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Keywords:

  • CloudSat;
  • mass-dimensional relationship;
  • MetUM;
  • particle size distribution function;
  • Rayleigh–Gans theory;
  • scattering

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Habit mixture models and limitations of applying the concept of effective dimension at 94 GHz
  5. 3. Methodology of calculating the equivalent Ze and testing the ensemble model
  6. 4. A tropical and midlatitude parametrization of IWC and Ze
  7. 5. Model comparisons against CloudSat and evaluation of the MetUM global forecast model
  8. 6. Summary and discussion
  9. Acknowledgements
  10. References

In this paper an ensemble model of ice crystals previously used to simulate the short-wave scattering properties of cirrus is now applied to simulate its equivalent radar reflectivity (Ze) at 94 GHz. It is shown that the ensemble model conserves the mass of aggregating ice crystals when compared against in situ derived mass-dimensional (m-D) relationships. The ensemble model derived m-D relationship is applied to the Rayleigh–Gans approximation to obtain a new parametrized radar reflectivity forward model for general circulation models (GCMs). The derived forward model is parametrized as a function of ice mixing ratio and in-cloud temperature, and it is shown that the forward model error is generally well within ±2 dBZe using a linear fit; this new parametrization negates the need for an ‘effective diameter’.

The Met Office Unified global Model (MetUM) predictions of ice water content (IWC) and Ze are compared against profiled in situ microphysical probe estimates of IWC and Ze, based on in situ estimates. The in situ IWC profiles were obtained from a midlatitude cirrus case during an airborne campaign around the UK. The paper demonstrates that towards cloud-bottom and cloud-top the MetUM prediction of IWC is generally within and outside the experimental uncertainty, respectively. The MetUM forward simulation of Ze assumes two particle size distributions (PSDs) of differing shapes and it is shown that the broader PSD simulates Ze better when compared against Ze based on in situ estimates for all altitudes. For the same case the PSD assumed in the CloudSat retrieval of IWC is also investigated and it is speculated that it could be too narrow towards cloud-bottom. The paper demonstrates the need for consistent PSDs when forward modelling Ze at 94 GHz, and the forward radar model error in the MetUM should be better characterized. Copyright © 2011 British Crown copyright, the Met Office. Published by John Wiley & Sons Ltd.


1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Habit mixture models and limitations of applying the concept of effective dimension at 94 GHz
  5. 3. Methodology of calculating the equivalent Ze and testing the ensemble model
  6. 4. A tropical and midlatitude parametrization of IWC and Ze
  7. 5. Model comparisons against CloudSat and evaluation of the MetUM global forecast model
  8. 6. Summary and discussion
  9. Acknowledgements
  10. References

The most recent fourth assessment report of the Intergovernmental Panel on Climate Change (IPCC) (IPCC, 2007) concluded that one of the largest uncertainties in predicting climate change is the coupling between clouds and the Earth's climate system. One such cloud that adds to the uncertainty in predicting climate change is cirrus (or ice crystal cloud). At any one time in the midlatitudes, cirrus can cover about 30% of the Earth's surface, and in the Tropics this coverage can increase to about 60–70% (Wylie and Menzel, 1999; Stubenrauch et al., 2006; Sassen et al., 2008). With such a spatial and temporal coverage it is hardly surprising that cirrus is an important component of the Earth–atmosphere radiation balance and hydrological cycle (Mitchell et al., 1989; Stephens et al., 1990, 2002; Liou and Takano, 1994; Donner et al., 1997; Edwards et al., 2007; Baran, 2009; Waliser et al., 2009).

To determine the radiative and hydrological impact of cirrus on a global scale there now exists, since April 2006, a constellation of multi-sensor Earth-orbiting satellites called the A-Train (Stephens et al., 2002), which nearly simultaneously sample the same cloud in different regions of the electromagnetic spectrum. The A-Train consists of instruments such as the MODerate-resolution Imaging Spectroradiometer (MODIS), which covers the spectral range 0.4 to 14.4 µm; the Cloud-Aerosol LIdar with Orthogonal Polarization instrument (CALIOP), which operates at 0.53 and 1.06 µm; the Polarization and Anisotropy of Reflectances for Atmospheric Sciences coupled with Observations from a Lidar (PARASOL), which covers the solar spectrum between 0.44 and 1.02 µm; and the 94 GHz vertical cloud-profiling radar called CloudSat.

With such a wide spectral coverage that the A-Train now offers it is necessary to develop theoretical scattering models of cirrus that are physically consistent across the electromagnetic spectrum rather than in just one particular region of the spectrum (Baran, 2009). In a recent paper by Zhang et al. (2009) it is argued that there should be one cirrus ice crystal model that is used to generate a set of optical properties which can then be used to generate global cirrus climatologies from space-based measurements. However, the first step must be to demonstrate that the ice crystal optical properties are physically consistent across differing regions of the electromagnetic spectrum (Baran and Francis, 2004). With the advent of CloudSat such ice crystal models should also be applicable to the frequency of 94 GHz, and this also requires them to predict the correct ice mass to within current levels of uncertainty.

In this article the ice mass consistency of a previously developed ensemble model of ice crystals used to simulate the short-wave scattering properties of cirrus (Baran and Labonnote, 2007) is tested against in situ derived m-D relationships found in the literature. The ensemble model predicted m-D relationship is then applied to simulate the equivalent radar reflectivity (Ze) at 94 GHz from in situ estimates of ice water content (IWC) and in-cloud temperature measurements obtained in the midlatitudes and Tropics.

From the Ze simulations, a parametrized Ze forward model is developed for general circulation models (GCMs). Moreover, the dependency of Ze on the assumed particle size distribution (PSD) is also investigated by using the CloudSat-retrieved IWC and Met Office Unified global Model (MetUM) simulations of Ze. Therefore, this article is about whether the same ensemble model used for visible light scattering calculations can also be consistently applied to simulate Ze at 94 GHz and the dependency of Ze on the assumed PSD.

The article is split into the following sections. Section 2 describes habit mixture models, and in particular the ensemble model of Baran and Labonnote (2007), and the limitations of applying the concept of effective dimension at 94 GHz. Section 3 describes the methodology of calculating Ze and tests the ensemble model in predicting the ice crystal mass of cirrus. Section 4 describes the parametrization of Ze in terms of the ice mixing ratio and cloud temperature, and the tropical and midlatitude data used for the parametrization. Section 5 briefly describes the Cirrus and Anvils: European Satellite and Airborne Radiation (CAESAR) measurement campaign of flying in, above and below cirrus (Baran etal., 2009) and the cirrus case used in this paper. Section 5.1 discusses the suite of microphysical instrumentation that was onboard the aircraft during the flight, as well as the in situ estimation of IWC. Section 5.2 tests the assumed PSD used in the retrieval of CloudSat IWC. Section 5.3 presents results of comparisons between the MetUM IWC and Ze simulations and the in situ estimates. Finally, section 6 summarizes the findings of this work.

2. Habit mixture models and limitations of applying the concept of effective dimension at 94 GHz

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Habit mixture models and limitations of applying the concept of effective dimension at 94 GHz
  5. 3. Methodology of calculating the equivalent Ze and testing the ensemble model
  6. 4. A tropical and midlatitude parametrization of IWC and Ze
  7. 5. Model comparisons against CloudSat and evaluation of the MetUM global forecast model
  8. 6. Summary and discussion
  9. Acknowledgements
  10. References

To conserve ice mass and to ensure that the scattering properties of ice crystal models are physically consistent across the electromagnetic spectrum, it is now generally accepted that ensembles or habit mixtures of ice crystals are better at achieving this than single ice crystal models (Foot, 1988; Francis et al., 1999; Liou etal., 2000; Baran et al., 2001; Baum et al., 2005). Baum et al. (2005) proposed a weighted habit mixture model consisting of droxtals, six-branched bullet-rosettes, solid hexagonal ice columns, hexagonal ice plates, hollow hexagonal ice columns and hexagonal ice aggregates. This weighted habit mixture model is now commonly applied to the retrieval of cirrus properties from MODIS (Platnick et al., 2003; Hong et al., 2007), and Baum et al. (2005) demonstrated that the habit mixture model conserves ice mass. This same habit mixture model was used by Hong etal. (2008) to compute Ze at 94 GHz using 1119 PSDs obtained from a number of midlatitude and tropical field campaigns. Hong et al. (2008) showed that the same habit mixture model used for the interpretation of MODIS radiometric measurements could also be applied to interpret radar reflectivity measurements made at 94 GHz, thereby demonstrating the physical consistency of the ice crystal model across the electromagnetic spectrum.

A further habit mixture model called the ‘ensemble model’ was proposed by Baran and Labonnote (2007) and this model becomes progressively more complex as a function of ice crystal maximum dimension. The model is shown in Figure 1, and consists of six elements; the first element is the solid hexagonal ice column of aspect ratio unity, representing the smallest ice crystals in the PSD. As the maximum dimension increases the elements become progressively more spatial and complex; this is achieved by arbitrarily attaching other hexagonal elements to each other, until by the sixth element, a ten-element chain is constructed, and this represents the largest ice crystals in the PSD. It was shown in Baran and Labonnote (2007) that by randomizing the reflected and refracted ray-paths and by introducing spherical air inclusions into each of the model elements, the ensemble model replicates one day of space-based global measurements of the spherical albedo. Moreover, Baran et al. (2009, 2011) demonstrated that when the ensemble model is combined with the PSD scheme of Field etal. (2007) the ensemble model could replicate for a number of midlatitude and tropical cirrus cases the cloud's volume extinction coefficient, the total solar optical depth, IWC and ice water path (IWP) to within current experimental uncertainties. The IWC and IWP were estimated by assuming that the effective density of the aggregating ice crystals in the ensemble model varied as a function of ice crystal maximum dimension. Baran et al. (2009, 2011) demonstrated that given a universal PSD scheme such as that of Field etal. (2007), the fundamental radiative parameters of cirrus could be predicted without the need for an effective dimension. The universal PSD scheme of Field et al. (2007) is described later, but first the meaning of an effective dimension is discussed. The ice crystal effective dimension of the PSD or effective diameter, De, is given, after Foot (1988) and Francis et al. (1994), by:

  • equation image(1)

where ρ is the density of solid ice, Ai is the mean cross-sectional area of the ith bin so ΣniAi is therefore the cross-sectional area density of the integrated PSD in units of m−1. Other definitions of De are explored by McFarquhar and Heymsfield (1998). Therefore, according to Eq. (1), De is an area-weighted size which is ultimately related to the bulk extinction coefficient of the cloud, if in the regime of geometric optics (see Wyser and Yang (1998) and Baran (2009) and references therein on the radiative importance of De). Due to the fundamental link between De and the solar radiative properties of the cloud, De is often used in the remote sensing of cirrus and in GCM cloud schemes for predicting the radiative properties of cirrus (see for example Hong et al. (2007) and Edwards et al. (2007)). However, De only has physical meaning at solar wavelengths where the ratio of ice crystal size to incident wavelength is large; at wavelengths where this ratio becomes small, such as in the infrared region, the concept breaks down as shown by Mitchell (2002) and Baran (2005). Thus De cannot be consistently applied across the electromagnetic spectrum to describe the radiative properties of cirrus.

thumbnail image

Figure 1. The Baran and Labonnote (2007) six-member ensemble model of cirrus ice crystals. The first element is represented by (a) the hexagonal ice column, assumed to have an aspect ratio (length-to-diameter) of unity. The second element is represented by (b) the six-branched bullet-rosette. Then with increasing ice crystal maximum dimension, D, the particles increase in complexity forming the (c) three-branched hexagonal aggregate, (d) five-branched hexagonal aggregate, (e) eight-element chain hexagonal aggregate, and (f) ten-element hexagonal chain aggregate. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

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An additional difficulty with the definition of De as given by Eq. (1) arises when ice crystals become aggregated. The aggregation of ice crystals is an important crystal growth process in the evolution of cirrus as well as in the development of precipitation (Heymsfield et al., 2002; Field et al., 2005). It is now well known that the mass of aggregating ice crystals is approximately ∝ (ice crystal maximum dimension)2 or ∝ D2; this relationship has been shown to be universal by a number of authors (Westbrook et al., 2004a, 2004b) but the relationship was theoretically predicted by Westbrook etal. (2004b). Therefore, any aggregating ice crystal model that is proposed must be shown to approximately follow this mass-D relationship. In the presence of aggregation the numerator of Eq. (1), the IWC, is ∝ D2 and in the denominator the cross-sectional area is also ∝ D2, then De just becomes a constant value which is not physically meaningful. Note also, in order to simulate Ze any ice crystal aggregating model must also be shown to follow the m-D2 relationship.

To circumvent the physical inconsistency inherent in De it is clearly more desirable to parametrize the optical properties of cirrus in general circulation models as functions of GCM prognostic variables such as the ice mixing ratio (qi) or IWC and in-cloud temperature. Such parametrizations have been proposed by Mitchell et al. (2008) and Baran et al. (2009), and argued for by Baran (2009). However, to link the GCM prognostic variable qi between the cloud and radiation schemes the same universal PSD should be utilized. Such a universal PSD scheme has been proposed by Field et al. (2005, 2007). In these articles many in situ measurements of the PSD were obtained in the midlatitudes and Tropics between the temperatures of 0°C and −60°C and they found that the many in situ PSDs could be represented by one universal PSD (a fixed PSD shape normalized by the 2nd and 3rd moments of the midlatitude and tropical PSDs). The 2nd moment (IWC) can be related to any other moment through power laws dependent on the in-cloud temperature. Given IWC and in-cloud temperature the initial PSD can be generated as demonstrated by Field et al. (2005, 2007) and Baran et al. (2011). This universal PSD scheme is independent of ice crystal shape assumptions, which means that it can be consistently applied to any ensemble model of cirrus ice crystals.

In the next section the methodology of predicting Ze using the ensemble model and testing its prediction of ice mass is described.

3. Methodology of calculating the equivalent Ze and testing the ensemble model

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Habit mixture models and limitations of applying the concept of effective dimension at 94 GHz
  5. 3. Methodology of calculating the equivalent Ze and testing the ensemble model
  6. 4. A tropical and midlatitude parametrization of IWC and Ze
  7. 5. Model comparisons against CloudSat and evaluation of the MetUM global forecast model
  8. 6. Summary and discussion
  9. Acknowledgements
  10. References

The units of the equivalent radar reflectivity factor, Ze, are expressed in mm6 m−3 and are usually transformed into dBZ via 10log10Ze, where Ze is defined (Atlas et al., 1995; Hong et al., 2008) as:

  • equation image(2)

where in Eq. (2) the constant equation image, λ is the incident wavelength in m, |K|2 is the dielectric factor assumed to have a value of 0.75 at 94 GHz (this value of |K|2 has been assumed since it is the value used to calibrate the CloudSat radar), and the choice of the dielectric factor is dictated by convention to ensure that for water droplets Z = ∫N(D)D6dD, where N(D) is the droplet size distribution function. The constant C in Eq. (2) has a value of 4.520 × 10−13 m4, σb (D) is the radar backscattering cross-section in units of m2 and n(D) is the PSD in units of m−4. The units of the integrand in Eq. (2) are SI (m6 m−3); to convert these to mm6 m−3 the integrand must be multiplied by a factor 1018. In this article the PSD is generated using the parametrization due to Field etal. (2007).

In Eq. (2) σb(D) is computed from Rayleigh–Gans theory using the formulation given in Westbrook et al. (2006), who relate σb(D) directly to the ice crystal mass, m, via:

  • equation image(3)

where ρi is the density of solid ice assumed to be 920 kg m−3, ε is the dielectric constant of solid ice and f (D) is the form factor which represents the deviation of the Rayleigh approximation as the size parameter (ratio of the circumference of a sphere to the incident wavelength) increases beyond unity. The form factor has been previously computed by Westbrook et al. (2006, 2008) for aggregating ice crystals. Since the form factor presented in Westbrook et al. (2008) has been computed for aggregating ice crystals, the same form factor is used in this paper and applied to Eq. (3). In Westbrook et al. (2006) the general conditions under which the Rayleigh–Gans approximation may be safely employed to compute σb(D) at the frequency of 94 GHz are extensively discussed. They conclude that the Rayleigh–Gans approximation could be safely applied because of (i) the relatively low value of ε at 94 GHz, (ii) the spatial nature of the assumed aggregates which would not promote strong electromagnetic coupling between individual monomers, i.e. multiple scattering between monomers could be ignored, and (iii) the relatively small size parameter of each individual monomer that make up the aggregate at the radar frequency of 94 GHz. In this article the ensemble model shown in Figure 1 is also of a spatial nature and so this model should also satisfy the three conditions given above. However, satisfying condition (ii) is the most problematic of all the conditions as this depends on how well separated the individual monomers that make up the aggregate are. The validity of the Rayleigh–Gans approximation under condition (ii) has been further investigated by C. Westbrook (personal communication) by assuming aggregates of bullet-rosettes; note that the second element of the ensemble model is the bullet-rosette as shown in Figure 1(b). It was found that when compared to calculations based on the discrete dipole approximation (Draine and Flatau, 1994) the Rayleigh–Gans approximation uniformly underestimated the backscattering cross-section by about 15%. This underestimation of the backscattering cross-section using Eq. (3) translates into a radar reflectivity error of about 0.5 dBZe. However, given that the error in the CloudSat measured radar reflectivity is ±2 dBZ the error in the Rayleigh–Gans approximation due to the neglect of multiple scattering between monomers can be considered small for the purposes of this article.

To predict σb(D), the mass term in Eq. (3) needs to be formulated for the ensemble model. The three-dimensional geometry of the ensemble model has been previously specified in Baran and Labonnote (2007). The mass, m, of the ensemble model, summed over the PSD, is given by:

  • equation image(4)

where V(D) is the geometric volume of the ice crystal ensemble and ρe(D) is the ice crystal effective density. In this paper ρe(D) is defined as:

  • equation image(5)

where Vs(D) is the volume of the circumscribing sphere and ρi is the density of solid ice. To predict the total ensemble ice crystal mass, ρe is applied when D > 100 µm, and for D ≤ 100 µm the solid density of ice is assumed. To test the ensemble model prediction of the total ice crystal mass using Eq. (4) a parametrization of the mass-D relationship is used from Field et al. (2008). In Field et al. (2008) aircraft measurements were made of the IWC, PSDs and environmental subsaturation, which were obtained during a Lagrangian spiral descent through a tropical anvil cloud between the temperatures of about −8°C and 0°C. During the spiral descent the IWC was measured to be between about 0.1 g m−3 and 1.0 g m−3; from these measurements the best fit between ice crystal mass, m, and D was found to be m = 0.024D1.85 with a pre-factor error of about ±45%. To test the ensemble model, PSDs are generated using the tropical parametrization due to Field et al. (2007) at two assumed temperature values, these being −8.0°C and 0°C. At each of the temperature values the IWC is assumed to vary between 0.1 g m−3 and 1.0 g m−3. In Figure 2(a) and (b) the ±45% uncertainty in the in situ ice crystal mass using m = 0.024D1.85 is shown as dotted open circles, and the total ice crystal mass predicted by the ensemble model using Eq. (4) and Eq. (5) as filled triangles. Also presented in the same figure is the best mass-D fit to the ensemble model, shown as filled circles, and the ice crystal mass predicted assuming the solid hexagonal ice aggregate due to Yang and Liou (1998), shown as asterisks. Figure 2(a) and (b) show that the ensemble model prediction of the ice crystal mass is generally between the ranges of experimental uncertainty, with the predictions being at the lower and higher ends of the uncertainty at the lowest and highest values assumed for the IWC, respectively. In contrast the solid hexagonal ice aggregate model substantially overpredicts the upper uncertainty of ice crystal mass by about an order of magnitude for all values of IWC, a finding consistent with Baum et al. (2005). The figures demonstrate that for the simulation of the equivalent radar reflectivity in regions of high IWC, ice crystal models that are spatial should be preferred. Also, the best-fit mass-D relationship to the ensemble model shown in Figure 2(a) and (b) was found to be (SI units):

  • equation image(6)
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Figure 2. Ice crystal mass (kg) plotted against IWC (g m−3) assuming temperatures of −8.0°C and 0°C. (a) The ice crystal mass at a temperature of −8.0°C showing the range in the experimental uncertainty (circles with dots), the mass prediction by the ensemble model (filled triangles), the mass-dimensional relationship 0.04D2 (filled circles) and the hexagonal ice aggregate model (asterisks); (b) same as (a) but at the temperature of 0.0°C.

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This mass-dimensional relationship was found by varying the pre-factor and keeping the exponent set to 2 until the difference between Eq. (6) and the ensemble model mass was best minimized. It is shown in Figure 2(a) at the temperature of −8.0°C that Eq. (6) can overestimate and underestimate the ensemble model predicted mass at the lowest and highest values used for the IWC, respectively. At the lowest IWC of 0.1 g m−3, Eq. (6), at worst, overestimates the ensemble model mass by a factor of about 1.7, though, as IWC increases, the factor in overestimation rapidly decreases to about 1.04 with an IWC of 0.6 g m−3. For IWC > 0.6 g m−3, Eq. (6) then slightly underestimates the ensemble model mass by at most a factor of 1.1 with an IWC of 1.0 g m−3. Figure 2(b) at the temperature of 0.0°C shows a similar behaviour to Figure 2(a) with Eq. (6) generally well within a factor 1.5 of the ensemble model predicted mass. It was previously discussed in the introduction that the mass of aggregating ice crystals should be proportional to approximately the square of D, and this general relationship appears to be quite well approximated by the ensemble model of Baran and Labonnote (2007), especially in the regions of high IWC, where the occurrence of precipitating aggregated ice crystals will be more important (Field et al., 2008). Considering that the error in the estimation of ice crystal mass is usually quoted as ±50% (Heymsfield et al., 2002) then Eq. (6) is sufficiently accurate for the purposes of this article. Therefore, such a simple mass-dimensional relationship that approximates the ensemble model mass well can easily be applied to Eq. (3) to compute the Rayleigh–Gans backscattering cross-section from which the equivalent radar reflectivity can then be estimated using Eq. (2). Although the ensemble model mass-D relationship was derived from tropical experimental measurements this does not exclude it from being applied to midlatitude PSDs because the model is a representation of the aggregation process, which is universal and independent of the assumed initial monomer (Westbrook et al., 2004b). Another mass-D relationship is the Brown and Francis (1995) expression represented by Eq. (13), see section 5.1, and this relationship was entirely based on aircraft data obtained off the northeast coast of Scotland. However, this does not mean that it cannot be applied to tropical data or any other part of the midlatitudes since it too is a representation of the universal aggregation process.

In the next section, Eq. (6) is used as the basis for computing the equivalent radar reflectivity in tropical and midlatitude regions.

4. A tropical and midlatitude parametrization of IWC and Ze

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Habit mixture models and limitations of applying the concept of effective dimension at 94 GHz
  5. 3. Methodology of calculating the equivalent Ze and testing the ensemble model
  6. 4. A tropical and midlatitude parametrization of IWC and Ze
  7. 5. Model comparisons against CloudSat and evaluation of the MetUM global forecast model
  8. 6. Summary and discussion
  9. Acknowledgements
  10. References

In section 2 it was argued that due to the physical inconsistency of De it is more useful to directly link GCM prognostic variables with the scattering properties of cirrus. Likewise for the simulation of Ze in general circulation models it would also be desirable to parametrize this quantity in terms of qi and in-cloud temperature.

To derive a new radar reflectivity forward model, Eq. (6) is applied to Eq. (3) to compute the Rayleigh–Gans backscattering coefficient, and then Ze is estimated using Eq. (2). The PSDs applied to Eq. (2) are derived from the parametrization due to Field et al. (2007). The IWC is then directly parametrized in terms of Ze and in-cloud temperature for both the Tropics and midlatitudes, allowing estimates of IWC from measurements of Ze and in-cloud temperature. Moreover, for application to GCMs Ze is also parametrized in terms of qi in units of kg/kg and in-cloud temperature so that the equivalent radar reflectivity can be directly simulated in GCMs. Simulating the CloudSat radar reflectivity in an operational global forecast model has been achieved by Bodas-Salcedo et al. (2008) who used the Met Office global forecast MetUM model.

Firstly, the midlatitude and tropical campaigns used to generate the PSDs are briefly described.

Most of the estimates of IWC and in-cloud temperature measurements used for the parametrizations in this article were previously compiled for a project called CIrrus microphysical properties and their effect on RAdiation: survey and integration into climate MOdels using combined SAtellite observations (CIRAMOSA). One of the purposes of this project was to compile a database of midlatitude and tropical in situ measurements of cirrus environmental properties such as in-cloud temperature and humidity as well as estimates of IWC and ice crystal size distribution functions. The microphysical and macrophysical properties were then used to parametrize the single-scattering properties of cirrus for application to a GCM (Edwards et al., 2007). The midlatitude and tropical campaigns were predominantly located around northern Europe and in the central equatorial Pacific, respectively. A description of the campaigns can be found in Table I, which gives the name of each campaign, the location, date and the source from where the data was obtained. From the midlatitude and tropical databases described in Table I a total number of 1210 IWC estimates and 1530 in-cloud temperature measurements were extracted. The total number of IWC estimates and in-cloud temperature measurements used in this article represent a range in IWC and in-cloud temperature values of between about 1.0 × 10−5 g m−3 to 1.0 g m−3 and −65.0°C to 0°C, respectively. This range in IWC and in-cloud temperature space should be sufficient to simulate the radar reflectivity at 94 GHz on a global scale for application to GCMs. As previously stated, the in situ estimates of IWC and in-cloud temperature are used to generate the PSDs using the parametrization due to Field et al. (2007). This parametrization of the PSD is preferred since the impact of ice crystal shattering on the probe inlets is specifically removed from the parametrization (Field et al., 2007). The problem of particle shattering on the probe inlets is now known to cause an artificial increase in the number concentration of ice crystals less than several hundred microns in size (Field et al., 2003; Heymsfield, 2007; McFarquhar et al., 2007; Korolev etal., 2011). To remove this artificial increase in the number concentration of ice crystals less than several hundred microns in size from the PSD the inter-arrival time of ice crystals is measured and those with short inter-arrival times are removed from the measured PSD (Field et al., 2003); this filtering procedure was applied in the analysis of Field et al. (2005, 2007). In a more recent paper by Korolev et al. (2011) it is demonstrated that filtering by itself may not remove all shattered artefacts and that specially designed tips, placed on the probe inlets, are also required to prevent shattering. However, this article is principally concerned with IWC and radar reflectivity, and for these quantities shattering does not have a significant impact. This is because IWC and radar reflectivity are determined by the 2nd and 4th moments of the PSD, respectively, which generally means that ice crystal sizes greater than several hundred microns contribute most to IWC and radar reflectivity. Indeed, in Field et al. (2006) the contribution of ice crystal shattering to the 2nd moment of the PSD was generally shown to be less than 10%. In Korolev et al. (2011) it is stated that the impact of shattering on the derived IWC and radar reflectivity is generally well within a factor 2 and at most 20%, respectively. The impact of shattering on the radar reflectivity translates into about 1 dBZ, noting that the uncertainty in the measured CloudSat radar reflectivity is ±2 dBZ. Therefore, given that this article is principally about the simulation of radar reflectivity, the Field et al. (2007) PSDs should be representative of midlatitude and tropical cirrus.

Table I. A description of the midlatitude and tropical field campaigns used in this article, their name, location, date and source of data.
NameLocationDateSource
  1. The campaigns had the following names: the EUropean and Cloud Radiation EXperiment (EUCREX), the Fram Strait Cyclone Experiment (FRAMZY), Cirrus and Anvils: European Satellite and Airborne Radiation measurements project (CAESAR), and the Central Equatorial Pacific Experiment (CEPEX).

EUCREX45°N–55°N5–30 April 1994Raschke et al. (1998)
FRAMZY77°N–88°N3–24 April 1999Brümmer et al. (2001)
CAESAR51°N–58.5°N2005–2006Baran et al. (2009)
CEPEXEquatorial PacificMarch 1993McFarquhar and Heymsfield (1996)

Applying Eq. (6) to Eq. (3) and using the in situ estimated IWC and in-cloud temperature to estimate the midlatitude and tropical PSDs, Ze from Eq. (2) is obtained in dBZe, noting that the CloudSat detection limit is −28 dBZ. The range of midlatitude and tropical radar reflectivity in dBZe as a function of IWC and temperature is shown in Figure 3(a) and 3(b), respectively. Figure 3(a) generally shows a trend in dBZe which is that at the colder temperatures and lower IWCs Ze can be as low as −50 dBZe but as temperature and IWC increase Ze also increases to about 15 dBZe at the highest IWC and warmest temperature. This behaviour is physically sensible since at the lowest IWCs and coldest temperatures the PSDs will be narrower and the occurrence of smaller ice crystals will dominate the PSD, so the equivalent radar reflectivity as a result will be low. As the IWCs and temperatures increase, the PSDs become broader resulting in larger ice crystals occurring in the PSD which in turn results in higher dBZe. The tropical dBZe simulations are shown in Figure 3(b) and the general trend in dBZe is similar to Figure 3(a), though at the very coldest temperatures of about −70°C and lowest IWC the Ze can be as low as approximately −80 dBZe. Note also, in contrast to the midlatitudes, high Ze approaching about 10 dBZe can also occur at temperatures <−50°C but at very high IWCs approaching about 1 g m−3 the Ze can reach approximately 13 dBZe, indicating the possible presence of very large ice crystals in deep tropical convection.

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Figure 3. The ensemble model predicted effective radar reflectivity in dBZe plotted as a function of IWC and in-cloud temperature for (a) the midlatitudes and (b) the Tropics. This figure is available in colour online at wileyonlinelibrary.com/journal/qj

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Given the physically realistic behaviour of dBZe as shown in Figure 3(a) and (b) it would be useful to obtain a three-dimensional fit between IWC, Ze and in-cloud temperature so that, given measurements of Ze and in-cloud temperature, IWC could then be directly estimated. Previously, there have been a number of empirical studies that have proposed relationships between Ze and IWC and/or De of the ice crystal PSD and in-cloud temperature (Liu and Illingworth, 2000; Boudala et al., 2002; Sassen et al., 2002; Garrett et al., 2003; Hogan et al., 2006; Sayres et al., 2008; Baran et al., 2009). In this article parametrizations of IWC = f(tc, Ze) and Ze = f(tc, qi), where tc is the in-cloud temperature, are offered for both the midlatitudes and Tropics and are described in the following subsections.

4.1. The midlatitudes: IWC = f(tc, Ze) and Ze = f(tc, qi)

From Figure 3(a) it can be seen that both IWC and dBZe (implying Ze) can significantly differ in order of magnitude. In order to reduce this range both IWC and Ze were firstly transformed into log10 space. Transforming Ze and IWC into log10 space and using a least squares fit minimizes the percentage error in Ze for a given IWC or IWC for a given Ze, with a uniform weight across the whole range of Ze and IWC. On the other hand, a linear fit to Ze and IWC would have minimized the absolute error, and hence would have weighted Ze and IWC to the largest cloud values, with the lowest Ze and IWC values having no influence.

The parametrizations were obtained by randomly selecting 50% of the midlatitude and tropical data so that a total number of 605 and 765 points were used for each of the fits, respectively. Using the log10 transformation and 50% of the data it was found that both IWC and Ze could be adequately parametrized using a linear equation for both the midlatitudes and Tropics. For the midlatitudes the following parametrizations for IWC and Ze were obtained:

  • equation image(7)

where in Eq. (7) tc and Ze are in units of K and mm6 m−3, respectively (these units are used in all parametrizations that follow), and the coefficients are given in Table II.

  • equation image(8)

where in Eq. (8) qi is in units of kg/kg and the coefficients are given in Table II.

Table II. The values for each of the midlatitude and tropical linear coefficients an, bn, cn, where n = 0–3, used in Eqs (7)–(10).
nabc
0−1.8099−0.00820.6908
1−0.15910.02211.4427
2−1.93720.00780.6847
3−0.16330.02141.4556

4.2. The Tropics: IWC = f(tc, Ze) and Ze = f(tc, qi)

For the Tropics the same procedure as outlined in subsection 4.1 is followed and the following parametrizations for IWC and Ze are found:

  • equation image(9)

where in Eq. (9) the coefficients are given in Table II.

  • equation image(10)

where in Eq. (10) qi is expressed in the same units as before and the coefficients are given in Table II.

Each of the parametrizations given by Eqs (7)–(10) were tested on the other 50% of the data not used to obtain Eqs (7)–(10). The accuracy of the predicted IWC using Eqs (7) and (9) is shown in Figure 4(a) in terms of the relative percentage error, χ, which is defined as:

  • equation image(11)

where in Eq. (11) IWCt is the test data, which is based on the previous 50% of the data that was randomly selected, and IWCp is the predicted IWC. The error in the forward modelling of Ze using Eqs (8) and (10) is shown in Figure 4(b) in units of dBZe, where the error in dBZe is defined as dBZet − dBZep, and the superscripts have the same meanings as before. Figure 4(a) shows that for IWC = f(tc, Ze) χ is generally well within ±20% for both the midlatitudes and Tropics, though at the warmest temperatures the error can increase to about 30% at most. Whilst for Ze = f(tc, IWC) shown in Figure 4(b) the error in dBZe is generally well within ±1 dBZe, and at the warmest temperatures the error in dBZe rises to about 1.5 dBZe in the Tropics and just over 2 dBZe in the midlatitudes. Given that the error in estimating in situ IWC or ice crystal mass is usually conservatively estimated as ±50% and dBZe is proportional to the mass squared (Heymsfield et al., 2002; Field et al., 2007), then the error in equivalent radar reflectivity due to uncertainties in mass is about ±3 dBZe. Therefore, the parametrization of IWC and Ze given by Eqs (7)–(10) can be considered to be sufficiently accurate for the purposes of this article. Figure 4(a) suggests that given Ze and tc, then IWC can be estimated to generally well within ±20%, and Figure 4(b) suggests that given qi and tc, the radar reflectivity at 94 GHz can be estimated to generally well within ±2 dBZe. Note that the error in the CloudSat radar reflectivity is ±2 dBZ.

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Figure 4. (a) The relative percentage error in the linear parameterized fit for IWC = f(tc, Ze), and (b) the error in dBZe for the linear parameterized fit (Ze = f(tc, qi)), where the squares with dots and circles with dots represents the midlatitudes and Tropics, respectively.

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In the next section the usefulness of simulating the radar reflectivity at 94 GHz in a GCM and combining these simulations with in situ estimates of IWC is demonstrated in helping to diagnose potential GCM errors.

5. Model comparisons against CloudSat and evaluation of the MetUM global forecast model

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Habit mixture models and limitations of applying the concept of effective dimension at 94 GHz
  5. 3. Methodology of calculating the equivalent Ze and testing the ensemble model
  6. 4. A tropical and midlatitude parametrization of IWC and Ze
  7. 5. Model comparisons against CloudSat and evaluation of the MetUM global forecast model
  8. 6. Summary and discussion
  9. Acknowledgements
  10. References

In this section the ensemble model derived mass-dimensional relationship used in simulating the equivalent radar reflectivity is compared against CloudSat measurements of radar reflectivity. Moreover, IWC estimates obtained from the CAESAR campaign (Baran et al., 2009) are used to evaluate the MetUM in predicting the prognostic variable IWC and simulating the radar reflectivity. Very briefly, the CAESAR campaign took place during the winter and autumn of 2007 when the FAAM (Facility for Airborne Atmospheric Measurements) BAe-146 G-LUXE aircraft flew a number of flights as part of flying in, above and below cirrus around the United Kingdom located over the sea.

In this article, one case from CAESAR is used to evaluate the MetUM; this case is named B262 and consisted of sampling optically thin cirrus preceding a frontal system. The detailed flight pattern used during the CAESAR campaign to statistically characterize the microphysical and macrophysical properties of cirrus has already been described in Baran et al. (2009) and for the case B262 used in this article a similar flight pattern to that previously described was used. The B262 frontal cirrus case occurred on 25 January 2007 over the North Sea, covering the latitudinal and longitudinal region of about 56°N to 58.4°N and about 2°E to 4°E, respectively. The next subsection briefly describes the in situ microphysical instrumentation used and the method adopted to estimate IWC from the in situ probes.

5.1. The in situ instrumentation and estimation of IWC

The main in situ microphysical instruments that were on board during B262 were the imaging PMS 2D-C probe and the small ice detector (SID-2). The PMS 2D-C probe measures the ice crystal size distribution function between about 25 to 800 µm. However, the PMS 2D-C probe has difficulties in sampling ice crystals less than 100 µm in size due to imaging problems (Strapp et al., 2001). Therefore, in this article the PMS 2D-C size bins less than 100 µm are ignored. Since the sample volume of the 2D-C probe is small in order to ensure a good statistical representation of the PSD for the larger ice crystal sizes, which contribute most to the IWC, the integration time during B262 was 60 s. To measure the PSD for ice crystal sizes less than 100 µm, SID-2 (Cotton et al., 2010) was used. This instrument can measure the ice crystal size distribution function between about 3 µm and 100 µm diameter, as well as the particle phase and particle size. Therefore, by combining SID-2 and the PMS 2D-C probe good characterization of the size spectra can be obtained. Both the 2D-C and SID-2 probes also measure the inter-arrival time of the ice crystals, and subsequent analysis of these data for both instruments showed no evidence of ice crystal shattering (Field et al., 2003) on the probe inlets, probably due to the generally small ice crystal sizes observed in this particular cirrus case.

In order to convert the measured size spectra to an IWC using the 2D-C and SID-2 probes, mass-dimensional relationships must be assumed. In the case of SID-2, the probe characterizes the ice crystal size in terms of the equal area spherical radius (Hirst et al., 2001; Cotton et al., 2010); the IWC is estimated using the following relation:

  • equation image(12)

where in Eq. (12) ρi has been previously defined, Nt is the total number concentration, and r is the equal area radius of the sphere.

For the 2D-C probe the ice crystal mass is estimated using the Brown and Francis (1995) and Francis (1995) mass-dimensional relationship, which is given by:

  • equation image(13)

where in Eq. (13) Mi is the particle mass in units of milligrams and equation image is the mean diameter (average of the maximum dimension in the x- and y-axes of the 2D-C image) of the ice particle in the ith size bin in units of millimetres.

The IWC estimated from the 2D-C probe is then given by:

  • equation image(14)

It should be noted here that Eq. (14) is only applied to size bins > 100 µm. The total IWC is found by adding the two estimates from the probes,

  • equation image(15)

The likely error in determining the IWC using the 2D-C is about ±50% (Heymsfield et al., 2002). The error in determining the IWC from the SID-2 probe is likely to be similar, with the error mostly due to uncertainties in the sampling volume and lack of knowledge of the ice crystal habit. The in-cloud temperature was measured using a 32 Hz Rosemount de-iced temperature sensor (described in Lawson and Cooper (1990)). The in-cloud temperature measurements were averaged up to 1 second data. The cloud-top and -bottom were defined by the 2D-C measured ice crystal number density being greater than 1000 m−3.

The reason why B262 was used for this article was because both SID-2 and the PMS 2D-C probe were on board the aircraft and in this case the deepest vertical ascending and descending profiles were obtained. Table III describes the profile ascent and descent times and altitudes as well as the temperature range measured during each profile. The profiles described in Table III cover a wide range of temperature and altitude and represent the only continuous profiles obtained during B262. In order to smooth profiles 8 and 9 so that high-frequency components were removed, a running mean of 35 s was found to be adequate.

Table III. The B262 profiles used in this article showing the profile date, profile start and end time (UTC), the profile altitude and the measured temperature range.
ProfileDateStart(h:min:s:)End(h:min:s:)Altitude (km)Temperature (K)
825/01/200713:52::3514:08::3110.54–6.22209–245
925/01/200714:13::5814:30::366.09–10.44244–209

From the estimated total IWC and in-cloud temperature obtained for each profile, the PSDs were generated using the midlatitude parametrization due to Field et al. (2007). These midlatitude PSDs together with Eq. (6) were applied to Eqs (3) and (2) to obtain the radar reflectivity in dBZe. The MetUM simulation of the radar reflectivities has already been described in Bodas-Salcedo etal. (2008) but in this article the simulations assume the Wilson and Ballard (1999) and Field et al. (2007) PSDs, hereinafter referred to as WB99 and Field07, respectively. This aspect was not considered by Bodas-Salcedo etal. (2008).

Before comparing the MetUM predicted IWC and radar reflectivity with the in situ derived values we first examine the dependence of the radar reflectivity on assumed PSDs using CloudSat.

5.2. Comparisons against CloudSat

During B262 there was a CloudSat overpass at about 1240 UTC; however, as can be seen from Table III, the deepest profiles 8 and 9 were not obtained until about 1–2 hours after the overpass had occurred. During this elapsed time it is probable that the cirrus had significantly evolved, making direct comparison between the MetUM predicted IWC and CloudSat retrieved IWC impossible, though these data will be used in the next section. However, in this section it is still possible to make direct comparisons between the CloudSat radar reflectivity measurements and two independent habit mixture model predictions of the equivalent radar reflectivity. Moreover, the equivalent radar reflectivity predicted by the two models is also compared against an independent parametrization of the 94 GHz radar reflectivity due to Hogan et al. (2006). Hogan et al. (2006) used ground-based scans from a 3 GHz radar collocated with the UK Met Office C-130 aircraft for a number of midlatitude frontal cirrus cases to parametrize the in situ estimated IWC as a function of equivalent radar reflectivity and in-cloud temperature. The results were then extrapolated to 94 GHz using Mie theory; the parametrization at 94 GHz is given in Table II of their paper. The Hogan et al. (2006) and Hong et al. (2008) parametrizations of the 94 GHz radar reflectivity are based on a number of in situ derived PSDs whilst the ensemble model predictions are based on the Field et al. (2007) parametrized PSDs. The Field et al. (2007) parametrization is based on the same source of PSDs used in the Hong et al. (2008) and Hogan et al. (2006) studies. Therefore, since the CloudSat retrieved IWC is based on a PSD assumption, the validity of this assumption is examined in this section by using the CloudSat retrieved IWC to forward model the radar reflectivity at 94 GHz using the two habit mixture models and the Hogan et al. (2006) parametrization.

To forward model the equivalent radar reflectivity, use is made of the CloudSat radar-only level 2B IWC product (Austin et al., 2009) and the in situ measured in-cloud temperature, on the assumption that the cloud temperature at the CloudSat retrieved altitudes remains constant in time. The precise relationship between IWC and Ze as a function of temperature for the Baum et al. (2005) habit mixture model used in this article is given in Table I of Hong et al. (2008). In the case of the ensemble model, the PSD is generated from the CloudSat retrieved IWC and in situ measured in-cloud temperature as described in section 3 and then the equivalent radar reflectivity is simulated using the ensemble mass-dimensional relationship applied to Eqs (3) and (2).

Comparisons between the CloudSat measured radar reflectivity and the forward simulation of the equivalent radar reflectivity using the two habit mixture models and parametrization assuming four CloudSat retrieved IWC profiles are shown in Figure 5(a)–(d) as a function of in-cloud temperature. Note that the sensitivity of the CloudSat radar reflectivity is not less than −28 dBZe (Austin et al., 2009), therefore CloudSat measurements significantly <−28 dBZe are not shown in the figure. Firstly, it can be seen from Figure 5(a)–(d) that the Hong et al. (2008) parametrization and the ensemble model are generally well within ±4 dBZe for all temperatures. However, towards cloud-top or at colder temperatures the ensemble model and Hong et al. (2008) parametrization are generally in good agreement. Figure 5 also shows that the ensemble model most closely follows the Hogan et al. (2006) parametrization; indeed, the ensemble model for temperatures between about −35°C and less than −45°C is within 1 dBZe of the parametrization.

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Figure 5. Comparison of the CloudSat measured radar reflectivity (±2 dBZ error bars) with the radar reflectivity predicted by the parametrized habit mixture due to Hong etal. (2008) (×), the ensemble model (open circles) and the Hogan et al. (2006) parametrization (open squares), plotted as a function of temperature for four CloudSat profiles: (a) profile 1, (b) profile 2, (c) profile 3 and (d) profile 4, that occurred during the B262 flight.

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Interestingly, when the habit mixture models and parametrization are compared against the CloudSat measured radar reflectivity in Figure 5(a)–(d) there is a general divergence between the forward simulations and measurements towards the cloud-base, and the radar reflectivity simulations are significantly greater than the measurements for the given retrieved IWC. This result towards cloud-base implies that the CloudSat retrieved IWC is too large for the given measured radar reflectivity, since this IWC results in the simulated radar reflectivity being greater than the measurements. The physical reason for this divergence could be due to the assumed PSD used in the CloudSat retrieval of IWC. At warmer temperatures the PSD becomes broader due to larger ice crystals being formed towards cloud-base (Field et al. (2007), and references therein). If the PSD is too narrow, i.e. too many small ice crystals, this will force the retrieval into giving an overestimate of IWC; this appears to be the case in Figure 5(a)–(d). Further evidence for this interpretation comes from Fig. 10 of Field07, where the parametrized PSD is compared against other PSDs such as Houze et al. (1979), and in that figure it can be seen that at warmer temperatures for both midlatitude and tropical cirrus the fourth moment of the PSD or radar reflectivity diverges between the PSDs significantly. In fact, the Houze et al. (1979) PSD predicts significantly greater radar reflectivity at warmer temperatures, due to a broader PSD, relative to the Field07 parametrization. At colder temperatures the PSDs converge. Somewhat similar behaviour can be seen in Figure 5(a)–(d) of this article where the models and parametrization tend to converge towards the CloudSat measurements at cloud-top but diverge towards cloud-bottom. Therefore, in order to fit the measured CloudSat radar reflectivity towards cloud-bottom, the 1D-variational scheme of Austin et al. (2008) assumes for the retrieval of IWC a narrower PSD relative to the two habit mixture models and parametrization.

In the next subsection the mass-dimensional relationship derived from the ensemble model is used to simulate the in situ radar reflectivity using profiles 8 and 9 from B262, since this model most closely follows the Hogan et al. (2006) parametrization, and these simulations are used to compare against the global MetUM radar reflectivity simulations.

5.3. Comparing the global MetUM against in situ estimates of IWC and dBZe

In order to obtain meaningful comparisons between the 40 km global MetUM model and the in situ estimates of IWC and ensemble model derived dBZe, at each of the model levels the nearest model grid point to the aircraft position was selected. The average distance between each of the model grid points and the aircraft position was found to be between about 17 km and 24 km for profiles 8 and 9, respectively. To compare against the aircraft in situ data, MetUM diagnostics were produced every 3 hours from each of the four analyses per day (i.e. 0000, 0600, 1200 and 1800 UTC) and the T + 3 forecast states. Instantaneous model data along the B262 flight track were extracted from the closest forecast time of (T12 + 3). With this approach, the large-scale atmospheric circulation is represented as accurately as possible within the limits of the data assimilation system, so the errors in the position of the front should be small. Figure 6(a) and 6(b) show the comparisons between the in situ estimated IWC and ensemble model derived dBZe against the equivalent model fields for profile 8, respectively. Figure 6(a) shows that towards profile-bottom, between the altitudes of about 7000 m and 9000 m, the MetUM model is generally within the in situ estimated IWC uncertainty. However, towards profile-top the model is well outside the lowest uncertainty range of the in situ IWC estimates. Interestingly, the comparisons of dBZe shown in Figure 6(b) demonstrate that the MetUM simulated radar reflectivity at altitudes greater than about 7000 m tend to systematically decrease relative to the global model IWC assuming the WB99 PSDs. For instance, between the altitudes of about 7500 m and 9500 m, the global MetUM model tends to predict an IWC that is within the estimated IWC uncertainty. However, at the same model levels the MetUM simulated dBZe tends towards the lower end of the dBZe uncertainty assuming the WB99 PSDs. Towards profile top the MetUM simulation of dBZe at an altitude of about 10000 m is considerably below the lower range of the estimated dBZe uncertainty compared to that found for the IWC. However, the global MetUM model simulated radar reflectivity assuming the Field07 PSDs shows uniformly that as a function of altitude the dBZe tends to be brighter than that predicted by the WB99 PSDs. Moreover, the simulated radar reflectivity assuming the Field07 PSDs tends to be within the upper levels of the in situ estimated uncertainty, except at the highest altitude of 10130 m.

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Figure 6. Comparisons between the global MetUM predictions of IWC and dBZe and in situ estimates of IWC and dBZe for profile 8. (a) The altitude plotted against IWC where the in situ estimate of total IWC (SID2 + 2DC) is shown as the full bold line and the ±50% uncertainties in the in situ estimate is represented by the dashed-dotted (+50%) (SID2 + 2DC + U) and dashed line (−50%) (SID2 + 2DC − U), respectively. The global MetUM predictions of IWC are represented by the filled circles (MetUM global). (b) The same as (a) but for the MetUM simulated equivalent radar reflectivity in dBZe at 94 GHz assuming the WB99 (filled circles) and Field07 (open circles) PSDs compared against the ensemble mass-dimensional relationship (0.04D2) dBZe–. The ±50% uncertainty in the ensemble dBZe is represented by the dashed-dotted (+50%) (0.04D2 +U) and dashed line (−50%) (0.04D2 − U), respectively. For illustrative purposes the CloudSat radar reflectivity sensitivity of −28 dBZ is shown as the dashed vertical line.

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Profile 9 shows comparisons between the MetUM predictions and aircraft estimations (Figure 7(a) and (b)). Figure 7(a) shows that for IWC the MetUM prediction at profile-bottom at an altitude of about 6000 m is within the upper range of the estimated IWC uncertainty. Between the altitudes of about 7000 m and 8300 m the MetUM prediction of IWC is outside the estimated IWC uncertainty. However, at altitudes greater than 9000 m the MetUM prediction of IWC is within the range of the estimated IWC uncertainty. The general trend of the MetUM simulated dBZe assuming WB99 for profile 9 shown in Figure 7(b) tends to be similar to that shown in Figure 6(b). In contrast to WB99 the Field07 PSDs simulate a radar reflectivity that is generally either at the lower or upper end of the in situ estimates, showing overall an improvement over the WB99 simulations. This behaviour of the MetUM simulated dBZe, assuming the WB99 PSDs being shifted to below or towards the lower range of the in situ derived dBZe uncertainty relative to its prediction of IWC, is apparent at the altitudes of about 9200 m, 7000 m and 6000 m and is a similar trend to that shown for profile 8.

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Figure 7. The same as Figure 6 but for profile 9.

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Figures 6(b) and 7(b) show there is a systematic bias in the MetUM simulated dBZe towards the lower end or below the in situ estimated dBZe uncertainty, even at altitudes where the corresponding IWC is within the estimated experimental uncertainty if the WB99 PSDs are assumed. The physical reasons for this behaviour in simulated MetUM dBZe is not just due to the model predicting insufficient IWC but may also be due to an unrepresentative PSD being assumed. Further evidence for the wrong shape of the PSD being assumed in the MetUM is shown in Field07. The Field07 article demonstrates that there are too many small ice crystals towards cloud-top in the MetUM model; this would have the impact of lowering the dBZe and could account for why the simulated MetUM dBZe has a low bias relative to the in situ estimates if WB99 is assumed.

Although, MetUM simulations of the 94 GHz radar are useful at diagnosing systematic model errors such as too-low IWC in midlatitude systems (Bodas-Salcedo et al., 2008), understanding the behaviour of dBZe requires a combination of model simulation and aircraft in situ sampling of IWC and the evolution of the PSD. This section highlights the need for a better characterization of forward modelling errors in GCMs.

6. Summary and discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Habit mixture models and limitations of applying the concept of effective dimension at 94 GHz
  5. 3. Methodology of calculating the equivalent Ze and testing the ensemble model
  6. 4. A tropical and midlatitude parametrization of IWC and Ze
  7. 5. Model comparisons against CloudSat and evaluation of the MetUM global forecast model
  8. 6. Summary and discussion
  9. Acknowledgements
  10. References

In this article an ensemble model of ice crystals that has been previously used to predict the solar radiative properties of cirrus has been applied to predict the equivalent radar reflectivity at 94 GHz. It has been shown that in regions of high IWC the ensemble model of Baran and Labonnote (2007), using an effective density derived from the model, predicts to within experimental uncertainty the mass of aggregating ice crystals. Moreover, it was shown that the predicted mass follows closely, and to generally well within a factor 2, a mass-dimensional relationship of the form 0.04D2. Previous theoretical studies have shown that the mass of aggregating ice crystals should be ∝ D2 (Westbrook et al., 2004b). The ensemble model derived mass-dimensional relationship was then generally applied to compute the 94 GHz radar reflectivity of cirrus using the Rayleigh–Gans approximation.

Using IWC estimates and in-cloud temperature measurements from previous midlatitude and tropical aircraft field campaigns, a total of 2740 PSDs were generated using the Field07 parametrization. These PSDs were then applied to the ensemble model to simulate the 94 GHz radar reflectivity, and these simulations were used to parametrize the tropical and midlatitude IWC as a function of Ze and in-cloud temperature. Moreover, a similar parametrization was also developed for the simulation of midlatitude and tropical Ze for GCMs as a function of the ice mixing ratio and in-cloud temperature. It was demonstrated that the three-dimensional linearly fitted parametrizations could accurately simulate the data to generally well within a relative accuracy of ±20% for the IWC fit and to within ±1 dBZe for the Ze fit. The parametrizations can be easily applied to measurements consisting of Ze and in-cloud temperature to estimate IWC or simulate Ze in GCMs directly from the ice mixing ratio and in-cloud temperature fields. These parametrizations can be directly related to GCM fields without using diagnosed quantities such as the ‘effective ice crystal dimension’. Moreover, the parametrizations can also be applied in regions of high IWC without the need to correct for aggregating ice crystals.

A case-study was used to compare the CloudSat measured radar reflectivity with the simulated radar reflectivity using the ensemble model and a habit mixture model due to Baum et al. (2005) which was parametrized in Ze space by Hong etal. (2008). It was shown that the habit mixture model was generally well within ±4 dBZe of the ensemble model as a function of temperature, and that towards profile-top both models were within a few dBZe. Interestingly, both models tended to generally significantly diverge from the CloudSat measurements towards cloud-base. It was speculated that this behaviour between the models and CloudSat was due to the assumed PSD used for the retrieval of IWC being too narrow. The ensemble model was, however, shown to follow most closely an independent parametrization of the 94 GHz radar reflectivity developed by Hogan et al. (2006) to generally within 1 dBZe for most of the temperatures considered. However, it was also shown that the Hong et al. (2008) habit mixture model tended to diverge from the Hogan et al. (2006) parametrization towards cloud bottom by about 2–3 dBZe.

The case-study was also used to test the Met Office global MetUM simulation of the IWC and radar reflectivity in dBZe against the aircraft in situ estimates. The comparisons showed that the Met Office global model prediction of IWC tended to be within the experimental uncertainty towards the middle and bottom of the cloud profiles, though at profile-top there was a systematic prediction of low IWC. Interestingly, the Met Office global model simulation of dBZe showed a general low dBZe bias relative to the in situ estimates even in regions where the MetUM model predicted an IWC that was within the experimental uncertainty, if the WB99 PSDs were assumed. There was a general improvement in MetUM simulated dBZe, relative to the in situ estimates, if the WB99 PSDs were replaced by Field07. The results presented in this paper are consistent with the previous findings of Field et al. (2007) and Bodas-Salcedo et al. (2008) in terms of too many small ice crystals and a low IWC bias in midlatitude systems, respectively. In order to circumvent such consistency problems in the assumed PSD it is recommended that a universal PSD, such as the Field et al. (2007) parametrization, is adopted for simulating the radar reflectivity and retrieval of IWC.

The article demonstrates that further in situ measurements of IWC and PSDs are required to evaluate GCMs, and reliance on satellite-only measurements is not sufficient to physically understand systematic errors in GCMs. Clearly, there is a need for better characterization of forward modelling errors in GCMs.

Acknowledgements

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Habit mixture models and limitations of applying the concept of effective dimension at 94 GHz
  5. 3. Methodology of calculating the equivalent Ze and testing the ensemble model
  6. 4. A tropical and midlatitude parametrization of IWC and Ze
  7. 5. Model comparisons against CloudSat and evaluation of the MetUM global forecast model
  8. 6. Summary and discussion
  9. Acknowledgements
  10. References

The authors wish to thank the two anonymous reviewers who have helped to improve the quality of this article. The FAAM facility jointly funded by the Met Office and Natural Environment Research Council and mission scientists as well as the technical staff for providing the data used in this article are also thanked. Alejandro Bodas-Salcedo was supported by the Joint DECC/Defra Met Office Hadley Centre Climate Programme (GA01101). NASA and the State University of Colorado are also acknowledged for making the CloudSat data freely available.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Habit mixture models and limitations of applying the concept of effective dimension at 94 GHz
  5. 3. Methodology of calculating the equivalent Ze and testing the ensemble model
  6. 4. A tropical and midlatitude parametrization of IWC and Ze
  7. 5. Model comparisons against CloudSat and evaluation of the MetUM global forecast model
  8. 6. Summary and discussion
  9. Acknowledgements
  10. References