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Description: Lake systems are important paleoclimate archives that preserve ecosystem and hydrologic responses to critical periods in Earth history, such as carbon cycle perturbations and glacial-interglacial cycles. Geochemical measurements of biogenic carbonate (for example, δ18O, δ13C, 87Sr/86Sr, [Li], [U], [Sr], and [Mg]) are indicators of hydrologic variability in lake systems throughout the geologic record. In this study, we present a new closed-basin lake modeling approach, HyBIM (the Hydrologic Balance Inverse Model), that employs a system of total differential equations and uses the measured δ18O, Sr/Ca, and Mg/Ca of biogenic carbonate to determine changes in temperature, runoff, and lake evaporation. Using equally-spaced time steps, these equations are simultaneously solved to constrain the hydrologic parameters of the lake as recorded in biogenic carbonate. We use a Monte Carlo approach to account for uncertainty in the input parameters, such as δ18O temperature relationships, partition coefficient uncertainty, and watershed solute chemistry. For illustrative purposes, we apply the model to two ostracod valve datasets covering different timescales: (1) the Cretaceous Songliao Basin, northeast China, and (2) Holocene Lake Miragoane, Haiti. Modern water measurements of water isotopes and cation concentrations from each location are required as model inputs. We compare our modeling results with author interpretations and geologic observations. The modeling approach presented in this study can be applied to other closed-basin lake records, can be modified for other calcifying species (for example, gastropods or mollusks) or with calibration to inorganic lacustrine carbonate. In addition, this approach holds promise for extension with additional proxy measurements (that is, δD, U/Ca or Li/Ca) and changing source area on tectonic timescales using proxies that reflect changing source lithology (that is, Sr and Pb isotopes). Future incorporation of age model uncertainty in the Monte Carlo approach will also provide utility by quantifying temporal uncertainty on the hydrologic response recorded by lake sediments.