A joint state and parameter estimation scheme for nonlinear dynamical systems

We present a novel algorithm for concurrent model state and parameter estimation in nonlinear dynamical systems. The new scheme uses ideas from three dimensional variational data assimilation (3D-Var) and the extended Kalman filter (EKF) together with the technique of state augmentation to estimate uncertain model parameters alongside the model state variables in a sequential filtering system. The method is relatively simple to implement and computationally inexpensive to run for large systems with relatively few parameters. We demonstrate the efficacy of the method via a series of identical twin experiments with three simple dynamical system models. The scheme is able to recover the parameter values to a good level of accuracy, even when observational data are noisy. We expect this new technique to be easily transferable to much larger models.

A moving-point approach to model shallow ice sheets: a study case with radially symmetrical ice sheets

Predicting the evolution of ice sheets requires numerical models able to accurately track the migration of ice sheet continental margins or grounding lines. We introduce a physically based moving-point approach for the flow of ice sheets based on the conservation of local masses. This allows the ice sheet margins to be tracked explicitly. Our approach is also well suited to capture waiting-time behaviour efficiently. A finite-difference moving-point scheme is derived and applied in a simplified context (continental radially symmetrical shallow ice approximation). The scheme, which is inexpensive, is verified by comparing the results with steady states obtained from an analytic solution and with exact moving-margin transient solutions. In both cases the scheme is able to track the position of the ice sheet margin with high accuracy.

Interactions between wind-blown snow redistribution and melt ponds in a coupled ocean–sea ice model

Introducing a parameterization of the interactions between wind-driven snow depth changes and melt pond evolution allows us to improve large scale models. In this paper we have implemented an explicit melt pond scheme and, for the first time, a wind dependant snow redistribution model and new snow thermophysics into a coupled ocean–sea ice model. The comparison of long-term mean statistics of melt pond fractions against observations demonstrates realistic melt pond cover on average over Arctic sea ice, but a clear underestimation of the pond coverage on the multi-year ice (MYI) of the western Arctic Ocean. The latter shortcoming originates from the concealing effect of persistent snow on forming ponds, impeding their growth. Analyzing a second simulation with intensified snow drift enables the identification of two distinct modes of sensitivity in the melt pond formation process. First, the larger proportion of wind-transported snow that is lost in leads directly curtails the late spring snow volume on sea ice and facilitates the early development of melt ponds on MYI. In contrast, a combination of higher air temperatures and thinner snow prior to the onset of melting sometimes make the snow cover switch to a regime where it melts entirely and rapidly. In the latter situation, seemingly more frequent on first-year ice (FYI), a smaller snow volume directly relates to a reduced melt pond cover. Notwithstanding, changes in snow and water accumulation on seasonal sea ice is naturally limited, which lessens the impacts of wind-blown snow redistribution on FYI, as compared to those on MYI. At the basin scale, the overall increased melt pond cover results in decreased ice volume via the ice-albedo feedback in summer, which is experienced almost exclusively by MYI.

Processes controlling surface, bottom and lateral melt of Arctic sea ice in a state of the art sea ice model

We present a modelling study of processes controlling the summer melt of the Arctic sea ice cover. We perform a sensitivity study and focus our interest on the thermodynamics at the ice–atmosphere and ice–ocean interfaces. We use the Los Alamos community sea ice model CICE, and additionally implement and test three new parametrization schemes: (i) a prognostic mixed layer; (ii) a three equation boundary condition for the salt and heat flux at the ice–ocean interface; and (iii) a new lateral melt parametrization. Recent additions to the CICE model are also tested, including explicit melt ponds, a form drag parametrization and a halodynamic brine drainage scheme. The various sea ice parametrizations tested in this sensitivity study introduce a wide spread in the simulated sea ice characteristics. For each simulation, the total melt is decomposed into its surface, bottom and lateral melt components to assess the processes driving melt and how this varies regionally and temporally. Because this study quantifies the relative importance of several processes in driving the summer melt of sea ice, this work can serve as a guide for future research priorities.

Comparison of terrain following and cut cell grids using a non-hydrostatic model

Terrain following coordinates are widely used in operational models but the cut cell method has been proposed as an alternative that can more accurately represent atmospheric dynamics over steep orography. Because the type of grid is usually chosen during model implementation, it becomes necessary to use different models to compare the accuracy of different grids. In contrast, here a C-grid finite volume model enables a like-for-like comparison of terrain following and cut cell grids. A series of standard two-dimensional tests using idealised terrain are performed: tracer advection in a prescribed horizontal velocity field, a test starting from resting initial conditions, and orographically induced gravity waves described by nonhydrostatic dynamics. In addition, three new tests are formulated: a more challenging resting atmosphere case, and two new advection tests having a velocity field that is everywhere tangential to the terrain following coordinate surfaces. These new tests present a challenge on cut cell grids. The results of the advection tests demonstrate that accuracy depends primarily upon alignment of the flow with the grid rather than grid orthogonality. A resting atmosphere is well-maintained on all grids. In the gravity waves test, results on all grids are in good agreement with existing results from the literature, although terrain following velocity fields lead to errors on cut cell grids. Due to semi-implicit timestepping and an upwind-biased, explicit advection scheme, there are no timestep restrictions associated with small cut cells. We do not find the significant advantages of cut cells or smoothed coordinates that other authors find.

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.

Bayesian analysis of uncertainty in the GlobCover 2009 land cover product at climate model grid scale

Land cover data derived from satellites are commonly used to prescribe inputs to models of the land surface. Since such data inevitably contains errors, quantifying how uncertainties in the data affect a model’s output is important. To do so, a spatial distribution of possible land cover values is required to propagate through the model’s simulation. However, at large scales, such as those required for climate models, such spatial modelling can be difficult. Also, computer models often require land cover proportions at sites larger than the original map scale as inputs, and it is the uncertainty in these proportions that this article discusses. This paper describes a Monte Carlo sampling scheme that generates realisations of land cover proportions from the posterior distribution as implied by a Bayesian analysis that combines spatial information in the land cover map and its associated confusion matrix. The technique is computationally simple and has been applied previously to the Land Cover Map 2000 for the region of England and Wales. This article demonstrates the ability of the technique to scale up to large (global) satellite derived land cover maps and reports its application to the GlobCover 2009 data product. The results show that, in general, the GlobCover data possesses only small biases, with the largest belonging to non–vegetated surfaces. In vegetated surfaces, the most prominent area of uncertainty is Southern Africa, which represents a complex heterogeneous landscape. It is also clear from this study that greater resources need to be devoted to the construction of comprehensive confusion matrices.

Decadal predictions with the HiGEM high resolution global coupled climate model: description and basic evaluation

This paper describes the development and basic evaluation of decadal predictions produced using the HiGEM coupled climate model. HiGEM is a higher resolution version of the HadGEM1 Met Office Unified Model. The horizontal resolution in HiGEM has been increased to 1.25◦ × 0.83◦ in longitude and latitude for the atmosphere, and 1/3◦ × 1/3◦ globally for the ocean. The HiGEM decadal predictions are initialised using an anomaly assimilation scheme that relaxes anomalies of ocean temperature and salinity to observed anomalies. 10 year hindcasts are produced for 10 start dates (1960, 1965,..., 2000, 2005). To determine the relative contributions to prediction skill from initial conditions and external forcing, the HiGEM decadal predictions are compared to uninitialised HiGEM transient experiments. The HiGEM decadal predictions have substantial skill for predictions of annual mean surface air temperature and 100 m upper ocean temperature. For lead times up to 10 years, anomaly correlations (ACC) over large areas of the North Atlantic Ocean, the Western Pacific Ocean and the Indian Ocean exceed values of 0.6. Initialisation of the HiGEM decadal predictions significantly increases skill over regions of the Atlantic Ocean,the Maritime Continent and regions of the subtropical North and South Pacific Ocean. In particular, HiGEM produces skillful predictions of the North Atlantic subpolar gyre for up to 4 years lead time (with ACC > 0.7), which are significantly larger than the uninitialised HiGEM transient experiments.

Surface Urban Energy and Water Balance Scheme (SUEWS): development and evaluation at two UK sites

The Surface Urban Energy and Water Balance Scheme (SUEWS) is evaluated at two locations in the UK: a dense urban site in the centre of London and a residential suburban site in Swindon. Eddy covariance observations of the turbulent fluxes are used to assess model performance over a twoyear period (2011-2013). The distinct characteristics of the sites mean their surface energy exchanges differ considerably. The model suggests the largest differences can be attributed to surface cover (notably the proportion of vegetated versus impervious area) and the additional energy supplied by human activities. SUEWS performs better in summer than winter, and better at the suburban site than the dense urban site. One reason for this is the bias towards suburban summer field campaigns in observational data used to parameterise this (and other) model(s). The suitability of model parameters (such as albedo, energy use and water use) for the UK sites is considered and, where appropriate, alternative values are suggested. An alternative parameterisation for the surface conductance is implemented, which permits greater soil moisture deficits before evaporation is restricted at non-irrigated sites. Accounting for seasonal variation in the estimation of storage heat flux is necessary to obtain realistic wintertime fluxes.

An idealized study of coupled atmosphere-ocean 4D-Var in the presence of model error

Atmosphere only and ocean only variational data assimilation (DA) schemes are able to use window lengths that are optimal for the error growth rate, non-linearity and observation density of the respective systems. Typical window lengths are 6-12 hours for the atmosphere and 2-10 days for the ocean. However, in the implementation of coupled DA schemes it has been necessary to match the window length of the ocean to that of the atmosphere, which may potentially sacrifice the accuracy of the ocean analysis in order to provide a more balanced coupled state. This paper investigates how extending the window length in the presence of model error affects both the analysis of the coupled state and the initialized forecast when using coupled DA with differing degrees of coupling. Results are illustrated using an idealized single column model of the coupled atmosphere-ocean system. It is found that the analysis error from an uncoupled DA scheme can be smaller than that from a coupled analysis at the initial time, due to faster error growth in the coupled system. However, this does not necessarily lead to a more accurate forecast due to imbalances in the coupled state. Instead coupled DA is more able to update the initial state to reduce the impact of the model error on the accuracy of the forecast. The effect of model error is potentially most detrimental in the weakly coupled formulation due to the inconsistency between the coupled model used in the outer loop and uncoupled models used in the inner loop.

South Atlantic Ocean cyclogenesis climatology simulated by regional climate model (RegCM3)

A detailed climatology of the cyclogenesis over the Southern Atlantic Ocean (SAO) from 1990 to 1999 and how it is simulated by the RegCM3 (Regional Climate Model) is presented here. The simulation used as initial and boundary conditions the National Centers for Environmental Prediction-Department of Energy (NCEP/DOE) reanalysis. The cyclones were identified with an automatic scheme that searches for cyclonic relative vorticity (zeta(10)) obtained from a 10-m height wind field. All the systems with zeta(10) a parts per thousand currency sign -1.5 x 10(-5) s(-1) and lifetime equal or larger than 24 h were considered in the climatology. Over SAO, in 10 years were detected 2,760 and 2,787 cyclogeneses in the simulation and NCEP, respectively, with an annual mean of 276.0 +/- A 11.2 and 278.7 +/- A 11.1. This result suggests that the RegCM3 has a good skill to simulate the cyclogenesis climatology. However, the larger model underestimations (-9.8%) are found for the initially stronger systems (zeta(10) a parts per thousand currency sign -2.5 x 10(-5) s(-1)). It was noted that over the SAO the annual cycle of the cyclogenesis depends of its initial intensity. Considering the systems initiate with zeta(10) a parts per thousand currency sign -1.5 x 10(-5) s(-1), the annual cycle is not well defined and the higher frequency occurs in the autumn (summer) in the NCEP (RegCM3). The stronger systems (zeta(10) a parts per thousand currency sign -2.5 x 10(-5) s(-1)) have a well-characterized high frequency of cyclogenesis during the winter in both NCEP and RegCM3. This work confirms the existence of three cyclogenetic regions in the west sector of the SAO, near the South America east coast and shows that RegCM3 is able to reproduce the main features of these cyclogenetic areas.

Modeling study of the aspect ratio influence on urban canopy energy fluxes with a modified wall-canyon energy budget scheme

The influence of the aspect ratio (building height/street canyon width) and the mean building height of cities on local energy fluxes and temperatures is studied by means of an Urban Canopy Model (UCM) coupled with a one-dimensional second-order turbulence closure model. The UCM presented is similar to the Town Energy Balance (TEB) model in most of its features but differs in a few important aspects. In particular, the street canyon walls are treated separately which leads to a different budget of radiation within the street canyon walls. The UCM has been calibrated using observations of incoming global and diffuse solar radiation, incoming long-wave radiation and air temperature at a site in So Paulo, Brazil. Sensitivity studies with various aspect ratios have been performed to assess their impact on urban temperatures and energy fluxes at the top of the canopy layer. In these simulations, it is assumed that the anthropogenic heat flux and latent heat fluxes are negligible. Results show that the simulated net radiation and sensible heat fluxes at the top of the canopy decrease and the stored heat increases as the aspect ratio increases. The simulated air temperature follows the behavior of the sensible heat flux. (C) 2010 Elsevier Ltd. All rights reserved.

STUDY OF THE EQUATORIAL ATLANTIC OCEAN MIXING LAYER USING A ONE-DIMENSIONAL TURBULENCE MODEL

The General Ocean Turbulence Model (GOTM) is applied to the diagnostic turbulence field of the mixing layer (ML) over the equatorial region of the Atlantic Ocean. Two situations were investigated: rainy and dry seasons, defined, respectively, by the presence of the intertropical convergence zone and by its northward displacement. Simulations were carried out using data from a PIRATA buoy located on the equator at 23 degrees W to compute surface turbulent fluxes and from the NASA/GEWEX Surface Radiation Budget Project to close the surface radiation balance. A data assimilation scheme was used as a surrogate for the physical effects not present in the one-dimensional model. In the rainy season, results show that the ML is shallower due to the weaker surface stress and stronger stable stratification; the maximum ML depth reached during this season is around 15 m, with an averaged diurnal variation of 7 m depth. In the dry season, the stronger surface stress and the enhanced surface heat balance components enable higher mechanical production of turbulent kinetic energy and, at night, the buoyancy acts also enhancing turbulence in the first meters of depth, characterizing a deeper ML, reaching around 60 m and presenting an average diurnal variation of 30 m.

Precipitation diurnal cycle and summer climatology assessment over South America: An evaluation of Regional Climate Model version 3 simulations

Regional Climate Model version 3 (RegCM3) simulations of 17 summers (1988-2004) over part of South America south of 5 degrees S were evaluated to identify model systematic errors. Model results were compared to different rainfall data sets (Climate Research Unit (CRU), Climate Prediction Center (CPC), Global Precipitation Climatology Project (GPCP), and National Centers for Environmental Prediction (NCEP) reanalysis), including the five summers mean (1998-2002) precipitation diurnal cycle observed by the Tropical Rainfall Measuring Mission (TRMM)-Precipitation Radar (PR). In spite of regional differences, the RegCM3 simulates the main observed aspects of summer climatology associated with the precipitation (northwest-southeast band of South Atlantic Convergence Zone (SACZ)) and air temperature (warmer air in the central part of the continent and colder in eastern Brazil and the Andes Mountains). At a regional scale, the main RegCM3 failures are the underestimation of the precipitation in the northern branch of the SACZ and some unrealistic intense precipitation around the Andes Mountains. However, the RegCM3 seasonal precipitation is closer to the fine-scale analyses (CPC, CRU, and TRMM-PR) than is the NCEP reanalysis, which presents an incorrect north-south orientation of SACZ and an overestimation of its intensity. The precipitation diurnal cycle observed by TRMM-PR shows pronounced contrasts between Tropics and Extratropics and land and ocean, where most of these features are simulated by RegCM3. The major similarities between the simulation and observation, especially the diurnal cycle phase, are found over the continental tropical and subtropical SACZ regions, which present afternoon maximum (1500-1800 UTC) and morning minimum (0900-1200 UTC). More specifically, over the core of SACZ, the phase and amplitude of the simulated precipitation diurnal cycle are very close to the TRMM-PR observations. Although there are amplitude differences, the RegCM3 simulates the observed nighttime rainfall in the eastern Andes Mountains, over the Atlantic Ocean, and also over northern Argentina. The main simulation deficiencies are found in the Atlantic Ocean and near the Andes Mountains. Over the Atlantic Ocean the convective scheme is not triggered; thus the rainfall arises from the grid-scale scheme and therefore differs from the TRMM-PR. Near the Andes, intense (nighttime and daytime) simulated precipitation could be a response of an incorrect circulation and topographic uplift. Finally, it is important to note that unlike most reported bias of global models, RegCM3 does not trigger the moist convection just after sunrise over the southern part of the Amazon.

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

fit the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten. this paper presents an extension of it previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D hock tube problem, 2D impinging jet and 2D/3D broken clam flows. Furthermore, these results are compared with existing analytical and experimental data. And third, it presents the application of the numerical method for solving 3D free surface flow problems. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved,