Rotating shallow water flow under location uncertainty with a structure-preserving discretization

We construct the generalized inverse of a global numerical weather prediction (NWP) model, in order to prepare initial conditions for the model at time “t=0 hrs”. The inverse finds a weighted, least-squares best-fit to the dynamics for −24<t<0, to the previous initial condition att=−24, and to data att=−24,t=−18,t=−12 andt=0. That is, the inverse is a weak-constraint, four-dimensional variational assimilation scheme. The best-fit is found by solving the nonlinear Euler-Lagrange (EL) equations which determine the local extrema of a penalty functional. The latter is quadratic in the dynamical, initial and data residuals. The EL equations are solved using iterated representer expansions. The technique yields optimal conditioning of the very large minimization problem, which has ∼109 hydrodynamical and thermodynamical variables defined on a 4-dimensional, space-time grid.

The presence of cities affects local ecosystems by changing the surface energy balance and introducing anthropogenic heat, greenhouse gases, and air pollutants into the atmosphere. Currently, over 50% of the global population resides in urban areas, which increases their exposure to risks related to extreme weather and climate change. To better forecast weather and address climate adaptation and mitigation challenges, numerical weather prediction (NWP) models are beginning to integrate urban physics. However, the absence of high-quality and comprehensive urban morphology data such as building heights and footprints is still a challenge. This study introduces a high-resolution (500 m) global database developed using open data sources to support regional and global weather and climate modeling and enhance the representation of urbanization in NWP models. WUMPOD contains following urban morphological parameters; MH (mean building height), STDH (standard deviation of building height), HGT (area weighted mean building height), LP (building plan area fraction), LB (building surface to plan area fraction), LF (frontal aspect ratio for cardinal directions of 0, 45, 90, and 135 degrees), LC (complete aspect ratio), H2W (height to width ratio), HI [0-75 m] (percentage distribution of building heights at every 5 m up to 75 m), Z0M, ZDM (Roughness length and displacement height according to Macdonald et al. (1998) for 0, 45, 90, and 135 directions), Z0S, ZDS (Roughness length and displacement height according to Grimmond and Oke (1999)), Z0R, and ZDR (Roughness length and displacement height according to Raupach (1994) for 0, 45, 90, and 135 directions) and urban fraction (from WorldCover 2021). The World Urban Morphological Parameter Open Dataset (WUMPOD) is available at https://doi.org/10.5281/zenodo.10039127. The dataset will be incorporated in the development of a global ancillary and a contribution to the UK Met Office Momentum partnership.

Since 1970, tropical cyclone (TC) track forecasts have improved steadily in the Atlantic basin. This improvement has been linked primarily to advances in numerical weather prediction (NWP) models. Concurrently, with few exceptions, the development and operational use of statistical track prediction schemes have experienced a relative decline. Statistical schemes provided the most accurate TC track forecasts until approximately the late 1980s. In this note, it is shown that increased reliance on the global NWP models does not always guarantee the best forecast. Here, Hurricane Ivan is used from the 2004 Atlantic TC season as a classical example, and reminder, of how strong climatological signals still can add substantial value to TC track forecasts, in the form of improved accuracy and increased timeliness at minimal computational cost. In an 8-day period in early September 2004, Hurricane Ivan was repeatedly, and incorrectly, forecast by 12 operational NWP models to move with a significant northward (poleward) component. It was found that the mean 24-h trajectory forecasts of a consensus of five commonly used NWP track prediction aids had a statistically significant right-of-track bias. Furthermore, the official track forecasts, which relied heavily on erroneous numerical guidance over this period, were also found to have significant poleward trajectory errors. At the same time, a climatology-based prediction technique, drawn entirely from the historical record of motion characteristics of TCs in geographical locations similar to Ivan, correctly and consistently indicated a more westward motion component, had a small directional spread, and was supported by a large number of archived cases. This climatological signal was in conflict with the deterministic NWP model output, and it is suggested that the large errors in the official track forecast for TC Ivan could have been reduced considerably by taking into greater account such a strong climatological signal. The potential impact of such an error reduction is a saving of lives and billions of dollars in both actual damage and unnecessary evacuations costs, for just this one hurricane. We also suggest that this simple strategy of examining the strength of the climatological signal be considered for all TCs to identify cases where the NWP and official forecasts differ significantly from strong, persistent climatological signals.

Warm conveyor belts (WBCs) are large-scale ascending airstreams found in extratopical cyclones. They constitute a major source of upper tropospheric/lower stratospheric (UTLS) water vapor&amp;#8212;a potent greenhouse gas&amp;#8212;and hydrometeors, which can form cirrus clouds. Therefore, WCBs play an important role for Earth&amp;#8217;s radiative budget. Additionally, WCBs transport large amounts of heat across latitudes and can influence large scale upper tropospheric circulation after their dissipation, underscoring their significance for Earth&amp;#8217;s weather and climate.Recent studies using high-resolution, convection-permitting simulations have shown that convection is a prominent feature of WCBs, with convective air parcels transporting significantly more hydrometeors into the UTLS than their slower-ascending counterparts. Furthermore, the cloud and precipitation development in convective air parcels is dominated by different processes than in slower ascending air. However, the global numerical weather prediction and climate models commonly used to assess the climatological and future impacts of WCBs operate at coarse grid resolutions (15&amp;#8211;50 km) that are not convection-permitting, relying instead on convection parametrization schemes. The widely used Tiedtke-Bechtold convection parameterization scheme is designed to simulate heat, moisture, and momentum transport in convective systems but includes only basic representations of cloud microphysics. This raises the question of whether low-resolution simulations fail to accurately represent the transport of hydrometeors into the UTLS by WCBs when compared to high-resolution, convection-permitting simulations.To address this, we analyze two simulations of the same WCB&amp;#8212;one convection-permitting and one using convection parameterization&amp;#8212;with a specific focus on vapor and hydrometeor transport. Our results show that the WCB in the high-resolution simulation transports substantially larger amounts of hydrometeors into the UTLS, while UTLS vapor conditions remain comparable between the two simulations. Microphysics processes also shift from liquid-dominated to frozen-dominated depending on the grid-scale.

Atmospheric aerosols have a significant impact on cloud formation and life cycle. Aerosols enhance cloud formation and affect microphysical and radiative properties of clouds by acting as Cloud Condensation Nuclei (CCN). Aerosol-cloud interactions are very complex, and thus accurate global-scale simulations are challenging. Aerosol-cloud interactions occur at a microscopic level, but cloud systems are often on a scale of tens or hundreds of kilometers. Accurate modeling of all aerosol-cloud processes at such a large scale is computationally demanding. Therefore, models simulating aerosols and their interactions with radiation and clouds, are usually greatly simplified, making them inaccurate. In this study, the accuracy of a simple aerosol model HAM-Lite will be enhanced with a machine-learning component, and the enhanced model will be coupled with a global kilometer-scale Numerical Weather Prediction (NWP) model OpenIFS. OpenIFS is used for global climate simulations and weather forecasting. It is an easy-to-use version of Integrated Forecasting System (IFS) by the European Centre for Medium-Range Weather Forecasts (ECMWF). IFS models the atmosphere in EC-Earth 3 climate model and it is developed by the European Consortium of National Meteorological Services and Research Institutes. OpenIFS will be the main atmospheric model in the upcoming EC-Earth version 4. HAM-Lite is a simplified version of a more complex aerosol model HAM-M7. While HAM-M7 includes seven log-normal aerosol modes and a total of twenty-five tracers, HAM-Lite describes only four tracers. HAM-M7 calculates microphysical processes, like nucleation, condensation and coagulation, as well as other processes like emissions and dry and wet deposition. HAM-Lite simplifies the processes by assuming constant hygroscopicity and very simplified calculations for extinction. These simplifications make the model computationally lighter. Since aerosol hygroscopicity and extinction are highly simplified in HAM-Lite, we will incorporate machine learning methods to provide a more accurate representation, bringing its performance closer to that of HAM-M7. Training data for the machine learning component will be produced with HAM-M7 coupled with OpenIFS. The new enhanced HAM-Lite aerosol model will also be coupled with OpenIFS for improved global scale simulations. By coupling the new enhanced aerosol model with the climate model, the aim is to make the system more accurate without significantly increasing the computational cost. Results from OpenIFS, with and without the enhanced aerosol model, will be compared to in situ measurements, satellite data, and simulations with other models. Expectation is that OpenIFS, coupled with the light aerosol module and machine learning methods, will achieve higher accuracy with reduced computational cost compared to OpenIFS coupled with HAM-M7. This research is funded by the European Union's Horizon EU -project Digital Twin of Earth System for Cryosphere, Land Surface, and Related Interactions – TerraDT 101187992.

Warm conveyor belts (WCBs) associated with extratropical cyclones transport air from the lower troposphere into the tropopause region and contribute to upper-level ridge building and the formation of blocking anticyclones. Recent studies indicate that this constitutes an important source and magnifier of forecast uncertainty and errors in numerical weather prediction (NWP) models. However, a systematic evaluation of the representation of WCBs in NWP models has yet to be determined. Here, we employ the logistic regression models developed in Part I to identify the inflow, ascent, and outflow stages of WCBs in the European Centre for Medium-Range Weather Forecasts (ECMWF) subseasonal reforecasts for Northern Hemisphere winter in the period January 1997 to December 2017. We verify the representation of these WCB stages in terms of systematic occurrence frequency biases, forecast reliability, and forecast skill. Systematic WCB frequency biases emerge already at early lead times of around 3 days with an underestimation for the WCB outflow over the North Atlantic and eastern North Pacific of around 40% relative to climatology. Biases in the predictor variables of the logistic regression models can partially explain these biases in WCB inflow, ascent, or outflow. Despite an overconfidence in predicting high WCB probabilities, skillful WCB forecasts are on average possible up to a lead time of 8–10 days with more skill over the North Pacific compared to the North Atlantic region. Our results corroborate that the current limited forecast skill for the large-scale extratropical circulation on subseasonal time scales beyond 10 days might be tied to the representation of WCBs and associated upscale error growth.

In this study we examine the determination accuracy of both the mean radiant temperature (Tmrt) and the Universal Thermal Climate Index (UTCI) within the scope of numerical weather prediction (NWP), and global (GCM) and regional (RCM) climate model simulations. First, Tmrt is determined and the so-called UTCI-Fiala model is then used for the calculation of UTCI. Taking into account the uncertainties of NWP model (among others the HIgh Resolution Limited Area Model HIRLAM) output (temperature, downwelling short-wave and long-wave radiation) stated in the literature, we simulate and discuss the uncertainties of Tmrt and UTCI at three stations in different climatic regions of Europe. The results show that highest negative (positive) differences to reference cases (under assumed clear-sky conditions) of up to -21°C (9°C) for Tmrt and up to -6°C (3.5°C) for UTCI occur in summer (winter) due to cloudiness. In a second step, the uncertainties of RCM simulations are analyzed: three RCMs, namely ALADIN (Aire Limitée Adaptation dynamique Développement InterNational), RegCM (REGional Climate Model) and REMO (REgional MOdel) are nested into GCMs and used for the prediction of temperature and radiation fluxes in order to estimate Tmrt and UTCI. The inter-comparison of RCM output for the three selected locations shows that biases between 0.0 and ±17.7°C (between 0.0 and ±13.3°C) for Tmrt (UTCI), and RMSE between ±0.5 and ±17.8°C (between ±0.8 and ±13.4°C) for Tmrt (UTCI) may be expected. In general the study shows that uncertainties of UTCI, due to uncertainties arising from calculations of radiation fluxes (based on NWP models) required for the prediction of Tmrt, are well below ±2°C for clear-sky cases. However, significant higher uncertainties in UTCI of up to ±6°C are found, especially when prediction of cloudiness is wrong.

The Beginnings of Numerical Weather Prediction and General Circulation Modeling: Early Recollections

Artificial intelligence and numerical weather prediction models: A technical survey

Human‐induced changes in atmospheric composition, particularly from aerosols and ozone pollution, significantly impact weather forecasting. Establishing a chemical weather model is essential to more accurately and effectively account for these effects. The stratosphere serves as primary ozone reservoir, but the Chinese Unified Atmospheric Chemistry Environment (CUACE) model lacks a dedicated stratospheric module, limiting accurate simulation of stratospheric ozone variability. Therefore, a stratospheric module is developed within CUACE and coupled online to the global weather prediction model, forming a novel global chemical weather (GCW) model. Critical technical advancements in parallel computation acceleration, optimized array conversion, precision interpolation, stratospheric boundary definition, and standardized unit conversion collectively enhance forecasting timeliness and stability. Benchmarked against reanalysis data, the GCW model successfully captures stratospheric ozone spatial distribution (R2 = 0.64–0.90), with radiative feedback implementation reducing stratospheric temperature prediction biases by 1.8–5.4 K. The newly established GCW model enhances environmental forecasts and climate resilience strategies.

One of the sources of uncertainties in climate models and numerical weather prediction (NWP) models is cirrus clouds. They are highly sensitive to subgrid-scale dynamics, such as gravity waves (GWs) and turbulence, making them challenging to model in detail within coarse-resolution settings.&amp;#160; Additionally, their net radiative effect remains poorly understood, highlighting the importance of accurately representing their microphysical properties as one of the main areas of focus for research and model refinement.The current work focuses on a coupled approach to GW&amp;#8211;ice microphysics interactions and its application in the global NWP model ICON. The ice scheme, developed by Dolaptchiev et al. (J. Atmos. Sci., 2023), describes GW-induced homogeneous nucleation of ice crystals and proposes a prototype parameterization used in this study. The representation of a local GW field is diagnosed using the Multi-Scale Gravity Wave Model (MS-GWaM) parameterization. MS-GWaM parameterization supports multiple GW source types, and allows for 3D GW propagation, enhancing its physical realism. The full coupling of GW forcing, along with feedback from the new scheme into the overall microphysics and radiation schemes, has been implemented in a test regime in ICON model.To validate the approach and assess the impact of GWs, several global ICON simulations were conducted. The results show a significant influence of GWs on ice number density, indicating higher concentrations of ice crystals in tropical regions. These findings highlight the potential of the coupled approach to improve predictions of cloud microphysics and their radiative impacts. Further investigations will explore the role of different GW sources and account for the superposition of GWs, offering deeper insights into the broader effects of GW representation on global atmospheric processes.

Lakes influence the structure of the atmospheric boundary layer and, consequently, the local weather and local climate. Their influence should be taken into account in the numerical weather prediction (NWP) and climate models through parameterisation. For parameterisation, data on lake characteristics external to the model are also needed. The most important parameter is the lake depth. Global database of lake depth GLDB (Global Lake Database) is developed to parameterise lakes in NWP and climate modelling. The main purpose of the study is to upgrade GLDB by use of indirect estimates of the mean depth for lakes in boreal zone, depending on their geological origin. For this, Tectonic Plates Map, geological, geomorphologic maps and the map of Quaternary deposits were used. Data from maps were processed by an innovative algorithm, resulting in 141 geological regions where lakes were considered to be of kindred origin. To obtain a typical mean lake depth for each of the selected regions, statistics from GLDB were gained and analysed. The main result of the study is a new version of GLDB with estimations of the typical mean lake depth included. Potential users of the product are NWP and climate models.

The global navigation satellite system (GNSS) can provide centimeter positioning accuracy at low costs. However, in order to obtain the desired high accuracy, it is necessary to use high-quality atmospheric models. We focus on the troposphere, which is an important topic of research in Brazil where the tropospheric characteristics are unique, both spatially and temporally. There are dry regions, which lie mainly in the central part of the country. However, the most interesting area for the investigation of tropospheric models is the wet region which is located in the Amazon forest. This region substantially affects the variability of humidity over other regions of Brazil. It provides a large quantity of water vapor through the humidity convergence zone, especially for the southeast region. The interconnection and large fluxes of water vapor can generate serious deficiencies in tropospheric modeling. The CPTEC/INPE (Center for Weather Forecasting and Climate Studies/Brazilian Institute for Space Research) has been providing since July 2012 a numerical weather prediction (NWP) model for South America, known as Eta. It has yield excellent results in weather prediction but has not been used in GNSS positioning. This NWP model was evaluated in precise point positioning (PPP) and network-based positioning. Concerning PPP, the best positioning results were obtained for the station SAGA, located in Amazon region. Using the NWP model, the 3D RMS are less than 10 cm for all 24 h of data, whereas the values reach approximately 60 cm for the Hopfield model. For network-based positioning, the best results were obtained mainly when the tropospheric characteristics are critical, in which case an improvement of up to 7.2 % was obtained in 3D RMS using NWP models.

In the absence of convection permitting numerical weather prediction (NWP) ensembles, the most recent deterministic NWP precipitation forecast is usually addressed. However, the exact intensity, location and timing of a deterministic precipitation forecast is not always reliable because of the chaotic nature and complexity of precipitation formation mechanisms. This study examines a way to optimize the use of precipitation forecasts for deterministic NWP models. More specifically, it suggests using a spatially smoothed time‐lagged ensemble (TLE) to obtain more reliable precipitation forecasts. A global NWP model (integrated forecast system—IFS) and a regional convection permitting NWP model (COSMO) over the Eastern Mediterranean during the period 2016–2018 were used for the analysis. First, the paper defines light, light–moderate and moderate intensities for 6 hr accumulated precipitation (6hAP) and investigates the corresponding definitions for 1 hr accumulated precipitation (1hAP). Next, fractional skill score (FSS) are used to estimate the optimal spatial smoothing scale of a deterministic precipitation forecast for the three intensity categories for the 6hAP and 1hAP. The FSS is also used to compare COSMO and IFS deterministic precipitation forecasts, and to analyse the skill degradation with the forecast range. It is quantitatively shown that the useful scale of precipitation forecasts is smaller for larger accumulation time intervals. Finally, precipitation forecasts for TLE are formed from successive smoothed deterministic forecasts and compared with the most recent deterministic forecast. It is found that, on average, TLEs have better skills for both 6hAP and 1hAP. The reason for this improvement in skill is illustrated using a case study as an example.

Prediction of tropical cyclones (TCs) beyond a week is challenging but of great importance for disaster prevention and mitigation. We propose a hybrid machine learning (ML)/physics‐based modeling framework to extend TC forecasts to 2 weeks. This framework integrates a recently launched ML‐based global weather prediction model (Pangu) and the high‐resolution physics‐based regional weather research and forecasting (WRF) model. The Pangu model shows promise in enhancing the accuracy of predictions for large‐scale circulation and TC tracks, while the high‐resolution WRF model is capable of capturing the core processes underlying TC evolution. To capitalize on the complementary strengths of both the Pangu and WRF models in predicting TCs, the framework comprises three key components: downscaling the Pangu model using the WRF model, adjusting large‐scale circulation through spectral nudging driven by the Pangu model forecasts, and updating sea surface temperature using an ocean mixed‐layer model. These components also ensure the framework's feasibility for real‐time TC forecasting. The prediction skill of the framework has been demonstrated for five long‐lived TCs across various basins from 2018 to 2023. Results indicate that the hybrid ML/physics‐based modeling framework decreased the 2‐week mean TC track and intensity errors by 59% and 32% compared to the global numerical weather prediction models, by 2% and 59% compared to the ERA5‐driven Pangu model, and by 32% and 23% compared to the ERA5‐driven WRF model, respectively. This implies that the framework has great potential to be used for 2‐week extended prediction of TCs.