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Agricultural and Forest Meteorology 232 (2017) 489–499

Contents lists available at ScienceDirect

Agricultural and Forest Meteorology

j our na l ho me page: www.elsev ier .com/ locate /agr formet

easonal and inter-annual variability of soil moisture stress functionn dryland wheat field, Australia

enkata Radha Akuraju a,∗, Dongryeol Ryu a, Biju George b, Youngryel Ryu c,ithsiri Dassanayake a

Department of Infrastructure Engineering, The University of Melbourne, Parkville, Victoria, 3010, AustraliaIntegrated Water and Land Management Program, ICARDA, Cairo, EgyptDepartment of Landscape Architecture and Rural Systems Engineering, Seoul National University, Seoul, Republic of Korea

r t i c l e i n f o

rticle history:eceived 16 September 2015eceived in revised form 5 October 2016ccepted 6 October 2016

eywords:vapotranspirationoot zone soil moistureegetation biomasset radiation

a b s t r a c t

It is assumed that the ratio of actual evapotranspiration (AET) to potential evapotranspiration (PET) ismostly controlled by the soil water content available for ET. This control is formulated using the soilmoisture stress function (SSF), where the evaporative fraction (EF) or the fraction of the AET to PET (fPET)is assumed to be either a linear or a non-linear function of soil moisture. We examine the effectivenessof the soil moisture stress function to quantify soil moisture control on EF or fPET over a dryland wheatfield in Victoria, Australia. Micrometeorological observations from two cropping seasons were used forthe analysis. The efficacy of a root-density-weighted soil moisture estimate in predicting EF and fPET wasinvestigated as against the commonly assumed fixed-depth root zone soil moisture. However, resultsindicate a strong relationship between EF and available soil water fraction (AWF) in the root zone onlywhen solar radiation is higher than 5 MJ/m2/day. As the rooting depth increases with vegetation growth,

SSF exhibits the strongest correlation with AWF for increasing soil profile depth. In the early and harvest-ing crop growth stages, ET is constrained mostly by surface soil moisture (0–5 cm). In the mid-growthstages, ET is strongly influenced by soil moisture in the root zone (0–60 cm). The shape of SSF, however,changes significantly between the two years (2012 and 2013). It is inferred that different temporal rainfallpatterns between the years caused wheat’s different response to water stress.

© 2016 Elsevier B.V. All rights reserved.

. Introduction

Water shortage is one of the significant issues currently beingxperienced throughout the developing world. Ensuring freshwa-er availability to meet the needs of urban, rural and agriculturalctivities is already a challenge in many parts of the world (Godfrayt al., 2010; Hamdy et al., 2003). Nearly seventy-five percent oflobal freshwater is used for agriculture annually (Wallace, 2000)nd a majority of the water consumed in agriculture returns to thetmosphere via evapotranspiration (ET). Consequently, an accuratestimation of ET over agricultural fields can provide critical infor-ation about their water use across various scales and, in turn, crop

ater productivity.

ET is also one of the most important components of terrestrialater balance contributing to hydrological and biophysical systems

∗ Corresponding author.E-mail address: avenkataradha@gmail.com (V.R. Akuraju).

ttp://dx.doi.org/10.1016/j.agrformet.2016.10.007168-1923/© 2016 Elsevier B.V. All rights reserved.

modelling and applications. ET is controlled by various environ-mental conditions such as available energy, vegetation conditionand available soil moisture (Detto et al., 2006; Ryu et al., 2008;Vivoni et al., 2008; Wetzel and Chang, 1987). However, for a givenPET or a reference ET estimated using solar radiation, air temper-ature, wind speed, and relative humidity, it is generally assumedthat AET is mainly constrained by soil moisture (Jung et al., 2010;Teuling et al., 2006). A typical approach to characterize ET is tocalculate potential evapotranspiration (PET) and then employ afunction accounting for the constraint by soil moisture (Akurajuet al., 2013; Lai and Katul 1999; Mahfouf et al., 1996).

The correlation between AET-to-PET ratio (denoted by fPEThereafter) or the evaporative fraction (EF), represented by soilmoisture stress function (SSF) and soil moisture is a potential wayof estimating root zone soil moisture (RZSM) over large vegeta-

tive regions using remote sensing and data assimilation methods(Crow et al., 2006; Hain et al., 2012; Norman et al., 1995; Wanget al., 1980). Therefore, an accurate representation of ET vs. SM iscritical to enable regional to global scale RZSM estimation.

4 Forest Meteorology 232 (2017) 489–499

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90 V.R. Akuraju et al. / Agricultural and

Several studies have examined the sensitivity of fPET to SM,nd the influence of meteorological conditions on the relationship.or example, relative transpiration rate has been formulated as aunction of SM and PET (Denmead and Shaw, 1962). Some studiesropose that the sensitivity of fPET to SM also constrained by croprowth stages (Fischer and Kohn, 1966; Vivoni et al., 2008; Weit al., 2014). A large number of agronomic studies have reported orssumed a linear correlation between ET or fPET and SM in wheatrops (Baier, 1969; Eagleman and Decker, 1965; Liu et al., 2002;an et al., 2011; Vivoni et al., 2008; Wetzel and Chang, 1987).

Recent advances in remote sensing demonstrate the potentialse of EF or fPET, surface temperature, and normalized differenceegetation index (NDVI) in estimating SM. For example, satellite-erived NDVI and surface skin temperature have been shown toave a significant correlation with SM (Carlson et al., 1981; Wangt al., 2007). The combined use of surface temperature and NDVITs/NDVI) based on their non-linear relationship satisfactorily esti-

ated surface SM information (Komatsu, 2003; Merlin et al., 2010,008; Noilhan and Planton, 1989). In a series of novel attempts, theurface thermal infrared (TIR) data or surface soil moisture derivedrom soil latent heat flux was assimilated into land surface modelso predict soil moisture (Anderson et al., 2007; Crow et al., 2006;as and Mohanty, 2006; Hain et al., 2011, 2009; Li et al., 2010; Scottt al., 2003). Most remote sensing approaches assume a simple andonstant linear or non-linear relationship between EF/fPET and SMver each site (Akuraju et al., 2013; Hain et al., 2009; Scott et al.,003).

Furthermore, seasonal and inter-annual variability of EF/fPET toZSM has not been rigorously examined due to the lack of con-inuous observations such as optical and thermal infrared datand SM measurements. Also, the effect of net radiation, vegeta-ion biomass (represented by NDVI), crop physiology and rainfallattern (temporal) on the ET vs. RZSM relationship has not beenhoroughly examined yet. Since transpiration is driven by ‘plantvailable water’ in the root zone (Albergel et al., 2008; Lai and Katul,999; Li et al., 1999; Molz and Remson, 1970), EF and fPET derivedrom vegetated land surfaces may vary with plant growth and phe-ological stage. The studies mentioned above did not evaluate theelationship between EF (or fPET) and RZSM at various crop growthtages.

In this study, EF derived from field observations were used forSF to obtain the available water fraction (AWF) on the surface andt various layers of the root zone. AWF is the plant available wateretween field capacity and wilting point, which can be used as

proxy for SM at different depths. The root zone soil moisture,specially in remote sensing methods, is defined as the arithmeticverage of soil moisture at different depths, which disregards themportance of dynamic root distribution at different crop pheno-ogical stages. However, in practice, it is very difficult to measurectual root distribution. In order to estimate plant root distribution,e employed a field-proven cropping system simulation model,gricultural Production Systems sIMulator (APSIM) (www.apsim.

nfo), which was later used to calculate the root-density-weightedWF in the root zone.

The objectives of this study are to: (1) examine the seasonal andnterannual variability of SSF, vegetation biomass and net radiationn two cropping seasons; (2) investigate how surface or root zoneoil moisture control on EF varies with net radiation, soil wetnessnd season; and (3) determine the meteorological and biophysi-al factors controlling the relationship between EF and RZSM in aheat field site. Continuous measurements of hydrometeorologi-

al variables such as evapotranspiration, net radiation, vegetation

henology and biomass, and profile soil moisture content collected

rom the wheat site were used to examine the relationship betweenF and surface or root zone soil moisture.

Fig. 1. Location of study sites at Dookie, Victoria, Australia.

2. Materials and methods

2.1. Description of the study site

The study was conducted at the agricultural research farm ofthe Dookie Agriculture farm, The University of Melbourne, located220 km northeast of Melbourne (36◦37′S, 145◦70′E, at 185 m alti-tude), Victoria, Australia. Fig. 1 shows the geographical location ofthe study site. The climate is Mediterranean semi-arid with hot/drysummers and cold/wet winters (Bell et al., 2012). Relative humidityis on average 10% in January–February and 90% in July–August. Theaverage annual rainfall of the study area typically varies between450 mm and 770 mm (BOM, 2015).

The overall study consisted of two field sites. Site 1 was a pas-tureland with forage lucerne rotationally grazed by sheep. Site 2was cultivated with wheat in 2012–2013. Each site was instru-mented with automated meteorological sensors, which consistedof meteorological sensors and profile soil moisture and tempera-ture sensors (refer to Table 1 for details). The soil moisture andtemperature sensors recorded measurements over the top 1.2-msoil profile at five intervals. This paper presents the data collectedfrom Site 2 grown to wheat. Fig. 1 shows the study sites.

2.2. Data collection

Turbulent fluxes, surface reflectance, and soil moisture weremeasured using a suite of tower-based sensors. Eddy covariancesystem consisting of a sonic anemometer with an open path IRGAgas analyser (LI-7500, LI-COR, Inc., USA) was installed 2.6 m aboveground level to estimate latent heat (LE) and sensible heat flux(H). A CNR1 net radiometer (KIPP & ZONEN, The Netherlands) wasinstalled at 5.7 m height to measure net radiation.

Ground-based surface reflectance was measure using SKR-1850 and SKR-1870A radiometers (Skye Instruments Ltd, UK)which were installed at 5.7 m height at six channels with wave-lengths 527–537, 565–575, 620–670, 837–877, 1228–1248, and2110–2148 nm. Surface reflectance allows the calculation of veg-etation indices such as NDVI (Normalized Difference VegetationIndex) to represent vegetation dynamics. Soil and vegetationsurface temperatures were measured using an infrared radia-tion sensor. Five capacitance soil moisture probes (CS616) were

installed vertically to measure soil moisture at average depths of0–5 cm, 0–30 cm, 30–60 cm, 60–90 cm, and 90–120 cm.

Air temperature and relative humidity were measured usinga HMP45C probe (Campbell Scientific). Barometric pressure was

V.R. Akuraju et al. / Agricultural and Forest Meteorology 232 (2017) 489–499 491

Table 1Description of parameters measured at the Study Site.

Variables measured Sensor (model &manufacturer) Height or depth (m) Frequency of Measurement

Shortwave and longwave radiations Net radiometer(CNR1, Kipp & Zonen)

5.7 m 30 min

Air temperature and relative humidity Temperature and relative humidityprobe(HMP45C, Campbell Scientific)

2.6 m 30 min

Actual ET Open path gas analyser (LI-7500,LI-COR),Sonic anemometer (CSAT3, CampbellScientific)

2.6 m 20 Hz

Wind speed and wind direction R. M. Young Wind sentry set(03101, Campbell Scientific)

2.6 m 30 min

Thermal infrared radiation Infrared radiometer sensor(SI-111, Apogee)

5.7 m 5 min

Visible and NIR radiation Radiation sensors(SKR-1850 and SKR-1870A, Skyeinstruments Ltd)

5.7 m 5 min

Soil moisture Soil moisture probes (5)(CS616, Campbell Scientific)

0–0.005, 0–0.3,0.3–0.6, 0.6–0.9and 0.9–1.2

30 min

Soil heat flux Soil heat flux plates (2)(CN3 Middleton, HFP01, Hukseflux)

0.008 30 min

Soil temperature Temperature probes (6) 0.002,0.005,0.1, 0.2,0.5 and 30 min

ronics

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2ct12Didasotwoe

2

ws

(T107, Campbell Scientific)Barometric pressure Barometer (CS105, Vaisala)

Rainfall Rain gauge (TR-525I, Texas Elect

easured using a Vaisala CS105 barometric pressure sensor. Windpeed and wind direction were measured using R.M. Young (Camp-ell Scientific) Wind sentry set. Soil heat flux was measured usingwo soil heat flux plates placed at 8 cm depth below the TCAV-Lveraging soil thermocouple. A TCAV-L averaging soil thermocou-le probe, consists of four temperature probes installed at 2 cmnd 6 cm depth that measures average soil temperature near theoil heat flux plates. A separate set of temperature probes wasnstalled at 10 cm, 20 cm, 50 cm and 95 cm depths to measure soilemperature profiles. A set of buriable time-domain reflectome-ers (TDR) was added to the ground sensing network at averageepths of 30–60 cm, 60–90 cm and 90–120 cm for calibrating capac-

tance moisture probes. Precipitation was measured using a tippingucket rain gauge. This amount was verified periodically with rain-all accumulation measured independently from a cylindrical rainauge. Average crop height was measured periodically during bothropping seasons. A summary of the sensors deployed and theireasurement intervals is illustrated in Table 1.

This paper used the data acquired at Site 2 between 15 August012 and 31 December 2013, covering two cropping seasons. Dataollection in 2012 started 90 days after wheat was sown, missinghe initial germination and foundation stages. Crops were sown on5 May (DOY 136) and 24 May (DOY 144), respectively in 2012 and013 seasons and were harvested on 9 December (DOY 344) and 7ecember (DOY 357) in the respective years. Therefore, the grow-

ng period of wheat in the Site 2 was 208 and 197 days respectively,uring the cropping seasons in 2012 and 2013. The growing periodsre consistent with the average growing period of winter wheat inoutheast Australia (Bowden and Edwards, 2008). Growth stagesf wheat can be divided into germination, foundation, construc-ion, production and harvesting. The growth stages in this studyere divided into initial, mid-growth and harvest stages based

n vegetation biomass over the ground, rooting depth, and cropvapotranspiration (Allen et al., 1998).

.3. Data preparation

The sampling frequency of the eddy covariance measurementsas 20 Hz, which was converted to 30-min time series for analy-

is. Actual evapotranspiration (AET) was derived from latent heat

0.951.2 30 min

) 1 30 min

flux measurements. EF was approximately zero during night timeand positive during the daytime. Daytime EF was used in this studybecause it accounts for a large proportion of daily ET, and EF showstrivial variation and is nearly constant during the daytime (Crago,1996a, 1996b; Farah et al., 2004; Gentine et al., 2007; Li et al.,2008; Nichols and Cuenca, 1993). EF was calculated as the aver-age of EFs derived from the 30-min latent heat and sensible heatflux measurements (Shuttleworth and Gurney, 1989). Our flux datarevealed that mean standard deviation of EF during the daytime (10a.m.–5 p.m.) was 0.08 and 0.05 during mid-day (12–2 p.m.). It wasobserved that since EF is nearly constant during mid-day, it wasthe most appropriate time to calculate EF (Eq. (1)). Outliers dueto excessive rainfall events and low solar radiation were excludedfrom the dataset. The energy balance closure in the Site 2 is 0.84for years 2012 and 2013, which indicates reasonably good energybudget closure during the study period.

EF = 1n

2pm∑

i=12pm

LEiLEi + Hi

(1)

All meteorological and ground measurements were recorded at30-min intervals while surface reflectance was recorded at 5-minintervals. Data gaps were filled in by a linear interpolation method.For instance, in the case of missing soil moisture data, the scat-tered data gaps were filled using linear interpolation. The surfacereflectance dataset was aggregated to a 30-min average to matchthe observation time scale of the other measurements. NDVI valueswere calculated as an average of the mid-day values to reduce theextreme atmospheric scattering on surface reflectances. The Skyesensors consisted of upward and downward sensors. The upwardsensors had a diffuser to measure hemisphere irradiance while thedownward sensors recorded ground or canopy reflectance. Unde-sirable atmospheric conditions such as non-uniform cloud coverstill can cause errors in the time series of NDVI. These errors in theNDVI dataset were smoothened out by applying the Savitzky-Golayfilter to the raw NDVI time series (Chen et al., 2004).

To assess the tower-based NDVI observations, the 16-day MODIScomposite NDVI (MOD13Q, 250-m resolution) was compared withthe field observations (see Fig. 9). The correlation between thetower-based and MODIS-derived NDVI values was 0.86 over the

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92 V.R. Akuraju et al. / Agricultural and

uration of ground observation. The root-mean-squared differenceRMSD) and bias in comparison with the tower-based NDVI were.14 and 0.11, respectively. Tower and MODIS NDVI products werevident for two cropping seasons of wheat for the years 2012 and013.

Meteorological variables collected from the site were used toalculate potential evapotranspiration. In this study, PET was cal-ulated using the Priestley-Taylor equation (Priestley and Taylor,972). This equation has been applied widely in remote sensing-ased two-source energy balance methods to estimate potentialanopy transpiration in agriculture landscapes (Anderson et al.,997, 2007; Crow et al., 2006; Norman et al., 1995).The Priestley-aylor equation can be denoted as:

ET = ˛�

� + �

Rn�

(2)

here PET is potential evapotranspiration in mm/day, � isriestley-Taylor coefficient, which is set to 1.26, Rn is net radia-ion in MJ/m2/day, � is the slope of the saturated vapour pressureurve in kPa/◦C, � is the psychrometric constant inkPa/◦C, and � ishe latent heat of vaporization that is equal to 2.45 MJ/kg. The mete-rological data used for PET calculations were daily net radiation,lbedo and air temperature, which were measured on the tower.

Soil moisture is dependent on specific conditions (e.g., soilexture, structure, and organic content) and may not correctly rep-esent the water content available for transpiration. Therefore, wesed an alternative definition, Available Water Fraction (AWF) inhis study (Brisson, 1998). Extraction of soil moisture via tran-piration/bare soil evaporation is usually assumed to occur whenoil moisture content is between the field capacity and the wilt-ng point/residual moisture content. In this study, AWF in the soilrofile was obtained using the following equation:

WF = � − �wp�fc − �wp

(3)

here � is measured soil moisture content, �wp and �fc are the soiloisture content at wilting point and field capacity, respectively.

.4. Description of APSIM

APSIM is one of the most widely used farming system modellingrameworks used for a wider range of climatic and soil conditions

ith almost all the commonly grown crops and pasture speciesAsseng et al., 1998; Kloss et al., 2012; Wang et al., 2009). It hashe potential to simulate soil water dynamics and the effects of soilroperties and conditions, including effects of soil water availabilityn crop growth and development. In this study, APSIM was used toimulate root depth, root length density and plant available soilater within the crop root zone.

The APSIM model is suitable to simulate evapotranspiration andoil moisture by combining crop growth simulation and soil waterodules (see the documentation for more details). Moreover, thisodel not only provides PET but also provides soil evaporation

nd crop transpiration separately at daily time steps (Foale et al.,004; Inman-Bamber and McGlinchey, 2003; McMaster et al., 2011;ang et al., 2004; Zhang et al., 2010). Soil moisture derived from

he model was compared with soil moisture observations collectedrom the study site.

There are 11 phenological stages in APSIM wheat module. Theiming of each stage is induced by the accumulation of “ther-

al time” that is calculated using daily maximum and minimumemperatures and adjusted by crop/cultivar specific genetics and

nvironmental factors. The length of each phase is determinedy the fixed thermal time. Biomass accumulation calculated fromadiation is interception limited by soil water stress. APSIM cal-ulates the radiation interception using the leaf area index and

t Meteorology 232 (2017) 489–499

the radiation extinction coefficient, which vary with plant den-sity. Actual daily biomass accumulation is water limited whereaspotential biomass accumulation is limited only by energy. Waterlimiting biomass accumulation is calculated as the ratio of dailywater update and crop water demand. Crop water demand is theamount of water the crop would have transpired in the absence ofsoil water constraint.

The rooting depth in APSIM is a function of growth stage, rootdepth growth rate, temperature factor, soil water factor and soilwater available factor and root exploration factor in each layer. Formore details on the formulation of these factors, see (Keating et al.,2003). Potential crop water uptake and actual water uptake dependon root density in the soil profile. Potential water uptake is thesum of root water uptake from each soil layer occupied by roots.Actual water uptake is limited by radiation or soil water available.In APSIM, PET is calculated using the Priestley-Taylor method. If thepotential soil water supply from the profile exceeds demand, thenactual water uptake is removed from the profile in proportion tothe potential water uptake in each layer. If the soil water uptakeis less than the demand, then actual water uptake is equal to thecomputed potential uptake.

2.5. Numerical simulation using APSIM

In this study, APSIM version 7.6 continuous wheat module wasused to simulate the 2012 and 2013 cropping seasons of field exper-iments conducted at Dookie experimental site. The meteorologicaldata on daily maximum and minimum temperatures, solar radia-tion, and precipitation were used for the model simulation. Wheatcultivar Gregory, a medium-maturing (200–210 days) cultivar thatis most commonly grown in Victoria, Australia, was used for thesimulation. Simulations for the years 2012 and 2013 were con-ducted separately with actual sowing and harvesting dates. Thesimulation started with the sowing dates of May 15, 2012, and May24, 2013, respectively.

A standard nitrogen fertilizer was applied at sowing as perindustry practice. The spacing between rows was maintained as40 cm with a plant population of 150 plants per square meter.Since the soil type at the Study Site was clay loam, soil type Redso-dosol (Boorhman N0554-YP) was selected from the standard APSIMsoil database. The soil profile consisted of four layers: 0–30 cm,30–60 cm, 60–90 cm and 90–120 cm. The soil parameters used forsimulation were bulk density, air-dry soil moisture, the lower limit(permanent wilting point), drainage upper limit (field capacity) andsaturated soil water content at the relevant depths given in Table 2.

APSIM was initiated on 1 January in both 2012 and 2013 whenthe soil profile was considered to be at the lower limit of availablewater. The simulation was carried out on a daily time step, and soilmoisture, root length and root density in each layer were reported.

3. Results and discussion

A considerable inter-annual variability in SSF was observedbetween the 2012 and 2013 cropping seasons, which is discussed inSection 3.5. Seasonal variations of EF, AET, PET, soil moisture fromfield observations and APSIM results are presented in the followingsections.

3.1. Evaporative fraction (EF)

Fig. 2 presents daily time series of EF, NDVI, and rainfall inthe 2012 and 2013 cropping seasons. EF showed large daily varia-

tions mixed with low-frequency seasonal fluctuations. EF was morescattered with low solar radiation values removed for better visu-alization, which subsequently removed some rainfall days. DailyEF variation was closely related to individual precipitation events

V.R. Akuraju et al. / Agricultural and Forest Meteorology 232 (2017) 489–499 493

Table 2Soil profile parameters used in the simulations.

Soil layer(cm)

Bulk density(g/cm3)

Air dry moisture content(m3 m−3)

Lower limit of moisturecontent(m3 m−3)

Drained upper limit ofmoisture content(m3 m−3)

Moisture contentat saturation(m3 m−3)

0–30 1.2 0.053 0.073 0.328 0.34830–60 1.3 0.120 0.14060–90 1.3 0.115 0.13590–120 1.3 0.115 0.135

F

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ig. 2. Daily time series of EF, NDVI and Rainfall from 15 Aug 2012 to 31 Dec 2013.

hereas low-frequency seasonal fluctuation in EF was inducedrimarily by the gradual change in solar radiation and resulting veg-tation phenology (indicated by NDVI). Peak EF values coincidedith precipitation events and ET in general decreased with the

rowth of wheat into the summer. This indicated that precipitation-nduced increase in soil moisture has an immediate influence onF.

Vegetation cover increased rapidly in the beginning (data col-ection started 90 days after wheat was sown in 2012) and reachedts maximum after 40 days (DOY 270). NDVI values decreased

onotonically, reflecting the likely influence of bare soil/harvestedondition of wheat. EF was dominant due to bare soil evaporationrom January to May 2013, during which time there was no veg-tation control on EF. EF was more driven by solar radiation andvailable soil moisture from the surface. The wheat crop was sownn 24 May 2013 and EF values dramatically changed with vege-ation phenology. EF was comparatively low in the early growthtages, nearly constant during the mid-growth stage, and signif-cantly low in the harvesting stage. EF values plummeted as theensible heat flux was high due to the absence of vegetation afterarvesting.

Overall, EF values increased with vegetation cover and reflectedhe bare soil evaporation at the end of both years. The seasonalattern of NDVI and EF were similar, and the relationship was morecattered when NDVI values were low. Specifically, the influence ofare soil evaporation on EF was dominant during this period.

.2. AET and PET

Fig. 3a shows the AET values measured by an eddy covariancenstrument and PET calculated using the Priestley-Taylor equa-ion. PET for the entire study period was an average 3.65 mm/dayhereas mean AET was 0.89 mm/day. Maximum PET value

8.34 mm/day) was observed on DOY 5 in 2013 as a result ofigh solar radiation (11.72 MJ/m2/day). The lowest PET value0.80 mm/day) was a result of low net radiation (0.45 MJ/m2/day)n DOY 259 in 2013. Since PET primarily depends on solar radiation

nd temperature, it showed distinctive seasonal characteristics inwo seasons: the hot and dry (summer) season in November-Aprilnd the warm and wet (crop growing) season in May-October. HighET values were observed in the summer period and low PET in the

0.432 0.452 0.301 0.321 0.452 0.472

crop growing period of winter-spring. In contrast, AET was highduring the crop growing period due to active crop transpiration andhigh soil moisture content. In summer, AET was low due to lowsoil moisture availability. PET assumes adequate water supply tothe crop whereas the process of AET depends on water and energyavailability. In case the net radiation was higher than thresholdlevel (section 3.5), AET mostly controlled by available soil mois-ture. In this situation, the ratio of AET to PET (fPET) can be used asan indicator of soil moisture stress.

Fig. 3b shows the patterns of EF and fPET obtained from datacollected from the Study Site. EF and fPET show different patternsin the dry and wet seasons. During the dry season, the differencebetween EF and fPET was less when compared to the wet season.Most of the data points in the wet season were widely spread dueto lower net radiation. For instance, 29 mm of rainfall was receivedon DOY 280 in 2012 which led to similar AET and PET of 2 mm/dayon DOY 281 due to an increase in soil moisture and less energyavailable. In this situation, the fPET value was significantly highercompared to EF. Overall, the analysis indicated that EF and fPETwere correlated well with an R2 value of 0.65 after filtering out thelow net radiation days.

3.3. Soil moisture

Soil moisture at different depths measured by soil moisturecapacitance probes was converted to volumetric soil moisture mea-surements. Fig. 4 shows the amount of rainfall and soil moistureresponse to rainfall events during the study period. Surface soilmoisture (0–5 cm) and soil moisture from 0 to 30 cm depth showedsignificant responses to rainfall, whereas the soil moisture from 30to 60 cm, 60–90 cm, and 90–120 cm depths displayed little or noresponse to the rainfall.

Surface soil moisture (0–5 cm) and soil moisture from 0 to 30 cmdepth were near field capacity when data collection started in2012, but dried up slowly until it reached the residual water con-tent (0–5 cm) or wilting point (0–30 cm) on DOY 57 in the 2013dry summer. Soil moisture values from 30 to 60 cm, 60–90 cm and90–120 cm depths remained low and stable during the 2012 crop-ping season. As shown in Fig. 4, the soil moisture values in 30–60 cmand 90–120 cm depths showed steep increases during the wet sea-son of 2013. We suspected that this might be due to fast infiltrationof rainfall through macro pores or groundwater reached the sensorsat these depths, saturating the clayey soils for a prolonged period.

3.4. APSIM results

APSIM was used to simulate soil moisture in daily time stepsfor 2012 and 2013 cropping seasons separately. A comparisonbetween modeled and observed soil moisture values for 0–30 cmand 30–60 cm depths in 2012 and 2013 (Fig. 5a and b) show aclose agreement between both, especially at 0–30 cm and 30–60 cmdepths of the soil profile. Soil moisture predictions were highly sen-

sitive to rainfall trends in these two layers. It can be said that APSIMwas accurately simulating soil water-plant-atmospheric interac-tions. However, it overestimated soil moisture from the 0–30 cmdepth in the 2012 cropping season due to the assumption of initial

494 V.R. Akuraju et al. / Agricultural and Forest Meteorology 232 (2017) 489–499

Fig. 3. (a) Comparison of AET and PET from 15 Aug 2012 to 31 Dec 2013. (b) Comparison of EF and fPET for the years 2012 and 2013.

Fd

ssmrdtisr

wttdft

F

ig. 4. Rainfall (mm) and soil moisture (volumetric in%) observations at differentepths.

oil moisture conditions. Initial soil moisture conditions that wereet as per field observations for the 2013 cropping season, whereodeled and observed soil moisture conditions were highly cor-

elated for the 2013 season. The APSIM soil moisture for 30–60 cmepth closely follows observed values in the 2012 season. However,here was a large discrepancy between them during the wet seasonn 2013. As discussed earlier, this was the result of the wet front waslowly reaching into the lower clayey layers after a certain level ofainfall accumulation only visible in observed soil moisture.

Root zone primarily depends on crop type, crop phenology, andater availability at different depths. Root length density is impor-

ant for root water uptake and difficult to measure in the field. In

his study, APSIM was used to obtain root length and root lengthensity of wheat in daily time steps. Since most of the roots were

ound in the top 60 cm (see Fig. 6), the root zone of wheat was takeno be 60 cm. Fig. 6 presents the APSIM-simulated root distribu-

ig. 5. (a) Comparison of observed and APSIM simulated soil moisture from 0 to 30 cm. (b

Fig. 6. APSIM simulated root distribution in the 2013 cropping season.

tion in each layer for a growing period in 2013. The representativeproportion of roots for each layer was calculated from the rootlength density in each layer obtained from APSIM. The soil moistureweighted by the layer-by-layer root proportion was obtained torepresent the root zone soil moisture (RZSM) theoretically affectingET.

3.5. Relationship between EF and AWF

Both EF and fPET were used to build a relationship with AWFat different depths. Since EF and fPET showed a good correlation

during two cropping seasons, only EF was used in the subsequentanalysis against AWF.

The correlation between EF and AWF was initially analyzed withvarying of net radiation thresholds. An important hypothesis here

) Comparison of observed and APSIM simulated soil moisture from 30 to 60 cm.

V.R. Akuraju et al. / Agricultural and Forest Meteorology 232 (2017) 489–499 495

e at di

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Fig. 7. The root-mean-square error (RMSE) vs. sample siz

s that, beyond a certain threshold of net radiation (Rn), there exists strong relation between EF and AWF. This potential was exam-ned through root-mean-square error (RMSE) analysis based on theest fits between EF and AWF in both years as shown in Fig. 8c and. For instance, the RMSE values were calculated from observedF and predicted EF values obtained from a non-linear fit in 2012ropping season. Fig. 7 shows the RMSE and sample size after filter-ng the number of samples using different net radiation thresholds.he analysis started with an RMSE of 0.116 and 96 samples and

ncreased with 0.5 MJ/m2/day net radiation threshold intervals forhe 2012 experimental data. RMSE values decreased with increasedet radiation threshold levels and reduced number of samples.owever, decreasing RMSE represents a better model evaluationut led to substantial reduction in the number of samples. Ashown in Fig. 7a, RMSE was 0.088 and stable until 5 MJ/m2/day andncreased thereafter, also removing a large number of samples.

Fig. 7b shows the RMSE analysis for the 2013 cropping period.he RMSE value was almost constant until 3.5 MJ/m2/day and

ncreasing until 5 MJ/m2/day. Beyond 5 MJ/m2/day net radiationhreshold, RMSE was stable and still led to a substantial reductionn number of samples. Based on RMSE variations from the two crop-ing seasons at different net radiation thresholds, it was noted thatet radiation of less than 5 MJ/m2/day is influencing the relationetween EF and AWF. EF or fPET showed good correlation with soiloisture at different depths beyond this net radiation threshold.

he Spearman rank correlation analysis (results not shown) alsoupport the same threshold net radiation (5 MJ/m2/day) for theffective EF vs. AWF relationship. To analyze the effectiveness ofF and AWF, rainfall days that led to high EF values were excludedrom further analysis. This exclusion significantly improved the cor-elation coefficient between EF and SM from 0.68 to 0.73 in 2012nd 0.73 to 0.85 in 2013.

Under soil moisture limited conditions, considerable variabilityas observed between EF and AWF in the 2012 and 2013 cropping

easons. To obtain a better understanding the effect of vegetationhenology on this relationship was analyzed. Fig. 8 shows the rela-ionship between EF and AWF in terms of cumulative NDVI, whichepresents crop growth stages (represented by different symbolsn the figure).

The correlation between EF and AWF varied with the depthf soil moisture. AWF values close to 1 represent field capacitynd most of the points greater than 0.8 can be found at initialrop growth stages. At this stage, evapotranspiration is likely to beccurred due to bare soil evaporation or transpiration due to shal-

ow root depth. Beyond this threshold, the EF and AWF relationship

as dependent on available energy. In mid-growth stages, the cor-

elation between EF and AWF 0–5 cm was significantly differentn two cropping seasons. As the crop reaches the harvesting stage,

fferent net radiation thresholds in (a) 2012 and (b) 2013.

another level of linear relationship can be seen between EF andAWF (Fig. 8a and b) due to low or no vegetation biomass.

The correlation between EF and AWF 0–30 cm was differentin two cropping seasons. During initial and harvesting stages, soilmoisture showed levels near the field capacity in the early growingperiod but approached wilting points towards the harvesting sea-son, and EF varied independent of soil moisture in these periods,as shown in Fig. 8c and d. It can be observed that the initial stagein 2012 has limited data points compared to the 2013 croppingseason due to a delay in data collection. In the mid-growth stage,the interaction between EF and AWF moved from the right to theleft reflecting crop growth and moisture availability. However, thecorrelation was significantly different in the two cropping seasons.Moreover, there is a non-linear relationship between EF and AWF0–30 cm in the 2012 cropping season and a linear relationship in2013.

The interaction between EF and AWF 0–60 is not statisticallysignificant in the two cropping seasons. As shown in Fig. 8d, AWFvalues were close to 0, representing the wilting point and most ofthe data points from late mid-growth stage and harvesting stage.At this stage, there was no correlation between EF and AWF dueto low moisture availability. In 2013, most of the data points wereclose to 1 from initial growth stage and some points from the mid-growth stage. It can be presumed that roots extract water from thetop 0–30 cm, and that no relationship exists at this depth.

Root depth and root distribution vary with crop phenology, soilmoisture at different depths exhibit a different relationship with EF.Since root water uptake is proportional to root distribution overdifferent depths of soil moisture, weighted root zone soil mois-ture based on root distribution was used to represent root zonesoil moisture. As discussed earlier, WRZSM calculated from APSIMroot distribution and soil moisture observations at different depthswere converted to available water fraction in the weighted rootzone (WRZAWF).

The correlation between EF and WRZAWF is similar to thecorrelation between EF and AWF 0–30 cm. However, adding rootdistribution term did not show any significant improvement toobtain AWF in the root zone compared to the AWF 0–30 cm inthis study. Figs. 8g and h show there is a non-linear relationshipbetween EF and WRZAWF in 2012 cropping season and a linear rela-tionship in 2013. The inter-annual variability of SSF likely accountsfor the differences in meteorological conditions considering thatother factors such as crop type, soil properties, and application offertilizers remained similar in the analysis years.

3.6. Net radiation and air temperature

Net radiation and air temperature are two crucial parameters forcrop water demand and transpiration. The correlation between EF

496 V.R. Akuraju et al. / Agricultural and Forest Meteorology 232 (2017) 489–499

Fig. 8. Scatterplots of Evaporative Fraction (EF) and Available Water fraction (AWF) with respect to cumulative NDVI. (a) EF vs. AWF 0–5 cm in 2012 (b) EF vs. AWF 0–5 cmin 2013 (c) EF vs. AWF 0–30 cm in 2012 (d) EF vs. AWF 0–30 cm in 2013 (e) EF vs. AWF 30–60 cm in 2012 (f) EF vs. AWF 30–60 cm in 2013 (g) EF vs. WRZ (Weighted RootZone) AWF in 2012 (h) EF vs. WRZAWF in 2013.

V.R. Akuraju et al. / Agricultural and Forest Meteorology 232 (2017) 489–499 497

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Fig. 10. Crop height (cm) in the 2012 and 2013 cropping seasons.

Fig. 9. Comparison of MODIS and Tower-based NDVI for 2012 and 2013.

nd AWF assumes water-limited ET generation and consequentlyet radiation greater than a critical level. EF may exhibit almosto correlation with AWF in low net radiation days (cloudy days).eyond a certain net radiation threshold (see Section 3.7), therexists a significant relationship between EF and AWF. Therefore,he variability in net radiation and air temperature in two crop-ing seasons were analyzed. Daily net radiation was compared toifferentiate both years in terms of available energy. The cumula-ive net radiation in 2012 was approximately 9% lower than thatn 2013, and the cumulative mean air temperature in 2012 was 8%ower than that in 2013. Annual variability observed in EF and AWFelationship which can be inferred due to differences in availablenergy. However, less than 10% difference between observations inhe 2012 and 2013 cropping seasons may not have much influencen the relationship between EF and AWF, indicating that the differ-nce between available energy and air temperature in both yearss negligible.

.7. Vegetation biomass and crop height

Vegetation biomass plays a vital role in the exchange of energynd water between the soil and the atmosphere. Variability in veg-tation biomass in the two seasons was compared to analyze theffect of vegetation biomass on the relationship between EF andWF. NDVI is a popular vegetation index widely used to repre-ent vegetation biomass (Box et al., 1989; Jin et al., 2014; Psomast al., 2011; Zheng et al., 2004). Fig. 9 shows time series of NDVI ofwo cropping seasons in the years 2012 and 2013. Bare soil condi-ions in January 2012 (dry summer in the study site) provided lowDVI values. In February-April, vegetation cover increased due to

he growth of weeds in response to late summer rainfall events.egetation biomass began to increase rapidly after sowing on DOY36 in 2012; AET was constrained by both soil evaporation and cropranspiration (Allen et al., 1998; Lauenroth and Bradford, 2006).

As shown in Fig. 9, vegetation biomass reached to maximum onOY 266 during the mid-growth stage, representing peak biomassf the wheat crop. As root depth increases with crop growth, therop extracts water from the root zone, and AET is more constrainedy transpiration than evaporation. From October to November, aecrease in vegetation biomass was reflected as the crop reachedarvesting stage. The wheat crop was harvested on DOY 344 in 2012nd sown again on DOY 144 in 2013. The second cropping seasonould be clearly observed from DOY 144 to 341 in 2013 (Fig. 9). Thishows the variation in vegetation biomass (represented by NDVI)rom sowing to harvesting in two cropping seasons. Overall, theurves were similar in both cropping seasons and the difference

etween vegetation biomass in both years is negligible to justify EFnd AWF relationship between the years.

Since vegetation biomass represented by NDVI did not show anyignificant physiological differences between two cropping sea-

Fig. 11. Monthly rainfall distribution in 2012 and 2013.

sons, crop height measured in both seasons were compared asshown in Fig. 10. Crop height in the 2012 cropping season reached95 cm whereas the maximum crop height was approximately 80 cmin the 2013 cropping season. So crop growth differences betweenthe two years may be responsible for the distinctive EF patternsbetween 2012 and 2013.

3.8. Rainfall

The amount of rainfall received in 2012 and 2013 was 479 mmand 398 mm, and the number of rainfall days during the actual crop-ping period were 66 and 77, respectively. Even though the totalrainfall received in 2012 was greater than that in 2013, the amountreceived during the actual cropping season (May–November) wassignificantly greater in 2013 (267 mm) than in 2012 (176 mm).In 2012, however, the large amount of rainfall received duringJanuary–April (260 mm in 2012 and 79 mm in 2013) resulted in wetsoil moisture conditions during the wheat sowing period. Unlikein 2012, lower rainfall distribution from the January-April rainfallresulted in drier soil moisture conditions in 2013.

There was no significant difference in total rainfall received dur-ing the 2012 and 2013 cropping seasons. However, high rainfallamount antecedent to sowing in the 2012 (Fig. 11) provided wetsoil conditions leading to high EF values in the initial growth stage.Later, low rainfall distribution towards the end of the crop growthperiod led to available water fraction being closer to zero, causing

a steep decrease in EF. As shown in Fig. 8c, most of the data pointsin 2012 mid-growth, and harvesting stages were near to wiltingpoint.

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Rainfall distribution from January-April provided dry soil mois-ure conditions for sowing in 2013. High rainfall distribution duringhe crop growing season provided wet soil moisture conditionsrom the initial growth stage to harvesting. Fig. 8d shows how EFalues were gradually decreasing with a gradual decrease in soiloisture and crop phenology.

Soil moisture showed levels near the field capacity in the earlyrowing period but approaches wilting point towards the harvest-ng season, and EF varied independent of soil moisture during theseeriods. This indicates that both ends of the growing period mayot be suitable for the application of the proposed approach. Theehavioral difference of EF vs. AWF between 2012 and 2013 wasainly evident in the latter part of the mid-growth stage where

WF dropped gradually in 2013 while it remained constant in 2012ntil it dropped steeply in the latter part of the mid-growth sea-on. We attribute this difference to the difference in soil wetnesst the beginning of the cropping seasons in 2012 and 2013. Whilehe soil maintained wet conditions from the pre-sowing period in012, the soil was drier during the sowing season and in the earlyart of the growing period in 2013 due to the low spring rainfall.ven though EF levels in 2013 were as high as in 2012 in the earlyart of the mid-growth stage, but it dropped gradually afterwardsntil harvesting stage.

As discussed earlier, all meteorological conditions that influencehe relationship between EF and AWF had negligible variations inoth years. Therefore, moisture availability in the root zone androp growth are the primary sources that distinguish the relation-hip between EF and AWF. Crop growth differences (see Section 3.7)ossibly caused by different rainfall patterns may be responsible

or the distinctive EF patterns between 2012 and 2013. EF gradu-lly decreases during 2013 cropping season that responds stronglylinearly) to water availability in the root zone. High soil moistureonditions in the initial crop growth stage in 2012 correspondedo constant EF values until it dropped steeply at the end of the

id-growth stage. This shows that there was a strong non-linearelationship between EF and AWF in the 2012 cropping season.

. Conclusions

Continuous observations from the wheat study site during tworopping seasons were used to describe the relationship betweenoil moisture stress function and root zone soil moisture. The vari-bility in SSF can be attributed to energy-limited conditions andater-limited conditions. Under energy-limited conditions, ET is

ot strongly related to soil moisture. Under water-limited condi-ions, the variability in evapotranspiration is constrained by soil

oisture and crop growth stage. If the soil moisture is below theilting point, evapotranspiration is not constrained by soil mois-

ure. Evapotranspiration is strongly constrained by soil moisture,here soil moisture lies between the wilting point and field capac-

ty.The variability in SSF varied with crop growth stages and depth

f soil moisture. Theory suggests that the root depth varies withegetation phenology, and that maximum root depth can be founduring mid-growth stages. In the initial crop growth stage, most ofhe data points were closer to field capacity, and EF varied indepen-ent of AWF 0–5 cm (surface). There were two different levels of

inear interactions between EF and AWF 0–5 in the mid-growth andarvesting stages. In the mid-growth stage, SSF was mostly con-rolled by vegetation biomass (transpiration from the root zone)hich showed high EF values. In the crop harvesting stage, the

ower level of EF values was evident due to little or no transpiration.The EF and AWF interactions in the root zone vary with crop-

ing season. In the initial and crop harvesting stages, EF is notonstrained by AWF in the root zone. In the mid-growth stage, EF

t Meteorology 232 (2017) 489–499

is strongly influenced by AWF in the root zone. The relationshipbetween EF and AWF in the root zone was non-linear in the 2012cropping season and linear in the 2013 cropping season. Variabilityin the relationship between EF and AWF was due to the markeddifference in rainfall distribution and crop growth. Our analysissuggests that the relation between EF and AWF 0–30 cm is equallyscalable to WRZAWF in this study.

The relationship between EF and AWF was influenced by netradiation, vegetation biomass, and critical soil moisture conditions.This study helps to understand the interactions between EF andAWF in the root zone and the feasibility of SSFs in RZSM estimations.The results of this study show that the shape of SSF substantiallyvaries from year to year based on rainfall distribution and cropgrowth.

Acknowledgements

The authors would like to thank the Australian Centre for Inter-national Agriculture Research (ACIAR) for sponsoring this researchunder the John Allwright Fellowship. The authors are grateful toRodger Ian Young and Robert Pipunic for their valuable support indata collection.

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