Intercomparison of general circulation models for hot extrasolar planets

We compare five general circulation models (GCMs) which have been recently used to study hot extrasolar planet atmospheres (BOB, CAM, IGCM, MITgcm, and PEQMOD), under three test cases useful for assessing model convergence and accuracy. Such a broad, detailed intercomparison has not been performed thus far for extrasolar planets study. The models considered all solve the traditional primitive equations, but employ di↵erent numerical algorithms or grids (e.g., pseudospectral and finite volume, with the latter separately in longitude-latitude and ‘cubed-sphere’ grids). The test cases are chosen to cleanly address specific aspects of the behaviors typically reported in hot extrasolar planet simulations: 1) steady-state, 2) nonlinearly evolving baroclinic wave, and 3) response to fast timescale thermal relaxation. When initialized with a steady jet, all models maintain the steadiness, as they should—except MITgcm in cubed-sphere grid. A very good agreement is obtained for a baroclinic wave evolving from an initial instability in pseudospectral models (only). However, exact numerical convergence is still not achieved across the pseudospectral models: amplitudes and phases are observably di↵erent. When subject to a typical ‘hot-Jupiter’-like forcing, all five models show quantitatively di↵erent behavior—although qualitatively similar, time-variable, quadrupole-dominated flows are produced. Hence, as have been advocated in several past studies, specific quantitative predictions (such as the location of large vortices and hot regions) by GCMs should be viewed with caution. Overall, in the tests considered here, pseudospectral models in pressure coordinate (PEBOB and PEQMOD) perform the best and MITgcm in cubed-sphere grid performs the worst.

A numerical model of the ionospheric signatures of time-varying magnetic reconnection: II. Measuring expansions in the ionospheric flow response

A numerical model embodying the concepts of the Cowley-Lockwood (Cowley and Lockwood, 1992, 1997) paradigm has been used to produce a simple Cowley– Lockwood type expanding flow pattern and to calculate the resulting change in ion temperature. Cross-correlation, fixed threshold analysis and threshold relative to peak are used to determine the phase speed of the change in convection pattern, in response to a change in applied reconnection. Each of these methods fails to fully recover the expansion of the onset of the convection response that is inherent in the simulations. The results of this study indicate that any expansion of the convection pattern will be best observed in time-series data using a threshold which is a fixed fraction of the peak response. We show that these methods used to determine the expansion velocity can be used to discriminate between the two main models for the convection response to a change in reconnection.

Impacts of increasing the aerosol complexity in the Met Office global numerical weather prediction model.

The inclusion of the direct and indirect radiative effects of aerosols in high-resolution global numerical weather prediction (NWP) models is being increasingly recognised as important for the improved accuracy of short-range weather forecasts. In this study the impacts of increasing the aerosol complexity in the global NWP configuration of the Met Office Unified Model (MetUM) are investigated. A hierarchy of aerosol representations are evaluated including three-dimensional monthly mean speciated aerosol climatologies, fully prognostic aerosols modelled using the CLASSIC aerosol scheme and finally, initialised aerosols using assimilated aerosol fields from the GEMS project. The prognostic aerosol schemes are better able to predict the temporal and spatial variation of atmospheric aerosol optical depth, which is particularly important in cases of large sporadic aerosol events such as large dust storms or forest fires. Including the direct effect of aerosols improves model biases in outgoing long-wave radiation over West Africa due to a better representation of dust. However, uncertainties in dust optical properties propagate to its direct effect and the subsequent model response. Inclusion of the indirect aerosol effects improves surface radiation biases at the North Slope of Alaska ARM site due to lower cloud amounts in high-latitude clean-air regions. This leads to improved temperature and height forecasts in this region. Impacts on the global mean model precipitation and large-scale circulation fields were found to be generally small in the short-range forecasts. However, the indirect aerosol effect leads to a strengthening of the low-level monsoon flow over the Arabian Sea and Bay of Bengal and an increase in precipitation over Southeast Asia. Regional impacts on the African Easterly Jet (AEJ) are also presented with the large dust loading in the aerosol climatology enhancing of the heat low over West Africa and weakening the AEJ. This study highlights the importance of including a more realistic treatment of aerosol–cloud interactions in global NWP models and the potential for improved global environmental prediction systems through the incorporation of more complex aerosol schemes.

Reducing noise associated with the Monte Carlo Independent Column Approximation for weather forecasting models

The Monte Carlo Independent Column Approximation (McICA) is a flexible method for representing subgrid-scale cloud inhomogeneity in radiative transfer schemes. It does, however, introduce conditional random errors but these have been shown to have little effect on climate simulations, where spatial and temporal scales of interest are large enough for effects of noise to be averaged out. This article considers the effect of McICA noise on a numerical weather prediction (NWP) model, where the time and spatial scales of interest are much closer to those at which the errors manifest themselves; this, as we show, means that noise is more significant. We suggest methods for efficiently reducing the magnitude of McICA noise and test these methods in a global NWP version of the UK Met Office Unified Model (MetUM). The resultant errors are put into context by comparison with errors due to the widely used assumption of maximum-random-overlap of plane-parallel homogeneous cloud. For a simple implementation of the McICA scheme, forecasts of near-surface temperature are found to be worse than those obtained using the plane-parallel, maximum-random-overlap representation of clouds. However, by applying the methods suggested in this article, we can reduce noise enough to give forecasts of near-surface temperature that are an improvement on the plane-parallel maximum-random-overlap forecasts. We conclude that the McICA scheme can be used to improve the representation of clouds in NWP models, with the provision that the associated noise is sufficiently small.

Imbalanced land-surface water budgets in a numerical weather prediction system

There has been a significant increase in the skill and resolution of numerical weather prediction models (NWPs) in recent decades, extending the time scales of useful weather predictions. The land-surface models (LSMs) of NWPs are often employed in hydrological applications, which raises the question of how hydrologically representative LSMs really are. In this paper, precipitation (P), evaporation (E) and runoff (R) from the European Centre for Medium-Range Weather Forecasts (ECMWF) global models were evaluated against observational products. The forecasts differ substantially from observed data for key hydrological variables. In addition, imbalanced surface water budgets, mostly caused by data assimilation, were found on both global (P-E) and basin scales (P-E-R), with the latter being more important. Modeled surface fluxes should be used with care in hydrological applications and further improvement in LSMs in terms of process descriptions, resolution and estimation of uncertainties is needed to accurately describe the land-surface water budgets.

Efficient incorporation of channel cross-section geometry uncertainty into regional and global scale flood inundation models

This paper investigates the challenge of representing structural differences in river channel cross-section geometry for regional to global scale river hydraulic models and the effect this can have on simulations of wave dynamics. Classically, channel geometry is defined using data, yet at larger scales the necessary information and model structures do not exist to take this approach. We therefore propose a fundamentally different approach where the structural uncertainty in channel geometry is represented using a simple parameterization, which could then be estimated through calibration or data assimilation. This paper first outlines the development of a computationally efficient numerical scheme to represent generalised channel shapes using a single parameter, which is then validated using a simple straight channel test case and shown to predict wetted perimeter to within 2% for the channels tested. An application to the River Severn, UK is also presented, along with an analysis of model sensitivity to channel shape, depth and friction. The channel shape parameter was shown to improve model simulations of river level, particularly for more physically plausible channel roughness and depth parameter ranges. Calibrating channel Manning’s coefficient in a rectangular channel provided similar water level simulation accuracy in terms of Nash-Sutcliffe efficiency to a model where friction and shape or depth were calibrated. However, the calibrated Manning coefficient in the rectangular channel model was ~2/3 greater than the likely physically realistic value for this reach and this erroneously slowed wave propagation times through the reach by several hours. Therefore, for large scale models applied in data sparse areas, calibrating channel depth and/or shape may be preferable to assuming a rectangular geometry and calibrating friction alone.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Understanding advances in the simulation of the Madden-Julian Oscillation in a numerical weather prediction model.

The Madden-Julian Oscillation (MJO) is the dominant mode of intraseasonal variability in the Trop- ics. It can be characterised as a planetary-scale coupling between the atmospheric circulation and organised deep convection that propagates east through the equatorial Indo-Pacific region. The MJO interacts with weather and climate systems on a near-global scale and is a crucial source of predictability for weather forecasts on medium to seasonal timescales. Despite its global signifi- cance, accurately representing the MJO in numerical weather prediction (NWP) and climate models remains a challenge. This thesis focuses on the representation of the MJO in the Integrated Forecasting System (IFS) at the European Centre for Medium-Range Weather Forecasting (ECMWF), a state-of-the-art NWP model. Recent modifications to the model physics in Cycle 32r3 (Cy32r3) of the IFS led to ad- vances in the simulation of the MJO; for the first time the observed amplitude of the MJO was maintained throughout the integration period. A set of hindcast experiments, which differ only in their formulation of convection, have been performed between May 2008 and April 2009 to asses the sensitivity of MJO simulation in the IFS to the Cy32r3 convective parameterization. Unique to this thesis is the attribution of the advances in MJO simulation in Cy32r3 to the mod- ified convective parameterization, specifically, the relative-humidity-dependent formulation for or- ganised deep entrainment. Increasing the sensitivity of the deep convection scheme to environmen- tal 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 transition to deep convection. Results from this thesis suggest that a tropospheric moisture control on convection is key to simulating the interaction between the physics and large-scale circulation associated with the MJO.

Black-box decomposition approach for computational hemodynamics: One-dimensional models

Increasing efforts exist in integrating different levels of detail in models of the cardiovascular system. For instance, one-dimensional representations are employed to model the systemic circulation. In this context, effective and black-box-type decomposition strategies for one-dimensional networks are needed, so as to: (i) employ domain decomposition strategies for large systemic models (1D-1D coupling) and (ii) provide the conceptual basis for dimensionally-heterogeneous representations (1D-3D coupling, among various possibilities). The strategy proposed in this article works for both of these two scenarios, though the several applications shown to illustrate its performance focus on the 1D-1D coupling case. A one-dimensional network is decomposed in such a way that each coupling point connects two (and not more) of the sub-networks. At each of the M connection points two unknowns are defined: the flow rate and pressure. These 2M unknowns are determined by 2M equations, since each sub-network provides one (non-linear) equation per coupling point. It is shown how to build the 2M x 2M non-linear system with arbitrary and independent choice of boundary conditions for each of the sub-networks. The idea is then to solve this non-linear system until convergence, which guarantees strong coupling of the complete network. In other words, if the non-linear solver converges at each time step, the solution coincides with what would be obtained by monolithically modeling the whole network. The decomposition thus imposes no stability restriction on the choice of the time step size. Effective iterative strategies for the non-linear system that preserve the black-box character of the decomposition are then explored. Several variants of matrix-free Broyden`s and Newton-GMRES algorithms are assessed as numerical solvers by comparing their performance on sub-critical wave propagation problems which range from academic test cases to realistic cardiovascular applications. A specific variant of Broyden`s algorithm is identified and recommended on the basis of its computer cost and reliability. (C) 2010 Elsevier B.V. All rights reserved.

Iterative strong coupling of dimensionally heterogeneous models

In this article we address decomposition strategies especially tailored to perform strong coupling of dimensionally heterogeneous models, under the hypothesis that one wants to solve each submodel separately and implement the interaction between subdomains by boundary conditions alone. The novel methodology takes full advantage of the small number of interface unknowns in this kind of problems. Existing algorithms can be viewed as variants of the `natural` staggered algorithm in which each domain transfers function values to the other, and receives fluxes (or forces), and vice versa. This natural algorithm is known as Dirichlet-to-Neumann in the Domain Decomposition literature. Essentially, we propose a framework in which this algorithm is equivalent to applying Gauss-Seidel iterations to a suitably defined (linear or nonlinear) system of equations. It is then immediate to switch to other iterative solvers such as GMRES or other Krylov-based method. which we assess through numerical experiments showing the significant gain that can be achieved. indeed. the benefit is that an extremely flexible, automatic coupling strategy can be developed, which in addition leads to iterative procedures that are parameter-free and rapidly converging. Further, in linear problems they have the finite termination property. Copyright (C) 2009 John Wiley & Sons, Ltd.

A hands-on approach for fitting long-term survival models under the GAMLSS framework

In many data sets from clinical studies there are patients insusceptible to the occurrence of the event of interest. Survival models which ignore this fact are generally inadequate. The main goal of this paper is to describe an application of the generalized additive models for location, scale, and shape (GAMLSS) framework to the fitting of long-term survival models. in this work the number of competing causes of the event of interest follows the negative binomial distribution. In this way, some well known models found in the literature are characterized as particular cases of our proposal. The model is conveniently parameterized in terms of the cured fraction, which is then linked to covariates. We explore the use of the gamlss package in R as a powerful tool for inference in long-term survival models. The procedure is illustrated with a numerical example. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

Influence diagnostics in nonlinear mixed-effects elliptical models

In this work we propose and analyze nonlinear elliptical models for longitudinal data, which represent an alternative to gaussian models in the cases of heavy tails, for instance. The elliptical distributions may help to control the influence of the observations in the parameter estimates by naturally attributing different weights for each case. We consider random effects to introduce the within-group correlation and work with the marginal model without requiring numerical integration. An iterative algorithm to obtain maximum likelihood estimates for the parameters is presented, as well as diagnostic results based on residual distances and local influence [Cook, D., 1986. Assessment of local influence. journal of the Royal Statistical Society - Series B 48 (2), 133-169; Cook D., 1987. Influence assessment. journal of Applied Statistics 14 (2),117-131; Escobar, L.A., Meeker, W.Q., 1992, Assessing influence in regression analysis with censored data, Biometrics 48, 507-528]. As numerical illustration, we apply the obtained results to a kinetics longitudinal data set presented in [Vonesh, E.F., Carter, R.L., 1992. Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17], which was analyzed under the assumption of normality. (C) 2009 Elsevier B.V. All rights reserved.

Skovgaard`s adjustment to likelihood ratio tests in exponential family nonlinear models

Likelihood ratio tests can be substantially size distorted in small- and moderate-sized samples. In this paper, we apply Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-321] adjusted likelihood ratio statistic to exponential family nonlinear models. We show that the adjustment term has a simple compact form that can be easily implemented from standard statistical software. The adjusted statistic is approximately distributed as X(2) with high degree of accuracy. It is applicable in wide generality since it allows both the parameter of interest and the nuisance parameter to be vector-valued. Unlike the modified profile likelihood ratio statistic obtained from Cox and Reid [Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference. journal of the Royal Statistical Society B49, 1-39], the adjusted statistic proposed here does not require an orthogonal parameterization. Numerical comparison of likelihood-based tests of varying dispersion favors the test we propose and a Bartlett-corrected version of the modified profile likelihood ratio test recently obtained by Cysneiros and Ferrari [Cysneiros, A.H.M.A., Ferrari, S.L.P., 2006. An improved likelihood ratio test for varying dispersion in exponential family nonlinear models. Statistics and Probability Letters 76 (3), 255-265]. (C) 2008 Elsevier B.V. All rights reserved.

SPECIAL CHARACTERIZATIONS OF STANDARD DISCRETE MODELS

This article presents important properties of standard discrete distributions and its conjugate densities. The Bernoulli and Poisson processes are described as generators of such discrete models. A characterization of distributions by mixtures is also introduced. This article adopts a novel singular notation and representation. Singular representations are unusual in statistical texts. Nevertheless, the singular notation makes it simpler to extend and generalize theoretical results and greatly facilitates numerical and computational implementation.

Three-dimensional, fully adaptive simulations of phase-field fluid models

We present an efficient numerical methodology for the 31) computation of incompressible multi-phase flows described by conservative phase-field models We focus here on the case of density matched fluids with different viscosity (Model H) The numerical method employs adaptive mesh refinements (AMR) in concert with an efficient semi-implicit time discretization strategy and a linear, multi-level multigrid to relax high order stability constraints and to capture the flow`s disparate scales at optimal cost. Only five linear solvers are needed per time-step. Moreover, all the adaptive methodology is constructed from scratch to allow a systematic investigation of the key aspects of AMR in a conservative, phase-field setting. We validate the method and demonstrate its capabilities and efficacy with important examples of drop deformation, Kelvin-Helmholtz instability, and flow-induced drop coalescence (C) 2010 Elsevier Inc. All rights reserved