Improved Calculation Model of Floating Ball Coverage Evaporation Based on Robust Regressio

YAN Xin-jun, ZHAO De-xin, SHI Ke-bin, HAN Ke-wu, WANG Jin-han

Journal of Changjiang River Scientific Research Institute ›› 2026, Vol. 43 ›› Issue (8) : 36-44.

PDF(8041 KB)
PDF(8041 KB)
Journal of Changjiang River Scientific Research Institute ›› 2026, Vol. 43 ›› Issue (8) : 36-44. DOI: 10.11988/ckyyb.20250440
Water Resources

Improved Calculation Model of Floating Ball Coverage Evaporation Based on Robust Regressio

Author information +
History +

Abstract

[Objective] Traditional evaporation models are limited in floating ball coverage scenarios by complex parameterization, reliance on sensible heat flux data, and cumbersome aerodynamic calculations. This study aims to develop a highly accurate evaporation prediction formula with simplified parameters, adaptable to varying coverage ratios, to provide a reference for water resource quantification. [Method] Based on the Priestley-Taylor model, a modified model was developed by introducing correction term g(m) to address evaporation prediction under floating ball coverage. By analyzing the relationship between coverage ratio and latent heat flux, exponential (for high-temperature seasons) and linear (for transition seasons) correction forms were determined. Robust regression was employed to minimize the impact of outliers. The optimal model was selected through model comparison and cross-validation. [Result] (1) The response relationship between latent heat flux and floating ball coverage ratio exhibited significant monthly variations. At high-temperatures during high-radiation season (June-August), the exponential correction yielded the best fit (R2≥0.985), whereas the linear correction performed better during the transition seasons (March-May and September-October) (R2≥0.986). (2) The exponential model demonstrated superior adaptability and predictive advantages for floating ball evaporation. Over the entire experimental period, it achieved a Willmott’s index of agreement (D) of 0.986, a Nash-Sutcliffe efficiency (NSE) of 0.947, a root mean square error (RMSE) of 0.54 mm/d, and a mean absolute error (MAE) of 0.43 mm/d, with strong parameter stability and no systematic bias. (3) The model also showed good adaptability during external validation under high-coverage conditions (NSE=0.734, D=0.890). [Conclusion] The proposed modified model establishes a unified prediction framework based on basic meteorological parameters for varying floating ball coverage ratios. It enables precise estimation of evaporation processes across different coverage levels, providing an efficient and practical computational method for water resource management in arid regions.

Key words

floating ball coverage / evaporation prediction model / water surface evaporation / robust regression / Priestley-Taylor model

Cite this article

Download Citations
YAN Xin-jun , ZHAO De-xin , SHI Ke-bin , et al . Improved Calculation Model of Floating Ball Coverage Evaporation Based on Robust Regressio[J]. Journal of Changjiang River Scientific Research Institute. 2026, 43(8): 36-44 https://doi.org/10.11988/ckyyb.20250440

References

[1]
韩克武, 侍克斌, 严新军, 等. 干旱区平原水库防蒸发节水控盐及效益分析[J]. 水利科技与经济, 2019, 25(7):44-50.
(Han Kewu, Shi Kebin, Yan Xinjun, et al. Benefit Analysis on Water Savings Efficiency and Salt Reduction of Anti-evaporation in Plain Reservoir in Arid Area[J]. Water Conservancy Science and Technology and Economy, 2019, 25(7): 44-50. (in Chinese))
[2]
孜来布·阿布来题. 新疆近10年降雨量与地表径流时空变化研究[J]. 水利科技与经济, 2025, 31(2): 134-138.
(Zilaibu Abulai. Temporal and Spatial Changes of Rainfall and Surface Runoff in Xinjiang in Recent 10 Years[J]. Water Conservancy Science and Technology and Economy, 2025, 31(2): 134-138. (in Chinese))
[3]
Li S, Li J, Du W, et al. Combining Satellite Images and the Hydraulic Engineering Archive to Map the Processes of Reservoir Construction in Xinjiang[J]. Remote Sensing, 2024, 16(2): 328.
Reservoirs are essential hydraulic facilities for water resource allocation in Xinjiang. Since the 1950s, many reservoirs have been constructed for oasis water resource utilization in Xinjiang, enhancing the storage capacity of water resources. There are a few intact and open reservoir archives containing both geolocations and hydraulic attributes, such as the reservoir completion year, which can facilitate our understanding of the correlation between hydraulic engineering and oasis expansion. This paper mapped all the reservoirs of Xinjiang using Sentinel-2 MSI images from 2022. It associated their attributes with the reservoir’s extent, such as the capacity, area, complete year, altitude, etc., by consulting historical almanac data to establish a full elemental dataset with both geographic and attribute information. Furthermore, the spatial variability and historical process of the reservoirs were discussed against geomorphic information and oasis evolution. The results showed that 804 reservoirs were mapped cumulatively in Xinjiang up to 2022, and 1960–1980 and 2005–2010 are the rapidly developed periods. The construction history of the reservoirs indicates that reservoirs’ locations have the spatial tendency to shift from being in oasis plain areas to mountainous areas, and the newly built reservoirs showed a trend of miniaturization in area and maximization in volume.
[4]
毛海涛, 王正成, 王晓菊, 等. 北疆平原水库水面蒸发模型的建立与关键参数确定[J]. 农业工程学报, 2018, 34(6): 129-136.
(Mao Haitao, Wang Zhengcheng, Wang Xiaoju, et al. Establishment of Water Surface Evaporation Model and Determination of Key Parameters for Plain Reservoir in Northern Xinjiang[J]. Transactions of the Chinese Society of Agricultural Engineering, 2018, 34(6): 129-136. (in Chinese))
[5]
虞志刚, 陈远生, 罗文哲, 等. 新疆小海子水库水面蒸发估计与蒸发抑制关键影响因素分析[J]. 水电能源科学, 2025, 43(4): 94-97, 11.
(Yu Zhigang, Chen Yuansheng, Luo Wenzhe, et al. Estimation of Water Surface Evaporation and Analysis of Key Influencing Factors of Evaporation Inhibition in Xiaohaizi Reservoir in Xinjiang[J]. Water Resources and Power, 2025, 43(4): 94-97, 11. (in Chinese))
[6]
韩克武, 侍克斌, 严新军, 等. PE浮球覆盖下干旱区平原水库静水水面蒸发抑制率研究[J]. 水资源与水工程学报, 2017, 28(4): 235-239.
(Han Kewu, Shi Kebin, Yan Xinjun, et al. Study on the Inhibition Rate of the still Water Evaporation under the PE Floating Ball Coverage in Arid Zone Plain Reservoir[J]. Journal of Water Resources and Water Engineering, 2017, 28(4): 235-239. (in Chinese))
[7]
Priestley C H B, Taylor R J. On the Assessment of Surface Heat Flux and Evaporation Using Large-scale Parameters[J]. Monthly Weather Review, 1972, 100(2): 81-92.
[8]
韩克武, 侍克斌, 严新军, 等. Priestley-Taylor模型在浮球覆盖下水面蒸发量估算中的应用[J]. 应用基础与工程科学学报, 2024, 32(2):479-487.
(Han Kewu, Shi Kebin, Yan Xinjun, et al. Application of Priestley-Taylor Model in the Estimation of Water Surface Evaporation Covered by Spheres[J]. Journal of Basic Science and Engineering, 2024, 32(2): 479-487. (in Chinese))
[9]
Han Kewu, Shi Kebin, Yan Xinjun. Evaporation Loss and Energy Balance of Agricultural Reservoirs Covered with Counterweighted Spheres in Arid Region[J]. Agricultural Water Management, 2020, 238:106227.
[10]
徐思远, 严新军, 王海涛, 等. 浮球覆盖下水面能量平衡再建与蒸发模型研究[J]. 长江科学院院报, 2024, 41(3): 22-29.
Abstract
针对干旱区平原水库蒸发强烈导致水资源利用率低的问题,选用黑色高密度聚乙烯(HDPE)浮球作为干旱区平原水库节水材料。通过理论分析、建模与室外试验三者结合,对完整非冰冻期内浮球覆盖下水面蒸发、水体能量平衡组分变化分布的响应机理进行研究,并在此基础上建立相应的水面蒸发量计算模型。结果显示:相较于自由水面,73%的浮球覆盖率下的整体水面净辐射吸收率减小约12.6%,其月均蒸发所需潜热通量减少了61.8%,约为148.73 W/m<sup>2</sup>,水体的感热通量和蓄热通量也有较大的变化。通过对彭曼模型的能量项和空气动力项进行修正,建立的覆盖条件下的水面蒸发量计算模型具有较高的精度。
(Xu Siyuan, Yan Xinjun, Wang Haitao, et al. Reconstruction of Water Surface Energy Balance and Evaporation Model under Floating Ball Coverage[J]. Journal of Changjiang River Scientific Research Institute, 2024, 41(3): 22-29. (in Chinese))
[11]
王少华, 叶自强, 陈金法, 等. 采用稳健回归算法的绝缘子污闪电压预测方法[J]. 电网技术, 2010, 34(12):131-135.
(Wang Shaohua, Ye Ziqiang, Chen Jinfa, et al. A Method to Predict Pollution Flashover Voltage of Insulators Based on Robust Regression[J]. Power System Technology, 2010, 34(12): 131-135. (in Chinese))
[12]
Han Kewu, Shi Kebin, Yan Xinjun, et al. Comparison of Evaporation Estimation Methods for Water Surface under Floating Coverage in Arid Areas[J]. Agricultural Water Management, 2022, 264: 107534.
[13]
Hao Guochen, Han Kewu, Shi Kebin. Effect of Floating Balls on Evaporation Inhibition, Surface Energy Balance and Biological Water Quality Parameters at Different Coverage Fractions[J]. Agricultural Water Management, 2023, 287: 108460.
[14]
Hao Guochen, Shi Kebin, Han Kewu. Evaluating the Impact of Floating Spheres on Evaporation Reduction and Water Salinity Control in Reservoirs[J]. Agricultural Water Management, 2025, 312: 109440.
[15]
韩克武, 侍克斌, 杨云鹏, 等. 配重浮球覆盖下干旱区平原水库节水率研究[J]. 干旱区地理, 2020, 43(3):644-651.
(Han Kewu, Shi Kebin, Yang Yunpeng, et al. Water Saving Efficiency of Weighted Floating Balls Covering Plain Reservoir in Arid Area[J]. Arid Land Geography, 2020, 43(3): 644-651. (in Chinese))
[16]
赵玲玲, 王中根, 夏军, 等. Priestley-Taylor公式的改进及其在互补蒸散模型中的应用[J]. 地理科学进展, 2011, 30(7): 805-810.
(Zhao Lingling, Wang Zhonggen, Xia Jun, et al. Improved Priestley-Taylor Method and Its Application in Complementary Relationship Evapotranspiration Model[J]. Progress in Geography, 2011, 30(7): 805-810. (in Chinese))
Priestley-Taylor method is developed under the condition of non advection water vapour transport, however, this assumption is hardly satisfied in reality. Some researches introduced the parameter in order to eliminate the error brought by the non-advection assumption. According to many researches, the value of parameter has some uncertainty. This paper tries to introduce an advection coefficient to reflect the influence of advection on evaporation. The case analyses suggest that this method could provide the minimum energy for calculating evaporation in winter. Compared with the original formula, the calculation accuracy of evaporation has been effectively improved, especially in winter and summer.
[17]
孙媛媛, 尹志明. 基于M估计稳健回归的多谐波源责任区分[J]. 中国电机工程学报, 2012, 32(31): 166-173, 233.
(Sun Yuanyuan, Yin Zhiming. Quantifying Harmonic Responsibilities of Multiple Harmonic Sources Based on M-estimation Robust Regression[J]. Proceedings of the Chinese Society for Electrical Engineering, 2012, 32(31): 166-173, 233. (in Chinese))
[18]
徐思远. 浮球覆盖对水面蒸发的影响及蒸发模型研究[D]. 乌鲁木齐: 新疆农业大学, 2023.
(Xu Siyuan. Study on theInfluence of Floating Ball on Water Surface Evaporation and Evaporation Model[D]. Urumqi: Xinjiang Agricultural University, 2023. (in Chinese))
[19]
Shalaby M M, Nassar I N, Abdallah A M. Evaporation Suppression from Open Water Surface Using Various Floating Covers with Consideration of Water Ecology[J]. Journal of Hydrology, 2021, 598: 126482.
[20]
李菲菲, 饶良懿, 吕琨珑, 等. Priestley-Taylor模型参数修正及在蒸散发估算中的应用[J]. 浙江农林大学学报, 2013, 30(5): 748-754.
(Li Feifei, Rao Liangyi, Kunlong, et al. Parameter Corrections for the Priestley-Taylor Model and Applications in Evapotranspiration Estimation[J]. Journal of Zhejiang A&F University, 2013, 30(5): 748-754. (in Chinese))
PDF(8041 KB)

Accesses

Citation

Detail

Sections
Recommended

/