An improved representation of the raindrop size distribution for single-moment microphysics schemes



We analyse observations of the size distribution of raindrops from a variety of cloud types and precipitation rates. The measurements show a transition from large raindrops observed in convective showers and frontal rainbands to higher concentrations of much smaller drizzle drops observed in stratocumulus clouds. The observations are used to develop an improved parametrization of the raindrop size distribution that better captures the observed transition for use in single-moment microphysics schemes. Sensitivity tests are performed in both climate and numerical weather prediction versions of the Met Office Unified Model to demonstrate that the new parametrization leads to improvements in various precipitation and cloud-related metrics. Copyright © 2012 British Crown copyright, the Met Office. Published by John Wiley & Sons Ltd.

1. Introduction

Clouds have long been recognised to play a critical role in the climate system through their influence on the radiative, thermodynamic and dynamic processes of the atmosphere. They are also a key component of the hydrological cycle of the earth–atmosphere system. Including a realistic representation of clouds and precipitation is therefore required for general circulation models (GCMs) that are used for either numerical weather prediction (NWP) or climate modelling. However, the microphysical processes that control the evolution of clouds and precipitation tend to occur on much smaller spatial scales than the typical grid-box sizes used in GCMs, and hence parametrizations are used to relate the models' grid-box mean parameters to these unresolved sub-grid processes. These parametrizations are typically designed and evaluated using observations or models that explicitly resolve the process under investigation.

In terms of precipitation, Stephens et al. (2010) perform a comparison of several state-of-the-art GCMs against observations from the CloudSat spaceborne profiling cloud radar (Stephens et al., 2008) and conclude that there is a ‘dreary state of model depiction of the real world’. There are numerous other studies that use satellite observations to evaluate precipitation in GCMs, e.g. Bodas-Salcedo et al. (2008, 2011), that also highlight large biases in current models. One of the errors that is common to the above studies is the finding that, for low-level clouds below the freezing level, there is a tendency for the models to predict excessive drizzle and rain. Bodas-Salcedo et al. (2008) show that this is particularly apparent in regions dominated by stratocumulus cloud. This is consistent with the results of Abel et al. (2010), who evaluate the performance of the Met Office Unified Model (MetUM) against observations from the VAMOS (Variability of the American Monsoon Systems) Ocean–Cloud–Atmosphere–Land Study Regional Experiment (VOCALS-REx) field project in the Southeast Pacific (Wood et al., 2011), and show that an overprediction of drizzle from stratocumulus is one of the model errors that needs to be addressed.

In this study we focus on one aspect of the parametrization of cloud microphysical processes in GCMs, namely the physical assumptions used to represent the raindrop size distribution (DSD). As precipitation rate is sensitive to particle size (larger drops fall faster), it is apparent that errors in the representation of the rain DSD could contribute to the high drizzle and rain rates found in these models. The article is organised as follows. Section 2 gives an overview of how the rain DSD is commonly represented in GCMs. Observations are then used in section 3 to characterise how the rain DSD changes across a range of cloud types and precipitation rates. We then discuss the limitations of some of the current parametrizations used in GCMs in accurately representing the observations, and modify one of the schemes to give a better representation of the measurements. Sensitivity tests with the new parametrization are then performed in the MetUM and evaluated against observations in section 5. A summary and discussion is then presented in section 6.

2. Rain DSD assumptions

Computational limitations currently prohibit the inclusion of cloud microphysics schemes that explicitly calculate the evolution of the particle size distribution (so called bin schemes) within GCMs. The approach that is typically used involves parametrizations that assume some functional form of the DSD and predict one or more moments of the distribution (so called bulk schemes). Although there are numerous bulk microphysics schemes with varying degrees of complexity described in the literature, the DSD of rain in these schemes is typically represented with either a gamma distribution (Ferrier, 1994; Morrison et al., 2005) or an exponential distribution (Lin et al., 1983; Rutledge and Hobbs, 1983; Fowler et al., 1996; Wilson and Ballard, 1999; Seifert and Beheng, 2006; Morrison and Gettelman, 2008; Thompson et al., 2008). The gamma distribution is given by

equation image(1)

where N(D) is the number concentration of droplets as a function of diameter, D. N0, λ and µ are the intercept, slope and shape parameters of the distribution. The exponential distribution is a specific form of Eq. (1) with µ = 0 and has previously been shown to provide a good description of the DSD observed in both drizzling stratocumulus (Wood, 2005b) and from heavier precipitation (Marshall and Palmer, 1948).

Many of the aforementioned bulk parametrizations only predict the mass mixing ratio of rain, qR, and assume that the DSD is represented by a Marshall–Palmer exponential size distribution which uses a fixed value of the intercept parameter N0 = 8 × 106 m−3m−1. qR is related to the rain DSD by

equation image(2)

where ρw is the density of liquid water. More complex bulk schemes have been included in GCMs that predict an additional moment of the distribution such as the number concentration of raindrops. This gives an additional degree of freedom in the representation of the DSD (variable N0 for example), enabling a better description of the DSDs that are observed in real clouds and predicted by bin schemes. An alternative to including an additional prognostic variable in a model, and therefore computationally cheaper approach, is to attempt to predict N0 from the qR alone. This method is currently used in the MetUM which predicts N0 from λ using the relation

equation image(3)

with the slope parameter λ expressed as a function of qr following

equation image(4)

where ρair is the density of air and Γ is the Gamma function. The current Global Atmosphere 3.0 configuration of the MetUM (Walters et al., 2011) uses an exponential distribution (µ = 0) with the parameters x1 = 26.2 and x2 = 1.57, hereafter referred to as the MetUM GA3.0 DSD. A slightly different method is used by Thompson et al. (2008) who vary the intercept parameter with the model-predicted qR using the equation

equation image(5)

where N1 = 9×109 m−3m−1, N2 = 2×106 m−3m−1 and qR0 = 1×10−4 kg kg−1. After N0 is calculated, Eq. (4) is solved for λ assuming an exponential size distribution such that x1 = N0, x2 = 0 and µ = 0. Both the MetUM GA3.0 and Thompson et al. (2008) methods attempt to represent the observed transition (as will be shown in this study) from high concentrations of drizzle-sized drops (approximately 50 ≤ D < 500µm) in stratocumulus clouds to DSDs that are dominated by lower concentrations of large millimetre-sized raindrops in heavy precipitation. Including an accurate representation of these characteristics of the rain DSD in different cloud types is important for predicting key parameters such as the precipitation rate R which is calculated following

equation image(6)

where V(D) is the terminal velocity of water droplets in air. It is also important for other microphysical process rates that depend on particle size such as accretion and evaporation. However, the relations described by Eqs (3) and (5) are poorly constrained by observations. There is therefore a requirement to characterise how N0 and λ vary across a wide range of rain rates from light drizzle to heavy precipitation in order to understand the limitations of these relations and develop improvements if appropriate.

3. Observed rain DSDs

3.1. Data

DSD data analysed in this study were collected from in situ aircraft measurements in stratocumulus and trade-wind cumulus clouds. In all cases the clouds were composed of hydrometeors in the liquid phase only. Table 1 gives a summary of the datasets that are used. The stratocumulus data are from the second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) field campaign off the coast of California in the Northeast Pacific (vanZanten et al., 2005), the VOCALS-REx field campaign off the coast of Chile and Peru in the Southeast Pacific (Wood et al., 2011), and from eleven flights in UK oceanic waters and one flight from the Azores in the Northeast Atlantic (Wood, 2005a). The trade-wind cumulus cloud data used are from the Rain in Cumulus over the Ocean (RICO) field campaign which was based in the Caribbean in the vicinity of the island of Antigua (Rauber et al., 2007). For each dataset we characterise N0 and λ by fitting exponential distributions to the measured DSDs as described in section 3.2.

Table 1. Summary of the aircraft field experiments and instrumentation used to measure the rain DSD.
Field campaignLocationAircraftCloud typeInstrumentation Reference
  • The FSSP was used only when the CDP optical heater failed.

VOCALS-RExSoutheast PacificFAAM BAe-146ScCDP; CIP-15Wood et al. (2011)
VOCALS-RExSoutheast PacificNSF/NCAR C-130ScCDP/FSSP; 2DCWood et al. (2011)
DYCOMS-IINortheast PacificNSF/NCAR C-130ScFSSP; 260XvanZanten et al. (2005)
VariousUK and AzoresMRF C-130ScFSSP; 2DCWood (2005a, 2005b)
RICOCaribbeanNSF/NCAR C-130CuFSSP; 2DC/2DPRauber et al. (2007)

We complement the stratocumulus and trade-wind cumulus aircraft datasets analysed in this study with reported measurements of N0 and λ from precipitation events in other cloud systems. These are derived from surface-based disdrometer measurements of the rain DSD in strong convective showers and widespread stratiform rain at various locations around the world (Waldvogel, 1974; Sauvageot and Lacaux, 1995; Tokay et al., 2001) and from aircraft measurements in frontal clouds around the UK (Field, 2000). Only data from the Field (2000) measurements at temperatures higher than 2 °C are used in order to minimise any contamination from ice particles.

In addition to these measurements, high temporal resolution (32 s) ground-based remote-sensing retrievals of the sub-cloud rain DSD are also utilised. The retrievals use a technique based on the ratio of the backscatter from two different wavelength lidars and include estimates of N0 and λ (Westbrook et al., 2010). Data are taken from a case with drizzle/light rain falling beneath stratus cloud on 6 October 2008 at the Chilbolton Observatory which is located in the south of England.

3.2. Fitting the observed DSDs

The instruments used to characterise the cloud and precipitation size distribution are described in detail in the relevant references in Table 1. These instruments measure the concentration of hydrometeors as a function of particle size (in discrete size bins). In brief, cloud droplets (approximately 2 < D < 47µm) are measured with either a Forward Scattering Spectrometer Probe (FSSP) or a Cloud Droplet Probe (CDP). Drizzle-sized drops (D ≥ 50µm) measured in stratocumulus clouds are measured with various optical array probes (2DC/CIP-15/260-X) depending on the aircraft and experiment. In addition to the 2DC, a 2DP optical array probe is also used to characterise larger rain drops (D ≥ 600µm) measured in the cumulus clouds observed in RICO. Composite size distributions that combine the data from the different instruments are produced by linear interpolation in logN(D)–logD co-ordinates.

We calculate individual DSDs using measurements made by the aircraft within cloud and averaging over a suitable time interval. Cloudy data points are defined using a minimum threshold for the total cloud droplet number concentration Nd of 5 cm−3 as measured by the FSSP or CDP. For stratocumulus clouds the averaging time interval used is 120 s, which has been assessed in previous analyses of drizzle DSDs (vanZanten et al., 2005) and corresponds to a horizontal length-scale of approximately 12 km. This is a pragmatic choice which aims to compromise between increasing the sampling statistics of the larger drizzle drops which can contribute significantly to the precipitation rate whilst maintaining a measure of variability on small spatial scales. For the RICO data, a shorter averaging time period of 15 s (length-scale of about 1.5 km) is used. This is primarily driven by the smaller physical sizes of the clouds in the trade-wind cumulus regime. However, the concentration of raindrops is much higher in the cumulus clouds sampled in RICO than in the stratocumulus data, and so the sampling statistics of large drops are not compromised.

Exponential distributions are then fitted to the precipitation-sized drops in the time-averaged DSDs using a least-squares curve-fitting algorithm. The fitting procedure accounts for uncertainties in the individual size bins by weighting the data with the Poissonian counting error. This primarily impacts the measurements of the larger particles as the number of raindrops tends to decrease with particle size. An additional fractional error is also applied to each size bin in order to account for uncertainties in the size-dependant sample area of the optical array probes (Heymsfield and Parrish, 1978). This error is estimated by calculating how the sample area changes at D values corresponding to the lower and upper edges of each size bin, and determining the subsequent uncertainty in the measured concentration. This primarily affects the smaller size bins of the optical array probes where the sample area changes rapidly with D. For the stratocumulus data, the fit is applied to drizzle-sized drops which are defined as particles with D ≥ 50µm. For the cumulus data, the fit is applied to the mode of the measured size distribution which represents the precipitation-sized particles. As will be shown below, in order to achieve a good fit, this can require increasing the minimum D used in the fitting algorithm. However we only use DSDs where the fit represents more than 95% of the measured qR above 50 µm. In total, the above procedure resulted in 812 DSDs from the stratocumulus datasets and 104 DSDs from the trade-wind cumulus dataset.

Figure 1 shows examples of the measured DSD and the fitted exponential distribution for a drizzling case in stratocumulus (R = 0.33 mm day−1) and for two cases with heavier precipitation in trade-wind cumulus clouds (R = 54.7 and 508.5 mm day−1). Two modes are evident in the measured DSDs which are plotted with filled black circles. The mode at smaller sizes represents the population of cloud droplets and the shoulder that extends to larger sizes represents the precipitation-sized particles to which the fit is applied. The emergence of larger drops with increasing rain rate is clearly evident in the observations. To test how well the fitted exponential distributions represent the measured data (D ≥ 50µm) we normalise each DSD by the fitted N0 and λ parameters in a similar manner to Wood (2005b). Figure 2 presents the data for each cloud type plotted as equation image against λD, with the grey shading representing the percentiles of equation image data points that fall within each λD bin. As an example, the light grey shading represents the 5th–95th percentiles of data points from all of the DSDs in a given cloud type. Also shown with a dashed line is the universal exponential function Nexp(D) = exp(−λD). If the data were perfectly represented by the fitted exponential distributions, then they would lie along the dashed line. For the stratocumulus cloud, the data follow the Nexp(D) curve which shows that the fitted function is a good description of the measured DSDs. For the cumulus DSDs, the data are well represented by the fit for values of λD larger than about 0.5. Below this, the data deviate from the Nexp(D) curve. The histogram in the top panel of Figure 2(b) shows that all particles with D ≥ 200µm have λD > 0.5 and are therefore well described by the fit. The histogram also shows that a fraction of particles in the cumulus DSDs at 50 ≤ D < 200µm are not described by the fit. These generally correspond to particles in the tail of the mode of the measured distribution that characterizes cloud droplets as shown by the examples in Figure 1(b, c), and are not representative of the main population of precipitation-sized droplets to which the fit is applied. It is important to note that these cloud droplets do not contribute significantly (< 5%) to the total mass of particles with D ≥ 50µm.

Figure 1.

Example DSDs from the (a) FAAM BAe-146 aircraft in stratocumulus cloud (R = 0.33 mm day−1), (b) the NSF/NCAR C-130 aircraft in cumulus cloud (R = 54.7 mm day−1), and (c) from the NSF/NCAR C-130 aircraft in cumulus cloud (R = 508.5 mm day−1). Data are shown using filled circles and the fitted exponential distribution is shown by a solid line. The equivalent DSD calculated using the various model parametrizations with the same qR as the fitted exponential distribution are also shown.

Figure 2.

Normalised DSDs, equation image, plotted against λD from (a) all stratocumulus data (812 DSDs) and (b) all cumulus data (104 DSDs). For each cloud type, the top panel shows a histogram of the percentage of data points from all individual DSDs as a function of λD. The black histogram represents droplets with D ≥ 50µm. In (b), additional histograms are shown for droplets with 50 ≤ D < 200µm (light grey) and with D ≥ 200µm (dark grey). The normalised DSDs are shown in the bottom panels. The grey shading denotes the percentiles of equation image data points that fall within each λD bin. The universal exponential distribution Nexp(D) = exp(−λD) is shown as a dashed line.

4. Parametrization of the rain DSD

Figure 3 presents a summary of how N0 varies as a function of λ from all of the datasets described in section 3.1. This includes measurements from a variety of cloud types and spans a wide range of rain rates from 0.01 to > 1000 mm day−1. Lines of constant R are shown with short-dashed lines. R is calculated as a function of N0 and λ by numerical integration of Eq. 2 using the V(D) relation from the measurements of Beard (1976). The integration is performed over a D range of 0 to 10 mm which covers the relevant drop sizes, with small ΔD increments of 2µm. It is clear that there is a trend to larger values of N0 and λ as R decreases. This indicates that there is an increased concentration of smaller droplets in the mode of the DSD that characterises the precipitation particles at lower values of R. This is also evident in the example DSD shown in Figure 1. At the heaviest precipitation rates, the DSD tends to a Marshall–Palmer-like distribution with N0 values ranging from approximately 1×106 to 1×108 m−3m−1. The transition to light drizzle in stratocumulus clouds corresponds with an increase in N0 to values as high as 1×1011 m−3m−1.

Figure 3.

N0 as a function of λ. The measured DSDs are denoted by various symbols. The short-dashed black lines show lines of constant rain rate calculated at T = 20°C and P = 1013 hPa. The long-dashed white line is a fit to the measured data. The black solid line represents the Marshall and Palmer (1948) relation, the long-dashed black line the Thompson et al. (2008) relation and the solid white line the MetUM GA3.0 parametrization.

Also plotted in Figure 3 are lines showing how N0 changes with λ for the parametrizations described in section 2. The solid black line shows the Marshall–Palmer relation which has a constant N0. This provides a reasonable representation of the DSD parameters for moderate and heavy rain rates, but is unable to capture the observed transition to higher values of N0 in lighter rain/drizzle produced by boundary-layer stratus and stratocumulus clouds. The relations used in the MetUM GA3.0 (Eq. (3)) and in the Thompson et al. (2008) scheme (Eq. (5)) are shown with solid white and dashed black lines respectively. Both relations show an increase in N0 with increasing λ as observed, but it is clear that the majority of measured data points do not lie along the lines showing the parametrizations. In order to better represent the observations, we fit the power law described by Eq. (3) to the measured N0 and λ points. The fitted parameters are x1 = 0.22 and x2 = 2.20. The fit is shown with a white dashed line in Figure 3 and provides a much better representation of the measured DSDs.

We now assess how the different DSD parametrizations impact the R that would be calculated from a model that uses a single-moment microphysics scheme with qR as the prognostic variable. For each of the observed DSDs, the measured qR and R are calculated by numerical integration of Eqs (2) and (6) using the fitted exponential distributions which are characterised by N0 and λ. The V(D) relation of Beard (1976) is used in the calculation of R. Equations (3) and (4) are then solved to calculate the equivalent DSD that each of the different parametrizations would predict from the measured qR. A model-predicted R is then calculated from the parametrized DSDs in a consistent manner to the measured DSDs. This enables the bias in the model-predicted R (which results solely from an incorrect representation of the DSD) to be assessed i.e. assuming that the model is able to predict the observed qR from other microphysical processes such as collision–coalescence or from the melting of ice particles.

Figure 4 presents scatter plots of the measured versus predicted R. The black dashed lines show the 1:1 line. It is clear that the Marshall–Palmer relation provides a good estimate of precipitation rates larger than about 10 mm day−1, but significantly overestimates R in drizzling stratocumulus by as much as a factor of 10. The relation used in the MetUM GA3.0 also has a high bias in the predicted R for light rain/drizzle but to a lesser degree than the Marshall–Palmer relation. The Thompson et al. (2008) parametrization provides a good representation of both drizzle and very heavy rainfall, but tends to underestimate intermediate values of R (∼ 5–200 mm day−1). In contrast, the new relation derived in this study from fitting the observed DSD parameters is better able to capture the measured R across six orders of magnitude from very light drizzle to heavy precipitation. The scatter around the 1:1 line is reduced, indicating a much smaller bias in the predicted rain rate than the other DSD parametrizations.

Figure 4.

Rain rate calculated from integrating the fitted exponential DSDs, RDSDmeasured, plotted against the rain rate calculated with the various model parametrizations using the same qR as the fitted exponential DSDs, RDSDparameterized. The symbols represent the individual measurements (same symbols as in Figure 3). The black dashed line is the 1:1 line.

The performance of the different parametrizations can be understood from looking at the example DSDs shown in Figure 1. For the stratocumulus case, the DSD calculated using the Thompson et al. (2008) parametrization and using the relation from this study are both in good agreement with the observations, whereas the MetUM GA3.0 and Marshall–Palmer relations predict much larger raindrops and hence overestimate R. For the intermediate rain case in cumulus cloud shown in Figure 1(b), the MetUM GA3.0, Marshall–Palmer and the new relation are in much better agreement with the observed DSD than that predicted by the Thompson et al. (2008) parametrization. In this case the Thompson et al. (2008) parametrization does not capture the larger rain drops and hence underestimates R. For the heavier rain case in cumulus cloud shown in Figure 1(c), all four schemes predict the observed DSD reasonably well.

The evaporation rate of raindrops in subsaturated air is also sensitive to particle size. Figure 5 shows how the evaporation rate varies as a function of R for an idealised case that is similar to sub-cloud environmental conditions below marine stratocumulus. The evaporation rate is calculated by integrating the fits to the observed DSDs following the equation described in Wilson and Ballard (1999). Also depicted are lines showing the evaporation rate calculated using the same method, but replacing the observed DSDs with those predicted by the different parametrizations. It is clear that the new DSD relation better represents the observations at the low precipitation rates (< 10 mm day−1) typical of drizzle or light rain falling beneath stratocumulus or stratus boundary layer clouds. Because the MetUM GA3.0 and Marshall–Palmer DSD relations predict much larger rain drops at these values of R, they tend to underestimate the evaporation rate. In contrast, at R ∼ 10 to 100 mm day−1, the Thompson et al. (2008) scheme tends to predict higher evaporation rates than calculated from the observed DSDs and from the other parametrizations.

Figure 5.

Evaporation rate of droplets as a function of rain rate (with symbols and lines as in Figure 3). The evaporation rate is calculated by integrating the DSDs following Wilson and Ballard (1999). The environmental conditions are relative humidity 80%, temperature 17°C and pressure 1000 hPa.

5. Global model simulations

A series of sensitivity tests in the MetUM were performed to evaluate the impact of changing the representation of the rain DSD in a GCM. Simulations were performed with the model run in both climate and NWP mode to evaluate the response across a variety of time-scales and resolutions. In both cases, the control simulation used the GA3.0 configuration of the model (Walters et al., 2011).

5.1. Climate model simulations

The model was run in climate mode for December 2006 at a horizontal resolution of N96 (1.875° longitude by 1.25° latitude) with 85 vertical levels below 85 km, quadratically spaced so that the vertical resolution is increased towards the surface. A time step of 20 min was used in the simulations. Two additional simulations were run, with the only change to the model being that the rain DSD parametrization was modified from the GA3.0 control version to (i) the new relation derived in section 4 and (ii) the Marshall–Palmer size distribution.

Figure 6 shows the surface precipitation rate averaged over December 2006 for the three simulations and observations from version 2.1 of the Global Precipitation Climatology Project (GPCP). The GPCP product combines observations from a variety of different satellite platforms with surface rain-gauge data (Adler et al., 2003) and has been shown to be in good agreement with independent estimates from the CloudSat radar over Oceanic regions (Stephens et al., 2008). Also highlighted in Figure 6 are regions of persistent marine stratocumulus in the Northeast and Southeast Pacific and the South Atlantic. The GPCP observations show that in much of these stratocumulus regions the monthly mean precipitation rate is less than 0.1 mm day−1, whilst the GA3.0 control simulation typically has higher values between 0.1 and 0.2 mm day−1. This appears to be consistent with the results presented in Figure 4 which show that, for typical rain rates observed in stratocumulus clouds, the DSD assumption in the model will tend to overestimate the rain rate by approximately a factor of two or three. The simulation with the Marshall–Palmer DSD is significantly worse, with surface mean precipitation rates between 0.2 and 0.4 mm day−1 in these regions. This overestimation is again consistent with the results in Figure 4. The simulation with the new representation of the rain DSD reduces the surface precipitation rate to values typically below 0.1 mm day−1, which is much closer to the GPCP observations. Investigation of the microphysical process rates in the model shows that this reduction in surface precipitation with the new DSD parametrization results from a combination of lower sedimentation rates and an increase in the evaporation rate of the drizzle droplets falling below the stratocumulus cloud (as expected from Figures 4 and 5). It can also be seen in Figure 6 that in regions of much heavier precipitation, such as the intertropical convergence zone or midlatitude storm tracks, the control simulation is very similar to the new parametrization which is expected from Figures 1, 3 and 4, which show that both schemes predict similar DSDs at high rain rates.

Figure 6.

December 2006 monthly mean surface precipitation rate from (a) GPCP observations, and model simulations using (b) the control GA3.0 DSD, (c) the new DSD, and (d) the Marshall–Palmer DSD relations. The boxes highlight regions of persistent marine stratocumulus in the Northeast and Southeast Pacific and the South Atlantic.

Figure 7 shows histograms of the 94 GHz radar reflectivity as a function of height for observations from the CloudSat space-borne radar and for the three model simulations. The data are from December 2006 and averaged over the Northeast Pacific box shown in Figure 6. The other stratocumulus regions show the same features. For the simulations, the radar reflectivity profiles are calculated from the model-predicted condensed water and precipitation amounts using the Cloud Feedback Model Intercomparison Project (CFMIP) Observational Simulator Package (COSP; Bodas-Salcedo et al., 2011). It is worth highlighting that radar reflectivity is proportional to D6 and so is highly sensitive to changes in the rain DSD. The CloudSat observations show that the low-level cloud below about 2 km is characterised by a peak at about–26 dBZ which is representative of very weakly (or non-)precipitating cloud and a continuous transition to higher values of radar reflectivity which represent heavier drizzle/rain. The GA3.0 control simulation does not show this transition, with the largest occurrence of reflectivities between –10 and 0 dBZ, which indicates that the frequency of precipitation and/or the particle size of the drizzle from the stratocumulus cloud is overestimated. The simulation that uses the Marshall–Palmer DSD is even worse, with the peak now more intense and closer to 0 dBZ. An improvement is seen in the simulation which uses the new DSD relation, with a reduction in the intensity of the peak reflectivity and a shift in the location of the peak to values below–10 dBZ. There are also increased occurrences of reflectivity values below–20 dBZ although these remain less frequent than in the CloudSat observations. The differences in the radar reflectivity profiles at higher altitudes are associated with ice particles and are discussed in Bodas-Salcedo et al. (2008).

Figure 7.

Histograms showing the 94 GHz radar reflectivity as a function of height (a) measured by CloudSat, and simulated in the MetUM using (b) the control GA3.0 DSD (c) the new DSD and (d) the Marshall–Palmer DSD relations. The colour bar represents the percentage of data points that fall within each bin of the height–radar reflectivity histograms. Data are taken from December 2006 in the North Pacific box shown in Figure 6. There are no CloudSat data in the 0–1 km altitude bin in order to minimise contamination of the radar echo from the surface return.

To demonstrate that the reduction in drizzle is a robust feature of the model across longer time-scales, we evaluate the response of the mean climate with additional 10-year atmosphere/land-only climate simulations forced by observed sea-surface temperatures and covering the period 1980 to 1990. Table 2 presents the mean error in a selection of precipitation and cloud-related metrics for the control and new DSD simulations as evaluated against observed climatologies. Results are shown for averages over the globe, the Tropics, Europe and the Northeast Pacific. In the Northeast Pacific region, which shows the same features as the other major stratocumulus regions, there is a reduction in surface precipitation with the new DSD relation which reduces the mean error in the model. A significant improvement can also be seen in the probability of dry day occurrence which is defined as < 0.1 mm day−1 in surface precipitation. The control simulation suffered from a large negative bias (i.e. not enough dry days) which primarily resulted from persistent drizzle. This metric has been improved in all of the regions where there is a tendency for the control simulation to underpredict dry day occurrence, suggesting that the new DSD relation has also improved light rain/drizzle in areas away from the major marine stratocumulus decks highlighted in Figure 6. In the global and tropical regions, there are small decreases in the mean error in precipitation which slightly improve the bias in the model. An interesting feedback in precipitation is apparent in the European region. In the control simulation there is an underprediction in the mean precipitation which is improved in the simulation using the new DSD relation. The increase in the dry day occurrence metric shows that there is a reduction in light drizzle over Europe, suggesting that the increase in the mean value has resulted from more frequent or more intense heavier rainfall events.

Table 2. A selection of mean errors of precipitation and cloud-related metrics from the 10-year climate simulations using the control GA3.0 and new DSD relations. The observational datasets used for the comparisons are GPCP (Adler et al., 2003) for surface precipitation and dry day probability, ERA-40 (Uppala et al., 2005) for precipitable water content, and ISCCP (Rossow and Schiffer, 1999) for cloud amount. The rightmost column shows the difference in the mean error between the simulations normalised by the observed value and expressed as a percentage. Values in bold indicate parameters where there is an improvement with the new DSD relation compared to the observed value.
Metric (units)ObservedMetUM GA3.0New DSD100(δ2δ1)
 valueerror (δ1)error (δ2)equation image
  1. Tropics: 20°S–20°N. Europe: 15°W–30°E, 30–70°N. Northeast Pacific: 140–110°W, 15–35°N.

Surface precipitation (mm day−1)2.6610.3600.359–0.05
Probability of a dry day (fraction)0.550–0.199–0.1528.49
Precipitable water content (kg m−2)24.31–1.35–1.091.10
Total cloud amount (fraction)0.626–0.0020.0101.96
Surface precipitation (mm day−1)3.5080.8300.829–0.05
Probability of a dry day (fraction)0.561–0.242–0.17711.7
Precipitable water content (kg m−2)40.54–3.31–2.811.21
Total cloud amount (fraction)0.602–0.054–0.0421.88
Surface precipitation (mm day−1)2.383–0.372–0.3401.35
Probability of a dry day (fraction)0.529–0.090–0.0615.58
Precipitable water content (kg m−2)15.49–0.55–0.271.77
Total cloud amount (fraction)0.5630.0620.0803.25
Northeast Pacific
Surface precipitation (mm day−1)0.6770.0650.057–1.08
Probability of a dry day (fraction)0.808–0.191–0.08812.8
Precipitable water content (kg m−2)27.27–3.36–3.081.03
Total cloud amount (fraction)0.693–0.078–0.0523.66

Table 2 also summarises changes in the precipitable water content in the different regions. It is clear that in all regions there was a dry bias in the control simulations compared to the European Centre for Medium-range Weather Forecasts ERA-40 reanalysis (Uppala et al., 2005), which is reduced with the new DSD relation. This largely results from an increase in the evaporation of drizzle/raindrops and lower surface precipitation rates, leading to more water being retained in the atmospheric column. This also leads to an increase in convective activity in the model which is likely to be the source of the improvement in the mean error of surface precipitation over European regions. There is also an increase in the total cloud cover in all regions compared with the cloud climatology from ISCCP (Rossow and Schiffer, 1999). The increase in total cloud cover has led to improvements in regions where there was a deficit in the control simulation (marine stratocumulus and Tropics) and a degradation in regions that overpredicted cloud (Europe and global). It should be noted that, although the mean error in the global cloud cover is higher with the new DSD relation, there is a small reduction in the root-mean-squared error compared with ISCCP.

5.2. NWP simulations

The effects on short-range forecasts are evaluated with a set of 20 NWP case-studies using the testing strategy outlined in Walters et al. (2011). The case-studies consist of ten 5-day forecasts selected from the December to February (DJF) 2008/9 and 2009/10 seasons and ten 5-day forecasts selected from the June to August (JJA) 2008 and 2009 seasons. The forecasts are initialised using the Met Office operational analysis at 1200 UTC, with each case separated by approximately two weeks to reduce the synoptic correlation between cases. Each forecast is run at a horizontal resolution of N320 (0.5625° longitude by 0.375° latitude) with the same vertical resolution in the troposphere as the climate model and slightly degraded resolution in the stratosphere. A time step of 12 min is used in the simulations.

Figure 8 shows a verification of the JJA forecasts against land-based observations in the extratropical Northern Hemisphere (20–90°N) of mean-sea-level pressure, temperature at screen height, relative humidity at screen height, 6 h accumulated precipitation, fractional cloud cover and visibility. These show a marked reduction in the mean forecast error for all parameters with the new DSD relation. The DJF case-studies show mainly neutral results and are therefore not shown. It is evident from Figure 8 that the new DSD relation reduces the positive mean error for accumulated precipitation shown in the control simulation which forecasts too much precipitation. Equitable threat scores (not shown) also show that there is a positive frequency bias in the prediction of low-rain-rate events, i.e. they are predicted too often, and the new DSD relation reduces this bias. Visibility forecasts are also improved, which likely results from increased evaporation of drizzle drops, cooling and moistening the lower atmosphere and therefore increasing the frequency of low-visibility conditions such as fog. The tendency for cooling and moistening of the sub-cloud layer from additional evaporation also improves the verification of temperature and relative humidity at the screen level. As discussed in Walters et al. (2011), the warm bias in the control GA3.0 simulation seen over Northern Hemisphere land during JJA was the primary reason that some minor changes have to be made to the GA3.0 physics for operational NWP use. It is possible that the overprediction of light rain was one of the causes of this warm bias. It is also clear that cloud cover was typically underpredicted and the new DSD relation has increased the cloud cover, improving the verification. Finally, small improvements can also be seen in the mean-sea-level pressure verification.

Figure 8.

Mean forecast error from the ten NWP case-studies in JJA as a function of forecast range for surface observations of (a) mean-sea-level pressure, (b) temperature at screen height, (c) relative humidity at screen height, (d) 6 h accumulated precipitation, (e) fractional cloud cover, and (f) visibility. These mean errors are calculated as the forecast value minus the observed value of a given parameter and averaged over all land-based observations in the extratropical Northern Hemisphere (20–90°N). The error bars denote the standard deviation of the mean errors from the ten individual case-studies. Results are shown for simulations using the control GA3.0 and the new DSD relations.

6. Conclusions

In this study we analysed observations of the size distribution of raindrops from a range of cloud types and precipitation rates. The observations show a marked transition from high concentrations of small drizzle drops measured in stratocumulus clouds to lower concentrations of much larger raindrops found in strong convective showers or widespread frontal rainbands. The measurements are used to illustrate the limitations of some single-moment microphysics schemes used in current GCMs which describe the rain DSD with an exponential distribution. In particular the Marshall–Palmer relation is shown to significantly overestimate drizzle/light rain rates because it does not represent the observed increase in the intercept parameter of the distribution with decreasing rain rate. The other parametrizations tested do attempt to represent this transition, but are shown to either overestimate light drizzle rates in the case of the MetUM GA3.0 scheme or underestimate intermediate rain rates in the case of the Thompson et al. (2008) scheme. An improved parametrization for use in single-moment microphysics schemes which predict the mass mixing ratio of rain is then developed to better represent the observations. The rain DSD is described by an exponential function with variable intercept and slope parameters of the distribution following Eqs (3) and (4) with x1 = 0.22, x2 = 2.20 and µ = 0. It is shown to better capture the measured rain rate across a range of scales from light drizzle to heavy precipitation. It is also shown to better represent the evaporation rate of droplets at low rain rates typical of boundary-layer stratocumulus or stratus clouds. An advantage of the new relation is that it can be easily implemented into GCMs that use one of the numerous single-moment bulk microphysics schemes described in the literature which depict the size distribution of raindrops with an exponential distribution (e.g. Lin et al., 1983; Rutledge and Hobbs, 1983; Fowler et al., 1996; Wilson and Ballard, 1999; Thompson et al., 2008). It is noted that, although a wide range of cloud types have been included in the observational dataset used for this study, additional measurements of the rain DSD from climatological regimes not sampled could be employed in future work to further assess the wider applicability of the new parametrization.

Sensitivity tests were performed within the GA3.0 configuration of the MetUM run in both climate and NWP modes in order to look at the impact of changing the parametrization of the rain DSD in the model. The climate simulations with both the control MetUM GA3.0 and the Marshall–Palmer DSD relations show an excess in the monthly mean surface precipitation rates in regions dominated by stratocumulus cloud when compared to observations from version 2.1 of the Global Precipitation Climatology Project. The surface precipitation rate is reduced in these regions when the new DSD relation is implemented in the model and is in better agreement with the observations. A significant increase in the frequency of dry days is shown across all regions of the globe which better matches the observed climatology. This highlights that the new DSD relation has also reduced the overprediction of light rain/drizzle in areas away from the major marine stratocumulus decks.

A comparison of reflectivity profiles from simulations in the MetUM with both the Marshall–Palmer and GA3.0 representations of the DSD against measurements from the CloudSat space-borne radar also shows significant biases in the modelled characteristics of precipitation from low-level clouds, with the simulations predicting much higher radar reflectivities than observed. This bias is not unique to the MetUM GA3.0, and has been shown to be common to many state-of-the-art GCMs (Bodas-Salcedo et al., 2011; Stephens et al., 2010). A significant reduction in the bias is found with the new rain DSD relation implemented in the MetUM, although it is evident that the model still does not capture the correct frequency distribution of reflectivity in low-level clouds. The CloudSat observations show a peak in the reflectivity of about–26 dBZ which is indicative of very weakly (or non-)precipitating cloud, whereas the model predicts a peak between–10 and 0 dBZ with the new DSD relation. It is not clear from the work in this study if this difference in the reflectivity from low-level clouds results from errors in the sub-grid representation of precipitation in the model or from errors in other assumptions used within the cloud microphysics scheme. However Boutle and Abel (2012) present comparisons of high-resolution NWP simulations of the stratocumulus-topped boundary layer with radar reflectivity observations from a cloud radar. They show that the bias in the simulated reflectivity can be significantly reduced when the DSD relation derived in this study is combined with changes to the autoconversion rate (which controls the conversion of cloud water to precipitation) in the MetUM microphysics scheme. In addition to the changes made by Boutle and Abel (2012), further investigation on the representation of subgrid-scale variability of precipitation in coarse-resolution GCMs, and the inclusion of aerosol–cloud interactions such as that discussed in Wilkinson et al. (2012), are warranted in future studies.

Verification of the NWP forecasts against surface observations in the extratropical Northern Hemisphere also show encouraging improvements in the performance of the simulations with the new DSD relation. In addition to an improvement in the surface precipitation forecast, the new DSD relation also tends to increase the evaporation of falling droplets in the sub-cloud layer because the drizzle droplets are represented by smaller particles than in the control simulation. This tends to cool and moisten the boundary layer which reduces a warm and dry bias in the model. This also leads to an improved verification of both cloud cover and visibility.


We would like to thank Chris Westbrook for the provision of the Chilbolton lidar data and Rob Wood for the MRF C-130 stratocumulus dataset. Ian Crawford and Jonathan Crosier are thanked for providing the FAAM BAe-146 VOCALS-REx cloud physics data. The NSF/NCAR C-130 aircraft VOCALS-REx, DYCOMS-II and RICO datasets were obtained from the NCAR/EOL data archive. Alejandro Bodas-Salcedo is thanked for advice on using the COSP simulator in the MetUM. Richard Cotton is thanked for useful discussions on fitting the observed particle size distributions.