Agricultural Water Management 179 (2017) 92–102 2524 Contents lists available at ScienceDirect Agricultural Water Management journal homepage: www.elsevier.com/locate/agwat Assessing FAO-56 dual crop coefficients using eddy covariance flux partitioning Ray G. Anderson a,∗ , Joseph G. Alfieri b , Rebecca Tirado-Corbalá c,1 , Jim Gartung c , Lynn G. McKee b , John H. Prueger d , Dong Wang c , James E. Ayars c , William P. Kustas b a US Salinity Laboratory, USDA-Agricultural Research Service, George E. Brown Jr. Salinity Laboratory, 450 W. Big Springs Rd., Riverside, CA, 92507-4617, USA2 b Hydrology and Remote Sensing Laboratory, USDA-Agricultural Research Service, 10300 Baltimore Ave., Bldg. 007 BARC-WEST, Beltsville, MD, 20705, USA c Water Management Research, USDA-Agricultural Research Service, San Joaquin Valley Agricultural Sciences Center, 9611 S. Riverbend Ave., Parlier, CA, 93648-9757, USA d National Laboratory for Agriculture and the Environment, USDA-Agricultural Research Service, 2110 University Blvd., Ames, IA 50011, USA a r t i c l e i n f o Article history: Received 4 February 2016 Received in revised form 27 July 2016 Accepted 31 July 2016 Available online 8 August 2016 Keywords: FAO-56 Eddy covariance Flux partitioning Crop coefficients Evapotranspiration a b s t r a c t Current approaches to scheduling crop irrigation using reference evapotranspiration (ET0 ) recommend using a dual-coefficient approach using basal (Kcb ) and soil (Ke ) coefficients along with a stress coefficient (Ks ) to model crop evapotranspiration (ETc ), [e.g. ETc = (Ks *Kcb + Ke )*ET0 ]. However, determining Ks , Kcb , and Ke from the combined evapotranspiration (ET) is challenging, particularly for Ke , and a new method is needed to more rapidly determine crop coefficients for novel cultivars and cultivation practices. In this study, we partition eddy covariance ET observations into evaporation (E) and transpiration (T) components using correlation structure analysis of high frequency (10–20 Hz) observations of carbon dioxide and water vapor (Scanlon and Sahu, 2008) at three irrigated agricultural sites. These include a C4 photosynthetic-pathway species (sugarcane—Sacharum officinarum L.) and a C3 pathway species (peach—Prunus persica) under sub-surface drip and furrow irrigation, respectively. Both sites showed high overall Kc consistent with their height (>4 m). The results showed differences in Ke , with the subsurface drip-irrigated sugarcane having a low Ke (0.1). There was no significant relationship (r2 < 0.05) between root zone soil volumetric water content (VWC) in sugarcane and observed Kcb *Ks , indicating that there was no stress (Ks = 1), while the peach orchard showed mid-season declines in Kcb *Ks when VWC declined below 0.2. Partitioning of Kc into Kcb and Ke resulted in a better regression (r2 = 0.43) between the Normalized Differential Vegetation Index (NDVI) and Kcb in sugarcane than between NDVI and Kc (r2 = 0.11). The results indicate the potential for correlation structure flux partitioning to improve crop ET coefficient determination by improved use of eddy covariance observations compared to traditional approaches of lysimeters and microlysimeters and sap flow observations to determine Kc , Ke , Ks , and Kcb . Published by Elsevier B.V. ∗ Corresponding author. E-mail addresses: ray.anderson@ars.usda.gov, r.g.anderson@gmail.com (R.G. Anderson), joe.alfieri@ars.usda.gov (J.G. Alfieri), rebecca.tirado@upr.edu (R. Tirado-Corbalá), jim.gartung@ars.usda.gov (J. Gartung), lynn.mckee@ars.usda.gov (L.G. McKee), john.prueger@ars.usda.gov (J.H. Prueger), dong.wang@ars.usda.gov (D. Wang), james.ayars@ars.usda.gov (J.E. Ayars), bill.kustas@ars.usda.gov (W.P. Kustas). 1 Present address: Crops and Agro-Environmental Science Department, University of Puerto Rico, PO Box 9000, Mayagüez, Puerto Rico, 00681-9000 USA. 2 Note: The U.S. Department of Agriculture (USDA) prohibits discrimination in all its programs and activities on the basis of race, color, national origin, age, disability, and where applicable, sex, marital status, familial status, parental status, religion, sexual orientation, genetic information, political beliefs, reprisal, or because all or part of an individual’s income is derived from any public assistance program. (Not all prohibited bases apply to all programs.) Persons with disabilities who require alternative means for communication of program information (Braille, large print, audiotape, etc.) should contact USDA’s TARGET Center at (202) 720-2600 (voice and TDD). To file a complaint of discrimination, write to USDA, Director, Office of Civil Rights, 1400 Independence Avenue, S.W., Washington, D.C. 20250-9410, or call (800) 795-3272 (voice) or (202) 720-6382 (TDD). USDA is an equal opportunity provider and employer. http://dx.doi.org/10.1016/j.agwat.2016.07.027 0378-3774/Published by Elsevier B.V. R.G. Anderson et al. / Agricultural Water Management 179 (2017) 92–102 1. Introduction Agricultural irrigation is the largest anthropogenic use of fresh water (Döll and Siebert, 2002). Accurately parameterizing crop water demand is critical to optimizing irrigation amounts and timing, maximizing crop growth and water productivity, and minimizing losses due to over-irrigation or crop stress from under irrigation (Doorenbos et al., 1979; Steduto et al., 2012). One major approach for calculating crop evapotranspiration (ET) is described in the Food and Agricultural Organization Irrigation and Drainage paper 56 (FAO-56 – Allen et al., 1998). FAO-56 combines a reference evapotranspiration (ET0 ), characterizing meteorological evaporative demand, along with a crop coefficient representing agricultural field characteristics, including crop type, plant density, phenology, soil water content status, and others. The FAO-56 method can be run with either a single crop coefficient (Kc ) or a dual crop coefficient approach that separately represents soil evaporation (Ke ) and plant transpiration and stress (Kcb and Ks ). Currently, numerous hydrologic models combine a multiple coefficient approach with FAO-56 ET0 (Raes et al., 2009; Rosa et al., 2012). Using a dual coefficient approach may be more appropriate for many cropping systems with technologies such as drip irrigation (Paço et al., 2012), plastic or organic mulching (Ding et al., 2013; Odhiambo and Irmak, 2012), partial root zone drying (O’Connell and Goodwin, 2007), and deficit irrigation (Ferreira et al., 2012). These techniques minimize soil evaporation and maximize water productivity, and, as such, it is important for irrigation studies to be able to independently determine and assess Kcb , Ks , and Ke . Despite the increasing relevance of using the dual crop coefficient approach for modeling crop ET, determination of Kcb , Ks , and Ke is challenging. The most commonly used methods for observing crop ET, including soil water balance (Bodner et al., 2007), lysimetry (Liu and Luo, 2010), and micrometeorological approaches including eddy covariance (EC) (Paço et al., 2006; Zhang et al., 2013), surface renewal (Testi et al., 2004) and Bowen ratio energy balance (InmanBamber and McGlinchey, 2003; Todd et al., 2000), cannot partition ET into evaporation (E) and transpiration (T). The FAO-56 approach and other studies rely on analyzing individual irrigation events and determining Kcb after an irrigation event when the soil surface is dry and E is very low or negligible (Allen et al., 1998; Benli et al., 2006). Other crop water use studies incorporate modeling to determine Kcb and Ke from the single coefficient (Kato and Kamichika, 2006). Separate E and T measurements are ideally needed to determine Kcb , Ks , and Ke . Direct observations of E and T, including microlysimetery (Liu et al., 2002) and sap flow techniques (Rana et al., 2005) observe small areas relative to the whole field and have similar issues of spatial representativeness (Kool et al., 2014; Williams et al., 2004). Another option for partitioning of fluxes is micrometeorological observations of isotopic fluxes (mainly 18 O and 13 C), which can be used to partition fluxes due to isotopic discrimination during photosynthesis and evaporation (Griffis et al., 2004; Zhang et al., 2011). However, this method has substantial methodological challenges due to uncertainty over the relationship between isotopic discrimination and land-atmospheric exchange processes at differing sites (Griffis et al., 2011; Sutanto et al., 2014); it also is considerably more expensive than EC. Due to expense and challenges of measuring E or T, numerous studies measure either E or T and determine the other component by residual (Ferreira et al., 2012; Liu et al., 2002). Recently a method of partitioning EC fluxes was developed based on flux-variance similarity theory, which uses parameterized leaf-level water use efficiency and analysis of the correlation structure of high frequency CO2 and H2 O time series observations from each flux averaging interval (Scanlon and Sahu, 2008; Scanlon and Kustas 2010, 2012). This method (hereafter called “EC FP”) enables separation of EC fluxes into E and T without additional observa- 93 tions. In this study, we conceptually demonstrate how EC FP can be applied to efficiently determine Kcb *Ks and Ke from EC observations in irrigated agricultural fields. Using observations during stressed and non-stressed periods, we illustrate how Ks can be separated from Kcb *Ks . We apply EC FP to three sites in two, contrasting irrigated agricultural systems. The first two sites are sub-surface drip-irrigated sugarcane (Sacharum officinarum L.) fields located in Hawaii, USA, while the third site is a furrow-irrigated peach orchard (Prunus persica) in California, USA. Finally, we illustrate how EC FP can also be used to enable soil moisture and satellite observations for quantifying Kcb , Ks , and Ke in operational settings for irrigation management. 2. Materials and methods 2.1. Flux partitioning and crop coefficient calculation EC FP relies on applying flux variance similarity (Scanlon and Sahu, 2008) to high frequency wind velocity and CO2 and H2 O concentration observations. We followed Scanlon and Kustas (2010, 2012) for data processing to determine half hourly partitioned fluxes. Briefly, Reynolds averaging and density fluctuation corrections were made to the data, and then wavelet filtering was applied to remove the impact of large-scale, low-frequency atmospheric processes (Reynolds, 1895; Scanlon and Sahu, 2008; Webb et al., 1980). Wavelet size decreased until an analytic solution was found to satisfy similarity theory with the given leaf-level water use efficiency (WUE), which is the ratio of leaf-level CO2 assimilation to transpiration, and resultant stomatal and non-stomatal components (Scanlon and Kustas, 2010). Along with the high frequency atmospheric time series data, WUE is the only other input used in the EC FP model. WUE was estimated following Campbell and Norman (1998) (see also Eq. (1) in Scanlon and Kustas, 2012). Intercellular H2 O assumed to be the saturation vapor pressure of the parameterized leaf temperature, while intercellular CO2 (ci ) is parameterized differently for the C3 and C4 photosynthetic pathways. For the C4 sugarcane sites, ci is estimated as a constant fraction (0.44) of atmospheric CO2 (ca ) (Kim et al., 2006). For the C3 peach orchard, the ci /ca ratio is a function of vapor pressure deficit (VPD) following Katul et al. (2009) as shown below: ci =1− ca  ˛ 0.5 ca D0.5 (1) Where ␣ is the diffusivity of CO2 to H2 O (1.6), D is VPD, and ␭ is a parameter describing the relationship between ci and ca . ␭ was set at 22 following the leaf-level analyses presented in Katul et al. (2009). We scaled the half hourly partitioned fluxes to daily fractions of transpiration (FT ) and evaporation (FE ) following Eqs. (2) and (3): FT = 1 j 1 FE = j T+ j 1 j 1 T+ T j 1 (2) E E j 1 (3) E Where T and E are the evaporation and transpiration outputs from the EC FP program and summation subscripts 1 and j denote the first and last periods of a day where the EC FP program finds a solution. Periods where the program does not come to a solution are excluded from the summation. If j < 8 for a given day, Eqs. (2) and (3) are not run, FT and FE are assumed to be missing for those days, and the dual crop coefficients are not calculated. We chose 8 periods (4 h) to reduce potential time of day biases in calculating FT and FE while still maximizing the number of days where the crop coefficients are calculated. FT and FE can be used to partition the 94 R.G. Anderson et al. / Agricultural Water Management 179 (2017) 92–102 Fig. 1. Map of peach study site. (a) Map of United States with southern San Joaquin Valley, California, highlighted. (b) False color image of southern San Joaquin Valley (Landsat 8 platform—June 13, 2016) with peach orchard indicated. For maps of the Hawaiian sugarcane study sites, please refer to Anderson et al. (2015a,b) or Zhang et al. (2015). single crop coefficient (Kc ) into Kcb *Ks and Ke following Eqs. (4) and (5): Kcb ∗ Ks = FT ∗ Kc (4) Ke = FE ∗ Kc (5) Two-week, running means of Kcb *Ks and Ke are calculated from the daily data. Ks can be separated from Kcb during periods of the growing season following onset of stress when canopy cover is relatively constant and Kcb can be assumed to be a constant as shown in Eq. (6): KS (t2 ) = Kcb ∗ Ks (t2 ) Kcb ∗ Ks (t1 ) (6) where t1 and t2 can either be two times in space or two differing values of soil moisture or salinity stress; Kcb *Ks can be determined for each time from Eq. (5); and t1 is assumed to be before onset of stress. Appropriate times for t1 and t2 need to be assessed by a combination of crop cover data and ancillary observations (soil water content/matric potential and salinity content), which may indicate onset of stress. 2.2. Study sites Two agricultural production systems and three fields were used to evaluate EC FP and crop coefficients. One system (two fields) was two-year, sub-surface drip irrigated sugarcane (Sacharum officinarum L. cv. H65-7052) on a commercial plantation in Maui, Hawaii, United States. Data from these fields (hereafter denoted Windy and Lee), and the plantation’s cultivation practices have been reported elsewhere (Anderson and Wang, 2014; Anderson et al., 2015a,b; Tirado-Corbalá et al., 2015; Zhang et al., 2015) and are briefly discussed here. Windy and Lee were planted in May and March 2011, respectively, and harvested in June 2013 and November 2012, respectively, with towers removed 2–6 weeks prior to harvest. For R.G. Anderson et al. / Agricultural Water Management 179 (2017) 92–102 analyses of Kc , data from Windy was truncated to 600 days after planting (DAP) for comparison with the shorter record from Lee. In both fields, we observed existing farm agronomic practices. The farm scheduled irrigations based on reference ET from its own inhouse weather station network and customized crop coefficients. The Windy and Lee fields and data have several characteristics that make them a particularly useful testbed for assessing crop coefficients with EC FP, including (1) minimal (<150 mm) growing season precipitation due to the fields leeward location and Maui’s drought during the data collection period, (2) presence of a layer of sugarcane residue (also known as “trash”) during the middle and later parts of the growing season that minimize E, and (3) high photosynthetic and evaporative fluxes. For these two fields we used a custom Penman-Monteith based ET0 equation due to divergence between the FAO-56 ET0 and measured ET under high wind speeds as reported by Anderson et al. (2015b). The second production system is a mature cling peach orchard (Prunus persica—cv. Ross) located on a commercial farm (Fig. 1) in the San Joaquin Valley of California, United States (36.4582◦ N, 119.5793◦ W, and 86 m elevation for eddy covariance tower site). The orchard soil is a coarse-loamy, alluvial soil, Wasco Series (Soil Survey Staff, 2016). The climate is typical of the region with warm to hot, dry summers (maximum air temperature of ∼40 ◦ C) and cool, rainy winters; average annual (1981–2010) precipitation is 256 mm (PRISM Climate Group, 2016). The 8.3 ha (20 acre) orchard was planted in 1998 with a spacing of 6.1 m (20 feet) between rows and 3.0 m (10 feet) between trees within rows. The trees were planted on a small raised berm (width of ∼150 cm) in between two furrows (bottom width ∼125 cm, maximum depth 25 cm). The trees were trimmed to a height of 4.1 m (13.5 ft.) at the end of each season, and regrew to a maximum height of 6 m during the growing season. There was no lateral trimming (reduction of canopy width) during the growing season. During the growing season, the orchard was fully vegetated (LAI exceeding 3 m2 m−2 ; fractional canopy cover exceeding 80%). The farmer irrigated based on his experience and assessment of crop and soil conditions. The farm used surface water or groundwater depending upon water availability. During normal periods, the orchard was irrigated to meet full evaporative demand with furrows filled approximately once every 4–12 days (irrigation application depth of 52–58 mm per event) depending upon meteorological demand and proximity to harvest. However, the farm’s well ran dry during part of the 2014 drought-affected growing season, and the farmer was unable to fully irrigate during this season. Leaf growth usually started in March with harvest in early August and leaf senescence in late November. Like the sugarcane fields, the peach orchard had little (or no) precipitation during the growing season and also had high evaporative and photosynthetic fluxes. For this orchard, ET0 was provided by the Spatial California Irrigation Management Information (Spatial CIMIS) product (Hart et al., 2009). 2.3. Eddy covariance (EC) and soil volumetric water content (VWC) observations Details about the sugarcane EC towers, associated meteorological and soil instrumentation, and data processing are reported elsewhere (Anderson and Wang, 2014; Anderson et al., 2015a,b). Both sugarcane sites were instrumented with open-path infrared gas analyzers (IRGAs). Both fields had adequate fetch distance and conditions. In each field, VWC was observed at 20 cm depth near the tower site with water content time-domain reflectometers underneath the cane row and in between each set of drip lines. Sensors were custom calibrated for each field’s soil texture, and a water retention curve was measured for each soil from Tempe cell samples (Anderson et al., 2015b). As discussed in Anderson et al. (2015b), VWC observations were not possible in the Lee field due 95 to rockiness. Precipitation data from both sites was measured at an on farm weather station network with a station within 1500 m of each EC tower. Like the sugarcane fields, the instrumentation in the peach orchard also consisted of an IRGA (Licor 7500, Licor Inc., Lincoln, Nebraska, USA3 ) and 3D sonic anemometer (CSAT3, Campbell Scientific Inc., Logan, Utah, USA). These instruments were mounted on a custom, non-guyed, telescoping pole which was adjusted to keep the cross bar with the EC instruments ∼2–2.5 m above the top of the canopy depending upon the time of year and expected change of canopy height. A four component net radiometer (CNR1, Hukseflux, Delft, Netherlands) was mounted at the top of the telescoping pole, 70 cm above the EC instruments. Along with the IRGA and sonic anemometer, there was an integrated air temperature and relative humidity sensor (HMP45C, Vaisala, Vantaa, Finland). Due to the relatively small dimensions of the field, 400 m east-west and 200 m north-south, the tower was not installed in the center of the field, but instead in the southeast quadrant of the field (30 m north of the south edge of the field and 118 m west of the eastern edge of the field). This placement resulted in better fetch distance to the north and west, which takes advantage of the predominant northwesterly winds at this site. An on-site rain gauge (TE525WS, Texas Electronics, Dallas, Texas, USA) was installed at the beginning of 2013; rain data prior to 2013 came from the CIMIS station at Parlier, California (station #44). There was also an extensive soil heat flux and moisture monitoring array that included 8 locations immediately around the tower; three were located on the berm 0.5 m away from the trunk of a peach tree oriented perpendicular to the berm and 45◦ between perpendicular and parallel to the berm. The other 5 locations were located perpendicular to the mound in line with the same peach tree and were located at 1.5 m (furrow bottom), 2.1 m (furrow edge), and 2.75 m, 3.75 m, and 4.75 m away from the tree, with the last three locations being on the inter-row between the irrigation furrows. At each location type-T, copper-constantan, soil thermocouples were placed at 2 and 6 cm depths to monitor near surface soil heat storage. A heat flux plate (HFT3, REBS, Seattle, Washington, USA) was installed at 8 cm to measure soil heat flux, and soil water content was measured using an impedance dielectric sensor (Hydra Probe II, Stevens Water Monitoring Systems, Inc., Portland, Oregon, USA), also placed at 8 cm depth. We used the manufacturer’s default calibration to convert dielectric readings to soil volumetric water content; the default calibration has a standard deviation of 0.01 m3 m−3 for loamy soils similar to the peach orchard soil. Soil volumetric water content at field capacity (−0.020 MPa) was measured with a pressure plate while permanent wilting point (−15 MPa) was measured with a dew point hygrometer (WP4C, Decagon Devices, Pullman, Washington, USA) to avoid overestimation at lower soil water potential (Bittelli and Flury, 2009). Data from the sonic anemometer and IRGA were recorded at 20 Hz during the first two growing seasons of observation (2012 and 2013) and 10 Hz during the 2014 season. After the first two seasons, the flux collection rate was changed to 10 Hz to make data processing, handling, and storage more logistically feasible. Evaluation of flux spectra and energy budget closure did not indicate missing energy and mass transport in the 10–20 Hz range which would bias ET observations. Flux data were processed to 15 min averaging intervals using open-source software (EddyPro® (v5.0—Advanced mode), released by LI-COR Biosciences, Lincoln, Nebraska USA—http://www.licor.com/eddypro) with custom setting and corrections identical to those used by Anderson et al. 3 Mention of trade names or commercial products in this publication is solely for the purpose of providing specific information and does not imply recommendation or endorsement by the U.S. Department of Agriculture. R.G. Anderson et al. / Agricultural Water Management 179 (2017) 92–102 2.4. Satellite remote sensing observations For the sugarcane fields, we calculated Normalized Differential Vegetation Index (NDVI) using reflectance data from the MODerate resolution Imaging Spectroradiometer (MODIS), Terra 250m, 16 day vegetation product (product ID: MOD13Q1 v.5 – Huete et al., 2002). Following Anderson et al. (2015a), reflectance data were extracted for the pixel overlapping the tower footprint using the Oak Ridge National Laboratory subsetting and visualization tool (http://daac.ornl.gov/cgi-bin/MODIS/GLBVIZ 1 Glb/modis subset order global col5.pl). NDVI observations for the peach orchard EC tower were obtained from the Landsat 7 satellite using the TOPS Satellite Irrigation Management System (SIMS) platform (http://ecocast.arc.nasa.gov/dgw/sims/ – Melton et al., 2012). Although TOPS SIMS produces fractional canopy cover (Fc ) estimates, we chose to use their NDVI values for comparison with the sugarcane fields and due to erratic mid-season patterns in SIMS provided Fc that diverged from non-gap filled Landsat NDVI. 3. Results Table 1 Precipitation days (greater than 1.5 mm) for Maui sugarcane sites. The number of additional smaller precipitation events (0.25–1.5 mm) was less than 10 for each tower site. These are excluded for brevity and because of their negligible contribution to the hydrologic fluxes for each site. DAP – Windy Precipitation (mm) – Windy DAP – Lee Precipitation – Lee 129 203 214 216 271 272 299 300 301 302 405 498 598 1.5 2 3.3 9.7 1.8 18 4.1 22.4 6.4 10.9 3.3 7.1 2.3 219 257 259 313 314 315 341 342 343 345 540 3.8 3.8 3.8 3.6 2.8 17.5 2.3 2.8 19.8 2.5 2.8 10 8 −1 (2015a). When winds came between 130◦ and 230◦ , fetch conditions were assumed to be inadequate, and data during these periods were gap-filled. Gap filling and energy budget closure (Reichstein et al., 2005; Leuning et al., 2012) also followed the procedure used by Anderson and Wang (2014) and Anderson et al. (2015a), with the addition that fluxes coming from the south with unsuitably short fetches were considered as missing and correspondingly gap filled. All other meteorological and soil data were averaged over the 15 min intervals as the EC data. ET0 (mm day ) 96 6 4 2012 running 2013 running 2014 running 2012 daily 2013 daily 2014 daily 2 3.1. Micro-meteorological observations, ET0 , and EC ET Details of the micrometeorological, ET0 , and EC ET observations for the Maui sugarcane sites are reported elsewhere (Anderson and Wang, 2014; Anderson et al., 2015a,b) with key aspects briefly discussed here. The overall quality of the EC ET observations was excellent, with energy balance approaching full closure (97%) at Windy, few daytime gaps at Lee that would affect ET sums, and 90% flux footprints that were well within field boundaries at both fields (Anderson et al., 2015b). Both fields exhibited moderate daily ET and ET0 , with mean ET values of 3.2 and 3.1 mm day−1 in Windy and Lee, respectively, and mean ET0 of 3.8 and 4.1 mm day−1 . The limited seasonality and moderate rates of EC ET and ET0 are consistent with Hawaiian climatology with limited temperature ranges (seasonal maximum daily temperature range of ∼4 ◦ C) and relatively mild maximum daily temperatures of less than 30 ◦ C. Cumulative precipitation for both sites was less than 100 mm during the period of analysis (Table 1). With respect to the peach orchard, the EC tower had a reasonable energy closure on a daily basis with measured turbulent fluxes comprising 83% of radiometric fluxes. 10% of the turbulent flux periods (friction velocity greater than 0.1 m s−1 ) needed to be gap filled due to the wind coming from a southerly direction with unsuitably short fetch length. The mean 70% flux footprint length during turbulent periods was 109 m while the mean 90% footprint length was 163 m, which both lie within the field boundaries for predominant wind directions. The climatology for the peach site is characteristic of the San Joaquin Valley and is briefly discussed here with respect to the 2012–2014 tower record. The site has high solar irradiance with a mean of 21.4 MJ m−2 day−1 and a maximum of 33.0 MJ m−2 day−1 . Mean air temperature during the entire study period was 17.3◦ C with daily average temperatures ranging from −0.5 to 29.3◦ C for the coldest and warmest days. Wind speeds were 0 50 100 150 200 250 300 DOY Fig. 2. Reference ET (ET0 ) for the Peach orchard. Data are plotted against Day of Year (DOY) for each of the three years presented. Points show daily values while the lines show a two week running mean of daily values. relatively low with a mean value of 1.2 m s−1 and daily averages ranging from 0.5 to 2.9 m s−1 . ET0 and ET at the peach orchard had strong seasonality with high peak daily fluxes (Figs. 2 and 3). During the non-dormant periods of the year (Day of Year (DOY) between 50 and 300), ET0 ranged between 1.4 and 9.2 mm day−1 , with a mean of 5.7 mm day−1 . Cumulative ET0 was similar for the two years with complete growing seasons (2013 and 2014), with 2013 having a cumulative ET0 of 1383 mm and 2014 an ET0 of 1411 mm. Actual ET tracked ET0 closely, with ET ranging between 0.6 and 9.0 mm day−1 with a mean of 5.2 mm day−1 . Tree trimming, which occurred during the dormant season, had no apparent impact on ET or Kc . With respect to cumulative seasonal totals, 2013 and 2014 showed significant (p < 0.001) difference with ET, with 2013 having cumulative ET of 1360 mm and 2014 having an ET of 1059 mm. The ET patterns for 2012 and 2013 closely followed ET0 while 2014 showed some substantial late season decreases in ET (differences of up to 4 mm day−1 compared to 2012 and 2013) due to irrigation deficits resulting from the farmer’s well failure. 3.2. Single and dual crop coefficients Single crop coefficients (Kc ) are presented for the sugarcane sites (Fig. 4) and the peach orchard (Fig. 5). For the sugarcane, both fields 97 R.G. Anderson et al. / Agricultural Water Management 179 (2017) 92–102 10 0.6 K Lee running e K Windy running 0.5 e 8 Ke Lee K Windy −1 ET (mm day ) 0.4 Ke 6 2012 daily 2013 daily 2014 daily 2012 running 2013 running 2014 running 2 0 50 100 150 200 0.1 0 0 250 300 Fig. 3. Eddy covariance measured evapotranspiration (ET) for the Peach orchard. Data are plotted against Day of Year (DOY) for each of the three years presented. As with Fig. 2, points show daily values while the lines show a two week running mean of daily values. 1.4 1.2 1 Kc 0.8 0.6 K Lee running c 0.4 K Windy running c K Lee 0.2 c K Windy c 100 200 300 DAP 400 500 600 Fig. 4. Single crop coefficients (Kc ) from the Windy and Lee field. Kc is calculated by dividing measured eddy covariance ET by the custom Penman-Monteith reference ET for these sites. Data are plotted against Days After Planting (DAP). As in Fig. 2, points show daily values while the lines show a two week running mean of daily values for both sites. 1.4 1.2 1 Kc 0.8 0.6 2012 running 2013 running 2014 running 2012 daily 2013 daily 2014 daily 0.4 0.2 100 150 200 250 100 200 300 DAP 400 500 600 Fig. 6. Soil evaporation coefficients (Ke ) from the Windy and Lee field determined by the EC-FP method and Eq. (5). Lines, points, and x-axis represent same temporal periods as Fig. 4. DOY 0 50 0.3 0.2 4 0 0 e 300 DOY Fig. 5. Single crop coefficients (Kc ) from the Peach orchard. Kc is calculated by dividing eddy covariance ET by Spatial CIMIS reference ET for the location. Data are plotted against Day of Year (DOY) for each of the three years presented. As in Fig. 2, points show daily values while the lines show a two week running mean of daily values. showed a similar maximum and season end Kc and curvilinear Kc form with respect to days after planting (DAP), with maximum Kc exceeding 1.2 between 200 and 250 DAP with a gradual decline to ∼0.4 at 600 DAP. Overall Kc appears to be slightly out of phase (∼50 days) between the two sites with Lee having a later phase than Windy. This could be due to slightly slower development of Lee due to its planting earlier in the spring, which corresponds to the sugarcane farm’s own internal Kc curve with slower increases in Kc for late winter/early spring planting compared to late spring/summer planting. The field with earlier relative EC tower establishment (Windy) showed a rapid increase in Kc from 0.5 at 75 DAP to the maximum values. For both fields, peak Kc corresponded with a period of relatively rapid growth in both sugarcane fields as well as the Hawaiian winter with slightly lower temperatures and reduced ET0 . For the peach orchard (Fig. 5), Kc was relatively low and variable (0.4–0.6), and then rapidly increased around DOY 100 with leaf emergence. From DOY 100 (April 8–9) to DOY 250 (September 5–6), Kc ranged between 0.9 and 1.1 for the two years with adequate irrigations (2012 and 2013 – Fig. 5). From DOY 250 until leaf senescence at DOY 300, Kc increases slightly, but this occurs at a time of rapidly decreasing ET0 , thus suggesting that this increase is a result of actual ET decreasing slightly slower than ET0 . In 2014, Kc initially shows the same pattern as 2012 and 2013, but the impacts of the farm’s well failure become apparent with significant minima in Kc at about DOY 160, 235, and 275. Soil evaporation coefficients (Ke ) at both sugarcane sites decreased with increasing crop age, cover, and residue deposition on the ground, but showed significant variation and correspondence with precipitation (Fig. 6; Table 1). Maximum Ke decreased from ∼0.3 to less than 0.1 with increasing DAP in both fields. Over the study period, mean Ke was 0.13 in Lee and 0.15 in Windy. Again, there were some phase differences between the sites, but also some localized discrepancies as well with a spike in the Lee field Ke at ∼225 DAP, and a spike in Windy field Ke at ∼400 DAP. In the peach orchard, Ke was substantially higher than at the sugarcane sites, as would be expected with furrow irrigation with exposed soil compared to shallow sub-surface drip with substantial surface residue. Between seasons, the Ke for the peach orchard in 2013 was substantially higher than 2012 or 2014. This higher Ke in 2013 may be due to the higher ecosystem respiration observed by an independent partitioning approach (Reichstein et al., 2005). As observed using Reichstein et al.’s (2005) approach, ecosystem respiration was 1061 kg C ha−1 from DOY 110 to 300 in 2013 while it was only 832 kg C ha−1 in 2012 for the same period. Gross photosynthesis during this time period for the two seasons was much closer (1067 98 R.G. Anderson et al. / Agricultural Water Management 179 (2017) 92–102 1.4 1 1.2 1 Kcb*Ks 1.2 1.4 2012 running 2013 running 2014 running 2012 daily 2013 daily 2014 daily Ke 0.8 0.8 0.6 0.6 K *K Lee running 0.4 cb cb 0.4 0.2 s K *K Lee cb s K *K Windy 0.2 0 50 s K *K Windy running cb 0 0 100 150 200 250 100 200 s 300 DAP 400 500 600 300 DOY Fig. 7. Soil evaporation coefficients (Ke ) from the Peach orchard. Ke is calculated by equation 5. Lines, points, and x-axis represent same temporal periods as Fig. 5. Fig. 8. Basal crop coefficient and stress coefficient (Kcb *Ks ) from the Windy and Lee field. Kcb *Ks is calculated by Eq. (4). Lines, points, and x-axis represent same temporal periods as Fig. 4. 1.4 Table 2 Precipitation days (greater than 1.5 mm) for peach orchard site during the period between Day of Year (DOY) 50 and DOY 300. DOY Precipitation (mm) 4/11/2012 4/13/2012 4/25/2012 2/19/2013 3/7/2013 3/8/2013 3/31/2013 5/7/2013 2/26/2014 2/27/2014 2/28/2014 3/29/2014 3/30/2014 3/31/2014 4/25/2014 102 104 116 50 66 67 151 127 57 58 59 88 89 90 115 18.2 26.9 6.8 6.6 2.3 5.6 5.8 15.1 5.3 5.3 20.3 4.6 3.0 5.6 33.27 and 1007 kg C ha−1 for 2012 and 2013, respectively). The reason for increased respiration during 2013 is unclear, but it should be noted that the winter of 2012–2013 was exceptionally dry, and decomposition of woody debris and other residue from the 2012 growing season may have been delayed until the 2013 growing season when irrigation water would have increased microbial activity. As carbon and water fluxes are tightly coupled in the EC FP algorithm, increased respiration would result in a greater proportion of total ET being partitioned to evaporation, thus increasing Ke and confounding the FP algorithm Early summer in 2012 and 2014 had similar Ke values near 0.2; divergence between 2012 and 2014 in later summer followed the divergence in overall water status and Kc between the two years quite well; Ke values were under 0.05 for the most water-stressed parts of the 2014 season (Fig. 7 and Table 2). Basal crop/stress coefficients (Kcb *Ks ) for the sugarcane sites followed the same pattern as Kc , but with lower magnitudes (Fig. 8). Kcb *Ks values ranged from 0.35 to 1 in both fields with the maximum values again coming about 200–250 DAP. After 300 DAP, there was less variability in Kcb *Ks with a linear decrease from 0.8 to less than 0.4. Mean Kcb *Ks was 0.74 in Lee and 0.68 in Windy over the entire study period. Similar to the Kc curve, Kcb *Ks appeared to have a phase discrepancy between the two fields that could be related to differences in planting time. With the peach orchard, Kcb *Ks increased rapidly with leaf out around DOY 100 (Fig. 9). 2012 had the highest overall Kcb *Ks , with values ranging from ∼0.7 to 1.2 1 Kcb*Ks Date 2012 running 2013 running 2014 running 2012 daily 2013 daily 2014 daily 0.8 0.6 0.4 0.2 0 50 100 150 200 250 300 DOY Fig. 9. Basal crop coefficient and stress coefficient (Kcb *Ks ) from the Peach orchard. Kcb *Ks is calculated by Eq. (4). Lines, points, and x-axis represent same temporal periods as Fig. 5. ∼1.0. 2013 and 2014 had similar, lower values of Kcb *Ks . The seasonality of Kcb *Ks in 2014 was more closely tied to overall Kc and water stress, while 2013’s pattern correlates with the issues with Ke discussed above. Peach volumetric water content (VWC) during the three seasons showed patterns consistent with observed crop coefficient values (Fig. 10). Maximum mean daily VWC was over 0.3 m3 m−3 except for 2014, which also showed the longest periods between irrigation events consistent with the farm’s well failure. 3.3. Relationship between crop coefficients, remotely sensed vegetation, and soil moisture At the sugarcane sites, Kcb *Ks had a significantly stronger relationship with MODIS NDVI than Kc (Fig. 11), with the r2 of Kcb *Ks -NDVI of 0.43 and the r2 of Kc -NDVI of 0.11. Both types of coefficients had substantial scatter, and the relationship did not change considerably when the relationships in each field were analyzed separately. We did not attempt to separate out water-stressed periods at the sugarcane sites because there were no stressed periods at Windy and there were no good soil moisture observations at Lee (Anderson et al., 2015b). The correlation for NDVI-Kc is much weaker than reported for other crops. One possible explanation 99 R.G. Anderson et al. / Agricultural Water Management 179 (2017) 92–102 1.4 0.5 2012 2013 Peach ET coefficient 2014 0.3 3 −3 VWC (m m ) 0.4 m =1.60±0.36 Kc 1.2 mKcb=0.82±0.29 b =−0.18±0.24 Kc 1 b =0.13±0.20 Kcb 0.8 0.6 r2 =0.79 Kc r2 =0.61 Kcb NDVI−K regression 0.4 c NDVI−K 0.2 regression cb 0.2 K c K cb 0 0.2 0.1 0 50 100 150 200 250 300 DOY Fig. 10. Daily mean volumetric water content (VWC) shown for the furrow bottom sensors (8 cm depth) shown for the three seasons. Field capacity (green line) and permanent wilting point (red line) are shown as horizontal lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) 0.3 0.4 0.5 0.6 Landsat 7 NDVI 0.7 0.8 0.9 Fig. 12. Relationship between Landsat 7 (L7) NDVI and single and basal/stress coefficients for the peach orchard. Plotted values are average Kc and Kcb *Ks values for each 16-day L7 overpass period. Data are shown from 2012 and the early portions of the 2014 season that were not confounded by uncertainty in the FP algorithm (2013—see paragraph 2 of Section 3.2) or water stress (later 2014). Regression statistics including slope (mKc and mKcb ), intercept (bKc and bKcb ), and coefficient of determination (r2 Kc and r2 Kcb ) are shown. 1 m =3.17±0.70 Kcb 0.9 b =0.11±0.12 Kcb m =0.62±0.46 Kc 1.2 mKcb=1.34±0.40 b =0.42±0.31 Kc 1 b =−0.19±0.27 0.8 r2 =0.50 s Kcb Peach K *K Kcb 0.8 0.6 r2 =0.11 Kc r2 =0.43 0.6 0.5 Kcb 0.4 VWC−K 0.3 2012 2014 NDVI−K regression 0.4 c NDVI−K cb 0.2 K K 0 0.3 0.7 cb Windy and Lee ET coefficients 1.4 0.4 regression 0.2 0.05 c cb 0.5 0.6 0.7 MODIS Terra NDVI 0.8 0.1 0.15 0.2 0.25 0.3 0.35 VWC (m3 water m−3 soil) cb regression 0.4 0.45 0.5 0.9 Fig. 11. Combined relationship between the MODIS Normalized Differential Vegetation Index (NDVI) and single and basal/stress coefficients for the Maui sugarcane sites. Plotted values are average Kc and Kcb *Ks values for each 16-day MODIS overpass period. Regression statistics including slope (mKc and mKcb ), intercept (bKc and bKcb ), and coefficient of determination (r2 Kc and r2 Kcb ) are shown. is that there were relatively few MODIS overpass dates at earlier growth stages with lower NDVI values (NDVI < 0.5), which results in a lower dynamic range for NDVI and which may give the NDVIKc relationships more scatter than they would have over an entire crop cycle. Another explanation for the poor r2 is the role of understory leaves in contributing to sugarcane transpiration. As Hawaiian sugarcane ages and is dried down, lower leaves on the stalk lose greenness while the top leaves (most visible to satellites) are still green. With respect to the peach orchard, there were significantly stronger relationships between Kcb -NDVI and Kc -NDVI (Fig. 12) during well-watered periods (2012 and early 2014). For both Kc and Kcb , the relationship with NDVI had a coefficient of determination greater than 0.6. The peach site also had a greater range of NDVI values (0.3–0.8) to compare against the crop coefficients. The peach site had stronger r2 between NDVI and Kc than Kcb . This might be due to dark, wet soil which would have a higher NDVI, thus resulting in a positive NDVI-Ke relationship (Bausch, 1993). Fig. 13. Relationship between peach basal coefficients and shallow soil volumetric water content (VWC—m3 H2 O m−3 soil volume). VWC is measured at 8 cm beneath the furrow and plotted for contrasting wet and water stressed growing seasons of 2012 and 2014. For both years, plotted daily coefficients are from the months of May through August when Kcb is relatively constant. Regression equation is shown for VWC less than 0.2 m3 m−3 for both years as this is the VWC at which substantial declines in Kcb *Ks are observed Regression statistics including slope (mKcb ), intercept (bKcb ), and coefficient of determination (r2 Kcb ) are shown. With respect to the relationship between soil moisture and crop coefficients, there was no significant correlation (r2 = 0.05) between root zone VWC in Windy and mid-period Kcb *Ks (data not shown), thus indicating that these data cannot be used to assess Ks relationships. This was not surprising given that root-zone VWC remained near field capacity for the entire study period. Even near the minimum VWC of 0.23, matric stress was minimal at −33 kPa (Anderson et al., 2015b). This was also in line with Anderson et al.’s (2015b) statistical testing of the days before and after irrigation, which showed no increase in ET in days immediately after irrigation, thus further discounting the likelihood of water stress. With respect to the peach orchard, the 2012 and 2014 growing seasons provide an interesting contrast between a well-watered and water-stressed season. For our assessment of VWC, we used the two sensors closest to the bottom of the irrigation furrow as our 100 R.G. Anderson et al. / Agricultural Water Management 179 (2017) 92–102 proxy for root zone soil water content. The relationship between the VWC average of these two sensors and Kcb *Ks during the middle of the growing season is shown in Fig. 13. VWC at field capacity and permanent wilting point were 33% and 3%, respectively. We assume that Kcb is relatively constant during this period, and can see that Kcb *Ks declines significantly below VWC of about 0.2–0.25, which indicates that the fraction of depletion of plant available water (field capacity-permanent wilting point) prior to onset of stress is between 0.27–0.43. We developed a regression equation for VWC-Kcb *Ks for VWC below 0.2. Based on this regression, for example, we would expect Ks to decrease from 1 to 0.57 as VWC decreased from 0.2 to 0.1. The VWC at which Ks starts to decrease below 1 can be imprecise, but a figure such as Fig. 13 can help independently determine this relationship. 4. Discussion and conclusions 4.1. Comparison of EC FP coefficients to literature values Maximum observed single coefficients (Kc ) for the peach and sugarcane towers compared favorably with FAO-56 published values and adjustments for canopy cover and height (Allen et al., 1998; Allen and Pereira, 2009). Maximum fraction canopy cover (Fc ) from TOPS-SIMS for the peach orchard was 0.7–0.8, which suggests a Kcmid of 1.15–1.2 based on Allen and Pereira (2009). This value was slightly above our observed mean mid-season Kc of ∼1.1 during 2012 and 2013. Similarly, the literature value of Kcmid for sugarcane (1.25 – Allen et al., 1998) is also above our observed maximum Kc of 1.1–1.15. We note the inherent daily variation in Kc observations with micrometeorology that other researchers have found in sugarcane and peach (Inman-Bamber and McGlinchey, 2003; Paço et al., 2012). Where differences exist are around the relative shape of the Kc curve, with our peach orchard showing a more rapid increase to Kc than previous studies in California (Ayars et al., 2003). With our sugarcane sites, we note that Olivier and Singels (2012) also found a relatively short Kcmid period and reduction in Kc which they attributed to sugarcane residue (trash) suppressing E and slightly reducing overall ET. While our sugarcane sites were technically sub-surface drip irrigated, the drip lines were buried very close to the surface (0–5 cm) with some locations having drip line on the surface. This shallowness combined with the higher initial Ke (∼0.3 maximum), leads us to surmise that burying the drip line had little impact on Ke . Determination of dual crop coefficients (Ke , Kcb , and Ks ) is more challenging due to challenges in independently observing transpiration and evaporation and relatively fewer studies publishing dual coefficients. FAO-56 and its extension models for Ke (Allen et al., 1998, 2005) rely on parameterizing maximum Ke as the difference between maximum observed Kc and Kcb , with reductions in Ke modeled as the soil dries. da Silva et al. (2012) evaluated the dual crop coefficient approach over Brazilian sugarcane and found mid-season Ke values on the order of ∼0.1, which is similar to our results. In peach, Abrisqueta et al. (2013) parameterized Ke from soil moisture profile observations in the inter row to calculate Kcb . Like us, they found significant seasonal scatter and year to year variation in Kcb with a maximum Kcb of approximately 1. With respect to stress coefficients, both peach and sugarcane are known to have a high sensitivity to deficit irrigation (Mata et al., 1999; Robertson et al., 1999). Girona et al. (2002) found a 50% relative reduction in ET with a 0.1 m3 m−3 reduction in total plant available water once the deficit threshold had been reached. This corresponds well with our observed decrease in Kcb *Ks from 0.75 to 0.4 when soil VWC dropped from 0.2 to 0.1 m3 m−3 . 4.2. Integration of EC FP to modeling and decision support infrastructure EC has been frequently used in recent studies in a wide variety of agricultural systems to assess water use (see, for example, Amayreh and Al-Abed (2005), Cammalleri et al. (2013), Facchi et al. (2013), Li et al. (2008), and Rajan and Maas, (2014) in addition to studies cited in the introduction for just a few examples). There are increasingly large databases of EC data (e.g. Fluxnet—http://fluxnet. fluxdata.org) with improved site coverage as new data are added. Most of these network-level syntheses focus on analysis and dissemination of processed fluxes as opposed to providing the raw, high-frequency, atmospheric time series. EC FP could be applied retroactively to previously gathered EC data to determine individual processes and fluxes from modeling components. Using EC FP can also assess T and E separately without the requirement of additional instrumentation such as sap flow sensors or microlysimeters that have spatial footprints that are much smaller than an EC tower. As farmers change drip irrigation spacing and use different amounts and types of mulches, canopy structures and planting densities; EC FP can help rapidly assess controls on Ke , Kcb , and Ks in new production systems and canopy environments. Increased accuracy of Ke , Kcb , and Ks will be useful for hydrologic and soil models that rely on crop coefficients to parameterize boundary model conditions. The results of EC FP can also be integrated into decision support frameworks for irrigation management. As an example, consider the relationship between Kcb *Ks and furrow bottom soil water content during the mid-summer at the peach orchard (Fig. 13). While this shallow measurement location is not in the middle of the root zone, it does have two advantages for management purposes. One, it sits near the interface between the peach root zone and the furrow, so it can capture water dynamics and plant stress. Second, and perhaps more critically, it is at a depth and location that can be easily accessed by a farmer for periodic sampling of water content. Using a relationship such as the one presented in Fig. 13, a farmer could easily and rapidly check his field for moisture stress by assessing soil at this position at multiple sites in the field. This would enable more efficient irrigation scheduling without a large investment in fixed, in-situ, water content sensors. Depending upon the data and available modeling frameworks, other simple field checks or site based instrumentation could be developed to predict Ks and thus schedule irrigation at the onset of stress to maximize irrigation efficiency. 4.3. Conclusions In this study, we analyzed three eddy covariance (EC) sites in two contrasting agricultural systems to demonstrate how a fluxvariance based partitioning algorithm can be used to partition evapotranspiration into basal, soil evaporation, and stress coefficients for determination of agricultural water consumption. Our maximum basal and combined coefficients were similar to previous studies for similar crop cover conditions, but we did find a differing shape of the Kcb curve compared with FAO-56. Partitioning EC fluxes also improved the relationship between Kcb and satellite vegetation cover in sugarcane. Analysis of partitioned coefficients against soil moisture indicated a lack of water stress at one of the sugarcane sites while illustrating how the Ks relationship could be determined at a peach orchard. Future work is needed to validate EC FP against independent transpiration and evaporation measurements across a variety of crops, crop cover (bare soil to full canopy cover), and irrigations practices. The results illustrate the value applying flux partitioning to determine dual crop coefficients from EC measured ET data across a variety of agricultural production systems. This type of analysis will become increasingly feasible as the prevalence of EC sites increases due to decreases in R.G. Anderson et al. / Agricultural Water Management 179 (2017) 92–102 monetary and logistical costs; this analysis may also be feasible for existing tower data if the high frequency EC tower data are shared on commonly used data repositories (e.g. Ameriflux and Fluxnet). Acknowledgements We thank the editors and two anonymous reviewers for their constructive critiques on a previous version of this manuscript. We thank Hawaiian, Commercial and Sugar Company for access to the Maui sites and Ryan Palm, for access to the peach orchard. We thank our cooperators on the Maui project and Stella Zambrzuski and Alex Jimenez from ARS Parlier and Dennise Jenkins from ARS Riverside for field assistance in the orchard. Dennise also measured the water retention curve from the orchard site. 30 min flux data for the Maui sites are available on the Ameriflux website. This study was supported by the United States Department of Agriculture-Agricultural Research Service, National Program 211: Water Availability and Watershed Management (project numbers 2036-61000-015-00, 2034-13000-011-00, and 8042-13611-028-00) and National Program 212: Climate Change, Soils, and Emissions (project number 5030-11610-002-00) and by the Office of Naval Research. References Abrisqueta, I., Abrisqueta, J.M., Tapia, L.M., Munguía, J.P., Conejero, W., Vera, J., Ruiz-Sánchez, M.C., 2013. 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