Model emulation to understand the joint effects of ice-nucleating particles and secondary ice production on deep convective anvil cirrus
Authors: Hawker Rachel E. , Miltenberger Annette K. , Johnson Jill S. , Wilkinson Jonathan M. , Hill Adrian A. , Shipway Ben J. , Field Paul R. , Murray Benjamin J. , Carslaw Ken S. 
Published: December 2021

Abstract. Ice crystal formation in the mixed-phase region of deep convective clouds can affect the properties of climatically important convectively generated
anvil clouds. Small ice crystals in the mixed-phase cloud region can be formed by heterogeneous ice nucleation by ice-nucleating particles (INPs) and
secondary ice production (SIP) by, for example, the Hallett–Mossop process. We quantify the effects of INP number concentration, the temperature
dependence of the INP number concentration at mixed-phase temperatures, and the Hallett–Mossop splinter production efficiency on the anvil of an
idealised deep convective cloud using a Latin hypercube sampling method, which allows optimal coverage of a multidimensional parameter space, and
statistical emulation, which allows us to identify interdependencies between the three uncertain inputs. Our results show that anvil ice crystal number concentration (ICNC) is determined predominately by INP number concentration, with the temperature
dependence of ice-nucleating aerosol activity having a secondary role. Conversely, anvil ice crystal size is determined predominately by the
temperature dependence of ice-nucleating aerosol activity, with INP number concentration having a secondary role. This is because in our simulations
ICNC is predominately controlled by the number concentration of cloud droplets reaching the homogeneous freezing level which is in turn determined
by INP number concentrations at low temperatures. Ice crystal size, however, is more strongly affected by the amount of liquid available for riming
and the time available for deposition growth which is determined by INP number concentrations at higher temperatures. This work indicates that the
amount of ice particle production by the Hallett–Mossop process is determined jointly by the prescribed Hallett–Mossop splinter production
efficiency and the temperature dependence of ice-nucleating aerosol activity. In particular, our sampling of the joint parameter space shows that
high rates of SIP do not occur unless the INP parameterisation slope (the temperature dependence of the number concentration of particles which
nucleate ice) is shallow, regardless of the prescribed Hallett–Mossop splinter production efficiency. A shallow INP parameterisation
slope and consequently high ice particle production by the Hallett–Mossop process in our simulations leads to a sharp transition to a cloud with
extensive glaciation at warm temperatures, higher cloud updraughts, enhanced vertical mass flux, and condensate divergence at the outflow level, all of
which leads to a larger convectively generated anvil comprised of larger ice crystals. This work highlights the importance of quantifying the full
spectrum of INP number concentrations across all mixed-phase altitudes and the ways in which INP and SIP interact to control anvil properties.