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Keywords:

  • Unified Model;
  • humidity;
  • entrainment

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Gregory–Rowntree convection scheme
  5. 3. Further CRM analysis from a EUROCS case
  6. 4. Formulation and single-column testing of simple adaptive detrainment
  7. 5. Performance in the full NWP model
  8. 6. Combination with other possible changes
  9. 7. Towards adaptive entrainment?
  10. 8. Conclusions
  11. Acknowledgement
  12. References

Mass-flux convection schemes continue to play key roles in large-scale atmospheric modelling. Currently, however, the specification of detrainment seems a potential weakness. Using cloud-resolving model results from the European Cloud Systems (EUROCS) humidity case, we consider how detrainment adapts to its environment and formulate a minimal-complexity description of partial detrainment in convective cloud fields. This can be viewed as an approximation to the behaviour of a multi-plume scheme. The algorithm is straightforwardly implemented within the Gregory–Rowntree convection scheme as an extension of its original partial-detrainment scheme. Numerical weather prediction tests in the Met Office Unified Model show significant benefits in full-model performance. © 2011 Crown Copyright, the Met Office. Published by JohnWiley & Sons Ltd.


1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Gregory–Rowntree convection scheme
  5. 3. Further CRM analysis from a EUROCS case
  6. 4. Formulation and single-column testing of simple adaptive detrainment
  7. 5. Performance in the full NWP model
  8. 6. Combination with other possible changes
  9. 7. Towards adaptive entrainment?
  10. 8. Conclusions
  11. Acknowledgement
  12. References

Convective cloud parametrization remains a critical component of large-scale atmospheric modelling. The mass-flux approach in its many guises has become the predominant technique.

The Met Office Unified Model (MetUM) has used the mass-flux scheme of Gregory and Rowntree (1990) with some success over several years within a unified numerical weather prediction (NWP) and climate modelling system (Martin et al., 2006). However, increasingly detailed diagnostic evidence of climate and NWP performance, together with various process studies, points to areas for improvement.

The outstanding challenges for convection parametrization, including behaviour on diurnal, intraseasonal and other time-scales, have lent considerable attention to more radical approaches involving forms of explicit representation (Grabowski and Moncrieff, 2004). There are also new approaches to ‘conventional’ parametrization (e.g. turbulence-based approaches such as that of Grant and Lock, 2004). Nevertheless, there is also strong motivation to improve existing mass-flux schemes, noting e.g. the significant improvements reported by Bechtold et al.(2008) within the ECMWF system.

In the present article, therefore. we examine the scope for incremental improvement in the Gregory–Rowntree (G–R) scheme, and in particular we revise its treatment of convective detrainment.

Entrainment and detrainment are classical issues in the study of convective clouds. Blyth (1993) reviews a considerable amount of literature focused on spatial or microphysical structure at the individual cloud level.

However there are also outstanding issues in modelling the cloud ensemble that depend on the variation between clouds. In fact, at the ensemble level the termination of different clouds at different heights itself counts as a form of detrainment. This deceptively simple point is one of the reasons for the widespread use of explicit multiple plumes in convection parametrization, e.g. following Arakawa and Schubert (1974).

We present here a simple representation of detrainment at the level of the cloud ensemble, intended to capture statistically the variation in termination level. There is some connection with previous observational and laboratory evidence discussed by Taylor and Baker (1991). We implement our ‘adaptive detrainment’ within the existing partial-detrainment module of the G–R scheme and test its NWP performance in the MetUM.

The outline of this article is as follows. In section 2 we summarize our convection-scheme formulation, in section 3 we consider cloud-resolving model (CRM) evidence, in section 4 we construct an adaptive-detrainment parametrization and in section 5 we illustrate the full-model performance tests that led to this change being adopted operationally. In sectopm 6 we discuss further issues related to shallow convection, entrainment and humidity.

2. The Gregory–Rowntree convection scheme

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Gregory–Rowntree convection scheme
  5. 3. Further CRM analysis from a EUROCS case
  6. 4. Formulation and single-column testing of simple adaptive detrainment
  7. 5. Performance in the full NWP model
  8. 6. Combination with other possible changes
  9. 7. Towards adaptive entrainment?
  10. 8. Conclusions
  11. Acknowledgement
  12. References

We now briefly summarize the main features of the G–R convection scheme as used in the MetUM.

The G–R scheme is based on the work of Gregory and Rowntree (1990), and is essentially a single-plume mass-flux scheme. As with other mass-flux schemes (e.g. Tiedtke, 1989), it has at its core the computation of a bulk updraught mass-flux Mu, based on equations of the form

  • equation image(1)

where equation image is entrainment and δ detrainment.

The mass-flux updraught calculation is accompanied by calculations of bulk scalar properties for the updraught, including temperature and humidity. The entrainment parameter equation image represents a rate of dilution of the updraught plume by the environment per unit height ascended. The environment is identified with the grid-point mean values. Generically the updraught equation for a scalar φ takes the form

  • equation image(2)

where φue are the updraught and environmental values respectively and Sφ denotes any specific source terms. For a simple passive scalar φ, the convective terms in the environmental tendency equations are

  • equation image(3)

where ρ is density. The first term on the right-hand side has the form of a subsidence (downward advection) in the non-cloudy environment, whilst the second is thought of as the detrainment of updraught properties into the environment.

Specific humidity qu is carried as one of the main updraught variables, and is of course not a passive scalar. In the updraught, condensation is assumed to occur at saturation, with accompanying release of latent heat accounted for in the parcel temperature equation. This process is partially opposed by plume dilution, due to entrainment from the subsaturated environment. Liquid water is assumed to convert to rain above a concentration of 1 g kg−1.

Since the original paper of Gregory and Rowntree (1990), the scheme has been extended in various ways, including the addition of precipitating downdraughts and a change to a CAPE closure time-scale determining the overall convection rate after Fritsch and Chappell (1980). However the representation of equation image and δ remain at the core of the scheme and its performance.

In the present paper we look particularly at detrainment in the G–R scheme. The original scheme incorporates two types of detrainment, ‘forced detrainment’ δf (due to loss of buoyancy of the core updraught) and ‘mixing detrainment’ δm (due to episodic events associated with mixing and evaporative cooling at cloud edges).

In principle the forced detrainment already includes a buoyancy-sensitive detrainment that might seem relevant to our needs. However this is based on a small buoyancy threshold of 0.2 K, which lacks any physical scaling, and the algorithm tends to do too much or too little.

Our main aim here is to rework and improve the G–R forced detrainment in a more physically satisfactory manner. We shall also make some physically motivated changes to the mixing detrainment.

3. Further CRM analysis from a EUROCS case

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Gregory–Rowntree convection scheme
  5. 3. Further CRM analysis from a EUROCS case
  6. 4. Formulation and single-column testing of simple adaptive detrainment
  7. 5. Performance in the full NWP model
  8. 6. Combination with other possible changes
  9. 7. Towards adaptive entrainment?
  10. 8. Conclusions
  11. Acknowledgement
  12. References

Here we motivate our changes to parametrization partly by further analysis of the European Cloud Systems (EUROCS) humidity case (Derbyshire et al., 2004). That test case is relevant here as much for its forcing specification as for the particular sensitivities considered. The forcing design allows some feedback with the large-scale and allows convective heating profiles to adapt their shape much more than under conventional prescribed large-scale forcing.

The EUROCS intercomparison showed that, almost independently of the humidity problem, the original G–R scheme had difficulty adapting the shape of its mass-flux profiles to different environments. Specifically, it showed a strong tendency for an elevated mass-flux peak that did not compare well with any of the CRM results. We therefore investigated its messages for detrainment and entrainment.

Figure 1 shows the buoyant cloudy updraught mass fluxes for the EUROCS simulations, based on the Met Office Cloud Resolving Model at 250 m horizontal resolution. The values are slightly smaller than those plotted in Derbyshire et al. (2004), because the present diagnosis is restricted to buoyant cloudy updraughts (BCu), a definition more compatible with the assumptions of the present mass-flux scheme.

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Figure 1. Convective core (buoyant cloudy updraught) mass flux Mu in the EUROCS humidity case (see text) for four values of the target relative humidity parameter RHt: 0.9 (solid), 0.7 (dotted), 0.5 (dashed) and 0.25 (dash–dotted).

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Figure 2 shows the variation in core updraught-area fraction au with environmental humidity. As well as a pronounced anvil development above around 5 km, strong variation of the core area fraction with its humidity environment is also seen lower down.

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Figure 2. Core area fraction au in the EUROCS humidity case. Line styles as in previous figure.

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Figure 3 shows that the core mean updraught velocity wu varies remarkably little with the environmental humidity parameter RHt, and hence that the mass-flux variation comes mainly from the variation in au. In turn Figure 4 shows that the buoyancy excess Tv′ (which presumably ‘drives’ wu) is only weakly sensitive to RHt.

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Figure 3. Core mean updraught velocity wu. Line styles as in previous figure.

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Figure 4. Core virtual temperature excess profiles. Line styles as in previous figure.

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Together these results strongly suggest that the core area is adapting to its environment so as to limit the variation of updraught thermodynamic properties, under significant changes in RHt.

There may be a connection with the results of Emanuel and Bister (1996) and Shutts and Gray (1999) in radiative–convective equilibrium problems. Under changes in forcing strength, they also found that it was mainly the core cloud area rather than the updraught strength that adapted.

Although we shall ultimately focus mainly on detrainment here, we evaluate entrainment as a stepping stone to the diagnosis of detrainment as well as for its own sake. We compute entrainment in the bulk core updraught by the method of Swann (2001), as a residual in the budget for updraught specific humidity qu after diagnosing conversion terms such as condensation directly in the CRM (more details in that reference). This is a relatively robust method owing to the strong humidity contrast between plume and environment.

Entrainment results for the EUROCS humidity case are shown in Figure 5. Above 2 km, the G–R entrainment is not far from the values of equation image diagnosed from the CRM and shows no consistent trend with RHt. In the lower layers, a possible revised entrainment of equation image = 1/z fits the results slightly better in the lower layers. The diagnosed values below around 1 km are of questionable relevance.

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Figure 5. Entrainment diagnosed from the EUROCS humidity CRM runs (see text). The bold line shows the corresponding G–R parametrization and the bold dashed line a simple alternative function equation image = 1/z. Otherwise line styles are as previously.

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In the layer 1–2 km, the shallow regime (dot–dashed line) gives noticeably higher entrainment than the others. Since the EUROCS case varies the target humidity profiles only above 2 km, this suggests non-local impacts, possibly via the overall cloud depth and properties. Given that we now diagnose a separate shallow regime, the message for changing entrainment in our scheme is unclear (see section 6 for further discussion).

Finally (see Figure 6) we diagnose detrainment as δ = equation imagelnMu/∂z. Evidently detrainment in the CRM exceeds the G–R mixing detrainment for each of the subcases. A consistent trend of significant decrease of detrainment with RHt is also seen at all heights from the cloud base to at least 5 km.

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Figure 6. Detrainment from the EUROCS humidity case diagnosed as explained in the text. The bold line shows the G–R mixing detrainment. Otherwise line styles are as previously.

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Above about 6 km, associated with the dominance of anvils (cf. Figure 2), the detrainment analysis effectively breaks down, giving negative detrainment. Clearly the notion of ‘cores’ interacting directly with ‘clear air’ becomes problematic in those regions. However, the major divergence between the humidity subcases essentially arises in the lowest 5 km.

Our purpose here in reanalyzing the EUROCS case is not to tune our scheme strongly to a single process-study but to extract conceptual lessons motivating structural improvement. Above all, we see a need for greater adaptivity in detrainment than in the standard G–R scheme.

4. Formulation and single-column testing of simple adaptive detrainment

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Gregory–Rowntree convection scheme
  5. 3. Further CRM analysis from a EUROCS case
  6. 4. Formulation and single-column testing of simple adaptive detrainment
  7. 5. Performance in the full NWP model
  8. 6. Combination with other possible changes
  9. 7. Towards adaptive entrainment?
  10. 8. Conclusions
  11. Acknowledgement
  12. References

4.1. Statistical modelling of partial detrainment

The EUROCS intercomparison of Derbyshire et al. (2004) and our further analysis of section 3 show that the original G–R scheme does not capture well the adaptive partial detrainment seen in our CRM comparison data. This problem can be traced to the unrealistic detrainment of a classical single plume at a single ‘final height’.

We investigated therefore whether the effective behaviour of a multiple-plume convection scheme might be more adaptive in a useful manner, and whether some of its adaptive detrainment could be matched within a bulk scheme like G–R.

The use of multiple plumes has a long pedigree, notably in Arakawa and Schubert (1974). It is easily seen that plumes of different thermodynamic properties, and hence buoyancy, will detrain at different heights in a manner that depends on the environment. Hence the aggregate behaviour of such a multi-plume ensemble (irrespective of its detailed specification) implies some form of adaptive detrainment. Simple experimentation with specified ensemble distributions rapidly bears out this generic finding.

In the Arakawa–Schubert scheme the partial detrainment behaviour is closely coupled to a strong form of quasi-equilibrium and to other assumptions that we do not wish to ‘hardwire’ into our scheme. However, from any multi-plume model, as indeed from a CRM, we can diagnose effective bulk parameters for entrainment and detrainment in each case. We seek here to distil the essence of statistical detrainment in the simplest most generic manner, with minimal assumptions and without introducing any new scales.

As noted above, in principle the G–R scheme already includes a simple statistical model of partial detrainment as the plume buoyancy falls to 0.2 K. The bulk plume is deemed to shed neutrally buoyant material; the loss of the least buoyant material tends to sustain the mean buoyancy of the remaining material. However, there is no physical scaling of this effect and in practice at current model vertical resolutions the original forced detrainment scheme is found to be ineffective and unsatisfactory.

Our strategy here is to improve the G–R forced detrainment by dispensing with the unphysical scale and treating the plume buoyancy distribution within the convective ensemble as self-scaling, in the sense that its shape is generic or known.

4.1.1. Idealized reference distributions

As an idealized benchmark case for self-scaling distributions we consider a family of power-law functions. Specifically, we take the mass flux to be distributed over the parcel buoyancy θv′ with a weighting of the form [1 − θv′/(θv′)m]γ, where (θv′)m is the local maximum value and γ a constant exponent determining the distribution shape.

Figure 7 illustrates these ‘γ distributions’ for three values γ = 0,1,2, i.e. uniform, linear or quadratic distributions.

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Figure 7. Family of idealized mass-flux distributions over buoyancy with the form m = [1 − θv′/(θv′)m]γ for various values of the shape parameter γ.

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Our choice of idealized distributions is in a sense for convenience, yet not entirely arbitrary. These are in fact the only distributions that preserve their shape under detrainment of the least buoyant elements. Most plausible distribution shapes can be roughly catered for within this family. The case of large γ becomes asymptotically exponential, whilst a narrow distribution around a point value (cf. the narrow distributions found by Kuang and Bretherton (2006) around cloud base) can also be formally treated as the case γ [RIGHTWARDS ARROW] −1.

The initial height for a benchmark case does not need to correspond to the base of a convecting layer. We could for instance focus on the upper half of the cloud layer, with much of the variability viewed as generated within the lower cloud layer rather than in the subcloud layer.

As a guide to what is realistic, CRM evidence concerning distributions will be discussed later, but first we simply consider each idealized distribution as an ensemble of plumes, the aggregate behaviour of which we might wish to match with a bulk parametrization.

4.1.2. Simplest dry test problem

Our simplest reference case for statistical detrainment will be an ensemble of dry parcels ascending adiabatically. We assume that each parcel terminates at its individual level of neutral buoyancy relative to some environmental profile equation image.

In this simplest problem, for notational brevity, we may write θ instead of θv, as in a dry case they are the same. We specify the statistical distribution as a mass-flux distribution function m over the buoyancy-like variable θ.

First of all consider a flat distribution m(θ) of plume buoyancy across the ensemble between θ0 and θm, i.e. the case γ = 0. Each plume is assumed to ascend from an initial height where θ0 equals the environmental value θe. (If θ0> θe, then the ensemble will ascend without detrainment up to a height where θe(z) does match θ0.)

We are particularly interested in the behaviour of this ensemble relative to a single plume of the same mean buoyancy, i.e. with equation image.

In Figure 8 we sketch the ensemble behaviour under our simple assumptions. For convenience we take the environmental profile θe to increase linearly with z, but this is not fundamental (the argument can be rewritten in θ-coordinates). The simple plume conserves its θ with height, but the ensemble increases its mean θ by shedding the least buoyant members. The maximum height of the ensemble will be determined by its most buoyant member, i.e. by θe(z) = θm, so in θ-coordinates the plume effectively ascends twice as far as the corresponding single plume with the same initial mean buoyancy.

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Figure 8. Simple dry ensemble problem illustrating our approach and contrasting an ensemble (bold curves) with a conventional single plume (dashed). (a) Uniform mass-flux distribution over θ at the initial height. (b) Mean parcel θ profiles for the ensemble (bold), environment (θe, solid) and the equivalent single plume (dashed). (c) Mass-flux profile under detrainment at neutral buoyancy (bold) compared with the equivalent single plume (dashed).

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Equivalently, the decline in relative plume buoyancy is compensated for by the loss of neutrally buoyant material. The single plume loses buoyancy with height relative to its environment at a rate ∂θe/∂z. The ‘ensemble plume’ loses relative buoyancy with height at a reduced rate equation image, which we interpret by saying that the buoyancy loss is 50% compensated by selective detrainment. That is, the decline in mean relative buoyancy is reduced to (1 − Rdet)∂θe/∂z, where here the ‘compensation parameter’ equation image.

The selective detrainment of material at neutral buoyancy obeys a simple and general relationship between its impacts on mass flux and on plume mean buoyancy respectively. The neutral elements carry no buoyancy flux (because their relative buoyancy is zero) and hence their detrainment conserves the overall buoyancy flux ′. A 1% loss (say) in M is compensated for by a 1% gain in the buoyancy of the plume (relative to the environment) by selective detrainment.

Given this compensating relationship between mass flux and buoyancy detrainment, we can now write the mass flux impacts and thermodynamic impacts together using the ‘fractional buoyancy compensation’ Rdet (here equation image) in the form

  • equation image(4)
  • equation image(5)

where δf is the rate of selective detrainment forced by loss of buoyancy and (lnθv/∂z) is the fractional rate of decline in parcel buoyancy due to other (non-detrainment) terms, i.e. before we apply the selective detrainment.

The combination of (4) and (5), together with the choice of equation image, gives us an adaptive forced-detrainment parametrization that exactly matches this dry adiabatic test problem both locally and in its height profile.

4.1.3. Dry problem with varying distributions

We now extend our dry test case by considering more general values of γ, i.e. more general power-law distribution shapes for the reference ensemble.

After a little algebra (integrating over the ensemble), these statistical distributions obey the following bulk properties.

  • (1)
    The maximum buoyancy in the ensemble exceeds the mean buoyancy by a factor (γ + 2). (This is a factor of 2 for the uniform distribution of Figure 8 or a factor of 3 for the linear distribution of Figure 9.)
  • (2)
    As in G–R, the loss of neutral buoyant material by this mechanism raises the mean buoyancy of the ensemble to preserve the overall buoyancy flux. In this way, a proportion Rdet of the decline in mean buoyancy is compensated for by selective detrainment, where
    • equation image(6)
    or equivalently
    • equation image(7)
    The proportion compensated for therefore takes values of 1/2 for the uniform distribution of Figure 8 or 2/3 for the linear distribution of Figure 9.
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Figure 9. Dry adiabatic ensemble problem, plots as in Figure 8 but now with a non-uniform (‘linear’) mass-flux distribution m = [1 − θv′/(θv′)m]γ, with γ = 1.

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It can be seen that these properties (1) and (2) are consistent in their prediction for the final height of the ensemble: both imply the ensemble rises higher than a single plume with the same mean initial buoyancy, by a factor γ + 2 = 1/(1 − Rdet) in θ-coordinates.

This wider class of test problems can all be handled by the G–R scheme if we make a simple change to its ‘partial detrainment’ specification. Specifically, we adopt (4) and (5) based on choosing the appropriate Rdet matched to the distribution through (6). Our detrainment parametrization can then again exactly match our dry adiabatic test problems.

4.1.4. Application to a moist plume ensemble

Obviously our real aim is to apply our detrainment algorithm to the parametrization of a cloud ensemble. Moist problems are physically more complex than our idealized dry problems, but we can still specify and match a range of idealized benchmark cases.

In particular, the basic moist adiabatic problem goes through as before; as usual the ‘condensation heating’ terms in ∂qsat/∂z can be incorporated into the environmental moist stability profiles without affecting the detrainment specification.

We can also handle other physical terms if they do not substantially affect the shape of the distribution; shifts in the mean alone are equivalent to changes in the environmental θe and can be handled by our algorithm without modification.

For instance, the loss of buoyancy due to entrainment can be incorporated in the analysis if we are prepared to treat it as constant across the distribution, i.e. if we approximate ‘evaporation terms’ like equation image(quqe) from the cloud ensemble mean, where qe is the environment value.

Under these assumptions, adaptive detrainment again matches a self-preserving exact solution, essentially as above but with the inclusion of moisture and (simplified) entrainment.

In the dry problem we showed how the detrainment parameter Rdet relates to the distribution shape in these idealized examples.

Figure 10 shows a probability density function (pdf) for core cloud material from two of the EUROCS CRM runs and at two heights. In each case, for comparison, a linear fit (γ = 1) to the positively buoyant part of the distribution is plotted. This fits plausibly though not perfectly; a slight curvature is detectable and might justify slightly higher γ. The linear fit γ = 1 would imply Rdet = 2/3.

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Figure 10. Buoyancy pdfs (solid curves) within the population of cloudy updraught points from the CRM simulations above, at heights of 2.5 or 7.5 km and for RHt = 0.5 or 0.7, as labelled. In each panel, the bold line shows a straight-line fit to the positive-buoyancy side of the distribution.

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The case of a narrow distribution, with a single strong peak at a non-zero value of θv′ (essentially the single-plume limit), could be represented by γ [RIGHTWARDS ARROW] −1 and Rdet [RIGHTWARDS ARROW] 0, although such behaviour is not evident in Figure 10.

Values of Rdet could be evaluated for any distribution shape. Given the various approximations made, we regard Rdet as slightly tunable and in practice have used values between 0.5 and 0.75, corresponding to γ between 0 and 2. Clearly there is scope for more detailed investigation of distributions across a wider range of simulations.

Although our illustrations and tests have been based on constant values of Rdet (or γ), independent of height or convection regime, this is not essential. Adaptive detrainment is a local algorithm and could be applied pragmatically with variable Rdet. For instance, low values of Rdet could be applied at heights or in regimes where the core distribution was viewed as narrow, i.e. the bulk updraught viewed as relatively homogeneous.

Clearly also our simple adaptive detrainment cannot capture all physical effects. In particular, it neglects changes to the distribution shape, e.g. due to partial mixing (cf. Blyth, 1993). Such effects need to be represented separately (within our scheme by ‘mixing detrainment’).

4.2. Additional revisions to mixing detrainment

As discussed above, the G–R scheme includes two types of detrainment, ‘forced’ and ‘mixing’ detrainment. ‘Adaptive detrainment’ is a reworking of the forced detrainment component but we also modified the mixing detrainment component slightly.

In the original G–R scheme, mixing detrainment was set to a fixed fraction of entrainment, equation image. However, if it represents evaporative cooling then δm should physically be sensitive to environmental humidity. We therefore modified the original assumption and replaced the fixed fraction by a simple function δm = (1 − RH)equation image, where RH is the environmental relative humidity. As this was viewed as physically more satisfactory it was adopted within the ‘adaptive’ package (including all the tests shown here).

There is scope for further scientific development of this mixing development component, but separate tests suggested that the impact of this change was limited.

4.3. RH-dependent CAPE closure

Our CRM comparison has some messages for convective ‘closure’, i.e. the specification of cloud-base mass flux. Forms of CAPE closure are widely used following Fritsch and Chappell (1980); these link the CAPE consumption by convective tendency terms to the actual CAPE divided by a prescribed time-scale τCAPE. In other words, we effectively renormalize the whole mass-flux profile and its associated tendency terms (∂φ/∂t)conv so that

  • equation image(8)

where the integral is taken over the convective layer and the integrand is approximately related to the total convective heating (integrated Q1). The CAPE is normally taken from the dilute parcel ascent.

In the EUROCS case, both the cloud-base mass flux and the CAPE vary relatively little with RHt, and this is true whether we use the adiabatic CAPE or actual parcel CAPE (cf. Figure 4). However, the integrated convective heating and CAPE consumption vary strongly with RHt and so the CRM results do not support a fixed time-scale relating CAPE to CAPE consumption.

The MetUM has for some time allowed an RH-dependent CAPE closure option inspired loosely by the original EUROCS humidity-case results. Figure 11 shows the CRM-diagnosed overall CAPE time-scales based on the ratio of actual parcel CAPE to CAPE consumption in the conventional Fritsch–Chappell sense.

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Figure 11. Dependence of bulk time-scales on RHt diagnosed from CRM (bold: based on total Q1; solid: based on ‘positive-only’ contributions; dotted: subsidence term only –see text). Values for bold and solid curves at the lowest RHt exceed 20 h and are left out of range because clearly these attempted scalings are no longer viable in that regime.

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We diagnosed these time-scales in three different ways because of questions about CAPE closure in convective regimes with little or no precipitation. CAPE closure is fundamentally linked to the notion that deep convection (with its relatively high precipitation efficiency) essentially warms the convecting layer towards a natural threshold profile. This warming can be broadly linked to the subsidence term in mass-flux schemes. In general, where condensation efficiency < 100% there is also some cooling from detrainment of the condensate. As condensation efficiency falls towards zero, the CAPE consumption normally becomes small as there is no net latent heating. Here, therefore, as alternatives to conventional measures of CAPE consumption we tried (i) integrating over only positive values of the apparent convective heating Q1 and (ii) taking only the subsidence term.

By all of these measures we see a strong systematic variation of the CAPE time-scale with RH in the CRM. A simple interpretation is that the cloud-base mass fluxes seem to be relatively independent of RHt, so that the differences seen in entrainment and detrainment imply systematic variation in ‘CAPE consumption’ with RHt.

The RH-dependent CAPE option in the MetUM allows the CAPE time-scale to vary with a bulk relative humidity equation image over the cloud layer, computed as a mass-weighted mean of the relative humidity at each level. Specifically, we take

  • equation image(9)

so that the dependence is linear between the cut-off at 60% relative humidity at the dry end and a moist cut-off by a ‘fastest’ time-scale τ1, typically 10 min. These results broadly support a linear dependence over the moister range, although there is an indication of stronger RH dependence in the driest case. In that case, though, we would expect to diagnose shallow rather than deep convection and hence would use a separate scheme.

The RH–CAPE closure is used in all the MetUM comparisons shown in this article.

4.4. Testing in the single-column model

We tested our adaptive detrainment in the single-column (SCM) version of the MetUM with two testbeds.

First we used the EUROCS humidity case of Derbyshire et al. (2004). Figure 12 shows the SCM comparison between the original (non-adaptive) and the new (adaptive) versions. As the MetUM has been radically revised since that intercomparison (including a completely new dynamical core plus major changes to the coupling between convection and the boundary layer), we do not expect to reproduce closely the SCM results of the earlier version (4.5). Nevertheless the control (non-adaptive) shows essentially the same behaviour as before, with sharp elevated mass-flux peaks. Evidently the adaptive-detrainment version shows a more gradual detrainment and greater discrimination between the relative-humidity cases.

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Figure 12. Updraught mass fluxes (12 h averaged) for the SCM experiment under the EUROCS humidity case testbed (line styles as in Figure 1), with and without adaptive detrainment.

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A slight exception to this generally smoother behaviour is seen around 2 km. This reflects the discontinuity in the EUROCS humidity specification at that height. By its nature, the adaptive detrainment tends to respond to such features whereas the original scheme tends either to ignore them or to terminate completely.

Although noticeably better than the non-adaptive scheme, the adaptive version cannot be claimed to match the CRM results exactly. We return to some of the shallow convection issues in section 6 below.

Secondly we used a forcing dataset based on field data from the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA–COARE) (Bechtold et al., 2010). The TOGA–COARE dataset covers the period 1 November 1992–28 February 1993. Our case study is a period of 12 days starting on 9 January (case 5b of the Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS: Randall et al., 2003) working group on precipitating convectively driven cloud systems). This period has a phase of suppressed convection (days 3–6), overlapped by a transitional period (days 5–8), which in turn overlaps an active phase (days 6–12).

The TOGA–COARE single-column case shows broadly the expected behaviour. Figure 13 shows that our detrainment changes reduce the upper-level mass fluxes in each of the periods: suppressed, transitional or active.

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Figure 13. Impact of detrainment changes on GCSS Case 5b SCM runs for (a) suppressed, (b) transitional and (c) active periods. Control :solid line; adaptive: dotted. Plots show the average mass flux in steps diagnosed as deep convection.

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As is usual in the current configurations of the MetUM, the proportion of time steps diagnosed with deep convection is rather low (around 25% in the control and 20% in the adaptive run). This reflects the use of a basic CAPE closure time-scale of 30 min, considerably faster than those shown in Figure 11.

In all the periods, the deep convection mass flux shows a more gradual detrainment at upper levels, as in the idealized EUROCS SCM. However in our TOGA–COARE SCM case the maximum convecting level is essentially unchanged, perhaps reflecting the nature of prescribed forcing in this approach.

4.5. Aquaplanet sensitivity tests

The aquaplanet configuration of a GCM (e.g. Inness et al., 2001) provides a useful intermediate testbed between the SCM (which lacks dynamical feedback) and the full model.

We tested our detrainment changes in the aquaplanet at N48 resolution (i.e. 96 points E–W by 73 points N–S) and 38 levels, with 12 levels in the boundary layer. We used a 30 min time step and an RH-dependent CAPE closure time-scale. The sea-surface temperature (SST) was constant with longitude and its latitude dependence followed the ‘control’ specification of Neale and Hoskins (2001). The aquaplanet was run for 40 days from a startdump taken from an aquaplanet with several years integration. Top-of-atmosphere incoming radiation was prescribed at spring equinox values.

Results for mass flux (not shown) were similar to those seen in the SCM. Results for convective temperature increments are shown in Figure 14. Significant additional heating is found in the intertropical convergence zone (ITCZ) from about 8–12 km, linked to a greater depth of convection.

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Figure 14. Aquaplanet impacts: zonal mean of convective temperature increment (K day−1) for a zonally symmetric SST. (a) Adaptive detrainment scheme, (b) control and (c) difference (adaptive − control). Contour interval 2K day−1 for (a) and (b), but 0.5K day−1 for (c).

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In the aquaplanet results, as in our EUROCS SCM results, the adaptive detrainment significantly raises the top of the convecting layer in a manner not seen in our TOGA–COARE SCM comparisons. This may be because the EUROCS SCM forcing specification was designed to allow some feedback with the large-scale environment, in order better to capture the behaviour seen in a three-dimensional model.

5. Performance in the full NWP model

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Gregory–Rowntree convection scheme
  5. 3. Further CRM analysis from a EUROCS case
  6. 4. Formulation and single-column testing of simple adaptive detrainment
  7. 5. Performance in the full NWP model
  8. 6. Combination with other possible changes
  9. 7. Towards adaptive entrainment?
  10. 8. Conclusions
  11. Acknowledgement
  12. References

The adaptive detrainment became operational in the global NWP version of the MetUM at cycle G39 in March 2006. It formed part of a more comprehensive physics package that included revisions to boundary-layer mixing over both land and ocean (Brown et al., 2008) and changes to surface scalar transfer over the oceans to bring the wind-speed dependence into better agreement with observations (Edwards, 2007). A discussion of adaptive detrainment impacts on systematic errors in predictions at 15 day and climate time-scales is given in Martin et al. (2010). Here we focus on short-range (1–5 day) forecasts in terms of the changes to diabatic forcing, thermodynamic mean state and the resulting impacts on the mean tropical circulation.

We discuss results from two boreal summer trials of adaptive detrainment. The first is a month-long trial of the adaptive detrainment from 18 July 2004–18 August 2004. The global NWP model is run at N216 (60 km) horizontal resolution and 38 vertical levels and the model formulation for the control is that operational at model cycle G38 (13 December 2005–14 March 2006: see Allan et al. (2007) for a detailed description). The control and experiment are each run with their own 3D-Var data-assimilation cycle and forecasts out to six days ahead are made from the 0000 UTC and 1200 UTC analyses. The changes in the vertical distribution of convective mass fluxes (Figure 12) and convective heating (Figure 14) due to adaptive detrainment produce a reduced warm-temperature bias at 500 hPa and reduced cold bias at 250 hPa in day 5 forecasts in the Tropics verified against radiosondes (Figure 15).

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Figure 15. Tropical (20°N–20°S) objective temperature verification statistics against radiosondes for temperature profiles (versus pressure) for the July 2004 trial of adaptive detrainment (see text). Plots compare control forecast (bold) against the experiment including adaptive detrainment (grey) for (a) mean bias and (b) RMS temperature errors respectively.

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The time series of the 500 hPa bias shows that these improvements appear in all days of the trial and are very systematic. Similar improvements are also seen in the RMS error (Figure 16). The more continuous detrainment also results in more moisture being detrained between the freezing level and the tropopause, resulting in reduced humidity biases (not shown).

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Figure 16. Temperature verification, as in previous figure but this time showing the time series of mean error (upper) and RMS error (lower) in 500 hPa temperatures over the tropical domain for each day 5 (T + 120) forecast in the trial. As before, plots compare the control forecast (bold) against the experiment including adaptive detrainment (grey) for (a) mean bias and (b) RMS temperature errors respectively.

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The second trial period covered 27 July 2005–25 August 2005 and was run with 4D-Var data assimilation. This trial had a more complete range of diagnostics, allowing us to explore changes in diabatic heating and overall thermal balance. We follow a similar approach to Rodwell and Palmer (2007), analysing all of the components in the model's tropical thermal balance including the balance residual, which provides a measure of the overall error in the temperature field. The experiment in this trial includes adaptive detrainment and also the other physics components made operational at cycle G39. Although all G39 physics is present, the dominant component in the thermodynamic changes was the adaptive detrainment (for verification see figure 6 of Martin et al. (2010) and also the impact on short-range objective verification due to adaptive detrainment discussed above). The model resolution in this trial was N320 (40 km) and 50 vertical levels.

As seen earlier, the main impact of the adaptive detrainment is to produce smoother convective mass-flux profiles and more gradual detrainment throughout the troposphere (Figure 12). This has a significant impact on the parametrized diabatic heating, in terms of both the vertical distribution and the vertically integrated heating, the latter manifest through a general reduction in precipitation over the tropical oceans.

The tropical thermal balance in the 24 h forecasts of the control show an imbalance between the parametrized diabatic heating and the dynamics (Figure 17(c)). There is a residual cooling of ∼1 K day−1 across the tropopause, which may be due to excessive cooling from the parametrizations (Figure 17(a)). The change in thermal balance (experiment − control) due to the revised physics shows that the tropical diabatic heating is reduced at mid levels but increased in the upper troposphere. This is consistent with convection penetrating higher in the model atmosphere, also seen in the aquaplanet tests of adaptive detrainment (Figure 14). The dynamics responds to the changes in diabatic forcing with a warming at mid levels (less ascent) and a cooling at the tropopause. The dynamical tendencies are of opposite sign but do not exactly balance the changes in the parametrized heating.

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Figure 17. Thermal budget from T + 24 h forecasts during 27 July–25 August 2005. The solid contours show the heating rates from the control experiment. The coloured shading is the change in heating rates (experiment − control). All of the parametrized terms and the dynamical terms are shown, along with the overall residual (parametrized + dynamics) in the model's thermal balance. Units are K day−1.

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Consequently there is a significant (and beneficial) change in the residual tendency. The warming at the tropopause (0.4 K), cooling in the mid-troposphere (∼0.3 K) and warming in the boundary layer combine to reduce the residual (by ∼50%) and improve the thermal balance. This is consistent with the improvements seen in the temperature verification, particularly the halving of the biases in the mid-troposphere and tropopause (Figure 16).

For the individual terms making up the parametrized diabatic heating, convective heating dominates the overall signal (Figure 17(d)). However, there are smaller changes in radiative heating components, with less short-wave (SW) absorption and reduced long-wave (LW) cooling at the tropical tropopause attributable to reductions in cloud. The SW and LW changes tend to counteract each other, so the overall change in net radiative heating is a small cooling of −0.2 K in the tropical upper troposphere (not shown). The signal in the large-scale precipitation (Figure 17(h)) is due to enhanced precipitation formation. The warming at 10 km is from latent heating due to condensation and the cooling at 5 km from the evaporation of precipitation.

One would expect the systematic changes in vertical diabatic heating profiles and improved thermodynamic state (temperatures and humidity) to have an impact on the tropical circulation (Hartmann et al., 1984) and this is clearly seen in both 15 day forecasts and Atmospheric Model Intercomparison Project climate simulations (Martin et al., 2010). For 5 day forecasts the impact of the revised physics package, and in particular the adaptive detrainment, was seen in the reduction of operational systematic errors in the tropical mean circulation following the G39 physics change in March 2006.

An example is the 850 hPa velocity potential field (Figure 18). During June–August (JJA) 2004, prior to adaptive detrainment, the global NWP model suffered from excessive convergence (ascent) in the Indian Ocean region and excessive divergence (descent) in the East Pacific, symptomatic of too strong a Walker circulation across the Pacific. In JJA 2006 the excessive convergence in the Indian Ocean was reduced dramatically. In the East Pacific the large excessive divergence was reduced but replaced by a convergent error localized further east over central South America. At 200 hPa we also see similar reduced biases in the divergent flow, but of opposite sign. Similar signals were seen in the trials of adaptive detrainment. The reduced divergent errors over the Indian Ocean and Pacific are consistent with an improved Walker circulation and this is apparent in the rotational flow (not shown). At low levels the rapid growth of excessive easterly wind stresses seen previously in the model is reduced, and this has been linked to improvements in the simulation of the El Niño Southern Oscillation (ENSO) at climate time-scales (Martin et al., 2010).

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Figure 18. June–August (JJA) 850 hPa divergent flow (velocity potential): (a) Met Office analysis for JJA 2004 and 2006, showing velocity potential (contours) and divergent wind, (b) day 5 mean error in JJA 2004 and (c) day 5 mean error in JJA 2006. Units are 106 m2 s-2.

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6. Combination with other possible changes

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Gregory–Rowntree convection scheme
  5. 3. Further CRM analysis from a EUROCS case
  6. 4. Formulation and single-column testing of simple adaptive detrainment
  7. 5. Performance in the full NWP model
  8. 6. Combination with other possible changes
  9. 7. Towards adaptive entrainment?
  10. 8. Conclusions
  11. Acknowledgement
  12. References

We see adaptive detrainment as addressing a key problem with the original G–R formulation. Our simple, physically motivated change leads naturally to a smoother detrainment as buoyancy declines, without introducing any new or unphysical length-scales and with significant benefits in model performance.

However, adaptive detrainment on its own does not address all the issues raised by the EUROCS case and other process studies. In particular, our modified detrainment as it stands does not fully capture the shallow convective regime.

In our current scheme this is not a critical fault, because we treat shallow convection as a separate category based on a prediagnosis of convective depth and then the adoption of substantially higher equation image and δ (all the results shown here use the deep convection scheme). Ideally, though, a deep convection scheme should have some ability to handle relatively suppressed regimes.

To see whether we could match the CRM mass-flux profiles more closely in the driest regime, we experimented with further changes to mixing detrainment and entrainment (Figure 19). Doubling our RH-sensitive mixing-detrainment specification does improve the profile shapes quantitatively. In a second test, loosely inspired by our CRM analysis above, we set equation image = 1/z. This second test has a bigger impact on the shallow regime and confirms that adaptive detrainment can cooperate with increased entrainment to give strong net detrainment.

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Figure 19. As Figure 12, but testing further parametrization changes within the adaptive-detrainment version, as discussed in the text. (a) Increased mixing detrainment; (b) increased entrainment.

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The cooperation between entrainment and adaptive detrainment can be shown analytically. Locally, adaptive detrainment is a linear function of the buoyancy decline, which in turn can be broken down into a sum of entrainment and other terms. Hence we can attribute a component of the adaptive detrainment

  • equation image(10)

as ‘caused’ by entrainment. The ratio of this extra detrainment to the entrainment varies essentially as the plume moist static energy excess divided by the plume buoyancy excess. When the environment is particularly dry or the buoyancy excess particularly weak, the ratio will exceed unity and entrainment will therefore lead to net detrainment. We view this behaviour as reasonable and consistent with our knowledge of these regimes.

In summary, our adaptive detrainment is compatible with other changes, such as increased entrainment, which may help to represent the transition to a shallow regime.

7. Towards adaptive entrainment?

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Gregory–Rowntree convection scheme
  5. 3. Further CRM analysis from a EUROCS case
  6. 4. Formulation and single-column testing of simple adaptive detrainment
  7. 5. Performance in the full NWP model
  8. 6. Combination with other possible changes
  9. 7. Towards adaptive entrainment?
  10. 8. Conclusions
  11. Acknowledgement
  12. References

Having presented a model for adaptive detrainment, a further question obviously arises about whether entrainment should also adapt to its environment, and if so how. In fact, different conceptual models give opposite pictures of adaptive entrainment.

7.1. Entrainment determined by natural selection from a diverse population?

Suppose that we view convection as intrinsically involving a diverse population of plumes with varying entrainment rates (Kuang and Bretherton (2006) comment that such a model can capture many aspects of their CRM simulations). Given sufficient variability, a positive dependence of aggregate entrainment on humidity (or instability) then naturally emerges from this ensemble. This follows since plumes that entrain ‘too much’ outgrow their strength and drop out from the ensemble. The statistical process is easily shown in toy models similar to our investigations of detrainment.

In summary, under a ‘natural selection’ view of convection, in a favourable environment for convection the bulk ensemble is constrained to entrain more.

7.2. Entrainment determined by dominant cloud sizes?

However another plausible conceptual model is as follows.

Convective populations tend to be dominated by the biggest clouds or cells. The size of these clouds may be viewed as scaling with the total convection depth, together with other cloud-system parameters. In a favourable environment for convection, we may expect bigger clouds with more nearly adiabatic cores, and hence the aggregate entrainment may in fact be less.

7.3. Implications of cloud-size effects for the instantaneous determination of the convective regime

We have two plausible mechanisms giving opposite dependences of bulk entrainment on the ‘favourability’ of the environment for convection. To develop a model of adaptive entrainment, it seems we need to decide which view is right or which mechanism is stronger.

Our CRM results in section 3 suggested that entrainment was slightly higher in the drier, less ‘favourable’ convective regimes, a finding consistent with standard assumptions in shallow-convection parametrizations. Perhaps this explains why shallow convection poses a challenge to multiple-plume schemes, which naturally embody the natural selection mechanism.

However, if we do accept the dominant cloud-size mechanism of section 6.2 as correct or stronger, with lower entrainment in a deeper cloud layer, then a problem arises for the parametrization of convection from instantaneous profiles. If equation image indeed decreases as a function of overall cloud depth, then a marginal (e.g. moist-neutral) profile can be expected to have more than one solution for the convective regime.

This is because marginal situations are inherently susceptible to small changes, and even a small increase in entrainment is likely to switch the diagnosis from ‘deep’ to ‘shallow’. Hence these marginal profiles can be expected to support either (i) shallow clouds entraining strongly and hence limiting their depth or (ii) deep clouds with much more protected cores reaching a moist adiabatic height.

Such non-uniqueness of instantaneous diagnosis (owing to the interactive behaviour of entrainment) has implications for modelling non-equilibrium convective development. If the equilibrium problem were robust, then one would expect non-equilibrium effects to be short-lived, persisting essentially over the lifetime of individual cells. However, there is evidence that non-equilibrium effects persist over considerably longer time-scales. In Derbyshire et al. (2004), even with relaxation of the mean fields on a 1 h time-scale, a systematic evolution was discernible for around 12 h. Compare also the systematic evolution of convective cloud fields over several hours shown by Khairoutdinov and Randall (2006).

Ultimately there could be a need to treat the ‘convective regime’ (and its link to entrainment) as an initial value problem. Piriou et al. (2007) found in SCM tests that, of a number of structural changes to their parametrization, perhaps the most effective measure giving a realistic delay to the diurnal cycle was a simple non-dimensional prognostic parameter ζ governing convective organization and hence entrainment.

In summary, our CRM results provided limited evidence that entrainment should also be adaptive, but different conceptual models imply quite different behaviour. Hence we consider that adaptive entrainment raises bigger questions and requires further research.

8. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Gregory–Rowntree convection scheme
  5. 3. Further CRM analysis from a EUROCS case
  6. 4. Formulation and single-column testing of simple adaptive detrainment
  7. 5. Performance in the full NWP model
  8. 6. Combination with other possible changes
  9. 7. Towards adaptive entrainment?
  10. 8. Conclusions
  11. Acknowledgement
  12. References

The representation of moist convection in atmospheric models is undergoing a range of innovations large and small. As well as new structural ideas there are also incremental approaches, which also draw on results from cloud-resolving studies. It is of scientific as well as practical importance to test the scope for incremental improvement of current methods, e.g. as in Bechtold et al. (2008).

The G–R scheme has been used with some success for many years in the MetUM. In seeking to improve it to meet current challenges, we looked to some of the headline lessons from CRM studies. For us the EUROCS case (Derbyshire et al., 2004) exposed most fundamentally the weakness in its detrainment specification and motivated a rethinking of this component.

The revised ‘adaptive detrainment’ presented here is deliberately simple, and introduces no new dimensional parameters (indeed it removes one unscaled temperature parameter). This was based on CRM evidence that the bulk plume parameters such as core area adjust so that the plume buoyancy is robust. In the CRM, the variation in core updraught velocity and core buoyancy across the EUROCS humidity subcases is strikingly small compared with the variation in mass flux and core area fraction, and this supports the notion that the cloud area ‘adapts’ by shedding material to maintain buoyancy.

Our ‘adaptive detrainment’ scheme thus links the mass flux more closely to the parcel buoyancy profile. This significantly improves the shapes of individual mass-flux profiles but does not fully explain variation with RHt. Our mixing detrainment captures a little more. The EUROCS test case would be better captured by increasing the role of our RH-sensitive mixing detrainment (doubling it or more). Adaptive detrainment is compatible with further changes to entrainment, which could go further towards a truly ‘shallow’ regime.

It was not our intention here to tune strongly to the EUROCS humidity case, nor to any single process study. In particular, for the present, within the MetUM system we prefer to continue to represent shallow convection with a separate shallow-convection scheme after Grant and Lock (2004), with which the enhanced equation image and larger δ are broadly consistent. Further fundamental issues including time dependence were discussed in section 6.

Our simple adaptive detrainment concept could be applied in other plume-based schemes. It appears to be the simplest way of representing statistical detrainment of a broad pdf of thermodynamic properties, without introducing additional scales.

The non-dimensional ‘adaptivity’ parameter Rdet could itself be made adaptive if desired and could allow for narrow as well as broad distributions.

Tests in the full NWP model showed that the the impact of adaptive detrainment projected strongly (and favourably) on to the major biases in temperature, humidity and circulation. The model verification was thus significantly improved and the change was adopted operationally.

The results of our relatively simple and physically motivated changes, and of other work both here and elsewhere, illustrate the possibility that some of the problems with convection parametrization stem from specific issues and that further progress is possible.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. The Gregory–Rowntree convection scheme
  5. 3. Further CRM analysis from a EUROCS case
  6. 4. Formulation and single-column testing of simple adaptive detrainment
  7. 5. Performance in the full NWP model
  8. 6. Combination with other possible changes
  9. 7. Towards adaptive entrainment?
  10. 8. Conclusions
  11. Acknowledgement
  12. References