Deep learning approaches have been widely adopted for precipitation nowcasting in recent years. Previous studies mainly focus on proposing new model architectures to improve pixel-wise metrics. However, they frequently result in blurry predictions which provide limited utility to forecasting operations. In this work, we propose a new Fourier Amplitude and Correlation Loss (FACL) which consists of two novel loss terms: Fourier Amplitude Loss (FAL) and Fourier Correlation Loss (FCL). FAL regularizes the Fourier amplitude of the model prediction and FCL complements the missing phase information. The two loss terms work together to replace the traditional $L_2$ losses such as MSE and weighted MSE for the spatiotemporal prediction problem on signal-based data. Our method is generic, parameter-free and efficient. Extensive experiments using one synthetic dataset and three radar echo datasets demonstrate that our method improves perceptual metrics and meteorology skill scores, with a small trade-off to pixel-wise accuracy and structural similarity. Moreover, to improve the error margin in meteorological skill scores such as Critical Success Index (CSI) and Fractions Skill Score (FSS), we propose and adopt the Regional Histogram Divergence (RHD), a distance metric that considers the patch-wise similarity between signal-based imagery patterns with tolerance to local transforms. Code is available at https://github.com/argenycw/FACL

翻译：近年来，深度学习技术已广泛应用于降水临近预报领域。先前的研究主要集中于提出新的模型架构以改进逐像素评估指标。然而，这些方法常导致预测结果模糊，对实际预报业务的应用价值有限。本研究提出了一种新颖的傅里叶振幅与相关性损失函数，该函数包含两个创新损失项：傅里叶振幅损失与傅里叶相关性损失。傅里叶振幅损失对模型预测的傅里叶振幅进行正则化约束，而傅里叶相关性损失则补充了缺失的相位信息。这两个损失项协同工作，可在基于信号的时空预测问题上替代传统的$L_2$损失函数（如均方误差和加权均方误差）。本方法具有通用性、无参数依赖和高效性的特点。通过在一个合成数据集和三个雷达回波数据集上的大量实验表明，该方法在提升感知质量指标和气象学技能评分方面效果显著，仅需以微小的逐像素精度和结构相似性为代价。此外，为改善临界成功指数和分数技巧评分等气象技能评分的误差容限，我们提出并采用了区域直方图散度——一种考虑基于信号的图像模式间区块相似性、且对局部变换具有容忍度的距离度量。相关代码已发布于 https://github.com/argenycw/FACL