A comparative method to evaluate and validate stochastic parametrizations

There is a growing interest in using stochastic parametrizations in numerical weather and climate prediction models. Previously, Palmer (2001) outlined the issues that give rise to the need for a stochastic parametrization and the forms such a parametrization could take. In this article a method is presented that uses a comparison between a standard-resolution version and a high-resolution version of the same model to gain information relevant for a stochastic parametrization in that model. A correction term that could be used in a stochastic parametrization is derived from the thermodynamic equations of both models. The origin of the components of this term is discussed. It is found that the component related to unresolved wave-wave interactions is important and can act to compensate for large parametrized tendencies. The correction term is not proportional to the parametrized tendency. Finally, it is explained how the correction term could be used to give information about the shape of the random distribution to be used in a stochastic parametrization. Copyright © 2009 Royal Meteorological Society

Computationally efficient expressions for the collision efficiency between electrically charged aerosol particles and cloud droplets

A multiple factor parametrization is described to permit the efficient calculation of collision efficiency (E) between electrically charged aerosol particles and neutral cloud droplets in numerical models of cloud and climate. The four-parameter representation summarizes the results obtained from a detailed microphysical model of E, which accounts for the different forces acting on the aerosol in the path of falling cloud droplets. The parametrization's range of validity is for aerosol particle radii of 0.4 to 10 mu m, aerosol particle densities of I to 2.0 g cm(-3), aerosol particle charges from neutral to 100 elementary charges and drop radii from 18.55 to 142 mu m. The parametrization yields values of E well within an order of magnitude of the detailed model's values, from a dataset of 3978 E values. Of these values 95% have modelled to parametrized ratios between 0.5 and 1.5 for aerosol particle sizes ranging between 0.4 and 2.0 mu m, and about 96% in the second size range. This parametrization speeds up the calculation of E by a factor of similar to 10(3) compared with the original microphysical model, permitting the inclusion of electric charge effects in numerical cloud and climate models.

The cumulus-capped boundary layer. I: Modelling transports in the cloud layer

Scalar-flux budgets have been obtained from large-eddy simulations (LESs) of the cumulus-capped boundary layer. Parametrizations of the terms in the budgets are discussed, and two parametrizations for the transport term in the cloud layer are proposed. It is shown that these lead to two models for scalar transports by shallow cumulus convection. One is equivalent to the subsidence detrainment form of convective tendencies obtained from mass-flux parametrizations of cumulus convection. The second is a flux-gradient relationship that is similar in form to the non-local parametrizations of turbulent transports in the dry-convective boundary layer. Using the fluxes of liquid-water potential temperature and total water content from the LES, it is shown that both models are reasonable diagnostic relations between fluxes and the vertical gradients of the mean fields. The LESs used in this study are for steady-state convection and it is possible to treat the fluxes of conserved thermodynamic variables as independent, and ignore the effects of condensation. It is argued that a parametrization of cumulus transports in a model of the cumulus-capped boundary layer should also include an explicit representation of condensation. A simple parametrization of the liquid-water flux in terms of conserved variables is also derived.

Mesoscale simulations of organized convection: importance of convective equilibrium

The validity of convective parametrization breaks down at the resolution of mesoscale models, and the success of parametrized versus explicit treatments of convection is likely to depend on the large-scale environment. In this paper we examine the hypothesis that a key feature determining the sensitivity to the environment is whether the forcing of convection is sufficiently homogeneous and slowly varying that the convection can be considered to be in equilibrium. Two case studies of mesoscale convective systems over the UK, one where equilibrium conditions are expected and one where equilibrium is unlikely, are simulated using a mesoscale forecasting model. The time evolution of area-average convective available potential energy and the time evolution and magnitude of the timescale of convective adjustment are consistent with the hypothesis of equilibrium for case 1 and non-equilibrium for case 2. For each case, three experiments are performed with different partitionings between parametrized and explicit convection: fully parametrized convection, fully explicit convection and a simulation with significant amounts of both. In the equilibrium case, bulk properties of the convection such as area-integrated rain rates are insensitive to the treatment of convection. However, the detailed structure of the precipitation field changes; the simulation with parametrized convection behaves well and produces a smooth field that follows the forcing region, and the simulation with explicit convection has a small number of localized intense regions of precipitation that track with the mid-levelflow. For the non-equilibrium case, bulk properties of the convection such as area-integrated rain rates are sensitive to the treatment of convection. The simulation with explicit convection behaves similarly to the equilibrium case with a few localized precipitation regions. In contrast, the cumulus parametrization fails dramatically and develops intense propagating bows of precipitation that were not observed. The simulations with both parametrized and explicit convection follow the pattern seen in the other experiments, with a transition over the duration of the run from parametrized to explicit precipitation. The impact of convection on the large-scaleflow, as measured by upper-level wind and potential-vorticity perturbations, is very sensitive to the partitioning of convection for both cases. © Royal Meteorological Society, 2006. Contributions by P. A. Clark and M. E. B. Gray are Crown Copyright.

The vibrational spectrum and ultimate modulus of polyethylene

We have performed the first completely ab initio lattice dynamics calculation of the full orthorhombic cell of polyethylene using periodic density functional theory in the local density approximation (LDA) and the generalized gradient approximation (GGA). Contrary to current perceptions, we show that LDA accurately describes the structure whereas GGA fails. We emphasize that there is no parametrization of the results. We then rigorously tested our calculation by computing the phonon dispersion curves across the entire Brillouin zone and comparing them to the vibrational spectra, in particular the inelastic neutron scattering (INS) spectra, of polyethylene (both polycrystalline and aligned) and perdeuteriopolyethylene. The F-point frequencies (where the infrared and Raman active modes occur) are in good agreement with the latest low temperature data. The near-perfect reproduction of the INS spectra, gives confidence in the results and allows Lis to deduce a number of physical properties including the elastic moduli, parallel and perpendicular to the chain. We find that the Young's modulus for an infinitely long, perfectly crystalline polyethylene is 360.2 GPa at 0 K. The highest experimental value is 324 GPa, indicating that current high modulus fibers are similar to 90% of their maximum possible strength.

Vertical velocity variance and skewness in clear and cloud-topped boundary layers as revealed by Doppler lidar

In this paper, observations by a ground-based vertically pointing Doppler lidar and sonic anemometer are used to investigate the diurnal evolution of boundary-layer turbulence in cloudless, cumulus and stratocumulus conditions. When turbulence is driven primarily by surface heating, such as in cloudless and cumulus-topped boundary layers, both the vertical velocity variance and skewness follow similar profiles, on average, to previous observational studies of turbulence in convective conditions, with a peak skewness of around 0.8 in the upper third of the mixed layer. When the turbulence is driven primarily by cloud-top radiative cooling, such as in the presence of nocturnal stratocumulus, it is found that the skewness is inverted in both sign and height: its minimum value of around −0.9 occurs in the lower third of the mixed layer. The profile of variance is consistent with a cloud-top cooling rate of around 30Wm−2. This is also consistent with the evolution of the thermodynamic profile and the rate of growth of the mixed layer into the stable nocturnal boundary layer from above. In conditions where surface heating occurs simultaneously with cloud-top cooling, the skewness is found to be useful for diagnosing the source of the turbulence, suggesting that long-term Doppler lidar observations would be valuable for evaluating boundary-layer parametrization schemes. Copyright c 2009 Royal Meteorological Society

Using Doppler radar with a simple explicit microphysics model to diagnose problems with ice sublimation depth-scales in forecast models

Several previous studies have attempted to assess the sublimation depth-scales of ice particles from clouds into clear air. Upon examining the sublimation depth-scales in the Met Office Unified Model (MetUM), it was found that the MetUM has evaporation depth-scales 2–3 times larger than radar observations. Similar results can be seen in the European Centre for Medium-Range Weather Forecasts (ECMWF), Regional Atmospheric Climate Model (RACMO) and Météo-France models. In this study, we use radar simulation (converting model variables into radar observations) and one-dimensional explicit microphysics numerical modelling to test and diagnose the cause of the deep sublimation depth-scales in the forecast model. The MetUM data and parametrization scheme are used to predict terminal velocity, which can be compared with the observed Doppler velocity. This can then be used to test the hypothesis as to why the sublimation depth-scale is too large within the MetUM. Turbulence could lead to dry air entrainment and higher evaporation rates; particle density may be wrong, particle capacitance may be too high and lead to incorrect evaporation rates or the humidity within the sublimating layer may be incorrectly represented. We show that the most likely cause of deep sublimation zones is an incorrect representation of model humidity in the layer. This is tested further by using a one-dimensional explicit microphysics model, which tests the sensitivity of ice sublimation to key atmospheric variables and is capable of including sonde and radar measurements to simulate real cases. Results suggest that the MetUM grid resolution at ice cloud altitudes is not sufficient enough to maintain the sharp drop in humidity that is observed in the sublimation zone.

A critique of neural networks for discrete-time linear control

This paper discusses the use of multi-layer perceptron networks for linear or linearizable, adaptive feedback.control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parametrization. A comparison is made with standard, non-perceptron algorithms, e.g. self-tuning control, and it is shown how gross over-parametrization can occur in the neural network case. Because of the resultant heavy computational burden and poor controller convergence, a strong case is made against the use of neural networks for discrete-time linear control.

The statistical properties of tropical ice clouds generated by the West-African and Australian monsoons from ground-based radar-lidar observations

In the present paper we characterize the statistical properties of non-precipitating tropical ice clouds (deep ice anvils resulting from deep convection and cirrus clouds) over Niamey, Niger, West Africa, and Darwin, northern Australia, using ground-based radar–lidar observations from the Atmospheric Radiation Measurement (ARM) programme. The ice cloud properties analysed in this paper are the frequency of ice cloud occurrence, cloud fraction, the morphological properties (cloud-top height, base height, and thickness), the microphysical and radiative properties (ice water content, visible extinction, effective radius, terminal fall speed, and concentration), and the internal cloud dynamics (in-cloud vertical air velocity). The main highlight of the paper is that it characterizes for the first time the probability density functions of the tropical ice cloud properties, their vertical variability and their diurnal variability at the same time. This is particularly important over West Africa, since the ARM deployment in Niamey provides the first vertically resolved observations of non-precipitating ice clouds in this crucial area in terms of redistribution of water and energy in the troposphere. The comparison between the two sites also provides an additional observational basis for the evaluation of the parametrization of clouds in large-scale models, which should be able to reproduce both the statistical properties at each site and the differences between the two sites. The frequency of ice cloud occurrence is found to be much larger over Darwin when compared to Niamey, and with a much larger diurnal variability, which is well correlated with the diurnal cycle of deep convective activity. The diurnal cycle of the ice cloud occurrence over Niamey is also much less correlated with that of deep convective activity than over Darwin, probably owing to the fact that Niamey is further away from the deep convective sources of the region. The frequency distributions of cloud fraction are strongly bimodal and broadly similar over the two sites, with a predominance of clouds characterized either by a very small cloud fraction (less than 0.3) or a very large cloud fraction (larger than 0.9). The ice clouds over Darwin are also much thicker (by 1 km or more statistically) and are characterized by a much larger diurnal variability than ice clouds over Niamey. Ice clouds over Niamey are also characterized by smaller particle sizes and fall speeds but in much larger concentrations, thereby carrying more ice water and producing more visible extinction than the ice clouds over Darwin. It is also found that there is a much larger occurrence of downward in-cloud air motions less than 1 m s−1 over Darwin, which together with the larger fall speeds retrieved over Darwin indicates that the life cycle of ice clouds is probably shorter over Darwin than over Niamey.

Implementation of a new urban energy budget scheme in the MetUM. Part I: Description and idealized simulations

This paper describes the formulation of a new urban scheme, MORUSES (Met Office–Reading Urban Surface Exchange Scheme) for use in the Met Office Unified Model. The implementation of the new scheme ensures that (1) the new scheme offers more flexibility in the parametrization of the building properties, and hence provides a more realistic representation of the fluxes; (2) the bulk outputs are in satisfactory agreement with previous observational studies; and (3) the impact of the new scheme on the energy balance fluxes is similar to the impact of the current urban scheme when set up to mimic it. As well as having a better physical basis, MORUSES also gains in flexibility in applications and adaptations to different urban materials as well as urban planning. The new scheme represents the urban area as a composition of two tiles, a canyon and a roof, using a simple 2D geometry. Sensitivity analysis to canyon geometry and thickness of the roof canopy emphasizes the gain in flexibility captured by the new scheme. Copyright © 2010 Royal Meteorological Society and Crown Copyright

Ensemble forecasts of a flood-producing storm: comparison of the influence of model-state perturbations and parameter modifications

High-resolution ensemble simulations (Δx = 1 km) are performed with the Met Office Unified Model for the Boscastle (Cornwall, UK) flash-flooding event of 16 August 2004. Forecast uncertainties arising from imperfections in the forecast model are analysed by comparing the simulation results produced by two types of perturbation strategy. Motivated by the meteorology of the event, one type of perturbation alters relevant physics choices or parameter settings in the model's parametrization schemes. The other type of perturbation is designed to account for representativity error in the boundary-layer parametrization. It makes direct changes to the model state and provides a lower bound against which to judge the spread produced by other uncertainties. The Boscastle has genuine skill at scales of approximately 60 km and an ensemble spread which can be estimated to within ∼ 10% with only eight members. Differences between the model-state perturbation and physics modification strategies are discussed, the former being more important for triggering and the latter for subsequent cell development, including the average internal structure of convective cells. Despite such differences, the spread in rainfall evaluated at skilful scales is shown to be only weakly sensitive to the perturbation strategy. This suggests that relatively simple strategies for treating model uncertainty may be sufficient for practical, convective-scale ensemble forecasting.

Evaluation of water and energy budgets in regional climate models applied over Europe

This study presents a model intercomparison of four regional climate models (RCMs) and one variable resolution atmospheric general circulation model (AGCM) applied over Europe with special focus on the hydrological cycle and the surface energy budget. The models simulated the 15 years from 1979 to 1993 by using quasi-observed boundary conditions derived from ECMWF re-analyses (ERA). The model intercomparison focuses on two large atchments representing two different climate conditions covering two areas of major research interest within Europe. The first is the Danube catchment which represents a continental climate dominated by advection from the surrounding land areas. It is used to analyse the common model error of a too dry and too warm simulation of the summertime climate of southeastern Europe. This summer warming and drying problem is seen in many RCMs, and to a less extent in GCMs. The second area is the Baltic Sea catchment which represents maritime climate dominated by advection from the ocean and from the Baltic Sea. This catchment is a research area of many studies within Europe and also covered by the BALTEX program. The observed data used are monthly mean surface air temperature, precipitation and river discharge. For all models, these are used to estimate mean monthly biases of all components of the hydrological cycle over land. In addition, the mean monthly deviations of the surface energy fluxes from ERA data are computed. Atmospheric moisture fluxes from ERA are compared with those of one model to provide an independent estimate of the convergence bias derived from the observed data. These help to add weight to some of the inferred estimates and explain some of the discrepancies between them. An evaluation of these biases and deviations suggests possible sources of error in each of the models. For the Danube catchment, systematic errors in the dynamics cause the prominent summer drying problem for three of the RCMs, while for the fourth RCM this is related to deficiencies in the land surface parametrization. The AGCM does not show this drying problem. For the Baltic Sea catchment, all models similarily overestimate the precipitation throughout the year except during the summer. This model deficit is probably caused by the internal model parametrizations, such as the large-scale condensation and the convection schemes.

Drag produced by trapped lee waves and propagating mountain waves in a two-layer atmosphere

The surface drag force produced by trapped lee waves and upward propagating waves in non-hydrostatic stratified flow over a mountain ridge is explicitly calculated using linear theory for a two-layer atmosphere with piecewise-constant static stability and wind speed profiles. The behaviour of the drag normalized by its hydrostatic single-layer reference value is investigated as a function of the ratio of the Scorer parameters in the two layers l_2/l_1 and of the corresponding dimensionless interface height l_1 H, for selected values of the dimensionless ridge width l_1 a and ratio of wind speeds in the two layers. When l_2/l_1 → 1, the propagating wave drag approaches 1 in approximately hydrostatic conditions, and the trapped lee wave drag vanishes. As l_2/l_1 decreases, the propagating wave drag progressively displays an oscillatory behaviour with l_1 H, with maxima of increasing magnitude due to constructive interference of reflected waves in the lower layer. The trapped lee wave drag shows localized maxima associated with each resonant trapped lee wave mode, occurring for small l_2/l_1 and slightly higher values of l_1 H than the propagating wave drag maxima. As l1a decreases, i.e. the flow becomes more non-hydrostatic, the propagating wave drag decreases and the regions of non-zero trapped lee wave drag extend to higher l_2/l_1. These results are confirmed by numerical simulations for l_2/l_1 = 0.2. In parameter ranges of meteorological relevance, the trapped lee wave drag may have a magnitude comparable to that of propagating wave drag, and be larger than the reference single-layer drag. This may have implications for drag parametrization in global climate and weather-prediction models.

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.

Evaluation of water and energy budgets in regional climate models applied over Europe

Abstract This study presents a model intercomparison of four regional climate models (RCMs) and one variable resolution atmospheric general circulation model (AGCM) applied over Europe with special focus on the hydrological cycle and the surface energy budget. The models simulated the 15 years from 1979 to 1993 by using quasi-observed boundary conditions derived from ECMWF re-analyses (ERA). The model intercomparison focuses on two large atchments representing two different climate conditions covering two areas of major research interest within Europe. The first is the Danube catchment which represents a continental climate dominated by advection from the surrounding land areas. It is used to analyse the common model error of a too dry and too warm simulation of the summertime climate of southeastern Europe. This summer warming and drying problem is seen in many RCMs, and to a less extent in GCMs. The second area is the Baltic Sea catchment which represents maritime climate dominated by advection from the ocean and from the Baltic Sea. This catchment is a research area of many studies within Europe and also covered by the BALTEX program. The observed data used are monthly mean surface air temperature, precipitation and river discharge. For all models, these are used to estimate mean monthly biases of all components of the hydrological cycle over land. In addition, the mean monthly deviations of the surface energy fluxes from ERA data are computed. Atmospheric moisture fluxes from ERA are compared with those of one model to provide an independent estimate of the convergence bias derived from the observed data. These help to add weight to some of the inferred estimates and explain some of the discrepancies between them. An evaluation of these biases and deviations suggests possible sources of error in each of the models. For the Danube catchment, systematic errors in the dynamics cause the prominent summer drying problem for three of the RCMs, while for the fourth RCM this is related to deficiencies in the land surface parametrization. The AGCM does not show this drying problem. For the Baltic Sea catchment, all models similarily overestimate the precipitation throughout the year except during the summer. This model deficit is probably caused by the internal model parametrizations, such as the large-scale condensation and the convection schemes.