  A comprehensive understanding of the behaviours of the various geophysical
processes and an effective evaluation of time series (else referred to as
"stochastic") simulation models require, among others, detailed investigations
across temporal scales. In this work, we propose a novel and detailed
methodological framework for advancing and enriching such investigations in a
hydroclimatic context. This specific framework is primarily based on a new
feature compilation for multi-scale hydroclimatic analyses, and can facilitate
largely interpretable feature investigations and comparisons in terms of
temporal dependence, temporal variation, "forecastability", lumpiness,
stability, nonlinearity (and linearity), trends, spikiness, curvature and
seasonality. Multifaceted characterizations are herein obtained by computing
the values of the proposed feature compilation across nine temporal resolutions
(i.e., the 1-day, 2-day, 3-day, 7-day, 0.5-month, 1-month, 2-month, 3-month and
6-month ones) and three hydroclimatic time series types (i.e., temperature,
precipitation and streamflow) for 34-year-long time series records originating
from 511 geographical locations across the contiguous United States. Based on
the acquired information and knowledge, similarities and differences between
the examined time series types with respect to the evolution patterns
characterizing their feature values with increasing (or decreasing) temporal
resolution are identified. Moreover, the computed features are used as inputs
to unsupervised random forests for detecting any meaningful clusters between
the examined hydroclimatic time series. This clustering plays an illustrative
role within this research, as it facilitates the identification of spatial
patterns (with them consisting an important scientific target in hydroclimatic
research) and their cross-scale comparison...
