  Using large-scale parallel numerical simulations we explore spatiotemporal
chaos in Rayleigh-B\'enard convection in a cylindrical domain with
experimentally relevant boundary conditions. We use the variation of the
spectrum of Lyapunov exponents and the leading order Lyapunov vector with
system parameters to quantify states of high-dimensional chaos in fluid
convection. We explore the relationship between the time dynamics of the
spectrum of Lyapunov exponents and the pattern dynamics. For chaotic dynamics
we find that all of the Lyapunov exponents are positively correlated with the
leading order Lyapunov exponent and we quantify the details of their response
to the dynamics of defects. The leading order Lyapunov vector is used to
identify topological features of the fluid patterns that contribute
significantly to the chaotic dynamics. Our results show a transition from
boundary dominated dynamics to bulk dominated dynamics as the system size is
increased. The spectrum of Lyapunov exponents is used to compute the variation
of the fractal dimension with system parameters to quantify how the underlying
high-dimensional strange attractor accommodates a range of different chaotic
dynamics.
