Signatures of warm carbon monoxide in protoplanetary discs observed with
  Herschel SPIRE
  Molecular gas constitutes the dominant mass component of protoplanetary
discs. To date, these sources have not been studied comprehensively at the
longest far-infrared and shortest submillimetre wavelengths. This paper
presents Herschel SPIRE FTS spectroscopic observations toward 18 protoplanetary
discs, covering the entire 450-1540 GHz (666-195 $\mu$m) range at R~400-1300.
The spectra reveal clear detections of the dust continuum and, in six targets,
a significant amount of spectral line emission primarily attributable to
$^{12}$CO rotational lines. Other targets exhibit little to no detectable
spectral lines. Low signal-to-noise detections also include signatures from
$^{13}$CO, [CI] and HCN. For completeness, we present upper limits of
non-detected lines in all targets, including low-energy transitions of H2O and
CH$^+$ molecules. The ten $^{12}$CO lines that fall within the SPIRE FTS bands
trace energy levels of ~50-500 K. Combined with lower and higher energy lines
from the literature, we compare the CO rotational line energy distribution with
detailed physical-chemical models, for sources where these are available and
published. Our 13CO line detections in the disc around Herbig Be star HD 100546
exceed, by factors of ~10-30, the values predicted by a model that matches a
wealth of other observational constraints, including the SPIRE $^{12}$CO
ladder. To explain the observed $^{12}$CO/$^{13}$CO ratio, it may be necessary
to consider the combined effects of optical depth and isotope selective
(photo)chemical processes. Considering the full sample of 18 objects, we find
that the strongest line emission is observed in discs around Herbig Ae/Be
stars, although not all show line emission. In addition, two of the six T Tauri
objects exhibit detectable $^{12}$CO lines in the SPIRE range.
