## A01 - Coupling a multiscale stochastic precipitation model to large scale atmospheric flow dynamics

**Head(s):** Prof. Dr. Henning Rust (FU Berlin), PD Dr. Peter Névir (FU Berlin), Dr. Péter Koltai (FU Berlin)

**Project member(s):** Dr. Annette Müller, Robert Polzin, Christoph Ritschel

**Participating institution(s):** FU Berlin

### Project Summary

Aiming at the efficient modelling of large scales for climate change studies, the objectives of this project are (O1) to develop a small scale stochastic model for convective activity and (O2) to describe convective feedback on the large scale atmospheric flow. This leads to a hybrid model with a stochastic component for a conceptual description of convection embedded in a deterministic atmospheric flow model – a so-called stochastic parametrisation.

During the first phase, we implemented and refined a multi-level stochastic precipitation model. These Poisson-cluster-type models consist of a hierarchy of Poisson-processes on different scales. The “rain cell” at the smallest scale bears some resemblance to the stochastic massflow component of the Plant–Craig scheme – a stochastic parametrisation for convection. The next level introduces a relation between individual rain cells in terms of a clustering on the meso-scale. A potential driver to control these small scale models is the Dynamic State Index (DSI), an “adiabaticity indicator”. This concept has been analytically transferred from the atmospheric root model (“primitive equations”) to the quasi-geostrophic and Rossby approximation. The latter is insensitive to small-scale processes and thus well suited as a large-scale driver controlling the small-scale precipitation model.

For the second funding period we plan the following contributions to our objectives.

**(O1) Downward coupling: large-scale flow driving small-scale convection.**

- To overcome limitations of the Poisson-cluster process, we pursue two approaches: a) Feature identification and tracking from visual data analysis combined with coherent set analysis to obtain a conceptual description of convection using characterisations motivated by the Poisson-cluster model. b) Data-based methods for direct probabilistic modelling of categorised vertical mass flow.

- Development of further DSI variants as indicators for general thermodynamic processes. Together with other parameters related to moisture processes, these build the set of potential control variables for convective activity. ** (O2) Upward coupling: small-scale convective feedback to large-scale flow.**

- A model for cloud characteristics relevant for the feedback is learned from available largeeddy simulations with the help of coherent set analysis.

- A conceptual characterisation of convection with associated cloud properties is used in conjunction with purely data-based dynamics-learning techniques to directly assemble a quantitative feedback function driving the large scale evolution.

We pursue these aims by application and simultaneous development of coherent set analysis, further by utilising data-based identification and investigation of non-linear systems. Including Péter Koltai as new PI provides the required expertise in these fields.

### Project publications

Müller, A. and Névir, P. and Klein, R.
(2018)
*Scale Dependent Analytical Investigation of the Dynamic State Index Concerning the Quasi-Geostrophic Theory.*
Mathematics of Climate and Weather Forecasting, 4
(1).
pp. 1-22.
ISSN 2353-6438 (online)

Koltai, P. and Lie, Han Cheng and Plonka, M.
(2018)
*Fréchet differentiable drift dependence of Perron--Frobenius and Koopman operators for non-deterministic dynamics.*
SFB 1114 Preprint in arXiv:1805.06719
.
pp. 1-24.
(Submitted)

Fackeldey, K. and Koltai, P. and Névir, P. and Rust, H.W. and Schild, A and Weber, M.
(2017)
*From Metastable to Coherent Sets – time-discretization schemes.*
SFB 1114 Preprint
.
pp. 1-13.
(Unpublished)

Fischer, M. and Ulbrich, U. and Rust, H.W.
(2017)
*A spatial and seasonal climatology of extreme precipitation return-levels: A case study.*
Spatial Statistics
.
pp. 1-25.
(In Press)

Hittmeir, S. and Klein, R. and Müller, A. and Névir, P.
(2017)
*The Dynamic State Index with Moisture and Phase Changes.*
SFB 1114 Preprint
.
pp. 1-12.
(Unpublished)

Nissen, K.M. and Ulbrich, U.
(2017)
*Increasing frequencies and changing characteristics of heavy precipitation events threatening infrastructure in Europe under climate change.*
Nat. Hazards Earth Syst. Sci., 17
.
pp. 1177-1190.

Mazza, E. and Ulbrich, U. and Klein, R.
(2017)
*The Tropical Transition of the October 1996 Medicane in the Western Mediterranean Sea: A Warm Seclusion Event.*
Monthly Weather Review, 145
.
pp. 2575-2595.
ISSN Online: 1520-0493 Print: 0027-0644

Ritschel, C. and Rust, H.W. and Ulbrich, U.
(2017)
*Precipitation extremes on multiple time scales -- Bartlett-Lewis Rectangular Pulse Model and Intensity-Duration-Frequency curves.*
Hydrol. Earth Syst. Sci.
.
pp. 1-20.
(Submitted)

O'Kane, T.J. and Monselesan, D.P. and Risbey, J.S. and Horenko, I. and Franzke, Ch.L.E.
(2017)
*On memory, dimension, and atmospheric teleconnection patterns.*
Math. Clim. Weather Forecast, 3
(1).
pp. 1-27.

Horenko, I. and Gerber, S. and O'Kane, T.J. and Risbey, J.S. and Monselesan, D.P.
(2017)
*On inference and validation of causality relations in climate teleconnections.*
In:
Nonlinear and Stochastic Climate Dynamics.
Cambridge University Press, pp. 184-208.
ISBN 9781107118140

Hirt, M. and Schielicke, L. and Müller, A. and Névir, P.
(2017)
*Statistical and dynamical analyses of atmospheric blocking with an idealized point vortex model.*
Tellus A
.
pp. 1-22.
(Submitted)

Fischer, M. and Rust, H.W. and Ulbrich, U.
(2016)
*Seasonal Cycle in German Daily Precipitation Extremes.*
Meteorologische Zeitschrift
.
pp. 1-11.
ISSN 0941-2948
(Submitted)

Horenko, I. and Gerber, S.
(2015)
*Improving clustering by imposing network information.*
Science Advances, 1
(7).
ISSN 2375-2548

O’Kane, T.J. and Risbey, J.S. and Monselesan, D.P. and Horenko, I. and Franzke, Ch.L.E.
(2015)
*On the dynamics of persistent states and their secular trends in the waveguides of the Southern Hemisphere troposphere.*
Climate Dynamics
.
ISSN Print: 0930-7575, Online: 1432-0894