GeoPriFormer: A Precipitation Spatial Interpolation Method with Geographic Priors Embedding

doi:10.19678/j.issn.1000-3428.0070260

Abstract

Abstract:

Current deep learning methods for precipitation spatial interpolation rely primarily on the spatial relationships between stations and often overlook the effective representation of regional features and their complex dependencies. In particular, this approach does not consider the relationship between precipitation and elevation. To address this issue, GeoPriFormer is proposed as a spatial interpolation method for precipitation that incorporates geographic priors. This method uses a Transformer as the backbone network and enhances feature representation by integrating geographic prior data. This integration improves the accuracy and reliability of precipitation spatial interpolation. An elevation-based multi-head attention submodule is introduced to better understand and adapt to the effects of complex terrain. Additionally, a Laplacian method learns the context-aware vector encoding of geographic coordinates, enhancing the model's understanding of spatial relationships and regional characteristics. Consequently, the feature representation is embedded with geographic priors. Comparative experiments conducted on the Henan, Beijing-Tianjin-Hebei, and Baden-Württemberg (BW) datasets show that GeoPriFormer outperforms the baseline models. For example, in the Beijing-Tianjin-Hebei dataset, the Root Mean Squared Error (RMSE) is reduced by 1.6%, the Mean Absolute Error (MAE) decreases by 5.1%, and the Nash-Sutcliffe's Efficiency (NSE) increases by 1.56%, indicating an improvement over the current dominant approaches.

Key words: precipitation spatial interpolation, Transformer model, geographic prior, elevation-based multi-head attention submodule, Laplacian method

摘要：

目前, 关于降水空间插值的深度学习方法仅依赖站点之间的位置关系, 忽略了区域内特征的有效表示以及复杂特征依赖关系, 尤其对降水与高程之间的关系考虑不足。为此, 提出地理先验嵌入的降水空间插值方法GeoPriFormer。该方法以Transformer作为主干网络, 通过引入地理先验数据来增强特征表示能力, 从而提高降雨空间插值的精度和可靠性。一方面, 引入高程-多头注意力子模块以提高模型对复杂地形影响的理解和适应能力; 另一方面, 使用拉普拉斯方法来学习地理坐标的上下文感知向量编码, 以增强模型对地点关系和区域特性的理解, 最终形成一个嵌入地理先验的特征表示。在河南、京津冀和德国的巴登-符腾堡州(BW)数据集上进行对比实验, 结果表明, GeoPriFormer均优于基线模型。以京津冀数据集为例, 均方根误差(RMSE)降低1.6%, 平均绝对误差(MAE)降低5.1%, 纳什效率系数(NSE)提升1.56%, 优于当前主流方法。

关键词: 降水空间插值, Transformer模型, 地理先验, 高程-多头注意力子模块, 拉普拉斯方法

WANG Xiaochuan, LIU Qingqing, WANG Chen, MU Hengchen, LIAO Yaoming, LIU Ruijun. GeoPriFormer: A Precipitation Spatial Interpolation Method with Geographic Priors Embedding[J]. Computer Engineering, 2026, 52(7): 179-188.

王晓川, 刘青青, 王晨, 牟恒辰, 廖要明, 刘瑞军. GeoPriFormer: 地理先验嵌入的降水空间插值方法[J]. 计算机工程, 2026, 52(7): 179-188.

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Figures/Tables 12

Fig.1 GeoPriFormer network framework

Fig.2 Multi-head attention mechanism

Fig.3 Geographic coordinate — Laplacian attention submodule

Fig.4 Elevation and distribution of meteorological stations in the Henan region

Fig.5 Elevation and distribution of meteorological stations in the Beijing — Tianjin — Hebei region

Fig.6 Spatial distribution map of daily cumulative precipitation in the Beijing — Tianjin — Hebei region on June 6, 2017

Fig.7 Scatter plot comparing the interpolation results of the Beijing — Tianjin — Hebei dataset with the actual values from observation stations

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