winter wheat - ASABE Technical Library

WINTER WHEAT (TRITICUM AESTIVUM L.) EVAPOTRANSPIRATION AND SINGLE (NORMAL) AND BASAL CROP COEFFICIENTS S. Irmak, K. Djaman, V. Sharma

ABSTRACT. Locally measured crop coefficients (Kc) are critical for accurately quantifying and evaluating crop evapotranspiration (ETc) under local climate, soil, and crop management practices. Data and information on winter wheat Kc values do not exist in Nebraska and are limited in the U.S. Great Plains in general. The objectives of this research were to measure ETc rates and develop growth-stage-specific single (normal) (Kc) and basal (Kcb) crop coefficients for winter wheat (Triticum aestivum L.) to provide data and information to producers, their advisors, and state and federal water regulatory and management agencies about the water use dynamics of winter wheat. Field experiments were conducted during two consecutive winter wheat growing seasons in 2008-2009 and 2009-2010 at the University of Nebraska-Lincoln South Central Agricultural Laboratory near Clay Center, Nebraska, in a 13.6 ha field. Hourly evapotranspiration was measured using a Bowen Ratio Energy Balance System (BREBS), and growth-specific single crop coefficients [grassreference (Kco) and alfalfa-reference (Kcr)] and grass- and alfalfa-reference basal crop coefficients (Kcbo and Kcbr, respectively) were developed from measured ETc and estimated grass- and alfalfa-reference (potential) evapotranspiration (ETo and ETr, respectively). The Kco, Kcr, Kcbo, and Kcbr values were developed as a function of days after planting (DAP) and thermal unit (TU, also known as growing degree days). Winter wheat grain yield averaged 4.55 tons ha-1 in both growing seasons. Water productivity (water use efficiency) was 0.76 kg m-3 in 2008-2009 and 0.93 kg m-3 in 2009-2010. Daily ETc increased with DAP in the pre-winter and post-winter periods. Maximum daily ETc was measured on 129 DAP (19 May 2009; 9.5 mm d-1) in 2008-2009 and on 137 DAP (24 May 2010; 10.6 mm d-1) in 2009-2010. Seasonal cumulative ETc was 600 mm during 2008-2009 and 490 mm during 2009-2010, and seasonal daily average ETc was 2.1 and 1.6 mm d-1 for the two growing seasons, respectively. Crop coefficients varied substantially with the growth and development stages. Twoyear average Kco values were 0.60, 1.30, and 0.30, and Kcr values were 0.40, 1.10, and 0.20 for the early-season, midseason, and late-season crop growth and development stages, respectively. Two-year average Kcbo values were 0.45, 1.30, and 0.30, while Kcbr values were 0.30, 1.05, and 0.20 for the same growth stages, respectively. On average, Kco and Kcbo were about 20% greater than Kcr and Kcbr, and Kco and Kcr were about 10% to 11% greater than Kcbo and Kcbr. The seasonal average Kcbo was 87% of Kco, and Kcbr was 89% of Kcr. Therefore, transpiration is expected to be about 87% to 89% of ETc, and soil evaporation would be expected to be about 11% to 13% of ETc, but these percentages varied during the season. For example, soil evaporation during the winter wheat dormancy period represented 21% and 10% of seasonal ETc in 2008-2009 and 2009-2010, respectively. The ratio of Kcbo to Kco ranged from 0.69 to 0.97, and the ratio of Kcbr to Kcr ranged from 0.63 to 0.98. A detailed Kc table was developed to present Kco, Kcr, Kcbo, and Kcbr values for different phenological and crop development stages. These values can be used by winter wheat producers, water regulatory agencies, and managers to evaluate water use of winter wheat with respect to availability and demand of water resources in soil and crop management and climatic conditions similar to those observed in south central Nebraska. Keywords. Basal crop coefficients, Evapotranspiration, Single crop coefficients, Winter wheat.

Submitted for review in November 2014 as manuscript number NRES 11083; approved for publication by the Natural Resources & Environmental Systems Community of ASABE in June 2015. The mention of trade names or commercial products is for the reader’s information and does not constitute an endorsement or recommendation by the authors or their institutions. The authors are Suat Irmak, ASABE Member, Distinguished Professor, Department of Biological Systems Engineering, University of Nebraska-Lincoln (UNL), Lincoln, Nebraska; Koffi Djaman, Research Scientist, Africa Rice Center (AfricaRice), Saint-Louis, Senegal; Vivek Sharma, ASABE Member, Post-Doctoral Research Associate, Department of Biological Systems Engineering, UNL, Lincoln, Nebraska. Corresponding author: Suat Irmak, 239 L.W. Chase Hall, Lincoln, NE 68583-0726; phone: 402-472-4865; e-mail: [email protected].

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heat (Triticum aestivum L.) is the third largest irrigated crop in the U.S. and a major crop throughout the world, especially in India, Pakistan, Russia, and China (Musick and Porter, 1990). In the last three decades, an increasing trend has been observed in wheat production in the U.S. with substantial increases in wheat exports, especially in 2007 and 2008, when average exports reached 31 million metric tons (Mt), comprising 25% of the world’s total wheat exports (FAO, 2008). In the U.S., wheat is generally grown in the Great Plains region with a variety of practices and yield differences. Midwestern states, including Nebraska, have extensive wheat cultivation under irrigated and rainfed

Transactions of the ASABE Vol. 58(4): 1047-1066

© 2015 American Society of Agricultural and Biological Engineers ISSN 2151-0032 DOI 10.13031/trans.58.11083

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conditions. Over the last decade, an overall increase of 26% was observed in wheat production in Nebraska. For example, in 2008, Nebraska harvested a total of 70,819 ha of irrigated wheat and 164,935 ha of rainfed wheat, with an average yield of 4.14 and 3.14 ton ha-1, respectively, in the ten-year period (USDA, 2008). Nebraska is the sixth largest wheat producer in the U.S., and in 2010 Nebraska’s wheat production revenue was valued at over $345 million. The productivity of wheat is largely limited by soil water availability, in addition to other yield-limiting factors such as climate, nutrient, soil properties, and management properties. However, detailed information on the evapotranspiration and crop coefficients for wheat, which are required for water resources demand, use, allocation, and management, is still lacking. Winter wheat has long been the mainstay of rainfed cropping systems in arid and semi-arid regions (and other climates) of the world, including Nebraska. Crop water productivity (CWP), also known as water use efficiency (WUE), under rainfed conditions is limited by the precipitation gradient and available soil water to meet crop evapotranspiration (ETc) for maximum productivity. One of the challenges in using data and information from other regions to determine local wheat water use and productivity relationships (Musick et al., 1994) is that winter wheat ETc, potential soil water conservation, grain yield, and related WUE show substantial variation with location. For example, in the northern Great Plains, fallowing the cropland every other year conserved 42 mm of water for the following wheat crop, of which only 17 mm water was taken up by wheat, resulting in a yield increase of 249 kg ha-1 (13.7%); however, the annual mean yield decreased by 782 kg ha-1 (43.1%) due to one year of fallow (Qiu et al., 2008). On the other hand, Nielsen et al. (2002, 2011) observed that winter wheat grain yields in the U.S. Central Great Plains increased by 141 kg ha-1 for every 10 mm increase in plantavailable water in the soil profile at planting and by 125 kg ha-1 for every 10 mm of wheat soil-water uptake after 130 mm of water use. Kang et al. (2003) reported winter wheat ETc varying from 213 to 227 mm under rainfed conditions and from 227 to 519 mm under different irrigation regimes, demonstrating significant variations in wheat water use, yield, and productivity between regions. The Food and Agriculture Organization (FAO) of the United Nations adopted a two-step methodology (FAO, 1998) to quantify water use of variety crops, including wheat. In this two-step approach, reference (potential) evapotranspiration (ETref) is calculated for a grass- or alfalfa-reference surface, which is subsequently related to crop ETc using a crop-specific coefficient (Kc), defined as the ratio of ETc to ETref. The crop coefficient is influenced by local environmental conditions and management practices (Hunsaker et al., 1995; Howell et al., 2006, Piccinni et al., 2009; Djaman and Irmak, 2013). Therefore, it is critical to develop Kc for local climate, soil conditions, and management practices to obtain more robust and accurate local water use estimates. Ko et al. (2009) reported winter wheat Kc that varied between 0.10 and 1.70 at Uvalde, Texas. Hunsaker et al. (2005) developed wheat basal coefficients as a function of Normalized Difference Vegetation Index (NDVI) for Arizona us-

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ing three-year field experiments that can potentially be used for real-time estimates of wheat water use in conditions where NDVI values can be obtained during the wheat growing season. Liu et al. (2002) reported winter wheat Kc of 0.60, 1.23 to 1.42, and 0.70 for the early-season, midseason, and late-season stages, respectively, for a five-year experiment. Zhang et al. (2004) reported winter wheat early-season, mid-season, and late-season Kc values of 0.37, 1.09 to 1.16, and 0.65, respectively. Ko et al. (2009) reported a third-degree power function of winter wheat Kc related to days after planting (DAP), while Kang et al. (2003) reported a fifth-order polynomial equation with significant correlations (R2 = 0.96) for winter wheat Kc as a function of DAP. These variations in Kc values for the same crop, especially for the mid-season growth and development stage, justify the need for developing local Kc values. Winter wheat ETc and Kc values have not been measured for modern cultivars in Nebraska climatic and management conditions and are extremely rare for the central Great Plains in general. The objectives of this research were to measure evapotranspiration and develop single (normal) and basal crop coefficients specific to winter wheat phenological stages in south central Nebraska climatic and soil and crop management conditions.

MATERIALS AND METHODS SITE DESCRIPTION, WEATHER CONDITIONS, AND CROP AND SOIL MANAGEMENT Field experiments were conducted for two consecutive winter wheat growing seasons (2008-2009 and 2009-2010) at the University of Nebraska-Lincoln South Central Agricultural Laboratory (40° 43′ N and 98° 8′ W, 552 m above mean sea level) near Clay Center, Nebraska. The field size is 524 m in the north-south direction and 258 m in the eastwest direction with a gentle 0% to 2% slope in the west-east direction. The soil at the experimental site is a Hastings silt loam, which is a well-drained upland soil (fine, montmorillonitic, and mesic Udic Argiustoll) with water holding characteristics of 0.34 m3 m-3 field capacity, 0.14 m3 m-3 permanent wilting point, and 0.53 m3 m-3 saturation point. The soil particle size distribution is 15% sand, 65% silt, and 20% clay, with 2.5% organic matter content in the topsoil (0 to 0.30 m soil layer) (Irmak, 2010). During the 2008-2009 growing season, a winter wheat variety of ART (agronomic disease tolerance; Hard Red Winter variety, ArgiPro, Syngenta Seeds, Inc.) was planted on 3 October 2008, emerged on 18 October, and was harvested on 9 July 2009. In the 2009-2010 growing season, the same wheat variety was planted on 30 September, emerged on 15 October, and was harvested on 4 July 2010. The seeding rate was 124 kg ha-1 in 2008-2009 and 122 kg ha-1 in 2009-2010. For both seasons, wheat was planted at 1.3 cm soil depth with 19 cm inter-row spacing, and the residue height remaining after harvest was 25 cm. The planting row direction was east-west in 2008-2009 and north-south in 2009-2010. In the 2008-2009 growing season, a total of 34.5 kg N ha-1 (28-0-0) and 9.5 kg P ha-1 (1034-0) were applied (drilled) to the experimental field uni-

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formly on 3 October 2008. In addition, a total of 92 kg ha-1 urea was broadcasted on 3 March 2009. In the 2009-2010 season, a total of 32 kg N ha-1 (28-0-0) and 18 kg P ha-1 (10-34-0) were applied in-furrow on 30 September 2009, and a total of 80 kg ha-1 urea was applied on 8 March 2010. The field was planted with soybean in the 2007 and 2008 summer growing seasons. In the 2008-2009 growing season, winter wheat was no-till drilled into the soybean residue on the remaining ridges from the previous crop season. In the 2009-2010 growing season, wheat was no-till drilled into the wheat stubble. Weed and pest control practices and soil management practices were uniformly applied to the entire field as needed. For weed control, a total of 2.5 LT ha-1 of Round-up Power Max was applied uniformly to the entire field on 17 September 2009 before planting. Even though the research was conducted in a 13.6 ha subsurface drip-irrigated field, no irrigation was needed based on the soil water status measurements, and the experiment was considered to be conducted under rainfed conditions. Winter wheat in south central Nebraska is usually not irrigated due to adequate precipitation during the winter wheat growing season. Detailed observations of crop growth stages were conducted and recorded in both growing seasons to determine Kc values for specific crop growth and development stages. PENMAN-MONTEITH MODEL FOR ESTIMATING REFERENCE (POTENTIAL) EVAPOTRANSPIRATION AND CROP COEFFICIENT (Kc) CALCULATIONS Daily grass-reference ET (ETo) and alfalfa-reference (potential) ET (ETr) were computed using the standardized ASCE Penman-Monteith equation (ASCE, 2005) with fixed stomatal resistance values for both grass- and alfalfareference surfaces:

ETref

  Cn 0.408Δ (Rn − G ) +  γ u 2 (es − ea ) T 273 +   mean = Δ + γ (1 + Cd u 2 )

(1)

where ETref is either grass- (ETo) or alfalfa-reference ET (ETr) (mm d-1), Rn is net radiation (MJ m-2 d-1), G is soil heat flux (MJ m-2 d-1, assumed to be zero for a daily time step), γ is the psychometric constant (kPa °C-1), Tmean is daily average air temperature (°C), u2 is wind speed at 2 m height (m s-1), (es − ea) is vapor pressure deficit (kPa), Δ is slope of saturation vapor pressure curve at air temperature (kPa °C-1), and Cn and Cd are constants that change with the reference surface and time step. Coefficients Cn and Cd are 900°C mm s3 Mg-1 d-1 and 0.34 s m-1 for a grass-reference surface and 1600°C mm s3 Mg-1 d-1 and 0.38 s m-1 for an alfalfa-reference surface, respectively, on a daily time scale (ASCE, 2005). Weather data used in equation 2 were measured from a Bowen Ratio Energy Balance System (BREBS) installed in the middle of the experimental field, which is also part of the Nebraska Water and Energy Flux Measurement, Modeling and Research Network (NEBFLUX; Irmak, 2010). For the same experimental field, it has been shown earlier that using weather data measured above an agronomic crop to calculate ETref closely resem-

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bles the values calculated using weather station dataestimated ETref (Irmak and Odhiambo, 2009; Skaggs and Irmak, 2012). A BREBS [Radiation and Energy Balance Systems (REBS), Bellevue, Wash.] was used to measure surface energy balance variables, including ETc, and other climatic variables (precipitation, maximum and minimum air temperature, maximum and minimum relative humidity, incoming shortwave radiation, and wind speed). All variables were sampled every 60 s and averaged and recorded every hour. A detailed description of the measurement of the microclimatic and climatic variables using BREBS was presented by Irmak (2010) and will not be repeated here. It was assumed that the BREBS-measured ETc represents field-average ETc. Both single and basal winter wheat crop coefficients (Kc, unitless) were derived from measured ETc (mm d-1) and estimated ETref (mm d-1): Kc =

ETa ETref

(2)

Evapotranspiration consists of soil evaporation (E) and plant transpiration (T), and basal Kc values are useful in terms of separating ETc into E and T. Detailed descriptions of the calculation procedures for single (normal) Kc and dual Kc are given in FAO-56 (FAO, 1998) and were followed in this research. Basal crop coefficients (Kcb) were developed to represent the portion of ETc that is used for E in conditions when the soil surface layer is dry, so that evaporation of water from the soil surface is minimal yet the average soil water content in the crop root zone is adequate to sustain crop transpiration at a potential rate. Approximate Kcb values for winter wheat were derived by removing the ETc and ETref data for the days when rain occurred and for the two or three days after the precipitation event. THERMAL UNIT (TU) The thermal or heat unit concept has been applied for decades to correlate phenological development in crops to predict sowing and maturity dates (Nuttonson, 1955; Mills, 1964). Heat units, also expressed as growing degree days (GDD), are frequently used to describe the timing of biological processes for characterizing the thermal response of crops in terms of growth. In general, GDD are used more frequently than DAP or days after emergence (DAE). Winter wheat single (normal) crop coefficients (Kc) and basal crop coefficients (Kcb) were related to thermal unit (TU) for both grass- and alfalfa-reference surfaces. TU (°C) is the accumulation of the daily air temperature, which is cumulative air temperature above the base temperature and is expressed as: TU =

 Tmax + Tmin  − Tbase  2  i =1 n

 

(3)

where Tmax is maximum air temperature (°C), Tmin is minimum air temperature (°C), Tbase is the base temperature threshold for winter wheat (0°C) (McMaster and Smika, 1988; McMaster and Wilhelm, 1997), and n is the number of days for which the TU is accumulated for during the

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winter wheat growing season. The base temperature for calculating growing degree days is the minimum threshold temperature at which plant growth continues. In this research, no upper limit air temperature threshold was applied. For the minimum air temperature threshold, values below 0°C were taken as 0°C because limited or no growth occurs below the lower limit (base) threshold air temperature. The upper limit air temperature threshold was withheld due to plant growth still occurring at higher temperatures than the commonly used threshold of 30°C, along with the known performance of the selected winter wheat hybrids at high temperatures in the region. SOIL WATER STATUS AND YIELD MEASUREMENTS Watermark Granular Matrix sensors (WGMS, Irrometer Co., Riverside, Cal.) were used to monitor soil matric potential (SMP) on an hourly basis to determine irrigation needs. The WGMS measured SMP values, which were then converted to soil water content in percent volume using pre-developed soil-water retention curves for the same research field (S. Irmak, 2006, unpublished research data; Irmak et al., 2014): θv = 3 × 10-6 × (SMP)2 − 0.0013 × (SMP) + 0.3764

(4)

where θv is the volumetric soil water content (% vol or m3 m-3), and SMP is the soil matric potential (kPa). The root mean squared error between neutron probe-measured soil water content and Watermark sensor-measured SMP, which was converted to soil water content using equation 4, was 0.024 m3 m-3. WGMS were installed at 0.30, 0.60, 0.90, and 1.20 m soil depths at six locations in the experimental field. Watermark Monitor dataloggers were used to record SMP throughout both winter wheat growing seasons. Soil temperature sensors were used to measure soil temperature to account for soil temperature influence on SMP, as outlined by Irmak et al. (2014) for soil temperatures different from 21.1°C.

At physiological maturity, winter wheat was harvested using a combine harvester. Winter wheat WUE was calculated as the ratio of field-average grain yield to ETc (mm). The WUE is expressed in kg m-3 on a unit water volume basis or in g kg-1 on a unit water mass basis, and Y is grain yield (g m-2).

RESULTS AND DISCUSSION WEATHER CONDITIONS DURING THE 2008-2009 AND 2009-2010 WINTER WHEAT GROWING SEASONS Measured weather data for the 2008-2009 and 20092010 growing seasons are presented in table 1. The longterm average annual precipitation at the experimental site is 722 mm with a significant interannual and within-season variability in magnitude and timing. Less seasonal (winter wheat growing season) precipitation was observed in the 2008-2009 growing season (560 mm) than in 2009-2010 (655 mm) (fig. 1). Adequate precipitation occurred during the winter wheat early stage (Feekes stage 1) and from Feekes stage 3 (late March) to harvest in July, and it was favorable for winter wheat production without any water deficit and irrigation needs (as later indicated by the soil water data). Air temperature decreased from planting to its lowest values of -22°C in mid-December of 2008 and to 26°C in mid-January of 2010 (table 1). From about 150 DAP, which coincided with the end of February, temperatures began to rise gradually and continued to increase until harvest in early July. The effect of temperature on winter wheat growth was evaluated through thermal unit accumulation and vapor pressure deficit (VPD) during the growing season. Wind speed was higher in 2008-2009 than in 20092010, with a seasonal average of 4.2 m s-1 in 2008-2009 and 3.8 m s-1 in 2009-2010 (table 1). Solar radiation and VPD had similar trends as air temperature, with very low VPD values during the 2009 winter. In the same period, maximum relative humidity was very high and close to

Table 1. Average weather conditions during the 2008-2009 and 2009-2010 winter wheat growing seasons measured at the research site (Tmax = maximum air temperature, Tmin = minimum air temperature, RHmax = maximum relative humidity, RHmin = minimum relative humidity, and VPD = vapor pressure deficit). VPD Tmax Tmin RHmax RHmin Solar Radiation Wind Speed (m s-1) (kPa) Season Month and Year (°C) (°C) (%) (%) (W m-2) October 2008 17.3 5.5 93.0 47.4 125.4 4.1 0.5 November 2008 9.2 -1.8 92.6 53.7 83.6 4.4 0.3 December 2008 4.2 -11.7 91.3 60.1 69.6 4.8 0.2 January 2009 6.8 -7.8 89.1 51.4 91.0 4.5 0.2 February 2009 6.1 -7.1 89.9 47.3 120.1 4.3 0.2 2008-2009 March 2009 10.6 -3.5 90.8 44.3 163.7 4.6 0.3 April 2009 15.7 2.7 91.2 43.1 207.6 5.0 0.5 May 2009 22.1 9.7 91.9 46.1 241.9 3.6 0.7 June 2009 25.8 15.5 95.4 57.4 209.0 2.6 0.6 July 2009 28.1 15.6 97.4 49.4 260.4 2.5 0.8 October 2009 12.1 2.0 96.9 61.2 98.2 3.9 0.2 November 2009 13.1 -0.2 95.7 49.1 93.6 3.3 0.3 December 2009 -3.7 -12.0 94.9 76.9 67.7 3.0 0.1 January 2010 -3.6 -10.0 96.8 82.4 81.6 3.6 0.0 February 2010 -1.3 -8.4 96.1 78.0 92.6 3.8 0.1 2009-2010 March 2010 9.6 0.4 93.9 64.1 130.5 4.6 0.2 April 2010 18.4 5.6 90.5 45.6 202.4 4.4 0.5 May 2010 19.5 9.2 93.6 57.8 223.9 3.9 0.4 June 2010 28.1 16.7 93.6 55.4 264.8 3.0 0.7 July 2010 28.1 17.1 95.6 54.8 233.2 2.9 0.7

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100%. Extreme cold air temperatures resulted in winter wheat dormancy with zero growth rates from December 2008 to late February 2009 and from December 2009 to late March 2010. Thermal unit increased dramatically from the end of March (about 180 DAP; Feekes stage 3) until harvest in early July, with seasonal cumulative thermal units of 2306°C and 2150°C in the 2008-2009 and 20092010 growing seasons, respectively. Air temperature is the

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main driving force in winter wheat development in cold regions (Xue et al., 2004), and the extreme cold temperatures in south central Nebraska, especially in the 2009 winter, substantially hindered winter wheat growth and prolonged its dormancy, while the 2008 winter was moderate and wheat began reviving on 16 January 2009 (116 DAP; Feekes stage 2) as compared to 29 March 2010 (table 1).

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Figure 2. Soil water content trends during the (a) 2008-2009 and (b) 2009-2010 winter wheat growing seasons. The 2009-2010 growing season includes data only from April through July due to the impact of freezing conditions on the Watermark soil matric potential sensors, which did not record data during the winter period.

SOIL WATER The average distribution of soil water content measured at six different locations across the field and in each of the four 0.30 m layers to a soil profile depth of 1.20 m are presented in figures 2a and 2b for the 2008-2009 and 20092010 growing seasons, respectively. For both growing seasons, the distribution of soil water content looks similar in terms of soil water content range. In the 2008-2009 grow-

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ing season, the soil water content was near field capacity from planting to the end of October, and it remained ample throughout October during plant establishment (fig. 2a). The soil water content decreased in the upper 0.30 m and 0.60 m soil layers during winter. However, after winter, the soil water content increased to near field capacity in late March and early April because of winter and abundant early spring precipitation (figs. 2a and 2b). As the winter wheat revived from dormancy in early spring, the soil water


content decreased due to soil evaporation and water uptake by the actively growing plants. In the 2009-2010 growing season, the soil water content of the first soil layer (0 to 0.30 m) was above 0.30 m3 m-3 throughout the spring, while the second layer (0.30 to 0.60 m) was much more depleted and was at 0.25 m3 m-3 around 20 May 2010. The soil water content in the 0-0.60 m soil layer increased after rain events on 10 April, 20 May, 13 June, and 21 June. The soil water content in the deeper layers decreased gradually, and the water content in the 0.60 to 0.90 m layer remained around 0.27 m3 m-3 from 8 May to 10 June and increased thereafter as a result of heavy rainfall of 46 mm on 12 June, another rainfall event of 23 mm on 13 June, and other substantial precipitation events of 60, 35, and 22 mm on 20, 21 and 22 June, respectively. On effective root zone (1.20 m) average basis, soil water content was consistently high, and there was no need for irrigation applications. Thus, it was considered that the winter wheat in both seasons did not experience water stress and would have similar growth, ETc, and Kc values as under irrigated conditions. During the period of soil water content measurements from 9 April to 30 June 2010, 398 mm of precipitation were recorded, which represented 61% of the season total precipitation with a relatively uniform temporal distribution. The differences in soil water distribution in terms of trends and magnitudes for both growing seasons were expected because of the differences in precipitation and water use between the two seasons. In addition, the field was planted with soybean before the 2008-2009 growing season, while the winter wheat for the 2009-2010 growing season was planted into the previous wheat crop’s stubble. This difference in residue cover would have an effect on soil water patterns between the two seasons. DAILY AND SEASONAL WINTER WHEAT EVAPOTRANSPIRATION The seasonal patterns in evapotranspiration rate are primarily driven by air temperature, solar radiation, water availability, and winter wheat growth stage. During the initial stage of the winter wheat, BREBS-measured daily ETc was low and much lower during the winter period due to low air temperatures, high relative humidity, short sunshine hours, and low incoming shortwave radiation. ETc during this period mainly results from soil water evaporation. Daily ETc in 2008-2009 varied from 0 mm on extremely cold days to 9.5 mm d-1 during the summer period with a seasonal average of 2.1 mm d-1, and it ranged from 0 to 10.6 mm d-1 with a seasonal average of 1.6 mm d-1 in 2009-2010. The seasonal total ETc was 600 mm and 490 mm during the 2008-2009 and 2009-2010 growing seasons, respectively (figs. 3a and 3b). Daily ETc was lowest during the extreme cold period of December through the end of February when the plants were in dormancy. From crop emergence to early December, ETc was reduced primarily to soil water evaporation during the winter due to the extreme cold temperatures and the frozen surface (visual observation of frozen soil and crop). During that period, ETc depended mainly on the aerodynamic variables and low air temperature, which restrict wheat growth, while low radiation and low vapor pressure result in low soil water evapo-

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ration rates (Zhang et al., 2004). After the dormancy period, ETc increased to the maximum value at the full crop development and reproductive stages that coincided with the second half of May and early June and declined toward the end of the growing season due to maturity and senescence. Maximum ETc occurred on 229 DAP (19 May 2009) in 2008-2009 and on 237 DAP (24 May 2010) in 20092010. Relative to thermal unit, the winter wheat growth can be divided into three periods, (1) active performance, (2) dormancy, and (3) post-dormancy, during which 12%, 21%, and 67% of ETc occurred in 2008-2009 and 11%, 10%, and 79% of ETc occurred in 2009-2010, respectively. Average daily ETc during these periods was respectively 1.17, 1.02, and 4.30 mm d-1 for the 2008-2009 growing season and 0.80, 0.42, and 4.01 mm d-1 for the 2009-2010 growing season. Winter wheat went into dormancy during the period from 2 December to 9 April in 2008-2009 (61 to 186 DAP) and during 4 December to 29 March in 2009-2010 (66 to 181 DAP). The 2008-2009 winter was warmer than the 2009-2010 winter with higher VPD (table 1); consequently, there was greater seasonal evapotranspiration in the 20082009 winter (fig. 3). Lower ETc values during the 20092010 growing season are attributed to lower VPD, which was almost null (very low) from the beginning of December through the end of February, and with almost null and negligible reference evapotranspiration (data not shown). Similar results were presented by Ko et al. (2009), who reported that wheat ETc measured with a weighing lysimeter ranged from 483 to 505 mm in Uvalde, Texas, over three years of research. Liu and Luo (2010) reported lower winter wheat ETc values ranging from 374 to 551 mm at Yucheng City in Shandong Province, China. Liu et al. (2002) also reported average winter wheat ETc of 453 mm for five growing seasons in the North China Plain, while Sun et al. (2006) reported winter wheat ETc between 192 and 464 mm at the same site. A much higher average value of 710 mm was reported by Musick and Porter (1990) in Texas. Howell et al. (1997) reported high measured wheat ETc, ranging from 791 to 957 mm, for a semi-arid and advective climate in Bushland, Texas. To further analyze the winter wheat ETc, cumulative ETc was calculated for each growth stage from emergence to harvest (table 2). Higher ETc values from emergence to Feekes stage 1 in both growing seasons were due to longer duration between emergence to Feekes stage 1, including the dormancy period. For example, in the 2008-2009 growing season, the winter wheat emerged on 18 October 2008, and the first shoot (Feekes stage 1) was observed on 11 March 2009. Overall, ETc values were higher in the 2008-2009 growing season over different growth stages, with maximum ETc occurring in the booting, flowering, and ripening stages. Wheat grain yield ranged from 0.33 to 7.99 t ha-1 in 2008-2009 and from 0.29 to 7.83 t ha-1 in 2009-2010, with a field-average yield of 4.55 t ha-1 in both growing seasons. Water productivity that was calculated from field-average ETc and field-average yield was 0.76 kg m-3 in 2008-2009 and 0.93 kg m-3 in 2009-2010. Dong et al. (2011) reported

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Days after Planting (DAP) Figure 3. Winter wheat daily and cumulative crop evapotranspiration (ETc) and observed phenological growth and development stages for the (a) 2008-2009 and (b) 2009-2010 growing seasons. Crop growth and development stages are marked with letters and blue squares on the x-axes: P = planting, E = emergence, H = harvest, and F = Feekes stage.

winter wheat WUE ranging from 1.30 to 2.16 kg m-3, from 1.75 to 2.41 kg m-3, and from 1.16 to 2.2 kg m-3 for three years in the North China Plain. They showed that WUE at grain yield level (i.e., photosynthetic and biomass level), for some cultivars, increased significantly with irrigation in the dry year, did not change in the normal year, and showed a clear decline in the above-average (wet) year. Similar interannual variation was observed by Su et al. (2007), who

1054

reported six-year average WUE ranging from 1.11 to 1.28 kg m-3 for the Loess Plateau in China. In terms of historical trend, Zhang et al. (2010) showed that WUE increased from 1.0 to 1.2 kg m-3 for cultivars from the early 1970s to 1.4 to 1.5 kg m-3 for recently released cultivars in the last decade. Much lower values of WUE, between 0.28 and 0.62 kg m-3, were reported by Aiken et al. (2013) for a semi-arid region (Colby, Kansas).


Table 2. Growth stages cumulative winter wheat evapotranspiration (ETc) for 2008-2009 and 2009-2010 growing seasons. Cumulative ETc Cumulative ETc Two-Year Average (2008-2009) (2009-2010) Cumulative ETc Winter Wheat Growth and Development Stage (mm) (mm) (mm) Emergence to Feekes 1: One shoot 129.52 61.83 95.68 Feekes 1 to Feekes 2: Tillering begins 7.92 8.22 8.07 Feekes 2 to Feekes 3: Tillers formed 15.01 13.26 14.13 Feekes 3 to Feekes 4: Leaf sheaths lengthen 21.65 24.14 22.89 Feekes 4 to Feekes 5: Leaf sheaths strongly erected 36.67 26.04 31.36 Feekes 5 to Feekes 6: First node visible 38.19 25.54 31.86 Feekes 6 to Feekes 7: Second node visible 33.57 23.44 28.51 Feekes 7 to Feekes 8: Last leaf visible 48.38 27.77 38.08 Feekes 8 to Feekes 9: Ligule of last leaf visible 41.74 43.91 42.82 Feekes 9 to Feekes 10: In boot 65.06 69.35 67.20 Feekes 10 to Feekes 10.1: Head visible 25.18 38.96 32.07 Feekes 10.1 to Feekes 10.5: Flowering 21.68 22.01 21.84 Feekes 10.5 to Feekes 11: Repining 73.57 91.21 82.39

GRASS- AND ALFALFA-REFERENCE SINGLE (NORMAL) CROP COEFFICIENTS (Kco AND Kcr) Figures 4 through 7 present the winter wheat single crop coefficients for both grass- and alfalfa-reference surfaces as a function of DAP and TU for both growing seasons. In general, Kc values were high in the early-season stages, gradually decreased toward the start of winter season (i.e., ~200 DAP), gradually increased again in spring, and reached minimum values toward harvest. The two-year average Kco values were 0.60, 1.30, and 0.30 for the earlyseason, mid-season, and late-season crop growth stages, respectively (figs. 4 and 5). Kcr varied from 0.14 to 1.40 (figs. 6 and 7) with average Kcr values of 0.40, 1.05, and 0.20 for the early-season, mid-season, and late-season stages, respectively. Similar results were reported by Ko et al. (2009), who observed wheat Kco values that varied between 0.10 and 1.70 at Uvalde, Texas. Liu et al. (2002) reported winter wheat Kco values of 0.60, 1.23 to 1.42, and 0.70 for the early-season, mid-season, and late-season stages, respectively, from a five-year experiment. The Kc values reported in table 12 of FAO-56 (FAO, 1998) for winter wheat are 0.40 to 0.70 for the initial growth stage (depending on freezing soil conditions), 1.15 for the mid-season stage, and 0.25 for the late growth stage. Liu et al. (1998) found Kc values of 0.70, 0.40, and 0.32 for winter wheat initial stage, frozen winter period, and late season growth stage, respectively. Winter wheat early-season, mid-season and lateseason Kco values of 0.37, 1.09 to 1.16, and 0.65, respectively, were reported by Zhang et al. (2004). Shahrokhnia and Sepaskhah (2013) reported single Kco values for the initial, mid-season, and end-season growth stages of wheat as 0.77, 1.35, and 0.26, respectively, and they reported that the measured Kc values were different from the FAO recommended values. Differences in Kc values between various studies can be largely attributed to the differences in cultivars, management practices, method used to quantify Kc values, climatic conditions, and perhaps more importantly soil and crop management practices, further justifying the need for developing local Kc values for accurate quantification of wheat water use. GRASS- AND ALFALFA-REFERENCE BASAL CROP COEFFICIENTS (Kcbo AND Kcbr) Grass- and alfalfa-reference basal crop coefficients as a function of DAP and TU for both growing seasons are pre-

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sented in figures 8 through 11. Values of Kcbo were within the ranges of 0.30 to 0.60, 1.15 to 1.36, and 0.30 to 0.23 for the early-season, mid-season, and late-season growth stages, respectively (figs. 8 and 9). The range of Kcbr for the same growth stages were 0.13 to 0.50, 0.85 to 1.10, and 0.13 to 0.20, respectively (figs. 10 and 11). On the other hand, average Kcbo values were 0.45, 1.30, and 0.30 for the early-season, mid-season, and late-season stages, while average Kcbr values were 0.30, 1.05, and 0.20 for the same growth stages, respectively. For all single and basal Kc curves, there were only a few days where Kc value was close to zero. Basal cop coefficient derived in this research are similar to the results of Liu and Luo (2010), who found winter wheat Kcbo to vary within 0.10 to 0.55, 1.00 to 1.50, and 0.10 to 0.80 for initial, mid-season, and late-season growth stages, respectively. Zhao et al. (2013) reported that calibrated Kcbo values for winter wheat were 0.25 for the initial and frozen soil periods, 1.15 for the mid-season, and 0.30 near harvest. Howell et al. (1995, 2006) reported Kcbo values for the early-season, mid-season, and late-season growth stages as 0.20, 0.80 to 1.00, and 0.30 to 0.60, respectively. The FAO-reported wheat Kcbo values are 0.15 to 0.50, 1.10, and 0.15 to 0.30, for the same growth stages, respectively. Shahrokhnia and Sepaskhah (2013) reported Kcbo values for the initial, mid-season, and end-season growth stages as 0.23, 1.14, and 0.13, respectively. Most of the aforementioned Kc values differed from the FAOreported values. Winter wheat crop coefficients were related to DAP and TU as base scales by sixth-order polynomial equations with coefficients of determination ranging from 0.40 to 0.78. A higher-order polynomial equation was developed to capture the subtle variability in Kc values with time and for practical implementation at other sites. Ko et al. (2009) reported a third-degree power function for winter wheat Kc related to DAP, while Kang et al. (2003) reported fifth-order polynomial equation with strong correlations (R2 = 0.96). In this research, crop coefficients during the winter period varied considerably and averaged 0.60 when related to ETo and 0.40 when related to ETr. These results are within the measured Kco range of -0.45 to 1.142 that averaged 0.81, 0.46, and 0.77 for three winter (dormant) seasons, respectively, as reported by Hay and Irmak (2009), while the Kco calculated with the FAO-56 method ranged from 0 to 1.20

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Days after Planting (DAP) Figure 4. Grass-reference single (normal) crop coefficients (Kco) of winter wheat as a function of days after planting (DAP) in the 2008-2009 and 2009-2010 growing seasons and pooled data: Kco pooled = -5.4336365E-13 × (DAP)6 + 4.141951E-10 × (DAP)5 − 1.1944436E-7 × (DAP)4 + 1.6329E-5 × (DAP)3 − 10.651547E-4 × (DAP)2 + 0.02847 × (DAP) + 0.397.

and averaged 0.53, 0.32, and 0.72 for the initial, midseason, and late-season stages, respectively. The variation in Kc values in the dormancy period might be due to the violation of the assumptions of the reference ET equations during non-growing periods, as in many regions because of vegetation dormancy, snow cover, and/or frozen soils, the surface conditions do not represent the assumed reference conditions. A number of factors may lead to unrealistic

1056

reference (potential) evapotranspiration and Kc estimates by combination methods, such as the ASCE Penman-Monteith equation. In addition, as reported by ASCE (2005) and Hay and Irmak (2009), unrealistic evapotranspiration estimates are possible during winter periods, especially in extremely cold winter climates, due to increased bulk surface resistance, change in the number of daytime hours to nighttime hours, greater influence of the aerodynamic com-


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Cumulative Thermal Units (°C) Figure 5. Grass-reference single (normal) crop coefficients (Kco) of winter wheat as a function of thermal unit (TU) in the 2008-2009 and 20092010 growing seasons and pooled data: Kco pooled = -7.0E-19 × (TU)6 + 5.66084E-15 × (TU)5 − 17.46399515E-12 × (TU)4 + 24.74797729938E-9 × (TU)3 − 156.305942715322E-7 × (TU)2 + 403.203773409052E-5 × (TU) + 0.29554501231487.

ponent of the combination equation relative to the radiation component during periods with low temperatures and high wind speeds, and unrealistic values of canopy resistance at low air temperatures. In this research, the assumed reference conditions when calculating ETref do not exist in south central Nebraska’s cold and windy conditions where the surface is snow-

58(4): 1047-1066

covered and/or frozen. The vertical superposed Kc values at thermal units of 435°C in figures 5, 7, 9, and 11 indicate the non-dependency of Kc to the plants, but dependency to the aerodynamic variables during the dormancy period. During extreme cold periods (i.e., 48 to 55 DAP), even though there was minimal accumulation of thermal unit, the Kc values varied from close to zero to 1.60 for Kco and to

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1.6 2008-2009

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Days after Planting (DAP) Figure 6. Alfalfa-reference single (normal) crop coefficients (Kcr) of winter wheat as a function of days after planting (DAP) in the 2008-2009 and 2009-2010 growing seasons and pooled data: Kcr pooled = -4.6378472E-13 × (DAP)6 + 3.5083E-10 × (DAP)5 − 9.98E-8 × (DAP)4 + 1.333095E-5 × (DAP)3 − 8.3846542E-4 × (DAP)2 + 0.021308 × (DAP) + 0.2721.

1.40 for Kcr due to the existence of ETc and ETref, creating a vertical distribution of Kc values in a very narrow range of TU. The Kc curves, as a function of DAP or TU, varied only slightly among seasons, indicating similar climatic and management practices as well as robustness (repeatability) of the measured crop coefficients. Even though there was only a slight difference between Kc values developed as a function of TU vs. DAP, it is recommended to use Kc and

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Kcb as a function of TU to avoid variability in within-season crop growth and development stage impact (due to differences in climate between years) on interannual variation in Kc values. The basal crop coefficient (Kcb) is defined as the ratio of ETc to ETref when the soil surface is dry and soil evaporation is minimal, but soil water availability remains nonlimiting for plant transpiration (Wright, 1982). Therefore,


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Cumulative Thermal Units (°C) Figure 7. Alfalfa-reference single (normal) crop coefficients (Kcr) of winter wheat as a function of thermal unit (TU) in the 2008-2009 and 20092010 growing seasons and pooled data: Kcr pooled = -1.2E-19 × (TU)6 + 1.90561E-15 × (TU)5 − 7.99359611E-12 × (TU)4 + 13.10334200509E-9 × (TU)3 − 8589.22065431722E-9 × (TU)2 + 0.00222334843969852 × (TU) + 0.247158155172662.

Kcbo × ETo is assumed to represents primarily the transpiration component of ETc. Based on the measured Kc values reported in table 3, the seasonal average grass-reference basal crop coefficient (Kcbo) is about 87% of Kco, and the alfalfa-reference basal crop coefficient (Kcbr) is 89% of Kcr. Therefore, transpiration is expected to be about 87% to 89% of ETc, and evaporation represents about 11% to 13%

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of ETc. In this research, soil water evaporation accounted for only a small proportion of evapotranspiration, decreased with DAP, and decreased with crop growth and development. However, the percentage of transpiration and evaporation varied during the season in both years. For example, soil water evaporation during the winter wheat dormancy period represented 21% and 10% of seasonal ETc in the

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Basal Crop Coefficient (Kcbo)

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Days after Planting (DAP) Figure 8. Grass-reference basal crop coefficients (Kcbo) as a function of days after planting (DAP) for the 2008-2009 and 2009-2010 growing seasons and pooled data: Kcbo pooled = -3.6534189E-13 × (DAP)6 + 2.6141452573E-10 × (DAP)5 − 69.66173847253E-9 × (DAP)4 + 86.827671480599E-7 × (DAP)3 − 5086.86264105137E-7 × (DAP)2 + 0.0121271355085331 × (DAP) + 0.353468133260731.

2008-2009 and 2009-2010 growing seasons, respectively. The ratio of Kcbo to Kco ranged from 0.69 to 0.97, and the ratio of Kcbr to Kcr ranged from 0.63 to 0.98. These results are close to those observed by Gao et al. (2005), who reported that soil evaporation was about 12% of ETc. However, Liu et al. (2002) and Kang et al. (2003) reported high-

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er evaporation rates of 30% and 33%, respectively, of the total seasonal winter wheat ETc. For practical application by practitioners, table 3 lists the two-year average Kco, Kcr, Kcbo, and Kcbr values for each winter wheat growth and development stage. All Kco, Kcr, Kcbo, and Kcbr values are those developed using thermal unit as a base scale. To ena-


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Cumulative Thermal Units (°C) Figure 9. Grass-reference basal crop coefficients (Kcbo) of winter wheat as a function of thermal unit (TU) in the 2008-2009 and 2009-2010 growing seasons and pooled data: Kcbo pooled = 1E-20 × (TU)6 + 7E-16 × (TU)5 − 4E-12 × (TU)4 + 8E-09 × (TU)3 − 5E-06 × (TU)2 + 0.0012 × (TU) + 0.3542.

ble daily calculations of Kc values in practice, winter wheat Kco, Kcr, Kcbo, and Kcbr equations as a function of DAP and TU (two-season pooled data) are provided in the Appendix.

58(4): 1047-1066

SUMMARY AND CONCLUSIONS Winter wheat daily evapotranspiration (ETc) was measured and growth-specific grass- and alfalfa-reference single (normal) crop coefficients (Kco and Kcr, respectively) and grass- and alfalfa-reference basal crop coefficients (Kcbo

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Basal Crop Coefficient (Kcbr)

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Days after Planting (DAP) Figure 10. Alfalfa-reference basal crop coefficients (Kcbr) of winter wheat as a function of days after planting (DAP) in the 2008-2009 and 20092010 growing seasons and pooled data: Kcbr pooled = -41.60568572742E-14 × (DAP)6 + 30.9795721203864E-11 × (DAP)5 − 87.0998122665609E-9 × (DAP)4 + 11.621613435019E-6 × (DAP)3 − 74.9086634264634E-5 × (DAP)2 + 0.0214010844091539 × (DAP) + 0.127676534863044.

and Kcbr, respectively) were developed as a function of days after planting (DAP) and thermal unit (TU; growing degree days) for south central Nebraska climatic and soil and crop management conditions for two consecutive winter wheat growing seasons (2008-2009 and 2009-2010). Daily ETc increased with DAP in the pre-winter period, stayed very low during extreme cold periods in winter, and increased

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again during the post-winter periods. Maximum ETc occurred on 229 DAP (19 May 2009) in the 2008-2009 growing season and on 237 DAP (24 May 2010) in the 2009-2010 growing season, which was primarily driven by air temperature, solar radiation, water availability, and winter wheat growth stage. The seasonal winter wheat ETc was 600 mm during the 2008-2009 growing season and 490 mm during


1.2 Basaal Crop Coefficient (Kcbr)

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Cumulative Thermal Units (°C) 1.2 Basal Crop Coefficient (Kcbr)

Pooled data 1.0 0.8 0.6 0.4 0.2

Kcb 2008-2009 Kcb(2008-2009)

Kcb(2009-2010) 2009-2010 Kcb

0.0 0

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Cumulative Thermal Units (°C) Figure 11. Alfalfa-reference basal crop coefficients (Kcbr) of winter wheat as a function of thermal unit (TU) in the 2008-2009 and 2009-2010 growing seasons and pooled data: Kcbr pooled = 55.3339791244E-20 × (TU)6 − 29.3881911924252E-16 × (TU)5 + 50.1338379896929E-13 × (TU)4 − 29.2401451730525E-10 × (TU)3 + 277.535380801621E-9 × (TU)2 + 4921.33090141017E-7 × (TU) + 0.199743914368643.

the 2009-2010 growing season. Winter wheat yield ranged from 0.33 to 7.99 t ha-1 in 2008-2009 and from 0.29 to 7.83 t ha-1 in 2009-2010, with field-average yields of 4.55 t ha-1 in both growing seasons. The water productivity calculated from field-average ETc and field-average yield was 0.76 kg m-3 in 2008-2009 and 0.93 kg m-3 in 2009-2010.

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Crop coefficients varied substantially with the growth and development stage. Two-year average Kco values were 0.60, 1.30, and 0.30, and Kcr values were 0.40, 1.10, and 0.20 for the early-season, mid-season, and late-season periods, respectively. Two-year average basal crop coefficient (Kcbo) values were 0.45, 1.30, and 0.30, while Kcbr values

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Table 3. Two-year average growth stage-specific grass- and alfalfareference single (normal) crop coefficients (Kco and Kcr, respectively) and grass- and alfalfa-reference basal crop coefficients (Kcbo and Kcbr, respectively) of winter wheat. Crop Coefficient Winter Wheat Growth and Development Stage Kco Kcr Kcbo Kcbr Feekes 1: One shoot 0.63 0.43 0.44 0.27 Feekes 2: Tillering begins 0.59 0.41 0.44 0.37 Feekes 3: Tillers formed 0.57 0.46 0.49 0.42 Feekes 4: Leaf sheaths lengthen 0.75 0.66 0.69 0.47 Feekes 5: Leaf sheaths strongly erected 0.84 0.78 0.78 0.67 Feekes 6: First node visible 0.86 0.64 0.63 0.54 Feekes 7: Second node visible 0.91 0.65 0.63 0.63 Feekes 8: Last leaf visible 1.00 0.78 0.90 0.68 Feekes 9: Ligule of last leaf visible 1.28 1.06 1.23 0.95 Feekes 10: In boot 1.22 1.02 1.18 1.00 Feekes 10.1: Head visible 1.33 1.09 1.21 1.00 Feekes 10.5: Flowering 1.33 1.06 1.27 1.00 Feekes 11: Repining 0.98 0.67 0.78 0.60

were 0.30, 1.05, and 0.20 for the same growth stages, respectively. For practical application by practitioners, the two-year average Kco, Kcr, Kcbo, and Kcbr values were tabulated for each winter wheat growth and development stage. Furthermore, to enable daily calculations of Kc values in practice, winter wheat Kco, Kcr, Kcbo, and Kcbr values as a function of DAP and TU (from two-season pooled data) were developed. Even though there was only a slight difference between Kc values developed as a function of TU vs. DAP, it is recommended to use Kc and Kcb as a function of TU to avoid variability in within-season crop growth and development stage impact (due to differences in climate between years) on interannual variation in Kc values. The results and findings of this research should be applicable to soil, climatic, and crop management conditions similar to those observed in south central Nebraska; caution should be used when extrapolating the results beyond these boundaries.

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APPENDIX The developed polynomial equations for estimating Kco, Kcr, Kcbo, and Kcbr values for winter wheat as a function of DAP and TU (two-season pooled data) are as follow: Kco pooled = -5.4336365E-13 × (DAP)6 + 4.141951E-10 × (DAP)5 − 1.1944436E-7 × (DAP)4 + 1.6329E-5 × (DAP)3 − 10.651547E-4 × (DAP)2 + 0.02847 × (DAP) + 0.397

(5)

Kcr pooled = -4.6378472E-13 × (DAP) + 3.5083E-10 × (DAP)5 − 9.98E-8 × (DAP)4 + 1.333095E-5 × (DAP)3 − 8.3846542E-4 × (DAP)2 + 0.021308 × (DAP) + 0.2721

(6)

6

Kco pooled = -7.0E-19 × (TU)6 + 5.66084E-15 × (TU)5 − 17.46399515E-12 × (TU)4 + 24.74797729938E-9 × (TU)3 − 156.305942715322E-7 × (TU)2 + 403.203773409052E-5 × (TU) + 0.29554501231487

(7)

Kcr pooled = -1.2E-19 × (TU)6 + 1.90561E-15 × (TU)5 − 7.99359611E-12 × (TU)4 + 13.10334200509E-9 × (TU)3 − 8589.22065431722E-9 × (TU)2 + 0.00222334843969852 × (TU) + 0.247158155172662

(8)

Kcbo pooled = -3.6534189E-13 × (DAP) + 2.6141452573E-10 × (DAP)5 − 69.66173847253E-9 × (DAP)4 + 86.827671480599E-7 × (DAP)3 − 5086.86264105137E-7 × (DAP)2 + 0.0121271355085331 × (DAP) + 0.353468133260731 6

(9)

Kcbo pooled = 1E-20 × (TU) + 7E-16 × (TU) − 4E-12 × (TU)4 + 8E-09 × (TU)3 − 5E-06 × (TU)2 + 0.0012 × (TU) + 0.3542 6

5

(10)

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Kcbr pooled = -41.60568572742E-14 × (DAP)6 + 30.9795721203864E-11 × (DAP)5 − 87.0998122665609E-9 × (DAP)4 + 11.621613435019E-6 × (DAP)3 − 74.9086634264634E-5 × (DAP)2 + 0.0214010844091539 × (DAP) + 0.127676534863044 Kcbr pooled = 55.3339791244E-20 × (TU)6 − 29.3881911924252E-16 × (TU)5 + 50.1338379896929E-13 × (TU)4 − 29.2401451730525E-10 × (TU)3 + 277.535380801621E-9 × (TU)2

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+ 4921.33090141017E-7 × (TU) + 0.199743914368643

(11)

(12)

where Kco = grass-reference single (normal) crop coefficient (unitless) Kcr = alfalfa-reference single (normal) crop coefficient (unitless) Kcbo = grass-reference basal crop coefficient (unitless) Kcbr = alfalfa-reference basal crop coefficient (unitless) DAP = days after planting (unitless) TU = thermal unit (growing degree days) (°C).
