Statistical characterisation of water vapour variability in the troposphere

Tropospheric water vapour plays an important role in thermodynamic
and radiative processes which have an immediate impact on the
weather and climate system. However, the processes that determine
the distribution of water vapour remain poorly understood. The
complexity arises out of a range of source and sink processes from
convective clouds on the kilometre scale to cloud systems
associated with motions on scales of a thousand or more kilometres,
as well as advection of water vapour as a passive tracer outside of
clouds. While large-scale advection of water vapour is well
represented in general circulation models, the simulation of
small-scale moist processes that are of central importance to the
representation of clouds are heavily dependent on
parameterisations. However, observations as well as processes that
determine the distribution of the water vapour field are
insufficiently explored, leading to constrained parameterisations
and therefore contributing significantly to the uncertainty of
numerical weather and climate predictions. Hence, a more accurate
description of the inhomogeneous water vapour field based on
high-resolution observations is required. This thesis investigates
a comprehensive data set of two-dimensional airborne water vapour
observations in the free troposphere collected by a Differential
Absorption Lidar (DIAL) in order to gain a height-resolved
statistical characterisation of the inhomogeneous water vapour
field. Structure functions, i.e., statistical moments up to the
fifth order of absolute increments over a range of scales, are
investigated and power-law behaviour or scale dependence is
identified over horizontal distances from about 5~km to 100~km. The
slope of the power-law fit, the so-called scaling exponent, is
found to take different values, depending on whether or not the
observations were taken in an air mass where convective clouds were
present. These results are consistent with a non-convective regime
that is dominated by large-scale advective processes, leading to
monofractal scaling, but strong localised input of small-scale
variability by convective circulations leading to intermittent
fields. Further, the observed power-law statistics are used to
evaluate the high-resolution numerical weather prediction model
COSMO-DE of the German weather service with regard to the
small-scale water vapour variability. The results of the scaling
exponent analysis of cloud-free and partly cloudy scenes suggest,
that the small-scale variance is modeled quite well in comparison
with the lidar observations. By using the advantage of the model
simulation where data is not limited to a specific flight path, the
influence of sampling limitation is estimated and is found to be
not significant. Further, the simulation provides humidity data in
and beneath clouds which allows for an estimation of the
uncertainty of data gaps in the lidar observations due to optically
thick clouds. The error is identified to be in a range of only few
percents. This thesis demonstrates that airborne DIAL observations
are useful to build up a height-resolved statistical
characterisation of tropospheric water vapour variability that
allows to distinguish physical mechansims that are responsible for
the water vapour distribution, to get new insights into stochastic
parameterisations and further to use the structure function method
as a suitable reality check of the numerical weather model
COSMO-DE.