Nationwide crop yield estimation based on photosynthesis and meteorological stress indices

Agricultural and Forest Meteorology 284 (2020) 107872

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Agricultural and Forest Meteorology journal homepage: www.elsevier.com/locate/agrformet

Nationwide crop yield estimation based on photosynthesis and meteorological stress indices

T

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Yang Chena, , Randall J. Donohueb,f, Tim R. McVicarb,f, François Waldnerc, Gonzalo Matad, Noboru Otad, Alireza Houshmandfard, Kavina Dayale, Roger A. Lawesd a

CSIRO Data61, Goods Shed North, 34 Village St, Docklands, VIC 3008, Australia CSIRO Land and Water, GPO Box 1700, Canberra, ACT 2061, Australia c CSIRO Agriculture and Food, 306 Carmody Rd, St Lucia QLD 4067, Australia d CSIRO Agriculture and Food, 147 Underwood Ave, Floreat WA 6014, Australia e CSIRO Agriculture and Food, College Rd, Sandy Bay TAS 7005, Australia f Australian Research Council Centre of Excellence for Climate Extremes, Canberra, ACT 2061, Australia b

A R T I C LE I N FO

A B S T R A C T

Keywords: Crop yield estimation Radiation use efficiency Stress index NDVI Remote sensing Canola Wheat Barley

There is considerable demand for nationwide grain yield estimation during the cropping season by growers, grain marketers, grain handlers, agricultural businesses, and market brokers. In this paper, we developed a semiempirical model (Crop-SI) to estimate the yield of the three major crops in the dryland Australian wheatbelt by combining a radiation use efficiency approach with meteorology driven Stress Indices (SI) at critical crop growth stages (e.g., anthesis and grain filling). These crop-specific SI (e.g., drought, heat and cold stress) help explain the impact of high spatial agro-environmental heterogeneity, which lead to substantial improvement in grain yield prediction. Crop-SI explains 87%, 69% and 83% of the observed field-scale grain yield variability with root mean square error of ~0.4, 0.4 and 0.5 t/ha for canola, wheat, and barley, respectively. At the pixel-level, Crop-SI reduces the relative error in grain yield estimation to 34%, 25%, and 20% for canola, wheat, barley, respectively, compared to two benchmark models. By incorporating water- and temperature-driven stresses, Crop-SI's predictive skill in highly variable environments is enhanced. As such, it paves the way for the next generation of agricultural systems models, knowledge products and decision support tools that need to operate at various scales.

1. Introduction Crop yield modelling has evolved since the 1980s and is used to answer questions in research knowledge synthesis, agronomic management practices, and national policy analysis (Boote et al., 1996; Vries, 1989; Whisler et al., 1986). For instance, meteorological-driven data assimilation models that simulate biological and physical processes in agricultural systems assist in pre-season and in-season management decisions to predict the effects of climatic change, leaching of agrichemicals, cultural practices, fertilisation, irrigation, and pesticide use (e.g. the Agricultural Production Systems sIMmulator – APSIM and WOrld FOod Studies – WOFOST; Holzworth et al., 2014; Keating et al., 2003; van Diepen et al., 1989). These ‘point-based’ models explain crop growth at one or multiple points in space based on underlying interactions among genotype, environment, and management strategies and require detailed inputs of data about local soils, crop management, and

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prevailing weather conditions to predict yield (Holzworth et al., 2014). It is not practical to parameterise such models over large areas (e.g., > 50, 000 km2), and as such, they have limited ability to reliably predict yields at regional to national scales (Ferencz et al., 2004; Lobell et al., 2015). Therefore, point-based simulations are usually extrapolated nationally for production analysis but the aggregated results cannot be used to describe spatial variations in actual yield that are driven by management strategies and agroecological heterogeneities (Hochman et al., 2016; Idso et al., 1977; Moran et al., 1997). The inherent limitations of point-based models can be addressed by using satellite-based models that estimate crop yield for large areas (Doraiswamy et al., 2003; Prasad et al., 2006; Serrano et al., 2000). Crop yield models based on remote sensing are generally classed into empirical models and semi-empirical models (Holloway and Mengersen, 2018; Lobell, 2013, see Table 1 for examples of each). Empirical models relate in situ yield observations to remotely-sensed

Corresponding author. E-mail address: [email protected] (Y. Chen).

https://doi.org/10.1016/j.agrformet.2019.107872 Received 22 March 2019; Received in revised form 10 December 2019; Accepted 12 December 2019 0168-1923/ © 2019 Elsevier B.V. All rights reserved.

Semi-empirical

Wheat and sorghum

Empirical

2

Canola, wheat, and barley

Wheat and canola

Corn and soybean

Wheat

Wheat and maize

Wheat

Wheat

Maize

Corn and soybean

Corn

Wheat, cotton, rice, and maize

Crop(s)

Model type

Yaqui Valley, Sonora, Mexico / N/R / N/R / Regional McLean County, Illinois, America / 24 fields / N/R / Regional Wheatbelt, Australia / 191 fields / N/R / Nationwide Wheatbelt, Australia / 291 fields / 95 ha on average / Nationwide

Australia / 125 fields / 110 ha / Nationwide Mas Badía, Girona, Spain / 3 fields / 4.5 m by 1.2 m / Field North Plain, China / 108 fields / N/R / Regional

Shelton, Nebraska, America / 20 fields / 7.3 m by 15.2 m / Field Iowa, America / 1 field / 47,348 km2 / Regional Kenya / 458 fields / 0.25–1 acre / Regional

Davis, California, America / 4 fields / 5 m by 15 m / Field North-west of Thessaloniki, Greece / 7 fields / 1.5 km by 1.5 km / Field

Location / number of fields / field size / modelling scale

Multispectral aerial photography

AVHRR

1997–1998

1982–2001

MODIS

MODIS

MODIS

2009–2015

2009–2015

Landsat

Model SE590 with detector CE390WBR AVHRR

MODIS

2005

1993–1994, 1999–2000

1992–1993

1992

2009–2015

Terra Bella

Advanced Very High Resolution Radiometer (AVHRR)

1986, 1988, 1989

2014–2015

Landsat Thematic Mapper (TM)

Remote sensing data

1978, 1979, 1981

Years of data

250 m / 16-day composite

250 m / 16-day composite

250 m / 8-day composite

30 m / N/A

30″ × 30″ grid cell (each cell being ~ 926 m by 725 m at 38.5°N) / 10 days

250 m / 16-day composite 30 cm / 18–43 days

1 m / N/A

8 km / monthly

NDVI

NDVI

NDVI

SR, NDVI

NDVI, SR

SR

Green chlorophyll vegetation index (GCVI), NDVI, and EVI NDVI

NDVI

GNDVI

NDVI

8 km / N/A

0.5 m / N/A

NDVI

Vegetation indices

30 m / N/A

Spatial resolution / temporal frequency

Monthly precipitation (mm), monthly average daily maximum and minimum temperatures ( °C) during the growing season

N/A

Daily average temperature ( °C) / solar radiation (W/m2) / precipitation (mm)

Daily interpolated mean, minimum, and maximum air temperature ( °C) / mean vapour pressure (kPa) / atmospheric pressure (kPa) / daily sunshine duration / precipitation (mm) N/A

16-day average rainfall (mm) and maximum temperature ( °C) N/A

Monthly average total precipitation (mm) / monthly surface air temperature ( °C) N/A

N/A

N/A

Daily air temperature (°C)

Meteorological data

(Hatfield, 1983)

(Quarmby et al., 1993)

R2 = 0.98

0.34 ≤ R2 ≤ 0.66 for wheat; 0.85 ≤ R2 ≤ 0.93 for cotton; 0.80 ≤ R2 ≤ 0.92 for rice; 0.82 ≤ R2 ≤ 0.94 for Maize 0.70 ≤ R2 ≤ 0.92

(Donohue et al., 2018)

R2 = 0.68 for wheat; R2 = 0.69 for canola

Crop-SI

(Doraiswamy et al., 2005)

SD = 0.5 t/ha for corns; SD = 0.2 t/ha for soybeans

(Lobell, 2013; Lobell et al., 2003)

(Mo et al., 2005)

R2 = 0.48 for winter wheat; 0.38 ≤ R2 ≤ 0.57 for maize

N/R

(Serrano et al., 2000)

SEM = 4.96 t/ha

(Kamir et al., 2020)

(Burke and Lobell, 2017)

0.15 ≤ R2 ≤ 0.40

R² = 0.77

(Prasad et al., 2006)

R2 = 0.78 for Corn; R2 = 0.86 for Soybean

(Shanahan et al., 2001)

Reference

Accuracy (reported)

Table 1 Summary of empirical and semi-empirical crop yield models using remotely sensed data to estimate crop yield. Records are sorted chronologically then alphabetically. R2: the coefficient of determination; SEM: the standard error of the mean; SD: The standard deviation. ‘N/R’ means not reported and ‘N/A’ means not applicable.

Y. Chen, et al.

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canopy-level NDVI to estimate photosynthetic activity globally. Although MODIS-based yield estimation is constrained by its spatial resolution at 250 m in assisting management strategies in a relatively small field, its daily revisit frequency (often slightly less due to the presence of clouds when imagery is acquired) allows crop biophysical processes that evolve rapidly to be monitored (Gao et al., 2006). According to the current literature (see Table 1), we hypothesise that a national crop yield monitoring system requires an efficient and repeatable model that accommodates both the biophysical process of carbon fixation and meteorological-driven stress factors that influence grain yield for the given biomass. This study, therefore, aims to improve remote sensing-based crop yield estimation by relating carbon estimation to drought, cold, and heat stress for canola, wheat, and barley in Australian dryland cropping systems. Specifically, our objectives are: (i) compare Crop-SI using the plant radiation use efficiency approach with other biomass-based semi-empirical models (i.e., C‐Crop and HF); and (ii) evaluate how canola, wheat, and barley yields relate to meteorological-driven environmental stress given the carbon fixation.

quantities such as Vegetation Indices (VIs; de Wit and van Diepen, 2008; Ferencz et al., 2004), which indicate plant biophysical conditions and above-ground biomass (Pinter Jr et al., 2003). Common VIs include the simple ratio (SR; Jordan, 1969), the Normalized Difference Vegetation Index (NDVI; Colwell, 1974), the Green Normalized Difference Vegetation Index (GNDVI; Gitelson et al., 1996), or the Enhanced Vegetation Index (EVI; Huete et al., 2002). Predictor variables in empirical models are either derived from single-date imagery or time series acquired (Quarmby et al., 1993). In the latter case, temporal metrics, such as the integral of NDVI over the course of the season, are related to crop yield but their performance was found to strongly vary with temporal resolution and cloudiness (Waldner et al., 2019). Empirical models have been widely criticised for their lack of generalisation—they tend to be specific to the climate and the agroecological conditions they are calibrated on and perform poorly in regions exhibiting a high spatial variability in agricultural production. Semi-empirical models focus on the biochemical mechanism of photosynthesis, dry matter (biomass) accumulation, and water consumption, and then apply a linear equation for yield estimates (e.g., Mo et al. 2005). For example, a linear equation, harvest function (HF; Whisler et al., 1986), estimates harvested grain (kg/ha) by modifying plant biomass in the form:

Yield = HI *DM

2. Study area and data pre-processing 2.1. Study area

(1)

Australia is a major agricultural producer and exporter. Depending on meteorological variability, approximately 40 to 50 million hectares are cropped annually (ABS, 2017). The intensively used Australian dryland agricultural system (e.g., colloquially known as the ‘wheatbelt’) is based on cereals (e.g., wheat, barley, and oats), oilseeds (e.g., canola), and legumes (e.g., lupins, chickpeas, field peas, and soybeans) in rotation with annual pastures and fallows. Rainfed agriculture occupies an extremely variable agroecological environment with respect to meteorology and soil type (Fig. 1), leading to the high temporal and spatial variations in Australian grain production (ABARES, 2018). The timing of maximum precipitation during the growing season varies spatially, as does the amount of annual precipitation through time with the Australian continent having the largest of variation of precipitation globally (McMahon et al., 1992).

where DM is total dry matter in Mo et al. (2005), and HI is the harvest index the fraction of DM that is crop yield which typically ranges from 0.25 to 0.3 for canola (Walton et al., 1999), from 0.33 to 0.6 for wheat (Dai et al., 2016), and from 0.4 to 0.6 for barley (Peltonen-Sainio et al., 2008) depending on cultivars and environmental stresses. Traditionally DM is determined by destructive measurements after oven drying, which is time-consuming and labour-intensive over large areas (Duncan et al., 1967; Hatfield, 1983; Idso et al., 1977). Remote sensing can monitor crop growth with high frequency and high spatial resolution, and have demonstrated a more accurate and efficient description of aboveground crop biomass for large areas (Ferencz et al., 2004; Lobell et al., 2003). The remote sensing-based harvest function is often extrapolated regionally or nationally for grain production assessment and policy analysis. It can be also aggregated to the field level because the DM of modern wheat cultivars varies across diverse climatic and soil conditions (Gaiser et al., 2010). HI was discarded in Donohue et al.’s (2018) carbon turnover model (C‐Crop). They used net primary productivity (NPP) integral to estimate biomass and related the above-ground biomass to the actual yield:

Yield = C*

2.2. Data and pre-processing 2.2.1. MODIS NDVI Collection 6 MODIS time-series NDVI (‘MOD13Q1’) were sourced from the USGS for the wheatbelt containing 7 scenes at 250 m resolution form 1 Jan 2009 to 31 Dec 2015. The MODIS NDVIs were generated at 16-day intervals based on product quality assurance and a constrained view angle approach to select a pixel to represent the composting period (Huete et al., 1999). When there are no pixels of acceptable quality available within a composting period, a lower quality observation with maximum NDVI was used for gap-fill the pixel (Huete et al., 1999).

(2)

where C* is calibrated above-ground carbon mass (gC/m2). In their study, C‐Crop explained 69% and 68% of the observed canola and wheat yield field-scale variation, respectively (Donohue et al., 2018). C‐Crop requires calibration of several crop-specific parameters (e.g., plant tissue respiration rates and leaf longevity) to estimate carbon loss caused by respiration and leaf turn-over. These parameters vary spatially (Reich et al., 1999) and this may result in over parameterisation. Moreover, year-to-year reported national yields fluctuate and can be induced by management strategies, growing season meteorology, weeds, diseases, and pests. Approximately 50% of the variability of Australian wheat yields are attributable to meteorological variation (Frieler et al., 2017). Our study describes a new semi-empirical model that accommodates the biophysical process of total carbon fixation (without consideration of energy loss through respiration) by photosynthesis. It also incorporates growing season meteorological variables that provide insight into soil water (Blum, 2009), hot (Deryng et al., 2014) and cold (Thakur et al., 2010) temperature processes that often affect crop yield. We evaluate the performance of Crop-SI to estimate crop yields at both field and nationwide scales with Moderate Resolution Imaging Spectroradiometer (MODIS) imagery. MODIS allows the daily observation of

2.2.2. Meteorological and terrain data Daily (2009–2015) data including precipitation, maximum and minimum air temperature were collected from SILO (Jeffrey et al., 2001). The meteorological raster data with 5 km by 5 km spatial resolution were then computed to monthly means for temperatures and accumulated precipitation as well as numbers of days of heat stress (i.e., ≥ 32.0 °C; Hatfield and Prueger, 2015) and frost stress (i.e., ≤ - 2.0 °C; Porter and Semenov, 2005) per month. Despite its coarse resolution, the meteorological data is expected to capture most of the spatial variability, especially as the terrain of Australian wheatbelt is generally flat. These meteorological-driven stresses for crop yield estimation are listed in Supplementary Material Table 1 to form a stress index (SI) for the model development. Topographic attributes were computed using the Shuttle Radar Topography Mission (Hensley et al., 2000) elevation data at 1″ resolution to estimate the ratio of shortwave irradiance at a 3

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Fig. 1. The seasonal (i.e., 22nd of April to 15th of November) accumulated precipitation (2009–2015) for the Australian wheatbelt. The wheatbelt area was masked based on the cropland (Teluguntla et al., 2018). The precipitation data was sourced from SILO (https://legacy.longfield.qld.gov.au/silo/) (Jeffrey et al., 2001). The field data include 57 canola fields, 190 wheat fields, and 68 barley fields we have GPS-based precision yield data across the wheatbelt.

atmospheric CO2 to in an area per unit time. The yield model is described as follows:

slopping-surface to that at a horizontal-surface (Wilson and Gallant, 2000). Both meteorological and terrain data are resampled to 250 m spatial resolution using nearest neighbour interpolation (Sibson, 1981). For more detailed assessment on the impacts of meteorological variability and techniques in downscaling on the yield prediction, see Anwar et al. (2015) and Brown et al. (2018).

y = a*C + b*SI

(3)

where y is grain yield estimation (t/ha), C is a remotely sensed indicator of carbon fixed by the plant during the growing season known as GPP integral (gC/m2) (Eq. (4)), and a and b are the model coefficients. Eq. (3) can be defined as the Crop-SI model (b ≠ 0) or a non-SI (b = 0) model. We derived carbon fixation (C) using a radiation use efficiency approach. For unstressed plants, radiation use efficiency (RUE) and the fraction of photosynthetically active radiation (fPAR) are usually used to estimate net carbon assimilation (Mo et al., 2005; Monteith, 1972,1977). The model requires dependent and independent variables as listed in Supplementary Material Table 3. Finally, we detail our calibration and validation protocol.

2.2.3. Observed yield data The observed yield data (57 canola fields, 170 wheat, and 64 barley fields) were collected across Australia's wheatbelt between 2009 and 2015 (Fig. 1) using yield monitoring systems mounted in the farmers’ grain harvesters (Supplementary Material Table 2); there are 315 unique field-year combinations in total with an average coverage of 95 ha. The data obtained by these commercial yield monitors were used to construct 5 m resolution yield data maps following Bramley and William's (2001) protocol. According to Donohue et al. (2018), varying the threshold that set the minimum allowable spatial overlap between MODIS 25 m NDVIs and the observed yield had no appreciable effect on yield estimation. Therefore, 5 m grid cell yield data were downscaled to 250 m cells of the remotely-sensed images using nearest neighbour interpolation (Sibson, 1981) for model calibration and validation. More specifically, the downscaled pixel value is a weighted average of the source pixel values within the area of the downscaled pixel.

3.1. RUE approach The metabolic link between GPP and NPP is determined by plant respiration (Amthor and Baldocchi, 2001). In spite of the fact that respiration leads to a large loss of carbon from plants, the ratio of NPP and GPP is relatively conservative, averaging 0.46 and ranging from 0.40 to 0.52 (Waring and Running, 1998). Growing season carbon fixation is given as:

3. Methods

C=

∫ϵ

ϵmax

min

The framework of implementation is shown in a flowchart (Fig. 2), which describes the process of crop yield estimation. A semi-empirical grain yield model was developed by relating remotely sensed gross primary productivity (GPP) integral to actual yield with respect to water, heat and cold stress. GPP is the rate of carbon fixed from

GPP (ϵ) dϵ

(4)

where C was described in Eq. (3), GPP (ϵ) is computed as PARϵ *fPARϵ *RUEϵ , and ϵ is the time step of the model (16-day period) (Leblon et al., 1991; Monteith, 1972, 1977), ϵmin and ϵmax represent the beginning and the end of the growing season. RUE is crop-specific 4

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Fig. 2. The implementation flowchart of the crop yield estimation. The shaded frames indicate the model required parameters and the dashed frames illustrate the links between parameters.

the GPP integral according to Eq. (4).

(Eq. (6)). Temporal variations in GPP during the growing season reflect the crop response to the environmental conditions (e.g., precipitation and temperature) at various phonological stages.

3.1.2. PAR Incoming solar radiation from approximately 390 to 710 nm is used in photosynthesis (McCree, 1971). The variability in PAR can be explained mostly by the variability in diffuse fraction (Whisler et al., 1986) and in the fraction of shortwave irradiance absorbed by the plant (Donohue et al., 2014). PAR (MJ/m2/d) is given as:

3.1.1. The growing season The date of sowing plays a key role in optimising flowering periods (Kirkland and Johnson, 2000). Early sowing may lead to insufficient biomass or frost damage, whereas late flowering may increase heat and water stress (Ozer, 2003). Emergence usually takes between 6 and 15 days after sowing depending on soil temperature, moisture and sowing depth (Hocking and Stapper, 2001). Delayed emergence may shorten the growing season and reduce yield potential (Liu et al., 2004). Emergence, therefore, varies depending on soil moisture content and soil temperature early in the season and management strategies (Karp and Shield, 2008). In dryland Australia, farmers typically sow in a window between late April and June (Zhang et al., 2006) Fig. 3 shows the average annual temporal distribution of time-series NDVI, fPAR, and GPP from 2009 to 2015 for canola, wheat, and barley, respectively, across the dataset. The earliest emergence date one week after the sowing window was approximately early-May (ϵmin = 8) by the trough of the averaged GPP curves (Fig. 3), when satellite begins to provide valid observations of crops during the growing season. NDVI and fPAR remain lower than 0.2 and 0.28 approximately before sowing season and then increases to the peak value of 0.8 (at ϵ from 15 to 16) and 0.7 (at ϵ from 14 to 16), and then reduces significantly to 0.2 after harvesting (ϵ ≥ 20) for cereals and canola, respectively. GPP fluctuates under 2 (gC/m2/d) before May (at ϵ ≤ 10) and increases rapidly until the peak value of 11 gC/m2/d, 8 gC/m2/d, and 9 gC/m2/d, respectively, for wheat, barley, and canola, is reached at ϵ equals to 15, 15, and 16. The maximum values of GPP, where most of the Australian cereal crops are in the flowering phase, is from lateJuly to early-September. In November GPP reduces to 2 gC/m2/d again, and the harvest date is defined as early-November (ϵmax = 20) corresponding to the division point of the GPP curve towards the end of the season. Accordingly, the growing season for major crops in dryland Australia is from late-April to late-November (Fig. 1). Therefore, carbon fixation by crops during the growing season were estimated based on

PAR = RO *τ∂*ρsw *h

(5)

where h is the constant value of 2.3 (molC/MJ) to approximately convert shortwave irradiance from a broadband energetic basis to a molar basis in the PAR wavelengths; RO*τ∂*ρsw represents non-planar shortwave irradiance; RO is top-of-atmosphere shortwave irradiance (MJ/m2/d) (Iqbal, 2012; Roderick, 1999); τ∂ is the atmospheric transmissivity calculated from the Bristow-Campbell relation (Bristow and Campbell, 1984; McVicar and Jupp, 1999) using 5 km resolution meteorological data from SILO; and ρsw is the ratio of irradiance at a sloping surface to that at a horizontal-surface (Wilson and Gallant, 2000). 3.1.3. RUE RUE is highly linear related to a diffuse fraction and photosynthetic carbon flux (Donohue et al., 2014):

RUEϵ = 0.024*fDϵ + 0.00061Ax

(6) 2

where Ax is a crop-specific parameter (μmolC/m /s) describing the maximum photosynthetic capacity and was set to 40, 45, and 23, for canola (Jensen et al., 1996), and wheat (Jensen et al., 1996), barley (Tambussi et al., 2005), respectively; fD is the ratio of diffuse to total solar irradiance ranging from 0.2 under clear skies to 1.0 under overcast skies (Roderick, 1999). 3.1.4. fPAR The fPAR is the fraction of PAR absorbed by a photosynthetic organism. Several approaches to retrieve fPAR from surface reflectance have been devised (Li et al., 2015; Verger et al., 2011). To simplify the 5

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Fig. 3. The scatter-plot matrix of NDVI, fPAR, and GPP (gC/m2/d) for canola, wheat, and barley. The first column on the left shows the distribution of aggregated NDVI, fPAR, and GPP against Crop-SI time-step ϵ , and the last two columns on the right indicate the pairwise relationships amongst them.

estimation of fPAR, we relied on the linear correlation between fPAR and rescaled MODIS NDVI by thresholds that represent bare soil and full cover:

and without SI to test the response of crop yield to meteorologicaldriven environmental stress during the growing season.

fPARϵ = 0.95*(NDVIϵ − NDVImin )/(NDVImax − NDVImin )

3.3. Calibration and validation

(7)

where NDVImin and NDVImax are the bare soil and full cover NDVI thresholds, respectively (Asrar et al., 1984; Carlson and Ripley, 1997). NDVImax is a crop-specific maximum NDVI that was computed based on the seven years’ MODIS NDVIs across the dataset; NDVImin is a local minimum value that was extracted for each field during this seven years to reduce the effect of background soil colour (Donohue et al., 2014).

The total amount of observations (in Supplementary Material Table 2) were then randomly split into two independent datasets for calibration (80% of the field-years) and validation (20% of the fieldyear) using Guyon's (1997) scaling law . To avoid autocorrelation issues of using pixels from the same field-years in both calibration and validation sets, pixels from one field-year could only be in one of the two datasets. Cross-validation was used for Eq. (3) parameter optimisation. Firstly, the calibration dataset (80% of the observation) was randomly divided into to a training (80% of the calibration dataset or 64% of the observation) and a hold-out set (20% of the calibration dataset or 16% of the observation). A predictive model was then developed on the training set and the model responses to the observations were tested by the hold-out set. The results of the hold-out set error provided an estimate of test error. Finally, we repeated the previous two steps 100 times to produce, on average, the best performance in all folds of the training set. An independent set (20%) of field-year combinations (including 11 canola fields, 34 wheat fields, and 12 barley fields) were then used to validate the model prediction. Model validation was performed at both the MODIS 250 m pixel scale and the field scale. The root mean square error (RMSE) was calculated to determine the accuracy of the yield prediction for the three crops. The RMSE was then divided by the mean of the observed yields to estimate the relative error (RE). The coefficient of determination (R2) was also calculated as the proportion of the response variable that was explained by the model. Predicted yield was compared with the observed yield maps for field-scale analysis. The

3.2. Meteorological-driven SI The stress index predictor (SI) was selected and integrated from the meteorological variables in Supplementary Material Table 1 using Support Vector Machines (SVMs; Weston et al., 2001). The SVM removes features with low variance and selects the most important features to establish a good predictor. The meteorological variability across Australia's wheatbelt from 2009 to 2015 is presented in Fig. 4. The SIs were generated based on a multiple linear regression using the selected meteorological variables. We assume that different crops have specific biochemical and physiological responses to the meteorological stresses during phenological development. Hence, the SI should vary across the crop types as different meteorological variables were selected and integrated to form unique crop-type based SI predictors. Moreover, the SI predictors were also defined monthly as various stressors experienced across the phenological stages impact yield differently. The maximum number of meteorological variables determined by SVMs are limited to three to control the model complexity and also avoid overfitting problems. We then compared the calibrated yield model with 6

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Fig. 4. The meteorological variables across the field-years (2009–2015) shown in Fig. 1 and Appendix 2. Part (a) monthly maximum temperature ( °C); (b) monthly minimum temperature ( °C); (c) monthly precipitation (mm/month); (d) monthly heat days (days/month); and (e) monthly frost days (days/month). The box extends from the 25th (Q1) to 75th (Q3) quartile of the data. The whiskers are located at a distance 1.5 times the Interquartile Range (Q3 - Q1) from the edges of the box, and the crosses that past the end of the whiskers are outliers.

the predictive model resulted in it reducing RMSE for ~0.13 t/ha and explaining 35%, 6%, and 13% more of the variation in the yields for canola, wheat, and barley, respectively. Based on the prediction improvements reported in Table 2, the meteorological-driven environmental stresses were included as an empirical component in the predictive model. We introduced averaged monthly maximum and minimum temperature and total precipitation (Supplementary Material Table 1) during the growing season to form SI as the secondary predictor. The patterns in SI for different crops are described in Table 3. The results indicate that: (i) precipitation indicates soil water deficit is critical at anthesis for both wheat and barley yield prediction; (ii) precipitation in the grain-filling period also has a significant contribution to barley yield prediction; (iii) wheat yield is more sensitive to heat stress in the grain-filling phase than barley; (iv) barely is more sensitive to heat stress in early vegetative stage; and (v) canola yield is more sensitive to heat and cold stress rather than soil

95% confidence intervals on the mean absolute error (MAE) values for the models were compared to analyse the differences (Payton et al., 2003). 4. Results 4.1. Meteorological-driven SI The canola non-SI yield model exhibited the lowest RMSE of ~0.6 t/ ha (Table 2) at the pixel level yet the model could not explain half the variability in the actual yield. Approximately 68% of the variability in the predicted wheat yield is linearly related to the pixel-level observations by the non-SI model and the RMSE of ~0.7 t/ha shows the unreliability for the yield estimation across the highly variable wheatbelt. The barley non-SI yield model produced R2 of 0.58 (RMSE of ~0.6 t/ha) and the lowest RE of 25%. By using SI explanatory parameters in

Table 2 Statistical performance on Non-SI model, Crop-SI, HF, and C‐Crop on 250 m pixel level for canola, wheat, and barley. For each crop, the number of 250 m pixels in the validation dataset are reported after the crop name. Model validation at pixel-level Crop (mean observed yield (t/ha), number of 250 m pixels)

Non-SI model R2 RMSE (t/ha)

RE

Crop-SI R2 RMSE (t/ha)

RE

HF R2

RMSE (t/ha)

RE

C-Crop R2 RMSE (t/ha)

RE

Canola (1.5 t/ha, 1606) Wheat (2.2 t/ha, 12,388) Barley (2.5 t/ha, 2508)

0.47 0.68 0.58

0.40 0.30 0.25

0.82 0.74 0.71

0.34 0.25 0.20

0.68 0.77 0.43

0.91 0.64 0.64

0.62 0.29 2.29

0.70 0.75 0.53

0.35 0.32 0.33

0.59 0.65 0.62

7

0.50 0.54 0.49

0.51 0.70 0.80

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Table 3 The comparison of model structures and coefficients for different crop types. The harvest indices (HIs) were calibrated individually for each crop.

HF C-Crop Crop-SI

Yield model

Canola

Wheat

Barley

Yield = HI*DM Yield = C* Yield = a*C + +b*SI

HI: 0.31 r10 = 0.19; λ = 0.21 SI: Tmax(Oct), Tmin(Oct)

HI: 0.62 r10 = 0.06; λ = 0.30 SI: P(Jul), P(Aug), Tmax(Oct)

HI:0.60 r10 = 0.02; λ = 1.00 SI: P(Oct), P(Aug), Tmax(Apr)

*HI is the harvest index; DM is total dry matter (t/ha). *C* is the above-ground biomass including senesces and dead litter (gC/m2). *a and b are model coefficients; T is air temperature ( °C); P is monthly total precipitation (mm/month).

Fig. 5. Scatter plots comparing modelled and observed canola (n = 1606), wheat (n = 12,388), and barley (n = 2508) yields on a 250 m pixel-level. The coloured dash lines delineate the upper and lower bounds of prediction confidence intervals (i.e., p = 0.01 and p = 0.05), the solid black line is the line of best fit, and the black dashed lines are the 1:1 line. From left to right, the 1st column shows HF predicted yields against the observed values; the 2nd column is the C-Crop estimated yields against the observed values; the 3rd column demonstrates Crop-SI predicted yields versus the observed values. From top to bottom, the 1st, 2nd, and 3rd row shows the model comparisons of canola, wheat, and barley yield, respectively. Table 4 The statistical comparison for the 95% confidence interval on the MAE. Canola

HF C-Crop Crop-SI

95% confidence MAE (t/ha) 0.76 0.41 0.39

Wheat interval Lower bound 0.72 0.37 0.35

Upper bound 0.79 0.45 0.43

95% confidence MAE (t/ha) 0.52 0.46 0.37

Barley interval Lower bound 0.51 0.44 0.35

8

Upper bound 0.54 0.47 0.39

95% confidence MAE (t/ha) 2.15 0.62 0.37

interval Lower bound 2.11 0.59 0.33

Upper bound 1.18 0.66 0.41

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carbon required for plant biomass accumulation and respiration during the growing season to enhance yield prediction. SI drives the plantspecific biophysical and biochemical process that influences the yield in response to precipitation and temperature stress at various phenological stages. We implemented a radiation use efficiency approach to estimate carbon fixation by photosynthesis per unit time by integrating GPP during the growing season. In contrast, other studies (Donohue et al., 2018; Gholz, 1982) integrate NPP integral for biomass production estimates. NPP integral based models could explain more than half of the variability in the observed yield (Serrano et al., 2000). They, however, could be over parameterised after accounting for energy loss due to cellular respiration (which depends on temperature) and maintenance of plant tissue (Amthor and Baldocchi, 2001). Moreover, the balance between photosynthesis, respiration, and growth could reflect the key role of nitrogen (Evans, 1989) that can be highly variable in management strategies across Australia (Van Herwaarden et al., 1998), and is difficult to estimate regionally and nationally (Serrano et al., 2000). The RUE method, without considering respiration, therefore, avoids the over parameterising issues of nationwide yield prediction and can be spatially implemented in highly variable cropping landscapes. C‐Crop is competitive to the calibrated Crop-SI for field-scale canola yield estimates (Fig. 6). This is due to the positive correlation between NPP integral and GPP integral modified by meteorological variabilities (Amthor and Baldocchi, 2001). The SI-based model reduces the RE of field-scale yield prediction by 9% and 8% for wheat and barley, respectively (Fig. 6). This improvement in predictive accuracy illustrates that meteorological variability substantially influences the yield variation given the carbon fixation for cereals across the country. Only using integrated GPP to estimate yield, however, is not reliable for crop yield prediction across areas with high temporal and spatial variabilities in meteorological (e.g., Australian wheatbelt) (Deryng et al., 2014; Hochman et al., 2017). While yield models based on biomass only (i.e., not including environmental stresses) can explain the majority of actual yield variation they also have a tendency to overestimate predictions so have large RE / RMSE statistics (compare Crop-SI with C‐Crop results at both the pixel-level (Fig. 5) and fieldlevel (Fig. 6)). Meteorological variables, therefore, should be used for regional to nationwide yield estimation with spatial and temporal variations in plant radiation use efficiency, to ultimately improve the model prediction in the spatial distribution of the yield across multiple climatic zones.

water deficit in the grain-filling phase than the cereals. 4.2. Model comparison The independent validation set was used to compare the results with a widely used harvest function (HF; Whisler et al., 1986) and a carbon turn-over model (C‐Crop; Donohue et al., 2018). These three model structures and coefficients for the three crop types are provided in Table 3. At pixel-level yield prediction, HF underestimates yields (Fig. 5), although the predicted yield is strongly linearly correlated to the observed values with a coefficient of determination of 0.68, 0.77, and 0.43 for canola, wheat, and barley, respectively. Table 4 shows HF produced the highest MAEs for all crop types. C‐Crop performed better than HF (p < 0.001) and reduced the RMSE from 1 t/ha to ~0.5 t/ha and from ~2.3 t/ha to ~0.8 t/ha, for canola and barley yields, respectively (Table 2 and Fig. 5). Compared to C‐Crop, Crop-SI yielded a higher prediction accuracy for wheat and barley (Table 4). It reduced RMSE for at least 0.16 t/ha and RE for 7% for wheat yield estimation (Table 2). It also explained an extra 18% of the variability and reduced RMSE by at least ~0.3 t/ha and RE by 13% for barley, comparatively. Despite the 95% confidence intervals on the MAE values for Crop-SI and C‐Crop overlap (C‐Crop: 0.37–0.45, Crop-SI: 0.35–0.43) for canola (Table 4). Crop-SI produced the highest R2 of 0.82 and lowest RMSE for canola yield prediction. In addition, Fig. 5 shows a narrower distance between the upper and lower bounds of the prediction confidence intervals (i.e., p = 0.01 and p = 0.05) for Crop-SI, which indicates less variance in the predicts for a new observation. For field-scale yield prediction, HF underestimates yields by approximately 0.9, 0.6 and 2.7 t/ha across canola, wheat, and barley field-years (Fig. 6), respectively, due to the simple application of harvest index (HI) to adjust the given biomass. It is not reliable for nationwide yield estimation in dryland Australian ecosystems due to the extreme variability in the meteorology. Comparing with HF, C‐Crop reduced RMSE of 0.5 t/ha and RE of 30% for canola yield prediction and explained an extra 10% and 30% of the variability in wheat and barley yields, respectively (Fig. 6). The right column in Fig. 6 shows the tighter the points hug the dashed lines and the better linear correlations between the predicted and the observed values. Crop-SI produced R2 of 87%, 69%, and 83% with RMSE of approximately 0.4, 0.4, and 0.5 t/ha canola, wheat, and barley yields, respectively (Fig. 6). HF tends to underestimate crop yields for all crops on both pixel and field scales (Figs. 5 and 6). Compared with HF, C‐Crop reduced the RE by approximately 30% and 68% for canola and barley yield prediction, respectively (Figs. 5 and 6). C‐Crop overestimates field-level barley yield (Fig. 6). Crop-SI takes advantages of rainfall and cold and heat stress during the growing season. It explains an additional 11% and 13% of the observed variability across the 250 pixel level for canola and barley, respectively, compared with C‐Crop (Fig. 5). Crop-SI yields the lowest RE of 29%, 20%, and 18% for field-level canola, wheat, barley yield estimation, respectively (Fig. 6).

5.2. Meteorological -driven SI HF relies on a constant HI to convert the given biomass to grain across a spatial large scale (e.g., the Australian wheatbelt), under or overestimation can be expected (Rötter et al., 2012). HI varies depending on cultivars and environmental stresses (Peltonen-Sainio et al., 2008), which should be calibrated year by year when dealing with yield prediction across a high spatial agro-environmental heterogeneity. In this study, HF underestimates yield by up to 2 t/ha and 4 t/ha when actual yield varied from 1 to 3 t/ha for canola fields and from 1 to 5 t/ ha for barley fields, respectively (Fig. 5). C‐Crop uses the above-ground biomass to estimate yields and takes into consideration the energy loss during respiration for biomass accumulation. It performs better than HF and reduces the 27% and 61% of RE for canola and barley yield prediction on pixel level (Fig. 5). C‐Crop, and other similar models, however, may overestimate wheat and barley yields during ‘haying off’, where more above-ground biomass early in the season lead to a decrease in tiller economy (e.g., surviving tillers) and an inability to complete grain filling (Van Herwaarden et al., 1998). Haying-off occurs under terminal water stress (Van Herwaarden et al., 1998). Therefore, using a biomass estimation based model which incorporated temperature and precipitation environmental stressors provided a more accurate approach to model crop yields across a region having high

5. Discussion 5.1. RUE approach Our study developed a simple, robust and repeatable model for a nationwide yield estimation with remote sensing and accounting for within growing season meteorological variability. This method accommodates the biophysical process of crop photosynthesis for carbon fixation using the radiation efficiency approach and environmental stress with respect to precipitation and temperatures. This study also identified in which critical months the meteorological-driven stress can improve yield prediction for the three main Australian wheatbelt crops due to their different response to temperature and precipitation at various phenological stages. The crop-specific SI modifies the amount of 9

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Fig. 6. Scatter plots comparing modelled and independent set observed canola (n = 11), wheat (n = 34), and barley (n = 12) yields at the field-scale. The coloured dash lines delineate the upper and lower bounds of prediction confidence intervals (i.e., p = 0.01 and p = 0.05), the solid black line is the line of best fit, and the black dashed lines are the 1:1 line. From left to right, the 1st column shows Crop-SI predicted yields against the observed values; the 2nd column is the C-Crop estimated yields against the observed values; the 3rd column demonstrates HF predicted yields versus the observed values. From top to bottom, the 1st, 2nd and 3rd row shows the model comparison on canola, wheat, and barley yield, respectively.

high temperatures influence canola yield for a given GPP integral (Table 3). The monthly minimum and maximum temperatures are often used to calculate the degree days for growth. The optimal temperature for canola growth ranges between 20–25 °C, and in the grain-filling period low temperature may slow down the canola growth and high temperatures can cause a substantial decline in the total number of branches and in the number of branches bearing mainly non-aborted pods (Brunel-Muguet et al., 2015). Therefore, canola yield estimation was enhanced by incorporating October (minimum and maximum) temperature-driven stress given the prior carbon fixation during the growing season. Accounting for the heat and cold stress during grainfilling reduces RMSE and RE and explains an additional 35% of the pixel-level canola yield variability (Table 2). For wheat, higher October temperatures increase the rate of grain fill (Table 2) and may shorten the time for grain-filling (Shah and Paulsen, 2003). The shorter grain-filling period, however, is not compensated by the higher rate of photosynthesis and the overall effect is a lower weight of grain (Shah and Paulsen, 2003). Moreover, soil moisture stress in anthesis can represent wasted nitrogen and increase the risk of crop haying-off (Van Herwaarden, 1996). Therefore, precipitation in July and August, and the late season high temperatures are important meteorological variables for wheat yield estimation. The hot

temporal and spatial variabilities in the agro-ecological environment. Figs. 5 and 6 demonstrate that Crop-SI provides the most accurate yield estimation on both pixel and field scales with the lowest prediction error across both scales. Crop-SI yields the highest R2 of 0.74 and 0.69 and the lowest RMSE of 0.54 and 0.39 t/ha for wheat yield prediction on pixel and field scales, respectively, in contrast to other empirical (Quarmby et al., 1993) and semi-empirical models (Donohue et al., 2018; Mo et al., 2005; Serrano et al., 2000) (see Table 1). The advantage of Crop-SI is taking meteorological-driven stress indices (e.g., water, heat and cold stress) into consideration to modify the estimated carbon fixation during the growing season. In dryland cropping systems, such differences in grain yield response to meteorological factors may be related to a wide range of biochemical, physiological, agronomic and ecological processes (Passioura, 2006; Wheeler et al., 2000). For example, grain yields are sensitive to brief episodes of drought, cold and hot temperatures if these coincide with critical stages of crop growth and development (e.g., anthesis and grain filling) (Wheeler et al., 2000). The critical stages for yield estimation are species-specific and the severity of response varies between crops (Dreccer et al., 2018). We found that early season biophysical processes of photosynthesis are critical for canola GPP integral (Fig. 3) and that late-season low and 10

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temperatures in grain filling and July/August precipitation in anthesis explained an extra 6% variation in actual wheat yield and reduced RMSE to 0.54 t/h when compared with the non-SI model (Table 2). SI for barley accommodates precipitation at anthesis and grainfilling phases, as well as an early-season high temperature (Table 3). Barley may be more prone to moisture stress later in the season (Dreccer et al., 2018) because soil water deficit indicates wasted moisture and nitrogen with the risk of barley haying off (Van Herwaarden et al., 1998). Hot temperatures not only influence the rate of growth but also determines the length of each phenological stage (Wheeler et al., 2000). For instance, maximum temperatures early in the season determines establishment as well as the length of the growing season (Hatfield and Prueger, 2015). Incorporating these environmental stresses explained an additional 13% of the variation for barley yield and reduced the RMSE by approximately 0.13 t/ha at the pixel level, compared with the non-SI model (Table 2). The SI-based barley model reduced RMSE by approximately 0.3 t/ha and RE by 13% on pixel scale, compared with C‐Crop predicted values (Fig. 5).

calibrations of these (semi) empirical models are expected with climate change. 6. Conclusion Estimating nationwide crop yields can be challenging due to high temporal and spatial variability in grain production, as it is the case in the Australian wheatbelt. With the objective of better-capturing variability, this study developed a parsimonious, robust and repeatable model (Crop-SI) to estimate wheat, barley and canola yields across Australia. Crop-SI combines a remotely-sensed description of plant carbon fixation during the growing season with stress indices derived from meteorological data. The stress indices significantly helped refine the model predictions because they capture environmental stresses (e.g., drought, cold and heat stress) experienced during critical growth stages which modify gain yield. As a result, the proposed model reduced the relative error to at best 18% compared to other models that can be easily calibrated across large areas. Given its high accuracy at both the pixel and field level, the outputs of Crop-SI are relevant across scales and can serve numerous applications requiring crop yield information. Ultimately, Crop-SI can be applied all globally provided that the appropriate yield, remotely-sensed and meteorological data are made available.

5.3. Limitations and future work Crop-SI was calibrated using yield data from different states, including Western Australia, South Australia, Victoria, and New South Wales. The number of observations (i.e., field-years) is not equally distributed across states (Supplementary Material Table 2): most are located in Western Australia and South Australia with fewer available from the eastern states. In the wheatbelt, winter dominant precipitation is evident in South Australia and Western Australia. In southern New South Wales and Victoria precipitation amounts are fairly uniformly distributed throughout the year, whereas summer dominant precipitation prevails in northern New South Wales and Queensland. The model does not account for non-growing-season precipitation that indicates available soil water before sowing, and these data would be required in the future to introduce such a parameter into model development. Future study should contribute to extensive yield map collection to enrich the calibration dataset and combine these data with a broader set of meteorological variables that extend back to December and January. The development of national digital agriculture system demands high spatial resolution time-series information to describe crop growth (Ferencz et al., 2004; Lobell et al., 2003), therefore finer spatial resolution data, such as Landsat, should be compared with the MODIS calibrated model on both national and field scales. Sentinel-2 should also be tested against MODIS in the future to reduce the time-step from 16 days to 5 days and also increase the spatial resolution so as to provide more detailed information for more practical and profitable decision making at sub-field scale. The current remote sensing-based methods are limited for in-season yield forecasting due to the high dependency on available observations of crop growth during the growing season. The more observation toward the end of the growing season the more aureate of the prediction. In Australia it generally after the green-up period as during this period the satellite captures most of the important information of crop growth. It is after peak greenness is reached when the satellite remote sensing ceased contributing new information and is when the meteorological variables become important. Global average temperatures have been expected to increase faster (0.2 °C per decade) for the next two and three decades with substantially larger trends for cropping areas (Solomon et al., 2007). The potential impact of meteorological change on world food supply suggests a decline in global crop production (Rosenzweig and Parry, 1994) and an increase in global food prices as well as the level of exposure of the global population to the risk of hunger (Parry et al., 2004). Weather-induced national crop-yield fluctuation is expected to increase under climate change (Pachauri et al., 2014) and should be included in studying crop yield variability across national and global scales. Yearly

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgment Appreciation is extended to numerous industry participants who provided training data in the form of yield maps, accessed by the project team. A special thank to Digiscape Future Science Platform, Commonwealth Scientific and Industrial Research Organisation for supporting this project. Randall J. Donohue and Tim R. McVicar acknowledge the support of the ARC Centre of Excellence for Climate Extremes (Australian Research Council grant CE170100023). Special gratitude to Nikhil Garg for his assistance in plotting statistical results. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.agrformet.2019.107872. References ABARES, 2018. Australian Crop report. Australian Bureau of Agricultural and Resource Economics and Sciences. pp. 26 Canberra. ABS, 2017. Themes: Land use On farms, Australia, Year Ended. Australian Bureau of Statistics. http://www.abs.gov.au/ausstats/[email protected]/mf/4627.0. Amthor, J.S., Baldocchi, D.D., 2001. Terrestrial higher plant respiration and net primary production. In: Saugier, B., Mooney, H.A. (Eds.), Terrestrial Global Productivity. Academic Press, San Diego, pp. 33–59. Anwar, M.R., et al., 2015. Climate change impacts on phenology and yields of five broadacre crops at four climatologically distinct locations in Australia. Agric. Syst. 132, 133–144. Asrar, G., et al., 1984. Estimating absorbed photosynthetic radiation and leaf area index from spectral reflectance in wheat. Agron. J. 76, 300–306. Blum, A., 2009. Effective use of water (EUW) and not water-use efficiency (WUE) is the target of crop yield improvement under drought stress. Field Crops Res 112 (2–3), 119–123. Boote, K.J., et al., 1996. Potential uses and limitations of crop models. Agron. J. 88, 704–716. Bramley, R. and Williams, S., 2001. A protocol for the construction of yield maps from data collected using commercially available grape yield monitors, Adelaide. Bristow, K.L., Campbell, G.S., 1984. On the relationship between incoming solar radiation and daily maximum and minimum temperature. Agric. For. Meteorol. 31 (2), 159–166. Brown, J.N., et al., 2018. Seasonal climate forecasts provide more definitive and accurate

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