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Short-range prediction of convective precipitation from weather radar observations is essential for severe weather warnings. However, deep learning models trained with pixel-wise error metrics tend to produce overly smooth forecasts that suppress intense echoes critical for hazard detection. This issue is exacerbated by insufficient multi-scale feature interaction and suboptimal fusion of heterogeneous geophysical inputs. We propose IMPA-Net (Integrated Multi-scale Predictive Attention Network), a deterministic 0-2 hour nowcasting framework that addresses these limitations through meteorologically-informed designs at the input, architecture, and loss function levels. A parameter-free Spatial Mixer reorganizes heterogeneous input channels at the mesoscale-$\gamma$ neighborhood (~2 km) via deterministic channel permutation, providing a structured cross-field prior. An integrated multi-scale predictive attention module serves as the spatiotemporal translator, capturing dynamics from mesoscale-$\beta$ to mesoscale-$\gamma$ scales. A Meteorologically-Aware Dynamic Loss employs three-level asymmetric weighting -- adapting across training epochs, storm intensity, and forecast lead time -- to counteract regression-to-the-mean. Evaluated against seven baselines on a multi-source radar dataset over eastern China, IMPA-Net raises the Heidke Skill Score at $\geq$45 dBZ from 0.049 (SimVP baseline) to 0.143 under matched settings. Relative to pySTEPS, it provides a better trade-off between severe-event detection and false-alarm control. Spectral analysis confirms preserved energy across mesoscale bands where competing methods show progressive smoothing. These improvements are shown within a single domain and convective regime; generalizability to other orographic and climatic regions remains to be tested.