High Resolution Limited Area Model Research Articles

Evaluation of an integrated modelling system containing a multi-layer perceptron model and the numerical weather prediction model HIRLAM for the forecasting of urban airborne pollutant concentrations

In this paper, a multi-layer perceptron (MLP) model and the Finnish variant of the numerical weather prediction model HIRLAM (High Resolution Limited Area Model) were integrated and evaluated for the forecasting in time of urban pollutant concentrations. The forecasts of the combination of the MLP and HIRLAM models are compared with the corresponding forecasts of the MLP models that utilise meteorologically pre-processed input data. A novel input selection method based on the use of a multi-objective genetic algorithm (MOGA) is applied in conjunction with the sensitivity analysis to reduce the excessively large number of potential meteorological input variables; its use improves the performance of the MLP model. The computed air quality forecasts contain the sequential hourly time series of the concentrations of nitrogen dioxide (NO 2) and fine particulate matter (PM 2.5) from May 2000 to April 2003; the corresponding concentrations have also been measured at two urban air quality stations in Helsinki. The results obtained with the MLP models that use HIRLAM forecasts show fairly good overall agreement for both pollutants. The model performance is substantially better, when the HIRLAM forecasts are used, compared with those obtained both using either HIRLAM analysis data or meteorological pre-processor, for both pollutants. The performance of the currently widely used statistical forecasting methods (such as those based on neural networks) could therefore be significantly improved by using the forecasts of NWP models, instead of the conventionally utilised directly measured or meteorological pre-processed input data. However, the performance of all operational models considered is relatively worse in the course of air pollution episodes.

Precipitation and evaporation budgets over the Baltic Proper: observations and modelling

Precipitation and evaporation budgets over the Baltic Sea were studied in a concerted project called PEP in BALTEX (Pilot study of Evaporation and Precipitation in the Baltic Sea), combining extensive field measurements and modelling efforts. Eddy-correlation-measurements of turbulent heat flux were made on a semi-continuous basis for a 12 month period at four well-exposed coastal sites in the Baltic Proper (the main basin of the Baltic Sea). Precipitation was measured at land-based sites with standard gauges and on four merchant ships travelling between Germany and Finland with the aid of specially designed ship rain gauges (SRGs). The evaporation and precipitation regime of the Baltic Sea was modelled for a 12 month period by applying a wide range of numerical models: the operational atmospheric High Resolution Limited Area Model (HIRLAM, Swedish and Finnish versions), the German atmospheric REgional-scale MOdel, REMO, the operational German Europe Model (only precipitation), the oceanographic model PRO...

Applicability of Large-Scale Convection and Condensation Parameterization to Meso-γ-Scale HIRLAM: A Case Study of a Convective Event

Abstract This paper presents a case study of a single cold air outbreak event with widespread convective precipitation over southern Finland on 25 May 2001. The purpose of the study is to investigate the applicability of the convection and condensation scheme of the High-Resolution Limited Area Model (HIRLAM) on meso-γ-scales. The study concentrates on the issue of grid-size-dependent convection parameterization. An explicit approach without the convection scheme is also examined. At the same time, the performance of an experimental nonhydrostatic version of HIRLAM is evaluated. Model simulations are conducted with three different horizontal grid spacings: 11, 5.6, and 2.8 km. Model results are compared to observed radar reflectivity data utilizing a radar simulation model, which calculates radar reflectivities from three-dimensional model output. The best results are obtained using nonhydrostatic dynamics and a grid-size-dependent convection scheme with a 5.6-km grid interval. However, even the best configuration still overestimates the area of strong reflectivity (intense precipitation). All the other combinations produce even stronger reflectivity. The grid-size-dependent convection parameterization is evidently beneficial at smaller grid spacings than 5.6 km. The nonhydrostatic model clearly outperforms its hydrostatic counterpart at the 5.6- and 2.8-km grid spacings, whereas with an 11-km grid interval, both models perform equally well.

Evaluation of two versions of the HIRLAM numerical weather prediction model during an air pollution episode in southern Finland

Abstract The main objective of this work is to evaluate the performance of two operational versions of the numerical weather prediction model HIRLAM (HIgh Resolution Limited Area Model) in severe wintertime air pollution conditions. The evaluation has been done by comparing the predicted temperature, wind speed and relative humidity with observational data during one specific episode in December 1995. Simulations were executed with versions 4.6.2 (operational 1999–2003) and 6.2.1 (operational since 2004) of the HIRLAM model. During 27–29 December 1995, an area of high pressure was formed over Southern Scandinavia and Finland, leading to the formation of an exceptionally strong ground-based temperature inversion. According to radiosonde measurements, the maximum strength of the inversion was 18 °C at Jokioinen. These conditions caused poor air quality for 2 days, especially in the Helsinki Metropolitan Area. The simulations with both model versions were able to predict the occurrence of the inversions, but the surface temperatures and wind speeds near the surface were generally overestimated, thus leading to underestimation of the strength of the inversion. However, the more recent model version performed better in predicting the ground-based inversions. The improved performance of the more recent model version is probably due to both the improved surface parameterisation and the better vertical resolution in the lowest atmospheric layers, compared with those of the older model version.

Probabilistic Forecasting of (Severe) Thunderstorms in the Netherlands Using Model Output Statistics

Abstract The derivation and verification of logistic regression equations for the (conditional) probability of (severe) thunderstorms in the warm half-year (from mid-April to mid-October) in the Netherlands is described. For 12 regions of about 90 km × 80 km each, and for projections out to 48 h in advance (with 6-h periods), these equations have been derived using model output statistics (MOS). As a source for the predictands, lightning data from the Surveillance et d’Alerte Foudre par Interférométrie Radioélectrique (SAFIR) network have been used. The potential predictor dataset mainly consisted of the combined (postprocessed) output from two numerical weather prediction (NWP) models. It contained 15 traditional thunderstorm indices, computed from the High-Resolution Limited-Area Model (HIRLAM), and (postprocessed) output from the European Centre for Medium-Range Weather Forecasts (ECMWF) model. The most important predictor in the thunderstorm forecast system is the square root of the ECMWF 6-h convective precipitation sum, and the most important predictor in the severe thunderstorm forecast system is the HIRLAM Boyden index. The success of the square root of the ECMWF 6-h convective precipitation sum as a thunderstorm predictor indicates that there is a strong relation between the forecast convective precipitation by the ECMWF model and the occurrence of thunderstorms, at least in the Netherlands up to 3 days in advance. The overall verification results for the 0000, 0600, 1200, and 1800 UTC runs of the MOS (severe) thunderstorm forecast system are good, and, therefore, the system was made operational at the Royal Netherlands Meteorological Institute (KNMI) in April 2004.

A Multi-Trajectory Chemical-Transport Vectorized Gear Model: 3-D Simulations and Model Validation

A new multi-trajectory highly vectorizable Gear chemical-transport model is discussed and tested against measurements from 25 sites in Europe for a two-week summer period. The simulations are compared with measurement data and with results of a Quasi-Steady-State Approximation (QSSA) based Lagrangian model using the EMEP mechanism. The model is developed from the Lagrangian EMEP model. The Regional Atmospheric Chemistry Mechanism (RACM) is used as the model’s chemical mechanism. To solve the stiff chemical rate equations, a sparse-matrix highly vectorizable Gear algorithm is used. The meteorological data used to run the model are obtained from the HIgh Resolution Limited Area Model (HIRLAM). The vectorized Gear based model improves the accuracy of the numerical solution for the chemistry compared with the QSSA based model. The differences between the two models are explained by alternative approaches of the chemical modules employed in the model: a Gear algorithm versus a QSSA solver, photolysis rate parameters in RACM are calculated from a radiation transfer code versus parameterized photolysis rate parameters used in the Lagrangian EMEP model, the RACM versus the EMEP atmospheric chemical mechanisms and two methods of aggregating the emissions of Volatile Organic Compounds (VOC). Photolysis rate parameters calculated from radiation codes (which are more accurate than simple parameterizations) and the Gear algorithm (which is a benchmark solver compared with the QSSA solver) are recommended for atmospheric chemistry modeling because of the high sensitivity of ozone concentrations to the chemical reaction scheme and to the photolysis rates (Stockwell and Goliff, 2004).

Estimation of Spatial Global Positioning System Zenith Delay observation error covariance

In this paper, we present new methods and estimates of the spatial (horizontal) covariance of the ground-based Global Positioning System Zenith Delay observation errors. An algorithm is developed which enables estimation of the observation error covariance as a linear combination of innovation covariances of Zenith Total Delay (ZTD) at ground-based receiver stations, surface pressure at synoptic stations and integrated water vapour at radiosonde stations, respectively. Innovation (observation minus model background) sequences computed with the High-Resolution Limited Area Model (HIRLAM) are used as statistical material for the estimation.We present a four-parameter exponential observation error covariance model for the ZTD horizontal observation error covariance. Seasonal and yearly mean models are provided for implementation into meteorological data assimilation systems.

Performance of HIRLAM in a Semiarid Heterogeneous Region: Evaluation of the Land Surface and Boundary Layer Description Using EFEDA Observations

Observations from the European Field Experiment in a Desertification-threatened Area (EFEDA) are used to evaluate the performance of the radiation, land surface, and boundary layer description of the numerical weather prediction (NWP) system High-Resolution Limited Area Model (HIRLAM) in semiarid conditions. Model analysis and 6-h forecast data of the fully coupled three-dimensional model are compared with the comprehensive dataset of a case study representing a sample of 22 days of anticyclonic conditions. Distributed micrometeorological surface stations, radiosondes, flux aircraft, and airborne lidar provide a unique validation dataset of the diurnal cycle of surface and boundary layer processes. The model surface, soil, and boundary layer are found to be too moist and slightly too cold during most of the diurnal cycle. The model radiation and surface energy budgets are biased toward more humid conditions. Model shortcomings are identified essentially in four areas. These are the moisture data assimilation, the landuse and soil classification with its associated physiographic database, the aerosol parameterization in the radiation code, and the boundary layer vertical resolution and entrainment description. Practical steps for immediate improvement of the model performance are proposed. They focus on the use of a land-use and soil classification and physiographic database adapted to Mediterranean landscapes, in combination with the inclusion of aerosol parameters in the radiation scheme, that account for the typically higher aerosol load of arid and semiarid environments.

Loading effects in Metsähovi from the atmosphere and the Baltic Sea

Abstract Loading by atmosphere and by the Baltic Sea cause gravity change at Metsahovi, located 15 km from the open sea. Gravity is changed by both the Newtonian attraction of the loading mass and by the crustal deformation. We have performed loading calculations using appropriate Green's function for both gravity and deformation, for both atmospheric and Baltic loading. The loading by atmosphere has been computed using a detailed surface pressure field from high resolution limited area model (HIRLAM) for north Europe up to 10° distances. Baltic Sea level is modelled using tide gauge records. Calculations show that 1 m of uniform layer of water corresponds to 31 nm s−2 in gravity and −11 mm in height. Modelled loading is compared with observations of the superconducting gravimeter T020 for years 1994–2002. The combination of HIRLAM and a tide gauge record decreases RMS of gravity residuals by 14% compared to single admittance in air pressure corrections without sea level data. Regression of gravity residuals on the tide gauge record at Helsinki (at 30 km distance) gives a gravity effect of 26 nm s−2 m−1 for Baltic loading. The gravity station is co-located with a permanent GPS station. We have also associated the loading effects of the atmosphere and of the Baltic Sea with temporal height variations. The range of modelled vertical motion due to air pressure was 46 mm and that due to sea level 18 mm. The total range was 38 mm. The effects of the Baltic Sea and of the atmosphere partly cancel each other, since at longer periods the inverse barometer assumption is valid. Regression of the modelled height on local air pressure gives −0.37 mm hPa−1, corresponding approximately to width 6° for pressure system. We have tested the models using one year of daily GPS data. Multilinear regression on local air pressure and sea level in Helsinki gives the coefficient −0.34 mm hPa−1 for pressure, and −11 mm m−1 for sea level. These match model values. Loading by air pressure and Baltic Sea explains nearly 40% of the variance of daily GPS height solutions.

An updated length‐scale formulation for turbulent mixing in clear and cloudy boundary layers

AbstractA new mixing‐length scale is presented for turbulence‐closure schemes, with special emphasis on neutral‐to‐convective conditions in clear and cloudy boundary layers. The length scale is intended for a prognostic turbulent‐kinetic‐energy closure. It is argued that present‐day length‐scale formulations may easily fail in one of two limiting situations. Schemes based on a local stability measure (e.g. the Richardson number) display unrealistic behaviour and instabilities in the convective limit. This strongly limits the representation of mixing in cloudy boundary layers. On the other hand, it is shown that non‐local parcel methods may misrepresent mixing near the surface. The new length‐scale formulation combines local and non‐local stability in a new way; it uses vertical integrals over the stability (the Richardson number) in a simple ‘parcel’ framework. The length scale matches with surface‐layer similarity for near‐neutral conditions and displays a realistic convective limit. The use of the length‐scale formulation can be extended easily to cloudy boundary layers. The scheme is numerically stable and computationally cheap. The behaviour of the length scale is evaluated in a single‐column model (SCM) and in a high‐resolution limited‐area model (LAM). The SCM shows good behaviour in three cases with and without boundary‐layer clouds. The prediction of the near‐surface wind and temperature in the LAM compares favourably with tower measurements at Cabauw (the Netherlands). Copyright © 2004 Royal Meteorological Society

Pollutant transport schemes integrated in a numerical weather prediction model: model description and verification results

AbstractRegional air pollution models are usually off‐line coupled with numerical weather prediction models. The present study, however, focuses on on‐line coupled modelling, for which the air pollution model is an integral part of the meteorological model. To this purpose, simulations of the first European Tracer Experiment (ETEX), which supplies the best suited verification data for dispersion modelling of a passive tracer, have been performed using versions of the Danish Meteorological Institute High Resolution Limited‐Area Model (DMI‐HIRLAM). Simulation results have been compared with observed values as well as with results from other models.The operational version of DMI‐HIRLAM using well‐known basic advection schemes has been tested, showing the need for improvements for air pollution purposes. The fourth‐order Bott algorithm for advection has thus been implemented in the semi‐Lagrangian version of DMI‐HIRLAM. Due to its practically perfect mass conservation properties and its low computational cost, this method turns out to be efficient for simulations of transport of pollutants in the atmosphere. This represents a first effort towards a fully integrated air pollution model, e.g. for forecasting purposes. Copyright © 2004 Royal Meteorological Society

Doppler Radar Wind Data Assimilation with HIRLAM 3DVAR

Abstract A Doppler radar wind data assimilation system has been developed for the three-dimensional variational data assimilation (3DVAR) scheme of the High Resolution Limited Area Model (HIRLAM). Radar wind observations can be input for the multivariate HIRLAM 3DVAR either as radial wind superobservations (SOs) or as vertical profiles of horizontal wind obtained with the velocity–azimuth display (VAD) technique. The radar wind data handling system, including data processing, quality control, and observation operators for the 3DVAR, are described and evaluated. Background error standard deviation (σb) in observation space for wind and radial wind have been estimated by the so-called randomization method. The derived values of σb are used in the quality control of observations and also in the assignment of radar wind observation error standard deviations (σo). Parallel data assimilation and forecast experiments confirm reasonably tuned error statistics and indicate a small positive impact of radar wind dat...

Three‐dimensional simulation of the ASTEX Lagrangian 1 field experiment with a regional numerical weather prediction model

AbstractThe Atlantic Stratocumulus Transition Experiment (ASTEX) first Lagrangian experiment (Lagrangian 1) is here simulated with a modified version of the regional forecast model HIRLAM (High Resolution Limited Area Model). The main modification is that moist turbulent fluxes are accounted for in the model. Trajectory calculations show good agreement with earlier estimations. The initially rather shallow stratocumulus topped marine boundary layer is deepening along the trajectory, and in the end cumulus clouds are formed that penetrate the boundary‐layer top. The model predicts this change in cloudiness, but the boundary layer is too shallow in the model. A simulation with modified initial conditions shows improved results, but is still too slow in increasing the boundary‐layer depth. Additional factors that influence the boundary‐layer growth are: the increase in sea surface temperatures, lower modelled wind speeds, low entrainment rates due to coarse vertical resolution, and synoptic‐scale subsidence.An anticyclone at the surface moved slightly northward during the simulation. The anticyclone was accompanied at 500 hPa by a deepening cyclone and, therefore, one would expect synoptic subsidence in the area of the Lagrangian 1. The modelled negative vertical wind component at the boundary‐layer top oscillates, and this is examined using spectral analysis. The results show that the vertical velocity is influenced by cumulus clouds on time‐scales up to 15 h with a peak at 9 h. The horizontal and vertical wavelengths of the vertical velocity disturbances are estimated from model output to be 400–500 km and 6–10 km, respectively. Using the estimated vertical wavelength and linear theory for hydrostatic inertia–gravity waves, a horizontal wavelength of 350–550 km was calculated for a frequency of 9 h. The model results thus indicate that these types of waves are responsible for the undulating vertical velocity.Finally, an estimation of the synoptic‐scale vertical velocity is calculated by filtering out all scales smaller than 15 h from the vertical velocity signal. This results in subsidence both at the beginning and the end of the Lagrangian with vertical velocities between −0.1 and −0.4 cm s−1. Copyright © 2004 Royal Meteorological Society

Assimilation of the GPS-derived integrated water vapour (IWV) in the MeteoSwiss numerical weather prediction model––a first experiment

A high resolution (7 km) limited area model called aLpine model (aLMo) is used for operational numerical weather prediction (NWP) at MeteoSwiss. A continuous data assimilation scheme based on the nudging technique produces the initial conditions for the forecast. Since November 2001 all standard meteorological observations have been routinely assimilated. The goal of this study is to evaluate the benefit of introducing GPS-derived integrated water vapour (IWV) in this scheme. In this first observing system experiment, data provided for COST action 716 “Exploitation of ground based GPS for climate and numerical weather prediction application” are used. A two week period in mid September 2001 was selected, characterized by an advective weather regime and intense precipitation events. On average observations from 80 European GPS sites are assimilated by the model. Results presented here are based on the aLMo assimilation cycle only, the impact on the forecast has not been evaluated. This experiment shows a tendency for GPS data to increase the model IWV amounts in the day-time, and shows a substantial impact of GPS in the southern part of the model domain. The negative bias of the model IWV daily cycle is mainly corrected by assimilating GPS data. An improvement of the daily precipitation cycle over Switzerland for the grid points below 800 m is also observed in the GPS run. The bias precipitation score confirms the better model performance when the GPS data are assimilated. This experiment has also revealed a weakness in the way the IWV is assimilated. In presence of highly inhomogeneous humidity fields an isotropic influence of the IWV increments can be detrimental. The first GPS assimilation results are considered encouraging but need to be consolidated. New assimilation experiments will be performed to investigate the GPS data impact for different weather regimes.

Effective Roughness Calculated from Satellite-Derived Land Cover Maps and Hedge-Information used in a Weather Forecasting Model

In numerical weather prediction, climate and hydrologicalmodelling, the grid cell size is typically larger than the horizontal length scales of variations in aerodynamicroughness, surface temperature and surface humidity. These local land cover variations give rise to sub-gridscale surface flux differences. Especially the roughness variations can give a significantly differentvalue between the equilibrium roughness in each of the patches as compared to the aggregated roughness value,the so-called effective roughness, for the grid cell. The effective roughness is a quantity that secures thephysics to be well-described in any large-scale model. A method of aggregating the roughness step changesin arbitrary real terrain has been applied in flat terrain (Denmark) where sub-grid scale vegetation-drivenroughness variations are a dominant characteristic of the landscape. The aggregation model is a physicaltwo-dimensional atmospheric flow model in the horizontal domain based on a linearized version of theNavier Stoke equation. The equations are solved by the Fast Fourier Transformation technique, hence the codeis very fast. The new effective roughness maps have been used in the HIgh Resolution Limited Area Model(HIRLAM) weather forecasting model and the weather prediction results are compared for a number of casesto synoptic and other observations with improved agreement above the predictions based on currentstandard input. Typical seasonal springtime bias on forecasted winds over land of +0.5 m s-1 and-0.2 m s-1 in coastal areas is reduced by use of the effective roughness maps.

Accuracy and Variability of GPS Tropospheric Delay Measurements of Water Vapor in the Western Mediterranean

Abstract As a preliminary step for assessing the impact of global positioning system (GPS) refractive delay data in numerical weather prediction (NWP) models, the GPS zenith tropospheric delays (ZTDs) are analyzed from 51 permanent GPS sites in the western Mediterranean. The objectives are to estimate the error statistics necessary for future assimilation of GPS ZTD data in numerical models and to investigate the variability of the data in this area. The time series, which were derived continuously from November 1998 to June 2001, are compared with independent equivalent values derived from radiosonde profiles and the High-Resolution Limited-Area Model (HIRLAM) NWP model. Based on over two years of data, the difference between radiosonde and GPS ZTD has a standard deviation of 12 mm of delay and a bias of 7 mm of delay. Some sites have biases as high as 14 mm of delay. The bimodal distribution of residuals, with a higher bias for daytime launches, indicates these biases may be due to radiosonde day–night ...

Validation and intercomparison of three mesoscale models on three FASTEX cloud systems: comparison with coarse‐resolution simulations

AbstractTaking advantage of the observations collected during the Fronts and Atlantic Storm‐Track EXperiment (FASTEX), three FASTEX midlatitude cloud systems are simulated with three state‐of‐the‐art, mesoscale, limited‐area models (the Met Office's Unified Model (UM), Met Éireann's High Resolution Limited Area Model (HIRLAM), and the French Laboratoire d'Aérologie research modèle de Méso‐échelle Non‐Hydrostatique (Méso‐NH)), at an 11 km horizontal resolution and with about 50 vertical levels. The dynamical, thermodynamic, cloud and precipitation fields obtained from these numerical integrations are then intercompared and validated against various observational sources, including radio‐ and dropsondes, satellite radiometer, and rain‐gauges. The similarities and the deficiencies of the three models are summarized in the paper. After this validation work, the mesoscale fields are degraded in resolution, so that they can be directly compared with the outputs of 300 km resolution simulations, run with Météo‐France's atmospheric general‐circulation model (AGCM) Action de Recherche Petite Echelle et Grande Echelle (ARPEGE). The deviations between the upscaled mesoscale models and the coarse AGCM turn out to be significant and highly dependent on the location relative to the storm, with, in particular, a large contrast between the trailing cold region and the warm sector with thick layer clouds, suggesting the existence of some deficiencies in the AGCM. Copyright © Royal Meteorological Society, 2003. Peter Clark's contribution is Crown copyright.

Nonhydrostatic generalization of a pressure-coordinate-based hydrostatic model with implementation in HIRLAM: validation of adiabatic core

A nonhydrostatic pressure-coordinate model of atmospheric dynamics is developed. The model filters acoustic mode. Internal acoustic waves are filtered using the assumption of non-divergence of motion in pressure-space. External (Lamb mode) waves are filtered using the surface pressure adjustment. The model is implemented in the framework of the numerical weather prediction model HIRLAM (High Resolution Limited Area Model) as an extension to the hydrostatic kernel. The integration scheme is either the explicit or semi-implicit Eulerian leapfrog time stepping. Due to the acoustic filtration, the explicit scheme supports quite large time-steps. To check the validity of the model, several flow experiments with artificial orography are performed. The hydrostatic and nonhydrostatic flow regimes are investigated. The results of different models are compared mutually and with the analytic solutions. The real situation simulations are also presented to show the model’s forecasting capabilities.

A numerical, high-resolution study of the life cycle of the severe storm over Denmark on 3 December 1999

A severe cyclone with destructive effects moved across Denmark during the evening of 3 December1999. A study, based on a numerical high-resolution limited area model simulation of this event, is presented. The development is of the frontal wave type. It can be interpreted qualitatively as aninteraction between a PV wave at the tropopause, a surface temperature wave on the polar frontand a low-level positive and upper-level negative PV anomaly generated by release of latent heat ofcondensation. In a run without this heat source the minimum sea level pressure in the cyclone increasedfrom 954 to 978 hPa. As a result of the PV anomaly interactions the surface cyclone moves from theanticyclonic to the cyclonic shear side of the upper-level jet during its evolution from an incipientlow to a mature cyclone. Its frontal structure evolves from an anticyclonic barotropic shear type toa barotropic type without shear. In the former state a low-level jet is confined to the warm sector ofthe surface cyclone. In the latter state a low-level bent-back front jet develops and becomes the mostintense low-level jet. The time-scale from initiation to maximum intensity of the jet is about 9 h. Therun without latent heat release develops similar, but weaker frontal structures, most notably a muchweaker bent-back front.

Comments on “A More Extensive Investigation of the Use of Ensemble Forecasts for Dispersion Model Evaluation”

In discussing the results obtained using the HighResolution Limited-Area Model (HIRLAM), Straume (2001) incorrectly credited to Mesinger (1984) the hybrid coordinate eta, which in the lowermost model layers follows the ground and in the upper layers follows the pressure surfaces. The hybrid coordinate eta with the described properties was proposed by Simmons and Burridge (1981). Although Mesinger considered his procedure to be a definition of a new coordinate and called it ‘‘eta,’’ Mesinger’s ‘‘eta coordinate’’ cannot in a strict sense be considered to be a valid coordinate system, given that it has continuum singularities above the edges