A comparison of GOCE and drifter-based estimates of the North Atlantic steady-state surface circulation

Over the last decade, due to the Gravity Recovery And Climate Experiment (GRACE) mission and, more recently, the Gravity and steady state Ocean Circulation Explorer (GOCE) mission, our ability to measure the ocean’s mean dynamic topography (MDT) from space has improved dramatically. Here we use GOCE to measure surface current speeds in the North Atlantic and compare our results with a range of independent estimates that use drifter data to improve small scales. We find that, with filtering, GOCE can recover 70% of the Gulf Steam strength relative to the best drifter-based estimates. In the subpolar gyre the boundary currents obtained from GOCE are close to the drifter-based estimates. Crucial to this result is careful filtering which is required to remove small-scale errors, or noise, in the computed surface. We show that our heuristic noise metric, used to determine the degree of filtering, compares well with the quadratic sum of mean sea surface and formal geoid errors obtained from the error variance–covariance matrix associated with the GOCE gravity model. At a resolution of 100 km the North Atlantic mean GOCE MDT error before filtering is 5 cm with almost all of this coming from the GOCE gravity model.

Gaussian anamorphosis in the analysis step of the EnKF: a joint state-variable/observation approach

The analysis step of the (ensemble) Kalman filter is optimal when (1) the distribution of the background is Gaussian, (2) state variables and observations are related via a linear operator, and (3) the observational error is of additive nature and has Gaussian distribution. When these conditions are largely violated, a pre-processing step known as Gaussian anamorphosis (GA) can be applied. The objective of this procedure is to obtain state variables and observations that better fulfil the Gaussianity conditions in some sense. In this work we analyse GA from a joint perspective, paying attention to the effects of transformations in the joint state variable/observation space. First, we study transformations for state variables and observations that are independent from each other. Then, we introduce a targeted joint transformation with the objective to obtain joint Gaussianity in the transformed space. We focus primarily in the univariate case, and briefly comment on the multivariate one. A key point of this paper is that, when (1)-(3) are violated, using the analysis step of the EnKF will not recover the exact posterior density in spite of any transformations one may perform. These transformations, however, provide approximations of different quality to the Bayesian solution of the problem. Using an example in which the Bayesian posterior can be analytically computed, we assess the quality of the analysis distributions generated after applying the EnKF analysis step in conjunction with different GA options. The value of the targeted joint transformation is particularly clear for the case when the prior is Gaussian, the marginal density for the observations is close to Gaussian, and the likelihood is a Gaussian mixture.

The first real-time worldwide ionospheric predictions network: an advance in support of spaceborne experimentation, on-line model validation, and space weather

We report on the first realtime ionospheric predictions network and its capabilities to ingest a global database and forecast F-layer characteristics and "in situ" electron densities along the track of an orbiting spacecraft. A global network of ionosonde stations reported around-the-clock observations of F-region heights and densities, and an on-line library of models provided forecasting capabilities. Each model was tested against the incoming data; relative accuracies were intercompared to determine the best overall fit to the prevailing conditions; and the best-fit model was used to predict ionospheric conditions on an orbit-to-orbit basis for the 12-hour period following a twice-daily model test and validation procedure. It was found that the best-fit model often provided averaged (i.e., climatologically-based) accuracies better than 5% in predicting the heights and critical frequencies of the F-region peaks in the latitudinal domain of the TSS-1R flight path. There was a sharp contrast however, in model-measurement comparisons involving predictions of actual, unaveraged, along-track densities at the 295 km orbital altitude of TSS-1R In this case, extrema in the first-principle models varied by as much as an order of magnitude in density predictions, and the best-fit models were found to disagree with the "in situ" observations of Ne by as much as 140%. The discrepancies are interpreted as a manifestation of difficulties in accurately and self-consistently modeling the external controls of solar and magnetospheric inputs and the spatial and temporal variabilities in electric fields, thermospheric winds, plasmaspheric fluxes, and chemistry.

An evaluation of decadal probability forecasts from state-of-the-art climate models

While state-of-the-art models of Earth's climate system have improved tremendously over the last 20 years, nontrivial structural flaws still hinder their ability to forecast the decadal dynamics of the Earth system realistically. Contrasting the skill of these models not only with each other but also with empirical models can reveal the space and time scales on which simulation models exploit their physical basis effectively and quantify their ability to add information to operational forecasts. The skill of decadal probabilistic hindcasts for annual global-mean and regional-mean temperatures from the EU Ensemble-Based Predictions of Climate Changes and Their Impacts (ENSEMBLES) project is contrasted with several empirical models. Both the ENSEMBLES models and a “dynamic climatology” empirical model show probabilistic skill above that of a static climatology for global-mean temperature. The dynamic climatology model, however, often outperforms the ENSEMBLES models. The fact that empirical models display skill similar to that of today's state-of-the-art simulation models suggests that empirical forecasts can improve decadal forecasts for climate services, just as in weather, medium-range, and seasonal forecasting. It is suggested that the direct comparison of simulation models with empirical models becomes a regular component of large model forecast evaluations. Doing so would clarify the extent to which state-of-the-art simulation models provide information beyond that available from simpler empirical models and clarify current limitations in using simulation forecasting for decision support. Ultimately, the skill of simulation models based on physical principles is expected to surpass that of empirical models in a changing climate; their direct comparison provides information on progress toward that goal, which is not available in model–model intercomparisons.

Estimating Lorenz's reference state in an ocean with a nonlinear equation of state for seawater

The study of the mechanical energy budget of the oceans using Lorenz available potential energy (APE) theory is based on knowledge of the adiabatically re-arranged Lorenz reference state of minimum potential energy. The compressible and nonlinear character of the equation of state for seawater has been thought to cause the reference state to be ill-defined, casting doubt on the usefulness of APE theory for investigating ocean energetics under realistic conditions. Using a method based on the volume frequency distribution of parcels as a function of temperature and salinity in the context of the seawater Boussinesq approximation, which we illustrate using climatological data, we show that compressibility effects are in fact minor. The reference state can be regarded as a well defined one-dimensional function of depth, which forms a surface in temperature, salinity and density space between the surface and the bottom of the ocean. For a very small proportion of water masses, this surface can be multivalued and water parcels can have up to two statically stable levels in the reference density profile, of which the shallowest is energetically more accessible. Classifying parcels from the surface to the bottom gives a different reference density profile than classifying in the opposite direction. However, this difference is negligible. We show that the reference state obtained by standard sorting methods is equivalent, though computationally more expensive, to the volume frequency distribution approach. The approach we present can be applied systematically and in a computationally efficient manner to investigate the APE budget of the ocean circulation using models or climatological data.

Wave spectra assimilation in typhoon wave modeling for the East China Sea

The East China Sea is a hot area for typhoon waves to occur. A wave spectra assimilation model has been developed to predict the typhoon wave more accurately and operationally. This is the first time where wave data from Taiwan have been used to predict typhoon wave along the mainland China coast. The two-dimensional spectra observed in Taiwan northeast coast modify the wave field output by SWAN model through the technology of optimal interpolation (OI) scheme. The wind field correction is not involved as it contributes less than a quarter of the correction achieved by assimilation of waves. The initialization issue for assimilation is discussed. A linear evolution law for noise in the wave field is derived from the SWAN governing equations. A two-dimensional digital low-pass filter is used to obtain the initialized wave fields. The data assimilation model is optimized during the typhoon Sinlaku. During typhoons Krosa and Morakot, data assimilation significantly improves the low frequency wave energy and wave propagation direction in Taiwan coast. For the far-field region, the assimilation model shows an expected ability of improving typhoon wave forecast as well, as data assimilation enhances the low frequency wave energy. The proportion of positive assimilation indexes is over 81% for all the periods of comparison. The paper also finds that the impact of data assimilation on the far-field region depends on the state of the typhoon developing and the swell propagation direction.

Probabilistic downscaling of remote sensing data with applications for multi-scale biogeochemical flux modeling

Upscaling ecological information to larger scales in space and downscaling remote sensing observations or model simulations to finer scales remain grand challenges in Earth system science. Downscaling often involves inferring subgrid information from coarse-scale data, and such ill-posed problems are classically addressed using regularization. Here, we apply two-dimensional Tikhonov Regularization (2DTR) to simulate subgrid surface patterns for ecological applications. Specifically, we test the ability of 2DTR to simulate the spatial statistics of high-resolution (4 m) remote sensing observations of the normalized difference vegetation index (NDVI) in a tundra landscape. We find that the 2DTR approach as applied here can capture the major mode of spatial variability of the high-resolution information, but not multiple modes of spatial variability, and that the Lagrange multiplier (γ) used to impose the condition of smoothness across space is related to the range of the experimental semivariogram. We used observed and 2DTR-simulated maps of NDVI to estimate landscape-level leaf area index (LAI) and gross primary productivity (GPP). NDVI maps simulated using a γ value that approximates the range of observed NDVI result in a landscape-level GPP estimate that differs by ca 2% from those created using observed NDVI. Following findings that GPP per unit LAI is lower near vegetation patch edges, we simulated vegetation patch edges using multiple approaches and found that simulated GPP declined by up to 12% as a result. 2DTR can generate random landscapes rapidly and can be applied to disaggregate ecological information and compare of spatial observations against simulated landscapes.

Low rank representation on Riemannian manifold of symmetric positive definite matrices

Sparse coding aims to find a more compact representation based on a set of dictionary atoms. A well-known technique looking at 2D sparsity is the low rank representation (LRR). However, in many computer vision applications, data often originate from a manifold, which is equipped with some Riemannian geometry. In this case, the existing LRR becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to applications. In this paper, we generalize the LRR over the Euclidean space to the LRR model over a specific Rimannian manifold—the manifold of symmetric positive matrices (SPD). Experiments on several computer vision datasets showcase its noise robustness and superior performance on classification and segmentation compared with state-of-the-art approaches.