clouds and radiation using radarlidar synergy to evaluate and

to Evaluate and Improve Models.
Malcolm Edward Brooks
A thesis submitted for the degree of Doctor of Philosophy
February 2005
Declaration
I confirm that this is my own work and the use of all material from other sources has been
properly and fully acknowledged.
i
Abstract
The large uncertainties in the cloud and radiation schemes used in General Circulation Mod-
els (GCMs) means there is the potential for large compensating errors, hindering future model
development and undermining the ability of GCMs to represent the interaction between clouds
and radiation. This presents the largest single uncertainty in predictions of future climate
change, and creates the need to evaluate clouds in GCMs.
In this thesis, radar and lidar observations are used to produce a climatology of cloud
fraction (cv) and ice water content (IWC) which is compared with colocated profiles from the
ECMWF global and Met Office mesoscale operational forecast models. A system is devised to
categorise profiles by meteorological regime. After accounting for observational issues, we find
the Met Office model predicts the frequency of cloud occurrence very well but underestimates
the mean cv by up to a factor of two. The ECMWF forecasts of cv are excellent, although it
overpredicts the depth of low cloud.
This thesis presents the first climatology of IWC from long-term radar observations and
shows that both models agree with the observed IWC to within the errorbars of the retrieval.
Using a radiative transfer model it is found that radiative impact of the observed ice clouds and
those in the Met Office model are comparable, due to the large observational uncertainties.
Most GCMs define cloud fraction by volume and use the Maximum-Random overlap
assumption; this underestimates the total column cloudiness (TCC) by 10% on a typical GCM
grid, highlighting the need to represent the complex sub-grid and inter-grid scale arrangement
of cloud. A parameterisation scheme is proposed where the sub-grid scale processes are rep-
resented to produce cloud fraction defined by area, while the inter-grid scale processes are
represented by the proposed Adjacent Level Partially Random overlap assumption. Combining
these parameterisations removes the underestimate of TCC.
ii
Acknowledgements
I am deeply grateful to my supervisor, Anthony Illingworth, whose incredible knowledge of
radar has been enlightening to experience and whose continual support and encouragement has
been vital in completing this thesis. Thanks also to Keith Shine and Alan O’Neill for their
alway useful insights which have greatly helped the development of this thesis.
A huge thank you is due to the various members of the Radar group especially Robin
Hogan(ator) and Ewan O’Connor, who are available with a wealth of radar and computing
information at their fingertips, combined with an easygoing manner, a sense of humour and
a taste for the occasional curry. Many thanks in general go to all the other PhD students at
Reading for providing all the necessary distractions to make a PhD last as long as this one has,
and generally making the Department such a good place to be.
I would also like to thank my Family for their continued, if often bemused, support, but
most of all I would like to thank my wife, Jacqueline, simply for putting up with Reading in
order for me to pursue my cloud obsession over the years - thank you for that.
Specific thanks go to all of the staff at RAL and Chilbolton for the observations which
have made this thesis possible, with specific thanks to: John Goddard, John Eastment, Charles
Wrench, Darcy Ladd and Charles Kilburn (with an extra appreciation of his excellent shopping
trolley control skills). Thanks also to those in the modelling community who have provided
their invaluable thoughts and even more invaluable data; Pete Clarke, Damian Wilson, Rich
Forbes, Adrian Tompkins and Christian Jakob. This research was funded by NERC, so thanks
to them as well.
Finally a general thanks to the CloudNet community; to the locus publicus!
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iv
Contents
1.3 This Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 The Representation of Cloud and Precipitation in GCMs 13
2.1 Model Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.2 ECMWF Operational Model . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Model Spin-Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1 Active Remote Sensing Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.1 Basic Principles of Radar . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.2 IWC Retrieval from Radar Z . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.3 Basic Principles of Lidar . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Instrumentation at Chilbolton . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2.1 Calibration of Broad Band Radiometers . . . . . . . . . . . . . . . . . 33
3.3 Retrieving Model Comparable Parameters . . . . . . . . . . . . . . . . . . . . 34
4 Radiative Transfer Modelling 38
4.1 The Edwards and Slingo Radiation Code . . . . . . . . . . . . . . . . . . . . . 38
4.2 Sensitivity Tests with the ES96 . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Blind Tests of EarthCARE retrievals . . . . . . . . . . . . . . . . . . . . . . . 49
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2.2 Mean Ice Water Content . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3 Problems with the Initial Comparisons . . . . . . . . . . . . . . . . . . . . . . 62
5.3.1 Error Characteristics of Cloud Fraction Means . . . . . . . . . . . . . 62
5.3.2 Assumptions Regarding Cloud Depth . . . . . . . . . . . . . . . . . . 63
5.3.3 Sampling Biases from Excluding Rain Events . . . . . . . . . . . . . . 64
5.3.4 Unobservable Cirrus . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.4 Comparing Observations with the Modified Model Data . . . . . . . . . . . . . 68
5.4.1 Mean Ice Water Content . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.4.2 Summer and Winter Comparison, ECMWF Model Changes . . . . . . 73
5.4.3 Correlations between Observed and Model Cloud Fractions . . . . . . 75
5.4.4 Distributions of Cloud Fraction and IWC. . . . . . . . . . . . . . . . . 76
5.4.5 Total Column Cloudiness . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.3.1 Long-Wave Emissivity . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.4.1 Cloud Fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
CONTENTS vii
7 The Definition of Cloud Fraction by Area and by Volume 137
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.3 Evaluating Cloud Fraction by Area and Volume . . . . . . . . . . . . . . . . . 141
7.4 Parameterising Cloud Fraction by Area . . . . . . . . . . . . . . . . . . . . . 144
7.5 Evaluation of the cv to ca Parameterisations . . . . . . . . . . . . . . . . . . . 150
7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
8.3 Biases in Current Overlap Assumptions . . . . . . . . . . . . . . . . . . . . . 163
8.3.1 Combined Biases from the Area/Volume Distinction and Overlap . . . 167
8.4 Parameterising Cloud Overlap . . . . . . . . . . . . . . . . . . . . . . . . . . 168
8.5 Evaluating the ALPR overlap Parameterisation . . . . . . . . . . . . . . . . . 172
8.5.1 Combining the Cloud Volume to Area Parameterisation, with ALPR
Overlap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Motivation
The representation of clouds in General Circulation Models (GCMs) is one of the major uncer-
tainties in current predictions of the future climate, due to the effect of clouds on the radiation
budget. The net effect of clouds on climate is a complex balance of the effects of scattering
of solar radiation and the absorption and emission of terrestrial radiation. Uncertainty in the
representation of clouds in GCMs is one of the major causes of the broad spread of predicted
future climate change through the complexity of the cloud-climate feedbacks. (Mitchell (2004),
Mitchell (2000), Stocker (2001)).
The magnitude of the impact that clouds can have on the climate system was shown
by Slingo (1990) who demonstrated in a GCM that the warming caused by the doubling of
atmospheric CO2 could be balanced by either an increase in the amount of low clouds or by
changes in the cloud droplet size distribution. Specifically a 15-20% increase in the cloud
amount of low clouds or a 20-35% increase in their water content was required to balance the
doubling of CO2, as was a 15-20% decrease in the effective radius (a radiative measure of the
“average” size the cloud droplets) of low clouds.
While the study of Slingo (1990) is a demonstration of the possible impacts of a cloud-
climate interaction, it is not in any way an estimate of the actual interactions, and the magnitude
and complexity of the cloud-climate interactions makes the estimation of these feedbacks very
difficult. A comparison of the cloud-climate feedbacks occurring in 19 different GCMs, by
Cess et al. (1990), found that when the spatial distribution of clouds is allowed to vary the
effect of temperature increases on the clouds in most models produced further temperature
increases i.e. the changes in clouds formed a positive feedback.
Analysis by Mitchell and Ingram (1992) describes the additional warming from cloud-
1
climate interactions as occurring by the temperature increases increasing the depth of vertical
motion in the atmosphere. This raises the tropopause and cirrus clouds to colder temperatures
(so the cirrus clouds emit less radiation to space) and also reduces the relative humidity and
cloud cover below, so reducing the planetary albedo. However, both the climate model compar-
isons of Arking (1991) and Cess et al. (1990) found that, by including variations of the cloud
optical properties, the cloud-climate feedbacks can vary greatly in both magnitude and sign.
In a more recent study Cess et al. (1996) recompared the same 19 GCMs to examine the
effect of the continual improvements which had been made and found that both the magnitude
and variability of the cloud-climate interactions had reduced, although it remained generally
positive. There remained, however, considerable variation between the models as to the bal-
ance between the effects of clouds on the solar shortwave (SW) and terrestrial longwave (LW)
radiation implying that, although the models were more in agreement, each model was arriving
at this agreement through a different balance between the SW and LW components.
These differences in the balances between different cloud feedback processes are, at least
in part, due to the large variations in the amount of cloud which these models produce. These
differences were quantified as part of the Atmospheric Model Intercomparison Project (AMIP)
described by Gates et al. (1999) who have compared the simulations of the climate between
1979-88 as produced by 24 different GCMs. In general, it was found that there was good
agreement between the large scale structures of the atmosphere, as predicted by the different
models, however the total cloudiness was found to vary hugely from model to model. The
errors in the distribution of cloud are being balanced by compensating errors in the radiation
calculations.
While this balance of errors enables the GCMs to produce a good description of the
current climate, the correct simulation of the mean distribution of cloud cover and the radiative
fluxes is a necessary, but by no means sufficient, test of a model’s ability to handle realistically
the cloud feedback processes relevant for climate change (Stocker (2001)). The substantial
disagreements between the distributions of cloud in the AMIP GCMs and the observed cloud
climatology suggests that the present generation of climate models fail this test.
Although this thesis will concentrate on the radiative impact of clouds, the importance
of the latent heat released by condensation plays a vital role in the development of all cloud
systems, from the smallest convective cloud to tropical and extratropical cyclones. The impor-
CHAPTER 1: Motivation 3
tance of representing the latent heat of condensation in GCMs has been known since Manabe
(1956) and the importance of ice sublimation in cloud dynamics stressed since Harris (1977).
Furthermore, an appropriate representation of clouds is a vital component in the prediction
of precipitation, which is one of the major aims in any Numerical Weather Prediction (NWP)
model.
In order to establish what is an appropriate distribution of cloud that a GCM or NWP
model should be able to reproduce, some cloud climatologies will be examined in section 1.1.
As this thesis will make extensive use of observations of cloud at the Chilbolton site, in Hamp-
shire, UK, this discussion will focus on the distribution of cloud over the UK and in the North-
ern Hemisphere in general. Following this, in section 1.2, we shall discuss how the fluxes of
radiation are calculated within a GCM, with particular reference to the uncertainties regarding
the representation of clouds in the radiation parameterisations.
1.1 Cloud Climatologies
Much work has been done in examining the distribution of clouds from satellite observations.
For example the International Satellite Cloud Climatology Project (ISCCP) has produced a
global cloud climatology from satellite radiances, as described by Rossow and Schiffer (1999).
The ISCCP global distribution of mean cloud amount, or total column cloudiness, between
1983 and 2001 is shown in Fig. 1.1. Total column cloudiness (TCC) is defined as the proportion
of the area viewed from space covered by any form of cloud at any height. The distribution of
cloud over the globe is far from uniform, with a maxima running around the equator and the
Indian Ocean due to tropical deep convective events and a second maxima in the extratropical
storm track regions between 40 and 60 north and south, over the oceans. There are distinct
cloud minima in the subtropics, with the exception of the stratocumulus regions on the western
coasts of South America and Africa. The global mean TCC is found to be 69%, while this rises
to a mean value of 72% over the northern midlatitudes.
This compares very well with more traditional observations presented by Warren et al.
(1986) who compiled global surface synoptic cloud observations over land during the period of
1971-1981 and who found that over the UK the mean TCC was 71%. This mean TCC shows
a degree of seasonal variation giving a peak TCC of 76% in the months of December, January,
Figure 1.1: ISCCP D2 total cloud
February, and a minimum of 69% during the months of March to August. With observations
restricted to surface observing sites (and ships with observers in the later work of Warren et al.
(1988)) such observations are difficult to analyse to give global or hemispheric mean values.
By comparison, as part of the Atmospheric Model Intercomparison Project (AMIP) Gates
et al. (1999) compared total cloud amount in 24 global climate models and found the mean
TCC to vary from just over 20% to 90% in northern midlatitudes.
By slightly improving the vertical resolution and sensitivity with which the satellite ob-
servations are analysed, Rossow and Schiffer (1999) shows mean cloud amounts (TCC) for
high clouds (pressure < 440 hPa) is 25%, mid-level cloud at 23%, and low clouds (pressure
> 680 hPa) at 24% coverage. Weare and the AMIP Modelling Groups (1996) compared the
zonally averaged amounts of high and low cloud in the AMIP models, bearing in mind the
improvements made to the ISCCP data in Rossow and Schiffer (1999). They showed that in
northern midlatitudes the zonal mean of high cloudiness is 25% in the observations and 10 to
20% in the models, while the AMIP zonal means of low cloudiness generally agree with the
modified ISCCP observations with a margin -10 to +30%. Out of all of the models discussed
the ECMWF model is one of the better performing models, while the Met Office Unified Model
is not discussed in this paper.
Cloud climatologies with better vertical resolution require the use of active sensors. Us-
ing vertically pointing lidar observations at the University of Utah, Sassen and Campbell (2001)
gives a detailed description of cirrus clouds that were observed. Unfortunately the inability of
lidar to penetrate lower cloud precludes the use of a lidar only retrieval of cloud properties for
a comparison with a GCM. Hogan et al. (2001) used three months of vertically pointing cloud
radar and lidar data at Chilbolton to produce a climatology of observed cloud fraction, with suf-
ficient vertical resolution that a direct comparison with a GCM is possible for the Chilbolton
site.
1.2 Radiative Transfer Models in GCMs
The calculation of the radiative fluxes through the atmosphere is a crucial and challenging com-
ponent of any atmospheric model. A GCM requires a representation of cloud properties on the
grid-box scale, and typically a GCM will have some representation of cloud water content and
cloud fraction (which is the proportion of a grid-box which contains cloud either by volume
(cv) or by area (ca)). The effect of the clouds on the radiative fluxes will therefore need to
be parameterised in terms of these variables, which means that a large number of assumptions
must be made. A requirement of any radiation parameterisation is that it provides a suitable de-
scription of the radiation budgets at the surface and the top of the atmosphere (TOA), while the
heating rates throughout the atmosphere are determined by divergence of the radiative fluxes.
Methods for computing the radiative fluxes have developed considerably since the fluxes
were tabulated by Brooks (1950). In order to produce an estimate of these parameters, with the
degree of accuracy approaching that which is required in an NWP model, the parameterisation
must include the effects of absorption and scattering by the most radiatively important gases;
water vapour, CO2 and O3, as well ice and liquid water clouds, while the introduction of other
trace gases and aerosols may be required for a greater degree of accuracy.
The main problem for the calculation of the radiative fluxes is that the atmosphere in a
GCM is not specified in terms of the atmosphere’s optical properties, and so these must be
determined from the parameters which are (or can be) readily supplied by the GCM (Stephens
(1984)). However, the need for accuracy must always be balanced against the need for com-
putational speed - the radiation calculations are usually the most computationally expensive
component of a GCM - and this implies that a high degree of approximation will often be
required.
In a GCM the calculation of the radiative fluxes is treated as a nested set of four integrals
(Stephens (1984)). Firstly the radiative fluxes must be considered over all wavelengths that
are active. This integration is performed by splitting the spectrum into a number of pseudo-
monochromatic spectral bands and calculating the optical properties and fluxes individually for
each band.
The optical properties of the atmosphere vary considerably with height due to the large
variations in temperature and the abundance of water vapour, O3 and clouds. In order to inte-
grate over the height of the atmosphere it is divided into levels and the scattering, absorption
and emission of radiation are determined within each level - in a GCM these would typically be
model levels. If a two stream approximation is made this integration is split into two streams of
radiation with one stream starting at the initial source of the radiation, and a second stream for
reflected/re-emitted radiation. For shortwave radiation this starts at the top of the atmosphere
working downward and then back up again, and vice-versa for the longwave flux calculations.
Within each layer radiation passes along all zenith angles. One method of integrating
along all zenith angles is that of Zdunkowski et al. (1982) who showed that this can be ap-
proximated by assuming that the flux of radiation passing through a slab can be represented
by the passage of a single beam of radiation along a representative zenith angle, often repre-
sented by multiplying optical properties of the layer by a “diffusivity factor” often taken to be
1.66, which is equivalent to a representative angle of roughly 53 (Stephens (1984)). The exact
method of solving this integral can vary depending on the approximation that has been made
(see Zdunkowski et al. (1980)).
Therefore, for each spectral band and at each model level the extinction, scattering and
absorption of radiation must be calculated along the path of this single representative beam (this
is the final integral). This is in itself a simple calculation, depending on the optical properties
of each layer.
The optical depth of each layer (τ) determines the reduction in the intensity of the radia-
tion (I) over the path of the beam through the layer.
I I0
= exp(−τ) or τ = −κext ρs , (1.1)
which can also be expressed in terms of is the mass extinction coefficient (κext ), where ρ is the
density of the medium and s the path length (the depth of the level multiplied by the “diffusivity
factor” as described above).
Once the amount of scattered/absorbed radiation is determined (I0 − I), the single scat-
tering albedo (ω0) determines the proportion of this radiation which is absorbed and how much
is scattered. An ω0 = 1 indicates a fully scattering medium, while an ω0 = 0 indicates a fully
absorbing medium.
Given that in this system of equations there are two directions, forwards and backwards
along the beam, all that remains to calculate the fluxes at both ends of the beam is the asym-
metry parameter (g). If g has a value of -1 then all the radiation is scattered in the backward
direction and if the value is 1 then all the radiation is scattered in the forward direction.
The calculation of the radiative fluxes therefore becomes an issue of parameterising κext ,
ω0 and g as functions of the parameters known on the model grid, with the boundary conditions
of incoming solar radiation at the top of the atmosphere and suitable surface properties. The
longwave calculations are slightly complicated by the addition of a Planck function to repre-
sent the emission of longwave radiation both at the surface and within each layer, where the
emissivity ε must also be determined.
While the optical properties of clear air are relatively easy to parameterise from the
known properties of the gases which make up its constituents, determining the optical proper-
ties of clouds is not as easy. Indeed Vogelmann and Ackerman (1995) found that the calculation
of downwelling shortwave flux at the surface (DSFs f c) below optically thick cirrus was partic-
ularly sensitive to g, to the extent that to calculate DSFs f c to within 5% required an accuracy of
g better than could be obtained from direct observations. As the optical properties of ice and
water clouds are so different, they are treated separately.
The optical properties of clouds are typically specified as a function of some measure
of the cloud particle size distribution. One commonly used measure is the effective radius, re,
which is defined as
n(r)r3dr R
n(r)r2dr (1.2)
where r is cloud particle radius and n(r)dD is the number concentration of droplets in the range
r to r + dr.
In general, increasing re will mean larger cloud particles so that, for a given mass of
condensate, there are fewer cloud particles and so a smaller extinction coefficient and a decrease
in the effect of clouds on the atmosphere. This is the mechanism for much of the cloud-climate
interactions discussed in papers such as Slingo (1990), Stephens et al. (1990) and Ou and Liou
(1995) which were discussed at the beginning of this chapter. It should be remembered that the
cloud particle size distribution is not a term which is directly calculated by a GCM, so it itself
must be parameterised, so adding a further level of uncertainty to the physical basis of radiative
transfer calculations used in GCMs.
There are a large number of parameterisation schemes in the literature for obtaining the
optical properties of clouds and for the purpose of this thesis it is not necessary to describe
any of them in detail. The common process used in most parameterisations is to make some
physical assumptions about the cloud particles and what determines the optical properties of an
individual cloud particle. These assumptions are then integrated over a set of (often observed)
particle size distributions to give mean values of the optical properties which can then be fitted
to the parameter of choice.
For water clouds this is relatively straight forward, as Mie theory can describe the optical
properties of spherical droplets with the required accuracy. As examples, this approach is
adopted in Slingo and Schrecker (1982), Slingo (1989) and Savijarvi et al. (1997).
For ice clouds assumptions must also be made about either the crystal habit or density
of the air-ice mixture (a specification of density is an implicit assumption of the crystal habit),
although there is considerable uncertainty in what is an appropriate choice. It is likely that there
is considerable variation in the size and shape which is appropriate to represent different clouds
across the globe, with tropical anvils containing smaller crystals (which were best described as
planar-polycrystals) than mid-latitude cirrus which contain larger, more columnar and dendritic
crystals (Mitchell and Arnott (1994) and Mitchell et al. (2004)).
The optical properties are then calculated for each crystal within a size distribution us-
ing methods such as Mie theory, Ray tracing using geometric optics or Anomalous Diffraction
Theory. For example Fu (1996) performed Geometric ray tracing calculations on ice particles
described by size distributions observed by flights in the FIRE campaign (Starr (1987)), assum-
ing hexagonal ice crystals which were randomly oriented in space. Mie theory was not used
as, after a series of observing campaigns in the late 1980s, it is generally regarded that Mie
theory does not adequately describe the shortwave (SW) properties of ice due to the complex
shapes or “habits” which ice crystals can form. Conversely Fu et al. (1999) shows that Mie
theory provides a good description of the long wave (LW) properties of ice clouds when the
assumptions about crystal habit conserve area and volume. This is analogous to the “equivalent
area” assumption made when calculating the optical properties of ice at radar wavelengths in
section 3.1.2.
The optical properties of a cirrus cloud may well be determined from the sort of assump-
tions discussed above, using in-situ observations of the size distribution, and applying these
assumptions within a radiative transfer model can often produce fluxes which compare well
with in-situ radiative observations, (e.g. Francis et al. (1994)) but the fact remains that GCMs
need to generalise the size distributions in some simple way. The variations of optical proper-
ties from cloud to cloud are not going to be adequately described in a GCM, and in effect the
optical and size parameterisations that are used in a GCM are those which will give the best
representation over all clouds. It is likely that this balance is due to a set of compensating errors
in any stage of the radiation code and the representation of clouds within the GCM. Disentan-
gling this problem will require a combination of better radiometric and cloud observations than
are currently available over long periods or with a global coverage.
The changing cloud particle size distributions causing the changes in optical properties is
the mechanism for much of the complexity of the cloud-climate interactions, as was mentioned
in the discussion of Slingo (1990) at the beginning of this chapter. A similar study by Hu
and Stamnes (2000) gave an even stronger sensitivity and found that a 2% increase in re per
degree of warming doubled the impact of doubling CO2. To examine the effect of the size
of ice crystals on the climate system, Ou and Liou (1995) used a 1D radiative equilibrium
model containing ice clouds where the mean size of the ice particle size distribution varied
with temperature, according to a parameterisation based on in-situ observations by Heymsfield
and Platt (1984), and found that the effect of climate warming was to increase the mean ice
particle size. Predominantly this makes the cirrus clouds more transparent to incoming solar
radiation so giving a warming (positive) feedback.
Although in this thesis the radiative effects of aerosols will the ignored, the effects are sig-
nificant. However, the optical properties of aerosols are more varied and uncertain than clouds
and additional uncertainties arise from the microphysical and radiative interactions which occur
between aerosols and clouds (Schwartz and Slingo (1995)).
In addition to the problem of determining the optical properties of clouds, uncertainties
arise due to the manner in which a radiative transfer model represents clouds within the levels
that the fluxes are integrated. Most radiative transfer models treat the fluxes through clear air
and cloudy air separately with an area of cloud (usually this is the cloud fraction by volume,
cv) and clear air within each grid box. When radiation passes from one partially cloudy level
to the another, whether the radiation from the clouds passes into clear air or into the cloud in
the next level is dependent on the cloud overlap assumption. These two issues are discussed at
length in chapters 7 and 8, along with a discussion of the effects of cloud inhomogeneity.
Although the parameterisation of cloud optical properties is important, the distributions
of cloud provided by the GCM to the radiative transfer model must also be correct. As an
indication of the required accuracy of the cloud parameters Vogelmann and Ackerman (1995)
estimated that, in order to calculate the net short wave fluxes passing through cirrus clouds to
within 5%, optical depth and therefore the ice water content (IWC) (from which the optical
depth is derived) must be known to within ±33% and ±12% for optical depths of 1 and 4
respectively. The vertical distribution of clouds is of particular importance for the calculation
of long wave fluxes, with Vogelmann and Ackerman (1995) estimating that to calculate the
top-of-atmosphere long wave fluxes to within 5% in mid-latitudes, cloud temperature must be
accurate to roughly ±9 and ±4.2 C for optical depths of 0.5 and 2.0 respectively. If the
environmental profile is well mixed, this corresponds to a difference in height of roughly 1km
and 0.5km.
1.3 This Thesis
The presence of clouds in the atmosphere brings two problems in the modelling of the radiative
fluxes; firstly the distribution of clouds must be correct, both in terms of the absolute amount
of cloud fraction and water contents, but also in terms of the cloud temperatures and heights.
Secondly the radiative transfer model must be able to accurately produce the correct fluxes
from these clouds.
The problem, in terms of GCM design and validation, is that observations of the radiative
fluxes at TOA are more easily and reliably obtained than cloud observations. Therefore if the
distribution of clouds is incorrect then the uncertainties in the modelling of radiative transfer
processes means that it is more than feasible that the GCM’s radiative transfer model will
contain compensating errors which are able to counteract the errors which would otherwise
be caused by the errors in the cloud distribution. If such a GCM were to be improved so
that it produced a more accurate distribution of cloud it is very likely that this would expose the
errors within its radiative transfer model which could be significantly detrimental to the GCM’s
usefulness as a forecast model or would introduce an imbalance in the GCM and so hamper its
ability to represent the current climate, so introducing a “climate drift”.
This means that it is essential to evaluate the clouds within GCMs using direct cloud
observations, so that the entanglement between the cloud and radiative processes can be unrav-
elled:
“In the long run, (climate) model development and observing program design are better
served by highlighting model-data discrepancies than by artificial agreement based on arbri-
trary assumptions.” - Del Genio et al. (1996)
In this thesis we will make extensive use of cloud radar and lidar observations from the
Chilbolton observatory in Hampshire, UK, in order to make direct comparisons between cloud
observations and the representation of these clouds in two state-of-the-art weather prediction
models from which profiles of cloud variables were extracted over the Chilbolton site. Where
it is feasible, this comparison will take a radiative perspective through the use of a radiative
transfer model.
The representation of clouds in GCMs will be discussed in chapter 2, with particular
reference to the models which will be used in this thesis, while chapter 3 presents an introduc-
tion to the theory and application of the radar and lidar observations. Sensitivity tests will be
discussed, in chapter 4, using the radiative transfer model which will be used in later chapters.
In chapter 5 the mean profiles and distributions of cloud parameters as observed and
forecast by the models will be compared, and this will be extended in chapter 6 to examine
the issues found in chapter 5 in more detail and develop a more radiative perspective. One of
the major issues in this chapter will relate to the representation of the complex sub-grid scale
geometry of clouds, which is all but ignored in most GCMs. This issue will be examined in
chapters 7 and 8 where the significance of this effect will be evaluated in terms of TCC and
proposed are parameterisations to represent the effect in GCM grid-boxes of all sizes.
In chapter 9 the findings of this thesis will be summarised and suggestions made for future
work. This is a particularly exciting area of research in that a huge amount of information is
being gathered by ground based observing campaigns such as the ARM and CloudNet projects
and the deployment of active cloud remote sensing instruments in space in the near future with
the CloudSat and EarthCARE missions.
CHAPTER TWO
Precipitation in GCMs
Although the clouds within a GCM are produced by the evolution of the large scale fields, such
as the temperature and humidity, the clouds also have a significant impact on these fields. It
has been clearly demonstrated that the latent heat released by condensation, the corresponding
evaporative cooling, and the variation in the radiative fluxes between clear and cloudy skies, all
have significant and local effects on the evolution of the large scale fields which need to be rep-
resented on a grid-box scale for an accurate forecast, particularly of the growth of extratropical
cyclones (Manabe (1956), Liou and Zheng (1984) and Forbes and Clarke (2003)). Therefore
a GCM requires a representation of clouds on the scale of the GCM grid-box; clouds cannot
simply be prescribed on a climatological basis, they must be an interactive part of the model.
In order to achieve this a GCM will typically predict a variable, or variables, to represent
the average cloud water content within the grid-box as well as a cloud fraction variable(s) which
represent the proportion of the grid-box which contains (a particular type of) cloud. As shown
schematically in Fig. 2.1 cloud fraction can be defined either as the proportion of the volume
filled with cloud (cv) or as the cloudy proportion of the area (ca), when viewed from above or
below. As cv is more easily related to the water content the majority of GCM cloud schemes
calculate cv. The difference between these two definitions of cloud fraction, and the possible
implications, are discussed in chapter 7.
There is a wide variety of different schemes for obtaining an estimate of the cloud water
content and fraction in a GCM. In order to represent the variation of clouds on the grid-box
scale (as opposed to prescribing climatological values) the cloud variables must either be di-
13
CHAPTER 2: The Representation of Cloud and Precipitation in GCMs 14
/C =a 3 2
1/vC = 2
Figure 2.1: Schematic of a distribution of cloud within a 3D grid-box, where the cloud fraction by volume (cv) is
1 2 , but the cloud fraction by area (ca) is 2
3 .
agnosed directly from the large scale variables or, when the cloud variables are themselves
prognostic variables, their tendencies need to be diagnosed. For the purposes of this discussion
we shall consider the cloud scheme to be composed of two separate, but highly linked com-
ponents: a condensation/precipitation model to predict the cloud/rain/snow water contents and
fluxes and a separate cloud fraction model to calculate the cloud fraction.
In the process of diagnosing the cloud water content, or their tendencies, the condensa-
tion/precipitation model will need to account for all of the major sources and sinks of water
in the atmosphere, as well as the partitioning the various types of water content which might
be represented in a model. A typical distinction would be between water vapour, cloud water,
cloud ice and rain; all of which have very different fallspeeds and optical properties which will
effect how each of these water quantities is transported within the model, and their radiative
impact.
While the process of partitioning the atmospheric water could be as simple as a diagnosis
based on the supersaturation of the water vapour, it could also invole many different water
contents such as the condensation/precipitation model described in Lin et al. (1983) which has
independent prognostic variables to account for water vapour, cloud water droplets, cloud ice,
rain, snow and finally graupel (hail). This requires 27 different transfer terms to account for the
various micro-physical processes which occur in the formation and dissipation of the different
types of water content. It is generally the case that such a complex model is not designed for
use in a GCM or NWP model, but in a very high resolution “Cloud Resolving Model” (CRM)
which explicitly resolves the turbulent cloud scale motion.
In a CRM the resolved cloud scale motion indicates that cloud formation occurs within
the entire grid-box, so by definition the box will be entirely empty, or entirely full, of cloud.
This ’on/off’ cloud model represents the simplest possible cloud model, and is a good descrip-
tion of reality only when the cloud scale motions are resolved. In a larger scale model such as
a GCM or NWP model the large scale air motions are resolved but the effects of the turbulent
motion must be parameterised. The variability of ascending and descending motion across the
grid-box means that there is a variability of temperature (T ) and specific humidity (q) across the
grid-box, and that the cloud fraction by volume (cv) would be defined as the proportion of the
grid-box which is supersaturated. The possibility of representing the sub-grid scale variability
of T and q across the grid-box implies that the definition of cloud cover could account for the
scales on which the turbulent motions occur, allowing for the definition of cloud fraction cloud
itself be scale dependent, and this will be discussed in chapter 7.
In order to calculate cv, it is therefore the job of the cloud model to represent the variabil-
ity of T and q across the grid-box, and this is what is a cloud model does regardless of whether
it relies on an empirically derived relationship between RH and cv, an approach adopted in
models such as Slingo (1980), Xu and Randall (1996) and Del Genio et al. (1996), or whether
the cloud model is based on a specific representation of the sub-grid variability of T and q such
those presented by Smith (1990), Tiedtke (1993) or Tompkins (2002). According to Tompkins
(2002), a well defined cloud and precipitation scheme is one where the water content produced
by the formation of a cloud will be consistent with the underlying assumptions about the dis-
tribution of T and q which produced the cv.
In this thesis extensive use is made of profiles of the atmospheric state over the Chilbolton
Observatory, in Hampshire, UK, as forecast by Met Office’s operational mesoscale model
(UKMO(mes)) and the European Centre for Medium-range Weather Forecasts’ operational
global model (ECMWF). In section 2.1 of this chapter these two models will be briefly de-
scribed with particular reference to their condensation/precipitation and cloud fraction models.
The appropriate use of these model profiles with respect to the “spin-up” of the model forecasts
will be discussed in section 2.2.
2.1 Model Profiles
The model profiles used in this thesis consist of hourly vertical profiles of temperature, pres-
sure, humidity, and various cloud variables which are extracted from the grid-box nearest the
Figure 2.2: 12 month running mean of R.M.S. error of the 500hPa height forecasts over Europe 72 hours into the
model forecast, verified against sonde observations, from Fuller (2000).
Chilbolton cloud observing site. The Met Office and ECMWF models represent two “state of
the art” weather prediction models. As a comparison of the quality of the forecasts produced
by various operational forecasting models around the world Fig. 2.2 shows the 12 month run-
ning mean root mean square (RMS) error in the forecasts of the height of the 500hPa surface
72 hours after the forecast was initialised (termed T+72), verified against sonde observations
over Europe. It can clearly be seen that the Met Office and ECMWF are consistently amongst
the best forecasts and during the 1999-2000 period (which forms the observing period for the
bulk of this thesis) the ECMWF and Met Office models were quite markedly the most accurate
operational forecast models in the world, with the ECMWF forecasts slightly more accurate
than the Met Office.
2.1.1 The UK Met Office Mesoscale Model
The Unified Model (UM) is the name given to the suite of atmospheric and oceanic numerical
models developed by the UK Met Office. The formulation of the models supports global and
regional domains and is applicable to a wide range of temporal and spatial scales that allow it
to be used for both Numerical Weather Prediction and climate modelling. The version of the
UM which was operational during the observing period examined in this thesis is described
qq sat
cv
Figure 2.3: Schematic diagram of the assumed distribution of humidity across a grid-box used in the Smith (1990)
cloud scheme.
by Cullen (1993). A hydrostatic version of the primitive set of equations is integrated using
finite-differences with split-explicit time integration, and 4th order Eulerian advection (Cullen
et al. (1991)). Variables are staggered on an Arakawa B grid in the horizontal and a Lorenz grid
in the vertical. During the observing period the Met Office global model runs with a 3D-VAR
data assimilation cycle four times per day with the Mesoscale model (UKMO(mes)) embedded
within the global model.
The condensation/precipitation model used in the UM is described by Wilson and Ballard
(1999), and uses prognostic variables for the cloud ice water content and the combined water
content of the water vapour and cloud liquid water content (excluding the ice).
Liquid water cloud formation is as described by Smith (1990) and is diagnosed when
supersaturation occurs at some point in the humidity distribution specified within the grid-box.
In this scheme the humidity distribution over a grid-box is assumed to be triangular, shown
schematically in Fig. 2.3, with the cloud fraction, cv, being the integral of this distribution
from saturation to the maximum q. The same process also defines the cloud liquid water
content (LWC or qc) as the same integral weighted by the degree of supersaturation. With
the assumption that the distribution is symmetric about the mean all that is needed to close the
system is a statement of the breadth of the distribution. This is specified by the critical relative
humidity (RHcrit ), defined as the RH at which part of the grid-box first becomes supersaturated,
so allowing the formation of a liquid water cloud. RHcrit varies slightly with height, but typical
values are 80 to 90%.
Ice nucleation occurs if certain criteria are met. Homogenous nucleation occurs if T <
−40C, and converts all cloud liquid water content to ice. Heterogenous nucleation occurs
when T < 10C and q exceeds a mixed-phase function specified by Gregory and Morris (1996),
and this works by adding very small quantities of ice nuclei (of negligible mass) to the grid-
box. Once the ice and liquid clouds have been defined the available water is partitioned by
the application of a range of transfer processes to represent vapour deposition and evaporation,
including the favourable vapour deposition onto the ice nuclei in the presence of liquid water
(the Bergeron-Findeisen process), and the riming of liquid water onto the ice. Rain is formed
either by gradual autoconversion or by melting snowflakes. Rain fallspeeds are calculated
assuming the size distribution of Marshall and Palmer (1948) and ice fallspeeds are calculated
using an an exponential ice particle size distribution which varies with temperature. These
particle size distributions are central to the calculation of the majority of the transfer processes.
Ice cloud fraction (cv) is calculated using an inverted version of the Smith (1990) scheme to
calculate cv from the IWC using the same assumptions as for the liquid water cloud.
Convective clouds are produced by the diagnostic, mass-flux based, convection scheme
of Gregory and Rowntree (1990) and do not contribute directly to the large scale clouds in
any way. The convection scheme does contribute to the large scale clouds by the detrainment
of humidity from the convecting plumes, so increasing RH in the environment, which will
produce clouds on some occasions but not others.
The UKMO(mes) outputs over Chilbolton are a time series of concatenated forecast runs
of the operational mesoscale model. The Met Office run their forecast model every 6 hours. A
global model run, with lower horizontal resolution, is used to provide boundary conditions to
the mesoscale model which is a regional model centred on the United Kingdom. The mesoscale
model has a resolution of 0.11 by x0.11 which is approximately 11km in mid-latitudes. It
has 38 levels in the vertical, with a spacing of around 400 m at 2 km and around 800 m at 10
km. It is run with a time-step of 5 minutes, although the variables of interest are output as a
snapshot consisting of a single time-step every hour.
2.1.2 ECMWF Operational Model
The ECMWF outputs are a time series of concatenated forecast runs of their operational global
model (as opposed to the ’Control’ or ’Ensemble’ models). The ECMWF model is a spectral
model, which solves the hydrostatic primitive equations represented in terms of spherical har-
monics. At the time of this comparison it was running with TL319 truncation, corresponding to
a horizontal resolution of around 60 km. The model was running with 50 vertical levels before
13th October 1999, and then 60 afterwards, with a spacing of around 400 m at 2 km and around
800 m at 10 km. The time-step of the model was 20 minutes, although the profiles output over
Chilbolton are again hourly snapshots. The ECMWF global model is run twice per day, at 00Z
and 12Z, with a 4D-VAR data assimilation cycle.
The ECMWF model uses the cloud fraction and condensation/precipitation models of
Tiedtke (1993) which holds both the cloud water content and fraction as prognostic variables.
These are advected through the model as tracers, each with sources and sinks to represent the
physical processes which effect them. The temperature is used to diagnose the partitioning of
the cloud water between the ice or liquid phases according to
L = 0 T ≤ Tice
L = 1 T ≥ T0 (2.1)
where L is the fraction of the total condensate in the liquid phase. Tice and T0 represent the
threshold temperatures between which mixed phase clouds are allowed to exist and are cur-
rently set at Tice = 250.16 K and T0 = 273.16 K.
The sources of cloud water and fraction included in the ECMWF model include cumulus
convection, boundary layer cloud and large scale/stratiform cloud. The convective cloud is
supplied by the mass-fluxes calculated by the convection scheme of Tiedtke (1989) and includes
both the plumes and anvils of deep convection. Sinks of cloud water and fraction include
evaporation and the rain and snow falling from the cloud.
The formation of large scale cloud actually uses the same assumptions of a triangular
distribution of humidity as the Smith (1990) scheme described in section 2.1.1, with RHcrit set
to 80% at 650 hPa, increasing to 100% as the boundary layer and tropopause are approached.
Once a cloud has formed, water content evaporates or precipitates from it, leaving the cloud
fraction unchanged, and if the situations are suitable, more cloud is added in later time-steps.
Compared to a diagnostic scheme, such as the Smith (1990) scheme, a prognostic cloud scheme
has a degree of memory from one time-step to the next.
The formation of rain from the water content is modelled as described by Sundquist et al.
(1989), which includes crude representations of the autoconversion and Bergeron-Findeisen
processes. Rain falls out of the profile in a single time-step, although it evaporates and inter-
acts with the cloud it encounters as it falls. Ice sedimentation is dealt with by splitting the
diagnosed IWC into two categories, defined as having a maximum dimension larger or smaller
than 100µm, as described in McFarquhar and Heymsfield (1997). Large ice crystals are as-
sumed to fall out of the model in a single time-step, while small ice crystals fall out in a single
time-step if they fall into clear sky, but if they fall into clouds they are allowed to settle with
an assumed fallspeed as given by Heymsfield and Donner (1990). The ice which falls out in
a single time-step is allowed to evaporate and melt as it falls, so effecting the environmental
profile and producing a more accurate prediction of surface rainfall.
Comparing the cloud and precipitation schemes used in the Met Office and ECMWF
models it is apparent they both have quite different emphases. The condensation/precipitation
model of the UM is much more physically based than that of the ECMWF, while the prognostic
clouds scheme in the ECMWF is more advanced than the cloud scheme in the UM. This reflects
the different emphases of the two institutions, with the Met Office acting as a National Weather
Centre, with part of its remit being the detailed forecasting of adverse weather conditions at
relatively short forecast lead times. For the accurate prediction of significant rainfall events the
very physically based condensation/precipitation scheme would be an advantage, especially
with higher resolution mesoscale models which aim to give an accurate representation of the
structure of individual rainfall events which has been found to be quite sensitive to the details
of the condensation/precipitation model (Forbes (2002)). By comparison the ECMWF aims
to produce medium range weather forecasts, where details such as exact rainfall rates and
structures are less important, but it is more important to get the cloud structures correct so that
the longer timescale radiative processes are well described.
2.2 Model Spin-Up
As we have discussed in sections 2.1.1 and 2.1.2 the profiles from the UKMO(mes) and
ECMWF models are available every 6 or 12 hours respectively. In order to meaningfully com-
pare the observed and modelled cloud profiles it is necessary to only use the model profiles
where the clouds have had time to be generated and reach an equilibrium within the model
forecast. This process is known as model spin-up, although it should be noted that it is not
confined to just the cloud variables within a GCM.
0 6 12 18 24 30 36 0.06
0.07
0.08
0.09
0.1
0.11
0.12
v
Figure 2.4: Mean values of Cloud fraction by volume (cv), varying with forecast lead time, averaged only below
a height of 12km, from hourly UKMO(mes) profiles over the Chilbolton site for the period May 1999 to May
2000.
As an investigation into the effects of model spin-up in the UKMO(mes), Fig. 2.4 shows
the mean values of cv in panel for forecast lead times of up to 36 hours. It can be seen that the
UKMO(mes) takes up to 8 hours for the cloud fraction to approach a stable level. Therefore,
unless specifically stated otherwise, all of the comparisons in the following chapters will use
the model profiles produced using each model forecast from its T+12 period until the next
forecast becomes available. This corresponds to analysing the T+12 to T+18 period for the
UKMO(mes), and the T+12 to T+36 period for the ECMWF.
CHAPTER THREE
Radar and Lidar Observations of Cloud
The most direct cloud observations come from in-situ observations taken from suitable plat-
forms such as aircraft or balloons. However, these observations are impractical to obtain for
monitoring over larger spatial or temporal scales, which are more suited to remote sensing,
either by passive or active means.
In passive remote sensing all of the information is obtained by analysis of the naturally
occurring electromagnetic radiation which is emitted or scattered by a body. Passive remote
sensing from space can produce datasets with truly global coverage, with the International
Satellite Cloud Climatology Project (ISCCP) being an example of a cloud dataset where data
from many different satellites over many years have been compiled to give global observations
of cloud over a period of almost 15 years (Rossow and Schiffer (1999)). Although such ob-
servations are of immense use for the evaluation of the representation of clouds in GCMs their
limited horizontal and vertical resolution (the ISCCP-D dataset classifies cloud in only three
vertical levels) precludes more detailed studies of cloud structure.
In active remote sensing, a pulse of radiation is emitted, usually in the form of a narrow
beam, and the radiation returned from any objects in its path is measured. The position of these
objects can be determined due to the accurate measurement of the timing delay between the
transmitted pulse and the pulses returned from objects within the beam, which enables active
sensors to make observations with very high spatial resolutions compared to passive remote
sensing.
Clouds and precipitation have been observed from the very beginning of microwave radar
(radio detection and ranging) in the 1940s, when “weather clutter” appeared on the screens of
the radar operators searching the skies and seas for enemy aircraft and ships. Since then a
22
CHAPTER 3: Radar and Lidar Observations of Cloud 23
body of theoretical and experimental work quickly developed to infer properties of the pre-
cipitation from the observed “clutter”. The ability of radar to detect precipitation over large
distances in near real time has made it an indispensable tool for short term weather forecasting,
or nowcasting, and research into precipitation processes (Atlas (1989)).
This chapter aims to provide a basic discussion of the theory of active remote sensing
which is relevant to the work contained in this thesis. This includes radar and lidar instruments
and the use radar to retrieve the Ice Water Content (IWC) of clouds. In section 3.2, there is
also a short discussion of the specific instruments at Chilbolton that are used in this thesis. This
is followed, in section 3.3, by an overview of how the radar and lidar observations are used to
produce cloud variables which have been averaged onto grids comparable with those of a GCM
or forecast model.
3.1 Active Remote Sensing Theory
All active remote sensing instruments work by transmitting a pulse of radiation with a power
Pt , and detecting the returned radiation at any given time with a power Pr. The distance (r)
between the instrument and the object returning the radiation is determined using the time
delay between the transmitted and received radiation.
Assuming that transmitted beam is filled with isotropic scatters the return power, Pr, is
dependent on
Pr ∝ Pt
σb, (3.1)
where the constant of proportionality is dependent on the wavelength and a multitude of prop-
erties of the individual radar system, such as the antenna gain and beam width. ∑ σb is the
apparent backscattering cross section of the scattering particles summed over the pulse vol-
ume V and is determined entirely by scattering properties of the targets at the wavelength
in question (Battan (1973)). This is considered an apparent cross section as it refers to the
backscattering cross section that the particles would have if they scattered isotropically.
The manner in which any object interacts with electromagnetic radiation is determined
by the ratio of its size to the wavelength of the radiation. For a spherical object of diameter D
we can define an electrical size a to normalise with respect to wavelength
a = πD λ
(3.2)
For a spherical object whose diameter (D) is small compared to the wavelength of the
passing radiation (a < 0.5), the Rayleigh scattering approximation can be used to determine
σb as
σb = π5
λ4 D6|K|2 (3.3)
where |K|2 is the dielectric factor which represents the ease or difficulty with which a dipole
can be induced in the scattering particle. This varies for different frequencies and tempera-
tures and can be calculated by various methods including the empirical formula of Liebe et al.
(1989). For liquid water droplets at 3GHz |K|2 = 0.93. For ice/snow particles, assuming that
these are homogenous mixtures of air and ice, |K(D)|2 ∝ ρ2 where ρ is the density of the air-ice
mixture.
As the size of the scattering particles begins to be comparable with the wavelength (a >
0.5) the Rayleigh approximation is no longer valid and the full solution given by Mie (1908),
for the σb of spheres, is needed:
σb = πD2
(n − 1)n(2n + 1)(an − bn) 2 (3.4)
where an and bn are coefficients of the scattering field involving Bessel and Hankel functions
which relate the scattering angle, electrical size and complex refractive index (Burgess and Ray
(1986)).
In order to compare these two scattering regimes it is useful to define a backscattering
cross-section which is normalised to the actual cross sectional area, or scattering efficiency
Q = 4σb πD2 , which is shown for the Rayleigh and Mie scattering approximations in Fig. 3.1,
for water droplets at 0C. This clearly shows that for small particles (a < 0.5) the Rayleigh
approximation is in good agreement with the more complete Mie solution, but as particles
become larger with respect to the wavelength the Rayleigh and Mie solutions diverge with the
Mie solution beginning a decaying oscillation to a limit where ’geometric optics’ applies.
Figure 3.1: Normalised backscatter cross sections for ice and water at 0C as determined using the Mie and
Rayleigh approximations. From Burgess and Ray (1986).
Due to the very different wavelengths employed by radar and lidar applications the σb
that is relevant for the two applications is very different. The two applications will therefore be
discussed separately from here on.
3.1.1 Basic Principles of Radar
The pertinent features of some of the typically used radar frequencies are presented in Table 3.1,
including the maximum diameter for which the Rayleigh scattering approximation is valid. As
most radars will observe hydrometeors almost entirely in the Rayleigh regime it is sensible to
consider the properties of these hydrometeors using the simpler Rayleigh theory and to consider
deviations from the Rayleigh theory where it is necessary.
In order to remove all of the instrumental variation in the returned power (Pr) detected by
a radar in equation (3.1) and assuming that σb can be calculated by the Rayleigh approximation
given in (3.3) the return power can easily be rewritten in terms of the radar reflectivity factor,
Z:
Frequency (GHz) Band Wavelength Maximum diameter Application
1.3 L 24 cm 38 mm wind profiler
3 S 10 cm 16 mm weather radar
5 C 6 cm 10 mm weather radar
10 X 3 cm 4.7 mm weather radar
35 Ka 8.6 mm 1.4 mm cloud radar
94 W 3.2 mm 0.5 mm cloud radar
Table 3.1: Maximum diameters for which the Rayleigh scattering approximation is assumed valid (a = 0.5) for a
selection of typical radar wavelengths.
which for a distribution of spherical water droplets simply becomes
Z =
Z in f
0 n(D)D6dD, (3.6)
where n(D)dD is the number concentration of droplets in the range D to D + dD. It should
be noted that the D6 term means that meteorological radars are significantly more sensitive to
detecting larger hydrometeors than small ones.
In linear terms Z has units mm6m−3 but as Z varies over many orders of magnitude it is
commonplace to use the logarithmic units of dBZ where
Z [dBZ] = 10 log10(Z [mm6m−3]). (3.7)
It is only recent technological developments that have enabled radar systems to be de-
veloped at higher frequencies, so giving the radar system sufficient sensitivity to detect clouds
as well as precipitation. The increased sensitivity of shorter wavelengths arises due to the de-
pendence of σb on 1 λ4 in (3.3). For applications where clouds rather than precipitation are of
interest, the additional sensitivity of the shorter wavelengths more than compensates for the
difficulties that arise due to the Mie scattering when larger hydrometeors, such as rain, are
observed.
As the wavelength of the radar decreases so the attenuation of the transmitted pulse in-
creases. This is due to the absorption of the transmitted pulse by water vapour and, particularly,
by liquid water. It should be noted that for cloud radars, especially at 94GHz, this represents
a serious issue when looking at liquid water clouds. In most cases, this may result in the loss
of 1 or 2 dBZ, but when the radar beam passes through very heavy precipitation the signal can
be entirely attenuated making quantitative use of the observed Z difficult and preventing the
detection of any cloud or precipitation which occurs above the heaviest region of precipitation.
3.1.2 IWC Retrieval from Radar Z
The IWC retrieval used in this thesis is an extension of that of Liu and Illingworth (2000),
in which values of Z and IWC were computed from ice particle spectra observed during the
EUCREX (European Cirrus and Radiation Experiment) and CEPEX (Central Equatorial Pacific
Experiment) flights. These values were binned into 6C temperature bins and a set of power
laws computed to calculate IWC from Z in each bin. The retrieval of Liu and Illingworth (2000)
was evaluated by Sassen et al. (2002) and was found to be one of the better Z to IWC retrievals,
and that the inclusion of temperature information does improve the retrievals.
However when applying this retrieval to cirrus clouds, which occupy more than one
temperature bin, the Liu and Illingworth (2000) retrieval produces sharp discontinuities in
IWC where the temperature changes from one bin to the next. Also at colder temperatures
(T < −55C), where there are fewer observations in the EUCREX flights, the Liu and Illing-
worth (2000) retrieval gives unusually high IWC.
In order to obtain a more useful retrieval the relationship between IWC and Z was re-
calculated, for a range of temperature bins, from the ice particle size spectra observed in the
EUCREX campaign, in a similar way to Liu and Illingworth (2000). The EUCREX dataset
consists of 10000 five-second averages of size spectra as measured by the 2D cloud and pre-
cipitation probes on the Met Office C130 aircraft in mid-latitude ice clouds. As discussed in
Francis et al. (1998) the 2D cloud and precipitation probe is known to underestimate the num-
ber of small cloud particles. This is one of the problems which is addressed in the recent work
of Hogan et al. (2005b) which will be discussed in section 6.4.
The underlying assumption in the calculation of Z from an ice size spectra is that ice
cloud particles are homogenous spheres of an air-ice mixture with a density (ρ) that varies
solely with particle diameter (D), so the radar reflectivity can be calculated from an ice crystal
size spectra as in Brown et al. (1995):
Z = 1
n(D)|K(D)|2 D6 γ(D) dD (3.8)
where n(D) is the number concentration, |K(D)|2 is the dielectric factor and γ(D) is the ratio
of the Mie to Rayleigh scattering, for particles with diameters in the range D to D + dD.
While it is true that ice cloud particles are not homogenous spheres this effect is to a
certain degree accommodated by the use of an observed relationship between the density (ρ)
of the air-ice mixture in the particles, and D. This relationship is vital as |K(D)|2 which for ice
is proportional to ρ2 and IWC is the integral of particle mass with D, so is also dependent on
the assumed density relationship. The Z, IWC relationships of Liu and Illingworth (2000) used
the density assumption of Hogan et al. (2000)
ρ = 0.175D−0.66 (3.9)
which is based on the relationship between ρ and D that is obtained from the observed cross
sectional area (A) from Francis et al. (1998), and the “equivalent area” assumption A = πD2/4.
The resultant density relationship is very similar to the density assumption of Mitchell (1996).
Based on these assumptions, Fig. 3.2 shows the relationship between IWC and Z for the
EUCREX observed ice size spectra, categorised according to temperature, and the resultant
best fits. As temperature increases, so the ice particles tend to be larger and give higher Z for a
given IWC. The effect is particularly strong for the lower values of Z.
Fig. 3.3(c) shows the variation of IWC with temperature for Z of 20 and -30 dBZ. Based
on the observation that there is no significant variation of IWC with temperature for Z of
20dBZ, and that there is a good log-linear relationship between IWC and T at -30dBZ the fits
in Fig. 3.2(b) were constrained to intersect yielding the following relationship for log10(IWC)
as a function of both Z (in dBZ) and temperature, as given in equation (3.10):
log10(IWC) = 0.000520 Z T + 0.0929 Z − 0.00605 T − 1.01 (3.10)
where IWC is in gm−3, Z is in dBZ and T is in C.
Figure 3.2: Ice water content (IWC) versus radar reflectivity (a) calculated from the EUCREX ice particle size
distributions categorised by temperature and (b) the resultant logarithmic fits. Curtesy of Robin Hogan.
Figure 3.3: (c) Variation of IWC with temperature for 2 Z values used to derive the fits in (d) of IWC versus Z for
all of the different temperature bins. Curtesy of Robin Hogan.
3.1.3 Basic Principles of Lidar
A lidar is an active remote sensing instrument which operates in the UV, visible or near-IR
region of the electromagnetic spectrum. The use of lasers as the transmitted pulse means that
a very narrow beam width is achievable without the comparatively large antenna required for a
radar system and the receiver systems resemble the telescopes used in visible astronomy, such
as avalanche photodiodes or photomultiplier tubes (O’Connor (2003)).
By comparison to the sizes of typical hydrometeors these wavelengths are usually much
smaller than the particles of interest, so the scattering efficiency (Q) is not dependent on size
of the particles, as shown in Fig.3.1, meaning that the backscattered power is dependent on the
actual cross section. This results in the observed attenuated backscatter β, which is defined as
the fraction of incident radiation scattered per steradian in the return direction is related to the
particle size distribution simply as
κβ ∝ ∑ vol
NDD2 (3.11)
where κ is a lidar ‘constant’, which varies dependent on the lidar calibration, and the optical
properties of the target precipitation. β has units of sr−1m−1.
In comparison to the Zreturned from a radar (equation 3.6, note the D6), the lidar return
is less dominated by the particle size, and more dependent on number density. It is therefore
able to distinguish the cloud base from any precipitation falling from the cloud (which has a
greater D, but smaller N), as well as detect the cloud base of even thin liquid water clouds
which would be unobservable by the radar alone. The disadvantage of the lidar instrument is
that the lidar beam is rapidly attenuated by the presence of even these thin clouds due to the
relatively greater dependence of the extinction coefficient on the number density. This means
that, although a lidar can detect many clouds which a radar would not be able to detect, a lidar
gives information only at or about cloud base.
The ability of a lidar to detect cloud base, combined with the ability of cloud radar to
penetrate to cloud top means that the use of co-located radar and lidar observations is able to
provide a complete description of the cloud boundaries. The use of a combination of radar and
lidar instruments in this manner is the most basic form of radar-lidar synergy.
3.2 Instrumentation at Chilbolton
The main radar used in this thesis was the zenith pointing 94 GHz Galileo cloud radar. The
radar operated quasi-continuously and in this thesis we will primarily be examining data taken
in the period 1 May 1999 to 26 May 2000.
During the majority of the 1999-2000 observing period the 94GHz radar was mounted
on the side of the 25m dish that is the antenna for the 3 GHz radar. This means that it was
very easy to calibrate the 94GHz radar by comparing the value of Z at 94 GHz with those at
3 GHz in drizzle, which Rayleigh scatters at both frequencies, while the 3-GHz weather radar
at Chilbolton was absolutely calibrated using the redundancy of the polarisation parameters in
heavy rain (Goddard et al., 1994). A disadvantage of this arrangement is that the 94GHz radar
would only be available as a vertically pointing cloud profiler while the 3GHz radar was not
in use. This would often occur when a heavy convective event was within the scanning range
of the 3GHz radar, or when the operators of the Chilbolton site were using the dish for other
contracted work relating to radio propagation research.
After the 94GHz radar was removed from the dish an additional calibration technique
was made possible by examining the relatively constant Z at 94 GHz, in heavy rain at 250m,
due to Mie scattering and attenuation as described in Hogan et al. (2003a). Combining these
two calibrations has enabled the calibration of the 94 GHz to be well determined throughout
the observing period.
For extra sensitivity the raw pulses were averaged over a 30 second period , which at
the start of this observing period gives sufficient sensitivity to observe cloud with a reflectivity
factor slightly less than -50dBZ at 1km, falling to -30dBZ at 10km. This sensitivity is sufficient
for the cloud radar to observe almost all cloud below 10km, with the exception of very thin
cirrus and drizzle free stratocumulus. Unfortunately, during the period of this study, a problem
was developing with the radar which gradually reduced the radar sensitivity.
May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun
−52
−50
−48
−46
−44
−42
−40
−38
1999 2000
Figure 3.4: Minimum detectable radar reflectivity (Z min) at 1km, over the period May 1999 to June 2000. The
increase is due to a developing hardware problem.
Fig. 3.4 shows variation with time of the minimum detectable Z at 1km and shows a
marked increase from -50dBZ to roughly -41dBZ during the May 1999 to May 2000 observing
period. In order to establish what clouds the radar would be able to observe at different heights
it is important to note that the minimum detectable Z increases with height. Fig. 3.5 shows
the minimum detectable Z with height for 1 May 1999 and 1 May 2000 and the corresponding
minimum observable IWC (IWCmin) found using equation (3.10).
The effect of attenuation by water vapour is corrected for using the temperature and
humidity profile from the Met Office operational mesoscale model (UKMO(mes)), coupled to
the line-by-line model for millimetre-wave attenuation of Liebe (1985).The effect of gaseous
attenuation is to increase the Zmin by between 1 and 3 dBZ. The pulse length of the radar leads
to a minimum vertical resolution of 60m.
Complementary instrumentation includes a zenith pointing 905nm Viasala CT75K lidar
ceilometer which is able to distinguish cloud base from precipitation and observe thin liquid
water clouds which the 94GHz radar cannot. The ceilometer records profiles of attenuated lidar
backscatter (β), with a resolution of 30m and 30s. For the purposes of this thesis it is a fully
automated and self contained unit which is able to determine cloud base from aerosol. The
ceilometer β is calibrated using the method of O’Connor et al. (2004) which examines cases
of total extinction of the lidar beam in stratocumulus by comparing the observed integrated
backscatter with that predicted by the emitted power using the invariance of the lidar extinction
to backscatter ratio for a distribution of cloud droplets. Data is also used from a drop counting
raingauge.
3
4
5
6
7
8
9
10
11
12
H ei
gh t (
May 1999 May 2000(b)
Figure 3.5: Estimated minimum detectable (a) reflectivity (Z min) and (b) ice water content (IWCmin), as a function
of height, for the Galileo 94GHz cloud radar on 1 May 1999 and May 1 2000. These are calculated from the
estimated minimum detectable Z at 1km, given in Fig. 3.4, with an attenuation correction of between 1 and 3dBZ,
and IWC derived from Zmin and UKMO(mes) temperature using equation (3.10).
3.2.1 Calibration of Broad Band Radiometers
To supply further complementary observations the Chilbolton observatory was equipped with
two sets of Pyrogeometers and Pyroanometers which measure the downwelling broad-band
fluxes of longwave and shortwave radiation respectively. The broad-band radiometers were in
place from October 2000 and operated continously, with occasional maintenence periods. The
Eppley units are on loan from the Met Office, and have recently been calibrated while the Kipp
& Zonen units have recently been purchased, and so are in need of cross calibration.
−15 −10 −5 0 5 10 15 20 −80
−60
−40
−20
0
20
40
60
80
Figure 3.6: Difference between downwelling longwave radiation measured by Kipp & Zonen CG4 and Epp-
ley pyrogeometers , plotted against Temperature of the Kipp & Zonen instrument. The observations taken at
Chilbolton Observatory from 30 November 2001 to 11 February 2002, excluding 27 December 2001 to 5 January
2002.
To this end, Fig 3.6 shows the difference between the two co-located observations of
downwelling longwave flux (DLFs), against the temperature of the Kipp & Zonen pyrogeome-
ter. It is found that the Kipp & Zonen instrument tends to record lower values of DLFs than the
Eppley unit, and that this is temperature dependent. By producing a linear fit between the dif-
ference between the Kipp & Zonen and Eppley observations and the Kipp & Zonen instrument
temperature, a correction factor is given in Fig. 3.6. Fig. 3.7 shows a frequency distribution
of the difference between observations before and after correction. It can be seen that the cor-
rection factor is successful in removing a significant bias (-7.8 W m−2) in the Kipp & Zonen
instrument. A standard deviation of 5.4 W m−2 is acceptable, given that a typical accuracy of a
BSRN calibrated pyrogeometer is 10 W m−2 (McArthur (1998)). Fig. 3.8 shows a similar fre-
quency distribution comparing the Eppley and Kipp & Zonen shortwave pyroanometers. There
is a minimal bias between the two observations, although there are many occasions where the
instruments are reading almost 150 W m−2difference, and contribute to over 2 3 of the standard
deviation. This is due to the shading of one instrument, while the other is in direct sunlight.
−80 −60 −40 −20 0 20 40 60 80 0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
F re
qu en
cy Uncorrected mean: −7.863 σ: 9.723 Corrected mean: 0 σ: 5.451
Figure 3.7: Frequency distribution of the difference
between colocated observations of downwelling long-
wave flux, with a Kipp & Zonen CG4 and Eppley Py-
rogeometers, in W m−2 Shown before and after cor-
recting the KZ, based on Fig 3.6.
−150 −100 −50 0 50 100 150 200 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
F re
qu en
between colocated observations of downwelling
shortwave flux, with Kipp & Zonen and Eppley
Pyroanometers, in W m−2.
3.3 Retrieving Model Comparable Parameters
An example of the raw radar and lidar observations, for 9 May 1999, are shown in frames (a)
and (b) of Fig. 3.9, with the IWC retrieved using equation (3.10) in frame (c).
In order to produce parameters which could be compared with the output from a forecast
model, the radar and lidar observations are processed with respect to a grid-box comparable to
those used in an NWP model or GCM. The average IWC is simply the mean value of IWC over
the pixels within the grid-box. The mean in-cloud IWC (IWCic) is the mean IWC, divided by
the cv (see Fig. 2.1 for a full definition of this term). To derive the cloud fraction from the radar
and lidar observations, the radar and lidar data are analysed in grid-boxes, which contain a large
number of the radar pixels, of height 60m and a time of 30s, corresponding to the sampling of
the instrument. The radar and lidar returns from each pixel are then analysed and each pixel
is determined as either cloudy or cloud free, producing a cloud mask. cv is then simply the
fraction of the pixels within grid-box which are deemed to be cloudy, while ca is the fraction
−40
−20
0
10 12
H ei
gh t (
0 2 4 6 8
10 12
H ei
gh t (
10−5
10−4
10−3
10 12
H ei
gh t (
10 12
H ei
gh t (
10−4
10−2
10 12
H ei
gh t (
v
0 3 6 9 12 15 18 21 24 0 2 4 6 8
10 12
H ei
gh t (
10−4
10−2
Figure 3.9: Time-height sections of: 94GHz Radar reflectivity, Lidar backscatter coefficient, the retrieved
IWCand the corresponding cloud mask (Tw = 0C isotherm). for 9 May 1999. As an example, this is grid-
ded onto the UKMO(mes) model grid with height and averaged over 1 hour, to produce an observed values of
cv and IWC comparable with the UKMO(mes) model.
of the area of the grid-box which contains cloud when viewed from above or below.
In order to determine whether an individual pixel is cloudy, we adopt the methodology
of Hogan et al. (2001). A radar return is determined to be from cloud when it is located either
above the freezing level (defined as the height at which the model wet bulb temperature is
0C), or above the lidar cloud base. This excludes any rain or drizzle falling from the base
of the cloud, or insects below cloud base, but retains the ice. Mittermaier and Illingworth
(2003) compared the freezing levels in the operational Met Office and ECMWF models and
found them to be in close agreement with the radar observations. Furthermore, the cloud base
observed by the lidar is checked for rapid, short-lived fluctuations in cloud base. Where the
cloud base descends 500m from one lidar profile to the next (i.e. in less than 30s), we assume
that the cloud base may have been obscured by a new, lower, cloud. If the higher cloud base is
observed again within 30 minutes, between any gaps in the lower cloud base, then we assume
that the higher cloud base is continuous, and is added to the cloud mask so removing the
ambiguity mentioned above, and also any vertical stripes of “cloud” above the melting layer,
where a low-level cloud obscures the cloud base for a few minutes.
Thin, non-precipitating liquid water clouds are also observed by the lidar which the radar
may not be able to detect. The bases of these clouds are clearly indicated by high values of
β (> 6 × 10−4sr−1 m−1) observed by the lidar, and are included in the cloud mask with an
assumed thickness of 180m (3 radar pixels). Fox and Illingworth (1997) showed that clouds
thicker than this typically develop sufficient drizzle droplets to become observable by the radar.
The resultant array of cloudy or non-cloudy pixels, hereafter referred to as the “cloud
mask”, as shown in Fig. 3.9(d), which forms a time-height section of cloud at the radar’s high
temporal (30 second) and spatial (60m) resolution, from which ca and cv are calculated as
described above.
The averaging period used for the majority of this thesis is 1 hour, with the exception
of Chapters 7 and 8 where the averaging period itself is a variable of interest. In the example
day shown in Fig. 3.9, frames (e) and (f) show the observed cv and IWC averaged onto the
UKMO(mes) model grid.
For example, using the 1 hour averaging period, at a height of 1km the vertical resolu-
tion of the UKMO(mes) and ECMWF models is approximately 200m. This means that each
observation of cv or IWC will be an average of approximately 400 radar/lidar pixels, thus re-
ducing the random errors in the retrieval of cv and IWC significantly. In chapter 5 an alternate
approach is investigated in which the averaging period at each model level is taken to be the
time taken to the model winds to travel horizontally across 1 model grid-box. However the
analysis performed with a varying averaging period is not found to give significantly different
results from those presented in this thesis.
A problem often enco

clouds and radiation using radarlidar synergy to evaluate and

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