Dominant Role of Initial Error in Weather Predictability Through the Study on Saturation Value

In this note, we consider numerical methods for a class of Hamiltonian systems that preserve the Hamiltonian. We show that the rate of growth of error is at most linear in time when such methods are applied to problems with period uniquely determined by the value of the Hamiltonian. This contrasts to generic numerical schemes, for which the rate of error growth is superlinear. Asymptotically, the rate of error growth for symplectic schemes is also linear. Hence, Hamiltonian-conserving schemes are competitive with symplectic schemes in this respect. The theory is illustrated with a computation performed on Kepler's problem for the interaction of two bodies.

The Pegasus breakup is characterized by distributions of the orbital parameters and radar cross section of the pieces. The accuracy of the Simplified General Perturbations 4 (SGP4) element sets for the Pegasus breakup has been examined using the Space Surveillance Performance Analysis Tool. A graph of the average error growth rate (EGR) of the Pegasus breakup element sets over time shows pronounced spikes on certain days. Comparing graphs of EGR versus BSTAR (the term in SGP4 that accounts for unmodeled in-track forces, including drag) for all the Pegasus breakup pieces on a day when the average EGR is low and a day when the average is high shows that the element sets with large BSTAR values are susceptible to large variations in EGR. A graph of the average EGR and daily maximum planetary geomagnetic index Ap over times shows that the spikes in EGR are associated with geomagnetic storms. To reduce the size of the spikes in EGR, the length of update interval (LUPI) for the batch differential corrections of the element sets was shortened. To support catalog maintenance of the Pegasus breakup pieces with shorter LUPIs, additional sensors were tasked for observations.

El Niño and the Southern Oscillation (ENSO) have a worldwide impact on seasonal to yearly climate. However, there are decadal variations in the seasonal prediction skill of ENSO in dynamical and statistical models; in particular, ENSO prediction skill has declined since 2000. The shortcomings of models mean that it is very important to study ENSO seasonal predictability and its decadal variation using observational/reanalysis data. Here we quantitatively estimate the seasonal predictability limit (PL) of ENSO from 1900 to 2015 using Nonlinear local Lyapunov exponent (NLLE) theory with an observational/reanalysis dataset and explore its decadal variations. The mean PL of sea surface temperature (SST) is high in the central/eastern tropical Pacific and low in the western tropical Pacific, reaching 12–15 and 7–8 months, respectively. The PL in the tropical Pacific varies on a decadal timescale, with an interdecadal standard deviation of up to 2 months in the central tropical Pacific that has similar spatial structure to the mean PL. Taking the PL of SST in the Niño 3.4 region as representative of the PL in the central/eastern tropical Pacific, there are clearly higher values in the 1900s, mid-1930s, mid-1960s, and mid-1990s, and lower values in the 1920s, mid-1940s, and mid-2010s. Meanwhile, the PL of SST in the Niño 6 region—whose average value is 7 months—is in good agreement with the PL of most regions in the western tropical Pacific, with higher values in the 1910s, 1940s, and 1980s and lower values in the 1930s, 1950s, and mid-1990s. In the framework of NLLE theory, the PL is determined by the error growth rate (representing the dissipation rate of the predictable signal) and the saturation value of relative error (representing predictable signal intensity). We reveal that the spatial structure of the mean PL in the tropical Pacific is determined mainly by the error growth rate. The decadal variability of PL is affected more by the variation of the saturation value of relative error in the equatorial Pacific, whereas the error growth rate cannot be ignored in the PL of some regions. As an important source of predictability in ENSO dynamics, the relationship between warm water volume and SST in the Niño 3.4 region has a critical role in the decadal variability of PL in the tropical Pacific through the error growth rate and saturation value of relative error. This strong relationship reduces the error growth rate in the initial period and increases the saturated relative error, contributing to the high PL.

Flooding is a recurring issue in North Barito Regency due to the overflow of the Barito River. Weather forecasts in the region rely mainly on Numerical Weather Prediction (NWP) models, which often fail to capture local details due to their grid-based homogenization. To address this limitation, statistical techniques such as Model Output Statistics (MOS) can enhance NWP outputs by representing local conditions more accurately . MOS establishes statistical relationships between response variables (predictands) and predictor variables derived from NWP outputs, enabling operational applications without the need for advanced instruments. This study utilizes rainfall data from 2021-2022 from the Beringin Meteorological Station in North Barito as the response variable, while data from the Integrating Forecasting System (IFS) model serve as the predictor variables. The Support Vector Machine (SVM) method is employed to identify the relationship between predictor and response variables. By integrating the MOS technique with the SVM method, this research aims to improve the accuracy of weather forecasting, particularly for short-term predictions in North Barito. This approach demonstrates the potential to enhance localized weather predictions by addressing the limitations of conventional NWP models. The results indicate a consistent reduction in RMSE across all experiments conducted. Furthermore, the SVM model showed notable improvements in bias values and exhibited a stronger correlation compared to the original outputs from the IFS model. The percentage improvement (%IM) in rainfall forecasts, following correction using the SVM model, increased by 5.03%. The percentage improvement (%IM) in rainfall forecasts, following correction using the SVM model, increased by 5.03% for use as a predictor variable in the applied SVM method. In contrast, a combination of surface pressure, temperature across various layers, and rainfall proved to be the the most effective input variables for enhancing the accuracy of weather forecasting in North Barito using the SVM model.

This work continues the generalized stability theory (GST) analysis of baroclinic shear flow in the primitive equations (PE), focusing on the regime in which the mean baroclinic shear and the stratification are of the same order. The Eady model basic state is used and solutions obtained using the PE are compared to quasigeostrophic (QG) solutions. Similar optimal growth is obtained in the PE and QG frameworks for eddies with horizontal scale equal to or larger than the Rossby radius, although PE growth rates always exceed QG growth rates. The primary energy growth mechanism is the conventional baroclinic conversion of mean available potential energy to perturbation energy mediated by the eddy meridional heat flux. However, for eddies substantially smaller than the Rossby radius, optimal growth rates in the PE greatly exceed those found in the QG. This enhanced growth rate in the PE is dominated by conversion of mean kinetic energy to perturbation kinetic energy mediated by the vertical component of zonal eddy momentum flux. This growth mechanism is filtered in QG. In the intermediate Richardson number regime mixed Rossby–gravity modes are nonorthogonal in energy, and these participate in the process of energy transfer from the barotropic source in the mean shear to predominantly baroclinic waves during the transient growth process. The response of shear flow in the intermediate Richardson number regime to spatially and temporally uncorrelated stochastic forcing is also investigated. It is found that a comparable amount of shear turbulent variance is maintained in the rotational and mixed Rossby–gravity modes by such unbiased forcing suggesting that any observed dominance of rotational mode energy arises from restrictions on the effective forcing and damping.

The annual-mean position errors (PE) of tropical cyclone (TC) track forecasts from three forecast agencies [WMO Regional Specialized Meteorological Center in Tokyo (RSMC-Tokyo), China Meteorological Administration (CMA), and Joint Typhoon Warning Center of the United States (JTWC)] are analyzed to document the past improvements and project future tendency in track forecast accuracy for TCs in the western North Pacific. An improvement of 48 h (2 days) in lead time has been achieved in the past 30 years, but with noticeable stepwise periods of improvements with superposed short-term fluctuations. The stepwise improvement features differ among the three forecast agencies, but are highly related to the development of objective forecast guidance and the application strategy. As demonstrated by an exponential model for the growth of PEs with lead time for TCs of tropical storm category and above, the improvements in the past 10 years have mainly been due to the reduction in analysis errors rather than the reduction in the error growth rate. If the current trend continues, a further 2-day improvement in TC track forecast lead times may be projected for the coming 15 years up to 2035, and we certainly have not reached yet the limit of TC track predictability in the western North Pacific.

We propose a dynamical mechanism for a strictly finite prediction horizon, i.e. a scenatio of chaotic motion where asymptotically a more precise knowledge of the initial condition does note translate into a longer closeness of the forecast to the truth. For this, we propose a class of hierarchical dynamical systems which possess a scale dependent error growth rate in the form of a power law. Actually, this is motivated by and consistent with well known hierarchies of patterns in atmospheric dynamics. This scale dependent error growth rate in form of a power law translates in power law error growth over time instead of exponential error growth as in conventional chaotic systems. The consequence is a strictly finite prediction horizon, since in the limit of infinitesimal errors of initial conditions, the error growth rate diverges and hence additional accuracy is not translated into longer prediction times. By re-analyzing data of the National Center for Environmental Protect Global Forecast System, a weather prediction model, published by Harlim et al (2005 Phys. Rev. Lett. 94 228501) we show that such a power law error growth rate can indeed be found in numerical weather forecast models and estimate it average maximal prediction horizon to about 15 d.

The rapid pace of urbanization worldwide has significantly altered local and global weather-climate interactions. Expanding urban areas modify land-atmosphere interactions, leading to changes in temperature, precipitation patterns, and extreme weather events. To better understand and mitigate urban-induced weather and climate effects, long-term, frequently updated urban datasets are essential. Such datasets enable accurate monitoring of urban expansion and its impact on atmospheric processes, ultimately improving weather forecasting capabilities. The Weather Research and Forecasting (WRF) model is a widely used numerical weather prediction tool, yet its urban representation remains constrained by the limited availability of continuous, high-resolution urban data. The accuracy of weather forecasts, particularly in and around urban areas, is dependent on how well the model represents urban land cover and surface characteristics. In this study, the authors present Normalized Difference Urban Index+ (NDUI+) dataset, a 30-meter, long-term, continuously updated urban dataset designed to enhance urban representation within WRF. This dataset uses AI-calibrated DMSP-VIIRS nighttime light images merged with Landsat NDVI (Normalized Difference Vegetation Index) to generate Normalized Difference Urban Index (NDUI) metric from 1999 to present. The integration of NDUI+ into WRF improves the characterization of urban areas, leading to more precise simulations of weather conditions. Results demonstrate that the enhanced urban representation significantly refines key meteorological variables such as temperature, humidity, and wind speed, yielding more reliable and accurate forecasts. The improved model performance underscores the necessity of incorporating high-resolution, frequently updated urban datasets to advance weather prediction capabilities, especially in rapidly urbanizing regions. By bridging the gap between urban data availability and numerical weather modeling, this study highlights the critical role of urban datasets in improving the accuracy of weather forecasts and understanding micro and meso-level urban-climate interactions.

A one-dimensional semi-implicit semi-Lagrangian (SISL) linear model and a nonlinear SISL global shallow-water model are employed to investigate the sensitivity of the solutions on (i) the order of interpolation applied at the departure points, (ii) trajectory uncentering adopted in recent studies to suppress computational gravitational noise, and (iii) the optimal truncation conditions. The linear model results show that the truncation errors associated with the semi-Lagrangian (SL) part of the SISL scheme dominate the error characteristics when the estimates of the departure point values are based on linear or quadratic polynomial Lagrangian interpolation. In these two cases, the rate of error growth is large and may significantly exceed the acceptable levels in operational numerical weather prediction. Application of cubic interpolation drastically reduces the overall truncation errors, and the accuracy is well within the acceptable range. In contrast with the schemes based on lower-order interpolation (linear or quadratic), the authors show that the truncation errors in the cubic interpolation case are almost entirely due to the semi-implicit (SI) part of the SISL scheme. It is apparent from the results that application of higher-order interpolation would not significantly improve the overall accuracy for fixed resolution in space and time. In the case of planetary-scale waves, uncentering tends to impose a more stringent upper limit on the choice of the size of time step compared to the fully centered scheme. Unlike the Eulerian numerical formulation case. this constraint arises from accuracy considerations rather than stability limitations. Therefore, although trajectory uncentering has recently been shown to be effective in suppressing undesirable gravitational computational noise, it must he applied cautiously as it may also degrade the low-frequency component of the flow that one wishes to preserve and predict. The synoptic-scale waves are relatively less sensitive to the damping associated with uncentering. For large-scale waves, use of coarser spatial resolution may even result in improved accuracy, provided that the size of the time step is chosen appropriately. Turning to the shallow-water model formulation, two kinds of simulations are performed to investigate the accuracy of the semi-Lagrangian numerical scheme. The method of prescribed solutions is adopted by introducing a forcing term in the mass continuity equation such that Rossby-Haurwitz functions are exact analytic solutions to the modified form of the shallow-water equations. We adopt the Arakawa C grid with a uniform grid size in the zonal and meridional directions of approximately 1.4°. The initial conditions are composed of planetary-scale Rossby-Haurwitz solutions and dominated by wavenumber 4 (R = 4). The first category of experiments consists of ten 5-day simulations. The Rossby-Haurwitz “exact” solutions for the modified shallow-water equations are adopted as the reference fields for assessing the model performance. Therefore, any departure of the numerical solution from the analytic solution represents a measure of the model error. As the size of the time step is increased, first the error decreases until it attains a minimum at approximately Δt = 30 min and then it begins to increase monotonically with further increase in the size of the time step. This development is also consistent with the results based on the analysis of the linear model. The second kind of experiment consists of another set of ten 5-day simulations based on the traditional identical-twin model design approach in which the control or “truth” run is based on a small time step of 10 min. In the rest of the runs under this category, the spatial resolution is again held fixed while the size of time step is progressively increased in each subsequent simulation from Δt = 10 min up to Δt = 120 min. The results show a monotonic relationship between the size of the time step and the global average rms error at day 5, with the larger time steps exhibiting greater error. We observe a regime of minimum error growth with increasing size of the time step in the intermediate range between 0.5 and 1.0 h. Based on the comparison between the results from the two categories of simulations, we infer that the results based on the identical twin experiment design could portray a misleading representation of the true truncation errors. We further note that the range of the size of time steps corresponding to the minimum numerical truncation errors in the first category of simulations coincides with the range of time steps, which exhibit minimum error truncation growth associated with the second category of experiments. This may eventually lead to the development of a practical procedure for identifying the optimal truncation conditions when the exact solutions to the governing system of equations are not known.

A theoretical analysis is presented for dispersion relation and growth rate in a Cherenkov free electron laser with finite axial magnetic field. It is shown that the growth rate and the resonance frequency of Cherenkov free electron laser increase with increasing axial magnetic field for low axial magnetic fields, while for high axial magnetic fields, they go to a saturation value. The growth rate and resonance frequency saturation values are exactly the same as those for infinite axial magnetic field approximation. The effects of electron beam self-fields on growth rate are investigated, and it is shown that the growth rate decreases in the presence of self-fields. It is found that there is an optimum value for electron beam density and Lorentz relativistic factor at which the maximum growth rate can take place. Also, the effects of velocity spread of electron beam are studied and it is found that the growth rate decreases due to the electron velocity spread.

Relaxation to steady states and dynamical exponents in deposition models

Aluminum-based metallic material as the frame or the skin material is widely used in vehicle industrial production. The electrostatic charge accumulate on the surface of the material,because of triboelectrifiction with space particles. And the electrostatic discharge would impact the vehicle or appliance around enormously. In order to study the triboelectrifiction, principle of space particle and space charge is analyzed and theoretical calculation formula is derivate. The fact is found that the charge of material is growth in negative index with time dependence, and get steady at the end. The saturation value and saturation time will be decrease when the charge factor of space charged particle increases. To make sure the conclusion is right, a part material of one aerial vehicle is taken into the test. From the experimental results of different material, angular velocity and contact area, the conclusion gotten above is proved by test data.

The stability properties of a vortex lens are studied in the quasi geostrophic (QG) framework using the generalized stability theory. Optimal perturbations are obtained using a tangent linear QG model and its adjoint. Their fine-scale spatial structures are studied in details. Growth rates of optimal perturbations are shown to be extremely sensitive to the time interval of optimization: The most unstable perturbations are found for time intervals of about 3 days, while the growth rates continuously decrease towards the most unstable normal mode, which is reached after about 170 days. The horizontal structure of the optimal perturbations consists of an intense counter-shear spiralling. It is also extremely sensitive to time interval: for short time intervals, the optimal perturbations are made of a broad spectrum of high azimuthal wave numbers. As the time interval increases, only low azimuthal wave numbers are found. The vertical structures of optimal perturbations exhibit strong layering associated with high vertical wave numbers whatever the time interval. However, the latter parameter plays an important role in the width of the vertical spectrum of the perturbation: short time interval perturbations have a narrow vertical spectrum while long time interval perturbations show a broad range of vertical scales. Optimal perturbations were set as initial perturbations of the vortex lens in a fully non linear QG model. It appears that for short time intervals, the perturbations decay after an initial transient growth, while for longer time intervals, the optimal perturbation keeps on growing, quickly leading to a non-linear regime or exciting lower azimuthal modes, consistent with normal mode instability. Very long time intervals simply behave like the most unstable normal mode. The possible impact of optimal perturbations on layering is also discussed.

The impact of various types of weather on aircraft operations for one airline for 3 yr at Atlanta Hartsfield International Airport is investigated. Impacts are expressed as delays defined in terms of the difference between the actual flight time and that projected by the air traffic control system assuming an accurate weather forecast. The impacts of weather events were measured as the difference between these delays in clear conditions and in various types of inclement weather. Fog and thunderstorms create delays in various phases of each flight. The resultant delays at Atlanta alone create costs amounting to over $6 million annually for the airline. More accurate forecasts have the potential to reduce these costs by allowing more accurate flight planning. Decreases in the number and length of delay over time suggest that improvements in forecasts have already had an economic benefit to the airline. Delays associated with three snowstorms were also investigated. Early morning storms, even when f...

MEPS Marine Ecology Progress Series Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsTheme Sections MEPS 281:27-35 (2004) - doi:10.3354/meps281027 Effects of phosphorus on the growth and nitrogen fixation rates of Lyngbya majuscula: implications for management in Moreton Bay, Queensland Ibrahim Elmetri1,2,*, Peter R. F. Bell1 1Division of Chemical Engineering, The University of Queensland, Brisbane, Queensland 4072, Australia 2Present address: Institute of Technology and Engineering, Massey University, Turitea, New Zealand *Email: i.elmetri@massey.ac.nz ABSTRACT: Significant acetylene reduction and therefore N2 fixation was observed for Lyngbya majuscula only during dark periods, which suggests that oxygenic photosynthesis and N2 fixation are incompatible processes for this species. Results from a series of batch and continuous-flow-culture reactor studies showed that the specific growth rate and N2 fixation rate of L. majuscula increased with phosphate (P-PO4) concentration up to a maximum value and thereafter remained constant. The P-PO4 concentrations corresponding to the maximum N2 fixation and maximum growth rates were ~0.27 and ~0.18 µM respectively and these values are denoted as the saturation values for N2 fixation and growth respectively. Regular monitoring studies in Moreton Bay, Queensland, show that concentrations of P-PO4 generally exceed these saturation values over a large portion of the Bay and therefore, the growth of the bloom-forming L. majuscula is potentially maximised throughout much of the Bay by the elevated P-PO4 concentrations. Results from other studies suggest that the elevated P-PO4 concentrations in the Bay can be largely attributed to discharges from waste-water treatment plants (WWTPs), and thus it is proposed that the control of the growth of L. majuscula in Moreton Bay will require a significant reduction in the P load from the WWTP discharges. If the current strategy of N load reduction for these discharges is maintained in the absence of substantial P load reduction, it is hypothesised that the growth of L. majuscula and other diazotrophs in Moreton Bay will increase in the future. KEY WORDS: Lyngbya majuscula · Nitrogen fixation · Phosphorus · Continuous culture · Growth kinetics · Moreton Bay Full text in pdf format PreviousNextExport citation RSS - Facebook - Tweet - linkedIn Cited by Published in MEPS Vol. 281. Online publication date: November 01, 2004 Print ISSN: 0171-8630; Online ISSN: 1616-1599 Copyright © 2004 Inter-Research.