Effectiveness of machine learning and deep learning models at county-level soybean yield forecasting 383Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398.DOI: 10.15201/hungeobull.72.4.4 Hungarian Geographical Bulletin 72 2023 (4) 383–398. Introduction Crop yield forecasting is crucial in agricul- tural decision-making for food security, crop insurance, and improving overall food pro- duction (Tantalaki, N. et al. 2019). Tradition- ally, farmers relied on their personal expe- rience and incorporated weather and other relevant data to forecast their individual crop yields and make informed decisions (Liakos, K. et al. 2018). However, this traditional ap- proach is associated with inherent uncertain- ties, particularly when extrapolated to large- scale scenarios, because of influencing fac- tors that differ depending on the region and crop type (Shahhosseini, M. et al. 2020). Crop yield forecasting and prediction are distinct approaches that differ in methodology and 1 Department of Geoinformatics, Physical and Environmental Geography, University of Szeged, Egyetem utca 2, 6722 Szeged, Hungary. Corresponding author’s e-mail: farmonov.nizom@stud.u-szeged.hu 2 Geospatial Sciences Center of Excellence, Department of Geography and Geospatial Sciences, South Dakota State University, Brookings, SD 57007, USA. 3 Department of State Cadastre, Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, National Research University, Tashkent, Uzbekistan 4 Department of Hydrology and Ecology, “TIIAME” NRU Bukhara Institute of Natural Resources Management, Gazli Avenue 32, Bukhara, Uzbekistan. 5 Department of Land Resources, Cadastre and Geoinformatics, Karshi Institute of Irrigation and Agrotech- nology, “TIIAME” National Research University, Karshi, Uzbekistan. Effectiveness of machine learning and deep learning models at county-level soybean yield forecasting Nizom FARMONOV 1, Khilola AMANKULOVA 1, Shahid Nawaz KHAN 2, Mokhigul ABDURAKHIMOVA 3, József SZATMÁRI 1, Tukhtaeva KHABIBA4, Radjabova MAKHLIYO 4, Meiliyeva KHODICHA5 and László MUCSI 1 Abstract Crop yield forecasting is critical in modern agriculture to ensure food security, economic stability, and effec- tive resource management. The main goal of this study was to combine historical multisource satellite and environmental datasets with a deep learning (DL) model for soybean yield forecasting in the United States’ Corn Belt. The following Moderate Resolution Imaging Spectroradiometer (MODIS) products were aggregated at the county level. The crop data layer (CDL) in Google Earth Engine (GEE) was used to mask the data so that only soybean pixels were selected. Several machine learning (ML) models were trained by using 5 years of data from 2012 to 2016: random forest (RF), least absolute shrinkable and selection operator (LASSO) regression, extreme gradient boosting (XGBoost), and decision tree regression (DTR) as well as DL-based one-dimensional convolutional neural network (1D-CNN). The best model was determined by comparing their performances at forecasting the soybean yield in 2017–2021 at the county scale. The RF model outperformed all other ML models with the lowest RMSE of 0.342 t/ha, followed by XGBoost (0.373 t/ha), DTR (0.437 t/ha), and LASSO (0.452 t/ha) regression. However, the 1D-CNN model showed the highest forecasting accuracy for the 2018 growing season with RMSE of 0.280 t/ha. The developed 1D-CNN model has great potential for crop yield forecasting because it effectively captures temporal dependencies and extracts meaningful input features from sequential data. Keywords: agriculture, remote sensing, farmers, random forest, soybean, machine learning Received September 2023, accepted October 2023. mailto:farmonov.nizom@stud.u-szeged.hu Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398.384 data utilization (Shahhosseini, M. et al. 2020). Forecasting entails using historical observa- tions to train a model and subsequently gen- erating forecasts by employing input features specific to the future (Paudel, D. et al. 2021). The forecasting process acknowledges the influence of various biotic and abiotic fac- tors on crop yield and necessitates a com- prehensive understanding and management of these elements for a full grasp of the yield dynamics. A critical issue is the scarcity of extensive data encompassing all pertinent factors on a large scale. Crop yield prediction differs from crop yield forecasting in that the former can uti- lize the target variable of the current year in the training phase (Shahhosseini, M. et al. 2020). Current crop yield prediction ap- proaches can be divided into two main cat- egories: physical models and statistical mod- els (Tripathy, R. et al. 2022). Physical models simulate crop-growing conditions in combi- nation with parameters that affect crop yield. Representative physical models include the Agricultural Production Simulator (Keating, B.A. et al. 2003) and Decision Support System for Agrotechnology Transfer (Jones, J.W. et al. 2003). Physical models are widely used, but they require extensive data for calibra- tion, which limits their capabilities for large- scale crop monitoring. In contrast, statistical models are simpler with fewer input require- ments, which make them very convenient for large-scale studies. Machine learning (ML) models use historical data to characterize the relationship between input variables and crop yield (Ma, Y. et al. 2021). A major advan- tage of ML models is that they can be used even when some specific crop parameters are not available. With the increased availabil- ity of data and computing power, robust ML methods have been developed and applied to crop yield prediction. The increased availability of extensive remote sensing data has greatly facilitated their utilization in various agricultural ap- plications, including crop classification, iden- tification, and drought characterization (Sun, J. et al. 2019; Khan, S.N. et al. 2023), which has opened new avenues for extracting meaning- ful input features from remote sensing data for crop yield prediction. Vegetation indi- ces (VIs) include factors such as greenness, vegetation health, and stress, and they have received substantial interest for research in vegetation dynamics (Panda, S.S. et al. 2010; Khan, K. et al. 2020). The normalized dif- ference vegetation index (NDVI) is widely used for crop health characterization and yield prediction (Fernandes, J.L. et al. 2017). The NDVI measures the difference in reflec- tance of near-infrared (Nir) and red light to capture variations in plant biomass and photosynthetic activity, which makes it very useful for assessing crop productivity. Other VIs that have been employed for crop yield prediction include the enhanced vegetation index (EVI), soil-adjusted vegetation index, and normalized difference water index. In addition to remote sensing data, some stud- ies have utilized climatic variables and soil data for crop yield prediction. Recent studies have combined remote sensing data with ML models for crop yield prediction (Shahhosseini, M. et al. 2020). For example, Piekutowska, M. et al. (2021) used multiple linear regression on phe- nological and meteorological data to pre- dict the potato yield and obtained a mean absolute percentage error of < 15 percent. Zeng, W. et al. (2018) used partial least- squares regression on weather data to pre- dict the sunflower yield with an accuracy of R2 = 0.69. Other ML models, including ran- dom forest (RF) (Khan, S.N. et al. 2022), sup- port vector regression (Khosla, E. et al. 2020), and decision tree regression (Khan, S.N. et al. 2022) have been used for crop yield prediction at different scales and with dif- ferent variables. In addition to conventional ML models, several deep learning (DL) mod- els have recently been applied to crop yield prediction (Kang, Y. et al. 2020). Sun, J. et al. (2019) used a convolutional neural network and long short-term memory (CNN-LSTM) model with Moderate Resolution Imaging Spectroradiometer (MODIS) data to pre- dict the soybean yield at the county level. 385Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398. Fig. 1. Map of the study area. For state codes see the text. They classified data into different stages of the crop-growing season and evaluated the model performance in the stages. The end-of- season models outperformed the in-season models. (Ma, Y. et al. 2021) used a Bayesian neural network (BNN) with VI, climate, and soil data to predict the corn yield at the coun- ty level. They compared the performances of several models and found that the BNN outperformed other ML models such as RF, support vector regression, and LSTM. Although Earth Observation Systems (EOS) play a crucial role in monitoring crop yield through satellite data, there exists a signifi- cant research gap in enhancing the integra- tion of multiplatform data, including data processing techniques, and the effective ap- plication of this technology in precision agri- cultural management. Novel research efforts are needed to bridge this gap and further optimize the utilization of EOS for informed decision-making in agriculture. In this study, we applied several ML and DL models to forecast the soybean yield of the United States (US) at the county level and evaluated their performances. The spatial patterns between the observed and forecast- ed yields were also analysed. To address the above tasks, the following research questions were selected: 1. What are the most significant input fea- tures to predict the crop yield at the county scale? 2. How does the deep learning-based 1D-CNN model compare to traditional ML models for forecasting soybean yield in the US Corn Belt using historical satellite and environmental data? Data Study area The study area comprised fourteen soybean- producing states: North Dakota (ND), South Dakota (SD), Nebraska (NE), Kansas (KS), Minnesota (MN), Iowa (IA), Missouri (MO), Arkansas (AR), Wisconsin (WI), Illinois (IL), Mississippi (MS), Michigan (MI), Indiana (IN), and Ohio (OH) (Figure 1). Most of the study area is in the Midwest, also known as the Corn Belt (Green, T.R. et al. 2018), and it is responsible for producing most of the corn Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398.386 and soybean in the US. Corn and soybean are often grown in rotation. The study area is primarily rainfed, and only a very small part is irrigated. Crop yield data County-level soybean yield data were ob- tained from the United States Department of Agriculture (USDA) for 2012–2021 (USDA/ NASS 2021). The data were originally in bushels per acre, but we converted the values to tons per hectare (t/ha). The crop yield data were used for training, testing, and validating the models considered in this study. Annual soybean yields at a county level were differ- ent in the years from 2012 to 2021 (Figure 2). Cropland data layer The cropland data layer (CDL) is a crop- specific land-cover data layer created for the continental US that is generated each year by using MODIS and ground truth data at a res- olution of 30 m (Boryan, C. et al. 2011). The CDL was developed by the Geospatial In- formation Branch, Spatial Analysis Research Section of the Research and Development Di- vision at the National Agricultural Statistics Service (NASS), which is part of the USDA. In this study, we utilized the CDL to create a mask that identifies soybean pixels while excluding other data. We also used the CDL to derive statistics that helped identify coun- ties with zero soybean pixels, which aided in the selection and exclusion of counties for further analysis. County boundaries The geographic boundaries of the counties in the study area were derived from the US Census Topologically Integrated Geographic Encoding and Referencing project, which provides accu- rate and comprehensive spatial data on county boundaries in the US (https://www.census.gov/ geographies/mapping-files/time-series/geo/ti- ger-line-file.html). The geographic boundaries were used to collect and represent county-level data each year within the specified period. Remote sensing and weather data We employed MODIS data from the NASA Earth Observing System Data and Information System (https://search. earthdata.nasa.gov/), which are collected at regular intervals of 16 days and are available at spatial resolutions of 250, 500, and 1,000 m. We utilized MODIS NDVI and EVI products from the MOD13Q1.061 Terra Vegetation Indices 16- Day Global 250 m data- set (Didan, K. 2021). The MOD09A1 product Fig. 2. Average soybean yield at the county level for 2012–2021. https://www.census.gov/geographies/mapping-files/time-series/geo/tiger-line-file.html https://www.census.gov/geographies/mapping-files/time-series/geo/tiger-line-file.html https://www.census.gov/geographies/mapping-files/time-series/geo/tiger-line-file.html https://search.earthdata.nasa.gov/ https://search.earthdata.nasa.gov/ 387Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398. provides a surface reflectance product for Terra MODIS bands 1–7 at a spatial reso- lution of 500 m and considers atmospheric conditions such as gases, aerosols, and Ray- leigh scattering. The reflectance of each pixel is selected from the best value of multiple ac- quisitions within an 8-day composite based on factors such as high observation coverage, low view angle, no clouds or cloud shadows, and aerosol loading (Vermote, E. 2021). The MOD11A2 product offers the average land surface temperature (LST) over 8 days at a spatial resolution of 1 km. The average LST for each pixel is calculated by taking the sim- ple average of all corresponding LST values collected from the MOD11A1 product with- in that specific 8-day period (Wan, Z. et al. 2021). The MOD11A2 product incorporates both daytime and night time surface tem- perature bands to account for long-term soil factors (Saravanan, V. and Tamburi, V.N. 2022). Meteorological data were obtained from Daymet (Thornton, M.M. et al. 2022) and included daily measurements of six parameters, of which four were selected as climatic factors: precipitation, vapour pres- sure, minimum temperature, and maximum temperature. These parameters are generated on a gridded surface with a resolution of 1 km × 1 km. Table 1 presents an overview of the satellite and climatic data utilized in this study. Data preprocessing The above datasets were preprocessed and downloaded by using Google Earth Engine (GEE) (Figure 3). All datasets were aggregat- ed to a temporal resolution of 16 days corre- sponding to the period of 14–31 July for con- sistency. This period was selected because it coincides with the peak vegetation phase of soybeans. We previously investigated the contributions of dynamic input features to the crop yield, including the growth stage and phenology. We found that VI data from mid-July are more significant to forecasting the soybean yield than from other periods. This period corresponds to the crucial pod- setting stage for soybeans. The significance of the dynamic input features implies that the presence of pods and leaves predominant- ly influences the soybean crop yield (Li, Y. et al. 2023). Thus, all data within this period should have a significant relationship with the crop yield. First, a dataset (e.g., MODIS NDVI) and the CDL were loaded into the GEE environment. The region of interest was selected, and both datasets were clipped to that region. We used the eq() function to create a binary mask based on the CDL values. Pixels with CDL values that corresponded to cropland were assigned a value of 1, while all other pixels were assigned a value of 0. We used the up- dateMask() function to apply the CDL mask to the MODIS NDVI dataset, which masked out all NDVI values that corresponded to non-cropland areas and left only soybean pixels. We then calculated the mean values of input features for each dataset at the county level. The soybean yield and input features were merged for each year using the county and year as common columns. Method Machine learning models We compared various ML models in an ef- fort to find a relationship between geospa- tial data and the soybean yield. We selected four different ML models: RF, least absolute shrinkable and selection operator (LASSO) regression, extreme gradient boosting (XG- Boost), and decision tree regression (DTR). In addition, we selected a one-dimensional convolutional neural network (1D-CNN) as a DL model. All models were trained, tested, and validated. Models were trained and test- ed on data for 2012–2016. The models were then validated by forecasting the soybean yield for 2017–2021. The ML models were implemented in Python 3.11.3 with the scikit- learn package (Pedregosa, F. et al. 2012). The 1D-CNN model was implemented in Keras Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398.388 (Ketkar, N. 2017), which is an open-source DL framework written in Python. RF estimates the crop yield by combining multiple regression trees. Each regression tree captures relationships between the input features and the target variable. Subsamples are randomly selected from the training set, which comprises 70 percent recorded yield samples and 30 percent test data. Each subsample is fitted to a regression tree. The final forecast is obtained by averaging the forecasts of all trees. RF has been demon- strated to be effective at mitigating overfit- ting (Wang, H. et al. 2016). We employed the Gaussian kernel function to investigate the non-linear association between input fea- tures (i.e., climatic and remote sensing data) and the target variable (i.e., crop yield). We applied RF to identify the most important input features utilizing Python 3.11.3 and the scikit-learn library, which offers Random Forest Regressor classes. LASSO regression uses linear regression to minimize the residual sum of squares while constraining the absolute values of coefficients below a specified threshold (Tibshirani, R. 1996). LASSO regression ad- dresses overfitting by automatically select- ing relevant input features, which leads to a more concise regression model. XGBoost is designed for tree boosting, which involves constructing multiple weak learners and combining their results to im- prove the regression or classification per- formance. It incorporates regularization techniques to prevent overfitting, and the weak learners can be regression trees or lin- ear models (Chen, T. and Guestrin, C. 2016; Table 1. Overview of the satellite and climatic data used in this study Data source Spatial resolution Temporal resolution Feature Products description MOD13Q1 250 m 16-day NDVI Vegetation index value at a per-pixel basis.EVI MOD09A1 500 m 8-day Red The surface spectral reflectance of Terra MODIS bands 1–7, accounting for atmospheric factors. It includes seven reflectance bands, a quality layer, and four observation bands. Pixel values are chosen based on criteria like extensive coverage, optimal view angle, clear sky conditions, and minimal aerosol. Nir Blue Green Nir 1 Swir 1 Swir 2 MOD11A2 1,000 m 8-day LST The 8-day period aligns with the ground track repeat period of the Terra and Aqua satellites. This product in- cludes day- and night-time LST bands, quality indicator layers, additional MODIS bands, and observation layers. Daymet 1,000 m Daily Precipitation Daymet V4 is an updated version that offers gridded estimates of daily weath- er parameters for Continental North America, Hawaii, and Puerto Rico. It addresses known issues by reducing timing bias, enhancing regression mod- els, and introducing a novel approach to handle high elevation temperature measurement biases. Water vapour Temperature min. Temperature max. 389Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398. Song, Y. et al. 2019). We opted to use XGBoost based on decision trees. XGBoost makes fore- casts by summing the weights of the leaves in all decision trees. We used the GridSearchCV package (Molinaro, A.M. et al. 2005) to de- termine the optimal parameters for XGBoost. DTR constructs a tree structure based on input features in the training data to forecast the target variable. It is suitable for both clas- sification and regression tasks and offers the benefit of interpretable results in the form of a tree. DTR utilizes binary splits to divide data into two groups and minimizes the sum of squared deviations from the mean within each group. This process is continued until a minimum node size specified by the user is achieved (San Millan-Castillo, R. et al. 2020). Finally, 1D-CNN is a type of neural net- work commonly used for sequential data analysis (Kiranyaz, S. et al. 2021). Different filters are applied to the input data to extract meaningful input features, which allows the model to learn the representation more ef- ficiently (Figure 4). The convolutional layers are followed by pooling layers that reduce the dimensions of data and only keep the Fig. 3. GEE-based data preprocessing workflow Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398.390 useful information. This information is then passed to fully connected (FC) lay- ers for the final forecast. We used a 1D-CNN compris- ing four convolu- tional layers, one max-pooling layer, and five FC layers followed by a drop- out layer and then the final FC layer for crop yield forecast- ing. We used three convolutional layers with 16–128 filters. The FC layers had 32–512 neurons. The dropout rate was set to 0.4. In Keras, training a DL model requires tuning sev- eral hyper-parame- ters to find the op- timal model, which include the learning rate, batch size, and optimization func- tion. We considered learning rates of 0.00001–0.01, batch sizes of 16–128, and the Adam op- timizer, which uses stochastic gradient descent to optimize the model performance and reduce the loss. Model evaluation We evaluated the model performances by us- ing several metrics. We used the R2 value to measure the proportion of variance explained by each model. We used the normalized root mean squared error (NRMSE%) and root mean squared error (NRMSE) to measure the forecasting error as a percentage area. We used the mean absolute error (MAE), which represents the average absolute difference be- tween the forecasted and actual values, and the mean squared error (MSE), which meas- ures the average squared difference between the forecasted and actual values. These met- rics are calculated as follows: (1) (2) (3) (4) (5) These metrics can be used to quantify the probability that a model correctly forecasts new samples from the underlying data dis- tribution . The residuals (ri) are the differ- ences between the predicted values (ypi) and actual labels (yi) as well as the average of the labels (y). Results Input feature importance We identified surface reflectance (SR) band 2, EVI, and NDVI as the most influential input features with importance scores of 0.30, 0.29, and 0.13, respectively (Figure 5). These input features exhibited strong predictive power, which indicates their significance to the crop yield. The LST was found to have moderate importance with a score of 0.08. Conversely, climatic data and other SR bands had rela- tively low importance scores of 0.01–0.05. These findings emphasize the potential of incorporating MODIS LST and SR data with climatic data to enhance the accuracy of crop yield forecasting models. Fig. 4. 1D-CNN model architecture 391Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398. Performance comparison of machine learning models The RF model consistently demonstrated the best performance across all metrics (Figure 6). The RF model had the highest R2 value of 0.75, which surpassed the R2 values of XGBoost (0.70), DTR (0.59), and LASSO regression (0.60). The RF model also had the lowest RMSE of 0.342 t/ha, MAE of 0.264 t/ha, MSE of 0.117 t/ha, and NRMSE of 8.4 percent. XGBoost had the second-best performance with an RMSE of 0.373 t/ha, MAE of 0.287 t/ha, MSE of 0.139 t/ha, and NRMSE of 9.15 percent. Therefore, the RF model was selected for forecasting the soybean yield. Crop yield forecasting The year-to-year results indicated that the RF model achieved MAE values of 0.112– 0.119 t/ha, RMSE values of 0.334–0.345 t/ha, R2 values of 0.75–0.77, and NRMSE% values of 7.85–8.46 percent (Figure 7). The best re- sults were obtained in 2021, for which the RF model achieved a MAE of 0.112 t/ha, RMSE of 0.334 t/ha, R2 of 0.77, and NRMSE% of 7.85 percent. 1D-CNN performance The 1D-CNN model was also applied to forecasting the soybean yield in the study area. Table 2 presents the fore- casting results for 2017–2021. Overall, the 1D-CNN model performed better than classi- cal ML models with MSE val- ues of 0.076–0.108 t/ha and R2 values of 0.76–0.86. The high- est R2 value was in 2021 while the lowest R2 value was in 2019. The scatterplots of the actual and forecasted yields were created for 2017–2021 (Figure 8). Spatial patterns of crop yield forecasts Spatial distribution of the forecasted soy- bean yields was generated over the period of 2017–2021 with the RF model (Figure 9). The soybean yield was forecasted as exceptional- ly high in the central and northeast (i.e., Iowa, Indiana, and Nebraska) at 1–5 t/ha while the observed yield was 1.0–4.5 t/ha. The error between the observed and forecasted yields was minimal, which indicated a high level of accuracy. The south (i.e., Arkansas and Mississippi) was forecasted with an average soybean yield of 2.0–3.5 t/ha, while Ohio in the west was forecasted with a soybean yield of 2.5–3.5 t/ha. The north (i.e., Minnesota and North Dakota) were forecasted with lower yields of 1.5–2.5 t/ha. The difference between the observed and forecast yields was not sub- stantial. However, these results do suggest that the growing conditions in the north were less favourable for soybean cultivation than elsewhere in the study area. The variations in yield across different regions can be at- tributed to a multitude of factors, including climate, soil quality, agricultural practices, and other local conditions. The central and Fig. 5. Importance of input features according to the random forest model Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398.392 Fig. 7. Scatterplots between actual and forecasted soybean yields for 2017–2021 with the RF model Fig. 6. Performance metrics of several ML models 393Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398. north-eastern states benefit from a highly conducive agricultural environment, which led to the forecast of higher yields. Converse- ly, the southern and northern states have less optimal conditions, which lowered the fore- casted yields. Note that these forecasts were based on the RF model’s analysis of historical data and other relevant factors. However, lo- cal factors, unforeseen events, and changes in agricultural practices can potentially affect the actual yield. Therefore, continuous moni- toring and adjustment of the model’s output to consider real-time data are essential for accurate and up-to-date forecasting. Discussion Input feature importance The RF model found the SR band 2, EVI, and NDVI as the most influential input features Fig. 8. Scatterplots between the actual and forecasted soybean yields for 2017–2021 with the 1D-CNN model Table 2. Performance of the 1D-CNN soybean yield forecast model for 2017–2021. Year MSE RMSE MAE R2 NRMSE t/ha % 2017 2018 2019 2020 2021 0.076 0.079 0.080 0.090 0.108 0.276 0.280 0.283 0.300 0.329 0.202 0.208 0.206 0.222 0.240 0.81 0.83 0.76 0.80 0.86 6.99 6.96 9.26 6.74 7.24 Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398.394 for forecasting the soybean yield in the study area, which is consistent with previous stud- ies that have highlighted the importance of VI data on crop yield forecasting. Sun, J. et al. (2019) demonstrated a strong correlation between MODIS SR data and soybean yield. Kuwata, K. and Shibasaki, R. (2016) found that EVI exhibited a significant relationship with corn yield. Our study reinforces the ex- isting literature by highlighting the signifi- cance of these VIs in different crop yield fore- casting models. The LST was found to have moderate importance for forecasting the soy- bean yield. This aligns with previous studies that have emphasized the effect of tempera- ture on crop development and productivity (Pede, T. et al. 2019; Mirhoseini, N. et al. 2022). Pede, T. et al. (2019) demonstrated the impor- tance of MODIS LST to corn yield forecasting before the harvesting stage, especially during periods of extreme drought and water stress. Thus, our study reaffirmed the importance of considering temperature in crop yield forecasting. The climatic data and other SR bands were assigned a lower importance for soybean yield forecasting. This is consistent with previous studies that have shown mixed results regarding the contribution of climatic variables to crop yield forecasting (Cai, Y. et al. 2019; Hunt, M.L. et al. 2019; Farmonov, N. et al. 2022). Hunt, M.L. et al. (2019) found that climatic variables had limited predictive power of the wheat yield, but Cai, Y. et al. (2019) reported that climatic factors had a stronger influence on the wheat yield in Aus- tralia. These discrepancies may arise due to Fig. 9. Spatial distributions of the forecasted soybean yield with the RF model and the observed soybean yield for 2017–2021. 395Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398. variations in the crop type, geographic loca- tion, and specific weather variables consid- ered. Nevertheless, our study highlights the potential of combining MODIS LST and SR data with climatic data to improve the accu- racy of crop yiefigld forecasting models. Model performance We compared the performances of four ML models for soybean yield forecasting and found that the RF model consistently outper- formed the others across all metrics with an RMSE value of 0.334 t/ha and R2 value of 0.77. These results are consistent with those of Ji, Z. et al. (2022) who used an RF model to predict the corn and soybean yields in the Corn Belt with R2 values of 0.55–0.75 and RMSE values of 1,000–1,500 kg/ha. Our findings align with previous studies that have reported the ef- fectiveness of the RF model at crop yield pre- diction (Barbosa dos Santos, V. et al. 2022; Dhillon, M.S. et al. 2023). Barbosa dos San- tos, V. et al. (2022) found that the RF model provided the most accurate soybean yield prediction in the Brazilian Cerrado with an R2 value of 0.81 and RMSE value of 176.93 kg/ha, whereas Dhillon, M.S. et al. (2023) success- fully applied the RF model to predicting the winter wheat and rapeseed yields in Germany. The robustness and flexibility of RF, combined with its ability to handle complex interactions and nonlinear relationships, make it a reliable choice for crop yield forecasting. However, the comparison between the RF and 1D-CNN models revealed that the latter generally outperformed the former with an R2 value of 0.86 in 2021 and RMSE value of 0.276 t/ha for 2017. This finding is consistent with other studies that have highlighted the effectiveness of DL models at crop yield pre- diction (Khaki, S. and Wang, L. 2019; Khaki, S. et al. 2020). Khaki, S. and Wang, L. (2019) employed a deep neural network for crop yield prediction and achieved better accuracy than with traditional ML models. Khaki, S. et al. (2020) developed a DL-based model to predict corn and soybean yields across the Corn Belt and demonstrated its superior performance. Our study adds to the growing body of literature supporting the potential of DL models for improving the accuracy of crop yield forecasting. Conclusions We explored the various contributions of dynamic input features to soybean yield forecasting and compared the performances of different ML models. The findings em- phasized the importance of VI data from mid-July, particularly SR band 2, EVI, and NDVI, to the soybean yield, which align with previous studies. The RF model consistently outperformed the other ML models in fore- casting the soybean yield. However, the 1D- CNN model performed even better, which highlights the potential of DL models for crop yield forecasting. The spatial patterns of the forecasted yields indicated higher yields in the central and north-eastern states and lower yields in the southern and northern states. These variations can be attributed to multiple factors, including the climate, soil quality, and local agricultural practices. Overall, this study provides insights into the importance of different input features to crop yield forecasting and the performances of ML and DL models. These findings can help researchers, practitioners, and policy- makers in making informed decisions to enhance crop productivity and ensure food security. Future research can focus on inte- grating additional variables and exploring advanced DL techniques to further improve the accuracy of crop yield forecasting. Disclosure statement: The authors report there are no competing interests to declare. Authors’ ORCID: Farmonov, N. – https://orcid.org/0000-0002-2491-9340 Amankulova, K. – https://orcid.org/0000-0001-6562-5616 Khan, S.N. – https://orcid.org/0000-0003-2185-7276 Szatmári, J. – https://orcid.org/0000-0002-7896-3363 Mucsi, L. – https://orcid.org/0000-0002-5807-3742 https://orcid.org/0000-0002-2491-9340 https://orcid.org/0000-0001-6562-5616 https://orcid.org/0000-0003-2185-7276 https://orcid.org/0000-0002-7896-3363 https://orcid.org/0000-0002-5807-3742 Farmonov, N. et al. Hungarian Geographical Bulletin 72 (2023) (4) 383–398.396 REFERENCES Barbosa dos Santos, V., Moreno Ferreira dos Santos, A., da Silva Cabral de Moraes, J.R., de Oliveira Vieira, I.C. and de Souza Rolim, G. 2022. Machine learning algorithms for soybean yield forecasting in the Brazilian Cerrado. Journal of the Science of Food and Agriculture 102. (9): 3665–3672. Available at https://doi.org/10.1002/jsfa.11713 Boryan, C., Yang, Z., Mueller, R. and Craig, M. 2011. 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