Accurate estimation of pan evaporation (Ep) is vital for the development of water resources and agricultural water management, especially in arid and semi-arid regions where it is restricted to set up the facilities and measure pan evaporation accurately and consistently. Besides, using pan evaporation estimating models and pan coefficient (kp) models is a classic method to assess the reference evapotranspiration (ET0) which is indispensable to crop growth, irrigation scheduling, and economic assessment. This study estimated the potential of a novel hybrid machine learning model Coupling Bat algorithm (Bat) and Gradient boosting with categorical features support (CatBoost) for estimating daily pan evaporation in arid and semi-arid regions of northwest China. Two other commonly used algorithms including random forest (RF) and original CatBoost (CB) were also applied for comparison. The daily meteorological data for 12 years (2006–2017) from 45 weather stations in arid and semi-arid areas of China, including minimum and maximum air temperature (Tmin, Tmax), relative humidity (RH), wind speed (U), and global solar radiation (Rs), were utilized to feed the three models for exploring the ability in predicting pan evaporation. The results revealed that the new developed Bat-CB model (RMSE = 0.859–2.227 mm·d−1; MAE = 0.540–1.328 mm·d−1; NSE = 0.625–0.894; MAPE = 0.162–0.328) was superior to RF and CB. In addition, CB (RMSE = 0.897–2.754 mm·d−1; MAE = 0.531–1.77 mm·d−1; NSE = 0.147–0.869; MAPE = 0.161–0.421) slightly outperformed RF (RMSE = 1.005–3.604 mm·d−1; MAE = 0.644–2.479 mm·d−1; NSE = −1.242–0.894; MAPE = 0.176–0.686) which had poor ability to operate the erratic changes of pan evaporation. Furthermore, the improvement of Bat-CB was presented more comprehensively and obviously in the seasonal and spatial performance compared to CB and RF. Overall, Bat-CB has high accuracy, robust stability, and huge potential for Ep estimation in arid and semi-arid regions of northwest China and the applications of findings in this study have equal significance for adjacent countries.

<p>Intercropping, growing at least two different crop species simultaneously in the same field, is a significant cropping system for global food security with more practice and attention recent years. The most remarkable advantage of intercropping is producing a higher yield or income due to more efficient use of agricultural sources. Specifically, the intercropping system utilizes nutrient and water more efficiently underground and intercepts more radiation aboveground. However, modeling intercropping system by crop model is still difficult and has two dominant challenges. One challenge is to quantify the competition of underground source between intercropped species, and the other one is to determine the radiation partitioning by intercropped species. With the view factor theory applied in radiation transmission, several models were established to simulate the light competition of strip intercropping, but most of the models ignore solar incident angles variation during one day and assume the indirect light traverse a whole hedgerow of the taller canopy. Although many models make great attempt on partitioning the indirect light, the extinction coefficient is not matched with the beer’s law. In our study, the radiation transmission model is based on geometrical relationships of crop height, calculating a beam transmission by spatial and temporal integration. Specifically, the same with direct light, the extinction coefficient of an indirect beam is established a numerical functional relation with the solar incident angle which is defined by crop heights and row widths of intercropped species. Furthermore, Gauss-Legendre integral formula are used to solve the indefinite integral caused by angular relationship during the temporal integration. The optimal number of nodes in Gauss-Legendre integral formula is five in our study and the error is generally less than 1%. Compared with existed models, the radiation interception model in our study is more stable and precise especially when the heights of crops are close or greatly discrepant. Further study including border row effect theory and heterogeneous canopy theory is also able to applied in our model.</p>

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