a. Diagnostic cloud liquid/ice condensate (DIAG)

Prior to 9 November 2010 (IFS cycle 36r3 and earlier), the operational IFS cloud scheme had one prognostic variable for subgrid cloud fraction and one for cloud condensate, and a diagnostic representation of precipitating rain and snow determined by autoconversion, evaporation, and melting parameterizations (Tiedtke 1993). In this scheme (referred to here as DIAG), a fixed diagnostic temperature-dependent function is used to partition the cloud condensate variable into liquid and ice in the mixed-phase temperature regime. The fraction of liquid water α in the total condensate amount is derived from data in Matveev (1984) and defined in the model as

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where T₀ = 0°C and T_ice = −23°C represent the threshold temperatures between which a mixed-phase cloud is allowed to exist. The fraction of supercooled liquid in the cloud ice/liquid mixture (solid line in Fig. 1) therefore decreases with decreasing temperature from all liquid at 0°C to all ice at −23°C and is a first approximation to the global mean distribution of supercooled liquid water occurrence. This has been a common approach for GCMs over the years and is still present in cloud parameterization schemes in a number of NWP and climate models (e.g., Del Genio et al. 1996; Zhao and Carr 1997; Lopez 2002; Boville et al. 2006; Bélair et al. 2009; Wu et al. 2010).

Frequency distribution of liquid water fraction as a function of temperature for the diagnostic temperature-dependent mixed-phase scheme (solid black line) and the new prognostic ice/liquid scheme (shading) during January 2011 (a) for the whole globe, (b) for the Arctic region (75°–90°N), and (c) for the tropics (10°S–10°N).

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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Frequency distribution of liquid water fraction as a function of temperature for the diagnostic temperature-dependent mixed-phase scheme (solid black line) and the new prognostic ice/liquid scheme (shading) during January 2011 (a) for the whole globe, (b) for the Arctic region (75°–90°N), and (c) for the tropics (10°S–10°N).

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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Frequency distribution of liquid water fraction as a function of temperature for the diagnostic temperature-dependent mixed-phase scheme (solid black line) and the new prognostic ice/liquid scheme (shading) during January 2011 (a) for the whole globe, (b) for the Arctic region (75°–90°N), and (c) for the tropics (10°S–10°N).

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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b. Prognostic cloud liquid and cloud ice condensate (PROG)

A major upgrade to the parameterization of cloud and precipitation was implemented in IFS cycle 36r4, operational at ECMWF from 9 November 2010. The new scheme (referred to here as PROG) has separate prognostic variables for cloud liquid condensate and cloud ice condensate, as well as prognostic variables for both rain and snow.

This removes the diagnostic temperature dependent liquid/ice phase split in the previous scheme and allows additional degrees of freedom to represent the wider variability of supercooled liquid water observed in the atmosphere. Cloud liquid water drops are formed when water saturation is reached, then the processes of ice crystal nucleation and diffusional growth determine the rate of conversion of supercooled liquid water to ice cloud. The parameterizations of ice nucleation and diffusional growth follow Rotstayn et al. (2000) [their Eqs. (2)–(5)], as summarized below.

Following Pruppacher and Klett (1997), the rate of growth of an ice crystal of mass M_i is

View Expanded

where C is the capacitance of the particle (related to the shape), S_i = (e/e_si − 1) is the ice supersaturation (ratio of vapor pressure e to the saturated vapor pressure with respect to ice, e_si), T is the air temperature, L_s is the latent heat of sublimation, R_υ is the gas constant for vapor, K_a is the heat conductivity of air, and χ is the diffusivity of water vapor in air, which varies inversely with pressure p, as χ = 2.21/p.

Equation (1) is integrated over the assumed ice particle size distribution to determine the gridbox mean ice deposition rate. In the current scheme, as in Rotstayn et al. (2000), the ice crystals are assumed to be monodispersed with all particles having equal diameter D_i and equal mass M_i (and therefore also equal density where ρ_i = 700 kg m⁻³). The cloud ice specific water content is therefore q_i =M_iN_i/ρ, where ρ is the density of air and N_i is the ice crystal number concentration defined below. The capacitance term C in Eq. (1) assumes ice crystals are spherical (C = D_i/2) where D_i = (6M_i/πρ_i)^1/3. Elimination of C in Eq. (1) then gives an equation for the rate of depositional growth of ice q_i as a function of number concentration, supersaturation, and specific ice water content:

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where β is a function of air density and temperature. The ice crystal number concentration N_i is given by the parameterization of Meyers et al. (1992) and, as the cloud is considered to be at water saturation in the model when considering the nucleation process and subsequent depositional growth, this is defined as

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The vapor pressures at ice saturation e_si and water saturation e_sl are dependent only on temperature so in this implementation the number of activated ice nuclei is also purely a function of temperature. The deposition process is active when there is liquid water present and so assumes that the vapor pressure e is at water saturation e_sl. When the liquid water is depleted, the deposition process becomes inactive, an approximation that will be addressed in the future. Equations (2) and (3) show the deposition rate is dependent on the amount of ice mass already in the grid box, increasing for higher ice water contents, and on the temperature through the ice crystal number concentration and supersaturation terms, increasing with decreasing temperature. The validity of the approximations and uncertainties in the ice nuclei concentration and deposition rate formulations described here are discussed in section 3.

The new scheme with separate liquid and ice prognostic variables and parameterized depositional growth allows supercooled liquid water to exist at all temperatures between 0°C and the homogeneous freezing threshold temperature defined as −38°C. At temperatures colder than this water droplets are assumed to freeze instantaneously and homogeneous nucleation of ice particles occurs when a critical supersaturation with respect to ice is reached in the clear air part of the grid box, as described in detail by Tompkins et al. (2007). For temperatures warmer than −38°C when supercooled liquid and ice coexist, they are assumed to be well mixed and distributed uniformly through the cloud, although alternative liquid-ice overlap assumptions can be made (Rotstayn et al. 2000).

It is the process of deposition representing the Wegener–Bergeron–Findeisen (WBF) process that largely determines the partition between liquid and ice in mixed-phase clouds in the scheme. Figure 1a shows the frequency distribution of the phase partition between ice and liquid cloud for a model forecast using the new scheme (PROG) compared to the previous diagnostic version (DIAG) for all cloud globally. It is seen that the “S” shape is reproduced from observations (e.g., Rotstayn et al. 2000). Compared to the default model, which sets liquid water fraction diagnostically to zero at −23°C, there are more occurrences of liquid water at temperatures colder than this threshold. The mode of the distribution still approximately follows the temperature-dependent function due to the diagnostic phase assumption remaining in the cloud source term from the convection parameterization, but variability is significantly increased. For example, 100% of cloud is all ice at −38°C, 100% is all liquid at +10°C, but at −10°C the cloud can vary from all ice, through varying fractions of supercooled liquid water, to all water. There is no liquid water at temperatures colder than around −38°C because of homogeneous freezing and there is increased occurrence of pure ice cloud at all temperatures colder than 0°C. Small ice fractions (i.e., liquid water fractions close to one) at temperatures warmer than 0°C are due to the fact that ice is allowed to fall and takes a finite time to melt. To highlight the regional variations of the phase partitioning, Figs. 1b and 1c show the frequency distribution of water fraction for the Arctic (75°–90°N) and the tropics (10°S–10°N), respectively. The impact of the diagnostic temperature-dependent mixed-phase function in the convective parameterization as a source of condensate is very clear in the tropics, and the higher occurrence of supercooled liquid water at colder temperatures is evident in the Arctic cloud.

The change to separate prognostic variables for liquid and ice is a major step forward in the representation of mixed-phase cloud in the IFS, but as will be shown in section 4, the additional degrees of freedom can also be detrimental to the forecast if all processes are not represented adequately. In particular, simulating the commonly observed thin liquid water layers at cloud top is difficult for typical global models with resolutions that are too coarse to represent the small-scale processes as well as deficiencies in the formulation of parameterizations. Some of these issues for the IFS are discussed in the following section.

a. Vertical resolution

The poorly resolved vertical profile of ice water content and supersaturation in the top few hundred meters of the cloud is likely to have a detrimental impact on the cloud-top supercooled liquid water layer. Observations, large-eddy simulations, and single-column model studies show ice water content increases, while the supersaturation decreases with distance downward from cloud top (Shupe et al. 2008b; BHF14). As seen in Eq. (2), the deposition rate is the product of these two terms. BHF14 describe a single-column model sensitivity study for a shallow supercooled liquid-water-topped cloud showing that the fastest deposition growth rates occur significantly below cloud top and that a higher proportion of the ice should sediment out of the grid layer due to the increasing profile of ice toward the base of the layer. They show that the persistence of the cloud-top SLW layer is particular sensitive to the vertical resolution of the model. When the cloud is well resolved with high vertical resolution the thermodynamic profile, deposition rate, and sedimentation are accurately represented and the smaller deposition rate at cloud top leads to a supercooled liquid water layer that is able to persist. However, with coarser vertical resolution representing the cloud with only one or two model layers, as is common in many GCMs, the assumption that the ice water content is uniform within the layer and the underestimate of ice sedimentation away from the cloud top leads to an overestimate of deposition rate and a more rapid depletion of the supercooled water layer.

Figure 2a shows the sensitivity of the supercooled liquid profile to the model’s vertical resolution. The control SCM run (black curve) with 60 vertical levels (layer thickness of about 210 m at 1-km height) produces a maximum liquid water content of about 0.08 g kg⁻¹. Increasing the vertical resolution to 137 levels (100-m-layer thickness at 1 km, red curve) almost triples the water amount in the topmost cloud layer. Ice water content is also increased, though only by about 50%.

b. Ice particle number concentration

The ice nuclei concentration (IN) is a large uncertainty due to the wide variability observed in the atmosphere (e.g., DeMott et al. 2010). The formulation of the deposition rate in Eq. (2) in the PROG version of the model makes it particularly sensitive to the parameterization of the number of nucleated ice particles. Equation (3) based on Meyers et al. (1992) is used here, but there are significant spatial and temporal variations and uncertainties with many proposed alternative parameterizations as a function of temperature and supersaturation (Cooper 1986; Prenni et al. 2007; DeMott et al. 2010). Prenni et al. (2007) describe observations of IN in the Arctic during M-PACE in the fall of 2004 with much lower IN concentrations observed than predicted by the Meyers et al. (1992) parameterization [see Eq. (3)]. They propose an alternative formulation that provides a better fit to the M-PACE data:

View Expanded

Figure 3a shows the two IN parameterizations from Eqs. (3) and (4), as well as other proposed formulations in the literature, as a function of temperature and assuming water saturation. For a given temperature, the number of IN can be different by orders of magnitude with a direct impact on the deposition rate in Eq. (2). The cloud in Fig. 2 is at about −10°C and so the Prenni et al. (2007) formulation decreases the deposition rate by about a factor of 5. The impact is to significantly increase the amount of SLW throughout the cloud, which leads to a more persistent and deeper Arctic boundary layer cloud as shown in Fig. 2b (blue curve versus black curve). However, although the Prenni et al. (2007) formulation may be a better representation of the observations for the M-PACE case, its validity throughout the entire global troposphere across different meteorological regimes is uncertain, as is also the case for other alternative formulations.

(a) Ice nuclei number concentration as a function of temperature for various parameterizations: Meyers et al. (1992), Prenni et al. (2007), Cooper (1986), and DeMott et al. (2010). (b) Bulk ice deposition rate as a function of ice water content for the Rotstayn et al. (2000) (solid line) and Wilson and Ballard (1999) (dashed line) parameterizations assuming water saturation at a temperature of −10°C and pressure of 950 hPa.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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(a) Ice nuclei number concentration as a function of temperature for various parameterizations: Meyers et al. (1992), Prenni et al. (2007), Cooper (1986), and DeMott et al. (2010). (b) Bulk ice deposition rate as a function of ice water content for the Rotstayn et al. (2000) (solid line) and Wilson and Ballard (1999) (dashed line) parameterizations assuming water saturation at a temperature of −10°C and pressure of 950 hPa.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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(a) Ice nuclei number concentration as a function of temperature for various parameterizations: Meyers et al. (1992), Prenni et al. (2007), Cooper (1986), and DeMott et al. (2010). (b) Bulk ice deposition rate as a function of ice water content for the Rotstayn et al. (2000) (solid line) and Wilson and Ballard (1999) (dashed line) parameterizations assuming water saturation at a temperature of −10°C and pressure of 950 hPa.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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c. Deposition rate formulation

The ice deposition growth rate parameterization from Rotstayn et al. (2000) described in section 2b has a number of simplifying assumptions such as the monodisperse size distribution, constant ice density, spherical particles, and lack of a ventilation enhancement term. An alternative formulation following Wilson and Ballard (1999) with an exponential size distribution, ventilation factor, and variable ice density is implemented in the single-column model to assess the impact on the SLW layer. Forbes and Clark (2003) [their Eqs. (1)–(12)] provide the details of the formulation of the deposition rate and show that it can be written in a similar form to Eq. (2):

View Expanded

where β′ is a function of air density and temperature, and the exponent γ takes a value close to ⅔ for small ice water contents and a value closer to 1 for larger ice water contents due to the dependence on the ice terminal fall speed in the ventilation factor. A comparison of the ice deposition rate for the Rotstayn et al. (2000) and Wilson and Ballard (1999) schemes as a function of ice water content is shown in Fig. 3b. The different exponent for the ice water content of ⅓ in Eq. (2) and ⅔ toward 1 in Eq. (5) result in large differences of the deposition rate for high and low ice water contents. The impact of the new deposition rate on the SCM Arctic case is shown in Fig. 2b (red line) and there is significantly less liquid water and ice in the profile. In fact, the initial ice water content is about 10⁻⁵ g kg⁻¹ and this results in a factor of 3 higher deposition rate (Fig. 3b) that removes all the SLW in the first few time steps and the cloud collapses. The main point of this result is to highlight the sensitive balance of processes in the cloud and the need for appropriate parameterizations of both the sources and sinks of SLW for a realistic simulation of mixed-phase boundary layer cloud.

d. Turbulent production of water saturation

In the absence of large-scale ascent, turbulent vertical motion can be sufficient to bring an air parcel to saturation and produce liquid condensate. Currently, the IFS represents enhanced turbulence driven by strong cloud-top cooling only in its stratocumulus boundary layer scheme (Köhler et al. 2011). This scheme requires a positive surface buoyancy flux to trigger, otherwise, the boundary layer is considered to be stable. This is problematic in the case of decoupled stratiform layers, such as might be found during the night over the winter continents or in the Arctic. It is likely that turbulence, and thus liquid production, will be underestimated in these cases. Inspiration for an improved treatment of turbulent-driven production of water saturation in mixed-phase clouds can be found, for example, in the works of Korolev and Field (2008), Hill et al. (2014), and Field et al. (2013). A revision of the boundary layer turbulent production of supercooled liquid water is part of future development plans for the IFS and cannot yet be included in the sensitivity tests here. Although clearly an important part of the mixed-phase problem, it is one of many.

e. A pragmatic reduction of cloud-top deposition (PROG+)

After implementation of the new prognostic (PROG) cloud scheme in the operational global ECMWF model in November 2010, a cold bias was reported in the forecast of 2-m temperatures over parts of Scandinavia during January 2011 (discussed in more detail in section 4c). This prompted an investigation that found a correlation between the increased temperature bias and regions of subfreezing boundary layer cloud with too little supercooled liquid water at cloud top.

The uncertainties in the mixed-phase processes discussed above were all possible contributors to the bias. However, any change to the model has to be appropriate for all the different meteorological regimes across the whole globe. In particular, supercooled liquid water is present in deep convective clouds in the tropics, clouds associated with frontal cyclones in midlatitudes, as well as high-latitude cloud layers. Initial testing of changes to the ice nucleation and deposition rate beneficial to the high-latitude boundary layer cloud were detrimental elsewhere in different meteorological regimes, suggesting too simplified an approach, missing processes or deficiencies in the parameterizations. Given the unique environment of the mixed-phase cloud top in the single-layer cloud, it was reasonable to also look at the role that vertical resolution plays in the cloud-top physics in the GCM, as highlighted in section 3a.

One solution in a GCM would be to increase the effective vertical grid resolution for the deposition and sedimentation part of the microphysical parameterization, with an associated increase in complexity and computational cost. An alternative is to formulate correction factors for the deposition rate and sedimentation rate, as described in BHF14. However, here a pragmatic solution was first investigated to assess the impacts of a reduction in cloud-top ice deposition rate on supercooled liquid water layers in the IFS, given the many uncertainties that affect this part of the cloud. In this formulation, the deposition rate is multiplied by a factor F_dep, which reduces the conversion rate from supercooled liquid water to ice near cloud top, defined as

View Expanded

where F_ref is a reference deposition rate factor of 0.1, Δz_cldtop is the distance in meters from the cloud-top layer (defined by the presence of supercooled liquid water and a cloud fraction threshold of 1%), Δz_ref is a reference depth set to 500 m, and F_T is a function of temperature from 0° to −23°C to reduce the impact of the modification with decreasing temperature (increasing altitude). This temperature dependence is rather arbitrary, but for this initial implementation was found to be beneficial, avoiding an increase in supercooled liquid water at very cold temperatures.

A modified version of the model (referred to here as PROG+) includes the above changes to the deposition parameterization to represent the effects of unresolved processes and deficiencies in the model parameterization in the mixed-phase cloud-top region.

Figure 2c shows the impact of the PROG+ modification on the SCM simulation of the Arctic boundary layer cloud at three different vertical resolutions. As expected, the SLW toward cloud top is increased significantly, by a factor of 3 to 0.23 g kg⁻¹ for the L60 model and increasing with vertical resolution to a value of 0.45 g kg⁻¹ for the L137 model. The cloud layer is deeper for all three resolutions and the depth more consistent across the resolutions. In addition, the ice water profile is largely unchanged and rather insensitive to the resolution.

Figure 2d illustrates the sensitivity of PROG+ to the parameter choices for F_ref and Δz_ref. The formulation is fairly insensitive to the choice of Δz_ref, which was chosen as 500 m based on the typical observed depth of cloud-top SLW layers (e.g., Shupe et al. 2008a). The scheme is more sensitive to the choice of F_ref. Following BHF14, a value of 0.8 (rather than the 0.1 chosen here) might be more appropriate to account for just the impact of assuming vertical homogeneity of ice condensate and temperature on the deposition rate. With this value, the cloud condensate still increases versus the control, but to a lesser degree.

It is apparent that the key factor of the above change to the deposition parameterization is to significantly reduce the deposition rate in the topmost layer of the cloud. Although a pragmatic approach, the aim is to compensate for some of the deficiencies in the parameterizations and inadequate vertical resolution in the mixed-phase cloud-top region, and to increase the SLW in high-latitude boundary layer cloud for an improved radiative impact. The modified scheme was implemented in the global model IFS cycle 37r3, operational from 15 November 2011 as an interim solution to address the near-surface temperature bias and is included in the evaluation results described in the next section.

a. Impact on Arctic mixed-phase boundary layer clouds during M-PACE

The U.S. Department of Energy ARM program operates observational sites at the North Slope of Alaska (NSA) at Barrow and Oliktok Point. Observations from NSA have been used previously to evaluate the ECMWF model’s performance in Arctic conditions. Beesley et al. (2000) note that the operational IFS in 1997 underestimated the fraction of liquid water in clouds observed during the SHEBA intensive observing period. When low clouds were present, the downwelling longwave radiation was underestimated. Xie et al. (2006) found a similar underestimate of liquid water fraction in the IFS for boundary layer clouds observed during M-PACE in the fall of 2004, and also linked the lack of cloud water with a substantial underestimation of surface downwelling longwave radiation. A single-layer mixed-phase cloud was observed during M-PACE on 9–10 October 2004 with a cloud-top temperature of about −15°C. This period was chosen for a model intercomparison study discussed in Klein et al. (2009). The IFS in single-column mode was part of the intercomparison and consistent with the earlier studies, the model was unable to partition the integrated water path correctly into liquid and ice phase, and significantly underestimated the amount of liquid in the cloud, underestimated the downward longwave, and overestimated the downward shortwave radiation at the surface.

To evaluate the IFS performance with the recent cloud scheme changes, the same two-day M-PACE single-layer cloud case study is revisited. A full description of M-PACE, including details on the ground-based active and passive sensors as well as in situ aircraft observations can be found in Verlinde et al. (2007). The observed cloud fraction, cloud liquid, and ice water contents for 9–10 October 2004 are shown in Fig. 4a. The cloud fraction is derived from the millimeter wavelength cloud radar (MMCR) and the micropulse lidar (MPL) and is available as part of the Cloud Modeling Best Estimate (CMBE) value-added product (Xie et al. 2010). The cloud water content shown here is derived using the Shupe–Turner algorithm (Shupe 2007; Turner 2007) and the 60-s in-cloud water content profiles have been averaged for each hour. The cloud liquid water mass is highest in the upper half of the cloud. The retrieval does not distinguish between suspended and precipitating ice, thus the ice water content in the right-hand panel of Fig. 4a shows a combination of both. It should be noted that the uncertainty associated with cloud water retrievals is not (yet) well defined and probably significant (Zhao et al. 2012). Klein et al. (2009) suggest rough uncertainty estimates of 20 g m⁻² for the liquid water path and a factor of 2 for the ice water content and path, although differences between retrievals can be larger than this.

(left) Cloud fraction, (middle) cloud liquid water contents, and (right) cloud ice water contents for a single-layer mixed-phase cloud observed during 9–10 Oct 2004 at the NSA site during MPACE. (a) Observations, (b) the DIAG model version, (c) the PROG model version, and (d) the PROG+ model version. Note the color scale is a factor of 5 different between the liquid and ice water content panels.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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(left) Cloud fraction, (middle) cloud liquid water contents, and (right) cloud ice water contents for a single-layer mixed-phase cloud observed during 9–10 Oct 2004 at the NSA site during MPACE. (a) Observations, (b) the DIAG model version, (c) the PROG model version, and (d) the PROG+ model version. Note the color scale is a factor of 5 different between the liquid and ice water content panels.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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(left) Cloud fraction, (middle) cloud liquid water contents, and (right) cloud ice water contents for a single-layer mixed-phase cloud observed during 9–10 Oct 2004 at the NSA site during MPACE. (a) Observations, (b) the DIAG model version, (c) the PROG model version, and (d) the PROG+ model version. Note the color scale is a factor of 5 different between the liquid and ice water content panels.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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The ECMWF model is initialized at 1200 UTC 8 October 2004 and integrated for 48 h from the operational analysis. To leave a spinup period and to define the time series so that maximum solar radiation is at the locally defined noon, forecast lead times from 21.5 to 45.5 h are used to form a 24-h time series for 9 October. A second forecast initialized at 1200 UTC 9 October is concatenated with the first to form the 2-day time series shown in Fig. 4. The forecast lead time is not critical for this case study as shorter lead times also gave similar results. Model data from the land and ocean grid points nearest to the Barrow site are chosen for the comparison with the ARM observations. Although the aircraft flights in the M-PACE campaign were over the ocean, the remote sensing and radiation instruments were on land. Figure 4 (and Fig. 6), therefore, show the data from the land point, whereas the liquid and ice water paths in Fig. 5 contain the model data for both land and ocean points for comparison with the remote sensing and aircraft data.

Liquid water path vs ice water path observed and modeled during the 48-h period from 0000 LT 9 Oct to 2300 LT 10 Oct. DIAG, PROG, and PROG+ are water paths from the three model versions at the land point closest to the NSA site at Barrow. The values for the closest ocean point are indicated by the gray markers and “o” suffix. MICROBASE and WANG stand for water paths retrieved using the Microbase and Wang algorithms, respectively. Two versions of the Shupe–Turner retrieval are shown, the standard retrieval (S-T/VAR) and a modified retrieval (S-T/MPACE) to better match in situ observations. AIR refers to the water paths derived from aircraft observations.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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Liquid water path vs ice water path observed and modeled during the 48-h period from 0000 LT 9 Oct to 2300 LT 10 Oct. DIAG, PROG, and PROG+ are water paths from the three model versions at the land point closest to the NSA site at Barrow. The values for the closest ocean point are indicated by the gray markers and “o” suffix. MICROBASE and WANG stand for water paths retrieved using the Microbase and Wang algorithms, respectively. Two versions of the Shupe–Turner retrieval are shown, the standard retrieval (S-T/VAR) and a modified retrieval (S-T/MPACE) to better match in situ observations. AIR refers to the water paths derived from aircraft observations.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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Liquid water path vs ice water path observed and modeled during the 48-h period from 0000 LT 9 Oct to 2300 LT 10 Oct. DIAG, PROG, and PROG+ are water paths from the three model versions at the land point closest to the NSA site at Barrow. The values for the closest ocean point are indicated by the gray markers and “o” suffix. MICROBASE and WANG stand for water paths retrieved using the Microbase and Wang algorithms, respectively. Two versions of the Shupe–Turner retrieval are shown, the standard retrieval (S-T/VAR) and a modified retrieval (S-T/MPACE) to better match in situ observations. AIR refers to the water paths derived from aircraft observations.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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The DIAG cloud scheme with the diagnostic temperature-dependent mixed-phase function produces a layer cloud with condensate primarily in the ice phase (Fig. 4b). Little liquid is present and it is distributed throughout the depth of the cloud, as the cloud is within the model defined mixed-phase from 0° to −23°C temperature regime. As precipitating snow is diagnostic in the DIAG cloud scheme, Fig. 4b only includes a contribution from cloud ice, so the total ice including the snow would be even higher and farther from the observed ice water path. In contrast, the PROG cloud scheme, with separate liquid water, ice and snow prognostic variables, significantly improves the phase partitioning of the modeled cloud (Fig. 4c). There is now more cloud liquid water than the combined frozen water content from ice and snow, and the supercooled liquid water layer is concentrated near the cloud top in closer agreement with the observed structure. Yet, the total condensate amount remains lower than observed and the model is unable to maintain the liquid layer throughout the 2-day period. The enhancement to the PROG version of the cloud scheme with reduced deposition rate near the cloud top (PROG+) increases the supercooled liquid water content and allows the liquid layer to persist throughout the 48-h period (Fig. 4d).

Figure 5 shows the vertically integrated liquid water path (LWP) and ice water path (IWP) from the IFS model versions for the land and the ocean grid points together with the available aircraft and remote sensing observations for the 2-day period. The IWP from DIAG contains only the contribution from the cloud ice whereas the PROG versions include both ice and snow. Three ground-based retrievals—MICROBASE (Dunn et al. 2011), Shupe–Turner [Shupe et al. (2005) and Turner (2005), referred to here as “S-T/VAR”], and Wang et al. (2004, referred to as “WANG”) are available as part of the ARM Cloud Retrieval Ensemble Dataset (Zhao et al. 2011, 2012). A second, modified version of the Shupe–Turner retrieval for the MPACE period is also included (“S-T/MPACE”). The ice retrieval has been adjusted in this latter version to yield results more consistent with in situ observations from the aircraft. The standard retrieval uses a variable, seasonally-dependent coefficient to the radar reflectivity power law (0.079 during M-PACE). However, comparison with in situ observations suggests that this coefficient is overestimated for the M-PACE case, and a lower coefficient (~0.04) is more appropriate (M. D. Shupe 2012, personal communication). It is this modified version (“S-T/MPACE”) that is used in Fig. 4a. Klein et al. (2009) derive an integrated water path from two research flights during the period, which are marked as “AIR” in Fig. 5. Note that in situ aircraft observations underestimate IWP, as the aircraft totals do not include all the ice from the subcloud air that the aircraft did not sample (Klein et al. 2009). The spread of observed IWP in particular illustrates the large uncertainty in ice water retrievals for Arctic mixed-phase clouds. The agreement for LWP is somewhat better. Nonetheless, all retrievals point toward a mixed-phase cloud dominated by the liquid water content.

As highlighted in Fig. 4, the DIAG version of the model with diagnostic mixed-phase assumption has much less supercooled liquid water than observed, around 10 g m⁻² for the land point compared to the observed estimates of 100–200 g m⁻², and a liquid water path fraction (ratio of LWP to total water path) of about 0.25, consistent with the temperature of the cloud of around −10° to −15°C (see diagnostic mixed-phase function in Fig. 1). The PROG model increases the LWP by a factor of 4 to 40 g m⁻², closer to observations but still significantly underestimated. The IWP is also slightly reduced, despite including the contribution from the prognostic snow category (not included in the DIAG version), giving a liquid water path fraction of about 0.6. The PROG+ version, with cloud-top enhancement, doubles the LWP without affecting the IWP giving a liquid water path fraction of about 0.75, closer to the observed fraction in the range 0.85–0.9 (based on the WANG and S-T/MPACE and aircraft retrievals in Fig. 5). However, the LWP over land is still underestimated compared to the observed estimates by up to a factor of 2. For the ocean point, where the surface is warmer and boundary layer turbulence is more active, all three model versions have higher IWP and the PROG versions also show a 50% increase in LWP.

Figure 6 shows a comparison of the corresponding surface irradiance and downward longwave radiation from the IFS model versions and observations during the 2-day period at the Barrow site. The DIAG model overestimates the surface irradiance by a factor of 2 (by 50 W m⁻²) and the downwelling longwave radiation at the surface is underestimated by 30 W m⁻² or more, consistent with earlier studies. The PROG model has an improved surface irradiance on the first day, but worse on the second day when the liquid cloud is depleted. Similarly, the downward longwave is significantly improved when supercooled liquid cloud is present, but has a worse agreement with observations than DIAG on the second day when the liquid cloud has dissipated. The closest fit to observations is the PROG+ model with just a 20 W m⁻² overestimate of surface irradiance on the first day and less than 10 W m⁻² on the second. The downward longwave difference from the PROG+ model is consistently the best throughout the period and only slightly underestimates the observations by about 10 W m⁻². These results highlight the importance of representing the supercooled liquid water at the cloud top for the correct radiation budget in the model.

(a) Surface irradiance and (b) downward longwave radiation time series, for the single-layer mixed-phase Arctic cloud at NSA during 9 and 10 Oct 2004 for the observations (black) and the three model versions, DIAG (blue), PROG (green), and PROG+ (red).

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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(a) Surface irradiance and (b) downward longwave radiation time series, for the single-layer mixed-phase Arctic cloud at NSA during 9 and 10 Oct 2004 for the observations (black) and the three model versions, DIAG (blue), PROG (green), and PROG+ (red).

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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(a) Surface irradiance and (b) downward longwave radiation time series, for the single-layer mixed-phase Arctic cloud at NSA during 9 and 10 Oct 2004 for the observations (black) and the three model versions, DIAG (blue), PROG (green), and PROG+ (red).

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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This case study covers only two days. However, a much longer record of surface radiation measurements is available from the NSA site at Barrow. Previous studies have shown that two persistent regimes are commonly observed at the site: a clear or nearly clear state with few optically thin clouds, and a cloudy state with liquid-containing stratiform clouds that have an emissivity close to one (Stramler et al. 2011; Morrison et al. 2012). These states are reflected in the surface longwave radiation with small net longwave radiation for the cloudy state and large negative net radiation (i.e., a surface heat loss) for the clear state. Figure 7 shows a histogram of the observed (black) and modeled (red) hourly mean net longwave surface radiation at NSA for two years: 2009 and 2013. In both years, the observations have a clear bimodal distribution with a peak around −15 W m⁻² corresponding to the cloudy state, and a peak near −50 W m⁻² corresponding to the clear state. The CMBE product is not yet available for the more recent period (2013), so the hourly mean surface net longwave radiation has been calculated from the 1-min quality controlled surface radiation product (QCRAD; Shi and Riihimaki 1994). The cloudy state occurs about twice as often as the clear state. The two years are chosen to coincide with years where the operational forecast model at ECMWF used the DIAG and PROG+ cloud schemes, though additional model changes were implemented between 2009 and 2013. Results are similar if different years (with DIAG/PROG+ in use) are chosen. The DIAG model does produce a bimodal distribution, but the relative frequency of the two modes is not captured well. The cloudy, warm state does not occur often enough, which is likely due to the scheme’s poor representation of supercooled liquid layers. The PROG+ model produces the cloudy state more frequently, but the two modes of the distribution are not as well separated as in the observations. The net longwave radiation associated with the cloudy state is still underestimated (i.e., surface heat loss overestimated). This may be due to a remaining underestimate of LWP (as seen in the 2-day MPACE case study), though incorrect cloud occurrence and base height are also potential error sources. The long-term radiation record confirms that the new cloud scheme is a step toward a more realistic representation of the cloudy state occurrence at NSA, though there is room for further improvements.

Net surface longwave radiation frequency distribution at the NSA site for (a) the observations (CMBE product, black) and the operational model with diagnostic mixed-phase (DIAG, red) for January–December 2009, and (b) the observations (QCRAD product, black) and operational model with prognostic mixed phase (PROG+, red) for January–December 2013.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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Net surface longwave radiation frequency distribution at the NSA site for (a) the observations (CMBE product, black) and the operational model with diagnostic mixed-phase (DIAG, red) for January–December 2009, and (b) the observations (QCRAD product, black) and operational model with prognostic mixed phase (PROG+, red) for January–December 2013.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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Net surface longwave radiation frequency distribution at the NSA site for (a) the observations (CMBE product, black) and the operational model with diagnostic mixed-phase (DIAG, red) for January–December 2009, and (b) the observations (QCRAD product, black) and operational model with prognostic mixed phase (PROG+, red) for January–December 2013.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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b. Impact on mixed-phase boundary layer clouds over the Southern Ocean

The advent of satellite-borne active sensors has provided new information about the vertical distribution of clouds over the Southern Ocean. In particular, cloud structure and cloud phase can be determined from combined radar and lidar observations from the CloudSat (Stephens et al. 2008) and CALIPSO (Winker et al. 2007) satellite data. The observations show that boundary layer clouds are the most common cloud type and dominate the cloud-radiative effect in the Southern Ocean region (Mace 2010; Verlinden et al. 2011; Haynes et al. 2011). Supercooled liquid water is often present in the areas dominated by boundary layer clouds (Hu et al. 2010). The Southern Ocean is also an area where many global models, including the IFS, struggle to represent the radiative budget correctly (Trenberth and Fasullo 2010; Bodas-Salcedo et al. 2012). This section examines the impact of the mixed-phase parameterization changes on cloud and radiation in the Southern Ocean region.

A product combining CALIPSO lidar and CloudSat radar observations with Moderate Resolution Imaging Spectroradiometer (MODIS) for a comprehensive cloud mask and target categorization [DARDAR (raDAR/liDAR)] is described in Delanoë and Hogan (2010). Strong lidar backscatter distinguishes boundary layer clouds containing liquid water from those with ice only. In combination with model-derived temperature information, cloud volumes containing supercooled liquid may be identified. The algorithm distinguishes hydrometeor targets containing ice, ice plus supercooled liquid, warm liquid, supercooled liquid without ice, and rain. Here, the two categories containing supercooled liquid (with or without ice) are grouped together, as are the categories for warm liquid and rain. There is just one ice category, with no distinction between “suspended ice” particles and “precipitating snow,” so the ice phase prognostic variables from the model are combined for the comparison.

Data from model forecasts initialized at 1200 UTC (using forecast hours 12–36) are extracted for grid points along the satellite track between 55° and 70°S. The 3-hourly model output is used, such that collocated observations and model results are never more than 1.5 h apart. A grid box falls into the “supercooled” category if the cloud liquid water content exceeds a threshold of 10⁻⁷ kg kg⁻¹ and the temperature is below freezing. A box is categorized as “ice” if the ice water content (ice only for DIAG and ice+snow for PROG and PROG+) exceeds the threshold while the liquid water content remains below the threshold.

Figure 8a shows a sample vertical cross section along the CALIPSO/CloudSat flight track over the Southern Ocean on 2 January 2007 for the “ice only” and “supercooled liquid” target categorization derived from the satellite products. The sea surface temperature along the track is below 0°C south of 60°S and rises to just under 3°C at 55°S at the far right of the section. This particular scene has all cloud below freezing and does not include any targets identified as warm liquid/rain, although in reality there is likely to be some mixed ice/rain close to the surface beneath the deeper frontal cloud in the northern part of the section. The main feature of the scene is the mixed-phase boundary layer cloud extending across 10° of latitude with supercooled liquid present in multiple layers but primarily near the cloud top. Note that the vertical extent and exact base of the lower layers is difficult to ascertain as the lidar signal is rapidly attenuated in the presence of liquid, and the radar retrieval becomes uncertain due to the sensitivity threshold and ground clutter near the surface.

Sample track of cloud phase categorization from (a) DARDAR product, and (b) the DIAG, (c) PROG, and (d) PROG+ model versions, for a CALIPSO/CloudSat track across the Southern Ocean on 2 Jan 2007. Black shading indicates the presence of supercooled liquid (with or without additional ice), while gray shading indicates the presence of frozen hydrometeors (cloud ice for DIAG, cloud ice or snow for PROG and PROG+).

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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Sample track of cloud phase categorization from (a) DARDAR product, and (b) the DIAG, (c) PROG, and (d) PROG+ model versions, for a CALIPSO/CloudSat track across the Southern Ocean on 2 Jan 2007. Black shading indicates the presence of supercooled liquid (with or without additional ice), while gray shading indicates the presence of frozen hydrometeors (cloud ice for DIAG, cloud ice or snow for PROG and PROG+).

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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Sample track of cloud phase categorization from (a) DARDAR product, and (b) the DIAG, (c) PROG, and (d) PROG+ model versions, for a CALIPSO/CloudSat track across the Southern Ocean on 2 Jan 2007. Black shading indicates the presence of supercooled liquid (with or without additional ice), while gray shading indicates the presence of frozen hydrometeors (cloud ice for DIAG, cloud ice or snow for PROG and PROG+).

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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The model data for the same cross section are shown in Figs. 8b–d. Even though the modeled clouds are displaced a few degrees in latitude, all three versions of the model show cloud structures similar to the observations with extensive mixed-phase boundary layer cloud across the scene, deeper ice-dominated cloud systems to the north and south and some ice cloud present toward the center of the scene. As a consequence of the diagnostic split used in the DIAG model to partition cloud water into ice and liquid, clouds between 0° and −23°C will always contain some liquid. Thus the boundary layer cloud in the DIAG model (Fig. 8b) is categorized as supercooled throughout its depth. Note, the shading indicates the target classification only, not the cloud fraction. Figure 8c shows the corresponding track for the PROG model version and includes the prognostic snow water content in the target categorization to correspond more closely with the hydrometeors in the observed ice category. The depth of the ice cloud, therefore, extends farther toward the surface. The PROG model produces a boundary layer cloud with multiple supercooled layers, with similarities to the observations. Yet, liquid is not consistently present near the cloud top (Fig. 8c) in contrast to that observed. This highlights the deficiencies in the model parameterizations that are unable to maintain enough supercooled liquid water at the cloud top. With the additional cloud-top deposition rate modification in the PROG+ model version, a consistent supercooled liquid layer is maintained at the cloud top throughout the scene (Fig. 8d), in closer agreement with the observations.

The track shown in Fig. 8 is a typical example for the Southern Ocean region, showing the model improvement in a qualitative manner. A quantitative comparison of the model and observations is performed for boundary layer clouds in the region. Nearly 15 000 grid boxes with boundary layer clouds over ocean (i.e., cloud base below 2.5 km and cloud no thicker than 3 km) were identified along the CloudSat/CALIPSO track between 55° and 70°S during January 2007. A comparison of the frequency of occurrence of supercooled liquid at the boundary layer cloud top gives a 76% occurrence in the observations and an 85% occurrence in the PROG+ version of the model. Huang et al. (2012) also found a range of frequency of occurrence, 80%–90%, of supercooled/mixed-phase low-altitude cloud tops derived from different data products over this region in summer from 4 years of data (CALIPSO, MODIS, and the combined DARDAR data used here). The results for January 2007 suggest the PROG+ model slightly overestimates the occurrence of supercooled liquid water at boundary layer cloud top, but it is in the right range given the uncertainties in the observations and in the assumed thresholds for the model water contents.

The radiative impact of the model changes in the Southern Ocean region is evaluated by comparison of the top-of-the-atmosphere net shortwave (SW) radiative fluxes against the Clouds and the Earth’s Radiant Energy System (CERES) satellite observations (Wielicki et al. 1998). An ensemble of four 1-yr low-resolution free-running simulations with the IFS (spectral truncation of T159 equivalent to a 125-km grid spacing) are performed for each of the model versions. Figure 9 shows the annual mean net SW from CERES and the model differences from the observations. The DIAG version in Fig. 9b highlights the main systematic errors, with too much reflection between 30°N and 30°S, particularly in regions of deep convection and shallow cumulus, and too little reflection in the coastal maritime stratocumulus regions and across the Southern Ocean south of 50°S. These differences are robust errors in the IFS, seen at different model horizontal resolutions and forecast time periods and have been persistent in the IFS model across many model versions.

Annual mean top-of-the-atmosphere net shortwave radiation (net SW) for (a) CERES observations, and the difference from CERES for the 4-member ensemble 1-yr IFS model simulations at T159 resolution (125-km grid resolution, 91 levels), for (b) DIAG, (c) PROG, and (d) PROG+. Hatched areas indicate regions of significance at the 5% level using a two-tailed t test.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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Annual mean top-of-the-atmosphere net shortwave radiation (net SW) for (a) CERES observations, and the difference from CERES for the 4-member ensemble 1-yr IFS model simulations at T159 resolution (125-km grid resolution, 91 levels), for (b) DIAG, (c) PROG, and (d) PROG+. Hatched areas indicate regions of significance at the 5% level using a two-tailed t test.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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Annual mean top-of-the-atmosphere net shortwave radiation (net SW) for (a) CERES observations, and the difference from CERES for the 4-member ensemble 1-yr IFS model simulations at T159 resolution (125-km grid resolution, 91 levels), for (b) DIAG, (c) PROG, and (d) PROG+. Hatched areas indicate regions of significance at the 5% level using a two-tailed t test.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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The change to the prognostic mixed phase (PROG) in Fig. 9c leads to less supercooled liquid water, with a reduction in the net SW error in the tropics (also due to warm-phase cloud microphysics changes in the model upgrade), but an increase in the net SW error in the Southern Ocean of around 10 W m⁻². The supercooled liquid water decreased in this region by up to 15 g m⁻² in the annual mean (not shown), particularly in the regions dominated by boundary layer cloud below 0°C. Figure 9d shows the PROG+ model difference versus CERES, which has a specific impact on the net SW in this band across the Southern Ocean, consistent with the regions of observed supercooled liquid water from the CALIPSO lidar (Hu et al. 2010). The liquid water path and net SW changes are reversed from the PROG simulation, increasing the LWP at high latitudes by 10–20 g m⁻² in the annual mean where the temperatures are below freezing, and reducing the net SW error by up to 10 W m⁻² (increased reflection) with a slight improvement compared to the original DIAG model version in Fig. 9b. The sensitivity of the shortwave to supercooled liquid water in this region has been suggested by others (e.g., Bodas-Salcedo et al. 2012), but the impact is quantified here, highlighting the need to have a realistic representation of mixed-phase clouds, the need to characterize these clouds from observations, and the need to improve our understanding of mixed-phase physical processes and how to formulate their parameterization in GCMs.

c. Impact on Northern Hemisphere high-latitude 2-m temperature over land

After implementation of the new prognostic (PROG) cloud scheme in the operational global ECMWF model in November 2010, a cold bias was reported in the forecast of 2-m temperatures over parts of Scandinavia during January 2011. This prompted an investigation, which found a correlation between the increased temperature bias and regions of low-level mixed-phase cloud, and motivated the cloud-top deposition rate modifications in the PROG+ model version described in this paper for an operational solution to the problem.

Figure 10 shows the 2-m temperature for 0000 UTC 4 January 2011 as an example of the problem. This was a month where there was persistent stratiform boundary layer cloud over Finland at temperatures below freezing. Figure 10a shows the operational analysis of 2-m temperature. The model with diagnostic mixed-phase (DIAG) has supercooled liquid throughout the cloud, as the temperatures are between −10° and −20°C, and is able to produce a reasonable 2-m temperature forecast (Fig. 10b). However, the PROG version of the model, operational at the time, is unable to retain much supercooled water in the cloud, resulting in excessive longwave cooling of the snow-covered land surface and a significant cold bias developing of up to −10°C (Fig. 10c). The increase in longwave cooling (more negative) in the PROG simulation is consistent with the second day of the M-PACE case described in section 3a, due to the lack of supercooled liquid in the cloud. The PROG+ model in Fig. 10d increases supercooled liquid water content in the stratiform cloud and reduced longwave surface cooling leads to near-surface temperatures over Finland in much closer agreement with observations and the analysis (Fig. 10a).

2-m temperature (°C) over northern Europe at 0000 UTC 4 Jan 2011 for (a) SYNOP observation analysis, and 60-h forecasts for (b) DIAG simulation, (c) PROG simulation, and (d) PROG+ simulation.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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2-m temperature (°C) over northern Europe at 0000 UTC 4 Jan 2011 for (a) SYNOP observation analysis, and 60-h forecasts for (b) DIAG simulation, (c) PROG simulation, and (d) PROG+ simulation.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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2-m temperature (°C) over northern Europe at 0000 UTC 4 Jan 2011 for (a) SYNOP observation analysis, and 60-h forecasts for (b) DIAG simulation, (c) PROG simulation, and (d) PROG+ simulation.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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Figure 11 shows the impact of the cloud-top deposition change in the PROG+ version compared to the PROG parameterization on the 2-m temperature for the whole month of January 2011. The impact of the increased supercooled liquid condensate and warming in the PROG+ simulation shown in the 4 January case study is clearly reflected in the monthly average over Scandinavia and eastern Europe (Fig. 11a) with an average warming of 1°–2°C, as well as over western Russia and North America. There is not just a change in the mean 2-m temperature, but also a decrease in the mean absolute error of 2-m temperature in large parts of Europe and North America (Fig. 11b) by a similar magnitude. Calculating the root-mean-square error of the 1000-hPa temperature for the Northern Hemisphere for the winter season 2010/11 also shows a significant 2% improvement throughout the first 5 days of the forecast (not shown). This example highlights the importance for weather forecasting of focusing future parameterization development on improving the representation of physical processes that determine the SLW topped boundary layer cloud.

Impact on 2-m temperature over land (72-h forecasts for January 2011) for supercooled liquid water changes (PROG+ minus PROG) for (a) mean temperature change (°C) and (b) change in mean absolute error (°C) when compared to 2-m temperature analyses using SYNOP stations.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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Impact on 2-m temperature over land (72-h forecasts for January 2011) for supercooled liquid water changes (PROG+ minus PROG) for (a) mean temperature change (°C) and (b) change in mean absolute error (°C) when compared to 2-m temperature analyses using SYNOP stations.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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Impact on 2-m temperature over land (72-h forecasts for January 2011) for supercooled liquid water changes (PROG+ minus PROG) for (a) mean temperature change (°C) and (b) change in mean absolute error (°C) when compared to 2-m temperature analyses using SYNOP stations.

Citation: Monthly Weather Review 142, 9; 10.1175/MWR-D-13-00325.1

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