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Abstract. Depressions – inwardly draining regions – are common to many landscapes. When there is sufficient moisture, depressions take the form of lakes and wetlands; otherwise, they may be dry. Hydrological flow models used in geomorphology, hydrology, planetary science, soil and water conservation, and other fields often eliminate depressions through filling or breaching; however, this can produce unrealistic results. Models that retain depressions, on the other hand, are often undesirably expensive to run. In previous work we began to address this by developing a depression hierarchy data structure to capture the full topographic complexity of depressions in a region. Here, we extend this work by presenting the Fill–Spill–Merge algorithm that utilizes our depression hierarchy data structure to rapidly process and distribute runoff. Runoff fills depressions, which then overflow and spill into their neighbors. If both a depression and its neighbor fill, they merge. We provide a detailed explanation of the algorithm and results from two sample study areas. In these case studies, the algorithm runs 90–2600 times faster (with a reduction in compute time of 2000–63 000 times) than the commonly used Jacobi iteration and produces a more accurate output. Complete, well-commented, open-source code with 97 % test coverage is available on GitHub and Zenodo. 

Abstract. Depressions – inwardly draining regions of digital elevation models – present difficulties for terrain analysis and hydrological modeling. Analogous “depressions” also arise in image processing and morphological segmentation, where they may represent noise, features of interest, or both. Here we provide a new data structure – the depression hierarchy – that captures the full topologic and topographic complexity of depressions in a region. We treat depressions as networks in a way that is analogous to surface-water flow paths, in which individual sub-depressions merge together to form meta-depressions in a process that continues until they begin to drain externally. This hierarchy can be used to selectively fill or breach depressions or to accelerate dynamic models of hydrological flow. Complete, well-commented, open-source code and correctness tests are available on GitHub and Zenodo. 

Let's Encrypt is a free, open, and automated HTTPS certificate authority (CA) created to advance HTTPS adoption to the entire Web. Since its launch in late 2015, Let's Encrypt has grown to become the world's largest HTTPS CA, accounting for more currently valid certificates than all other browser-trusted CAs combined. By January 2019, it had issued over 538 million certificates for 223 million domain names. We describe how we built Let's Encrypt, including the architecture of the CA software system (Boulder) and the structure of the organization that operates it (ISRG), and we discuss lessons learned from the experience. We also describe the design of ACME, the IETF-standard protocol we created to automate CA--server interactions and certificate issuance, and survey the diverse ecosystem of ACME clients, including Certbot, a software agent we created to automate HTTPS deployment. Finally, we measure Let's Encrypt's impact on the Web and the CA ecosystem. We hope that the success of Let's Encrypt can provide a model for further enhancements to the Web PKI and for future Internet security infrastructure.