSM-CROPGRO-Cotton for simulating effects of management and climate change on cotton growth and evapotranspiration in an arid environment. Trans. ASABE, 57(6), 1627-1642. https://doi.org/10.13031/trans.57.10612

Thorp, K. R., Hunsaker, D. J., Bronson, K. F., Andrade-Sanchez, P., & Barnes, E. M. (2017). Cotton irrigation scheduling using a crop growth model and FAO-56 methods: Field and simulation studies. Trans. ASABE, 60(6), 2023-2039. https://doi.org/10.13031/trans.12323

Thorp, K. R., Hunsaker, D. J., French, A. N., Bautista, E., & Bronson, K. F. (2015). Integrating geospatial data and cropping system simulation within a geographic information system to analyze spatial seed cotton yield, water use, and irrigation requirements. Precision Agric., 16(5), 532-557. https://doi.org/10.1007/s11119-015-9393-x

Thorp, K. R., Hunsaker, D. J., French, A. N., White, J. W., Clarke, T. R., & Pinter Jr, P. J. (2010). Evaluation of the CSM-CROPSIM-CERES-Wheat model as a tool for crop water management. Trans. ASABE, 53(1), 87-102. https://doi.org/10.13031/2013.29505

Trout, T. J., & DeJonge, K. C. (2017). Water productivity of maize in the U.S. high plains. Irrig. Sci., 35(3), 251-266. https://doi.org/10.1007/s00271-017-0540-1