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River network routing's significance in reach-level flood forecasting over extensive domains is growing, requiring considerable computational resources for modeling networks comprising thousands to millions of reaches. Parallel computation plays a central role in timely forecasting in such cases. However, the sequentiality of upstream-to-downstream flow paths within river networks poses a significant challenge for parallelization. This study introduces a family of stream orders and an associated order-based parallel routing approach. We assign each reach an order that falls between one more than the maximum order of its upstream reaches and one less than the order of its downstream reach. This strategy enables the parallel simulation of reaches with identical orders while sequentially processing those with different orders, thus maintaining the crucial upstream-to-downstream dynamic. To further enhance parallel scalability, we strategically relax the upstream-to-downstream relationship along the longest flow paths, dividing the network into independent subnetworks and introducing halo reaches to mitigate the impact of inexact inflows. We validate our approach using China's Yangtze River basin, the country's largest river network with 53,600 fully connected reaches. Employing a conceptual parallel execution machine, we demonstrate that our method achieves 80% parallel efficiency with up to 25 processors. By strategically introducing breakpoints, we further enhance scalability, enabling efficient simulations on 77 processors while maintaining 80% efficiency. These results highlight the scalability and efficiency of our methods for large-scale, high-resolution river network modeling within Earth system models. Our study also lays a theoretical groundwork for optimizing stream orders and halo reach placements, crucial for advancing river network modeling. [ABSTRACT FROM AUTHOR]