# Estimation of Corn Yield by Assimilating SAR and Optical Time Series Into a Simplified Agro-Meteorological Model: From Diagnostic to Forecast

Mael Ameline, Remy Fieuzal, Julie Betbeder, Jean-François Berthoumieu, Frederic Baup

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Mael Ameline, Remy Fieuzal, Julie Betbeder, Jean-François Berthoumieu, Frederic Baup. Estimation of Corn Yield by Assimilating SAR and Optical Time Series Into a Simplified Agro-Meteorological Model: From Diagnostic to Forecast. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2018, 11 (12), pp.4747-4760. 10.1109/JSTARS.2018.2878502. hal-04774393

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# Estimation of Corn Yield by Assimilating SAR and Optical Time Series Into a Simplified Agro-Meteorological Model: From Diagnostic to Forecast

Maël Ameline, Rémy Fieuzal, Julie Betbeder, Jean-François Berthoumieu, and Frédéric Baup

**Abstract**—The estimation of crop yield plays a major role in decision making and management of food supply. This paper aims to estimate corn dry masses and grain yield at field scale using an agro-meteorological model. The SAFY-WB model (simple algorithm for yield model combined with a water balance) is controlled by green area index (GAI) derived from optical satellite images (GAI<sub>opt</sub>), and the GAI derived from synthetic aperture radar (SAR) satellite images (GAI<sub>sar</sub>) acquired over two crop seasons (2015 and 2016) in the south-west of France. Landsat-8 mission provides the optimal data. SAR information ($\sigma_{VV}^{\circ}$, $\sigma_{VH}^{\circ}$, and $\sigma_{VH/VV}^{\circ}$) is provided by Sentinel-1A mission through two angular normalized orbits (30 and 132) allowing a repetitiveness from 12 to 6 days. $\sigma_{VH/VV}^{\circ}$ is successfully used to derive GAI<sub>sar</sub> ($R^2$ = 0.72, relative root mean square error (rRMSE) = 10.4%) over the leaf development stages of the crop cycle from a nonlinear function. Others SAR signal ($\sigma_{VV}^{\circ}$ and $\sigma_{VH}^{\circ}$) are too much related to soil moisture changes. At the opposite of GAI<sub>opt</sub>, GAI<sub>sar</sub> cannot be used alone in the model to accurately estimate vegetation parameters. Finally, the robustness of the results comes from the combination of GAI derived from SAR and optical data. In this condition, the model is able, thanks to the inclusion of a new “production module,” to simulate dry masses and yield ($R^2$ > 0.75 and rRMSE < 12.75%) with good performances in the diagnostic approach. In the context of forecast, results offer lower performances but stay acceptable, with relative errors inferior to 13.95% ($R^2$ > 0.69).

**Index Terms**—Biomass, corn, green area index (GAI), Landsat, maize, remote sensing, SAFY-WB, Sentinel-1, yield forecast.

Manuscript received May 24, 2018; revised September 27, 2018; accepted October 17, 2018. This work is part of the PRECIEL project, supported by ACMG, Agralis, Nouvelle-Aquitaine Region, European Union, and CESBIO and certified by Agri Sud-Ouest Innovation. (Corresponding author: Maël Ameline.)

M. Ameline is with the CESBIO, Université de Toulouse, CNES, CNRS, IRD, UPS, Toulouse 31400, France, and also with the Association Climatologique de Moyenne-Garonne et du Sud-ouest, Le Passage 47520, France (e-mail: mael.ameline@gmail.com).

R. Fieuzal and F. Baup are with the CESBIO, Université de Toulouse, CNES, CNRS, IRD, UPS, Toulouse 31400, France (e-mail: remy.fieuzal@cesbio.cnes.fr; frederic.baup@cesbio.cnes.fr).

J. Betbeder is with the CIRAD, UPR BSEF, Montpellier F-34398, France (e-mail: betbederjulie@gmail.com).

J.-F. Berthoumieu is with the Association Climatologique de Moyenne-Garonne et du Sud-ouest, Le Passage 47520, France (e-mail: acmg@acmg.asso.fr).

Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSTARS.2018.2878502

## I. INTRODUCTION

ULTIVATED throughout the world, corn (Zea mays L.) is the most produced cereal (almost 1.3 billion of tons in 2016, [1]). In France, it is the second most prevalently produced crop and is mainly cultivated in areas that are located in the south west (40% of the national production). Fine scale information about corn production over large area is needed for farmers and decision makers to forecast food security or economic impact from local to global scale [2]. To this end, numerous crop models have been developed over the last few decades {e.g., CERES [3], CROPSYST [4], GRAMI [5], STICS [6], WOFOST [7] (for more details see review on crop modeling production: [8]–[11])}. Many of them simulate plenty of variables [i.e., nitrogen consumption, phenological stages, energy fluxes, water balance, carbon allocation, green area index (GAI), grain yield, etc.] and require an accurate description (complete set of parameters used as input) of the surface. Such a list of crop parameters cannot be realistically measured at a regional or national scale (too much time consuming). This constraint is reinforced with the increase of fields and spatial heterogeneities intrinsic to large areas.

To overcome this limitation, several studies have shown interest in combining simplified crop models (inducing less input parameters), well-selected field data (lower time requirements), and remote-sensing images (large areas covered) to estimate crop production parameters (Aquacrop [12], SAFY [13], and GRAMI [5]). These models are all based on the efficiency theories of the plant using the Monteith equations [14]. Based on the growing degree-day base, they simulate the GAI from which the production of dry mass is directly derived. The oldest one, Aquacrop, is developed by the Food and Agriculture Organization and offers the best described water balance module (runoff, infiltration, and deep percolation). GRAMI and SAFY-WB (simple algorithm for yield model combined with a water balance) are, respectively, developed by the United States Department of Agriculture and by the CESBIO laboratory. For both, the vegetation part is driven by the same equations of Monteith. SAFY-WB integrates a simple water balance model since no hydrological model is implemented in GRAMI. The SAFY-WB model is retained since it has been validated for different crop types (wheat [13], [15], corn [16], [17], sunflower [18], and soybean [19]) in contrasting climatic conditions
<figure><img src="image_2.png" /></figure>

Source: SRTM 30m (NASA), Google Maps, data.gov.fr

<figure><img src="image_3.png" /><figcaption>Fig. 1. Location of the study site and the monitored corn fields (with zooms for the sampled fields: a, b, c, and d) in 2015 and 2016, superimposed with the Landsat-8 and Sentinel-1 swaths.</figcaption></figure>

(semiarid [20] and temperate), and is controlled by optical and/or synthetic aperture radar (SAR) remote sensing. Currently, with the high availability of Sentinel and Landsat missions, satellites are fully adapted for field monitoring [21] by providing timely and continuous information (few days of repeat cycle) at high spatial resolution (pixel size from 10 to 30 m for optical and microwave), over large areas (several hundred kilometers wide).

Often combined with simplified model, the contribution of optical images has been widely proved in literature in order to monitor, understand, and estimate crop production, especially

for corn. Mostly based on vegetation indices [2], [22] or radiative transfer models [23], biophysical crop parameters are derived, and then, are implemented into models. However, optical acquisitions are highly dependent on the weather conditions (e.g., cloud cover and haze), and the product derived from their use is nonguaranteed for final users.

In such a context, several studies emphasize the all-weather capability offered by multitemporal images provided by SAR sensors to retrieve biophysical parameters: GAI, biomass, and soil moisture [24]–[27]. This derived SAR information can be used directly, or implemented into agro-meteorological models
(coupling weather data and agronomic functioning model of crop) for estimating the grain mass production of wheat [28], soybean [19], sunflower [18], and other crops.

In this context, the objective of this study is to estimate grain corn yield, derived from dry masses (ear, plant, and total amount), at field scale using a simple agro-meteorological model controlled by optical and/or SAR satellite images acquired in the south-west of France. Two approaches are considered: 1) diagnostic and 2) forecast. The site and the data collection (in situ and satellite) are presented in Section II. The methodology is explained in Section III (SAR processing and optical processing to derive GAI, presentation of the model, and the associated new contribution). The results and discussion about the model performance in the diagnostic and forecast approaches are included in Section IV. The diagnostic approach aims to estimate grain yield from all the information acquired throughout the agricultural season, whereas the forecast approach aims to estimate grain yield by using an increasing number of satellite images according to their acquisition in time.

## II. MATERIALS

### A. Site Description

The study area, centered on the coordinates: 44.06° N, 0.42° E and covering a footprint of 110 km × 140 km, is located in the south-west of France over two French regions (Nouvelle-Aquitaine and Occitanie) (see Fig. 1). With a tempered climate, the area is mainly dedicated to the cultivation of seasonal crops, which fills 54% of the land (percentages based on the land cover map available in [29]). In the west part of the study site, soils are mostly sandy. They are more heterogeneous in the eastern part, depending on the relief and the proximity to large rivers, and dominated by the fraction of silt or clay (silty clay loam or silty loam soils as defined in [30]).

### B. In Situ Data

1) **Climatic Data:** Meteorological stations are implanted in the vicinity of each group of fields (since the required climatic variables are not freely available over the area) (see Fig. 1). The weather parameters are standardized at a daily time step and concern solar radiation, rainfall, air temperature, wind speed, and relative humidity. The reference crop evapotranspiration (ET₀) is then derived, based on the procedure described in [31].

The minimum values of ET₀ are observed in spring at 2 mm; they reach 5–6 mm during summer when the climatic demand is maximum (see Fig. 2). In 2016, these values are more heterogeneous due to the presence of clouds inducing lower radiative fluxes. The 2015 cultural period (from April to the end of October) is much drier than that of 2016, as evident from the amount of rainfall measuring 233 and 380 mm, respectively. In 2015, two dry periods without rainfall are observed, just after the sowing around the day 150 and during the flowering and the tassel emergence from days 170 to 195. In 2016, rainfalls are regularly distributed except at the end of summer from days 214 to 244. The cumulative degree day (using the 6-°C base) allows presenting the phenological stages (see Fig. 2) of corn based from sowing.

<figure><img src="image_4.png" /><figcaption>Fig. 2. Temporal evolution of the daily rainfall (blue bar) and ET₀ (black line) recorded by the station in the south-east of the study area (Fig. 1, zoom sampled field d), during the agricultural season of corn. Degree-day accumulation (6-°C base) is presented for fields “F1” and “F5” (associated with phenological stages’ observations in 2016).</figcaption></figure>

<table><caption>TABLE I
MAIN FEATURES OF THE CORN FIELD</caption><thead><tr><th>Year</th><th>2015</th><th>2016</th></tr></thead><tbody><tr><td><strong>n</strong></td><td>66</td><td>56</td></tr><tr><td><strong>Area</strong> (ha)</td><td>[3.1 42.3 9.6]</td><td>[3.1 62 11.9]</td></tr><tr><td><strong>Slope</strong> (°)</td><td>[0.3 11.2 4.3]</td><td>[0.4 9.7 4.0]</td></tr><tr><td><strong>Sowing day</strong></td><td>[94 127 103]</td><td>[104 128 121]</td></tr><tr><td><strong>Harvest day</strong></td><td>[237 288 241]</td><td>[263 294 273]</td></tr><tr><td><strong>Yield<sub>mea</sub></strong> (q.ha<sup>-1</sup>)</td><td></td><td></td></tr><tr><td>(15% moisture)</td><td>[31 145 109]</td><td>[46 152 109]</td></tr><tr><td><strong>Yield<sub>spa</sub></strong> (n)</td><td>60</td><td>51</td></tr></tbody></table>

2) **Field Information:** Field information is collected over 122 fields of corn (66 in 2015 and 56 in 2016) managed with conventional practices (without intercropping) (see Table I). The sizes of the fields are heterogeneous, with areas ranging from 3.1 to 62 ha for the biggest one. They are mostly distributed over hilly surface (slope of about 4°—or 7°—in average, and up to 11°). The fields monitored over the two years are comparable, regarding the sizes (averages of 9.6 and 11.9 ha) and the slopes (averages of 4.3° and 4°). The corn fields cultivated in 2015 show earlier dates of sowing and harvest (in average, days 103 and 241 compared to days 121 and 294 in 2016) and a shorter vegetative period (–35 days). In 2015, owing to a dry summer followed by thundershowers in some places, many farmers decided to harvest earlier in order to avoid yield losses.
<figure><img src="image_5.png" /><figcaption>Fig. 3. Example of a yield map produced over a heterogeneous area: (a) before been reshaped, and (b) after been reshaped.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. Comparison between yield measured after weighing and yield<sub>spa</sub> measured spatially over a nonreshaped field for the years 2015 and 2016 (15% grain moisture).</figcaption></figure>

Yield information is generally gathered from the farmer once the harvest has been weighed. Yet, some combine harvesters, which are coupled with positioning technologies, record the yield information instantaneously. This spatialized knowledge allows reshaping the field into homogeneous areas, following the agricultural practices (i.e., by separating the irrigated and nonirrigated fields, see Fig. 3).

The comparison between the weighed yields and those obtained from combine harvesters (see Fig. 4) ensures reliability and guarantees the spatialized yields (yield<sub>spa</sub>) to be used as “ground truth” with a high confidence index (R<sup>2</sup> > 0.82 and relative root mean square error (rRMSE) < 11%). In this case, the yield estimated from combine harvesters has not been reshaped to be consistent, in spatial scale, with those weighed. When spatialized data are not available (six fields in 2015 and 2016), the weighed yield is used as the reference. Displayed in the trade standard of moisture (15%), the yield values have the same range of variation (from 31 to 152 q.ha<sup>-1</sup>) over the two years, with 109 q.ha<sup>-1</sup> in average (see Table I).

3) *Ground Surveys*: Biomass measurements are performed following an elementary sampling unit protocol (ESU: 20 m ×

<table><caption>TABLE II
DATES OF BIOMASS MEASUREMENT DURING THE AGRICULTURAL SEASONS OF CORN (FROM APRIL TO OCTOBER) FOR THE YEARS 2015 AND 2016</caption><thead><tr><th>id</th><th>n</th><th>Date of sampling<br>(day of year)</th><th>Date of sampling<br>(°C.day)</th></tr></thead><tbody><tr><td>F1 (2015)</td><td>2</td><td>216, 236</td><td>1572, 1879</td></tr><tr><td>F2 (2016)</td><td>7</td><td>148, 174, 188, 209, 231,<br>249, 270</td><td>202, 508, 709, 1043,<br>1390, 1693, 1974</td></tr><tr><td>F3 (2016)</td><td>5</td><td>183, 201, 223, 241, 257</td><td>679, 944, 1261, 1558,<br>1801</td></tr><tr><td>F4 (2016)</td><td>6</td><td>147, 172, 194, 215, 236,<br>267</td><td>336, 621, 959, 1280,<br>1611, 2080</td></tr><tr><td>F5 (2016)</td><td>7</td><td>133, 148, 169, 195, 215,<br>232, 266</td><td>207, 345, 592, 978, 1292,<br>1567, 2088</td></tr><tr><td>F6 (2016)</td><td>7</td><td>133, 148, 169, 195, 215,<br>232, 266</td><td>207, 345, 592, 978, 1292,<br>1567, 2088</td></tr></tbody></table>

<table><caption>TABLE III
SATELLITE (SAR AND OPTICAL) FEATURES</caption><thead><tr><th>Mission</th><th>Sentinel-1A</th><th>Landsat-8</th></tr></thead><tbody><tr><td>Swath</td><td>250 km</td><td>185 km</td></tr><tr><td>Repetitivity</td><td>12 days</td><td>16 days</td></tr><tr><td>Resolution</td><td>20 x 5 m<sup>2</sup></td><td>30 x 30 m<sup>2</sup></td></tr><tr><td>Sensor features</td><td>5.405 GHz</td><td>B2: 0.45-0.52 µm (B)</td></tr><tr><td></td><td>Dual polarization (VV, VH)</td><td>B3: 0.53-0.60 µm (G)<br>B4: 0.63-0.68 µm (R)<br>B5: 0.85-0.89 µm (NIR)</td></tr></tbody></table>

20 m [33]) where five plants are weighed *in situ* before being dried at 65 °C with a minimum of 60 h. The fruit (ear), as yield component, is separated from the plant (stem and leaves) to obtain the ear dry mass (EDM<sub>mea</sub>), the plant dry mass (PDM<sub>mea</sub>), and the total dry mass (TDM<sub>mea</sub> = PDM<sub>mea</sub> + EDM<sub>mea</sub>). The values are expressed in quintal per hectare (q.ha<sup>-1</sup>) using the plant density information. In 2015, samples are collected on one field on two dates at the end of the crop cycle (days 216 and 236), whereas in 2016 they are collected over five fields all along the crop cycle from sowing to harvest [each three weeks over four fields (see Table II)]. The values of TDM<sub>mea</sub> range from 0.1 q.ha<sup>-1</sup> to a maximum of more than 220 q.ha<sup>-1</sup> reached a few days before the harvest [examples of two fields “F1” and “F5” presented in Fig. 6].

### C. Satellite data

1) *Optical Data:* Despite the launch of Sentinel 2A satellite in June 2015, images are only available for the second cultural year (from December). To be consistent between the two years, optical data exclusively come from the Landsat-8 OLI sensor, launched in 2013. The images are processed by a level-2A processor named MACCS [34], and are available free of charge at Theia land data services [32]. Main features of images are given in Table III (only the spectral bands used are presented).

From April to the end of October, 24 and 22 images are collected, respectively, in 2015 and 2016. This must be contrasted assuming that, in average in 2015, 58% of the information over the fields is worthless because of clouds. It is even worse in 2016 with 74% of the fields that are masked (see Fig. 5). In
<figure><img src="image_7.png" /><figcaption>Fig. 5. Time courses of optical and SAR (orb 30 and 132) acquisitions during the cultivation cycle of corn (from April to October) for the years 2015 and 2016. Cloud cover rate over fields are mentioned by black circle (information not provided for SAR data).</figcaption></figure>

the following, these images are used to calculate the normalized difference vegetation index (NDVI) [35].

2) Microwave Data: SAR images are provided by Sentinel-1A, freely available from the European Copernicus Services Data Hub [36]. The satellite features are presented in Table III, over the studied region (see Fig. 1) in ground range detected mode with an incidence angle ranged between 29.1° and 46.0°, following two orbits (#30 and #132) [37]. During the growing period of corn, 28 and 35 images are, respectively, acquired in 2015 and 2016. The images are preprocessed (radiometric calibration, Range Doppler terrain correction and resampled at 10 m spacing) using the SNAP software by european space agency (ESA) to obtain the sigma naught for the vertical/horizontal (VH) and Vertical/Vertical (VV) polarizations. The SAR signal is sensitive to the antenna incidence angle, an effect that can be reinforced by the local incidence angle observed over hilly landscape. It is necessary to acquire images at regular visit time using the same incidence angle [38]. Thereby, an angular normalization [19], [39] is applied from sowing to harvest to take into account the vegetation effect. Thanks to the swath overlap of the two orbits (#30 and #132), the monitored fields are finally observed every six days, whatever be the weather conditions (see Fig. 5)

$$ \sigma_{\text{norm}}^{0} = (\theta_{\sigma^{0}} - \theta_{\text{ref}}) \times \tau_{\text{mean}} + \sigma_{i}^{0} \quad (1) $$

where $\sigma_{\text{norm}}^{0}$ is the normalized SAR signal, $\theta_{\sigma^{0}}$ is the local incidence angle of the acquisition, $\theta_{\text{ref}}$ is the local incidence angle reference (37.5°), $\tau_{\text{mean}}$ is the average angular sensitivity (0.06 for VH and 0.07 dB.°⁻¹ for VV, calculated from backscattering coefficient and slope, derived from SAR images and shuttle radar topography mission (SRTM) digital elevation model, respectively), and $\sigma_{i}^{0}$ is the initial SAR signal.

3) SAR and Optical Signatures: The NDVI, SAR signals, and ground are presented as a function of the degree days (see Fig. 2), which allows aligning the profile to a unique sowing

reference (see Fig. 6). The evolution of the NDVI represents the dynamics of the photosynthetic activity. It increases from sowing to 1000 °C-day, then saturates and finally decreases during senescence phase (from around 1800 °C-day). This signal is not affected by soil moisture changes. On the opposite, the $\sigma_{VH}^{0}$ and $\sigma_{VV}^{0}$ signals are significantly affected by the variations of soil moisture (due to rains or irrigations) when the vegetative density is low (i.e., at the beginning of agricultural season and before the harvest) [see Fig. 6(e)–(h)] (confirmed by [38]). This phenomenon is strongly year dependent and is clearly visible in 2016 contrary to 2015. Indeed, rainfalls are more important during this period [see Fig. 6(f) and (h)] in 2016 and occur later in 2015 [Fig 6(e) and (g)]. The impact of irrigations or rainfalls decreases when the vegetation is fully developed from 900 to 1500 °C-day, as shown in [38] and [40]. The use of the ratio $\sigma_{VH/VV}^{0}$ overcomes this limitation for vegetation monitoring (compensation of soil moisture impacts) [38], [41]. From 0 to around 300 °C-day, this ratio slightly decreases to reach a minimum [see Fig. 6(i) and (j)] around four or five leaves and corresponds to a low rainfall period and a sustained evaporative demand (around 5 mm/day) accentuated by the vegetation demand (see Fig. 2). It contradicts the argument in [40], as no harrowing is practiced after sowing for any of the fields. Then, the SAR signal ($\sigma_{VH/VV}^{0}$) rises till a plateau (around 1000 °C-day) while the corn biomass still grows [39]. At the end of the agricultural season, the SAR signal decreases with disparities depending on the fields, due to harvest date variations (according to the growth duration of the variety). In 2015, this decline is less pronounced than in 2016. This phenomenon is due to the extension of the harvesting period in 2015 according to favorable climatic conditions (with some earlier harvests, see Table I). On the opposite, the signal significantly decreases in 2016, at the end of the growing season over a shorter period than in 2015. In this case, farmers have harvested their crops to prevent possible damages due to predicted heavy rains.
<figure><img src="image_8.png" /><figcaption>Fig. 6. Time courses of ground data (dry masses), NDVI, and the backscattering signals ($\sigma_{VH}^{\circ}$, $\sigma_{VV}^{\circ}$, and $\sigma_{VH/VV}^{\circ}$) observed over all the monitored corn fields for the years 2015 (a, c, e, g, and i) and 2016 (b, d, f, h, and j). The crosses “+” represent the values observed over the two sampled fields “F1” and “F5”; the gray bands represent the standard deviation of the median values (black line).</figcaption></figure>

### III. METHODOLOGY

As illustrated in Fig. 7, the methodology consists of assimilating the GAI s derived from optical satellite images and SAR satellite images into the SAFY-WB agro-meteorological model to simulate GAI simulated ($GAI_{sim}$) and dry masses (from which the yield is derived), following a diagnostic or a forecast approach. The main steps involved in estimating GAI from reflectances or backscattering coefficients are presented hereinafter, together with an overview of the SAFY-WB model and the description of the new proposed module, ending by the calibration and the validation procedures.

#### A. From Satellite to GAI Estimates

The first step consists in deriving the GAI from optical satellite data and the GAI from SAR satellite data. The time courses of GAI are derived from optical images using the tool BVNet developed by authors in [23]. The radiative transfer model PROSAIL is first used to constitute a training dataset, with the constraint of estimating reflectance (from 400 to 2500 nm) for a wide range of conditions regarding the crop biophysical

variables. Artificial neural networks (ANNs) are then trained on the dataset estimated from PROSAIL (considering reflectance as input variable, and GAI as output). Regarding GAI, the domain of validity of such approach ranges between 0 and 6 m².m⁻². The trained ANNs are finally applied to satellite images, using the green, red, and near-infrared reflectances. Such an approach has been validated in the south-west of France using optical images provided by Formosat-2, Spot-4, and Landsat-8, on independent ground measurements, showing accurate performance with a correlation of 0.92 and an RMSE of 0.4 m².m⁻² for corn (see [16]).

The sensitivity of the SAR signals to the GAI derived from optical satellite images ($GAI_{opt}$) are established using a non-linear regression, focusing on the period from the sowing date to the average SAR signal saturation (1000 °C.day, see Fig. 6). Analyses are based on images acquired in 2015, optical data being almost unusable in 2016, due to cloud cover (see Fig. 5). The relationships based on monopolarization are limited or not satisfactory to estimate the GAI (R² = 0.56, RMSE = 0.94 m².m⁻² for $\sigma_{VH}^{\circ}$; R² = 0.13, RMSE = 1.13 m².m⁻² for $\sigma_{VV}^{\circ}$) due to the sensitivity of these signals to the soil moisture. The best
<figure><img src="image_9.png" /><figcaption>Fig. 7. Workflow of the main steps involved to estimate corn yield assimilating satellite (SAR and optical) information in the SAFY-WB model following two approaches: diagnostic and forecast.</figcaption></figure>

performances are obtained with $\sigma_{VH/VV}^o$, showing high coefficient of determination ($R^2 = 0.72$, RMSE = 0.76 m$^2$.m$^{-2}$, see Fig. 8). It confirms that the ratio of polarization is more sensitive to the volume scattering and is less affected by rainfall.

Nevertheless, the residuals estimated between the regression model and GAI$_{opt}$ remain important (> 0.5 m$^2$.m$^{-2}$ and RMSE = 1.02 m$^2$.m$^{-2}$) when the ratio is greater than -7.5 dB. Consequently, the following equation is used to obtain the GAI derived from SAR satellite images (GAI$_{sar}$) inside the domain of validity [-12 dB, -7.5 dB], given by the analysis of the residual values:

$$GAI_{sar} = 90.52e^{0.69 \times \sigma_{VH/VV}^0} \quad (2)$$

## B. SAFY-WB Model

1) Model Presentation: The SAFY-WB model [15] simulates the temporal evolution of GAI (GAI$_{sim}$) and aerial dry masses (plant, ear and total masses simulated are noted PDM$_{sim}$, EDM$_{sim}$, and TDM$_{sim}$, respectively) from the day close of emergence (D$_0$) until harvest. The model runs at daily time steps, and physical processes are controlled by climatic variables and GAI. The daily dry matter production is proportional to the photosynthetically active radiation (PAR), according to the effective light-use efficiency (ELUE). GAI$_{sim}$ is then derived from the daily total dry matter

$$TDM_{doy} = TDM_{doy-1} + \Delta TDM_{doy} \quad (3)$$

with

$$\Delta TDM_{doy} = ELUE \times PAR_{doy} \times Sc \quad (4)$$

$$GAI_{doy} = GAI_{doy-1} + \Delta GAI_{doy} \quad (5)$$

with

$$\Delta GAI_{doy} = \Delta TDM \times SLA_{doy} \times PLI_{doy} \quad (6)$$

where SLA represents the specific leaf area, PLI represents the partition to leaf index, Sc represents the stress coefficient of water and temperature, and doy represents the day of year.

For a better description of the vegetation growth, the fixed parameter SLA is transformed to a dynamic variable, as proposed in [16] and [42]. In this paper, the daily values of SLA are derived from a degree-day reference, following a relationship estimated from *in situ* data (see Fig. 9).

2) Corn Production Module: The daily EDM$_{mea}$ production module has been implemented based on ground measurements of the TDM$_{mea}$ and the EDM$_{mea}$ (see Fig. 10).

Contrary to the use of a simple harvest index [16], [17], this approach allows simulating the evolution of the biomass allocated to the ear through the ratio between the TDM$_{mea}$ and the EDM$_{mea}$. The fraction of the biomass allocated to EDM$_{sim}$ daily increases following a degree-day reference, the remaining portion being assigned to the PDM$_{sim}$. The final yield is obtained
<figure><img src="image_10.png" /><figcaption>Fig. 8. Relationship between GAI<sub>opt</sub> derived from optical images and the ratio of SAR backscattering coefficients (σ<sup>o</sup><sub>VH/VV</sub>) and the associated residuals (based on the fit model) from sowing day (0 °C·day) to the 1000 °C·day.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 9. Evolution of the SLA (GAI<sub>opt</sub>/PDM<sub>mea</sub>) according to the cumulative degree day from the sowing.</figcaption></figure>

using the maximum of the EDM<sub>sim</sub> associated with the fraction of the EDM<sub>sim</sub> (integrating all the components of the ear) attributed to the grain part (determined in the calibration step). At a regional scale, various earliness indices of corn variety are sown depending on the climate and because of farmers strategies (e.g., to move forward the market prices) (see Table IV).

<figure><img src="image_12.png" /><figcaption>Fig. 10. Evolution of the ratio TDM<sub>mea</sub> / EDM<sub>mea</sub> according to the cumulative degree day from the sowing.</figcaption></figure>

<table><caption>TABLE IV
EARLINESS INDICES' VARIATION DEPENDING ON THE VARIETY OF CORN SEEDS ACCORDING TO THE CUMULATIVE DEGREE DAY FROM SOWING TO HARVEST (USING 6-°C BASE) [43]</caption><thead><tr><th>Earliness type</th><th>Degrees day (°C.day)</th><th>Variation from Ref. (%)</th><th>Number of fields (2015)</th><th>Number of fields (2016)</th></tr></thead><tbody><tr><td>Early</td><td>1740</td><td>-13.65</td><td>3</td><td>0</td></tr><tr><td>Mid-early</td><td>1800</td><td>-10.70</td><td>0</td><td>2</td></tr><tr><td>Mid-late</td><td>1940</td><td>-3.72</td><td>45</td><td>36</td></tr><tr><td>Late (ref)</td><td>2015</td><td>0</td><td>15</td><td>17</td></tr><tr><td>Very late</td><td>2090</td><td>3.72</td><td>3</td><td>0</td></tr></tbody></table>

<table><caption>TABLE V
VALUES OF THE MODEL PARAMETERS DEFINED IN THE CALIBRATION STEP ON THE FIELD "F5" IN THE YEAR 2016</caption><thead><tr><th></th><th>GAI<sub>sar</sub></th><th>GAI<sub>opt</sub></th><th>GAI<sub>sar+opt</sub></th><th>Range [17]</th></tr></thead><tbody><tr><td>P<sub>la</sub></td><td>0.22</td><td>0.15</td><td>0.10</td><td>[0.05 - 0.5]</td></tr><tr><td>P<sub>lb</sub></td><td>-10<sup>-4</sup></td><td>0.002</td><td>0.002</td><td>[10<sup>-5</sup> - 10<sup>-2</sup>]</td></tr><tr><td>S<sub>h</sub> (°C.day)</td><td>1516</td><td>1553</td><td>1456</td><td>[0 - 2000]</td></tr><tr><td>R<sub>a</sub> (°C.day)</td><td>12129</td><td>6425</td><td>8520</td><td>[0 - 10<sup>-5</sup>]</td></tr><tr><td>D<sub>0</sub> (doy)</td><td>121</td><td>134</td><td>137</td><td>[90 - 250]</td></tr><tr><td>ELUE (g.MJ<sup>-1</sup>)</td><td>3.72</td><td>4.42</td><td>3.91</td><td>[0.5 - 6]</td></tr></tbody></table>

This index represents the growth duration of the crop, which is dependent upon variety. It is expressed in degree days by the seed producers from sowing till 32%–35% of grain moisture. Earlier varieties have shorter growth duration until maturity. The new module integrates the earliness announced by the seed companies (from sowing to the harvested product), by varying the duration (using coefficients based on the earliness index of the calibrated field) of the S<sub>tt</sub> parameter of the model (value available in Table V) as follows:

$$S_{tt}(\text{var}) = S_{tt} * (1 + V_{\text{ref}}). \qquad (7)$$

### C. Calibration Step

The model is calibrated on field "F5" of corn (see Figs. 1 and 6, and Table II), selected among the monitored fields, because
it has the advantage of gathering all the ground and satellite observations. Moreover, no stress or damage has been observed on this field. Six target parameters (P<sub>la</sub>, P<sub>lb</sub>, S<sub>tt</sub>, R<sub>s</sub>, D<sub>0</sub>, and ELUE) are calibrated by minimizing the cost function based on the difference between the simulated values of the GAI<sub>sim</sub> and the TDM<sub>sim</sub>, and the GAI derived from satellites and the TDM<sub>mea</sub> is as follows:

$$C_{GAI} = \sqrt{N_{GAI_{mea}}^{-1} \sum_{0<t_i<2500} [GAI_{sim}(t_i) - GAI_{mea}(t_i)]^2} \quad (8)$$

$$C_{TDM} = \sqrt{N_{TDM_{mea}}^{-1} \sum_{0<t_i<2500} [TDM_{sim}(t_i) - TDM_{mea}(t_i)]^2} \quad (9)$$

$$\bar{C} = \text{sum} \left( \frac{GAI_{mea}^{-1} \times C_{GAI}}{TDM_{mea}^{-1} \times C_{TDM}} \right) \quad (10)$$

where GAI<sub>sim</sub> or TDM<sub>sim</sub> correspond to values simulated by the model at time t<sub>i</sub>, GAI measured (GAI<sub>mea</sub>) and TDM<sub>mea</sub> correspond to the values obtained from measurements (satellite or ground), N represents the number of data collected between the sowing (0 °C-day) and the harvest (2500 °C-day).

### D. Validation: From Diagnostic to Forecast

In the validation step, the model is applied to 66 and 55 fields of corn, independent from the calibration step in 2015 and 2016, respectively. D<sub>0</sub> and ELUE are optimized field-by-field by comparing the GAI<sub>sim</sub> and the GAI derived from satellite [13]. The values of the other parameters (P<sub>la</sub>, P<sub>lb</sub>, S<sub>tt</sub>, and R<sub>s</sub>) stay constant and come from the calibration step.

In the diagnostic approach, all the available satellite images are used to derive time series of GAI, which finally control the agro-meteorological model. This approach requires waiting till the end of the crop season to be implemented.

The aim of the forecast approach is to estimate the corn yield in near real time conditions. To this end, the D<sub>0</sub> parameter is fixed as the minimum of the σ°<sub>VH/VV</sub> [corresponding the four- or five-leaf stage as observed in Fig. 11 (top)]. Then, each 250 °C-day (from sowing till 2500 °C-day), the forecast is performed by taking into account all the images, i.e., GAI from both optical and SAR images (GAI<sub>sar+opt</sub>) successively acquired, and considering previous images to adjust the future prediction [see Fig. 11 (top)].

## IV. RESULTS AND DISCUSSION

### A. Calibration

The results (see Fig. 12) show that the GAI<sub>sim</sub> increases to reach a plateau around 1000/1200 °C-day (except for the “GAI<sub>sar</sub>”) where the plant progressively stops its leaf (and stem) development and reallocates the energy into the kernel production. At this step, the biomass is partitioned into EDM<sub>sim</sub> and PDM<sub>sim</sub>, thanks to the function of allocation to ear (see Fig. 10).

<figure><img src="image_13.png" /><figcaption>Fig. 11. Scheme of the methodology used in the forecast approach, concerning the estimation of D<sub>0</sub> and the number of images assimilated according to the range of temperature ([0–250 °C-day], [0–500 °C-day], ..., [0–2500 °C-day]).</figcaption></figure>

### TABLE VI

<table><caption>SUMMARY OF STATISTICAL PERFORMANCES OF THE CALIBRATION STEP USING “GAI<sub>sar</sub>,” “GAI<sub>opt</sub>,” AND “GAI<sub>sar+opt</sub>.” HERE, GAI<sub>opt</sub> IS USED AS REFERENCE TO BE CORRELATED TO GAI<sub>sim</sub> (NO GAI<sub>mea</sub> AVAILABLE). “a” AND “b” REPRESENT THE COEFFICIENTS OF THE LINEAR REGRESSION USED TO CORRELATE SIMULATION AND OBSERVATION</caption><thead><tr><th>Configuration</th><th>Model output</th><th>R<sup>2</sup></th><th>rRMSE (%)</th><th>n</th><th>a</th><th>b</th></tr></thead><tbody><tr><td rowspan="4">GAI<sub>sar</sub></td><td>GAI<sub>sim</sub></td><td>0.87</td><td>73.62</td><td>9</td><td>2.61</td><td>0.60</td></tr><tr><td>PDM<sub>sim</sub></td><td>0.98</td><td>14.71</td><td>7</td><td>1.27</td><td>57.49</td></tr><tr><td>EDM<sub>sim</sub></td><td>0.98</td><td>14.43</td><td>4</td><td>1.09</td><td>72.62</td></tr><tr><td>TDM<sub>sim</sub></td><td>0.98</td><td>17.60</td><td>7</td><td>1.16</td><td>104.86</td></tr><tr><td rowspan="4">GAI<sub>opt</sub></td><td>GAI<sub>sim</sub></td><td>0.98</td><td>12.18</td><td>9</td><td>1.05</td><td>-0.01</td></tr><tr><td>PDM<sub>sim</sub></td><td>0.98</td><td>15.71</td><td>7</td><td>1.27</td><td>29.69</td></tr><tr><td>EDM<sub>sim</sub></td><td>0.98</td><td>14.39</td><td>4</td><td>1.03</td><td>81.80</td></tr><tr><td>TDM<sub>sim</sub></td><td>0.97</td><td>19.61</td><td>7</td><td>1.12</td><td>93.17</td></tr><tr><td rowspan="4">GAI<sub>sar+opt</sub></td><td>GAI<sub>sim</sub></td><td>0.99</td><td>9.41</td><td>9</td><td>1.04</td><td>-0.01</td></tr><tr><td>PDM<sub>sim</sub></td><td>0.98</td><td>11.58</td><td>7</td><td>1.08</td><td>16.56</td></tr><tr><td>EDM<sub>sim</sub></td><td>0.98</td><td>11.31</td><td>4</td><td>0.89</td><td>63.54</td></tr><tr><td>TDM<sub>sim</sub></td><td>0.98</td><td>14.85</td><td>7</td><td>0.97</td><td>60.66</td></tr></tbody></table>

After 2000 °C-day, the crop finally enters its ripening period, the vegetation dries, and the mass production stops till the harvest. The model simulations, the values of model parameters, and the associated performances are, respectively, presented in Fig. 12, and in Tables V and VI.

The estimations of the parameters are close using “GAI<sub>sar+opt</sub>” and “GAI<sub>opt</sub>” to control the model with, respectively, emergence at days 134 and 137 (see Table V) and earlier when using “GAI<sub>sar</sub>.” In these cases the D<sub>0</sub> corresponds to the four- or five-leaf stage (see Fig. 2) from an agronomic perspective, few stages after emergence. The performances are comparable when the model is either controlled by “GAI<sub>opt</sub>” or “GAI<sub>sar+opt</sub>,” and the simulations well reproduce the GAI<sub>opt</sub> with a small error rate (R<sup>2</sup> > 0.98 and rRMSE < 12.18%) (see Fig. 13(a) and (b), and Table VI). The estimations of the dry masses (PDM<sub>sim</sub>, EDM<sub>sim</sub>, and TDM<sub>sim</sub>) are accurate, with high level of R<sup>2</sup> (>0.97) and reasonable rRMSE (inferior to 15.71%). On the opposite, the GAI<sub>sim</sub> is strongly overestimated (rRMSE = 73.62%), and the simulation exceeds 7 m<sup>2</sup>.m<sup>-2</sup> [see Fig. 13(a)] when the model is controlled by the “GAI<sub>sar</sub>” (which is not realistic for corn [17]). Nevertheless, thanks to the constraint of TDM<sub>mea</sub> in the cost function, the dry masses
<figure><img src="image_14.png" /><figcaption>Fig. 12. Comparison between observed (dots) and simulated (lines) GAI and dry masses (PDM, EDM, and TDM) when the model is controlled by: (a) “GAI<sub>sar</sub>,” (b) “GAI<sub>opt</sub>,” (c) “GAI<sub>sar+opt</sub>.”</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Fig. 13. Comparison between yield<sub>mea</sub> and yield<sub>sim</sub> simulated by assimilating (a) GAI<sub>opt</sub>, or (b) a combination of SAR and optical, GAI<sub>sar+opt</sub>, for the years 2015 and 2016.</figcaption></figure>

are more fairly estimated than the GAI<sub>sim</sub> with rRMSE from 17.60% (TDM) to 14.43% (EDM). The grain part (grain yield) of the ears is then calculated by dividing the measured yird, i.e., yield<sub>mea</sub> (133 q.ha<sup>-1</sup>) with the maximum EDM<sub>sim</sub> coming from the three types of GAI assimilated (221.78, 168.49, and 180.53 q.ha<sup>-1</sup> corresponding to assimilation of “GAI<sub>sar</sub>,” “GAI<sub>opt</sub>,” and “GAI<sub>sar+opt</sub>”). This part represents 60%, 79%, and 74%, respectively, of the maximum of EDM<sub>sim</sub>. The last two values are more consistent with ground measurements performed *in situ* (86% in mean on 10 samples), whereas the first one is too small, explained by the overestimation of EDM when the model is controlled by SAR data only. These coefficients are used in the following to derive yield<sub>sim</sub> from the maximum of EDM<sub>sim</sub>.

At the sight of the calibration results, the validation will be
performed by using only the GAI derived from optical images,
i.e., GAI<sub>opt</sub>, or the GAI derived from both SAR and optical
images, i.e., GAI<sub>sar+opt</sub>.

B. Diagnostic Approach

The performances associated with the estimations of the
crop variables (GAI, TDM, PDM, and EDM) are presented in

Table VII. Irrespective of the considered year, the GAI<sub>sim</sub> is well estimated with R<sup>2</sup> ranging from 0.95 to 0.99, and rRMSE inferiors to 21.23% (n > 745 in 2015 and n > 384 in 2016), and with regression function coefficients (a and b, corresponding to slope and offset) close to the perfect cases (1 and 0, respectively). In 2016, the dry masses’ estimations are better estimated using the GAI<sub>sar+opt</sub>. However, the precision is more heterogeneous depending on the considered variable. TDM and EDM are estimated with similar low errors (about 15% in mean using GAI<sub>sar+opt</sub>); whereas, for both configurations, the model has some difficulties to fairly estimate the PDM<sub>sim</sub> with rRMSE upper to 31.99%. Moreover, this last variable is strongly over-estimated as pointed out by the high value of coefficient “a” of the regression function (1.66 and 1.36 instead of 1.0) (see Table VII).

The combined use of SAR and optical data to control the
model (“GAI<sub>sar+opt</sub>”) improves the accuracy of the TDM<sub>sim</sub>
by reducing the rRMSE (–15%) and increasing the R<sup>2</sup> (+0.08).
The best estimates of the TDM<sub>sim</sub> are associated with accurate
simulated values of the EDM<sub>sim</sub> (variable of interest in yield
estimation) with rRMSE of 13.29% for the “GAI<sub>sar+opt</sub>.”

For both years and configurations, the model is able to repro-
duce with confidence the yield heterogeneities as illustrated in
<table><caption>TABLE VII
SUMMARY OF STATISTICAL PERFORMANCES DERIVED FROM THE RELATIONSHIPS BETWEEN SIMULATION AND OBSERVATION USING “GAI<sub>opt</sub>” AND “GAI<sub>sar+opt</sub>” TO CONTROL THE MODEL (VALIDATION STEP), PERFORMED FROM “n” POINTS, AND LINEAR REGRESSION FUNCTION IS CHARACTERIZED BY COEFFICIENTS “a” AND “b”</caption><thead><tr><th>year</th><th>Configuration</th><th>Model output</th><th>R<sup>2</sup></th><th>rRMSE (%)</th><th>n</th><th>a</th><th>b</th></tr></thead><tbody><tr><td rowspan="2">2015</td><td>GAI<sub>opt</sub></td><td>GAI<sub>sim</sub></td><td>0.95</td><td>21.23</td><td>747</td><td>0.93</td><td>0.06</td></tr><tr><td>GAI<sub>sar+opt</sub></td><td>GAI<sub>sim</sub></td><td>0.96</td><td>19.00</td><td>745</td><td>0.94</td><td>0.03</td></tr><tr><td rowspan="5">2016</td><td>GAI<sub>opt</sub></td><td>GAI<sub>sim</sub></td><td>0.99</td><td>12.42</td><td>384</td><td>0.99</td><td>-0.03</td></tr><tr><td></td><td>PDM<sub>sim</sub></td><td>0.85</td><td>43.76</td><td>19</td><td>1.66</td><td>81.24</td></tr><tr><td></td><td>EDM<sub>sim</sub></td><td>0.92</td><td>20.28</td><td>11</td><td>1.06</td><td>55.97</td></tr><tr><td></td><td>TDM<sub>sim</sub></td><td>0.87</td><td>31.83</td><td>19</td><td>1.02</td><td>238.85</td></tr><tr><td>GAI<sub>sar+opt</sub></td><td>GAI<sub>sim</sub></td><td>0.98</td><td>14.22</td><td>384</td><td>0.93</td><td>0.10</td></tr><tr><td></td><td>PDM<sub>sim</sub></td><td>0.88</td><td>31.99</td><td>19</td><td>1.36</td><td>37.67</td></tr><tr><td></td><td>EDM<sub>sim</sub></td><td>0.95</td><td>13.29</td><td>11</td><td>0.92</td><td>15.34</td></tr><tr><td></td><td>TDM<sub>sim</sub></td><td>0.95</td><td>16.50</td><td>19</td><td>0.88</td><td>114.41</td></tr></tbody></table>

Fig. 13. It reproduces the difference in biomass production between irrigated and nonirrigated fields, irrespective of the level of yield observed on ground. When the model is controlled by “GAI<sub>opt</sub>” [see Fig. 13(a)], the performances of yield estimation are better in 2015 (R<sup>2</sup> = 0.76 and rRMSE = 15.65%) than those in 2016 (R<sup>2</sup> = 0.69 and rRMSE = 16.44%). This result is explained by the higher number of optical images exploitable in 2015 (see Fig. 5). The performances of yield estimation vary directly as a function of the number of available optical data. The results are improved when SAR information is added as demonstrated over other crop type (sunflower, soybean, and wheat) [18], [19], [28]. In our case, the GAI<sub>sar</sub> fills the missing optical information at the beginning of the vegetative growth and allows estimating the D<sub>0</sub> parameter more accurately (especially in 2016 where cloud cover was important). In consequence, the performances are more stable in time or even improved (R<sup>2</sup> = 0.75 and rRMSE = 12.75% in 2015, R<sup>2</sup> = 0.77 and rRMSE = 12.07% in 2016) when using the “GAI<sub>sar+opt</sub>.” This consistency can also be notified by the slope of the linear regression (similar using the “GAI<sub>sar+opt</sub>” with a = 0.89 and 0.88 in 2015 and 2016).

At field scale, these results are better than those obtained in [16] (R<sup>2</sup> = 0.66) by using only optical satellite data. Nevertheless, the performances are lower than those obtained at regional scale using low spatial resolution images (R<sup>2</sup> = 0.92 and rRMSE = 4.6%) [16], or than those obtained using mechanistic models such as WOFOST (R<sup>2</sup> = 0.84) [44]. In the first case, low resolution images are less affected by the heterogeneities of fields and final performances are smoothed (as [45] in the U.S. Corn Belt), and the final product of the yield cannot be processed at field scale contrary to our approach. In the second case, the method is strongly limited to few fields as it requires detailed information, as nutrient for example.

<table><caption>TABLE VIII
SUMMARY OF STATISTICAL PERFORMANCES DERIVED FROM THE RELATIONSHIPS BETWEEN SIMULATION AND OBSERVATION USING “GAI<sub>sar+opt</sub>” TO CONTROL THE MODEL (WITH OR WITHOUT CONSIDERING THE EARLINESS INDEX)</caption><thead><tr><th></th><th colspan="2">2015</th><th colspan="2">2016</th></tr><tr><th></th><th>With earliness index</th><th>Without earliness index</th><th>With earliness index</th><th>Without earliness index</th></tr></thead><tbody><tr><th>R<sup>2</sup></th><td>0.75</td><td>0.75</td><td>0.77</td><td>0.74</td></tr><tr><th>rRMSE</th><td>12.75</td><td>12.62</td><td>12.07</td><td>12.61</td></tr></tbody></table>

<table><caption>TABLE IX
COMPARISON OF THE COEFFICIENT AND RRMSE ON YIELD ESTIMATES, ACCORDING TO THE USE OF ANGULAR NORMALIZATION ALGORITHM ON THE SAR SIGNAL</caption><thead><tr><th></th><th>With the<br>angular<br>normalization</th><th>R<sup>2</sup></th><th>rRMSE<br>(%)</th><th>Without<br>angular<br>normalization</th><th>R<sup>2</sup></th><th>rRMSE<br>(%)</th></tr></thead><tbody><tr><th>2015</th><td></td><td>0.75</td><td>12.75</td><td></td><td>0.73</td><td>12.78</td></tr><tr><th>2016</th><td></td><td>0.77</td><td>12.07</td><td></td><td>0.71</td><td>13.22</td></tr></tbody></table>

The benefit of earliness index is investigated in Table VIII, to evaluate the robustness of the approach when this information is not available. In 2015, the results show that there is no improvement on the yield estimate with or without considering the index. This result is explained by the specific climatic condition of this year. Indeed, the end of the crop season was particularly rainy (rain storm) and farmers decided to harvest the crop earlier to avoid damage and loss on corn production. Consequently, majority of the field have been harvested earlier, whatever be the crop variety. On the opposite, the result obtained in 2016 (standard year from a climatic point of view) shows that earliness index has positive effects on yield estimates (R<sup>2</sup> = 0.77 to 0.74). During this year, fields have been harvested according to their earliness indices. Whatever the considered year, the rRMSE stays constant using or not using the earliness index (≈12%–13%). These results demonstrated that the diagnostic approach stays operational even if no information is provided by the seed companies.

The impact of angular normalization function on grain yield retrieval is addressed in Table IX. The results show that, when backscattering coefficient is not normalized, the final yield estimation is slightly degraded for the two years (2015 and 2016) based on the coefficient of determination (–0.02 in 2015 and –0.06 in 2016) and the rRMSE (see Table IX). It demonstrates that the yield estimates stay acceptable without angular normalization, and that performances slightly increase when SAR signal is angular corrected.

In the following, only the GAI<sub>sar+opt</sub> are used for the forecast approach because of its lower dependence on cloud cover (considering the earliness index).

### C. Forecast Approach

The statistical performances (R<sup>2</sup> and rRMSE) associated with the estimates of yield<sub>sim</sub> using the forecast approach are presented in Fig. 14. Results show that forecast is not possible (R<sup>2</sup> < 0.44 and rRMSE > 21.47% in 2015; R<sup>2</sup> < 0.15 and
<figure><img src="image_16.png" /><figcaption>Fig. 14. Evolution of the statistical performances ($R^2$ and rRMSE) associated with the estimation of corn yield, by updating the assimilation of $GAI_{sar+opt}$ each 250 °C-day till 2500 °C-day in the years 2015 and 2016.</figcaption></figure>

$r$RMSE > 50.31% in 2016) during the first phenological stages of the crop development, until 1250 °C-day. The maximum of performances ($R^2$ > 0.69 and rRMSE < 13.95%) are obtained at about 1750/2000 °C-day, just after the fruit development (see Fig. 2). Then, performances are quite stable until the harvest (in mean, $R^2$ = 0.68 and rRMSE = 15% in 2015 and 2016), where ear/grain dry mass does not evolve anymore and only the vegetation moisture content decreases.

In the forecasting approach, few studies are available at a field scale as they mainly use optical information at low resolution (MODIS, [46] for corn). The accurate estimates of corn yield are consistent with agronomic studies, where early predictions are derived from statistical algorithms trained on ground measurements [47]–[50]. The proposed approach takes full advantage of the observation capabilities of satellite images, offering opportunities for monitoring large areas unlike empirical approaches often subservient to few surveyed plots. Moreover, the obtained performances confirm the usefulness of combining SAR and optical images for early yield estimates, and extend the promising results presented in [51] to successive agricultural seasons. It would be interesting, as in [52] (using SAR on rice crop), to mix historical (not available here) and real-time weather information to minimize uncertainties.

## V. CONCLUSION

The aim of this paper was to estimate corn dry masses (ear, plant, and total amount) and grain yield at field scale using an agro-meteorological model (SAFY-WB) controlled by $GAI_{opt}$ and/or $GAI_{sar}$ images. The methodology presented first the

estimation of GAI from SAR and optical satellite images, with the associated domain of validity. Contrary to optical data, the SAR data ($\sigma^o_{VH/VV}$) are not able to estimate GAI all along the crop cycle and saturate early in the crop season (around -7.5 dB). In parallel, the improvements of the model were presented with the inclusion of a new “production module,” which allows simulating the allocation of mass into the ears from the simulated TDM$_{mea}$ all along the crop cycle (the yield was then derived from the ear mass) taking into account the variety (through the earliness index).

The model was calibrated using three configurations: 1) $GAI_{sar}$; 2) $GAI_{opt}$; and 3) $GAI_{sar+opt}$. The results show that the use of $GAI_{opt}$ is well adapted to control the model along the crop cycle, with accurate estimates of dry masses (rRMSE < 19.61%). ON the opposite, the $GAI_{sar}$ cannot be used alone to reproduce the temporal behavior of GAI (rRMSE = 73.62%). When combined with $GAI_{opt}$, the $GAI_{sar}$ offers crucial information to determinate the parameters $D_0$ of the model, improving the performances of the dry masses and yield simulations, and its robustness irrespective of the cloud cover rate. Consequently, only the last two configurations ($GAI_{opt}$ and $GAI_{sar+opt}$) were retained for validation. Finally, in the diagnostic approach, the estimates of dry masses and GAI were improved especially for the TDM$_{sim}$ [by reducing the rRMSE (-15%) and increasing the $R^2$ (+0.08)], used to derive yield. Accordingly, yield performances were better and more stable in time when SAR data were combined to the optical ones (in mean $R^2$ = 0.76 and rRMSE = 12.5% in 2015/16). The consideration of the earliness index brought about positive effects for the yield estimation. This impact should be deeper investigated by considering more contrasted varieties of corn on other climatic conditions. Therefore, in the forecast approach, only $GAI_{sar+opt}$ was considered and results demonstrated that the yield is quite accurate ($R^2$ > 0.69 and rRMSE < 13.95%).

The use of only SAR or optical data is not sufficient to achieve corn monitoring, due to the low sensitivity of SAR signal to crop development and the uncertainty to obtain enough optical data because of cloud cover risk. Moreover, *in situ* dry masses remained necessary to apply this method year-to-year, as only one field (in 2016) was able to calibrate the model for two years. In the future, it would be interesting to develop new approaches to determine a satellite signal more sensitive to dry masses in order to improve yield forecasting. For this objective, other microwave frequencies could be investigated, especially those offered by ALOS-2 PALSAR sensors (L-band). At this frequency, the signal penetrates deeper into the vegetation layer, and saturates later (compared to C-band) according to the vegetation biomass. Others SAR techniques could be also investigated as PolInSAR ones.

With the purpose to deliver a service to the people in charge of forecasting the future yields, the performance of the forecast around 1500 °C-day is acceptable as it means delivering, around one month before the harvest, a spatialized information that will help the management of the storage infrastructure and the means to carry the grains from the fields. Of course, weather scourges such as hail, wind, and floods may reduce locally the estimated potential.
ACKNOWLEDGMENT

The authors are very grateful to the farmers involved, the ACMG (P. Debert, C. Cazenave, etc.), and the CESBIO (M. Battude, F. Helen, etc.) for their help.

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<figure><img src="image_17.png" /></figure>

Maël Ameline received the Master’s degree in geography with a specialization in remote sensing, GIS, and environment from the University of Rennes 2 in collaboration with the agronomy engineering school AgroCampus-Ouest, Rennes, France, in 2014. He is currently working toward the Ph.D. degree in remote sensing and agro-systems modeling at the University Paul Sabatier, Toulouse, France.

He worked on rice mapping and yield estimation based on remote sensing in Madagascar with the Center of Agricultural Research for Development, Reunion Island, France. He also acquired knowledge in web mapping and pedology by studying the impact of climate change on groundwater-irrigated agriculture of southern India, as an Intern with the Indo-French Cell on Water Science, Bengaluru, India.

<figure><img src="image_18.png" /></figure>

Rémy Fieuzal was born in Agen, France, in 1981. He received the M.S. degree in ecology, biostatistics, and modeling from the University Paul Sabatier, Toulouse, France, in 2007, and the Ph.D. degree in remote sensing and agronomy from the University Paul Sabatier, in 2013, for his work on the contributions of satellite radar data for estimating biophysical parameters of agricultural land.

He is working on image processing and analysis of satellite data acquired in optical and microwave domains, with the Centre d'Etudes Spatiales de la BIOsphère, Toulouse, France. His research interests include mapping of different surface parameters (leaf area index, biomass, irrigation, or top soil moisture) and agrosystems modeling.

<figure><img src="image_19.png" /></figure>

Julie Betbeder received the Master’s degree in environmental engineering from the Ecole Supérieure d’Agriculture, Angers, France, in 2010, and the Ph.D. degree in geography from the University of Rennes, Rennes, France, in 2015.

Her Ph.D. work involved littoral, environment, and remote Sensing (LETG Rennes COSTEL), on the evaluation of optical and radar SAR polarimetry data for the characterization of ecological continuities in European landscapes. She worked during her Postdoctorate (2015–2016) on the evaluation of the assimilation of optical and SAR data into agro-meteorological model for crop yield estimation in the Centre d’Etude Spatiale de la BIOsphère, Toulouse, France.

She is a Researcher with the Research Unit "Forests and Societies," the International Center of Agricultural Research for Development, Montpellier, France. Her research interest focuses on the impact of forest degradation on landscape functions in tropical forest landscapes. She is also working on the evaluation of remote sensing data for forest degradation quantification and characterization.

<figure><img src="image_20.png" /></figure>

Jean-François Berthoumieu received the M.S. degree in habitat and environment and the Ph.D. degree in fluid mechanics, option aérothermie, from the University Paul Sabatier, Toulouse, France, in 1976, 1979, respectively.

After the Postdoctorate at the Alberta Research Council, he worked during four years on the climatology study of storms and hail over the south-west of France. Then, he left the field of fundamental research to work with a farmer association (ACMG) where he developed technologies based upon probes and remote sensing for helping famers better manage their irrigation. He worked on four European Interreg programs where he found the limitation of optical and thermal images to provide a continuous service to farmers due to cloud cover. He met Frédéric Baup in 2011 and they decided to build a new program called PRECIEL in 2014 base upon SAR images with the objective of testing their potential for helping farmers on large scales to better manage agronomy and irrigation.

Dr. Berthoumieu is the President of a cluster called Water and Climate Adaptation and he reviews on atmospheric research for ELSEVIER.

<figure><img src="image_21.png" /></figure>

Frédéric Baup received the M.S. degree in microwaves and optical telecommunications, and the Ph.D. degree in SAR remote sensing, both from the University Paul Sabatier, Toulouse, France, in 2003, 2007, respectively.

Since 2008, he is a Researcher in microwave remote sensing with the Centre d'Etudes Spatiales de la Biosphère Laboratory, Toulouse, France. He has authored international journals. His research interests include microwave remote sensing applied to land surfaces and SAR image analysis to monitor spatio-temporal variations of soil (moisture and roughness) and vegetation (biomass) properties over agricultural or natural areas. His education interests are focused on physics and remote-sensing sciences.

Dr. Baup is a Principal Investigator of projects supported by the European Space Agency, Canadian Space Agency, Japan Aerospace Exploration Agency, and German Aerospace Center. He is a Reviewer for journals and conference proceedings.