Atmospheric Prediction Research Articles

An improved OIF Elman neural network based on CSO algorithm and its applications

In order to prevent air pollution and improve the living environment for residents, it is particularly important to carry out air quality forecasting. Air quality is affected by many factors, and showed significant non-linear features. Output–input feedback Elman (OIF Elman) neural network can effectively solve non-linear problems. However, the disadvantages of OIF Elman neural network are easy to fall into local minimum, slow convergence and inflexibility. Chicken swarm optimization (CSO) algorithm has high operating efficiency and fast convergence speed. Therefore, this paper proposes an air pollution prediction model for OIF Elman neural network based on the CSO algorithm (CSO-OIF Elman neural network model). Evaluation indicators are absolute average error and accuracy rate. The efficacy of the proposed model is compared with other models such as traditional Elman neural network model, OIF Elman neural network model and Elman neural network model based on CSO algorithm (CSO-Elman neural network model). The experimental results show that CSO-OIF Elman neural network model has the best accuracy and the smallest absolute average error value, and has higher nonlinear fitting capabilities and generalization capabilities. The establishment of this model can provide useful reference value for atmospheric prediction research.

The Sensitivity of British Weather to Ocean Tides

AbstractTides in shelf seas greatly impact ocean mixing and temperature structure. Using a regional‐coupled ocean–atmosphere prediction system, at ocean coastal process and atmosphere convection permitting scales, we assess the influence of tides on British weather by comparing simulations with and without tides. In summer, when seasonal stratification is particularly sensitive to tides, the sea‐surface temperature is up to 6 K cooler in simulations with tidal mixing. Tides cool the air temperature over the sea by up to 3 K, and nearby land by up to 1.4 K. The mean air temperature across Great Britain land areas cools by 0.3 K with tides. Changes in near‐surface stability result in decreases in summer mean wind speeds over the ocean. A 6% reduction in summer precipitation is found with tides, consistent with cooler temperatures. This study has implications for climate projections since global‐coupled models typically do not include tides.

Analysis and Projections of Rainfall using representative concentration pathways (RCPs) Scenarios in Sleman Yogyakarta

Climate change has affected many agricultural areas, and further problem in food security. One of indicator in climate change is the pattern of rainfall, then it is necessary to predict that. This research was conducted in Sleman due to this area has a lot of agricultural activities which greatly influence human life in Yogyakarta. Monthly rainfall data were obtained from Balai Besar Wilayah Sungai Serayu Opak (BBWSSO) from 1988 to 2019. Statistical Downscaling Model (SDSM) was used to downscale 21st century rainfall for 30 years in Sleman, Yogyakarta. Downscaling was performed on the basis of established relationships between historical data observed rainfall records from 7 stations and National Center for Environmental Prediction re-analysis large scale atmospheric predictors. General Circulation Models (GCMs) under Representative Concentration Pathways (RCPs) climate change with scenarios of RCP 2.6, RCP 4.5, and RCP 8.5. Rainfall prediction with RCP scenarios is needed to be used as a guide for adaptation of crops in agriculture because it relates to water availability.

Partial differential equations for oceanic artificial intelligence

The Sea Surface Temperature (SST) plays a significant role in analyzing and assessing the dynamics of weather and also biological systems. It has various applications such as weather forecasting or planning of coastal activities. On the one hand, standard physical methods for forecasting SST use coupled ocean- atmosphere prediction systems, based on the Navier-Stokes equations. These models rely on multiple physical hypotheses and do not optimally exploit the information available in the data. On the other hand, despite the availability of large amounts of data, direct applications of machine learning methods do not always lead to competitive state of the art results. Another approach is to combine these two methods: this is data-model coupling. The aim of this paper is to use a model in another domain. This model is based on a data-model coupling approach to simulate and predict SST. We first introduce the original model. Then, the modified model is described, to finish with some numerical results.

Toward the Improvement of High-Impact Probabilistic Forecasts with a Sensitivity-Based Convective-Scale Ensemble Subsetting Technique

AbstractEnsemble sensitivity analysis (ESA) is a useful and computationally inexpensive tool for analyzing how features in the flow at early forecast times affect different relevant forecast features later in the forecast. Given the frequency of observations measured between model initialization times that remain unused, ensemble sensitivity may be used to increase predictability and forecast accuracy through an objective ensemble subsetting technique. This technique identifies ensemble members with the smallest errors in regions of high sensitivity to produce a smaller, more accurate ensemble subset. Ensemble subsets can significantly reduce synoptic-scale forecast errors, but applying this strategy to convective-scale forecasts presents additional challenges. Objective verification of the sensitivity-based ensemble subsetting technique is conducted for ensemble forecasts of 2–5-km updraft helicity (UH) and simulated reflectivity. Many degrees of freedom are varied to identify the lead times, subset sizes, forecast thresholds, and atmospheric predictors that provide most forecast benefit. Subsets vastly reduce error of UH forecasts in an idealized framework but tend to degrade fractions skill scores and reliability in a real-world framework. Results reveal this discrepancy is a result of verifying probabilistic UH forecasts with storm-report-based observations, which effectively dampens technique performance. The potential of ensemble subsetting and likely other postprocessing techniques is limited by tuning UH forecasts to predict severe reports. Additional diagnostic ideas to improve postprocessing tool optimization for convection-allowing models are discussed.

Seasonality patterns and distinctive signature of latitude and population on ozone concentrations in Southern Ontario, Canada

Ozone is a serious health concern and the only major pollutant in Ontario that is increasing, despite major efforts to control atmospheric pollutants in North America. Ambient ozone levels are affected by local atmospheric conditions (temperature, humidity, radiation, precipitation) and the concentration of its main precursors, nitrogen oxides (NOx) and volatile organic compounds (VOCs). In the present study, our aim is to elucidate the day-to-day and seasonal variability of the influence of synoptic atmospheric descriptors on daily average ozone concentrations, as well as to establish a predictive framework of the likelihood of exceedance of harmful levels in Southern Ontario. Using 31 stations in Southern Ontario with daily ozone concentration data from 2007 to 2015, we developed parsimonious models using as predictors a suite of atmospheric variables, available from the National Centers for Environmental Prediction and the National Center for Atmospheric Research (NCEP/NCAR) reanalysis dataset, and terms that recreate the seasonality and weekend/weekday effects of the previous day ozone concentrations. In all sites, seasonal (among-month) variability was distinctly lower than within-month variability. Our analysis showed that the population size reduced the average ambient ozone concentrations, increased their variability, and decreased the predictive power of our models. Ambient ozone levels in higher latitude sites displayed stronger dependence on the antecedent conditions, whereas the human activities weakened the serial correlation in the ozone time series in urban areas. Seasonal changes in the magnitude and sign of the slopes of the atmospheric predictors were consistent within the spatial domain of our study: shortwave radiation consistently increased ambient ozone levels, temperature displayed a positive relationship during the summer but a negative one during the winter; humidity was characterized by a negative relationship with ozone; precipitation increased ozone during late summer and winter, with no consistent effect during the rest of the year; wind speed and direction also showed contrasting effects between summer and winter months. Seasonality strongly affected the probability of exceedance in low population sites but had a minor role in more densely populated areas, while the difference in ozone concentrations between weekend and weekdays increased in urban sites. Overall, our results suggest that population and seasonality of the prevailing ambient conditions affect the local daily average ozone concentrations by modulating the importance of different processes and can thus be used to understand why high ozone concentrations may occur locally even during winter months.

Dynamical Structures of Cross-Domain Forecast Error Covariance of a Simulated Tropical Cyclone in a Convection-Permitting Coupled Atmosphere–Ocean Model

AbstractUnderstanding the dynamics of the flow-dependent forecast error covariance across the air–sea interface is beneficial toward revealing the potential influences of strongly coupled data assimilation on tropical cyclone (TC) initialization in coupled models, and the fundamental dynamics associated with TC air–sea interactions. A 200-member ensemble of convection-permitting forecasts from a coupled atmosphere–ocean regional model is used to investigate the forecast error covariance across the oceanic and atmospheric domains during the rapid intensification of Hurricane Florence (2018). Forecast uncertainties in both atmospheric and oceanic domains, from an Eulerian perspective, increase with forecast lead time, mainly from TC displacement errors. In a storm-relative framework, the ensemble forecast uncertainties in both domains are predominantly caused by differences in the simulated storm intensity and structure. The largest ensemble spread in the atmospheric pressure, temperature, and wind fields can be found within the TC inner-core region. Alternatively, the largest ensemble spread in the upper-ocean currents and temperature fields are located along the cold wake behind the storm. Cross-domain ensemble correlations between simulated atmospheric (oceanic) observations and oceanic (atmospheric) state variables in the storm-relative coordinates are highly anisotropic, variable dependent, and ultimately driven by the dynamics of TC air–sea interactions. Meaningful and dynamically consistent cross-domain ensemble correlations suggest that it is possible to use atmospheric and oceanic observations to simultaneously update state variables associated with the coupled ocean–atmosphere prediction of TCs using strongly coupled data assimilation. Sensitivity experiments demonstrate that at least 60–80 ensemble members are required to represent physically consistent cross-domain correlations and minimize sampling errors.

Impact of the Mesoscale Range on Error Growth and the Limits to Atmospheric Predictability

AbstractGlobal numerical weather prediction (NWP) models have begun to resolve the mesoscale k−5/3 range of the energy spectrum, which is known to impose an inherently finite range of deterministic predictability per se as errors develop more rapidly on these scales than on the larger scales. However, the dynamics of these errors under the influence of the synoptic-scale k−3 range is little studied. Within a perfect-model context, the present work examines the error growth behavior under such a hybrid spectrum in Lorenz’s original model of 1969, and in a series of identical-twin perturbation experiments using an idealized two-dimensional barotropic turbulence model at a range of resolutions. With the typical resolution of today’s global NWP ensembles, error growth remains largely uniform across scales. The theoretically expected fast error growth characteristic of a k−5/3 spectrum is seen to be largely suppressed in the first decade of the mesoscale range by the synoptic-scale k−3 range. However, it emerges once models become fully able to resolve features on something like a 20-km scale, which corresponds to a grid resolution on the order of a few kilometers.

Pacific subsurface ocean temperature as a long-range predictor of South China tropical cyclone landfall

Seasonal forecasts of the tropical cyclones which frequently make landfall along the densely populated South China coast are highly desirable. Here, we analyse observations of landfalling tropical cyclones in South China and of subsurface ocean temperatures in the Pacific warm pool region, and identify the possibility of forecasts of South China tropical cyclone landfall a year ahead. Specifically, we define a subsurface temperature index, subNiño4, and build a predictive model based on subNiño4 anomalies with a robust double cross-validated forecast skill against climatology of 23%, similar in skill to existing forecasts issued much later in the spring. We suggest that subNiño4 ocean temperatures precede the surface El Niño/Southern Oscillation state by about 12 months, and that the zonal shifts in atmospheric heating then change mid-level winds to steer tropical cyclones towards landfall in South China. We note that regional subsurface ocean temperature anomalies may permit atmospheric predictions in other locations at a longer range than is currently thought possible.

Measuring the Risk of Supply and Demand Imbalance at the Monthly to Seasonal Scale in France

Transmission system operator (TSOs) need to project the system state at the seasonal scale to evaluate the risk of supply-demand imbalance for the season to come. Seasonal planning of the electricity system is currently mainly adressed using climatological approach to handle variability of consumption and production. Our study addresses the need for quantitative measures of the risk of supply-demand imbalance, exploring the use of sub-seasonal to seasonal forecasts which have hitherto not been exploited for this purpose. In this study, the risk of supply-demand imbalance is defined using exclusively the wind energy production and the consumption peak at 7 pm. To forecast the risks of supply-demand imbalance at monthly to seasonal time horizons, a statistical model is developed to reconstruct the joint probability of consumption and production. It is based on a the conditional probability of production and consumption with respect to indexes obtained from a linear regression of principal components of large-scale atmospheric predictors. By integrating the joint probability of consumption and production over different areas, we define two kind of risk measures: one quantifies the probablity of deviating from the climatological means, while the other, which is the value at risk at 95% confidence level (VaR95) of the difference between consumption and production, quantifies extreme risks of imbalance. In the first case, the reconstructed risk accurately reproduces the actual risk with over 0.80 correlation in time, and a hit rate around 70–80%. In the second case, we find a mean absolute error (MAE) between the reconstructed and real extreme risk of 2.5 to 2.8 GW, a coefficient of variation of the root mean square error (CV-RMSE) of 3.8% to 4.2% of the mean actual VaR95 and a correlation of 0.69 and 0.66 for winter and fall, respectively. By applying our model to ensemble forecasts performed with a numerical weather prediction model, we show that forecasted risk measures up to 1 month horizon can outperform the climatology often used as the reference forecast (time correlation with actual risk ranging between 0.54 and 0.82). At seasonal time horizon (3 months), our forecasts seem to tend to the climatology.

Joint analysis of convective structure from the APR-2 precipitation radar and the DAWN Doppler wind lidar during the 2017 Convective Processes Experiment (CPEX)

Abstract. The mechanisms linking convection and cloud dynamical processes are major factors in much of the uncertainty in both weather and climate prediction. Further constraining the uncertainty in convective cloud processes linking 3-D air motion and cloud structure through models and observations is vital for improvements in weather forecasting and understanding limits on atmospheric predictability. To date, there have been relatively few airborne observations specifically targeted for linking the 3-D air motion surrounding developing clouds to the subsequent development (or nondevelopment) of convective precipitation. During the May–June 2017 Convective Processes Experiment (CPEX), NASA DC-8-based airborne observations were collected from the JPL Ku- and Ka-band Airborne Precipitation Radar (APR-2) and the 2 µm Doppler Aerosol Wind (DAWN) lidar during approximately 100 h of flight. For CPEX, the APR-2 provided the vertical air motion and structure of the cloud systems in nearby precipitating regions where DAWN is unable to sense. Conversely, DAWN sampled vertical wind profiles in aerosol-rich regions surrounding the convection but is unable to sense the wind field structure within most clouds. In this paper, the complementary nature of these data are presented from the 10–11 June flight dates, including the APR-2 precipitation structure and Doppler wind fields as well as adjacent wind profiles from the DAWN data.

New atmospheric data model for constant altitude accelerated flight performance prediction calculations and flight trajectory optimization algorithms

This article presents a new method for storing and computing the atmospheric data used in time-critical flight trajectory performance prediction calculations, such as flight performance prediction calculations in flight management systems and/or flight trajectory optimization, of constant altitude cruise segments. The proposed model is constructed based on the forecast data provided by Meteorological Service Agencies, in a GRIB2 data file format, and the set of waypoints that define the lateral component of the evaluated flight profile(s). The atmospheric data model can be constructed/updated in the background or off-line, when new atmospheric prediction data are available, and subsequently used in the flight performance computations. The results obtained using the proposed model show that, on average, the atmospheric parameter values are computed six times faster than through 4D linear interpolations, while yielding identical results (value differences of the order of 10e−14). When used in flight trajectory performance calculations, the obtained results show that the proposed model conducts to significant computation time improvements. The proposed model can be extended to define the atmospheric data for a set of cruise levels (usually multiple of 1000 ft).

A web-based support system for biometeorological research.

Data are the fundamental building blocks to conduct scientific studies that seek to understand natural phenomena in space and time. The notion of data processing is ubiquitous and nearly operates in any project that requires gaining insight from the data. The increasing availability of information sources, data formats and download services offered to the users, makes it difficult to reuse or exploit the potential of those new resources in multiple scientific fields. In this paper, we present a spatial extract-transform-load (spatial-ETL) approach for downloading atmospheric datasets in order to produce new biometeorological indices and expose them publicly for reuse in research studies. The technologies and processes involved in our work are clearly defined in a context where the GDAL library and the Python programming language are key elements for the development and implementation of the geoprocessing tools. Since the National Oceanic and Atmospheric Administration (NOAA) is the source of information, the ETL process is executed each time this service publishes an updated atmospheric prediction model, thus obtaining different forecasts for spatial and temporal analyses. As a result, we present a web application intended for downloading these newly created datasets after processing, and visualising interactive web maps with the outcomes resulting from a number of geoprocessing tasks. We also elaborate on all functions and technologies used for the design of those processes, with emphasis on the optimisation of the resources as implemented in cloud services.

AIM CIPS PMC tracking wind product retrieval approach and first assessment

The refined Cloud Imaging and Particle-Size (CIPS) cloud wind tracking algorithm is elaborated and the wind product is assessed against the Navy Operational Global Atmospheric Prediction System - Advanced Level Physics and High Altitude (NOGAPS-ALPHA) winds and the horizontal wind model (HWM14) climatological winds. Multiple searching frame sizes are adopted to generate the preliminary wind sets which are then merged and further edited based on the clustering of the similar wind directions (±20°). The mean values of the clusters within the sampling grids of 1.5 ° × 1.5 ° or 4.5 ° × 4.5 ° are taken as the final wind product. At the coincidences the CIPS and NOGAPS winds show a moderate degree of deterministic consistency. We have further shown that on the orbit-to-orbit basis when the NOGAPS modeled ice and CIPS measured ice correlate better, the wind agreement is also better. The difference in the two wind sets is most likely attributed to the NOGAPS temperature being deviated from the true temperature that will affect the geostrophic component of the winds and also to the fact that the CIPS winds are often ageostrophic and are cascaded into smaller scales. The CIPS zonal (westward) winds are decreased and then reversed in early June and late August whereas in the core of the season they are stronger. This overall variation pattern is shared by both NOGAPS and HWM14 zonal winds. Both NOGAPS and HWM14 zonal winds exhibit ~8–10 m/s difference between cases using all local times (LTs) and the CIPS LT range 13–23 h due to the dominant diurnal migrating tides, and this may partially interpret the weaker CIPS zonal winds. The meridional (equatorward) winds do not follow any established intra-seasonal variation pattern but rather the variability is susceptible to the sampling longitudes/latitudes.

Forecasting sea level fluctuations caused by storm winds at the ports in Odesa Region of the north-western part of the Black Sea

Increasing the draught of ships that may be accepted by ports for loading at their loading berths is one of the main tasks aimed at development and freight turnover enhancement of sea trade ports located in Odesa Region of the north-western part of the Black Sea (cities of Chornomorsk, Odesa and Pivdennyi). An operational forecasting of short-term sea level fluctuations caused by storm winds presents a critical task for ensuring safe navigation across the ports’ water area and approach channels. The article is devoted to analysing and discussing the results of tests of a simplified 2D hydrodynamic model designed for forecasting such phenomena as upsurge and downsurge of the sea level caused by storm winds in the vicinity of sea ports in Odesa Region of the north-western part of the Black Sea. Spatio-temporal variability of wind conditions at the sea-to-atmosphere boundary was set based on the data retrieved from a 10-day synoptic forecast using global atmospheric prediction model GFS (Global Forecast System). The study analyses the results of forecast of significant (the ones exceeding 30 cm) short-term sea level drops and rises at the ports which were observed in 2016, 2017 and 2020.
 It was established that, in case of use of the GFS forecast data, the pattern of sea level denivellations caused by storm winds and their amplitude in the majority of events start approximating to the observed values provided the forecast has a 4-day lead time. Therefore the accuracy of wind conditions variability forecast with application of the GFS model having a longer lead advance time is not sufficient for forecasting the sea level fluctuations caused by storm winds. The study made it possible to get an acceptable equivalence between the values of sea level denivellation amplitudes which were forecast with a 1-to-3-day lead time and the ones observed afterwards. In particular, when the forecast lead time is equal to »2 days, in relation to the expected storm conditions, the average absolute error for the forecast of sea level fluctuations amplitude constituted 7-8 cm, while its permissible value was defined as 15 cm, and the average relative error – 16-18%. It allowed making a conclusion that a hydrodynamic model option, applied alongside with the forecasting information on wind conditions variability retrieved with the help of the GFS weather prediction model, may be used for operational forecasting of short-term sea level fluctuations caused by storm winds with the forecast lead time of up to 4 days.

Mantle redox state drives outgassing chemistry and atmospheric composition of rocky planets

Volcanic degassing of planetary interiors has important implications for their corresponding atmospheres. The oxidation state of rocky interiors affects the volatile partitioning during mantle melting and subsequent volatile speciation near the surface. Here we show that the mantle redox state is central to the chemical composition of atmospheres while factors such as planetary mass, thermal state, and age mainly affect the degassing rate. We further demonstrate that mantle oxygen fugacity has an effect on atmospheric thickness and that volcanic degassing is most efficient for planets between 2 and 4 Earth masses. We show that outgassing of reduced systems is dominated by strongly reduced gases such as text {H}_{2}, with only smaller fractions of moderately reduced/oxidised gases (text {CO}, text {H}_{2}text {O}). Overall, a reducing scenario leads to a lower atmospheric pressure at the surface and to a larger atmospheric thickness compared to an oxidised system. Atmosphere predictions based on interior redox scenarios can be compared to observations of atmospheres of rocky exoplanets, potentially broadening our knowledge on the diversity of exoplanetary redox states.

High-Resolution (2.5 km) Ensemble Precipitation Analysis across Canada

AbstractConsistent and continuous fields provided by precipitation analyses are valuable for hydrometeorological applications and land data assimilation modeling, among others. Providing uncertainty estimates is a logical step in the analysis development, and a consistent approach to reach this objective is the production of an ensemble analysis. In the present study, a 6-h High-Resolution Ensemble Precipitation Analysis (HREPA) was developed for the domain covering Canada and the northern part of the contiguous United States. The data assimilation system is the same as the Canadian Precipitation Analysis (CaPA) and is based on optimal interpolation (OI). Precipitation from the Canadian national 2.5-km atmospheric prediction system constitutes the background field of the analysis, while at-site records and radar quantitative precipitation estimates (QPE) compose the observation datasets. By using stochastic perturbations, multiple observations and background field random realizations were generated to subsequently feed the data assimilation system and provide 24 HREPA members plus one control run. Based on one summer and one winter experiment, HREPA capabilities in terms of bias and skill were verified against at-site observations for different climatic regions. The results indicated HREPA’s reliability and skill for almost all types of precipitation events in winter, and for precipitation of medium intensity in summer. For both seasons, HREPA displayed resolution and sharpness. The overall good performance of HREPA and the lack of ensemble precipitation analysis (PA) at such spatiotemporal resolution in the literature motivate further investigations on transitional seasons and more advanced perturbation approaches.

Chaos and information in two-dimensional turbulence

By performing a large number of fully resolved simulations of incompressible homogeneous and isotropic two dimensional turbulence, we study the scaling behavior of the maximal Lyapunov exponent, the Kolmogorov-Sinai entropy and attractor dimension. The scaling of the maximal Lyapunov exponent is found to be in good agreement with the dimensional predictions. For the cases of the Kolmogorov-Sinai entropy and attractor dimension the simple dimensional predictions are found to be insufficient. A dependence on the system size and the forcing length scale is found, suggesting non-universal behavior. The applicability of these results to atmospheric predictability is also discussed.

The Year of Polar Prediction in the Southern Hemisphere (YOPP-SH)

AbstractThe Year of Polar Prediction in the Southern Hemisphere (YOPP-SH) had a special observing period (SOP) that ran from 16 November 2018 to 15 February 2019, a period chosen to span the austral warm season months of greatest operational activity in the Antarctic. Some 2,200 additional radiosondes were launched during the 3-month SOP, roughly doubling the routine program, and the network of drifting buoys in the Southern Ocean was enhanced. An evaluation of global model forecasts during the SOP and using its data has confirmed that extratropical Southern Hemisphere forecast skill lags behind that in the Northern Hemisphere with the contrast being greatest between the southern and northern polar regions. Reflecting the application of the SOP data, early results from observing system experiments show that the additional radiosondes yield the greatest forecast improvement for deep cyclones near the Antarctic coast. The SOP data have been applied to provide insights on an atmospheric river event during the YOPP-SH SOP that presented a challenging forecast and that impacted southern South America and the Antarctic Peninsula. YOPP-SH data have also been applied in determinations that seasonal predictions by coupled atmosphere–ocean–sea ice models struggle to capture the spatial and temporal characteristics of the Antarctic sea ice minimum. Education, outreach, and communication activities have supported the YOPP-SH SOP efforts. Based on the success of this Antarctic summer YOPP-SH SOP, a winter YOPP-SH SOP is being organized to support explorations of Antarctic atmospheric predictability in the austral cold season when the southern sea ice cover is rapidly expanding.

A New Theoretical Framework for Understanding Multiscale Atmospheric Predictability

AbstractHere we present a new theoretical framework that connects the error growth behavior in numerical weather prediction (NWP) with the atmospheric kinetic energy spectrum. Building on previous studies, our newly proposed framework applies to the canonical observed atmospheric spectrum that has a −3 slope at synoptic scales and a −5/3 slope at smaller scales. Based on this realistic hybrid energy spectrum, our new experiment using hybrid numerical models provides reasonable estimations for the finite predictable ranges at different scales. We further derive an analytical equation that helps understand the error growth behavior. Despite its simplicity, this new analytical error growth equation is capable of capturing the results of previous comprehensive theoretical and observational studies of atmospheric predictability. The success of this new theoretical framework highlights the combined effects of quasi-two-dimensional dynamics at synoptic scales (−3 slope) and three-dimensional turbulence-like small-scale chaotic flows (−5/3 slope) in dictating the error growth. It is proposed that this new framework could serve as a guide for understanding and estimating the predictability limit in the real world.