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Study locations and rice data

The ML and DNN models were developed for the rice growing areas in the entire geographic regions of Cheorwon and Paju in South Korea (Fig.4). Then, the parameterised ML and DNN models were evaluated for the representative rice growing areas of Gimje, South Korea and Pyeongyang, North Korea. Cheorwon and Paju were selected as these areas are typical rice cultivation regions in the central portion of the Korean peninsula. The paddy rice cultivation regions in Cheorwon and Paju have areas of 10,169 and 6,625ha, respectively, representing 80.4% and 62.6% of the total staple croplands for each region, according to the Korean Statistical Information Service, KOSIS (https://kosis.kr/).

Study location boundary maps of (a) Cheorwon, (b) Paju, (c) Gimje in South Korea and (d) Pyeongyang in North Korea.

The leading rice cultivar in Cheorwon and Paju was Odae (bred by NICS in 1983), cultivated in more than 80% of the paddy fields during the study period, according to KOSIS. Rice seedlings were transplanted in these areas between May 15 and 20, deemed as the ideal transplanting period.

We used the temporal profiles of NDVI from the Terra MODIS MOD09A1 surface reflectance 8-day product with a spatial resolution of 500m, which were employed for the ML and DNN model input variable. This product is the composited imagery by selecting the best pixels considering the cloud and solar zenith during eight days33. It is essential to secure reliable and continuous phenological NDVI data for determining crop yield in monsoon regions like the current study area concerning input variables for the process-based crop model. Therefore, the cloud-contaminated pixels were interpolated with other poor quality pixels caused by aerosol quantity or cloud shadow using the spline interpolation algorithm during the rice-growing season to improve data quality during the monsoon season. This approach has been widely used in time series satellite imagery for interpolation34,35,36. The criteria for poor quality pixels for interpolation were determined from the 16-bit quality assurance (QA) flags from the MOD09A1 product33.

Furthermore, we estimated the incoming solar radiation on the surface (insolation) obtained from the COMS Meteorological Imager (MI). Insolation reflects the energy source of photosynthesis for the crop canopies. We adopted a physical model to estimate solar radiation by considering atmospheric effects such as aerosol, water vapour, ozone, and Rayleigh scattering37,38,39,40,41. Before estimating the solar radiation from the physical model, we classified clear and cloudy sky conditions because cloud effects should be considered for their high attenuation influences. If the pixel image was assigned as a clear sky condition, atmospheric parameterisations were performed for direct and diffuse irradiance owing to the effects of atmospheric constituents and solar-target-satellite sensor geometry40,42,43,44. If the pixel images were considered as under cloudy conditions, the cloud attenuation was calculated using a cloud factor for visible reflectance and the solar zenith angle42. Finally, the estimated solar radiation from COMS MI was used as one of the main input parameters of the RSCM system. Comprehensive descriptions of those parameters used for the physical model can be referenced from earlier studies41,43.

The maximum and minimum air temperature data were obtained from the Regional Data Assimilation and Prediction System (RDAPS) provided by the Korea Meteorological Administration (KMA, https://www.kma.go.kr). The spatial resolution of the RDAPS is 12km, and it is composed of 70 vertical levels up to about 80km. The global data assimilation and prediction system is provided at 3-h intervals for the Asian regions, and forecasts are performed four times a day (00, 06, 12, and 18 UTC) for 87h. In addition, the system is operated in a 6-h interval analysis-prediction-circulation system using the four-dimensional variational data assimilation45. The weather datasets were resampled to a spatial resolution of 500m using the nearest neighbour method that does not change the existing values to match the MODIS imagery.

The current study employed the RSCM to incorporate an ML and DNN procedure and then simulate rice growths and yields (Supplementary Fig. S1). We integrated an ML and DNN regressor into the RSCM-rice system based on the investigation of the ML or DNN regressors described in the following subsection. The ML or DNN scheme was implemented to improve the mathematical regression approach for the RS-based VIs and LAI relationships, as described below.

RSCM is a process-based crop model designed to integrate remotely sensed data, allowing crop modellers to simulate and monitor potential crop growth6. This model can accept RS data as input to perform its within-season calibration procedure5, wherein the simulated LAI values are compared to the corresponding observed values. Four different parameters (that is, L0, a, b, and c) are utilised in the within-season procedure to define the crop-growth processes based on the optimisation of LAI using the POWELL procedure46. In addition, these parameters can be calibrated using the Bayesian method to obtain acceptable values with a prior distribution that was selected based on the estimates from earlier studies6,47. The current research project applied consistent initial conditions and parameters to calibrate the RSCM-rice system.

The ML models investigated in this study were Polynomial regression, Ridge, Least Absolute Shrinkage and Selection Operator (LASSO), Support Vector Regression (SVR), RF, Extra Trees (ET), Gradient Boosting (GB), Histogram-based Gradient Boosting (HGB), Extreme Gradient Boosting (XGB), and Light Gradient Boosting machine regression (LightGB) regressors. These models are implemented in scikit-learn (https://scikit-learn.org/), while the DNN model (Supplementary Fig. S4) is implemented in Keras (https://keras.io/), which are achievable on Python (https://www.python.org/).

The Polynomial regression model is a particular regression model to overcome the limitations of simple linear regression by estimating the relationship with the Nth degree polynomial. The Ridge and Lasso additionally use l2-norm and l1-norm as constraints in the existing model. These characteristics of the models show better performance than the conventional linear regression, which uses the least-squares method to find appropriate weights and biases to reduce overfitting48,49.

The SVR allows the definition of the amount of allowable error and finds a hyperplane of higher dimensions to fit the data. The SVR is widely used for classification and numerical prediction and is less overfitting and easier to use than neural networks. However, it takes a long time to build an optimisation model, and it is difficult to interpret the results50.

The RF is an ensemble model that trains multiple decision tree models and aggregates its results. It has good generalisation and performance, is easy to tune parameters, and is less prone to overfitting. On the other hand, memory consumption is higher than in other ML models. Also, it is not easy to expect higher performance improvement even when the amount of training dataset increases. Extra trees increase randomness by randomly splitting each candidate feature in the tree, which can reduce bias and variance51. The difference from the RF is that ET does not use bootstrap sampling but uses the whole origin data when making decision trees. The GB belongs to the boosting series among the RF ensemble models, which combines weak learners to create strong learners with increased performance. Meanwhile, the GB training process is slow and not efficient in overfitting. There are HGB, XGB, and LightGB in the form of the GB that improve performance by increasing the training speed and reducing overfitting. The HGB speeds up the algorithm by grouping each decision tree with a histogram and reducing the number of features. The XGB improves learning speed through parallel processing and is equipped with functions necessary to improve performance compared to the GB, such as regularisation, tree pruning, and early stopping. The LightGBM significantly shortens the training time and decreases memory use by using a histogram-based algorithm without showing a significant difference in predictive performance compared to the XGBoost52.

The DNN increases the predictive power by increasing the hidden layer between the input and the output layers. Non-linear combinations between input variables are possible, feature weighting is performed automatically, and performance tends to increase as the amount of data increases. However, since it is difficult to interpret the meaning of the weights, there is a disadvantage in that the results are also difficult to interpret. In addition, when fewer training datasets are collected, the performance of the ML models mentioned above can be better53.

This study used satellite-based solar radiation and model-based maximum and minimum temperatures to estimate LAI values during the rice-growing seasons on the study sites (Cheorwon, Paju, Gimje, and Pyeongyang) for seven years (20112017), employing the ML and DNN regressors. We reproduced rice LAI values from the MODIS-based NDVI values using the empirical relationship between LAI and NDVI (Supplementary Fig. S2). Cheorwon and Paju datasets were used for the ML and DNN model development, while Gimje and Pyeongyang datasets were employed for the model evaluation. The target LAI variable data used for the model development showed characteristic seasonal and geographical variations (Supplementary Figs. S3 and S4). The model development datasets were divided into train and test sets with a 0.8 and 0.2 ratio using the scikit-learn procedure. All the ML and DNN regressors were trained and tested, obtaining appropriate hyperparameters. Alpha values for the Ridge and Lasso were determined as 0.1 and 0.01 based on a grid search approach with a possible range of values (Supplementary Fig. S5). The activation function employed for the DNN model was the rectified linear unit (ReLU), implementing six fully connected layers with a design of gradual increasing and decreasing units from 100 to 1,000 (Supplementary Fig. S6). The model was performed with a dropout rate of 0.17, the adam optimizer at a learning rate of 0.001, 1,000 epochs, and a batch size of 100. The DNN hyperparameters were determined based on a grid search approach and a trial and error approach, seeking minimum and steady losses for each study region (Supplementary Fig. S7).

We analysed the performance of the ML (that is, RF) and DNN regimes using two statistical indices in Python (https://www.python.org), namely the RMSE and the ME54. This index denotes the comparative scale of the residual variance of simulated data compared to the observed data variance. Furthermore, ME can assess the agreement between the experimental and simulated data, showing how well these data fit through the 1:1 line in a scatter plot. The index value can vary from to 1. We employed normalized ME for advanced interpretation, allowing for the ME measure in simulation estimation approaches used in model evaluation. Thus, ME=1, 0, and correspond to ME=1, 0.5, and 0, respectively. Therefore, the model is considered reliable if the ME value is nearer to 1, whereas the simulated data are considered less dependable if the ME value is close to 0.

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Incorporation of machine learning and deep neural network approaches into a remote sensing-integrated crop model for the simulation of rice growth |...