The composite-tendency Robert-Asselin-Williams (RAW) filter in semi-implicit integrations

Timediscretization in weatherandclimate modelsintroduces truncation errors that limit the accuracy of the simulations. Recent work has yielded a method for reducing the amplitude errors in leap-frog integrations from first-order to fifth-order.This improvement is achieved by replacing the Robert–Asselin filter with the Robert–Asselin–Williams (RAW) filter and using a linear combination of unfiltered and filtered states to compute the tendency term. The purpose of the present article is to apply the composite-tendency RAW-filtered leapfrog scheme to semi-implicit integrations. A theoretical analysis shows that the stability and accuracy are unaffected by the introduction of the implicitly treated mode. The scheme is tested in semi-implicit numerical integrations in both a simple nonlinear stiff system and a medium-complexity atmospheric general circulation model and yields substantial improvements in both cases. We conclude that the composite-tendency RAW-filtered leap-frog scheme is suitable for use in semi-implicit integrations.

Freshwater transport in the coupled ocean-atmosphere system: a passive ocean

Conservation of water demands that meridional ocean and atmosphere freshwater transports (FWT) are of equal magnitude but opposite in direction. This suggests that the atmospheric FWT and its associated latent heat (LH) transport could be thought of as a \textquotedblleft coupled ocean/atmosphere mode\textquotedblright. But what is the true nature of this coupling? Is the ocean passive or active? Here we analyze a series of simulations with a coupled ocean-atmosphere-sea ice model employing highly idealized geometries but with markedly different coupled climates and patterns of ocean circulation. Exploiting streamfunctions in specific humidity coordinates for the atmosphere and salt coordinates for the ocean to represent FWT in their respective medium, we find that atmospheric FWT/LH transport is essentially independent of the ocean state. Ocean circulation and salinity distribution adjust to achieve a return freshwater pathway demanded of them by the atmosphere. So, although ocean and atmosphere FWTs are indeed coupled by mass conservation, the ocean is a passive component acting as a reservoir of freshwater.

The equivalent-weights particle filter in a high-dimensional system

In general, particle filters need large numbers of model runs in order to avoid filter degeneracy in high-dimensional systems. The recently proposed, fully nonlinear equivalent-weights particle filter overcomes this requirement by replacing the standard model transition density with two different proposal transition densities. The first proposal density is used to relax all particles towards the high-probability regions of state space as defined by the observations. The crucial second proposal density is then used to ensure that the majority of particles have equivalent weights at observation time. Here, the performance of the scheme in a high, 65 500 dimensional, simplified ocean model is explored. The success of the equivalent-weights particle filter in matching the true model state is shown using the mean of just 32 particles in twin experiments. It is of particular significance that this remains true even as the number and spatial variability of the observations are changed. The results from rank histograms are less easy to interpret and can be influenced considerably by the parameter values used. This article also explores the sensitivity of the performance of the scheme to the chosen parameter values and the effect of using different model error parameters in the truth compared with the ensemble model runs.

The effect of the equivalent-weights particle filter on dynamical balance in a primitive equation model

The disadvantage of the majority of data assimilation schemes is the assumption that the conditional probability density function of the state of the system given the observations [posterior probability density function (PDF)] is distributed either locally or globally as a Gaussian. The advantage, however, is that through various different mechanisms they ensure initial conditions that are predominantly in linear balance and therefore spurious gravity wave generation is suppressed. The equivalent-weights particle filter is a data assimilation scheme that allows for a representation of a potentially multimodal posterior PDF. It does this via proposal densities that lead to extra terms being added to the model equations and means the advantage of the traditional data assimilation schemes, in generating predominantly balanced initial conditions, is no longer guaranteed. This paper looks in detail at the impact the equivalent-weights particle filter has on dynamical balance and gravity wave generation in a primitive equation model. The primary conclusions are that (i) provided the model error covariance matrix imposes geostrophic balance, then each additional term required by the equivalent-weights particle filter is also geostrophically balanced; (ii) the relaxation term required to ensure the particles are in the locality of the observations has little effect on gravity waves and actually induces a reduction in gravity wave energy if sufficiently large; and (iii) the equivalent-weights term, which leads to the particles having equivalent significance in the posterior PDF, produces a change in gravity wave energy comparable to the stochastic model error. Thus, the scheme does not produce significant spurious gravity wave energy and so has potential for application in real high-dimensional geophysical applications.

Twin experiments with the equivalent weights particle filter and HadCM3

This paper investigates the use of a particle filter for data assimilation with a full scale coupled ocean–atmosphere general circulation model. Synthetic twin experiments are performed to assess the performance of the equivalent weights filter in such a high-dimensional system. Artificial 2-dimensional sea surface temperature fields are used as observational data every day. Results are presented for different values of the free parameters in the method. Measures of the performance of the filter are root mean square errors, trajectories of individual variables in the model and rank histograms. Filter degeneracy is not observed and the performance of the filter is shown to depend on the ability to keep maximum spread in the ensemble.

SPARE-ICE: synergistic Ice Water Path from passive operational sensors

This article presents SPARE-ICE, the Synergistic Passive Atmospheric Retrieval Experiment-ICE. SPARE-ICE is the first Ice Water Path (IWP) product combining infrared and microwave radiances. By using only passive operational sensors, the SPARE-ICE retrieval can be used to process data from at least the NOAA 15 to 19 and MetOp satellites, obtaining time series from 1998 onward. The retrieval is developed using collocations between passive operational sensors (solar, terrestrial infrared, microwave), the CloudSat radar, and the CALIPSO lidar. The collocations form a retrieval database matching measurements from passive sensors against the existing active combined radar-lidar product 2C-ICE. With this retrieval database, we train a pair of artificial neural networks to detect clouds and retrieve IWP. When considering solar, terrestrial infrared, and microwave-based measurements, we show that any combination of two techniques performs better than either single-technique retrieval. We choose not to include solar reflectances in SPARE-ICE, because the improvement is small, and so that SPARE-ICE can be retrieved both daytime and nighttime. The median fractional error between SPARE-ICE and 2C-ICE is around a factor 2, a figure similar to the random error between 2C-ICE ice water content (IWC) and in situ measurements. A comparison of SPARE-ICE with Moderate Resolution Imaging Spectroradiometer (MODIS), Pathfinder Atmospheric Extended (PATMOS-X), and Microwave Surface and Precipitation Products System (MSPPS) indicates that SPARE-ICE appears to perform well even in difficult conditions. SPARE-ICE is available for public use.

A Variance-Minimizing Filter for Large-Scale Applications

A truly variance-minimizing filter is introduced and its per for mance is demonstrated with the Korteweg– DeV ries (KdV) equation and with a multilayer quasigeostrophic model of the ocean area around South Africa. It is recalled that Kalman-like filters are not variance minimizing for nonlinear model dynamics and that four - dimensional variational data assimilation (4DV AR)-like methods relying on per fect model dynamics have dif- ficulty with providing error estimates. The new method does not have these drawbacks. In fact, it combines advantages from both methods in that it does provide error estimates while automatically having balanced states after analysis, without extra computations. It is based on ensemble or Monte Carlo integrations to simulate the probability density of the model evolution. When obser vations are available, the so-called importance resampling algorithm is applied. From Bayes’ s theorem it follows that each ensemble member receives a new weight dependent on its ‘ ‘distance’ ’ t o the obser vations. Because the weights are strongly var ying, a resampling of the ensemble is necessar y. This resampling is done such that members with high weights are duplicated according to their weights, while low-weight members are largely ignored. In passing, it is noted that data assimilation is not an inverse problem by nature, although it can be for mulated that way . Also, it is shown that the posterior variance can be larger than the prior if the usual Gaussian framework is set aside. However , i n the examples presented here, the entropy of the probability densities is decreasing. The application to the ocean area around South Africa, gover ned by strongly nonlinear dynamics, shows that the method is working satisfactorily . The strong and weak points of the method are discussed and possible improvements are proposed.

Analysis Scheme in the Ensemble Kalman Filter

This paper discusses an important issue related to the implementation and interpretation of the analysis scheme in the ensemble Kalman filter . I t i s shown that the obser vations must be treated as random variables at the analysis steps. That is, one should add random perturbations with the correct statistics to the obser vations and generate an ensemble of obser vations that then is used in updating the ensemble of model states. T raditionally , this has not been done in previous applications of the ensemble Kalman filter and, as will be shown, this has resulted in an updated ensemble with a variance that is too low . This simple modification of the analysis scheme results in a completely consistent approach if the covariance of the ensemble of model states is interpreted as the prediction error covariance, and there are no further requirements on the ensemble Kalman filter method, except for the use of an ensemble of sufficient size. Thus, there is a unique correspondence between the error statistics from the ensemble Kalman filter and the standard Kalman filter approach

Assimilation of Geosat Altimeter Data for the Agulhas Current Using the Ensemble Kalman Filter with a Quasigeostrophic Model

The ring-shedding process in the Agulhas Current is studied using the ensemble Kalman filter to assimilate geosat altimeter data into a two-layer quasigeostrophic ocean model. The properties of the ensemble Kalman filter are further explored with focus on the analysis scheme and the use of gridded data. The Geosat data consist of 10 fields of gridded sea-surface height anomalies separated 10 days apart that are added to a climatic mean field. This corresponds to a huge number of data values, and a data reduction scheme must be applied to increase the efficiency of the analysis procedure. Further, it is illustrated how one can resolve the rank problem occurring when a too large dataset or a small ensemble is used.

Study on the application of cool paintings for the passive cooling of existing buildings in Mediterranean climates

Building roofs play a very important role in the energy balance of buildings, especially in summer, when they are hit by a rather high solar irradiance. Depending on the type of finishing layer, roofs can absorb a great amount of heat and reach quite high temperatures on their outermost surface, which determines significant room overheating. However, the use of highly reflective cool materials can help to maintain low outer surface temperatures; this practice may improve indoor thermal comfort and reduce the cooling energy need during the hot season.This technology is currently well known and widely used in the USA, while receiving increasing attention in Europe. In order to investigate the effectiveness of cool roofs as a passive strategy for passive cooling in moderately hot climates, this paper presents the numerical results of a case study based on the dynamic thermal analysis of an existing office building in Catania (southern Italy, Mediterranean area). The results show how the application of a cool paint on the roof can enhance the thermal comfort of the occupants by reducing the operative temperatures of the rooms and to reduce the overall energy needs of the building for space heating and cooling.

Cool roofs for passive cooling: performance in different climates and for different insulation levels in Italy

Roofs are severely hit by solar radiation in summer; hence the use of cool materials on the finishing layer provides a significant reduction in the heat flow entering the building, with sensible attenuation in the building cooling load. In this paper, a case study is presented, based on the dynamic simulation of an existing office building in Catania (southern Italy). Here, a part of the roof has been recently treated with a commercial cool paint, with the aim of improving thermal comfort in summer. Hence, the simulations represent a preliminary study that will allow assessing the expected effectiveness of the intervention. More in detail, the results of the simulations will be discussed in terms of both thermal comfort and energy savings, through the evaluation of parameters such as the roof surface temperature, the operative temperature and the cooling load for both conditions, i.e. with and without the cool paint. The paper also discusses the potential increase in the energy needs for winter heating, and looks at the overall annual balance in terms of primary energy; this is made by considering different climatic conditions and envelope characteristics. These aspects are usually not well highlighted in the current scientific literature.

Implicit equal-weights particle filter

Filter degeneracy is the main obstacle for the implementation of particle filter in non-linear high-dimensional models. A new scheme, the implicit equal-weights particle filter (IEWPF), is introduced. In this scheme samples are drawn implicitly from proposal densities with a different covariance for each particle, such that all particle weights are equal by construction. We test and explore the properties of the new scheme using a 1,000-dimensional simple linear model, and the 1,000-dimensional non-linear Lorenz96 model, and compare the performance of the scheme to a Local Ensemble Kalman Filter. The experiments show that the new scheme can easily be implemented in high-dimensional systems and is never degenerate, with good convergence properties in both systems.

The Diffusion Kernel Filter

A particle filter method is presented for the discrete-time filtering problem with nonlinear ItA ` stochastic ordinary differential equations (SODE) with additive noise supposed to be analytically integrable as a function of the underlying vector-Wiener process and time. The Diffusion Kernel Filter is arrived at by a parametrization of small noise-driven state fluctuations within branches of prediction and a local use of this parametrization in the Bootstrap Filter. The method applies for small noise and short prediction steps. With explicit numerical integrators, the operations count in the Diffusion Kernel Filter is shown to be smaller than in the Bootstrap Filter whenever the initial state for the prediction step has sufficiently few moments. The established parametrization is a dual-formula for the analysis of sensitivity to gaussian-initial perturbations and the analysis of sensitivity to noise-perturbations, in deterministic models, showing in particular how the stability of a deterministic dynamics is modeled by noise on short times and how the diffusion matrix of an SODE should be modeled (i.e. defined) for a gaussian-initial deterministic problem to be cast into an SODE problem. From it, a novel definition of prediction may be proposed that coincides with the deterministic path within the branch of prediction whose information entropy at the end of the prediction step is closest to the average information entropy over all branches. Tests are made with the Lorenz-63 equations, showing good results both for the filter and the definition of prediction.