# Evaluation of MODIS, Landsat 8 and Sentinel-2 Data for Accurate Crop Yield Predictions: A Case Study Using STARFM NDVI in Bavaria, Germany

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## Abstract

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^{2}) for the year 2019. For WW and OSR, the synthetic products’ high spatial and temporal resolution resulted in higher yield accuracies using LUE and WOFOST. The observations of high temporal resolution (8-day) products of both S-MOD13Q1 and L-MOD13Q1 played a significant role in accurately measuring the yield of WW and OSR. For example, L- and S-MOD13Q1 resulted in an R

^{2}= 0.82 and 0.85, RMSE = 5.46 and 5.01 dt/ha for WW, R

^{2}= 0.89 and 0.82, and RMSE = 2.23 and 2.11 dt/ha for OSR using the LUE model, respectively. Similarly, for the 8- and 16-day products, the simple LUE model (R

^{2}= 0.77 and relative RMSE (RRMSE) = 8.17%) required fewer input parameters to simulate crop yield and was highly accurate, reliable, and more precise than the complex WOFOST model (R

^{2}= 0.66 and RRMSE = 11.35%) with higher input parameters. Conclusively, both S-MOD13Q1 and L-MOD13Q1, in combination with LUE, were more prominent for predicting crop yields on a regional scale than the 16-day products; however, L-MOD13Q1 was advantageous for generating and exploring the long-term yield time series due to the availability of Landsat data since 1982, with a maximum resolution of 30 m. In addition, this study recommended the further use of its findings for implementing and validating the long-term crop yield time series in different regions of the world.

## 1. Introduction

- What is the optimal spatial resolution (10 m, 30 m, or 250 m)?
- What is the optimal temporal resolution (8 or 16 days)?
- Which is the suitable CGM (LUE or WOFOST)?

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, Bavaria covers almost one-fifth of Germany. The federal state is divided into 96 counties with 71 rural districts (so-called “Landkreise”) and 25 city districts (so-called “Kreisfreie Städte”). A brief description of the regions of Bavaria is shown in Figure A1.

#### 2.2. Data

#### 2.2.1. Satellite Data

#### 2.2.2. Climate Data

#### 2.2.3. InVeKos Data

#### 2.2.4. LfStat Data

#### 2.3. Method

#### 2.3.1. WOFOST

_{2}assimilation, transpiration, respiration, phenological development, and dry matter formation (crop biomass). The model states crop biomass as a function of solar radiation, temperature, and daily crop characteristics. LAI is a vital state variable in the WOFOST model to analyse dynamic growth processes. The model simulates the daily crop growth rate, the gross CO

_{2}assimilation rate that depends on the LAI, and incoming radiation. In addition, LAI is an essential parameter for the calculation of the potential transpiration in the model. The inputted LAI is calculated as a function of NDVI for WW and OSR (Table 3).

_{2}O) produced. Some fractions of the CH

_{2}O produced are used to provide energy for respiration (maintenance respiration), with the remaining energy converted into dry matter. The model calculates the growth rate as:

^{−1}d

^{−1}), A is the gross assimilation rate (kg CH

_{2}O ha

^{−1}d

^{−1}), R

_{m}is the maintenance respiration rate (kg CH

_{2}O ha

^{−1}d

^{−1}), and C

_{e}is the conversion efficiency (kg dry matter kg

^{−1}CH

_{2}O). Based on Monteith’s Principle of Light Use Efficiency, the calculation of total dry matter (kg dry matter ha

^{−1}yr

^{−1}) in the WOFOST model is equivalent to the net primary production (NPP) (kg ha

^{−1}yr

^{−1}) [20,63].

#### 2.3.2. LUE

^{−2}d

^{−1}), FPAR is the fraction of PAR absorbed by the canopy, ∈ is the actual Light Use Efficiency (g C M J

^{−1}), ∈

_{o}is the actual Light Use Efficiency (g C M J

^{−1}), Tmin

_{min}′ is the minimum of the minimum temperature (°C) index, VPD

^{’}is the vapour pressure deficit (kPa) index, and Ks is the soil moisture stress index. The temperature and vapour pressure indexes are calculated using the minimum and maximum values for the study region. The total aboveground biomass calculated by the LUE model is equivalent to the net primary productivity (NPP) (kg ha

^{−1}yr

^{−1}). A brief explanation of the model with a flow diagram is described in our previous study [5]. The specific model is not only selected for its performance but also its high processing speed and low requirement of input parameters compared to the other CGMs. The linear regression equations used to calculate crop yields of WW and OSR for different satellite biomass products using LUE are shown in Table A1.

**Table 4.**Description of model calibration values taken from the related literature for the WOFOST and LUE models, plus, the climate thresholds used to calculate the climate stress indexes used in the design of a model.

Parameter | Description | Model(s) | Value | Units | Reference | |
---|---|---|---|---|---|---|

ξ | Scattering coefficient | WOFOST | 0.2 | - | [60] | |

kdf | Diffusion coefficient | WOFOST | 0.72 | - | [72] | |

Am | Gross assimilation rate | WOFOST | 4 | g/m^{2} | [73] | |

Ce | Conversion coefficient | WOFOST | 0.0399 | - | [74] | |

∈_{o} | Light use efficiency | WOFOST&LUE | 3 | gC/MJ | [71] | |

Tmin min | Minimum of minimum temperature | WOFOST&LUE | −2 | °C | [67] | |

Tmin max | Maximum of minimum temperature | WOFOST&LUE | 12 | °C | [70] | |

VPD min | Minimum VPD | LUE | 1.3–1.5 | k Pa | [75,76] | |

VPD max | Maximum VPD | LUE | 3.6–4 | k Pa | [75,76] | |

Zr | Maximum root depth | WOFOST&LUE | 1.5–1.8 | m | [77] | |

P | Average fraction of TAW | WOFOST&LUE | 0.55 | - | [77] |

#### 2.3.3. Sensitivity Analysis

_{o}) values.

#### 2.3.4. Statistical Analysis

^{2}) and the precision (root mean square error (RMSE)) of the obtained results were calculated using a linear regression model (LRM), which aimed to establish a linear relationship between the referenced (independent variable) and modelled yields (dependent variable) of WW and OSR at different spatial (10, 30, and 250 m) and temporal (8 and 16 days) scales. The statistical parameters used to validate and compare the accuracies of the LUE- and WOFOST-modelled yields with the referenced yield are R

^{2}(Equation (5)), Mean Error (ME) (Equation (6)), RMSE (Equation (7), and relative RMSE (RRMSE) (Equation (8)). To compare the yield outputs of both models, this study considered RRMSE < 15% as good agreement, 15–30% as moderate agreement, and > 30% as poor agreement [78]. The lower the value of ME, RMSE, and RRMSE, the better the model performed.

_{i}is the predicted value, O

_{i}is the observed value, P’ is the predicted mean, O’ is the observed mean value, n is the total number of observations, referenced yield

_{y}is the LfStat yield of every district in 2019, and modelled yield

_{y}is the LUE-generated yield of every district in 2019. The results’ significance was obtained by observing the probability value (p-value) calculated using the LRM with a H

_{0}that no correlation exists between the referenced and the modelled or synthetic values and an H

_{1}that the correlation exists. The test was performed at a significance (or alpha (α)) of 0.05. A p-value lower than 0.05 indicates that the model is significant and rejects the H

_{0}that there is no correlation.

## 3. Results

#### 3.1. Evaluation of Real (MOD13Q1, Landsat, and Sentinel-2) and Synthetic (L-MOD13Q1 and S-MOD13Q1) Satellite NDVI Products

#### 3.2. Statistical Analysis of Crop Yields Obtained from LUE and WOFOST Models for WW and OSR Using Multisource Data in 2019

_{0}of the LRM that there is no relationship between the modelled and measured crop yield (Figure 6 and Figure 7). The linear regression equations obtained to calculate crop yields of WW and OSR for different satellite biomass products with both models are shown in Table A1. The R

^{2}values obtained from the S-MOD13Q1 NDVI (8 and 16 days) products have a higher accuracy compared to the L-MOD13Q1 (8 and 16 days) and MOD13Q1 (8 and 16 days). Based on the R

^{2}of the different spatial resolutions of the NDVI products for WW, the models’ descending order is LUE (S-MOD13Q1, 10 m, 8 days), LUE (S-MOD13Q1, 10 m, 16 days), LUE (L-MOD13Q1, 30 m, 8 days), LUE (L-MOD13Q1, 30 m, 16 days), WOFOST (S-MOD13Q1, 10 m, 8 days), WOFOST (L-MOD13Q1, 10 m, 8 days), LUE (MOD13Q1, 250 m, 8 days), WOFOST (S-MOD13Q1, 10 m, 16 days), WOFOST (MOD13Q1, 250 m, 8 days), WOFOST (MOD13Q1, 250 m, 16 days), WOFOST (L-MOD13Q1, 30 m, 16 days), and LUE (MOD13Q1, 250 m, 16 days), with R

^{2}values of 0.85, 0.85, 0.82, 0.78, 0.78, 0.75, 0.73, 0.73, 0.69, 0.65, 0.64, and 0.52, respectively. In general, the predicted values by both models with different satellite inputs follow a similar pattern, and none of the models can claim to outclass the others. However, the ME and RMSE values give a complete picture of the model comparisons (8-and 16-day products) and performances (i.e., their quality and precision) with every satellite input. The ME and RMSE of WW from the WOFOST (MOD13Q1 8-day) is slightly lower than the WOFOST (L-MOD13Q1 16-day and S-MOD13Q1 16-day); moreover, the RMSE of the WOFOST (S-MOD13Q1 and L-MOD13Q1 (8-day)) is lower than the WOFOST (MOD13Q1 16-day). The overall results of LUE inputting L-MOD13Q1, S-MOD13Q1, and MOD13Q1 8-to-16-days NDVIs range from 5.46 to 6.32 dt/ha (RMSE), 5.01 to 5.40 dt/ha, and 6.52 to 9.33 dt/ha.

^{2}of the different spatial resolutions of NDVI satellite products for OSR in descending order are LUE (S-MOD13Q1, 10 m, 8 days), LUE (L-MOD13Q1, 30 m, 8 days), LUE (S-MOD13Q1, 10 m, 16 days), LUE (L-MOD13Q1, 30 m, 16 days), LUE (MOD13Q1, 250 m, 8 days), WOFOST (S-MOD13Q1, 10 m, 8 days), WOFOST (L-MOD13Q1, 10 m, 8 days), LUE (MOD13Q1, 250 m, 16 days), WOFOST (S-MOD13Q1, 10 m, 16 days), WOFOST (L-MOD13Q1, 30 m, 16 days), WOFOST (MOD13Q1, 250 m, 8 days), and WOFOST (MOD13Q1, 250 m, 16 days), with R

^{2}values of 0.82, 0.80, 0.80, 0.78, 0.67, 0.64, 0.63, 0.63, 0.63, 0.62, 0.62, and 0.60, respectively. It showed that the LUE model is more accurate at different spatial scales than the WOFOST model. Moreover, the model resulted in higher accuracy for the 8-day products of S-MOD13Q1 and L-MOD13Q1 compared to their 16-day products. The overall results of LUE combining L-MOD13Q1, S-MOD13Q1, and MOD13Q1 8-to-16-days NDVIs range from 2.23 to 2.36 dt/ha (RMSE), 2.11 to 2.39 dt/ha, and 3.02 to 3.40 dt/ha.

^{2}and lower RMSE values than the non-fused products for WW and OSR. For example, L- and S-MOD13Q1 resulted in an R

^{2}= 0.72 and 0.76 and RMSE = 4.91 and 4.49 dt/ha, respectively, and MOD13Q1 resulted in an R

^{2}= 0.63 and RMSE = 5.85 dt/ha. Analysing the different temporal resolutions of 8- and 16-day products with LUE and WOFOST models, the 8-day products (median R

^{2}= 0.77, RMSE= 6.14 dt/ha) resulted in higher R

^{2}and lower RMSE than the 16-day products (median R

^{2}= 0.69, RMSE= 8.0 dt/ha) (Figure 9c,d).

#### 3.3. Spatial Analysis of Crop Yields Obtained from LUE and WOFOST Models for WW and OSR Using Multisource Data in 2019

#### 3.4. Sensitivity Analysis

^{2}and lower RMSE values compared with the yield values obtained during the sensitivity analysis (Figure 14). The overall accuracies obtained during the sensitivity analysis of both LUE and WOFOST were recorded as R

^{2}of 0.61 and 0.58 and RMSE of 6.13 dt/ha and 6.32 dt/ha, respectively (Figure 14). Including climate parameters improved both models’ performance, reducing the RMSE by −38% (LUE) and −11% (WOFOST) and increasing the R

^{2}from 19% to 12%, respectively.

#### 3.5. Suitable Crop Growth Model

^{2}, RMSE, RRMSE, and ME values of the model’s (LUE and WOFOST) performance, including climate stress factors’ effect on both WW and OSR in Bavaria in 2019 (Figure 15). The LUE model resulted in a higher R

^{2}(>0.78) for the 8- and 16-day products of L-MOD13Q1 and S-MOD13Q1 than the WOFOST model (R

^{2}< 0.71). Similarly, the RMSE and ME of these products show more accurate results with the LUE model (RMSE <4.5 dt/ha, ME <3.3 dt/ha) than the WOFOST model (RMSE < 7.0 dt/ha, ME < 6.0 dt/ha). MOD13Q1 8-day (R

^{2}< 0.66, RMSE < 5.19 dt/ha, ME < 4.03 dt/ha) achieved higher accuracy than MOD13Q1 16-day (R

^{2}< 0.62, RMSE < 7.10 dt/ha, ME < 5.86 dt/ha) with both LUE and WOFOST. The RRMSE for both models show better agreement (<15%) between the observed and modelled yields for all satellite products. However, the LUE model (<11.50%) showed an overall lower RRMSE than the WOFOST model (<13.67%) at different spatial and temporal scales. Irrespective of the crop type and satellite spatial scale, the LUE model obtained higher R

^{2}and lower RRMSE (average R

^{2}= 0.77, RRMSE = 8.17 %) than the WOFOST model (average R

^{2}= 0.66, RRMSE = 11.35%) (Figure 16).

#### 3.6. Visualisation of the Modelled Crop Biomass by the LUE Model in 2019

^{2}, respectively. These values were obtained considering the climate stress factors, such as temperature, VPD, and soil moisture stress. Every figure shows the difference between the 8-day and 16-day biomass products. The difference in 8- and 16-day WW products varies between −72.57 g/m

^{2}and 80.50 g/m

^{2}, respectively. The results indicate that for WW, S-MOD13Q1 had almost similar results at both temporal resolutions; however, a slight variation in L-MOD13Q1 was seen. For OSR, a little difference in the field-based biomass was observed in both 8- and 16-day products of Sentinel-2 and Landsat. The 8-day products in WW and OSR for L-MOD13Q1 and S-MOD13Q1 showed an overestimation in crop biomass compared to the 16-day products.

## 4. Discussion

#### 4.1. Importance of the Synthetic Data in Crop Yield Modelling

^{2}obtained for the agricultural class with both L-MOD13Q1 (R

^{2}= 0.60, RMSE = 0.11) and S-MOD13Q1 (R

^{2}= 0.68, RMSE = 0.13) through the STARFM are comparable to those obtained by other studies [20,39,40,87]. One of our previous studies stated the high potential of data fusion between Landsat and MCD43A4 MODIS products on achieving an R

^{2}of 0.61 and RMSE of 0.10 for WW biomass monitoring at Mecklenburg–West Pomerania in Germany [5]. The higher correlations between the observed and predicted NDVI values indicate the suitability of the algorithm for vegetation monitoring. Other studies with spatiotemporal data fusion have used NDVI as their primary input for applications such as crop biomass and yield monitoring [80,81,82,83,84,85,87,88,89]. The present study highlights the importance of the synthetic NDVI time series in crop yield modelling by analysing the accuracy assessment between the raw satellite imagery MOD13Q1 (without fusion) and L and S-MOD13Q1 (with fusion). The crop yield prediction results conclude the need for data fusion (obtaining high-resolution satellite data) for accurate crop yield prediction. Many studies demonstrated the potential of high spatial and temporal remote sensing data to describe the spatiotemporal variability of crop biophysical parameters [93], where the availability of Landsat and Sentinel-2 images offer new perspectives for crop monitoring and modelling.

^{2}= 0.72 and 0.76 and RMSE = 4.91 and 4.49 dt/ha) than the non-fused product (MOD13Q1: R

^{2}= 0.63 and RMSE = 5.85 dt/ha) for both WW and OSR irrespective of the crop model (LUE or WOFOST) (Figure 9a,b). While comparing the yield prediction accuracies of both fused products, S-MOD13Q1 results are more accurate than the L-MOD13Q1. Due to its higher temporal frequency, Sentinel-2 (5–6 days) had six cloud-free scenes (DOYs: 49, 81, 97, 113, 145, and 177) than the Landsat (16 days), with only four cloud-free scenes (DOYs: 49, 81, 145, and 177) available for the analysis (Figure 2). Due to this lower gap in Sentinel-2 DOYs, the NDVI-fused product (S-MOD13Q1) results in higher accuracy than the Landsat-based product (L-MOD13Q1) [4], which further improves the crop yield prediction accuracy of the former more than the latter. However, the L-MOD13Q1 product is still advantageous for generating and exploring the long-term yield time series due to the availability of Landsat data since 1982 with a maximum resolution of 30 m [10].

^{2}value of 0.86 for the LAI measurements using Sentinel-2 as shown by [94]. Dhillon et al. [5] measured the accuracy of LUE with MODIS and the STARFM; both proved to be more reliable and significant with high R

^{2}(>0.64, >0.82) and low RMSE (<650 g/m

^{2}, <600 g/m

^{2}), where MODIS resulted in lower accuracy due its coarser resolution. Further, Huang et al. [95] found that the low spatial resolution of MODIS degrades the output accuracy in crop modelling up to 60%.

^{2}= 0.77, RMSE = 6.14 dt/ha) show a better relationship between the referenced and modelled yields than the 16-day products (median R

^{2}= 0.69, RMSE = 8.0 dt/ha) (Figure 9c,d). Therefore, this study concludes that high spatial and temporal remote sensing products are essential for crop growth monitoring influenced by climatic factors [5,9].

#### 4.2. Importance of Linking Crop Growth Models with RS in Crop Yield Modelling

^{2}of 0.83 and RMSE of 581.82 g/m

^{2}, which is very close to the results obtained in the present study (R

^{2}= 0.81, RMSE = 5.17 dt/ha). Irrespective of the crop type and satellite spatial scale, the results of this study show that the LUE model (average R

^{2}= 0.77, RMSE = 4.45 dt/ha) performed more accurately than the WOFOST model (average R

^{2}= 0.66, RMSE = 7.75 dt/ha) (Figure 16).

^{2}of 0.77 and RMSE of 651 g/m

^{2}, which matches the results of the present study, where the model for WW resulted in an R

^{2}of 0.71 and RMSE of 7.75 dt/ha [5].

#### 4.3. Sensitivity Analysis

^{2}from 19% to 12%, respectively. Our previous study combined the machine learning approach with crop modelling to identify the impact of every climate element used in crop yield predictions [9]. This study found that solar radiation, soil moisture, and temperature are the most influential variables in increasing the yield accuracy for WW and OSR.

#### 4.4. Outlook

## 5. Conclusions

- (i)
- To discover the optimal spatial resolution for accurate crop yield predictions, this paper recommends S-MOD13Q1 (10 m) due to its lower uncertainty of mixed pixels information resulting in an increase in the accuracy and precision of the modelled yield. This study obtains higher crop yield accuracy with S-MOD13Q1 (R
^{2}= 0.76 and RMSE = 4.49 dt/ha) than L-MOD13Q1 and MOD13Q1 (R^{2}= 0.72 and 0.63 and RMSE = 4.91 and 5.85 dt/ha) for both WW and OSR, respectively. However, the L-MOD13Q1 product is more advantageous for generating and exploring the long-term yield time series due to the availability of Landsat data since 1982, with a maximum resolution of 30 m. - (ii)
- To investigate the optimal temporal resolution in yield forecasting, this paper recommends S-MOD13Q1 and L-MOD13Q1 (8-day) as they could improve the accuracy of yield prediction with detailed coverage of crop growth stages and briefly analyse the impact of climate variables simultaneously. The 8-day products (median R
^{2}= 0.77, RMSE= 6.14 dt/ha) show a better relationship of referenced yield with the modelled yield than the 16-day products (median R^{2}= 0.69, RMSE= 8.0 dt/ha). - (iii)
- To find the suitable crop model with the available input variables, this study finds the LUE model simpler, more reliable, and more accurate than the WOFOST model. Moreover, the LUE model inputs fewer variables, which makes the processing faster than the WOFOST model. Comparably, the LUE model results in a higher mean R
^{2}= 0.77 and RMSE = 4.45 dt/ha, while the WOFOST model results in a lower R^{2}= 0.66 and RMSE = 7.75 dt/ha for both WW and OSR yield validations in Bavaria in 2019.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Detailed map of administrative regions of Bavaria (Landkreise und Kreisfreie Städte in Bayern). The names of the districts are translated from German to English: Unterfranken as Lower Franconia, Mittelfranken as Middle Franconia, Oberfranken as Upper Franconia, Oberpfalz as Upper Palatinate, Oberbayern as Upper Bavaria, and Niederbayern as Lower Bavaria. (Source: https://www.gifex.com/, accessed on 12 January 2023).

**Figure A2.**Flowchart of the WOFOST model. (Source: [5]).

**Table A1.**Summary of linear regression equations used to calculate crop yield from biomass obtained from different satellite products (MOD13Q1, Landsat (L)-MOD13Q1, and Sentinel-2 (S)-MOD13Q1) for WW and OSR using LUE and WOFOST models. The yield obtained is in dt/ha.

Crop Type | Crop Model | Equation | R^{2} |
---|---|---|---|

WW | LUE | ${\mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{MOD13Q1}=-56.549+0.2231\ast {\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}_{MOD13Q1}$ | 0.73 |

WW | LUE | ${\mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{L-MOD13Q1}=22.278+0.0743\ast {\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}_{L-MOD13Q1}$ | 0.82 |

WW | LUE | ${\mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{S-MOD13Q1}=-14.377+0.147\ast {\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}_{S-MOD13Q1}$ | 0.85 |

WW | WOFOST | ${\mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{MOD13Q1}=52.533+0.0599\ast {\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}_{MOD13Q1}$ | 0.69 |

WW | WOFOST | ${\mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{L-MOD13Q1}=58.027+0.0537\ast {\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}_{L-MOD13Q1}$ | 0.75 |

WW | WOFOST | ${\mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{S-MOD13Q1}=58.670+0.0573\ast {\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}_{S-MOD13Q1}$ | 0.78 |

OSR | LUE | ${\mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{MOD13Q1}=-25.192+0.1158\ast {\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}_{MOD13Q1}$ | 0.67 |

OSR | LUE | ${\mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{L-MOD13Q1}=-5.823+0.0807\ast {\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}_{L-MOD13Q1}$ | 0.80 |

OSR | LUE | ${\mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{S-MOD13Q1}=-6.035+0.0816\ast {\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}_{S-MOD13Q1}$ | 0.82 |

OSR | WOFOST | ${\mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{MOD13Q1}=-4.4375+0.0721\ast {\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}_{MOD13Q1}$ | 0.62 |

OSR | WOFOST | ${\mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{L-MOD13Q1}=-16.345+0.089\ast {\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}_{L-MOD13Q1}$ | 0.63 |

OSR | WOFOST | ${\mathrm{Y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}}_{S-MOD13Q1}=-8.592+0.815\ast {\mathrm{B}\mathrm{i}\mathrm{o}\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}}_{S-MOD13Q1}$ | 0.64 |

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**Figure 1.**The conceptual framework of this study is divided into two parts: Part 1 states the data fusion for 2019 to investigate the synthetic NDVI time series product (this section was completed in our previous study [4]) and Part 2 estimates and validates the crop yield for Bavaria by inputting the fused L-MOD13Q1 time series and climate elements to a semi-empiric Light Use Efficiency (LUE) model. STARFM = Spatial and Temporal Adaptive Reflectance Fusion Model; NDVI = Normalised Difference Vegetation Index; L-MOD09GQ = Landsat-MOD09GQ; L-MOD09Q1 = Landsat-MOD09Q1; L-MCD43A4 = Landsat-MCD43A4; L-MOD13Q1 = Landsat-MOD13Q1; S-MOD09GQ = Sentinel-2-MOD09GQ; S-MOD09Q1 = Sentinel-2-MOD09Q1; S-MCD43A4 = Sentinel-2-MCD43A4; S-MOD13Q1 = Sentinel-2-MOD13Q1; LfStat = the Bayerisches Landesamt für Statistik (LfStat).

**Figure 2.**An overview of the study region. The LC map of Bavaria is obtained by combining multiple inputs of Landcover maps, such as Amtliche Topographisch-Kartographisches Informationssystem, Integrated Administration Control System (provides the crop field information), and Corine LC, into one map. Agriculture (peach green) dominates mainly in the northwest and southeast of Bavaria, while forest and grassland classes (dark green and yellow, respectively) dominate in the northeast and south. The district map of Bavaria overlays the LC map. The enlargement (displayed with a dark red box on the top right map) shows the urban area of the town Volkach, including the oil seed rape (OSR) fields (dark orange) and the winter wheat (WW) fields (dark green). A brief description of the regions of Bavaria is shown in Figure A1.

**Figure 3.**The cloud-free scenes are available for Landsat (in red box) and Sentinel-2 (in blue box) during the seasons of OSR and WW. Four cloud-free scenes were collected for the Landsat data and six were collected for the Sentinel-2 data. The maps show the NDVI values from −1 to 1 for Bavaria during 2019. The negative NDVI values indicate non-vegetated areas such as water bodies or barren land.

**Figure 4.**Field-wise comparison of STARFM and real-time NDVI values of (

**a**) MOD13Q1, (

**b**) Landsat 8, (

**c**) L-MOD13Q1, (

**d**) Sentinel-2, and (

**e**) S-MOD13Q1 on DOY 145 (25 May 2019) on WW fields. The image in (

**f**) shows the spatial location of 10,000 random points in Bavaria used to draw line and bar plots in Figure 5 for comparing the mean NDVI values on a DOY basis for the real and synthetic NDVI products.

**Figure 5.**The (

**a**) line and (

**b**) bar plots show the DOY-based and interquartile-range-based comparison of STARFM-generated NDVI values with their respective high-resolution input (Landsat (L) or Sentinel-2 (S)) and low-resolution input MOD13Q1, respectively. The comparison is based on the mean values extracted for 10,000 random points (whose spatial location is shown in Figure 4f) taken for the entire Bavaria.

**Figure 6.**The scatter plots (

**a**–

**l**) compare the accuracies of LUE- and WOFOST-modelled yields (inputting the 8- and 16-day MOD13Q1, L-MOD13Q1 and S-MOD13Q1) with the referenced yield of WW. The green dots represent WW. Every plot contains a solid line to visualise the correlation of pixels between the referenced and modelled yield values.

**Figure 7.**The scatter plots (

**a**–

**l**) compare the accuracies of LUE- and WOFOST-modelled yields (inputting the 8- and 16-day MOD13Q1, L-MOD13Q1, and S-MOD13Q1) with the referenced yield of OSR. The orange dots represent OSR. Every plot contains a solid line to visualise the correlation of pixels between the referenced and modelled yield values.

**Figure 8.**The violin plots compare the crop yields of referenced (at 95% confidence interval) and modelled yields obtained from multi-source data (MOD13Q1, L-MOD13Q1, and S-MOD13Q1) at 8 and 16 days of temporal scales of (

**a**,

**b**) WW and (

**b**,

**d**) OSR using the (

**a**,

**c**) LUE and (

**b**,

**d**) WOFOST models in 2019. The green-coloured text represents WW and the orange-coloured text represents OSR. The text values represent the median yield values of every product.

**Figure 9.**The box plots compare the accuracies (

**a**,

**c**) R

^{2}and (

**b**,

**d**) RMSE of referenced (at 95% confidence interval) and modelled yields obtained from multi-source data: MOD13Q1, L-MOD13Q1, and S-MOD13Q1 at temporal scales of 8 and 16 days.

**Figure 10.**Spatial distribution of referenced yields and predicted yields for WW using MOD13Q1 (8 and 16 days), L-MOD13Q1 (8 and 16 days), and S-MOD13Q1 (8 and 16 days) with LUE and WOFOST models for the state of Bavaria. The white colour represents no data available. A detailed map of the administrative regions of Bavaria is shown in Figure A1.

**Figure 11.**The dot plots show the region-wise distribution of referenced yields and modelled yields obtained from multi-source data (MOD13Q1 (8 and 16 days), L-MOD13Q1 (8 and 16 days), and S-MOD13Q1 (8 and 16 days)) for WW using (

**a**) LUE and (

**b**) WOFOST in 2019. The regional referenced yields are displayed in red dots.

**Figure 12.**Spatial distribution of referenced yields and predicted yields for OSR using MOD13Q1 (8 and 16 days), L-MOD13Q1 (8 and 16 days), and S-MOD13Q1 (8 and 16 days) with LUE and WOFOST models for the state of Bavaria. The white colour represents no data available. A detailed map of the administrative regions of Bavaria is shown in Figure A1.

**Figure 13.**The dot plots show the region-wise distribution of referenced yields and modelled yields obtained from multi-source data (MOD13Q1 (8 and 16 days), L-MOD13Q1 (8 and 16 days), and S-MOD13Q1 (8 and 16 days)) for OSR using (

**a**) LUE and (

**b**) WOFOST in 2019. The regional referenced yields are displayed in red dots.

**Figure 14.**The box plots show the comparison of accuracies (

**a**,

**c**) R

^{2}values and (

**b**,

**d**) RMSE values obtained from the referenced yields (at 95% confidence interval), with LUE (

**a**,

**b**) and WOFOST (

**c**,

**d**) modelled yields including climate stress factors (dark blue and pink) and the modelled yields excluding the climate stress factors (sensitivity analysis) (light blue and pink).

**Figure 15.**The dot plots show the comparison of accuracies for (

**a**) R

^{2}, (

**b**) RMSE, (

**c**) RRMSE, and (

**d**) ME values obtained from the referenced yields (at 95% confidence interval) for LUE (dark blue) and WOFOST (dark pink) models.

**Figure 16.**The box plots compare the accuracies for (

**a**) R

^{2}and (

**b**) RRMSE of referenced (at 95% confidence interval) and modelled yields obtained from multi-source data using LUE and WOFOST models in 2019.

**Figure 17.**Visualisation of field level biomass of L-MOD13Q1 and S-MOD13Q1 with 8 days, 16 days, and the difference (16–18 days) obtained using the LUE model for (

**a**) WW and (

**b**) OSR.

**Table 1.**A summary of the collected datasets for crop modelling of winter wheat (WW) and oil seed rape (OSR) in 2019. The satellite data used for crop yield modelling are synthetic L-MOD13Q1, S-MOD13Q1, and real Moderate Resolution Imaging Spectroradiometer (MODIS) MOD13Q1. The climate parameters are minimum temperature (°C) (Tmin), maximum temperature (°C) (Tmax), dewpoint temperature (°C) (Tdew), solar radiation (MJ m

^{−2}day

^{−1}) (Rs), sunshine duration (hours) (N), evaporation (mm) (Ep), transpiration (mm) (Tp), runoff (mm) (Roff), and precipitation (mm) (P). InVeKos data provide the fields of WW and OSR for Bavaria in 2019; the Bayerisches Landesamt für Statistik (LfStat) data provide the crop yield information (dt/ha) of WW and OSR at the district level of Bavaria in 2019.

Data | Product Name | Resolution (Spatial-Temporal) | References |
---|---|---|---|

Climate data | Tmin, Tmax, Tdew, Rs, N, Ep, Tp, Roff, P | 2000 m, 8 and 16 days | https://www.uni-augsburg.de/de/fakultaet/fai/geo/ (accessed on 21 June 2021) |

Satellite data | L-MOD13Q1 | 30 m, 8 and 16 days | [4] |

S-MOD13Q1 | 10 m, 8 and 16 days | [4] | |

MODIS (MOD13Q1) | 250 m, 8 and 16 days | https://lpdaac.usgs.gov/ (accessed on 21 June 2021) | |

Vector data | InVeKos | 2019 | www.ec.europa.eu/info/index_en (accessed on 21 June 2021) |

LfStat | 2019 | https://www.statistikdaten.bayern.de/genesis/online/ (accessed on 21 June 2021) |

**Table 2.**Statistical analysis between the NDVI values obtained from raw Landsat (L) and Sentinel-2 (S) images with synthetic images (L- and S-MOD13Q1) on different days of the year (DOY). The analysis shows the R

^{2}and mean RMSE obtained between the synthetic and reference NDVI in Bavaria for the land cover class of agriculture (which covers 31.67% of Bavaria) and for the overall classes (including agriculture, forest, urban, water, natural, semi-natural, and grassland) in 2019.

NDVI Product | LC Class | DOY | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

OSR | WW | ||||||||||

49 | 81 | 97 | Mean R ^{2} | Mean RMSE | 113 | 145 | 177 | Mean R ^{2} | Mean RMSE | ||

L-MOD13Q1 | Agriculture | 0.41 | 0.49 | - | 0.45 | 0.11 | - | 0.66 | 0.65 | 0.65 | 0.10 |

Overall | 0.43 | 0.50 | - | 0.47 | 0.11 | - | 0.61 | 0.62 | 0.62 | 0.11 | |

S-MOD13Q1 | Agriculture | 0.49 | 0.74 | 0.85 | 0.69 | 0.10 | 0.76 | 0.50 | 0.60 | 0.62 | 0.12 |

Overall | 0.48 | 0.67 | 0.80 | 0.65 | 0.13 | 0.81 | 0.64 | 0.65 | 0.70 | 0.13 |

**Table 3.**A summary of equations used to calculate LAI from NDVI satellite products for WW and OSR. These equations are derived from the growth stage of a crop until the flowering stage. The LAI product is used as an input to the WOFOST model.

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## Share and Cite

**MDPI and ACS Style**

Dhillon, M.S.; Kübert-Flock, C.; Dahms, T.; Rummler, T.; Arnault, J.; Steffan-Dewenter, I.; Ullmann, T.
Evaluation of MODIS, Landsat 8 and Sentinel-2 Data for Accurate Crop Yield Predictions: A Case Study Using STARFM NDVI in Bavaria, Germany. *Remote Sens.* **2023**, *15*, 1830.
https://doi.org/10.3390/rs15071830

**AMA Style**

Dhillon MS, Kübert-Flock C, Dahms T, Rummler T, Arnault J, Steffan-Dewenter I, Ullmann T.
Evaluation of MODIS, Landsat 8 and Sentinel-2 Data for Accurate Crop Yield Predictions: A Case Study Using STARFM NDVI in Bavaria, Germany. *Remote Sensing*. 2023; 15(7):1830.
https://doi.org/10.3390/rs15071830

**Chicago/Turabian Style**

Dhillon, Maninder Singh, Carina Kübert-Flock, Thorsten Dahms, Thomas Rummler, Joel Arnault, Ingolf Steffan-Dewenter, and Tobias Ullmann.
2023. "Evaluation of MODIS, Landsat 8 and Sentinel-2 Data for Accurate Crop Yield Predictions: A Case Study Using STARFM NDVI in Bavaria, Germany" *Remote Sensing* 15, no. 7: 1830.
https://doi.org/10.3390/rs15071830