# A Study of Forest Phenology Prediction Based on GRU Models
## 4 Discussion  
Modeling and predicting with limited data can be quite challenging. In this study, we utilized the GRU model to model GEI data and predict future forest phenology growth patterns. The results indicate that the GRU model is capable of predicting phenology with remarkable accuracy, aligning with our initial hypotheses. To elucidate this phenomenon, we extracted GEI data from forest images and attempted to predict it using the GRU model. We then validated our analysis using histograms, kernel density plots, and autocorrelation plots. Furthermore, we evaluated the model performance and predictive capabilities. The results indicate that: (1) the GRU model, after being trained and tested on the dataset, exhibited good similarity with the actual values, fulfilling the predictive requirements. (2) Validation, conducted through histograms, kernel density plots, and autocorrelation plots, demonstrated the reasonability of the testing data and confirmed the stability of the predictive model. (3) Model performance evaluation confirmed that the model accuracy meets the predictive requirements. (4) The GRU model is capable of predicting the forest's trends for the next 60 days. The GRU model has become a phenological prediction model. While many scholars have made predictions regarding other aspects of forestry [39, 40], phenology has not been given sufficient attention, even though it plays a crucial role in reflecting the impact of environmental changes on forest growth [41]. To demonstrate the predictive capabilities of GRU, we trained and tested the mode and found that it was capable of effectively predicting trend changes. The discrepancy between the real and predicted values observed in Figure 6 can be attributed to the memory control mechanism of the model. Specifically, the GRU model directly passes the information to the next unit without any control, and, in addition, it uses the reset gate to regulate the information from the previous time step when calculating the new memory h\({}^{(0)}\). The histograms and kernel density plots correspond correctly to the distribution of the data. For continuous variable data, histograms are constructed to understand the distribution, and kernel density plots are drawn to visualize the potential probability distribution of the data. The results showed that the distribution of the testing dataset of the GRU model was relatively consistent with the distribution of the histogram, and the data distribution of the GRU model remained constant and uniform. To demonstrate the probability density function of the random variable of the entire dataset, kernel density plots were used for analysis. It was found that the GRU model data showed a uniformly distributed and symmetrical distribution, indicating that the values were consistent and that the sample repeatability was good. This further confirms that the GRU model can be used as a phenology prediction model. Under the time series data prediction model, the correlation between predicted values and real values at different time periods was analyzed using autocorrelation analysis, which is used to measure the correlation between current sequence values and past sequence values [42]. The results showed that the autocorrelation coefficient values of the GRU model decreased smoothly, indicating that the model is very stable. This indicates that the GRU model measures a strong correlation and has good stability between the current and past sequence values. This is due to the simple structure of the GRU model, which leads to relatively greater stability. To evaluate the performance of the proposed model, real data was compared with predicted data using performance metrics such as MSE, RMSE, and MAE [43]. These metrics were chosen to measure the error rate of the model and provide a measure of the accuracy of the system's performance. The goodness of fit of any model can be explained by its error rate, and, therefore, MSE, RMSE, and MAE were used to assess the accuracy of the proposed model.