Relaxing the Tropics to an ‘observed’ state: analysis using a simple baroclinic model

The technique of relaxation of the tropical atmosphere towards an analysis in a month-season forecast model has previously been successfully exploited in a number of contexts. Here it is shown that when tropical relaxation is used to investigate the possible origin of the observed anomalies in June–July 2007, a simple dynamical model is able to reproduce the observed component of the pattern of anomalies given by an ensemble of ECMWF forecast runs. Following this result, the simple model is used for a range of experiments on time-scales of relaxation, variables and regions relaxed based on a control model run with equatorial heating in a zonal flow. A theory based on scale analysis for the large-scale tropics is used to interpret the results. Typical relationships between scales are determined from the basic equations, and for a specified diabatic heating a chain of deductions for determining the dependent variables is derived. Different critical time-scales are found for tropical relaxation of different dependent variables to be effective. Vorticity has the longest critical time-scale, typically 1.2 days. For temperature and divergence, the time-scales are 10 hours and 3 hours, respectively. However not all the tropical fields, in particular the vertical motion, are reproduced correctly by the model unless divergence is heavily damped. To obtain the correct extra-tropical fields, it is crucial to have the correct rotational flow in the subtropics to initiate the Rossby wave propagation from there. It is sufficient to relax vorticity or temperature on a time-scale comparable or less than their critical time-scales to obtain this. However if the divergent advection of vorticity is important in the Rossby Wave Source then strong relaxation of divergence is required to accurately represent the tropical forcing of Rossby waves.

The effect of doubled CO2 and model basic state biases on the monsoon-ENSO system. II: Changing ENSO regimes

Integrations of a fully-coupled climate model with and without flux adjustments in the equatorial oceans are performed under 2×CO2 conditions to explore in more detail the impact of increased greenhouse gas forcing on the monsoon-ENSO system. When flux adjustments are used to correct some systematic model biases, ENSO behaviour in the modelled future climate features distinct irregular and periodic (biennial) regimes. Comparison with the observed record yields some consistency with ENSO modes primarily based on air-sea interaction and those dependent on basinwide ocean wave dynamics. Simple theory is also used to draw analogies between the regimes and irregular (stochastically forced) and self-excited oscillations respectively. Periodic behaviour is also found in the Asian-Australian monsoon system, part of an overall biennial tendency of the model under these conditions related to strong monsoon forcing and increased coupling between the Indian and Pacific Oceans. The tropospheric biennial oscillation (TBO) thus serves as a useful descriptor for the coupled monsoon-ENSO system in this case. The presence of obvious regime changes in the monsoon-ENSO system on interdecadal timescales, when using flux adjustments, suggests there may be greater uncertainty in projections of future climate, although further modelling studies are required to confirm the realism and cause of such changes.

Can knowledge of the state of the stratosphere be used to improve statistical forecasts of the troposphere?

Recent analysis of the Arctic Oscillation (AO) in the stratosphere and troposphere has suggested that predictability of the state of the tropospheric AO may be obtained from the state of the stratospheric AO. However, much of this research has been of a purely qualitative nature. We present a more thorough statistical analysis of a long AO amplitude dataset which seeks to establish the magnitude of such a link. A relationship between the AO in the lower stratosphere and on the 1000 hPa surface on a 10-45 day time-scale is revealed. The relationship accounts for 5% of the variance of the 1000 hPa time series at its peak value and is significant at the 5% level. Over a similar time-scale the 1000 hPa time series accounts for 1% of itself and is not significant at the 5% level. Further investigation of the relationship reveals that it is only present during the winter season and in particular during February and March. It is also demonstrated that using stratospheric AO amplitude data as a predictor in a simple statistical model results in a gain of skill of 5% over a troposphere-only statistical model. This gain in skill is not repeated if an unrelated time series is included as a predictor in the model. Copyright © 2003 Royal Meteorological Society

Variational data assimilation for parameter estimation: application to a simple morphodynamic model

Data assimilation is a sophisticated mathematical technique for combining observational data with model predictions to produce state and parameter estimates that most accurately approximate the current and future states of the true system. The technique is commonly used in atmospheric and oceanic modelling, combining empirical observations with model predictions to produce more accurate and well-calibrated forecasts. Here, we consider a novel application within a coastal environment and describe how the method can also be used to deliver improved estimates of uncertain morphodynamic model parameters. This is achieved using a technique known as state augmentation. Earlier applications of state augmentation have typically employed the 4D-Var, Kalman filter or ensemble Kalman filter assimilation schemes. Our new method is based on a computationally inexpensive 3D-Var scheme, where the specification of the error covariance matrices is crucial for success. A simple 1D model of bed-form propagation is used to demonstrate the method. The scheme is capable of recovering near-perfect parameter values and, therefore, improves the capability of our model to predict future bathymetry. Such positive results suggest the potential for application to more complex morphodynamic models.

A simple theoretical model for the intensification of tropical cyclones and polar lows

A simple theoretical model for the intensification of tropical cyclones and polar lows is developed using a minimal set of physical assumptions. These disturbances are assumed to be balanced systems intensifying through the WISHE (Wind-Induced Surface Heat Exchange) intensification mechanism, driven by surface fluxes of heat and moisture into an atmosphere which is neutral to moist convection. The equation set is linearized about a resting basic state and solved as an initial-value problem. A system is predicted to intensify with an exponential perturbation growth rate scaled by the radial gradient of an efficiency parameter which crudely represents the effects of unsaturated processes. The form of this efficiency parameter is assumed to be defined by initial conditions, dependent on the nature of a pre-existing vortex required to precondition the atmosphere to a state in which the vortex can intensify. Evaluation of the simple model using a primitive-equation, nonlinear numerical model provides support for the prediction of exponential perturbation growth. Good agreement is found between the simple and numerical models for the sensitivities of the measured growth rate to various parameters, including surface roughness, the rate of transfer of heat and moisture from the ocean surface, and the scale for the growing vortex.

Simple general method of generating non-oxo, non-amavadine model octacoordinated vanadium(IV) complexes of some tetradentate ONNO chelating ligands from various oxovanadium(IV/V) compounds and structural characterization of one of them

A simple general route of obtaining very stable octacoordinated non-oxovanadium( IV) complexes of the general formula VL2 (where H2L is a tetradentate ONNO donor) is presented. Six such complexes (1-6) are adequately characterized by elemental analysis, mass spectrometry, and various spectroscopic techniques. One of these compounds (1) has been structurally characterized. The molecule has crystallographic 4 symmetry and has a dodecahedral structure existing in a tetragonal space group P4n2. The non-oxo character and VL2 stoichiometry for all of the complexes are established from analytical and mass spectrometric data. In addition, the non-oxo character is clearly indicated by the complete absence of the strong nu(v=o) band in the 925-1025 cm(-1) region, which is a signature of all oxovanadium species. The complexes are quite stable in open air in the solid state and in solution, a phenomenon rarely observed in non-oxovanadium(IV) or bare vanadium(IV) complexes.

Neurofuzzy state identification using prefiltering

A new state estimator algorithm is based on a neurofuzzy network and the Kalman filter algorithm. The major contribution of the paper is recognition of a bias problem in the parameter estimation of the state-space model and the introduction of a simple, effective prefiltering method to achieve unbiased parameter estimates in the state-space model, which will then be applied for state estimation using the Kalman filtering algorithm. Fundamental to this method is a simple prefiltering procedure using a nonlinear principal component analysis method based on the neurofuzzy basis set. This prefiltering can be performed without prior system structure knowledge. Numerical examples demonstrate the effectiveness of the new approach.

State estimation using model order reduction for unstable systems

The problem of state estimation occurs in many applications of fluid flow. For example, to produce a reliable weather forecast it is essential to find the best possible estimate of the true state of the atmosphere. To find this best estimate a nonlinear least squares problem has to be solved subject to dynamical system constraints. Usually this is solved iteratively by an approximate Gauss–Newton method where the underlying discrete linear system is in general unstable. In this paper we propose a new method for deriving low order approximations to the problem based on a recently developed model reduction method for unstable systems. To illustrate the theoretical results, numerical experiments are performed using a two-dimensional Eady model – a simple model of baroclinic instability, which is the dominant mechanism for the growth of storms at mid-latitudes. It is a suitable test model to show the benefit that may be obtained by using model reduction techniques to approximate unstable systems within the state estimation problem.

A stress relaxation model for the viscoelastic solids based on the steady-state creep equation

Creep and stress relaxation are inherent mechanical behaviors of viscoelastic materials. It is considered that both are different performances of one identical physical phenomenon. The relationship between the decay stress and time during stress relaxation has been derived from the power law equation of the steady-state creep. The model was used to analyse the stress relaxation curves of various different viscoelastic materials (such as pure polycrystalline ice, polymers, foods, bones, metal, animal tissues, etc.). The calculated results using the theoretical model agree with the experimental data very well. Here we show that the new mathematical formula is not only simple but its parameters have the clear physical meanings. It is suitable to materials with a very broad scope and has a strong predictive ability.

Data assimilation for state and parameter estimation: application to morphodynamic modelling

Data assimilation is predominantly used for state estimation; combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts we need good estimates of both the current system state and the model parameters. This paper presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three dimensional variational(3D-Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from SAR satellite imagery and a ship-borne survey is shown to significantly improve the predictive capability of the model over a 2 year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this paper considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D-Var data assimilation algorithm for joint state-parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation-based state-parameter estimation in coastal morphodynamic modelling.

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.

Atmospheric blocking in a high resolution climate model: influences of mean state, orography and eddy forcing

An underestimate of atmospheric blocking occurrence is a well-known limitation of many climate models. This article presents an analysis of Northern Hemisphere winter blocking in an atmospheric model with increased horizontal resolution. European blocking frequency increases with model resolution, and this results from an improvement in the atmospheric patterns of variability as well as a simple improvement in the mean state. There is some evidence that the transient eddy momentum forcing of European blocks is increased at high resolution, which could account for this. However, it is also shown that the increase in resolution of the orography is needed to realise the improvement in blocking, consistent with the increase in height of the Rocky Mountains acting to increase the tilt of the Atlantic jet stream and giving higher mean geopotential heights over northern Europe. Blocking frequencies in the Pacific sector are also increased with atmospheric resolution, but in this case the improvement in orography actually leads to a decrease in blocking

Changes in reactive stratospheric gases due to a change in Brewer–Dobson circulation: results from a simple model

Amounts of source gases with stratospheric sinks (CFCs, N2O, CH4) are affected by changes in Brewer–Dobson circulation. Source gases and their degradation products are important for atmospheric chemistry and climate. With a simple model, we examine how amounts and lifetimes of source gases and products depend on speed of the circulation. Transient results differ from steady-state and stratospheric results differ from those for stratosphere plus troposphere. Increases in speed increase the stratospheric burden of source gases, but reduce products and reduce total burdens and lifetimes of source gases

Present state of global wetland extent and wetland methane modelling: conclusions from a model inter-comparison project (WETCHIMP)

Global wetlands are believed to be climate sensitive, and are the largest natural emitters of methane (CH4). Increased wetland CH4 emissions could act as a positive feedback to future warming. The Wetland and Wetland CH4 Inter-comparison of Models Project (WETCHIMP) investigated our present ability to simulate large-scale wetland characteristics and corresponding CH4 emissions. To ensure inter-comparability, we used a common experimental protocol driving all models with the same climate and carbon dioxide (CO2) forcing datasets. The WETCHIMP experiments were conducted for model equilibrium states as well as transient simulations covering the last century. Sensitivity experiments investigated model response to changes in selected forcing inputs (precipitation, temperature, and atmospheric CO2 concentration). Ten models participated, covering the spectrum from simple to relatively complex, including models tailored either for regional or global simulations. The models also varied in methods to calculate wetland size and location, with some models simulating wetland area prognostically, while other models relied on remotely sensed inundation datasets, or an approach intermediate between the two. Four major conclusions emerged from the project. First, the suite of models demonstrate extensive disagreement in their simulations of wetland areal extent and CH4 emissions, in both space and time. Simple metrics of wetland area, such as the latitudinal gradient, show large variability, principally between models that use inundation dataset information and those that independently determine wetland area. Agreement between the models improves for zonally summed CH4 emissions, but large variation between the models remains. For annual global CH4 emissions, the models vary by ±40% of the all-model mean (190 Tg CH4 yr−1). Second, all models show a strong positive response to increased atmospheric CO2 concentrations (857 ppm) in both CH4 emissions and wetland area. In response to increasing global temperatures (+3.4 °C globally spatially uniform), on average, the models decreased wetland area and CH4 fluxes, primarily in the tropics, but the magnitude and sign of the response varied greatly. Models were least sensitive to increased global precipitation (+3.9 % globally spatially uniform) with a consistent small positive response in CH4 fluxes and wetland area. Results from the 20th century transient simulation show that interactions between climate forcings could have strong non-linear effects. Third, we presently do not have sufficient wetland methane observation datasets adequate to evaluate model fluxes at a spatial scale comparable to model grid cells (commonly 0.5°). This limitation severely restricts our ability to model global wetland CH4 emissions with confidence. Our simulated wetland extents are also difficult to evaluate due to extensive disagreements between wetland mapping and remotely sensed inundation datasets. Fourth, the large range in predicted CH4 emission rates leads to the conclusion that there is both substantial parameter and structural uncertainty in large-scale CH4 emission models, even after uncertainties in wetland areas are accounted for.

A simple method for integrating a complex model into an ensemble data assimilation system using MPI

This paper details a strategy for modifying the source code of a complex model so that the model may be used in a data assimilation context, {and gives the standards for implementing a data assimilation code to use such a model}. The strategy relies on keeping the model separate from any data assimilation code, and coupling the two through the use of Message Passing Interface (MPI) {functionality}. This strategy limits the changes necessary to the model and as such is rapid to program, at the expense of ultimate performance. The implementation technique is applied in different models with state dimension up to $2.7 \times 10^8$. The overheads added by using this implementation strategy in a coupled ocean-atmosphere climate model are shown to be an order of magnitude smaller than the addition of correlated stochastic random errors necessary for some nonlinear data assimilation techniques.