## 3 Results
### Experiment 1: Evaluation of SMF Model
#### 3.2.1 SMF Model Deduction
For example, S1 was the regression curve using the data from the first record to the eighth one. This regression curve was used by the SMF model to forecast the moisture value of the 9 th data sample. The S28 used the records from the 28 th to the 35 th, and the SMF model used this regression curve to forecast the moisture of the 36 th data sample. The results were closer to the observed moisture data samples than the regression curve for the whole dataset. The size of continuously sampled moisture records in a segment is known as the _extract window_, denoted as \(W\). Our objective was to determine a suitable \(W\) size to minimize the distance between the sampled data and the regression curve. The evaluated sizes of \(W\) included 6, 8, 10, 12, 14, 15, 20, 25, and 30. Figure 6 shows the results of the 1 st, 2 nd, and 3 rd order polynomial regression functions with 2, 3, and 4 h irrigation intervals. Here, the forecasting error is defined as \((M_{f}\)-\(M_{r})/M_{max}\). \(M_{f}\) is the forecasted moisture level using the regression function of the segmented sampled data, \(M_{r}\) is the real  
Figure 5: The regression function of the sampled moisture data. The dimension of moisture level is 0–1023. (**a**) The regression curves of the 2 nd, 3 rd, 4 th, 5 th, and 6 th order polynomial functions for total sampled data. (**b**) The air temperature of this experiment. (**c**) The air humidity of this experiment. (**d**) The segmented regression curves. The segment size in this figure is 8 continuously sampled moisture records. Each \(\text{S}_{\text{k}}|\text{k}=\{1,\,28,\,40,\,50,\,52,\,62\}\) in this figure is the regression curve using the data from the kth record to the (k + 8)th one. This regression curve is used by the SMF model to forecast the moisture value of the (k + 9)th sampled data. moisture value sampled by the sensors, and \(M_{max}\) is the maximal scale at which the sensors sample the moisture. Figure 6a-c shows the forecasting errors for different irrigation intervals. Figure 6d shows the non-segmented moisture records for comparison. The forecasting error evaluates the difference between the real capture voltage value of the YL-69 sensor and the deduced value from the SMF model. Figure 6a shows the forecasting errors for a 2 h irrigation interval from sensors placed at the 3 cm soil depth. The results indicated that the forecasting error was smaller if the applied window sizes were 8, 10, or 12; their average forecasting errors of the moisture level were 1.5-2.3, 1.5-3.1, and 2.3-3.7, respectively. Figure 6b shows the forecasting errors when the experiment used a 3 h irrigation interval. The lowest average forecasting errors on the moisture level were with window sizes 6 and 8 (1.5-6.1 and 0.8-3.1, respectively). Figure 6c shows the average errors of the 4 h irrigation interval. The errors in window sizes 8, 10, and 12 were lower than the others, at 1.5-4.6, 1.5-9.2, and 3.1-9.2, respectively. The experimental results suggest that a 2 nd-order regression function with a window size set to 8 gave the best forecasting accuracy. When all sampled data were used as the extract window, the forecasting errors on the moisture level in every irrigation interval were 17.5-36.6 shown as Figure 6d. This level of error cannot predict the true variation of soil moisture. The next experiment verified higher-order polynomial regression functions to discover which were best at forecasting. Figure 7a-c shows the forecasting errors for moisture at 2 cm, 3 cm, and 4 cm depths. For the data in every soil depth layer, this experiment used the 1 st, 2 nd, 3 rd, 4 th, and 5 th-order regression functions to forecast moisture. The results indicated that forecasting errors grew with the order of function. The 2 nd-order polynomial function had the smallest error on average. These results  
Figure 6: The forecasting accuracy of different window sizes. The sensors placed at the 3 cm depth layers of soil. The forecasting error is estimated in moisture levels. The dimension of moisture level is 0–1023.