An analysis of the vertical structure equation for arbitrary thermal profiles

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations

Ten priority science gaps in assessing climate data record quality

Decision makers need accessible robust evidence to introduce new policies in an effort to mitigate and adapt to climate change. There is an increasing amount of environmental information available to policy makers concerning observations and trends relating to the climate. However, this data is hosted across a multitude of websites often with inconsistent metadata and sparse information relating to the quality, accuracy and validity of the data. Subsequently, the task of comparing datasets to decide which is the most appropriate for a certain purpose is very complex and often infeasible. In support of the European Union’s Copernicus Climate Change Service (C3S) mission to provide authoritative information about the past, present and future climate in Europe and the rest of the world, each dataset to be provided through this service must undergo an evaluation of its climate relevance and scientific quality to help with data comparisons. This paper presents the framework for Evaluation and Quality Control (EQC) of climate data products derived from satellite and in situ observations to be catalogued within the C3S Climate Data Store (CDS). The EQC framework will be implemented by C3S as part of their operational quality assurance programme. It builds on past and present international investment in Quality Assurance for Earth Observation initiatives, extensive user requirements gathering exercises, as well as a broad evaluation of over 250 data products and a more in-depth evaluation of a selection of 24 individual data products derived from satellite and in situ observations across the land, ocean and atmosphere Essential Climate Variable (ECV) domains. A prototype Content Management System (CMS) to facilitate the process of collating, evaluating and presenting the quality aspects and status of each data product to data users is also described. The development of the EQC framework has highlighted cross-domain as well as ECV specific science knowledge gaps in relation to addressing the quality of climate data sets derived from satellite and in situ observations. We discuss 10 common priority science knowledge gaps that will require further research investment to ensure all quality aspects of climate data sets can be ascertained and provide users with the range of information necessary to confidently select relevant products for their specific application

Atmospheric Reanalyses-Recent Progress and Prospects for the Future. A Report from a Technical Workshop, April 2010

In April 2010, developers representing each of the major reanalysis centers met at Goddard Space Flight Center to discuss technical issues - system advances and lessons learned - associated with recent and ongoing atmospheric reanalyses and plans for the future. The meeting included overviews of each center s development efforts, a discussion of the issues in observations, models and data assimilation, and, finally, identification of priorities for future directions and potential areas of collaboration. This report summarizes the deliberations and recommendations from the meeting as well as some advances since the workshop

Advancing global & regional reanalyses

This report outlines the structure of and summarizes the recommendations made at the 5th International Conference on Reanalysis (ICR5), attended by 259 participants from 37 countries, in Rome (Italy), on 13-17 November 2017. It first summarizes the conference structure. Then, the key recommendations of ICR5 are given for the five main conference topics: production; observations (data rescue and preparation); data assimilation methods; quality assurance of reanalysis; and applications in science, services, and policymaking. Lastly, five high-level recommendations are proposed to managing agencies on how best to advance the field of reanalyses, which serves tens of thousands of users, via enhanced research, development, and operations

Atrasentan and renal events in patients with type 2 diabetes and chronic kidney disease (SONAR): a double-blind, randomised, placebo-controlled trial

Background: Short-term treatment for people with type 2 diabetes using a low dose of the selective endothelin A receptor antagonist atrasentan reduces albuminuria without causing significant sodium retention. We report the long-term effects of treatment with atrasentan on major renal outcomes. Methods: We did this double-blind, randomised, placebo-controlled trial at 689 sites in 41 countries. We enrolled adults aged 18–85 years with type 2 diabetes, estimated glomerular filtration rate (eGFR)25–75 mL/min per 1·73 m 2 of body surface area, and a urine albumin-to-creatinine ratio (UACR)of 300–5000 mg/g who had received maximum labelled or tolerated renin–angiotensin system inhibition for at least 4 weeks. Participants were given atrasentan 0·75 mg orally daily during an enrichment period before random group assignment. Those with a UACR decrease of at least 30% with no substantial fluid retention during the enrichment period (responders)were included in the double-blind treatment period. Responders were randomly assigned to receive either atrasentan 0·75 mg orally daily or placebo. All patients and investigators were masked to treatment assignment. The primary endpoint was a composite of doubling of serum creatinine (sustained for ≥30 days)or end-stage kidney disease (eGFR <15 mL/min per 1·73 m 2 sustained for ≥90 days, chronic dialysis for ≥90 days, kidney transplantation, or death from kidney failure)in the intention-to-treat population of all responders. Safety was assessed in all patients who received at least one dose of their assigned study treatment. The study is registered with ClinicalTrials.gov, number NCT01858532. Findings: Between May 17, 2013, and July 13, 2017, 11 087 patients were screened; 5117 entered the enrichment period, and 4711 completed the enrichment period. Of these, 2648 patients were responders and were randomly assigned to the atrasentan group (n=1325)or placebo group (n=1323). Median follow-up was 2·2 years (IQR 1·4–2·9). 79 (6·0%)of 1325 patients in the atrasentan group and 105 (7·9%)of 1323 in the placebo group had a primary composite renal endpoint event (hazard ratio [HR]0·65 [95% CI 0·49–0·88]; p=0·0047). Fluid retention and anaemia adverse events, which have been previously attributed to endothelin receptor antagonists, were more frequent in the atrasentan group than in the placebo group. Hospital admission for heart failure occurred in 47 (3·5%)of 1325 patients in the atrasentan group and 34 (2·6%)of 1323 patients in the placebo group (HR 1·33 [95% CI 0·85–2·07]; p=0·208). 58 (4·4%)patients in the atrasentan group and 52 (3·9%)in the placebo group died (HR 1·09 [95% CI 0·75–1·59]; p=0·65). Interpretation: Atrasentan reduced the risk of renal events in patients with diabetes and chronic kidney disease who were selected to optimise efficacy and safety. These data support a potential role for selective endothelin receptor antagonists in protecting renal function in patients with type 2 diabetes at high risk of developing end-stage kidney disease. Funding: AbbVie

Data Assimilation in the Presence of Forecast Bias: the GEOS Moisture Analysis

We describe the application of the unbiased sequential analysis algorithm developed by Dee and da Silva (1998) to the GEOS moisture analysis. The algorithm estimates the slowly varying, systematic component of model error from rawinsonde observations and adjusts the first-guess moisture field accordingly. Results of two seasonal data assimilation cycles show that moisture analysis bias is almost completely eliminated in all observed regions. The improved analyses cause a sizable reduction in the 6h-forecast bias and a marginal improvement in the error standard deviations. 1 Introduction Hidden beneath the computational complexities of atmospheric data assimilation systems lies a multitude of assumptions about the errors associated with observing and predicting atmospheric fields. Most of these assumptions are there for practical reasons, either because there is not enough information to remove them, or because they result in critical computational simplifications. Some, however, are ..

Simplification of the Kalman Filter for Meteorological Data Assimilation

We propose a new statistical data assimilation method that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated by simply advecting the mass error covariance field, by deriving the remaining covariances geostrophically, and by accounting for external model error forcing only at the end of each forecast cycle. This greatly reduces the cost of the forecast error covariance computation, which is the central and most expensive aspect of the Kalman filter algorithm. In simulations with a linear, one-dimensional shallow-water model and artificially generated data, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. These experiments are designed to isolate the effect of simplifying the forecast error covariance evolution. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI. ae 1 Introduction ..

Prescribed Solution Forcing Method for Model Verification

This paper describes a method for verifying the consistency and order of accuracy of a numerical implementation of a pde-model. We present an application example to a 3D hydrodynamic flow model. The general idea behind PSF By means of the PSF technique it is possible to thoroughly test the quality of a numerical approximation to a given mathematical model, by prescribing an analytical test solution to the model equations and solving the appropriate inhomogeneous version of the model which the test solution exactly satisfies. Suppose that the mathematical model is given by @U @t +D(U) = 0 (1) where U = U(x; t) is a vector function of unknown dependent variables, and D is a spatial differential operator defined on the model domain\Omega \Theta [t 0 ; T ]. The model implementation which is to be validated numerically solves Eq. (1) subject to initial and boundary conditions U = U 0 (x) at t = t 0 (2) B(U) = 0 for x 2 @\Omega ; t t 0 (3) where @\Omega is the boundary of the spat..