2.2.2. Yield Data

Australia's major dryland crops are selected for yield estimates and validation, including 35 fields of canola, 123 fields of wheat, and 52 fields of barley (Table S1, Supplementary Materials). The average area of these fields is ~112 ha with a standard deviation of ~69 ha. Using various yield monitoring systems mounted on grain harvesters operated by farmers, these observed data were collected at these sites across the country from 2009 to 2015 (Figure 1). The data obtained by these commercially available yield monitors were used to construct a yield data image at 5-m resolution [44], which was upscaled to 25 m and 250 m to match the Landsat and MODIS resolutions, respectively.

#### 2.2.3. Climate Data

Climate data were sourced from Science Information for Land Owners (SILO) which provides nationwide meteorological variables (e.g., maximum and minimum air temperature, and precipitation) at daily temporal frequencies by interpolating observations made by the Australian Bureau of Meteorology onto a 0.05◦ by 0.05◦ grid [37].

#### **3. Methods**

#### *3.1. Yield Prediction*

We use a semi-empirical model [C-Crop; 6]) because of its low data requirements for calibration across large areas. C-Crop correlates actual grain weight (t/ha) to end-of-season above-ground plant carbon mass (*C*), and the estimation of *C* is based on biophysical principles of plant photosynthesis [6]. *Ci* is estimated using the carbon mass (*Ci*−1) from the previous time step and the current period's allocated net assimilation flux *Ni* (gCm<sup>−</sup>2) minus the dead biomass that enters the litter store, and *i* (1–22) is the model time step (every 16 days in a calendar year).

$$\mathbb{C}\_{i} = (1 - \rho)(\mathbb{C}\_{i-1} + N\_i) \tag{1}$$

where ρ (periods<sup>−</sup>1) is the reciprocal of carbon longevity (i.e., the turn-over rate of plant live carbon into senesced tissue per time step *i*).

#### 3.1.1. Net Primary Productivity

Net primary productivity (NPP) is the rate of carbon assimilation from atmospheric CO2 to organic material (biomass) for a given area while accounting for the energy loss due to autotrophic respiration [6,45].

$$N\_i = 0.75 \left( G\_i \frac{fPAR\_i}{0.95} - 16r\_{10} \frac{C\_{i-1}}{cn} \sigma\_i \right) \tag{2}$$

where *fPARi* 0.95 is the fraction of total assimilation flux *Gi* allocated to the above-ground plant biomass (gCm<sup>−</sup>2) at time step *i*. The plant maintenance respiration is calculated as a function of leaf nitrogen, air temperature, and previous biomass *Ci*−1. *r*<sup>10</sup> is the plant tissue respiration rate at 10 ◦C; *cn* stands for plant carbon-to-nitrogen ratio; σ*<sup>i</sup>* is a scalar that modifies the respiration rate according to the daily air temperature [46].

## 3.1.2. Gross Primary Productivity

The total assimilation flux *Gi*, <sup>=</sup> also known as the gross primary productivity (GPP) (gCm−2·day<sup>−</sup>1), can be calculated using the remote sensing-based plant light use efficiency (LUE) approach. The chloroplasts use incoming solar radiation with a spectral range between 400 nm and 700 nm in photosynthesis [47].

$$G\_i = PAR\_i \times fPAR\_i \times RLE\_i \tag{3}$$

$$PAR = 2.3(R\_O \times \tau\_{\partial})\rho\_{\text{sw}} \tag{4}$$

where (*RO* × τ∂)ρ*sw* represents the shortwave irradiance (*Rs*), *RO* is daily top-of-atmosphere shortwave irradiance (J/m2/day) [48,49], τ∂ is atmospheric transmissivity calculated using the Bristow–Campbell relationship [50,51] calibrated for Australia, and ρ*sw* is the ratio of shortwave irradiance at a sloping surface to that at a horizontal surface [52].

*fPAR* is the portion of *PAR* that is absorbed by a photosynthetic organism, and it is estimated using a linear relation between *fPAR* and rescaled NDVI by thresholds (i.e., local minimum and crop-specific maximum NDVIs) [53,54]. *LUE* is highly linearly related to a diffuse fraction (*fD*) and photosynthetic carbon flux [55].

$$LILE\_i = 0.024 \times f\_{\rm Di} + 0.00061 A\_{\rm x} \tag{5}$$

where *Ax* is the maximum photosynthetic capacity (μmolCm−2·s<sup>−</sup>1), which is a crop-specific parameter; is 23, 40, and 45 for barley [56], canola [57], and wheat [57], respectively; *fD* is the ratio of diffused to total solar irradiance varying from 0.2 (under clear skies) to 1.0 (under overcast skies) [48]. For a full description of C-Crop, see Donohue et al. [6].

#### *3.2. Validation*

Two sets of data are used for validation and further analysis, depending on the pixel-level completeness of time-series Landsat NDVIs at 25-m pixel resolution across the growing season (*i*: 8–19) between April (DOY 113) and October (DOY 304) (Figure S3, Supplementary Materials). Firstly, the coordinates of complete time-series Landsat pixels are used to obtain the resampled MODIS, L–M blended, and observed yield data for validation at the 25-m resolution as the first dataset. Secondly, these complete time-series Landsat pixels are upscaled at 250 m pixel size to extract the MODIS and the L–M blended data with the same pixel size for the validation at the moderate resolution. Thirdly, the pixel-level yield predictions are aggregated for each respective field by averaging the yield values of the pixels within, for field-level validation. Fourthly, and finally, the predicted yields are evaluated using the model coefficient of determination (*R*2), the root-mean-square error (*RMSE*), and the mean bias error (*MBE*). The *R*<sup>2</sup> describes the proportion of the response variable that can be explained by the model. *RMSE* gives more weight to the largest errors, and the *MBE* indicates the systematic error of the model to under or overestimate. These procedures are then repeated for the second dataset created

according to the coordinates of incomplete time-series Landsat NDVIs at the 25-m pixel resolution. As C-Crop requires a time series of NDVI, the results are assessed without the incomplete time-series pixels of Landsat.
