Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

Towards the Use of Radar Winds in Numerical Weather Prediction

Numerical weather prediction (NWP) models provide the basis for weather forecasting by simulating the evolution of the atmospheric state. A good forecast requires that the initial state of the atmosphere is known accurately, and that the NWP model is a realistic representation of the atmosphere. Data assimilation methods are used to produce initial conditions for NWP models. The NWP model background field, typically a short-range forecast, is updated with observations in a statistically optimal way. The objective in this thesis has been to develope methods in order to allow data assimilation of Doppler radar radial wind observations. The work has been carried out in the High Resolution Limited Area Model (HIRLAM) 3-dimensional variational data assimilation framework. Observation modelling is a key element in exploiting indirect observations of the model variables. In the radar radial wind observation modelling, the vertical model wind profile is interpolated to the observation location, and the projection of the model wind vector on the radar pulse path is calculated. The vertical broadening of the radar pulse volume, and the bending of the radar pulse path due to atmospheric conditions are taken into account. Radar radial wind observations are modelled within observation errors which consist of instrumental, modelling, and representativeness errors. Systematic and random modelling errors can be minimized by accurate observation modelling. The impact of the random part of the instrumental and representativeness errors can be decreased by calculating spatial averages from the raw observations. Model experiments indicate that the spatial averaging clearly improves the fit of the radial wind observations to the model in terms of observation minus model background (OmB) standard deviation. Monitoring the quality of the observations is an important aspect, especially when a new observation type is introduced into a data assimilation system. Calculating the bias for radial wind observations in a conventional way can result in zero even in case there are systematic differences in the wind speed and/or direction. A bias estimation method designed for this observation type is introduced in the thesis. Doppler radar radial wind observation modelling, together with the bias estimation method, enables the exploitation of the radial wind observations also for NWP model validation. The one-month model experiments performed with the HIRLAM model versions differing only in a surface stress parameterization detail indicate that the use of radar wind observations in NWP model validation is very beneficial.

On the behaviour of some physical parameterization methods in high-resolution numerical weather prediction models

Modern-day weather forecasting is highly dependent on Numerical Weather Prediction (NWP) models as the main data source. The evolving state of the atmosphere with time can be numerically predicted by solving a set of hydrodynamic equations, if the initial state is known. However, such a modelling approach always contains approximations that by and large depend on the purpose of use and resolution of the models. Present-day NWP systems operate with horizontal model resolutions in the range from about 40 km to 10 km. Recently, the aim has been to reach operationally to scales of 1 4 km. This requires less approximations in the model equations, more complex treatment of physical processes and, furthermore, more computing power. This thesis concentrates on the physical parameterization methods used in high-resolution NWP models. The main emphasis is on the validation of the grid-size-dependent convection parameterization in the High Resolution Limited Area Model (HIRLAM) and on a comprehensive intercomparison of radiative-flux parameterizations. In addition, the problems related to wind prediction near the coastline are addressed with high-resolution meso-scale models. The grid-size-dependent convection parameterization is clearly beneficial for NWP models operating with a dense grid. Results show that the current convection scheme in HIRLAM is still applicable down to a 5.6 km grid size. However, with further improved model resolution, the tendency of the model to overestimate strong precipitation intensities increases in all the experiment runs. For the clear-sky longwave radiation parameterization, schemes used in NWP-models provide much better results in comparison with simple empirical schemes. On the other hand, for the shortwave part of the spectrum, the empirical schemes are more competitive for producing fairly accurate surface fluxes. Overall, even the complex radiation parameterization schemes used in NWP-models seem to be slightly too transparent for both long- and shortwave radiation in clear-sky conditions. For cloudy conditions, simple cloud correction functions are tested. In case of longwave radiation, the empirical cloud correction methods provide rather accurate results, whereas for shortwave radiation the benefit is only marginal. Idealised high-resolution two-dimensional meso-scale model experiments suggest that the reason for the observed formation of the afternoon low level jet (LLJ) over the Gulf of Finland is an inertial oscillation mechanism, when the large-scale flow is from the south-east or west directions. The LLJ is further enhanced by the sea-breeze circulation. A three-dimensional HIRLAM experiment, with a 7.7 km grid size, is able to generate a similar LLJ flow structure as suggested by the 2D-experiments and observations. It is also pointed out that improved model resolution does not necessary lead to better wind forecasts in the statistical sense. In nested systems, the quality of the large-scale host model is really important, especially if the inner meso-scale model domain is small.

Communicating probabilistic information from climate model ensembles—lessons from numerical weather prediction

Climate model ensembles are widely heralded for their potential to quantify uncertainties and generate probabilistic climate projections. However, such technical improvements to modeling science will do little to deliver on their ultimate promise of improving climate policymaking and adaptation unless the insights they generate can be effectively communicated to decision makers. While some of these communicative challenges are unique to climate ensembles, others are common to hydrometeorological modeling more generally, and to the tensions arising between the imperatives for saliency, robustness, and richness in risk communication. The paper reviews emerging approaches to visualizing and communicating climate ensembles and compares them to the more established and thoroughly evaluated communication methods used in the numerical weather prediction domains of day-to-day weather forecasting (in particular probabilities of precipitation), hurricane and flood warning, and seasonal forecasting. This comparative analysis informs recommendations on best practice for climate modelers, as well as prompting some further thoughts on key research challenges to improve the future communication of climate change uncertainties.

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.

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.

Weather forecasting for Eastern Amazon with OLAM model

O modelo OLAM tem como característica a vantagem de representar simultaneamente os fenômenos meteorológicos de escala global e regional através de um esquema de refinamento de grades. Durante o projeto REMAM, o modelo foi aplicado para alguns estudos de caso com objetivo de avaliar o desempenho do modelo na previsão numérica de tempo para a região leste da Amazônia. Estudos de caso foram feitos para os doze meses do ano de 2009. Os resultados do modelo para estes casos foram comparados com dados observados na região de estudo. A análise dos dados de precipitação mostrou que o modelo consegue representar a distribuição média da precipitação acumulada e os aspectos da sazonalidade da ocorrência dos eventos, mas não consegue prever individualmente a acumulação de precipitação local. No entanto, avaliação individual de alguns casos mostrou que o modelo OLAM conseguiu representar dinamicamente e prever, com alguns dias de antecedência, o desenvolvimento de fenômenos meteorológicos costeiros como as linhas de instabilidade, que são um dos mais importantes sistemas precipitantes da Amazônia.

Wind power forecasts using Gaussian processes and numerical weather prediction

Since wind at the earth's surface has an intrinsically complex and stochastic nature, accurate wind power forecasts are necessary for the safe and economic use of wind energy. In this paper, we investigated a combination of numeric and probabilistic models: a Gaussian process (GP) combined with a numerical weather prediction (NWP) model was applied to wind-power forecasting up to one day ahead. First, the wind-speed data from NWP was corrected by a GP, then, as there is always a defined limit on power generated in a wind turbine due to the turbine controlling strategy, wind power forecasts were realized by modeling the relationship between the corrected wind speed and power output using a censored GP. To validate the proposed approach, three real-world datasets were used for model training and testing. The empirical results were compared with several classical wind forecast models, and based on the mean absolute error (MAE), the proposed model provides around 9% to 14% improvement in forecasting accuracy compared to an artificial neural network (ANN) model, and nearly 17% improvement on a third dataset which is from a newly-built wind farm for which there is a limited amount of training data. © 2013 IEEE.

Exploiting ground-based measurements of the Global Positioning System for numerical weather prediction

Data assimilation provides an initial atmospheric state, called the analysis, for Numerical Weather Prediction (NWP). This analysis consists of pressure, temperature, wind, and humidity on a three-dimensional NWP model grid. Data assimilation blends meteorological observations with the NWP model in a statistically optimal way. The objective of this thesis is to describe methodological development carried out in order to allow data assimilation of ground-based measurements of the Global Positioning System (GPS) into the High Resolution Limited Area Model (HIRLAM) NWP system. Geodetic processing produces observations of tropospheric delay. These observations can be processed either for vertical columns at each GPS receiver station, or for the individual propagation paths of the microwave signals. These alternative processing methods result in Zenith Total Delay (ZTD) and Slant Delay (SD) observations, respectively. ZTD and SD observations are of use in the analysis of atmospheric humidity. A method is introduced for estimation of the horizontal error covariance of ZTD observations. The method makes use of observation minus model background (OmB) sequences of ZTD and conventional observations. It is demonstrated that the ZTD observation error covariance is relatively large in station separations shorter than 200 km, but non-zero covariances also appear at considerably larger station separations. The relatively low density of radiosonde observing stations limits the ability of the proposed estimation method to resolve the shortest length-scales of error covariance. SD observations are shown to contain a statistically significant signal on the asymmetry of the atmospheric humidity field. However, the asymmetric component of SD is found to be nearly always smaller than the standard deviation of the SD observation error. SD observation modelling is described in detail, and other issues relating to SD data assimilation are also discussed. These include the determination of error statistics, the tuning of observation quality control and allowing the taking into account of local observation error correlation. The experiments made show that the data assimilation system is able to retrieve the asymmetric information content of hypothetical SD observations at a single receiver station. Moreover, the impact of real SD observations on humidity analysis is comparable to that of other observing systems.

Studies on orographic effects in a numerical weather prediction model

Numerical models, used for atmospheric research, weather prediction and climate simulation, describe the state of the atmosphere over the heterogeneous surface of the Earth. Several fundamental properties of atmospheric models depend on orography, i.e. on the average elevation of land over a model area. The higher is the models' resolution, the more the details of orography directly influence the simulated atmospheric processes. This sets new requirements for the accuracy of the model formulations with respect to the spatially varying orography. Orography is always averaged, representing the surface elevation within the horizontal resolution of the model. In order to remove the smallest scales and steepest slopes, the continuous spectrum of orography is normally filtered (truncated) even more, typically beyond a few gridlengths of the model. This means, that in the numerical weather prediction (NWP) models, there will always be subgridscale orography effects, which cannot be explicitly resolved by numerical integration of the basic equations, but require parametrization. In the subgrid-scale, different physical processes contribute in different scales. The parametrized processes interact with the resolved-scale processes and with each other. This study contributes to building of a consistent, scale-dependent system of orography-related parametrizations for the High Resolution Limited Area Model (HIRLAM). The system comprises schemes for handling the effects of mesoscale (MSO) and small-scale (SSO) orographic effects on the simulated flow and a scheme of orographic effects on the surface-level radiation fluxes. Representation of orography, scale-dependencies of the simulated processes and interactions between the parametrized and resolved processes are discussed. From the high-resolution digital elevation data, orographic parameters are derived for both momentum and radiation flux parametrizations. Tools for diagnostics and validation are developed and presented. The parametrization schemes applied, developed and validated in this study, are currently being implemented into the reference version of HIRLAM.

On the impact of humidity observations in numerical weather prediction

The impact of humidity observations on forecast skill is explored by producing a series of global forecasts using initial data derived from the ERA-40 reanalyses system, in which all humidity data have been removed during the data assimilation. The new forecasts have been compared with the original ERA-40 analyses and forecasts made from them. Both sets of forecasts show virtually identical prediction skill in the extratropics and the tropics. Differences between the forecasts are small and undergo characteristic amplification rate. There are larger differences in temperature and geopotential in the tropics but the differences are small-scale and unstructured and have no noticeable effect on the skill of the wind forecasts. The results highlight the current very limited impact of the humidity observations, used to produce the initial state, on the forecasts.

Exploitation of Geostationary Earth Radiation Budget data using simulations from a numerical weather prediction model: Methodology and data validation

We describe a new methodology for comparing satellite radiation budget data with a numerical weather prediction (NWP) model. This is applied to data from the Geostationary Earth Radiation Budget (GERB) instrument on Meteosat-8. The methodology brings together, in near-real time, GERB broadband shortwave and longwave fluxes with simulations based on analyses produced by the Met Office global NWP model. Results for the period May 2003 to February 2005 illustrate the progressive improvements in the data products as various initial problems were resolved. In most areas the comparisons reveal systematic errors in the model's representation of surface properties and clouds, which are discussed elsewhere. However, for clear-sky regions over the oceans the model simulations are believed to be sufficiently accurate to allow the quality of the GERB fluxes themselves to be assessed and any changes in time of the performance of the instrument to be identified. Using model and radiosonde profiles of temperature and humidity as input to a single-column version of the model's radiation code, we conduct sensitivity experiments which provide estimates of the expected model errors over the ocean of about ±5–10 W m−2 in clear-sky outgoing longwave radiation (OLR) and ±0.01 in clear-sky albedo. For the more recent data the differences between the observed and modeled OLR and albedo are well within these error estimates. The close agreement between the observed and modeled values, particularly for the most recent period, illustrates the value of the methodology. It also contributes to the validation of the GERB products and increases confidence in the quality of the data, prior to their release.