Stochastic parameterization: uncertainties from convection

In 2005, the ECMWF held a workshop on stochastic parameterisation, at which the convection was seen as being a key issue. That much is clear from the working group reports and particularly the statement from working group 1 that “it is clear that a stochastic convection scheme is desirable”. The present note aims to consider our current status in comparison with some of the issues raised and hopes expressed in that working group report.

The core-periphery model with three regions and more

We determine the properties of the core-periphery model with three regions and compare our results with those of the standard 2-region model. The conditions for the stability of dispersion and concentration are established. As in the 2-region model, dispersion and concentration can be simultaneously stable. We show that the 3-region (2-region) model favours the concentration (dispersion) of economic activity. Furthermore, we provide some results for the n-region model. We show that the stability of concentration of the 2-region model implies that of any model with an even number of regions.

Breakdown of hydrostatic balance at convective scales in the forecast errors in the Met Office Unified Model

For data assimilation in numerical weather prediction, the initial forecast-error covariance matrix Pf is required. For variational assimilation it is particularly important to prescribe an accurate initial matrix Pf, since Pf is either static (in the 3D-Var case) or constant at the beginning of each assimilation window (in the 4D-Var case). At large scales the atmospheric flow is well approximated by hydrostatic balance and this balance is strongly enforced in the initial matrix Pf used in operational variational assimilation systems such as that of the Met Office. However, at convective scales this balance does not necessarily hold any more. Here we examine the extent to which hydrostatic balance is valid in the vertical forecast-error covariances for high-resolution models in order to determine whether there is a need to relax this balance constraint in convective-scale data assimilation. We use the Met Office Global and Regional Ensemble Prediction System (MOGREPS) and a 1.5 km resolution version of the Unified Model for a case study characterized by the presence of convective activity. An ensemble of high-resolution forecasts valid up to three hours after the onset of convection is produced. We show that at 1.5 km resolution hydrostatic balance does not hold for forecast errors in regions of convection. This indicates that in the presence of convection hydrostatic balance should not be enforced in the covariance matrix used for variational data assimilation at this scale. The results show the need to investigate covariance models that may be better suited for convective-scale data assimilation. Finally, we give a measure of the balance present in the forecast perturbations as a function of the horizontal scale (from 3–90 km) using a set of diagnostics. Copyright © 2012 Royal Meteorological Society and British Crown Copyright, the Met Office

Cloud-resolving model simulations with one- and two-way couplings via the weak temperature gradient approximation

A cloud-resolving model is modified to implement the weak temperature gradient approximation in order to simulate the interactions between tropical convection and the large-scale tropical circulation. The instantaneous domain-mean potential temperature is relaxed toward a reference profile obtained from a radiative–convective equilibrium simulation of the cloud-resolving model. For homogeneous surface conditions, the model state at equilibrium is a large-scale circulation with its descending branch in the simulated column. This is similar to the equilibrium state found in some other studies, but not all. For this model, the development of such a circulation is insensitive to the relaxation profile and the initial conditions. Two columns of the cloud-resolving model are fully coupled by relaxing the instantaneous domain-mean potential temperature in both columns toward each other. This configuration is energetically closed in contrast to the reference-column configuration. No mean large-scale circulation develops over homogeneous surface conditions, regardless of the relative area of the two columns. The sensitivity to nonuniform surface conditions is similar to that obtained in the reference-column configuration if the two simulated columns have very different areas, but it is markedly weaker for columns of comparable area. The weaker sensitivity can be understood as being a consequence of a formulation for which the energy budget is closed. The reference-column configuration has been used to study the convection in a local region under the influence of a large-scale circulation. The extension to a two-column configuration is proposed as a methodology for studying the influence on local convection of changes in remote convection.

Precipitation distributions for explicit versus parameterized convection in a large-domain high-resolution tropical case study

Global climate and weather models tend to produce rainfall that is too light and too regular over the tropical ocean. This is likely because of convective parametrizations, but the problem is not well understood. Here, distributions of precipitation rates are analyzed for high-resolution UK Met Office Unified Model simulations of a 10 day case study over a large tropical domain (∼20°S–20°N and 42°E–180°E). Simulations with 12 km grid length and parametrized convection have too many occurrences of light rain and too few of heavier rain when interpolated onto a 1° grid and compared with Tropical Rainfall Measuring Mission (TRMM) data. In fact, this version of the model appears to have a preferred scale of rainfall around 0.4 mm h−1 (10 mm day−1), unlike observations of tropical rainfall. On the other hand, 4 km grid length simulations with explicit convection produce distributions much more similar to TRMM observations. The apparent preferred scale at lighter rain rates seems to be a feature of the convective parametrization rather than the coarse resolution, as demonstrated by results from 12 km simulations with explicit convection and 40 km simulations with parametrized convection. In fact, coarser resolution models with explicit convection tend to have even more heavy rain than observed. Implications for models using convective parametrizations, including interactions of heating and moistening profiles with larger scales, are discussed. One important implication is that the explicit convection 4 km model has temperature and moisture tendencies that favour transitions in the convective regime. Also, the 12 km parametrized convection model produces a more stable temperature profile at its extreme high-precipitation range, which may reduce the chance of very heavy rainfall. Further study is needed to determine whether unrealistic precipitation distributions are due to some fundamental limitation of convective parametrizations or whether parametrizations can be improved, in order to better simulate these distributions.

Initialisation and predictability of the AMOC over the last 50 years in a climate model

The mechanisms involved in Atlantic meridional overturning circulation (AMOC) decadal variability and predictability over the last 50 years are analysed in the IPSL–CM5A–LR model using historical and initialised simulations. The initialisation procedure only uses nudging towards sea surface temperature anomalies with a physically based restoring coefficient. When compared to two independent AMOC reconstructions, both the historical and nudged ensemble simulations exhibit skill at reproducing AMOC variations from 1977 onwards, and in particular two maxima occurring respectively around 1978 and 1997. We argue that one source of skill is related to the large Mount Agung volcanic eruption starting in 1963, which reset an internal 20-year variability cycle in the North Atlantic in the model. This cycle involves the East Greenland Current intensity, and advection of active tracers along the subpolar gyre, which leads to an AMOC maximum around 15 years after the Mount Agung eruption. The 1997 maximum occurs approximately 20 years after the former one. The nudged simulations better reproduce this second maximum than the historical simulations. This is due to the initialisation of a cooling of the convection sites in the 1980s under the effect of a persistent North Atlantic oscillation (NAO) positive phase, a feature not captured in the historical simulations. Hence we argue that the 20-year cycle excited by the 1963 Mount Agung eruption together with the NAO forcing both contributed to the 1990s AMOC maximum. These results support the existence of a 20-year cycle in the North Atlantic in the observations. Hindcasts following the CMIP5 protocol are launched from a nudged simulation every 5 years for the 1960–2005 period. They exhibit significant correlation skill score as compared to an independent reconstruction of the AMOC from 4-year lead-time average. This encouraging result is accompanied by increased correlation skills in reproducing the observed 2-m air temperature in the bordering regions of the North Atlantic as compared to non-initialized simulations. To a lesser extent, predicted precipitation tends to correlate with the nudged simulation in the tropical Atlantic. We argue that this skill is due to the initialisation and predictability of the AMOC in the present prediction system. The mechanisms evidenced here support the idea of volcanic eruptions as a pacemaker for internal variability of the AMOC. Together with the existence of a 20-year cycle in the North Atlantic they propose a novel and complementary explanation for the AMOC variations over the last 50 years.

A mechanism for Atlantic multidecadal variability in the Kiel Climate Model

Atlantic Multidecadal Variability (AMV) is investigated in a millennial control simulation with the Kiel Climate Model (KCM), a coupled atmosphere–ocean–sea ice model. An oscillatory mode with approximately 60 years period and characteristics similar to observations is identified with the aid of three-dimensional temperature and salinity joint empirical orthogonal function analysis. The mode explains 30 % of variability on centennial and shorter timescales in the upper 2,000 m of the North Atlantic. It is associated with changes in the Atlantic Meridional Overturning Circulation (AMOC) of ±1–2 Sv and Atlantic Sea Surface Temperature (SST) of ±0.2 °C. AMV in KCM results from an out-of-phase interaction between horizontal and vertical ocean circulation, coupled through Irminger Sea convection. Wintertime convection in this region is mainly controlled by salinity anomalies transported by the Subpolar Gyre (SPG). Increased (decreased) dense water formation in this region leads to a stronger (weaker) AMOC after 15 years, and this in turn leads to a weaker (stronger) SPG after another 15 years. The key role of salinity variations in the subpolar North Atlantic for AMV is confirmed in a 1,000 year long simulation with salinity restored to model climatology: No low frequency variations in convection are simulated, and the 60 year mode of variability is absent.

The effects of explicit versus parameterized convection on the MJO in a large-domain high-resolution tropical case study. Part I: Characterization of large-scale organization and propagation

High-resolution simulations over a large tropical domain (∼20◦S–20◦N and 42◦E–180◦E) using both explicit and parameterized convection are analyzed and compared to observations during a 10-day case study of an active Madden-Julian Oscillation (MJO) event. The parameterized convection model simulations at both 40 km and 12 km grid spacing have a very weak MJO signal and little eastward propagation. A 4 km explicit convection simulation using Smagorinsky subgrid mixing in the vertical and horizontal dimensions exhibits the best MJO strength and propagation speed. 12 km explicit convection simulations also perform much better than the 12 km parameterized convection run, suggesting that the convection scheme, rather than horizontal resolution, is key for these MJO simulations. Interestingly, a 4 km explicit convection simulation using the conventional boundary layer scheme for vertical subgrid mixing (but still using Smagorinsky horizontal mixing) completely loses the large-scale MJO organization, showing that relatively high resolution with explicit convection does not guarantee a good MJO simulation. Models with a good MJO representation have a more realistic relationship between lower-free-tropospheric moisture and precipitation, supporting the idea that moisture-convection feedback is a key process for MJO propagation. There is also increased generation of available potential energy and conversion of that energy into kinetic energy in models with a more realistic MJO, which is related to larger zonal variance in convective heating and vertical velocity, larger zonal temperature variance around 200 hPa, and larger correlations between temperature and ascent (and between temperature and diabatic heating) between 500–400 hPa.

Modelling the diurnal cycle of tropical convection across the "Grey Zone"

We present the results of simulations carried out with the Met Office Unified Model at 12km, 4km and 1.5km resolution for a large region centred on West Africa using several different representations of the convection processes. These span the range of resolutions from much coarser than the size of the convection processes to the cloud-system resolving and thus encompass the intermediate "grey-zone". The diurnal cycle in the extent of convective regions in the models is tested against observations from the Geostationary Earth Radiation Budget instrument on Meteosat-8. By this measure, the two best-performing simulations are a 12km model without convective parametrization, using Smagorinsky style sub-grid scale mixing in all three dimensions and a 1.5km simulations with two-dimensional Smagorinsky mixing. Of these, the 12km model produces a better match to the magnitude of the total cloud fraction but the 1.5km results in better timing for its peak value. The results suggest that the previously-reported improvement in the representation of the diurnal cycle of convective organisation in the 4km model compared to the standard 12km configuration is principally a result of the convection scheme employed rather than the improved resolution per se. The details of and implications for high-resolution model simulations are discussed.

Understanding advances in the simulation of intraseasonal variability in the ECMWF model. Part I: the representation of the MJO

As a major mode of intraseasonal variability, which interacts with weather and climate systems on a near-global scale, the Madden – Julian Oscillation (MJO) is a crucial source of predictability for numerical weather prediction (NWP) models. Despite its global significance and comprehensive investigation, improvements in the representation of the MJO in an NWP context remain elusive. However, recent modifications to the model physics in the ECMWF model led to advances in the representation of atmospheric variability and the unprecedented propagation of the MJO signal through the entire integration period. In light of these recent advances, a set of hindcast experiments have been designed to assess the sensitivity of MJO simulation to the formulation of convection. Through the application of established MJO diagnostics, it is shown that the improvements in the representation of the MJO can be directly attributed to the modified convective parametrization. Furthermore, the improvements are attributed to the move from a moisture-convergent- to a relative-humidity-dependent formulation for organized deep entrainment. It is concluded that, in order to understand the physical mechanisms through which a relative-humidity-dependent formulation for entrainment led to an improved simulation of the MJO, a more process-based approach should be taken. T he application of process-based diagnostics t o t he hindcast experiments presented here will be the focus of Part II of this study.

Understanding advances in the simulation of intraseasonal variability in the ECMWF model. Part II: the application of process-based diagnostics

In Part I of this study it was shown that moving from a moisture-convergent- to a relative-humidity-dependent organized entrainment rate in the formulation for deep convection was responsible for significant advances in the simulation of the Madden – Julian Oscillation (MJO) in the ECMWF model. However, the application of traditional MJO diagnostics were not adequate to understand why changing the control on convection had such a pronounced impact on the representation of the MJO. In this study a set of process-based diagnostics are applied to the hindcast experiments described in Part I to identify the physical mechanisms responsible for the advances in MJO simulation. Increasing the sensitivity of the deep convection scheme to environmental moisture is shown to modify the relationship between precipitation and moisture in the model. Through dry-air entrainment, convective plumes ascending in low-humidity environments terminate lower in the atmosphere. As a result, there is an increase in the occurrence of cumulus congestus, which acts to moisten the mid troposphere. Due to the modified precipitation – moisture relationship more moisture is able to build up, which effectively preconditions the tropical atmosphere for the t ransition t o d eep convection. R esults from this study suggest that a tropospheric moisture control on convection is key to simulating the interaction between the convective heating and the large-scale wave forcing associated with the MJO.

Isomap nonlinear dimensionality reduction and bimodality of Asian monsoon convection

It is known that the empirical orthogonal function method is unable to detect possible nonlinear structure in climate data. Here, isometric feature mapping (Isomap), as a tool for nonlinear dimensionality reduction, is applied to 1958–2001 ERA-40 sea-level pressure anomalies to study nonlinearity of the Asian summer monsoon intraseasonal variability. Using the leading two Isomap time series, the probability density function is shown to be bimodal. A two-dimensional bivariate Gaussian mixture model is then applied to identify the monsoon phases, the obtained regimes representing enhanced and suppressed phases, respectively. The relationship with the large-scale seasonal mean monsoon indicates that the frequency of monsoon regime occurrence is significantly perturbed in agreement with conceptual ideas, with preference for enhanced convection on intraseasonal time scales during large-scale strong monsoons. Trend analysis suggests a shift in concentration of monsoon convection, with less emphasis on South Asia and more on the East China Sea.

On the potential of assimilating meteorological analyses in a global climate model for the purpose of model validation

A simple four-dimensional assimilation technique, called Newtonian relaxation, has been applied to the Hamburg climate model (ECHAM), to enable comparison of model output with observations for short periods of time. The prognostic model variables vorticity, divergence, temperature, and surface pressure have been relaxed toward European Center for Medium-Range Weather Forecasts (ECMWF) global meteorological analyses. Several experiments have been carried out, in which the values of the relaxation coefficients have been varied to find out which values are most usable for our purpose. To be able to use the method for validation of model physics or chemistry, good agreement of the model simulated mass and wind field is required. In addition, the model physics should not be disturbed too strongly by the relaxation forcing itself. Both aspects have been investigated. Good agreement with basic observed quantities, like wind, temperature, and pressure is obtained for most simulations in the extratropics. Derived variables, like precipitation and evaporation, have been compared with ECMWF forecasts and observations. Agreement for these variables is smaller than for the basic observed quantities. Nevertheless, considerable improvement is obtained relative to a control run without assimilation. Differences between tropics and extratropics are smaller than for the basic observed quantities. Results also show that precipitation and evaporation are affected by a sort of continuous spin-up which is introduced by the relaxation: the bias (ECMWF-ECHAM) is increasing with increasing relaxation forcing. In agreement with this result we found that with increasing relaxation forcing the vertical exchange of tracers by turbulent boundary layer mixing and, in a lesser extent, by convection, is reduced.

The energy-cycle analysis of the interactions between shallow and deep atmospheric convection

Interactions between different convection modes can be investigated using an energy–cycle description under a framework of mass–flux parameterization. The present paper systematically investigates this system by taking a limit of two modes: shallow and deep convection. Shallow convection destabilizes itself as well as the other convective modes by moistening and cooling the environment, whereas deep convection stabilizes itself as well as the other modes by drying and warming the environment. As a result, shallow convection leads to a runaway growth process in its stand–alone mode, whereas deep convection simply damps out. Interaction between these two convective modes becomes a rich problem, even when it is limited to the case with no large–scale forcing, because of these opposing tendencies. Only if the two modes are coupled at a proper level can a self–sustaining system arise, exhibiting a periodic cycle. The present study establishes the conditions for self–sustaining periodic solutions. It carefully documents the behaviour of the two mode system in order to facilitate the interpretation of global model behaviours when this energy–cycle is implemented as a closure into a convection parameterization in future.

The ocean's gravitational potential energy budget in a coupled climate model

This study examines, in a unified fashion, the budgets of ocean gravitational potential energy (GPE) and available gravitational potential energy (AGPE) in the control simulation of the coupled atmosphere–ocean general circulation model HadCM3. Only AGPE can be converted into kinetic energy by adiabatic processes. Diapycnal mixing supplies GPE, but not AGPE, whereas the reverse is true of the combined effect of surface buoyancy forcing and convection. Mixing and buoyancy forcing, thus, play complementary roles in sustaining the large scale circulation. However, the largest globally integrated source of GPE is resolved advection (+0.57 TW) and the largest sink is through parameterized eddy transports (-0.82 TW). The effect of these adiabatic processes on AGPE is identical to their effect on GPE, except for perturbations to both budgets due to numerical leakage exacerbated by non-linearities in the equation of state.