In this Supplementary Information document, we:1. Illustrate our firn densification correction for converting volume change to mass change.2. Describe our treatment of grounded subaqueous ice.3. Present the datasets we use to estimate temperature and precipitation on Svalbard (1936Svalbard ( -2010.4. Show the relationships between ∆h/∆t and climate parameters such as mean annual temperature, positive degree days, and total precipitation.5. Compare our results to literature estimates of historical and future glacier change on Svalbard.Note that our 1936/1938 models, including 5 meter resolution orthophotomosaics and digital elevation models (DEMs), and a vector shapefile containing outlines and attributes of the 1,888 glaciers on Svalbard, is available on the Norwegian Polar Institute (NPI) website (https: // publicdatasets. data. npolar. no/ ) and on Zenodo (https: // doi. org/ 10. 5281/ zenodo. 5644415 ). The DEMs and orthophotomosaics are divided into the 8 regions in Main text, Fig. 1d, and represent the unprocessed SfM output-i.e., before the co-registration procedure of Nuth & Kääb ( 2011) is applied to each glacier basin individually. We also provide the raw 3D point clouds as .laz files and an .xlsx file with the glacier-by-glacier statistics of area, volume, ∆h/∆t, ∆M/∆t, mean summer temperature, total solid precipitation, etc.

Satellite imagery offers an efficient and cost‐effective means of estimating water depth in shallow environments. However, traditional empirical algorithms for calculating water depth often are unable to account for varying bottom reflectance, and therefore yield biased estimates for certain benthic environments. We present a simple method that is grounded in the physics of radiative transfer in seawater, but made more robust through the calibration of individual color‐to‐depth relationships for separate spectral classes. Our cluster‐based regression (CBR) algorithm, applied to a portion of the Great Bahama Bank, drastically reduces the geographic structure in the residual and has a mean absolute error of 0.19 m with quantified uncertainties. Our CBR bathymetry is 3–5 times more accurate than existing models and outperforms machine learning protocols at extrapolating beyond the calibration data. Finally, we demonstrate how comparison of CBR with traditional models sensitive to bottom type reveals the characteristic length scales of biosedimentary facies belts.

In the past 3 billion years, significant volumes of carbonate with high carbon-isotopic (δ13C) values accumulated on shallow continental shelves. These deposits frequently are interpreted as records of elevated global organic carbon burial. However, through the stoichiometry of primary production, organic carbon burial releases a proportional amount of O2, predicting unrealistic rises in atmospheric pO2 during the 1 to 100 million year-long positive δ13C excursions that punctuate the geological record. This carbon–oxygen paradox assumes that the δ13C of shallow water carbonates reflects the δ13C of global seawater-dissolved inorganic carbon (DIC). However, the δ13C of modern shallow-water carbonate sediment is higher than expected for calcite or aragonite precipitating from seawater. We explain elevated δ13C in shallow carbonates with a diurnal carbon cycle engine, where daily transfer of carbon between organic and inorganic reservoirs forces coupled changes in carbonate saturation (ΩA) and δ13C of DIC. This engine maintains a carbon-cycle hysteresis that is most amplified in shallow, sluggishly mixed waters with high rates of photosynthesis, and provides a simple mechanism for the observed δ13C-decoupling between global seawater DIC and shallow carbonate, without burying organic matter or generating O2.

Carbonate mud represents one of the most important geochemical archives for reconstructing ancient climatic, environmental, and evolutionary change from the rock record. Mud also represents a major sink in the global carbon cycle. Yet, there remains no consensus about how and where carbonate mud is formed. Here, we present stable isotope and trace-element data from carbonate constituents in the Bahamas, including ooids, corals, foraminifera, and algae. We use geochemical fingerprinting to demonstrate that carbonate mud cannot be sourced from the abrasion and mixture of any combination of these macroscopic grains. Instead, an inverse Bayesian mixing model requires the presence of an additional aragonite source. We posit that this source represents a direct seawater precipitate. We use geological and geochemical data to show that “whitings” are unlikely to be the dominant source of this precipitate and, instead, present a model for mud precipitation on the bank margins that can explain the geographical distribution, clumped-isotope thermometry, and stable isotope signature of carbonate mud. Next, we address the enigma of why mud and ooids are so abundant in the Bahamas, yet so rare in the rest of the world: Mediterranean outflow feeds the Bahamas with the most alkaline waters in the modern ocean (>99.7th-percentile). Such high alkalinity appears to be a prerequisite for the nonskeletal carbonate factory because, when Mediterranean outflow was reduced in the Miocene, Bahamian carbonate export ceased for 3-million-years. Finally, we show how shutting off and turning on the shallow carbonate factory can send ripples through the global climate system.