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Field Crops Research 204 (2017) 180–190

Contents lists available at ScienceDirect

Field Crops Research

jou rn al hom ep age: www.elsev ier .com/ locate / fc r

mprovements to the Hybrid-Maize model for simulating maize yieldsn harsh rainfed environments

aishun Yang a,∗, Patricio Grassini a, Kenneth G. Cassman a, Robert M. Aiken b,atrick I. Coyne c

Department of Agronomy and Horticulture, University of Nebraska – Lincoln, P.O. Box 830915, Lincoln, NE 68583-0915, USAKansas State University Northwest Research-Extension Center, Colby, KS, USAKansas State University Agricultural Research Center, Hays, KS, USA

r t i c l e i n f o

rticle history:eceived 5 August 2016eceived in revised form 26 January 2017ccepted 27 January 2017

eywords:aize

rop modelater-limited yieldater deficit

roughtimulation

a b s t r a c t

This paper reports revisions in formulation and new features of the Hybrid-Maize model (released asHM2016), to better simulate yields in harsh rainfed environments. Revisions include updated subrou-tines for root growth and distribution within the soil profile, greater sensitivity of canopy expansion andsenescence to water deficits, an expanded kernel setting period, and soil evaporation as influenced bysurface cover with crop residues. The updated model also includes routines for simulating surface runoffand estimating soil water content at sowing based on simulation of soil water balance during the pre-ceding fallow period. Revisions of model functions were based on recent advances in understanding andquantification of maize response to environmental factors and management practices, as well as char-acteristics of new maize hybrids. More robust simulation of maize yield was obtained with the updatedmodel under rainfed conditions, especially in years and locations with severe drought or on soils withlimited water holding capacity. Capability to quantify soil water content at sowing and to perform batch

simulations makes HM2016 more useful for pre-season yield projections in years with below-normalsoil water recharge and for in-season yield forecasting across a wide range of environments. Revisionsto routines governing root distribution and kernel setting make HM2016 a more powerful tool for eval-uating hybrid-specific traits and crop management practices for ability to mitigate yield loss from waterdeficits and for identifying management options for individual production fields.

© 2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC

. Introduction

Crop simulation models have been widely used in research, edu-ation, extension, and to inform policy making (Bouman et al., 1996;inclair and Seligman, 1996; Boote et al., 2010). While performancef crop models is generally more robust under non-water stressonditions with good management of nutrients and biotic stresses,odel performance for crops that experience water deficits (e.g., in

arsh rainfed systems with low and highly variable rainfall or soils

ith limited water holding capacity) has been less satisfactory (Ko

t al., 2006; McMaster et al., 2011; Mastrorilli et al., 2003). Poorodel performance has been attributed to relatively poor under-

Abbreviations: LAI, leaf area index; WSI, water stress index; DS, developmenttage; RGR, root growth rate (for depth); ET, evapotranspiration; ET0, grass-eferenced evapotranspiration.∗ Corresponding author.

E-mail address: hyang2@unl.edu (H. Yang).

ttp://dx.doi.org/10.1016/j.fcr.2017.01.019378-4290/© 2017 The Author(s). Published by Elsevier B.V. This is an open access articl.0/).

BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

standing and quantification of several key physiological processesthat govern crop responses to limited water supply (Sinclair andSeligman, 1996; Roth et al., 2013) and phenotypic differences innew cultivars, compared to older ones, that are not yet used inmodel development and calibration (Boote et al., 1996). For maize(Zea mays L.) simulation models, several processes related to cropgrowth and yield formation under water deficit conditions havebeen suggested for improving some models, including crop rootdistribution and water uptake from soil (Hammer et al., 2009), leafexpansion and senescence (Ben Nouna et al., 2000; Cakir, 2004;Yang et al., 2009), and kernel setting (Andrade et al., 1999, 2002;Lizaso et al., 2007). In addition, the effects of crop residues coveringthe soil surface in conservation tillage systems on soil evaporationand surface runoff also need to be accommodated to improve modelsimulation of soil water balance throughout the growing season (Bu

et al., 2013).

The Hybrid-Maize model (Yang et al., 2004, 2006;http://hybridmaize.unl.edu/) is a computer simulation modelfor maize under non-limiting (fully-irrigated) or water-limited

e under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/

Research 204 (2017) 180–190 181

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rainfed or partially irrigated) conditions based on daily weatherata. Specifically, it allows users to: (a) assess yield potentialnd its variability at a given location based on historical weatherecords, (b) evaluate changes in yield potential using differentombinations of sowing date, hybrid maturity and plant density,c) identify optimal timing and amount of irrigation applicationsor highest yield and irrigation water use efficiency, and (d) maken-season yield forecasts based on real-time weather up to theurrent date and a probability distribution of final yield basedn historical weather records for the remainder of the growingeason. The Hybrid-Maize model does not account for yield lossesue to suboptimal nutrient management or from weeds, insectsnd pests, diseases, lodging, and other stresses.

The Hybrid-Maize model combines the strength of twoaize simulation approaches represented by Wageningen models,

ncluding WOFOST (Van Diepen et al., 1989) and INTERCOM (Kropffnd van Laar, 1993; Lindquist, 2001), and by the CERES-Maizeodel (Jones and Kiniry, 1986; Kiniry et al., 1997). The previous

ersions of the Hybrid-Maize were developed in 2004 (Yang et al.,004) and 2006 (Yang et al., 2006). Since then, research has led to

mproved understanding and quantification of crop growth pro-esses and responses to water deficit, and maize breeders haveontinued to improve drought tolerance and other traits of maizeybrids. These advances have not yet been incorporated into theybrid-Maize model to improve its robustness and applicabilitycross diverse environmental and management conditions.

Earlier versions of Hybrid-Maize have been used to assess maizeield potential and yield gaps (Van Wart et al., 2013; Farmaha et al.,016; van Ittersum et al., 2016), evaluate management optionsChen et al., 2011; Grassini et al., 2011a; Witt et al., 2006; Mengt al., 2013), the impact of climate change (Cassman et al., 2010;hen et al., 2013; Lobell et al., 2009; Meng et al., 2014), waterroductivity (Grassini et al., 2009, 2011b), yield and production

orecasting (Sibley et al., 2014; Morell et al., 2016), and nutri-nt management (Meng et al., 2012; Setiyono et al., 2011) acrossiverse maize systems and mostly favorable production envi-onments worldwide. Feedback about performance under severeater deficit, however, indicated room for model improvement.

ikewise, evolution of computer operating systems, software andardware continue to provide opportunities to improve function-lity of application software like Hybrid-Maize. As developers ofhe original Hybrid-Maize model, we also received feedback fromsers about opportunities for adding new model features and appli-ations, all of which provided motivation for revision of the model.

Specific objectives of this paper are to: (1) document revisions tohe Hybrid-Maize model as now included in HM2016, as comparedo the 2006 version (HM2006), with regard to root distribution,anopy expansion and senescence in response to crop water deficit,ernel setting, surface runoff, soil evaporation and crop transpira-ion, estimation of soil water content at sowing based on simulationf water balance during the fallow period, and a new batch run func-ion, and (2) evaluate the ability of the revised model to reproduce

wide range of measured maize yields from well-managed fieldtudies under rainfed and irrigated conditions. Description of theodel and a detailed user’s guide describing all model functions

nd underpinning equations can be found at www.hybridmaize.nl.edu.

. Revisions of model functions

.1. Root growth and soil profile distribution

In HM2006, root length distribution by soil depth largely fol-owed the CERES-Maize approach (Jones and Kiniry, 1986). Inssence, rooting depth progresses following growing degree days

Fig 1. Schematic representation of root length distribution in HM2016 and HM2006.

(GDD) accumulation and reaches the user specified maximumdepth at development stage (DS) 1.15. The rooting length distri-bution is V-shaped with the tip at the maximum rooting depth(Fig. 1). However, some studies have reported that roots of newmaize hybrids can reach 150 cm or more in soils without constraintsto root growth (Dardanelli et al., 1997; Djaman and Irmak, 2012;Tolk et al., 2016), and the effective lateral root length distribution ismore cylindrical in the upper rooting zone (0–30 cm) followed bya conical shape at lower depths (Hammer et al., 2009) (Fig. 1). Thissuggests that, given the same soil depth, the soil volume from whichthe maize root system acquires water (and nutrients) is greater thansimulated in HM 2006. In the revised routine of HM2016, maximumrooting depth still occurs at DS 1.15 (typically 5–7 days after silk-ing), but the increase of rooting depth (Depthroot) from emergenceto DS = 1.15 is simulated as a function of growing-degree days (GDD,Tbase = 10 ◦C) as follows:

ifDepthroot< Depthmax, thenDepthroot = sumGDD10 ∗ RGR

else, Depthroot = Depthmax

in which Depthmax is the user-specified maximum soil rootingdepth, sumGDD10 is the sum of growing degree days from ger-mination to a particular date, and RGR is the root growth rate (cmper GDD). RGR is calculated as potential hybrid rooting depth (oneof the hybrid-specific parameters that can be modified by the userand different from Depthmax) divided by sumGDD10 to DS 1.15.In general, root growth of most crops decreases substantially orceases at onset of rapid dry matter accumulation in reproductivestructures (Borg and Grimes, 1986). Although there are few data ongenotypic differences in potential rooting depth of modern hybrids,we expect most commercial hybrids can extract water from 1.5 mdepth which is the default setting for the hybrid-specific potentialrooting depth in HM2016. We do not recommend that users modifythis default value unless they have strong evidence that the hybridthey simulate has a deeper or shallower potential rooting depth.In contrast, Depthmax represents the depth of soil without phys-ical or chemical restrictions to root growth. Users should reducethe default value for simulations on soils with restrictions to root

growth at a shallower depth due to hard pans, bedrock, caliche,sand lens, soil toxicity, salinity, or acidity. For example, if there is ahard pan at 75 cm depth that roots do not penetrate, then Depthmax

should be set at 75 cm.

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During early growth when rooting depth is ≤30 cm, root lengthistribution is assumed to a be V shaped as described as Jones andiniry (1986):

Uweightabsolute = exp[−VDC ∗ Depthlayer/Depthroot]

Uweightrelative = WUweightabsolute/∑

WUweightabsolute

here WUweightabsolute and WUweightrelative are the absolute andelative water uptake weight of the layer, respectively, Depthlayers the depth of the layer (to its lower end), Depthroot is the currentooting depth, and VDC is the vertical distribution coefficient thatetermines the shape of the exponential function. The greater theDC, the greater the WUweight for upper layers. The default valuef VDC is set at 3.

As roots grow deeper (>30 cm), roots in the upper soil layerill likely cross into space occupied by neighboring roots, and

s a result, the effective extraction zone for individual plants willecome a cylindrical on top and a V shape underneath, similar tohe semicircular root profiles evaluated by Hammer et al. (2009).ield observations by Dwyer et al. (1988) also support this proposi-ion. It is assumed that this situation occurs when roots are deeperhan 30 cm and the relative water uptake weight of the top threeayers becomes equal:

Uweight1absolute = WUweight2

absolute = WUweight3absolute

Uweightrelative = WUweightabsolute/∑

WUweightabsolute

n which superscript 1, 2 and 3 denote layers 1, 2 and 3 with a depthf 10 cm for each layer.

.2. Impact of water deficit on canopy expansion and senescence

In Hybrid-Maize, daily crop water stress index (WSI) is defineds WSI = (1–Tranpactual/Transpmax), where Tranpactual is the actualaily crop transpiration rate, and Transpmax is the maximum tran-piration if the crop is well watered. In HM2006, crop water deficitffects canopy expansion by reducing photosynthesis and, hence,et assimilation to sustain leaf area expansion. Keating et al. (2003)uggest a greater reduction in canopy expansion rate due to theirect (i.e., other than mediated through carbon availability) impactf water deficit on leaf area expansion than currently used inM2006. Following Keating et al. (2003), daily leaf area expansion

PLAG) decreases linearly until WSI = 0.5 when leaf area expansioneases.

Canopy expansion stops at silking and senescence begins there-fter, although some leaf area senescence can occur earlier due togeing and light competition (Jones and Kiniry, 1986; Lizaso et al.,003). In addition to the leaf senescence caused by leaf aging, shad-

ng, and heat stress, which were already accounted for by HM2006Yang et al., 2006), HM2016 includes an additional routine thatccelerates canopy senescence due to water deficit: at WSI of 1i.e., full stress), LAI will decrease by a fixed fraction of current LAIdefault = 3% per day, but this value can be modified by users) and

linear interpolation is used to estimate the fraction of senescedeaf area for WSI ranging from 1 to 0 (Saseendran et al., 2008).

.3. Kernel setting

Kernel setting determines the size of the sink for maize grain fill-ng (Kiniry et al., 1992; Yang et al., 2004). How much of this ‘sink’ is

ealized will depend on daily net photosynthesis during grain fill-ng, contribution of carbohydrate reserves to kernels when daily dry

atter production and carbon remobilization from stem does noteet the demand for grain filling, and duration of the grain filling

rch 204 (2017) 180–190

period. HM2006 used the total dry matter produced from silkingto the start of effective grain filling for estimation of kernel setting(Yang et al., 2004). More recent studies suggest a wider window oftime for kernel setting determination (Otegui et al., 1995; Andradeet al., 1999; Otegui and Andrade, 2000). Therefore, in HM2016, acurvilinear function was used to set the number of viable grains perplant (GPP) based on the average plant growth rate (PSKER) duringa critical kernel setting window of 340 GDD8 (base temperature of8 ◦C) centered on silking date:

PSKER = sumP/(1 + GRRG) ∗ 1000/IDURP ∗ 3.4/5

GPP = G2 − 676/(PSKER/1000)

in which sumP (g CH2O plant−1) is the cumulative net dry mat-ter adjusted for maintenance respiration of grain (GRRG; 0.49 gCH2O g−1), IDURP is the duration in days of the 340 of GDD8 period,PSKER is the average daily dry matter accumulation per plant(mg d−1) during this period, G2 is the potential number of grainsper plant, and the value of 676 is the maximum kernel number perplant averaged for common hybrids in North America (Jones andKiniry 1986; Yang et al., 2016). The threshold value of PSKER forgrain setting is 1000 mg d−1 plant−1, as found by Tollenaar et al.(1992) and Andrade et al. (1999, 2002), which is slightly greaterthan the threshold for grain setting used in HM2006 (Yang et al.,2004).

2.4. Surface runoff

Surface runoff occurs when rainfall intensity exceeds the waterinfiltration rate. Field slope, soil drainage class, and the amount ofcrop residues on the soil surface largely determine the amount ofsurface runoff (Littleboy et al., 1992; Niehoff et al., 2002). A new rou-tine was added to HM2016 that estimates water loss from runoff tobetter account for water infiltration to soil, especially in fields withsteep terrain, soils with slow infiltration rates and/or little residuecover. The routine follows the simplified approach of Soltani andSinclair (2012):

ifrain + irrigation < = 0.2 × S, thenRunoff = 0

else, Runoff = (rain + irrigation − 0.2 ∗ S)2/(rain

+ irrigation + 0.8 ∗ S)

in which S (in cm) is the retention parameter and is estimated as:

S = 25.4 ∗ (100/CNadj − 1)

CNadj = CN − min(soilCoverFrac ∗ 0.25, 0.2)

in which CN is the curve number for a particular combination ofslope and drainage class based on Ritchie (1998) and CNadj is theadjusted CN after accounting for the fraction of soil covered bycrop residues (soilCoverFrac), and min is the function that takesthe minimum of two values in the parentheses. This subroutine ismost relevant for fields with relatively uniform slope that are notinfluenced by run-on from neighboring fields. Pictures for differ-ent soil cover conditions, and associated soil cover fractions, can beaccessed through a button in the Hybrid-Maize model user inter-

face to aid determination of the residue cover condition at the timeof sowing or initiation of the simulation during the fallow periodbefore sowing. Seasonal reduction of soil surface coverage due toresidue decomposition is not taken into account by the model.

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.5. Crop transpiration and soil evaporation

Daily grass-referenced evapotranspiration (ET0) is one of theaily weather inputs required to run Hybrid-Maize (Allen et al.,998). If ET0 is not available in the weather data, the model contains

utility program, called WeatherAid, to calculate ET0 from solaradiation, maximum and minimum temperature, air humidity, andind speed using the FAO Penman-Monteith method (Allen et al.,

998). HM2006 used the method of Driessen and Konijn (1992)or estimation of actual crop ET. The revised version adopted the

ethod of Allen et al. (1998) for the estimation of crop ET, whichs largely based on Ritchie (1972). ET0 from the weather input data

ust first be adjusted to reflect ET of a well-watered maize fieldith LAI >4, which typically has greater ET than a well-watered

hort grass due to differences in canopy height and aerodynamicoughness (Connor et al., 2011). Based on Allen et al. (1998), thedjustment is:

fLAI <= 3.5, thenadjCoef = 1

lseadjCoef = 1 + (LAI − 3.5) ∗ (1.2 − 1)/(4.5–3.5)

fadjCoef > 1.2, thenadjCoef = 1.2

djET0 = ET0 ∗ adjCoef

n which adjET0 is the ETO adjusted for maize canopy, and theenominator (4.5–3.5) is the range of LAI when the adjustmenttarts at LAI of 3.5 to the end of the transition when the adjustmentecomes the largest at 1.2 at LAI of 4.5. Maximum transpirationTranspmax) is then estimated to account for canopy size (i.e., LAI):

ranspmax = adjET0 ∗ (1 − exp(−LAI ∗ k))

n which k is the light extinction coefficient (default = 0.55). Poten-ial evaporation (Evappot) is estimated as:

vappot = adjET0 − Transpmax

Maximum evaporation (Evapmax) is estimated by accounting forhe effect of soil coverage by crop residues (Rosenberg et al., 1983):

vapmax = Evappot∗exp(−soilCoverFrac)

n which soilCoverFrac is the fraction of soil surface that is coveredy crop residues.

Actual soil evaporation (Evapact) is estimated using the 2-stageethod in Allen et al. (1998). Soil evaporation is assumed to occur

n the top 10 cm soil depth, and actual evaporation rate will be ataximum (Evapmax) when soil is wet (i.e., Stage-1):

vapact = Evapmax

Actual evaporation rate will begin decreasing, and does soontinuously, when soil water content drops below a thresholdStage-2). This threshold (stage2EvapWater) is estimated followingllen et al. (1998):

vapWatermax = (soilFCtheta − 0.5 ∗ soilPWPtheta) ∗ 10

tep2EvapWater = step2threshold ∗ EvapWatermax

aterForEvap = (soilTheta − 0.5 ∗ soilPWPtheta) ∗ 10

vapact = Evapmax∗waterForEvap/step2EvapWater

n which EvapWatermax is the maximum amount of water that canvaporate, soilTheta, soilFCtheta and soilPWPtheta are the topsoil

rch 204 (2017) 180–190 183

volumetric water contents, topsoil field capacity, and topsoil per-manent wilting point (all three in fraction), respectively, 10 is thedepth (in cm) of the evaporating soil depth, and stage2threshold isa fraction of EvapWatermax typically ranging from 0.5 to 0.7 and isset at 0.7 as default in HM2016.

2.6. Estimation of soil water recharge during the fallow period

Soil water content at sowing is the starting point for tracking soilwater balance throughout the growing season. In HM2016, userscan choose to start the water balance simulation up to 11 monthsbefore sowing and let the model simulate the soil water balanceand soil water content during the fallow period up to sowing date(Fig. 2). The model simulates the water input from precipitation andlosses from runoff, soil evaporation, and deep percolation duringthe fallow period to estimate soil water content at sowing in theseason to be simulated. This method is more reliable in environ-ments where precipitation during the fallow period mainly occursas rainfall rather than snowfall and where soil water does not freezeduring wintertime, which can limit infiltration of melting snow atthe soil surface.

2.7. Other revisions

The new version of the Hybrid-Maize has a batch run functionthat uses an Excel spreadsheet template to allow input settings fora single simulation on individual rows in the spreadsheet. Instruc-tions are provided on how to provide the input data. Using thisbatch function, users can run in one batch as many simulationsas one Excel spreadsheet can hold (i.e., more than one million inExcel 2007) and simulation results are saved to the same Excelfile. Using functions such as copy and paste can make the pro-cess of setting up a large number of simulations very time efficient.The entire HM2016 software package, including its utility programWeatherAid, has been upgraded to be fully compatible with thecurrent windows operation system, including Windows 7–8.

HM2016 also includes a new function to account for crop killingby frost when daily minimum temperature reaches −2 ◦C or below.This function, however, does not initiate until 30 days after emer-gence as the maize plant is more tolerant to frost damage duringthe early vegetative growth (Carter, 1995; Nielsen and Christmas,2005).

3. Datasets used for validation

Two datasets were used to validate HM2016 and for compar-ison to the previous version of Hybrid-Maize (HM2006). Dataset1 consisted of 47 year-site combinations in which maize yieldwas measured in field studies that explicitly strived for optimalmanagement to avoid yield loss from nutrient deficiencies, weeds,insects and disease, and weather, crop management, and soil datawere available (Table 1). This dataset included irrigated and rain-fed maize fields located in four major US maize producing states,including Illinois (IL), Kansas (KS), Iowa (IA) and Nebraska (NE). Anadditional three site-year dataset measured seasonal dynamics ofLAI, total aboveground biomass, as well as final grain yield. Theywere used to evaluate the model’s capacity for dynamic simulationof LAI and aboveground biomass.

In irrigated fields, water was applied to avoid water deficits.Weather data for each site was collected from a nearby stationin the High Plains Regional Climate Center (http://www.hprcc.unl.edu/) or the Illinois Climate network (http://www.isws.illinois.edu/

). Required soil properties for each rainfed field, including soil tex-ture and rooting depth, were measured in-situ or obtained from theUSDA-NRCS database via http://casoilresource.lawr.ucdavis.edu/gmap/. Simulations were based on crop management information

184 H. Yang et al. / Field Crops Research 204 (2017) 180–190

Fig. 2. Input setting page of the HM2016 model with new features for estimating soil water at sowing and soil water balance as influenced by surface runoff and soilevaporation, which in turn are as influenced by crop residue cover, slope, and drainage.

Table 1Dataset 1 used for evaluation of HM2006 and HM2016 under rainfed and irrigated conditions.

Locationa Crop season RMb (days) n Yieldc (Mg ha−1) Plant density (m−2) Sources

IrrigatedBellwood, NE 2003 114 1 16.8 7.7 Wortmann et al. (2009)Brunswick, NE 2003 110d 1 17.4 8.6 Wortmann et al. (2009)Cairo, NE 2003 114 1 17.3 8.0 Wortmann et al. (2009)Clay Center, NE 2002, 2005, 2006 112–114 3 14.5–16.2 6.9–7.3 Wortmann et al. (2009), Yang

and Irmak. (unpublished data)Edgar, NE 2007 114 1 13.6 7.1 Irmak et al. (2012)Geneva, NE 2007 110 1 13.3 7.1 Irmak et al. (2012)Hordville, NE 2007 114 1 12.8 6.7 Irmak et al. (2012)Lincoln, NE 1999, 2000, 2001, 2002, 2003 113–114 11 14.8–17.9 7.0–11.0 Yang et al. (2004), Yang et al.

(2006), Wortmann et al. (2009)Mead, NE 2002, 2007 114–116 3 13–15.5 6.8–7.2 Wortmann et al. (2009), Irmak

et al. (2012)North Platte, NE 2005, 2006 112 2 13.3–14.2 7.1 Yang and Irmak (unpublished

data)Paxton, NE 2003 110d 1 16.2 7.9 Wortmann et al. (2009)Scandia, KS 2003 115d 2 14–15.7 6.9–10.4 Dobermann and Walters

(2004)York, NE 2007 113 1 14.9 6.9 Irmak et al. (2012)West Point, NE 2007 111 1 15 6.6 Irmak et al. (2012)

RainfedChampaign, IL 2003 112d 1 16.4 8d Dobermann and Walters

(2004)Clay Center, NE 2005, 2006, 2012 110–114 4 3.9–11.7 5.6–7.1 Yang and Irmak (unpublished

data), Irmak (unpublisheddata)

Manchester, IA 2002 114 1 16.0 8.4 Yang et al. (2004)Mead, NE 2001, 2003, 2005, 2009, 2011 111–113 5 7.7–12.0 5.0–6.1 Yang et al. (2006), Suyker and

Verma (2009), Suyker(unpublished data)

Mead, NE 2009, 2011, 2013 111 3 9.4–11.2 5.0–6.0 Arkebauer (2014, unpublished)North Platte, NE 1992, 1993, 1994,1995, 2005, 2006 108–115 6 0.6–13 7.1–7.9 Payero et al., 2006; Yang and

Irmak (unpublished data)

a Locations and corresponding USA state (IL: Illinois; IA: Iowa; KS: Kansas; NE: Nebraska).b Relative maturity.c Measured yields at standard water content of 15.5%.d estimated.

H. Yang et al. / Field Crops Resea

Table 2Summary of Dataset 2 of the 33 field-years rainfed maize during 2001–2009 at Colby,KS (39.38 N, −101.17 W). Hybrid maturity in total GDD to black layer (base temper-ature = 10 ◦C) was 1414 for years 2001–2002, 1483 for years 2003–2006, and 1406for years 2004–2009.

Minimum Mean Maximum SD1

Soil available water in 1.5 mdepth at sowing, mm

42 121 242 45

Total rainfall from sowing tosilking, mm

88 147 262 54

Total rainfall from silking tomaturity, mm

71 122 202 45

Total rainfall from sowing tomaturity, mm

199 263 376 63

Total water supply2, mm 264 390 571 80Maximum LAI 0.4 2.7 1.6 0.4Grain yield dry matter, Mg ha−1 0 2.24 8.31 2.5Total aboveground biomass,

Mg ha−10.46 5.72 12.42 3.2

Harvest index 0 0.26 0.72 0.22

1 standard deviation.

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deficit. In 2013, however, HM2016 simulated faster leaf area senes-

2 Sum of soil available water in 1.5 m depth at sowing and the total in-seasonainfall from sowing to maturity.

rom the sources in Table 1 or our best estimate when informationas missing. Among the 47 cases, 17 were rainfed while 30 were

rrigated. This assessment substantially expands the evaluation ofM2006 performed by Grassini et al. (2009).

Dataset 2 consisted of 33 rotation-year combinations of rainfedaize during 2001–2009 in Colby, KS (Table 2). Except for 2001,

ach year had four rotation treatments, each of these treatmentsad a different previous crop. Hence, each treatment had differentoil water content at sowing time. Crop management followed bestanagement recommendations for rainfed maize in that region.

xcept for crop sequence, crop management in each year was con-istent for the four treatments relative to choice of hybrid, sowingate, plant population, nutrient inputs, and crop protection. Theeld had uniform silt-loam soil texture without restrictions to rootrowth to 1.5 m depth. The top 30 cm soil depth had a field capac-ty (FC) of 36% volumetric water content (%v/v) and a permanent

ilting point (PWP) of 14%v/v, while the subsoil had FC and PWPf 33%v/v and 13%v/v, respectively. Soil water content at sowingas measured at 30 cm increments using a neutron probe. Dailyeather data were obtained from an on-site weather station. Crop

henology was based on semi-weekly observations, and maximumAI represented LAI around silking. Crop failure (i.e., zero yield in002 and 2003) and below normal rainfall in some years (e.g., only99 mm in 2006) highlights the severe water limitation some ofhese crops experienced. Hence, this database provides a rigorousest of the revised model in very harsh environments for rainfed

aize production.

. Sensitivity analysis

Sensitivity analysis was performed to evaluate how simulationesults change as a result of the five major revisions in HM2016as described above) compared to HM2006. We used grain yieldnd stover biomass as the target variables for the sensitivity analy-is. Because all five of the major revisions would have the greatestmpact under drought conditions, we used the 33 cases of Dataset 2or the sensitivity analysis, which include a number of observationsnder severe water limitation. Each of the five major revisions was

ncorporated into HM2006 without changing the rest of the rou-ines, and the revised program was subsequently run for the 33

ases of Dataset 2. The simulated grain yields and stover biomassere compared with the corresponding results of HM2006 and theagnitude of the changes relative to simulations with HM2006

rch 204 (2017) 180–190 185

were used to assess how the major revisions have contributed toimprove simulation results.

5. Statistical analysis

The comparison of simulated and measured values for yield andother simulated variables were based on the root mean square error(RMSE) and mean error (ME), which were computed as follows:

RMSE =√∑

(S − M)2

n

ME = 1n

∑(S − M)

In which S is the simulated result, M the measured result, n thenumber of total pairs of simulated and simulated data. In addition,linear regression analysis was performed to assess biases in therelationship between simulated and observed yields.

6. Results

6.1. Grain yield and total aboveground biomass

For the total of 50 site-year observations under rainfed con-ditions, with moderate to severe water limitation in most cases,HM2016 simulated yield significantly better than HM2006 (Fig. 3).The coefficient of determination (r2) between simulated and mea-sured yields increased from 0.89 for HM2006 to 0.94 for HM2016.Relative to measured yields, RMSE decreased from 2.5 Mg ha−1

(HM2006) to 1.2 Mg ha−1 (HM2016), while ME dropped from1.9 Mg ha−1 (HM2006) to 0.5 Mg ha−1 (HM2016). Moreover, theslope of the regression equation between simulated and mea-sured yields improved from 0.79 for HM2006 to 0.96 for HM2016,while the intercept dropped from 2.92 Mg ha−1 (HM2006) to0.71 Mg ha−1 (HM2016). For cases where severe water deficitscaused dramatic yield losses, e.g. most cases at Colby, KS and manyat North Platte NE, simulated yields by HM2016 were in much bet-ter agreement with measured values than with HM2006. For the33 cases of Dataset 2 for which measurements of harvest index(HI) were available, simulated HI from HM2016 agreed better thanHM2006 with measured values as indicated by large reductions inRSME and ME (Fig. 4). For irrigated fields, however, there was no sig-nificant difference between the two versions of the model (HM2006simulation results not shown) and simulated yields agreed wellwith observed values (Panel C of Fig. 3). To summarize, HM2016 wasconsiderably more robust at reproducing measured yields, acrossa diverse range of environments and crop management practiceswith respect to sowing dates, hybrid maturity, and plant popula-tions without detectable bias across a range of yields from completecrop failure to 18 Mg ha−1.

6.2. Dynamics of biomass production and canopy senescence

Seasonal dynamics of total aboveground biomass and LAI weremeasured only at Mead, NE in 2011 and 2013. In 2011, bothHM2016 and HM2006 gave similar results in terms of seasonal pat-tern of aboveground biomass production and LAI. A full soil profilein terms of soil water content at sowing, total rainfall of 556 mmduring the growing season, and good rainfall distribution from sow-ing to maturity (inset in Fig. 5) indicated that 2011 was a relativelywet year at this location and therefore the crop did not suffer water

cence during the last phase of grain filling due to lack of rainfalland water deficits during this period (inset in Fig. 5). Further evi-dence of water deficit in 2013 comes from an irrigated simulation

186 H. Yang et al. / Field Crops Research 204 (2017) 180–190

Fig. 3. Simulated versus measured maize yields for rainfed fields (a) using HM2006 (left panel) and (b) using HM2016 (central panel), and (c) for both rainfed and irrigatedcrops using HM2016 (right panel) for Datasets 1 (in Table 1) and 2 (in Table 2). Root mean square error (RMSE), mean error (ME), and linear regression analysis parametersare indicated. Diagonal dashed line indicates y = x. Solid black lines show the fitted linear regression model. Encircled data point was excluded from the calculation of RMSE,ME and linear regression analysis because observed yield was affected by frost damage during grain filling. Justification for excluding the site with frost damage from allregressions comes from the fact that frost damage can be very site-specific because it is often associated with small differences in elevation within a relatively flat landscapedue to pooling of cold air. Therefore, frost damage may be larger or smaller in a given field compared to simulated damage from the closest weather station.

F HM2C

spid

6

aawmiwsateHvoa

ig. 4. Harvest index based on measured and simulated results using HM2006 andolby, KS (see Table 2).

cenario for total biomass and LAI (the dashed lines in the lowerart of Fig. 5), which showed that total biomass would continue to

ncrease and the LAI would decrease more slowly without watereficit during the later phase of grain filling.

.3. Kernel setting and duration of grain filling

Simulated maize kernel setting was evaluated for the 33 casest Colby, KS, which is a harsh environment for rainfed maize crops indicated by sparse in-season rainfall amounts (Table 2). Whenater deficit occurred during the kernel setting window (approxi-ately three weeks bracketing silking), HM2016 predicted a larger

mpact on kernel setting than HM2006 (Fig. 6). For the eight casesith crop failure (i.e., zero yield), HM2016 simulated zero kernel

etting rate (as% of maximum number of kernels of 675 per plant)nd only 9% and 10% kernel setting for other two cases. In con-rast, HM2006 simulated a much higher rate of kernel setting, andspecially in years with complete crop failure. Across the 33 cases,

M2016 simulated an average kernel setting rate of 42% while thealue from HM2006 was 57%, which documents the improvementf HM2016 in terms of quantifying the impact of drought stressround silking on maize kernel setting.

016 Dataset 2, which includes 33 rainfed maize crops grown during 2001–2009 at

The difference between HM2016 and HM2006 in responsive-ness of canopy senescence to water deficit was also shown in thesimulated drought-induced termination of crop growth and thusthe duration of the grain filling phase for the 33 cases at Colby, KS(Fig. 7). On average, HM2016 simulated 4 days shorter grain fill-ing duration than HM2006 with a range from 0 to 15 days, with themagnitude depending largely on the in-season rainfall in each year,especially during reproductive growth phases.

6.4. Sensitivity analysis

Among the five major revisions (i.e., revisions 1–5), root lengthdistribution and kernel setting had the greatest effects in a water-limited environment, but in opposite directions: the revised rootlength distribution resulted in higher grain yield, whereas therevised kernel setting led to lower grain yield (Fig. 8, left panel).On average, the absolute effect from kernel setting (59%) on grainyield is greater than that of root length distribution (43%), and

as a result, the net effect is expected to result in lower yields. Incomparison, the other revisions, including canopy expansion andsenescence, runoff and crop ET, did not have significant impactson simulated grain yield, with an average effect ranging from −1%

H. Yang et al. / Field Crops Research 204 (2017) 180–190 187

Fig. 5. Simulated and measured seasonal dynamics of total aboveground biomass (left panels) and LAI (right panels) using HM2016 and HM2006 for rainfed maize grown in2011 and 2013 at Mead, NE. The inserts in the right panels show daily rainfall amounts from sowing to physiological maturity. Rainfall in 2011 growing season was sufficientto meet plant water requirements throughout the growing season whereas there was a dry period during part of the grain filling in 2013. Because 2013 was a dry year,simulation of fully irrigated maize crop (the dashed line) was added to show the difference in total biomass and LAI between rainfed and fully irrigated crops. The field wason annual rotation with soybean, with maize sown in odd-numbered years.

F ber (i.m ing rat

tsciiti

tAesllC

ig. 6. Simulated maize kernel setting rate, expressed as% of maximum kernel numaize crops grown during 2001–2009 at Colby, KS (in Table 2). Average kernel sett

o −13%. Despite the relatively small effects from these other revi-ions within the limits of observations provided by Dataset 2, wean envision situations in which these factors may have greaternfluence on final yields. For example, the fields in which the exper-ments were conducted for Dataset 2 had relatively little slope andhus the runoff revision would not be expected to have a largenfluence.

The effects of model revisions on stover biomass were smallerhan the impact on yield, ranging, on average, from 8% to −9%.n exception was kernel setting, which has a large (58%) positiveffect on stover biomass when limited water supply reduces sink

ize (Fig. 8, right panel). This trend occurs because of (1) accumu-ation of photosynthate in stem (Christensen et al., 1981) and (2)ess use of carbohydrate reserve in stem for grainfilling (Hume andampbell, 1972). However, the magnitude of the increase in stover

e., 675 per plant), by HM2006 and HM2016 for Dataset 2, which includes 33 rainfede was 57% and 42% for HM2006 and HM2016, respectively.

biomass under reduced kernel setting is likely over-estimated asphotosynthetic rate is also likely to reduce when the sink size isreduced (Christensen et al., 1981) but the model lacks the feedbackmechanism.

7. Discussion

Modeling crop growth and yield under limited water supplyhas been a significant scientific challenge due to a large number ofinteracting soil and plant factors that determine the final impact ongrain and biomass yields. To meet the increasing demand for more

robust simulations in water-limited environments, we attemptedto revise the Hybrid-Maize model to improve its capacity to accountfor the impact of water deficits on maize development, growth,and yield. To that end, subroutines were revised with regard to

188 H. Yang et al. / Field Crops Resea

Fig. 7. Difference in the duration (HM2006 minus HM 2016, days) of grain filling asscw

sad(uaemlswHaea

ihpfh2ispss

FE*am

imulated by HM2006 and HM2016 for Dataset 2 (in Table 2) of the 33 rainfed maizerops grown during 2001–2009 at Colby, KS. The difference in simulated durationas, on average, 4.2 days shorter with HM2016 than by HM2006.

oil water balance, soil profile root distribution and water uptake,nd the impacts of water deficit on canopy expansion, senescence,ry matter production, and kernel setting. Compared to HM2006the earlier version), HM2016 (the revised version) produced sim-lation results in much better agreement with measured yield,boveground biomass, and harvest index, across a wide range ofnvironments with yields ranging from 0 to 18 Mg ha−1. Among theajor revisions, the revision of root distribution led to a greater root

ength density in the entire soil profile, resulting in higher grain andtover yields in water-limited environments. However, this effectas partly offset by reduced kernel setting that was simulated withM2016 due to the impact of drought stress on crop growth rateround silking stage. While the other revisions had relatively smallffects on grain and yield, together, on average, they contributed to

grain yield reduction of 1–13%.These model improvements are consistent with recent advances

n understanding the improved performance of newer maizeybrids in terms of stress resistance, including drought, com-ared to older hybrids, especially as related to the competition

or resources imposed by increasing inter-plant competition atigher plant densities (Tollenaar and Lee, 2002; Campos et al., 2004,006). Indeed, producer plant populations have increased steadily

n recent decades (Pioneer, 2014; Grassini et al., 2014), leaving a

maller lateral topsoil volume for water extraction by individuallants. This may lead to a change in root distribution from a Vhape throughout the profile to a combined cylindrical shape in top-oil and a V-shape below, thus increasing the soil volume for plant

ig. 8. Sensitivity analysis of each of the five major revisions in HM2016 (including root aT) on simulated grain yield (left panel) and stover biomass (right panel) for the 33 case100%. Positive and negative values indicate respective higher or lower values relative tond third quartiles, respectively, while the horizontal line band inside each box is the maximum and minimum values, respectively.

rch 204 (2017) 180–190

water acquisition, which may impart additional drought toleranceas suggested by Hammer et al. (2009).

In addition to improved sensitivity of kernel setting under waterdeficit, HM2016 better captures impact of limited water supplyduring grain filling through accelerated leaf senescence and, asa result, earlier termination of grain filling when there is persis-tent water deficit, as documented by Saini and Westgate (2000).These improvements are make the revised model considerablymore responsive in simulating maize yields in harsh rainfed envi-ronments like those found in the western US Corn Belt where cropwater deficit is likely to occur around pollination and during thegrain filling in a majority of years.

The inclusion of routines for water runoff can potentially makethe revised model more accurate at simulating soil water status infields with steep terrain and environments with high frequency ofintense rainfall events. The added effects of crop residue cover onwater runoff and soil evaporation make HM2016 simulations of soilwater balance more responsive to tillage method and conservationpractices.

Despite the improved predictive power of HM2016, relative toHM2006, there remain other impacts of severe water deficit thatare not yet effectively accounted forHM2016. These factors includereduction of effective LAI due to leaf rolling (Asim and Rabiye,2007), the increase in canopy temperature that occurs under waterlimited conditions (Gonzalez-Dugo et al., 2005), and heat stressduring pollination (Cicchino et al., 2013; Gabaldon-Leal et al., 2016).Each of these effects may last only a few hours during mid-dayheat and are difficult to quantify in models with a daily time steptemperature. Additional field data are also needed to develop andcalibrate useful subroutines for quantifying these effects on yield,and a model that runs on an hourly time step may be needed aswell.

8. Conclusion

Moderate to severe water deficit is common in many rain-fed maize production environments worldwide. Yield losses fromwater deficit result from a number of interacting processes thatinvolve soil water balance, crop growth, canopy senescence, and

kernel setting. Most of the processes are difficult to mathematicallydescribe and simulate in crop models. We revised the Hybrid-Maizemodel in an attempt to improve maize yield simulation underrainfed conditions with water deficit. The revisions and new rou-

nd distribution, canopy expansion and senescence, kernel setting, runoff, and crops of Dataset 2. The relative change was calculated as (HM2016–HM2006)/HM2006

those obtained using HM2006. The bottom and top of each box represent the firstedian, the x sign is the mean. The upper and lower end of the bars indicate the

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ines address those processes and the impact of water deficit onhem. Likewise, we improved simulation of soil evaporation, sur-ace runoff, and estimation of soil water content at sowing basedn the soil water balance during the fallow period up to sowingime. Together, these changes make the revised Hybrid-Maize moreobust at simulating yields over a wider range of environmentsnd field conditions. Consequently, these improvements make theodel more useful in research on crop traits and management

ptions to mitigate yield losses from water deficits, and for sup-orting in-season crop management decisions and yield forecasts.ocumentation of these changes as provided in this paper, and inreater detail in the users’ guide (Yang et al., 2016), will facilitateuture model development by others, and the HM2016 has beeneleased to the public and is available at http://hybridmaize.unl.du/.

cknowledgements

we thank Dr Suat Irmak (Department of Biological System Engi-eering, University of Nebraska – Lincoln) and Dr. Andrew SuykerSchool of Natural Resources, University of Nebraska – Lincoln) forroviding some of the data used in the study. We also thank Jennyees and Keith Glewen, Extension Educator of the University ofebraska for their feedback on applications of the Hybrid-Maizeodel.

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