Regular Latitude Longitude Research Articles

A Long-Time-Step-Permitting Tracer Transport Model on the Regular Latitude–Longitude Grid

A Long-Time-Step-Permitting Tracer Transport Model on the Regular Latitude–Longitude Grid

Physics-Inspired Adaptions to Low-Parameter Neural Network Weather Forecast Systems

Abstract Recently, there has been a surge of research on data-driven weather forecasting systems, especially applications based on convolutional neural networks (CNNs). These are usually trained on atmospheric data represented on regular latitude–longitude grids, neglecting the curvature of Earth. We assess the benefit of replacing the standard convolution operations with an adapted convolution operation that takes into account the geometry of the underlying data (SphereNet convolution), specifically near the poles. Additionally, we assess the effect of including the information that the two hemispheres of Earth have “flipped” properties—for example, cyclones circulating in opposite directions—into the structure of the network. Both approaches are examples of physics-informed machine learning. The methods are tested on the WeatherBench dataset, at a resolution of ∼1.4°, which is higher than many previous studies on CNNs for weather forecasting. For most lead times up to day +10 for 500-hPa geopotential and 850-hPa temperature, we find that using SphereNet convolution or including hemisphere-specific information individually leads to improvement in forecast skill. Combining the two methods typically gives the highest forecast skill. Our version of SphereNet is implemented flexibly and scales well to high-resolution datasets but is still significantly more expensive than a standard convolution operation. Finally, we analyze cases with high forecast error. These occur mainly in winter and are relatively consistent across different training realizations of the networks, pointing to flow-dependent atmospheric predictability.

Evaluation of native Earth system model output with ESMValTool v2.6.0

Abstract. Earth system models (ESMs) are state-of-the-art climate models that allow numerical simulations of the past, present-day, and future climate. To extend our understanding of the Earth system and improve climate change projections, the complexity of ESMs heavily increased over the last decades. As a consequence, the amount and volume of data provided by ESMs has increased considerably. Innovative tools for a comprehensive model evaluation and analysis are required to assess the performance of these increasingly complex ESMs against observations or reanalyses. One of these tools is the Earth System Model Evaluation Tool (ESMValTool), a community diagnostic and performance metrics tool for the evaluation of ESMs. Input data for ESMValTool needs to be formatted according to the CMOR (Climate Model Output Rewriter) standard, a process that is usually referred to as “CMORization”. While this is a quasi-standard for large model intercomparison projects like the Coupled Model Intercomparison Project (CMIP), this complicates the application of ESMValTool to non-CMOR-compliant climate model output. In this paper, we describe an extension of ESMValTool introduced in v2.6.0 that allows seamless reading and processing of “native” climate model output, i.e., operational output produced by running the climate model through the standard workflow of the corresponding modeling institute. This is achieved by an extension of ESMValTool's preprocessing pipeline that performs a CMOR-like reformatting of the native model output during runtime. Thus, the rich collection of diagnostics provided by ESMValTool is now fully available for these models. For models that use unstructured grids, a further preprocessing step required to apply many common diagnostics is regridding to a regular latitude–longitude grid. Extensions to ESMValTool's regridding functions described here allow for more flexible interpolation schemes that can be used on unstructured grids. Currently, ESMValTool supports nearest-neighbor, bilinear, and first-order conservative regridding from unstructured grids to regular grids. Example applications of this new native model support are the evaluation of new model setups against predecessor versions, assessing of the performance of different simulations against observations, CMORization of native model data for contributions to model intercomparison projects, and monitoring of running climate model simulations. For the latter, new general-purpose diagnostics have been added to ESMValTool that are able to plot a wide range of variable types. Currently, five climate models are supported: CESM2 (experimental; at the moment, only surface variables are available), EC-Earth3, EMAC, ICON, and IPSL-CM6. As the framework for the CMOR-like reformatting of native model output described here is implemented in a general way, support for other climate models can be easily added.

The E3SM Diagnostics Package (E3SM Diags v2.7): a Python-based diagnostics package for Earth system model evaluation

Abstract. The E3SM Diagnostics Package (E3SM Diags) is a modern, Python-based Earth system model (ESM) evaluation tool (with Python module name e3sm_diags), developed to support the Department of Energy (DOE) Energy Exascale Earth System Model (E3SM). E3SM Diags provides a wide suite of tools for evaluating native E3SM output, as well as ESM data on regular latitude–longitude grids, including output from Coupled Model Intercomparison Project (CMIP) class models. E3SM Diags is modeled after the National Center for Atmospheric Research (NCAR) Atmosphere Model Working Group (AMWG, 2022) diagnostics package. In its version 1 release, E3SM Diags included a set of core essential diagnostics to evaluate the mean physical climate from model simulations. As of version 2.7, more process-oriented and phenomenon-based evaluation diagnostics have been implemented, such as analysis of the quasi-biennial oscillation (QBO), the El Niño–Southern Oscillation (ENSO), streamflow, the diurnal cycle of precipitation, tropical cyclones, ozone and aerosol properties. An in situ dataset from DOE's Atmospheric Radiation Measurement (ARM) program has been integrated into the package for evaluating the representation of simulated cloud and precipitation processes. This tool is designed with enough flexibility to allow for the addition of new observational datasets and new diagnostic algorithms. Additional features include customizable figures; streamlined installation, configuration and execution; and multiprocessing for fast computation. The package uses an up-to-date observational data repository maintained by its developers, where recent datasets are added to the repository as they become available. Finally, several applications for the E3SM Diags module were introduced to fit a diverse set of use cases from the scientific community.

Deriving Arctic 2 m air temperatures over snow and ice from satellite surface temperature measurements

Abstract. The Arctic region is responding heavily to climate change, and yet, the air temperature of ice-covered areas in the Arctic is heavily under-sampled when it comes to in situ measurements, resulting in large uncertainties in existing weather and reanalysis products. This paper presents a method for estimating daily mean clear-sky 2 m air temperatures (T2m) in the Arctic from satellite observations of skin temperature, using the Arctic and Antarctic ice Surface Temperatures from thermal Infrared (AASTI) satellite dataset, providing spatially detailed observations of the Arctic. The method is based on a linear regression model, which has been tuned against in situ observations to estimate daily mean T2m based on clear-sky satellite ice surface skin temperatures. The daily satellite-derived T2m product includes estimated uncertainties and covers the Arctic sea ice and the Greenland Ice Sheet during clear skies for the period 2000–2009, provided on a 0.25∘ regular latitude–longitude grid. Comparisons with independent in situ measured T2m show average biases of 0.30 and 0.35∘C and average root-mean-square errors of 3.47 and 3.20 ∘C for land ice and sea ice, respectively. The associated uncertainties are verified to be very realistic for both land ice and sea ice, using in situ observations. The reconstruction provides a much better spatial coverage than the sparse in situ observations of T2m in the Arctic and is independent of numerical weather prediction model input. Therefore, it provides an important supplement to simulated air temperatures to be used for assimilation or global surface temperature reconstructions. A comparison of T2m derived from satellite and ERA-Interim/ERA5 estimates shows that the satellite-derived T2m validates similar to or better than ERA-Interim/ERA5 against in situ measurements in the Arctic.

Observed Daily Temperature Variability and Extremes over Southeastern USA (1978–2017)

This study presents an analysis of extreme temperature events over southeastern USA from 1978 to 2017. This region is part of the so-called ‘warming hole’ where long-term surface temperature trends are negative or non-significant, in contrast with the remainder of the country. This study examines whether this distinctive characteristic reflects on the region’s trends in temperature extremes. Daily maximum and minimum temperatures from the US Historical Climatology Network were used to compute extreme indices recommended by the Expert Team on Climate Change Detection and Indices. Temperature extreme indices computed for all stations using the RClimDex package were gridded onto a regular latitude–longitude grid, and a spatiotemporal analysis of associated trends was performed. The results point to a tendency toward warming due to increasing trends in the annual occurrence of the hottest day, the warmest night, warm days, warm nights, summer days, tropical nights, and warm spells, as well as decreases in cool nights, cool days, and frost days. Statistically significant trend changes over large portions of the Southeast were dominated by increases in the frequency of the coldest night, summer days, and warm nights, and decreases in cool nights and frost days. Comparison of our results with other global and regional studies indicate that most of the extreme temperature changes over the Southeast are consistent with findings from other parts of the United States (US) and the world. Overall, this study shows that being part of the ‘warming hole’ does not preclude southeastern US from an intensification of temperature extremes, whether it is an increase in warm extremes or a decrease in cold ones. Further, the results suggest that, should the current trends continue in the long term, the Southeast will not be considered as being part of a warming hole anymore.

Modeling Tangential Vector Fields on a Sphere

ABSTRACTPhysical processes that manifest as tangential vector fields on a sphere are common in geophysical and environmental sciences. These naturally occurring vector fields are often subject to physical constraints, such as being curl-free or divergence-free. We start with constructing parametric models for curl-free and divergence-free vector fields that are tangential to the unit sphere through applying the surface gradient or the surface curl operator to a scalar random potential field on the unit sphere. Using the Helmholtz–Hodge decomposition, we then construct a class of simple but flexible parametric models for general tangential vector fields, which are represented as a sum of a curl-free and a divergence-free components. We propose a likelihood-based parameter estimation procedure, and show that fast computation is possible even for large datasets when the observations are on a regular latitude–longitude grid. Characteristics and practical utility of the proposed methodology are illustrated through extensive simulation studies and an application to a dataset of ocean surface wind velocities collected by satellite-based scatterometers. We also compare our model with a bivariate Matérn model and a non-stationary bivariate global model. Supplementary materials for this article are available online.

SA-OBS: A Daily Gridded Surface Temperature and Precipitation Dataset for Southeast Asia

This study introduces a new daily high-resolution land-only observational gridded dataset, called SA-OBS, for precipitation and minimum, mean, and maximum temperature covering Southeast Asia. This dataset improves upon existing observational products in terms of the number of contributing stations, in the use of an interpolation technique appropriate for daily climate observations, and in making estimates of the uncertainty of the gridded data. The dataset is delivered on a 0.25° × 0.25° and a 0.5° × 0.5° regular latitude–longitude grid for the period 1981–2014. The dataset aims to provide best estimates of grid square averages rather than point values to enable direct comparisons with regional climate models. Next to the best estimates, daily uncertainties are quantified. The underlying daily station time series are collected in cooperation between meteorological services in the region: the Southeast Asian Climate Assessment and Dataset (SACA&D). Comparisons are made with station observations and other gridded station or satellite-based datasets (APHRODITE, CMORPH, TRMM). The comparisons show that vast differences exist in the average daily precipitation, the number of rainy days, and the average precipitation on a wet day between these datasets. SA-OBS closely resembles the station observations in terms of dry/wet frequency, the timing of precipitation events, and the reproduction of extreme precipitation. New versions of SA-OBS will be released when the station network in SACA&D has grown further.

NCAR_Topo (v1.0): NCAR global model topography generation software for unstructured grids

Abstract. It is the purpose of this paper to document the NCAR global model topography generation software for unstructured grids (NCAR_Topo (v1.0)). Given a model grid, the software computes the fraction of the grid box covered by land, the grid-box mean elevation (deviation from a geoid that defines nominal sea level surface), and associated sub-grid-scale variances commonly used for gravity wave and turbulent mountain stress parameterizations. The software supports regular latitude–longitude grids as well as unstructured grids, e.g., icosahedral, Voronoi, cubed-sphere and variable-resolution grids.

Operational surface UV radiation product from GOME-2 and AVHRR/3 data

Abstract. The surface ultraviolet (UV) radiation product, version 1.20, generated operationally in the framework of the Satellite Application Facility on Ozone and Atmospheric Chemistry Monitoring (O3M SAF) of the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) is described. The product is based on the total ozone column derived from the measurements of the second Global Ozone Monitoring Experiment (GOME-2) instrument aboard EUMETSAT's polar orbiting meteorological operational (Metop) satellites. Cloud cover is taken into account by retrieving cloud optical depth from the channel 1 reflectance of the third Advanced Very High-Resolution Radiometer (AVHRR/3) instrument aboard both Metop in the morning orbit and Polar Orbiting Environmental Satellites (POES) of the National Oceanic and Atmospheric Administration (NOAA) in the afternoon orbit. In addition, more overpasses are used at high latitudes where the swaths of consecutive orbits overlap. The input satellite data are received from EUMETSAT's Multicast Distribution System (EUMETCast). The surface UV product includes daily maximum dose rates and integrated daily doses with different biological weighting functions, integrated ultraviolet B (UVB) and ultraviolet A (UVA) radiation, solar noon UV index and daily maximum photolysis frequencies of ozone and nitrogen dioxide at the surface level. The quantities are computed in a 0.5°×0.5° regular latitude–longitude grid and stored as daily files in the hierarchical data format (HDF5) within 2 weeks from sensing. The product files are archived in the O3M SAF distributed archive and can be ordered via the EUMETSAT Data Centre.

Pangolin v1.0, a conservative 2-D advection model towards large-scale parallel calculation

Abstract. To exploit the possibilities of parallel computers, we designed a large-scale bidimensional atmospheric advection model named Pangolin. As the basis for a future chemistry-transport model, a finite-volume approach for advection was chosen to ensure mass preservation and to ease parallelization. To overcome the pole restriction on time steps for a regular latitude–longitude grid, Pangolin uses a quasi-area-preserving reduced latitude–longitude grid. The features of the regular grid are exploited to reduce the memory footprint and enable effective parallel performances. In addition, a custom domain decomposition algorithm is presented. To assess the validity of the advection scheme, its results are compared with state-of-the-art models on algebraic test cases. Finally, parallel performances are shown in terms of strong scaling and confirm the efficient scalability up to a few hundred cores.

A standard test case suite for two-dimensional linear transport on the sphere: results from a collection of state-of-the-art schemes

Abstract. Recently, a standard test case suite for 2-D linear transport on the sphere was proposed to assess important aspects of accuracy in geophysical fluid dynamics with a "minimal" set of idealized model configurations/runs/diagnostics. Here we present results from 19 state-of-the-art transport scheme formulations based on finite-difference/finite-volume methods as well as emerging (in the context of atmospheric/oceanographic sciences) Galerkin methods. Discretization grids range from traditional regular latitude–longitude grids to more isotropic domain discretizations such as icosahedral and cubed-sphere tessellations of the sphere. The schemes are evaluated using a wide range of diagnostics in idealized flow environments. Accuracy is assessed in single- and two-tracer configurations using conventional error norms as well as novel diagnostics designed for climate and climate–chemistry applications. In addition, algorithmic considerations that may be important for computational efficiency are reported on. The latter is inevitably computing platform dependent. The ensemble of results from a wide variety of schemes presented here helps shed light on the ability of the test case suite diagnostics and flow settings to discriminate between algorithms and provide insights into accuracy in the context of global atmospheric/ocean modeling. A library of benchmark results is provided to facilitate scheme intercomparison and model development. Simple software and data sets are made available to facilitate the process of model evaluation and scheme intercomparison.

Vorticity–divergence mass-conserving semi-Lagrangian shallow-water model using the reduced grid on the sphere

The semi-Lagrangian semi-implicit shallow water model on the sphere using the reduced latitude–longitude grid is presented. The key feature of the model is the vorticity–divergence formulation on the unstaggered grid. The new algorithm for the reconstruction of wind components from vorticity and divergence is described. The mass-conservative version of the model is developed. The conservative cascade scheme (CCS) by Nair et al. is modified to provide a locally-conservative semi-Lagrangian advection algorithm for the reduced grid. Some numerical advection tests are carried out to demonstrate the accuracy of the CCS with the reduced grid. The CCS-based discretization for the continuity equation and finite-volume Helmholtz problem solver are introduced to guarantee the mass-conservation.The results for shallow water tests on the sphere are presented. The results for different versions of the model are compared. They are also compared with the results for the same tests available in literature. The impact of the reduced grid is analyzed. The mass-conservative version of the model using the reduced grid with up to 20% reduction of grid points number has approximately the same accuracy as its non-conservative counterpart implemented on the regular latitude–longitude grid.

A class of deformational flow test cases for linear transport problems on the sphere

A class of new benchmark deformational flow test cases for the two-dimensional horizontal linear transport problems on the sphere is proposed. The scalar field follows complex trajectories and undergoes severe deformation during the simulation; however, the flow reverses its course at half-time and the scalar field returns to its initial position and shape. This process makes the exact solution available at the end of the simulation, and facilitates assessment of the accuracy of the underlying transport scheme. A procedure to eliminate possible cancellations of errors when the flow reverses is proposed. The test suite consists of four cases. Three are based on non-divergent flow fields and one on a divergent flow. The initial conditions are prescribed in terms of regular latitude–longitude spherical coordinates and are easy to implement. The divergent flow is specifically aimed for conservative global transport schemes to test for conservation, consistency and monotonicity (or positivity) of limiters/filters in a challenging flow environment. In the context of semi-Lagrangian schemes, the time-varying flow fields can be used to test trajectory algorithms where the exact trajectories do not follow great-circle arcs. The characteristics of the test cases are demonstrated with two different transport schemes.

Using temporal variability to improve spatial mapping with application to satellite data

AbstractThe National Aeronautics and Space Administration (NASA) has a remote‐sensing program with a large array of satellites whose mission is earth‐system science. To carry out this mission, NASA produces data at various levels; level‐2 data have been calibrated to the satellite's footprint at high temporal resolution, although there is often a lot of missing data. Level‐3 data are produced on a regular latitude—longitude grid over the whole globe at a coarser spatial and temporal resolution (such as a day, a month, or a repeat‐cycle of the satellite), and there are still missing data. This article demonstrates that spatio‐temporal statistical models can be made operational and provide a way to estimate level‐3 values over the whole grid and attach to each value a measure of its uncertainty. Specifically, a hierarchical statistical model is presented that includes a spatio‐temporal random effects (STRE) model as a dynamical component and a temporally independent spatial component for the fine‐scale variation. Optimal spatio‐temporal predictions and their mean squared prediction errors are derived in terms of a fixed‐dimensional Kalman filter. The predictions provide estimates of missing values and filter out unwanted noise. The resulting fixed‐rank filter is scalable, in that it can handle very large data sets. Its functionality relies on estimation of the model's parameters, which is presented in detail. It is demonstrated how both past and current remote‐sensing observations on aerosol optical depth (AOD) can be combined, yielding an optimal statistical predictor of AOD on the log scale along with its prediction standard error. The Canadian Journal of Statistics 38: 271–289; 2010 © 2010 Statistical Society of Canada

Geometrically Exact Conservative Remapping (GECoRe): Regular Latitude–Longitude and Cubed-Sphere Grids

Abstract Land, ocean, and atmospheric models are often implemented on different spherical grids. As a conseqence coupling these model components requires state variables and fluxes to be regridded. For some variables, such as fluxes, it is paramount that the regridding algorithm is conservative (so that energy and water budget balances are maintained) and monotone (to prevent unphysical values). For global applications the cubed-sphere grids are gaining popularity in the atmospheric community whereas, for example, the land modeling groups are mostly using the regular latitude–longitude grid. Most existing regridding schemes fail to take advantage of geometrical symmetries between these grids and hence accuracy of the calculations can be lost. Hence, a new Geometrically Exact Conservative Remapping (GECoRe) scheme with a monotone option is proposed for remapping between regular latitude–longitude and gnomonic cubed-sphere grids. GECoRe is compared with existing remapping schemes published in the meteorological literature. It is concluded here that the geometrically exact scheme significantly improves the accuracy of the resulting remapping in idealized test cases.

Monotone and Conservative Cascade Remapping between Spherical Grids (CaRS): Regular Latitude–Longitude and Cubed-Sphere Grids

Abstract A high-order monotone and conservative cascade remapping algorithm between spherical grids (CaRS) is developed. This algorithm is specifically designed to remap between the cubed-sphere and regular latitude–longitude grids. The remapping approach is based on the conservative cascade method in which a two-dimensional remapping problem is split into two one-dimensional problems. This allows for easy implementation of high-order subgrid-cell reconstructions as well as the application of advanced monotone filters. The accuracy of CaRS is assessed by remapping analytic fields from the regular latitude–longitude grid to the cubed-sphere grid. In terms of standard error measures, CaRS is found to be competitive relative to an existing algorithm when regridding from a fine to a coarse grid and more accurate when regridding from a coarse to a fine grid.

Moving Vortices on the Sphere: A Test Case for Horizontal Advection Problems

Abstract A new two-dimensional advection test on the surface of the sphere is proposed. The test combines a solid-body rotation and a deformational flow field to form moving vortices over the surface of the sphere. The resulting time-dependent deforming vortex centers are located on diametrically opposite sides of the sphere and move along a predetermined great circle trajectory. The horizontal wind field is deformational and nondivergent, and the analytic solution is known at any time. During one revolution around the sphere the initially smooth transported scalar develops strong gradients. Such an approach is therefore more challenging than existing advection test cases on the sphere. To demonstrate the effectiveness and versatility of the proposed test, three different advection schemes are employed, such as a discontinuous Galerkin method on a cubed-sphere mesh, a classical semi-Lagrangian method, and a finite-volume algorithm with adaptive mesh refinement (AMR) on a regular latitude–longitude grid. The numerical results are compared with the analytic solution for different flow orientation angles on the sphere.

Fibonacci grids: A novel approach to global modelling

Recent years have seen a resurgence of interest in a variety of non-standard computational grids for global numerical prediction. The motivation has been to reduce problems associated with the converging meridians and the polar singularities of conventional regular latitude–longitude grids. A further impetus has come from the adoption of massively parallel computers, for which it is necessary to distribute work equitably across the processors; this is more practicable for some non-standard grids. Desirable attributes of a grid for high-order spatial finite differencing are: (i) geometrical regularity; (ii) a homogeneous and approximately isotropic spatial resolution; (iii) a low proportion of the grid points where the numerical procedures require special customization (such as near coordinate singularities or grid edges); (iv) ease of parallelization. One family of grid arrangements which, to our knowledge, has never before been applied to numerical weather prediction, but which appears to offer several technical advantages, are what we shall refer to as ‘Fibonacci grids’. These grids possess virtually uniform and isotropic resolution, with an equal area for each grid point. There are only two compact singular regions on a sphere that require customized numerics. We demonstrate the practicality of this type of grid in shallow-water simulations, and discuss the prospects for efficiently using these frameworks in three-dimensional weather prediction or climate models. © Crown copyright, 2006. Royal Meteorological Society

Removal of Systematic Biases in S-Mode Principal Components Arising from Unequal Grid Spacing

Abstract Frequently, physical variables are analyzed using gridded fields, on regular latitude–longitude frameworks. Such networks often concentrate a disproportionate number of observations over polar regions. If these types of grids are used for an S-mode principal component analysis, they produce a bias of the component patterns toward the temporal patterns observed at higher latitudes. A method to potentially eliminate this effect, while employing the covariance similarity matrix, is to weight the variables by the square root of the cosine of the latitude of the point at which the datum was observed. However, this processing is not useful when using the correlation similarity matrix. In this case, a spatially uniform or equal density grid can be designed by means of the criteria of a constant density of points in each circle of latitude. Then, the variable values are linearly interpolated into this new equal-density grid. This technique is easy to program and to adapt to any regular latitude–longitude...