  Some properties of chaotic dynamical systems can be probed through features
of recurrences, also called analogs. In practice, analogs are nearest
neighbours of the state of a system, taken from a large database called the
catalog. Analogs have been used in many atmospheric applications including
forecasts, downscaling, predictability estimation, and attribution of extreme
events. The distances of the analogs to the target state condition the
performances of analog applications. These distances can be viewed as random
variables, and their probability distributions can be related to the catalog
size and properties of the system at stake. A few studies have focused on the
first moments of return time statistics for the best analog, fixing an
objective of maximum distance from this analog to the target state. However,
for practical use and to reduce estimation variance, applications usually
require not just one, but many analogs. In this paper, we evaluate from a
theoretical standpoint and with numerical experiments the probability
distributions of the $K$-best analog-to-target distances. We show that
dimensionality plays a role on the size of the catalog needed to find good
analogs, and also on the relative means and variances of the $K$-best analogs.
Our results are based on recently developed tools from dynamical systems
theory. These findings are illustrated with numerical simulations of a
well-known chaotic dynamical system and on 10m-wind reanalysis data in
north-west France. A practical application of our derivations for the purpose
of objective-based dimension reduction is shown using the same reanalysis data.
