Contemporaneously growing speleothems and their value to decipher in-cave processes

<p>Speleothems have been developed to be valuable climate archives. Albeit much progress has been made to understand speleothem proxies, it remains difficult to differentiate between a direct climate signal and variations, which occurred due to in-cave processes like prior calcite precipitation, CO<sub>2</sub> degassing or C exchange between dissolved inorganic C-species and cave air CO<sub>2</sub>. Here, we analyse palaeoclimate proxies of contemporaneously growing speleothems, which were extracted from the SISALv2 database (Comas-Bru et al., 2020). We argue that differences in their stable O and C isotopic composition as well as in their growth rate can only arise by differences of drip site specific conditions as climate conditions for pairs of contemporaneously growing speleothems are similar. To better understand differences in the isotopic composition and growth rate of contemporaneously growing speleothems, we investigate the in-cave processes by applying a speleothem isotope and growth model. The model is based on a Rayleigh process, which includes CO<sub>2</sub> degassing and CaCO<sub>3</sub> precipitation, HCO<sub>3</sub><sup>-</sup> <—> H<sub>2</sub>O buffering as well as CO<sub>2</sub> exchange and is able to calculate growth rates. The model accounts for CaCO<sub>3</sub> deposition as prior calcite precipitation as well as CaCO<sub>3</sub> deposition at the speleothem. We find that C-exchange processes are necessary to explain the linked isotopic and growth rate differences in speleothems.</p><p> </p><p><strong>References</strong></p><p>Comas-Bru, L., Atsawawaranunt, K., Harrison, S., SISAL working group members (2020): SISAL (Speleothem Isotopes Synthesis and AnaLysis Working Group) database version 2.0. University Of Reading.</p>

GENERALIZED RAYLEIGH AND JACOBI PROCESSES AND EXCEPTIONAL ORTHOGONAL POLYNOMIALS

We present four types of infinitely many exactly solvable Fokker–Planck equations, which are related to the newly discovered exceptional orthogonal polynomials. They represent the deformed versions of the Rayleigh process and the Jacobi process.

Some remarks on the Rayleigh process

The transition p.d.f. for a one-dimensional Rayleigh process in the presence of an absorption condition or a zero-flux condition in the origin is obtained in closed form. The first-passage-time problem through an arbitrary constant boundary is then considered and the moment-generating function is determined. In some particular cases the first-passage-time p.d.f. is explicitly derived. Use of some of these results is finally made to obtain the transition p.d.f. of the affine drift-linear infinitesimal-variance diffusion process when the origin is an entrance or a regular boundary in the presence of a reflection condition.

Some remarks on the Rayleigh process

The transition p.d.f. for a one-dimensional Rayleigh process in the presence of an absorption condition or a zero-flux condition in the origin is obtained in closed form. The first-passage-time problem through an arbitrary constant boundary is then considered and the moment-generating function is determined. In some particular cases the first-passage-time p.d.f. is explicitly derived. Use of some of these results is finally made to obtain the transition p.d.f. of the affine drift-linear infinitesimal-variance diffusion process when the origin is an entrance or a regular boundary in the presence of a reflection condition.