A new floating model level scheme for the assimilation of boundary layer top inversions: the univariate assimilation of temperature.

The assimilation of observations with a forecast is often heavily influenced by the description of the error covariances associated with the forecast. When a temperature inversion is present at the top of the boundary layer (BL), a significant part of the forecast error may be described as a vertical positional error (as opposed to amplitude error normally dealt with in data assimilation). In these cases, failing to account for positional error explicitly is shown t o r esult in an analysis for which the inversion structure is erroneously weakened and degraded. In this article, a new assimilation scheme is proposed to explicitly include the positional error associated with an inversion. This is done through the introduction of an extra control variable to allow position errors in the a priori to be treated simultaneously with the usual amplitude errors. This new scheme, referred to as the ‘floating BL scheme’, is applied to the one-dimensional (vertical) variational assimilation of temperature. The floating BL scheme is tested with a series of idealised experiments a nd with real data from radiosondes. For each idealised experiment, the floating BL scheme gives an analysis which has the inversion structure and position in agreement with the truth, and outperforms the a ssimilation which accounts only for forecast a mplitude error. When the floating BL scheme is used to assimilate a l arge sample of radiosonde data, its ability to give an analysis with an inversion height in better agreement with that observed is confirmed. However, it is found that the use of Gaussian statistics is an inappropriate description o f t he error statistics o f t he extra c ontrol variable. This problem is alleviated by incorporating a non-Gaussian description of the new control variable in the new scheme. Anticipated challenges in implementing the scheme operationally are discussed towards the end of the article

Representation of model error in a convective-scale ensemble prediction system

In this paper ensembles of forecasts (of up to six hours) are studied from a convection-permitting model with a representation of model error due to unresolved processes. The ensemble prediction system (EPS) used is an experimental convection-permitting version of the UK Met Office’s 24- member Global and Regional Ensemble Prediction System (MOGREPS). The method of representing model error variability, which perturbs parameters within the model’s parameterisation schemes, has been modified and we investigate the impact of applying this scheme in different ways. These are: a control ensemble where all ensemble members have the same parameter values; an ensemble where the parameters are different between members, but fixed in time; and ensembles where the parameters are updated randomly every 30 or 60 min. The choice of parameters and their ranges of variability have been determined from expert opinion and parameter sensitivity tests. A case of frontal rain over the southern UK has been chosen, which has a multi-banded rainfall structure. The consequences of including model error variability in the case studied are mixed and are summarised as follows. The multiple banding, evident in the radar, is not captured for any single member. However, the single band is positioned in some members where a secondary band is present in the radar. This is found for all ensembles studied. Adding model error variability with fixed parameters in time does increase the ensemble spread for near-surface variables like wind and temperature, but can actually decrease the spread of the rainfall. Perturbing the parameters periodically throughout the forecast does not further increase the spread and exhibits “jumpiness” in the spread at times when the parameters are perturbed. Adding model error variability gives an improvement in forecast skill after the first 2–3 h of the forecast for near-surface temperature and relative humidity. For precipitation skill scores, adding model error variability has the effect of improving the skill in the first 1–2 h of the forecast, but then of reducing the skill after that. Complementary experiments were performed where the only difference between members was the set of parameter values (i.e. no initial condition variability). The resulting spread was found to be significantly less than the spread from initial condition variability alone

Techniques and challenges in the assimilation of atmospheric water observations for numerical weather prediction towards convective scales

While contemporary Numerical Weather Prediction models represent the large-scale structure of moist atmospheric processes reasonably well, they often struggle to maintain accurate forecasts of small-scale features such as convective rainfall. Even though high-resolution models resolve more of the flow, and are therefore arguably more accurate, moist convective flow becomes increasingly nonlinear and dynamically unstable. Importantly, the models’ initial conditions are typically sub-optimal, leaving scope to improve the accuracy of forecasts with improved data assimilation. To address issues regarding the use of atmospheric water-related observations – especially at convective scales (also known as storm scales) – this paper discusses the observation and assimilation of water- related quantities. Special emphasis is placed on background error statistics for variational and hybrid methods which need special attention for water variables. The challenges of convective-scale data assimilation of atmospheric water information are discussed, which are more difficult to tackle than at larger scales. Some of the most important challenges include the greater degree of inhomogeneity and lower degree of smoothness of the flow, the high volume of water-related observations (e.g. from radar, microwave, and infrared instruments), the need to analyse a range of hydrometeors, the increasing importance of position errors in forecasts, the greater sophistication of forward models to allow use of indirect observations (e.g. cloud and precipitation affected observations), the need to account for the flow-dependent multivariate ‘balance’ between atmospheric water and both dynamical and mass fields, and the inherent non-Gaussian nature of atmospheric water variables

The ABC-DA system (v1.4): a variational data assimilation system for convective-scale assimilation research with a study of the impact of a balance constraint

Following the development of the simplified atmospheric convective-scale “toy” model (the ABC model, named after its three key parameters: the pure gravity wave frequency A, the controller of the acoustic wave speed B, and the constant of proportionality between pressure and density perturbations C), this paper introduces its associated variational data assimilation system, ABC-DA. The purpose of ABC-DA is to permit quick and efficient research into data assimilation methods suitable for convective-scale systems. The system can also be used as an aid to teach and demonstrate data assimilation principles. ABC-DA is flexible and configurable, and is efficient enough to be run on a personal computer. The system can run a number of assimilation methods (currently 3DVar and 3DFGAT have been implemented), with user configurable observation networks. Observation operators for direct observations and wind speeds are part of the current system, and these can, for example, be expanded relatively easily to include operators for Doppler winds. A key feature of any data assimilation system is how it specifies the background error covariance matrix. ABC-DA uses a control variable transform method to allow this to be done efficiently. This version of ABC-DA mirrors many operational configurations by modelling multivariate error covariances with uncorrelated control parameters, each with special uncorrelated spatial patterns. The software developed performs (amongst other things) model runs, calibration tasks associated with the background error covariance matrix, testing and diagnostic tasks, single data assimilation runs, and multi-cycle assimilation/forecast experiments, and it also has associated visualisation software. As a demonstration, the system is used to tackle a scientific question concerning the role of geostrophic balance (GB) to model background error covariances between mass and wind fields. This question arises because although GB is a very useful mechanism that is successfully exploited in larger-scale assimilation systems, its use is questionable at convective scales due to the typically larger Rossby numbers where GB is not so relevant. A series of identical twin experiments is done in cycled assimilation configurations. One experiment exploits GB to represent mass–wind covariances in a mirror of an operational set-up (with use of an additional vertical regression (VR) step, as used operationally). This experiment performs badly where error accumulates over time. Two further experiments are done: one that does not use GB and another that does but without the VR step. Turning off GB impairs the performance, and turning off VR improves the performance in general. It is concluded that there is scope to further improve the way that the background error covariance matrices are represented at convective scale. Ideas for further possible developments of ABC-DA are discussed

Methods of investigating forecast error sensitivity to ensemble size in a limited-area convection-permitting ensemble

Ensemble-based predictions are increasingly used as an aid to weather forecasting and to data assimilation, where the aim is to capture the range of possible outcomes consistent with the underlying uncertainties. Constraints on computing resources mean that ensembles have a relatively small size, which can lead to an incomplete range of possible outcomes, and to inherent sampling errors. This paper discusses how an existing ensemble can be relatively easily increased in size, it develops a range of standard and extended diagnostics to help determine whether a given ensemble is ‘large enough’ to be useful for forecasting and data assimilation purposes, and it applies the diagnostics to a convective-scale case study for illustration. Diagnostics include the effect of ensemble size on various aspects of rainfall forecasts, kinetic energy spectra, and (co)variance statistics in the spatial and spectral domains. The work here extends the Met Office’s 24 ensemble members to 93. It is found that the extra members do develop a significant degree of linear independence, they increase the ensemble spread (although with caveats to do with non-Gaussianity), they reduce sampling error in many statistical quantities (namely variances, correlations, and length-scales), and improve the effective spatial resolution of the ensemble. The extra members though do not improve the probabilistic rain rate forecasts. It is assumed that the 93-member ensemble approximates the error-free statistics, which is a practical assumption, but the data suggests that this number of members is ultimately not enough to justify this assumption, and therefore more ensembles are likely required for such convective-scale systems to further reduce sampling errors, especially for ensemble data assimilation purposes

Mine waste and acute warming induce energetic stress in the deep-sea sponge Geodia atlantica and coral Primnoa resedeaformis; results from a mesocosm study

There is the potential for climate change to interact with pollution in all of the Earth's oceans. In the fjords of Norway, mine tailings are released into fjords generating suspended sediment plumes that impact deep-sea ecosystems. These same deep-sea ecosystems are expected to undergo periodic warming as climate change increases the frequency of down-welling events in fjords. It remains unknown how a polluted deep-sea ecosystem would respond to down-welling because multiple stressors will often interact in unpredictable ways. Here, we exposed two deep-sea foundation species; the gorgonian coral Primnoa resedaeformis and the demosponge Geodia atlantica to suspended sediment (10 mg L−1) and acute warming (+5°C) in a factorial mesocosm experiment for 40 days. Physiology (respiration, nutrient flux) and cellular responses (lysosomal cell stability) were measured for both the coral and sponge. Exposure to elevated suspended sediment reduced metabolism, supressed silicate uptake and induced cellular instability of the sponge G. atlantica. However, combining sediment with warming caused G. atlantica to respire and excrete nitrogen at a greater rate. For the coral P. resedaeformis, suspended sediments reduced O:N ratios after 40 days, however, warming had a greater effect on P. resedaeformis physiology compared to sediment. Warming increased respiration, nitrogen excretion, and cellular instability which resulted in lower O:N ratios. We argue that suspended sediment and warming can act alone and also interact to cause significant harm to deep-sea biota, however responses are likely to be species-specific. Warming and pollution could interact in the deep-sea to cause mortality to the coral P. resedaeformis and to a lesser extent, the sponge G. atlantica. As foundation species, reducing the abundance of deep sea corals and sponges would likely impact the ecosystems they support.publishedVersio

Characterising the background errors for the boundary-layer capping inversion

The one-dimensional variational assimilation of vertical temperature information in the presence of a boundary-layer capping inversion is studied. For an optimal analysis of the vertical temperature profile, an accurate representation of the background error covariances is essential. The background error covariances are highly flow-dependent due to the variability in the presence, structure and height of the boundary-layer capping inversion. Flow-dependent estimates of the background error covariances are shown by studying the spread in an ensemble of forecasts. A forecast of the temperature profile (used as a background state) may have a significant error in the position of the capping inversion with respect to observations. It is shown that the assimilation of observations may weaken the inversion structure in the analysis if only magnitude errors are accounted for as is the case for traditional data assimilation methods used for operational weather prediction. The positional error is treated explicitly here in a new data assimilation scheme to reduce positional error, in addition to the traditional framework to reduce magnitude error. The distribution of the positional error of the background inversion is estimated for use with the new scheme

The effects of assimilating a sub-grid-scale sea ice thickness distribution in a new Arctic sea ice data assimilation system

In the past decade groundbreaking new satellite observations of the Arctic sea ice cover have been made, allowing researchers to understand the state of the Arctic sea ice system in greater detail than before. The derived estimates of sea ice thickness are useful but limited in time and space. In this study the first results of a new sea ice data assimilation system are presented. Observations assimilated (in various combinations) are monthly mean sea ice thickness and monthly mean sea ice thickness distribution from CryoSat-2 and NASA daily Bootstrap sea ice concentration. This system couples the Centre for Polar Observation and Modelling's (CPOM) version of the Los Alamos Sea Ice Model (CICE) to the localised ensemble transform Kalman filter (LETKF) from the Parallel Data Assimilation Framework (PDAF) library. The impact of assimilating a sub-grid-scale sea ice thickness distribution is of particular novelty. The sub-grid-scale sea ice thickness distribution is a fundamental component of sea ice models, playing a vital role in the dynamical and thermodynamical processes, yet very little is known of its true state in the Arctic. This study finds that assimilating CryoSat-2 products for the mean thickness and the sub-grid-scale thickness distribution can have significant consequences for the modelled distribution of the ice thickness across the Arctic and particularly in regions of thick multi-year ice. The assimilation of sea ice concentration, mean sea ice thickness and sub-grid-scale sea ice thickness distribution together performed best when compared to a subset of CryoSat-2 observations held back for validation. Regional model biases are reduced: the thickness of the thickest ice in the Canadian Arctic Archipelago (CAA) is decreased, but the thickness of the ice in the central Arctic is increased. When comparing the assimilation of mean thickness with the assimilation of sub-grid-scale thickness distribution, it is found that the latter leads to a significant change in the volume of ice in each category. Estimates of the thickest ice improve significantly with the assimilation of sub-grid-scale thickness distribution alongside mean thickness

Simplified Kalman smoother and ensemble Kalman smoother for improving reanalyses

The paper presents a simplification of the Kalman smoother that can be run as a post-processing step using only minimal stored information from a Kalman filter analysis, which is intended for use with large model products such as the reanalyses of the Earth system. A simple decay assumption is applied to cross-time error covariances, and we show how the resulting equations relate formally to the fixed-lag Kalman smoother and how they can be solved to give a smoother analysis along with an uncertainty estimate. The method is demonstrated in the Lorenz (1963) idealised system which is applied to both an extended and ensemble Kalman filter and smoother. In each case, the root mean square errors (RMSEs) against the truth, for both assimilated and unassimilated (independent) data, of the new smoother analyses are substantially smaller than for the original filter analyses, while being larger than for the full smoother solution. Up to 70% (40 %) of the full smoother error reduction, with respect to the extended (ensemble) filters, respectively, is achieved. The uncertainties derived for the new smoother also agree remarkably well with the actual RMSE values throughout the assimilation period. The ability to run this smoother very efficiently as a post-processor should allow it to be useful for really large model reanalysis products and especially for ensemble products that are already being developed by various operational centres