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Bayesian Optimal Sensor Augmentation Via Estimated Mutual Information

We consider the problem of designing a sensor network to most efficiently locate the source of a seismic event. The left panel of Figure 1 shows 982 possible sensor locations in a region of interest. The objective is to infer the unknown location of an earthquake, indicated by the gold dot for illustration purposes. Assume that three sensors have already been placed for data collection. Travel times of the P-wave from the source to the three sensors are observed and used to infer the unknown source location via a Bayesian statistical model described subsequently. The right panel of Figure 1 shows samples from the resulting posterior distribution for source location along with a posterior estimate of this location.

47 OTHER INSTRUMENTATION↗

California Trees Seasonally Use Augmented Water Sources: Water Isotope Tracking in a Groundwater‐Dependent Ecosystem

Sustainable groundwater management must account for the needs of groundwater dependent ecosystems. To understand the relationship of ecosystems and seasonal water use, we studied the stable isotope composition (δ 18 O and δ 2 H) of water in streamside trees in a semi-arid streamside environment (Livermore, California, USA). We sampled seven trees at two sites every other month from April 2024 through April 2025 for tree xylem stable water isotope signatures. These data were compared to potential source waters: precipitation, imported surface water, soil water and regional groundwaters. Large daily precipitation events were found to be isotopically similar to regional groundwater and were thus treated as one water source. A Bayesian mixing model using stable water isotopes was used to determine the ratios of these three potential source waters (small daily precipitation events, groundwater/large daily precipitation events and imported water) present in tree xylem water. On average, tree water sources include 32% imported water (SD = 9%), 35% small daily precipitation events (SD = 10%) and 33% groundwater (SD = 3%), with significant seasonal variation (t summer-winter = 30.8, p < 0.01), particularly drawing more imported water (more than 55%) in the summer. While small daily precipitation events contribute only 10% of the total precipitation in our dataset, it represents a third of water used by trees. In addition, while these ecosystems are designated as groundwater dependent ecosystems, the trees use approximately one third imported water and even more during dry summer months. This approach provides water managers with a practical tool for quantifying ecosystem water needs, supporting data-driven decisions and regulatory compliance. While California's Sustainable Groundwater Management Act emphasizes supporting groundwater dependent ecosystems, it allows flexibility in demonstrating benefits. In conclusion, our methodology provides a way to document that management actions (such as managed aquifer recharge with imported water) deliver measurable co-benefits to GDEs.

Geosciences↗