Eta Model Research Articles

How the ETAS models were created, used, and evolved -- Personal views and perspectives

Statistical seismology originated in Japan 130 years ago. Through the marriage with stochastic point processes in about half a century, we can now provide on-line estimation, real-time forecasting and direct diagnosis of seismic activity. This manuscript describes the origin and recent development of the ETAS models, their relationship to forecasting problems, and their diagnostic studies of the physical phenomena of seismic activity. I will take this opportunity to focus on my research experiences and views.

Bayesian Earthquake Forecasting Using Gaussian Process Modeling: GP-ETAS Applications

Abstract Numerous seismicity models are known to simulate different observed characteristics of earthquake occurrence successfully. However, their ability of prospective forecasting future events is a priori not always known. The recently proposed semiparametric model, Gaussian process epidemic-type aftershock sequence (GP-ETAS) model, which combines the ETAS model with GP modeling of the background activity, has led to promising results when applied to synthetic seismicity. In this study, we focus on the ability of GP-ETAS for different forecasting experiments in two case studies: first, the Amatrice, Italy, sequence during 2016 and 2017, and second, long-term seismicity in Southern California. The results indicate that GP-ETAS performs well compared with selected benchmark models. The advantages become particularly visible in cases with sparse data, in which GP-ETAS shows in general a more robust behavior compared to other approaches.

A dataset of high-resolution climate change projections over South America with bias correction

Accurate and detailed datasets are crucial for assessing climate change impacts. Regional climate models provide high-resolution simulations and are key tools but often exhibit systematic biases. Therefore, this paper presents a dataset derived from bias-corrected Eta regional model simulations and projections driven by four global CMIP5 models. The correction applied to daily precipitation, potential evapotranspiration, actual evapotranspiration, and 2-m air temperature, was conducted on a 0.2° x 0.2° grid over South America. The dataset covers two periods: 1976-2005 (baseline) and 2006-2099 (future) under RCP4.5 and RCP8.5 scenarios. Empirical quantile mapping was used to adjust the Eta model outputs to better match observational data. This method modified the accumulated probability curves of the Eta model outputs to align with observational curves for both baseline and future climates. Two observational datasets were used for correction and evaluation. The new dataset shows that bias correction significantly reduced the errors in the Eta simulations, especially for the frequent values of precipitation, potential evapotranspiration, and 2-m temperature, and also corrected the annual cycle and frequency distribution of these variables, approaching the observations. The pattern of extreme precipitation indices from the bias-corrected Eta dataset also reduced error. Bias correction was applied to future projections. The comparison against the raw Eta dataset showed that the trends of changes were preserved, but in general, the peaks of the changes were smoothed. As in the raw Eta dataset, the RCP8.5 scenario showed a higher change rate than RCP4.5. This work also revealed the large uncertainty of the observational dataset; some of the remaining errors after the bias correction were mostly due to differences between the two correction and evaluation observational datasets. The described dataset is freely available from the CNPq LattesData repository at the following link: https://doi.org/10.57810/lattesdata/WAVGSL.

Algorithms for Fitting the Space-Time ETAS Model to Earthquake Catalog Data: A Comparative Study

Algorithms for Fitting the Space-Time ETAS Model to Earthquake Catalog Data: A Comparative Study

Ensemble hydrological predictions at an intraseasonal scale through a statistical–dynamical downscaling approach over southwestern Amazonia

ABSTRACT We developed and analyzed the performance of an ensemble forecasting system for the Madeira River basin, the largest sub-basin of the Amazon, with forecasts up to 30 days under different hydrometeorological conditions. We used outputs from the regional Eta model of precipitation and global climatological data as inputs to a large-scale hydrological model. Bias correction of precipitation through quantile mapping significantly improved the results, achieving a hit rate >70%. The system demonstrated the ability to discriminate between high, medium, and low flow conditions. Forecast performance is better for larger catchment areas. This system is expected to increase decision-making efficiency for flood and drought situations in the largest Amazon tributary.

Four Storm Surge Cases on the Coast of São Paulo, Brazil: Weather Analyses and High-Resolution Forecasts

The coast of São Paulo, Brazil, is exposed to storm surges that can cause damage and floods. These storm surges are produced by slowly traveling cyclone–anticyclone systems. The motivation behind this work was the need to evaluate high-resolution forecasts of the mean sea-level pressure and 10 m winds, which are the major drivers of the wave model. This work is part of the activity in devising an early warning system for São Paulo coastal storm surges. For the evaluation, four case studies that had a major impact on the coast of São Paulo in 2020 were selected. Because storm surges that reach the coast may cause coastal flooding, precipitation forecasts were also evaluated. The mesoscale Eta model produces forecasts with a 5 km resolution for up to an 84 h lead time. The model was set up in a region that covers part of southeast and south Brazil. The ERA5 reanalysis was used to describe the large-scale synoptic conditions and to evaluate the weather forecasts. The cases showed a region in common between 35° S, 40° S and 35° W, 45° W where the low-pressure center deepened rapidly on the day before the highest waves reached the coast of São Paulo, with a mostly eastward, rather than northeastward, displacement of the associated surface cyclone and minimal or no tilt with height. The winds on the coast were the strongest on the day before the surge reached the coast of São Paulo, and then the winds weakened on the day of the maximum wave height. The pattern of the mean sea-level pressure and 10 m wind in the 36 h, 60 h, and 84 h forecasts agreed with the ERA5 reanalysis, but the pressure was slightly underestimated. In contrast, the winds along the coast were slightly overestimated. The 24 h accumulated precipitation pattern was also captured by the forecast, but was overestimated, especially at high precipitation rates. The 36 h forecasts showed the smallest error, but the growth in the error for longer lead times was small, which made the 84 h forecasts useful for driving wave models and other local applications, such as an early warning system.

Inclusion of the radiative effect of deep convective clouds in the Eta model simulations

AbstractConvective clouds play an important role in the local energy budget by directly interacting with solar and terrestrial radiation. However, radiation parameterization schemes of atmospheric models generally consider clouds produced from microphysics schemes or some other grid saturation criteria. Deep convective parameterization schemes tend to rain out the convective cloud before the radiation scheme perceives its water load. This may be a source of the positive bias of the incoming solar radiation at the surface. The objective of this work is to include the effects of deep convective clouds in the radiation scheme of the regional Eta model and to evaluate the impacts on the net radiative energy and other meteorological variables. The radiation scheme is the Rapid Radiative Transfer Model. The work is developed in four stages. The positive bias in the incoming solar radiation was diagnosed in the first stage. In the second stage, the parameters of the convective parameterization scheme were modified to increase convective precipitation. In the third stage, the parameters of the microphysics scheme were modified to increase explicit clouds. In the fourth and last stage, in addition to the previous modifications, the condensates from the convective parameterization were input into the radiation scheme. The runs were performed for a period of one summer rainy month with intense convective activity over South America. Including deep convective cloud condensates into the radiation scheme improved the cloud cover, the diurnal cycle of the surface net radiation, and the 2‐m temperature. However, the reduction of the net radiation at the surface caused the reduction of the available energy for convective instability and, consequently, the precipitation reduction. The results show the importance of including cumulus cloud water load in the radiative scheme for bias reduction in the radiative energy components.

Severe convective storms’ reproduction: empirical analysis from the marked self-exciting point processes point of view

The paper focuses on the evaluation of hailstorms’ and thunderstorms winds’ events in the United States of America, in the period from 1996 to 2022, under the marked spatio-temporal self-exciting point processes point of view. The aim of the present article is the assessment and description of the spatio-temporal spontaneous and reproducing activity of severe hailstorms’ and thunderstorms winds’ processes. The present application shows how the spatio-temporal pattern is well-fitted and clearly explainable, according to the flexible semi-parametric ETAS model fitting.

Projections of severe weather and the impacts on transmission line towers in Santa Catarina, Brazil, under future scenarios of global climate change

Transmission line towers are highly exposed to weather hazards. In southern Brazil, several damages to transmission lines have been reported due to severe weather events. Climate change projections indicate that the frequency and magnitude of extreme events may increase, making planning and adaptation of the transmission system exposure even more critical. In this work, we propose a severe weather index (SWI) as a proxy for detecting severe storms that can potentially result in extreme weather events. The SWI combines thresholds of instability indices based on observed severe events around the transmission tower-line systems. These indices were calculated using the downscaling by the Eta model at 20 km resolution of three global climate model projections and at 5 km of one global climate model for the historical period and the near future. The results show that the SWI captures the severe storms observed in the region. All downscaling projections agree with the increase of extreme weather events in the near future and the expansion of vulnerable areas. The constructed index can be employed to assess the risks and to plan the power transmission system better.

Evaluation of Precipitation Simulations at the Subseasonal Range in the Sao Francisco River Basin, Brazil

The objective of this work is to evaluate the subseasonal precipitation simulations of the Eta model during the onset of the rainy season in the Sao Francisco River Basin (SFB). Accumulated precipitation every 20 days in September and October (2011 to 2015) was evaluated based on subseasonal simulations (integration period of up to 60 days) of the Eta-20-km model, nested within the Climate Forecast System Reanalysis (CFSR), here called Eta-CFSR. MERGE precipitation data were used to evaluate Eta-CFSR simulated precipitation. A statistical method was employed to evaluate the model’s ability to simulate the onset of the rainy season in the Upper SFB. The main results are: i) The Eta-CFSR accurately represents the seasonality of the precipitation pattern in the SFB and the seasonal and interannual variation of the accumulated precipitation in all of the chosen three consecutive 20-day periods of years 2011 to 2015; ii) The model can represent the transition pattern from the dry to the rainy season, showing better results in 2011 and 2015, which were marked, respectively, by La Niña and El Niño, and by anomalies of sea surface temperature favorable and unfavorable for the occurrence of precipitation; iii) Although the model underestimates the amount of precipitation, it effectively captures the seasonal patterns and the onset of the rainy season, with a maximum advancement of two pentads in wetter years and delaying it in drier years.

Evaluation of Subseasonal Precipitation Simulations for the Sao Francisco River Basin, Brazil

Water conflicts have been a significant issue in Brazil, especially in the Sao Francisco River basin. Subseasonal forecasts, up to a 60-day forecast range, can provide information to support decision-makers in managing water resources in the river basin, especially before drought events. This report aims to evaluate 5-year mean subseasonal simulations generated by the Eta regional model for the period from 2011 to 2016 and assess the usefulness of this information to support decision-making in water resource conflicts in the Sao Francisco River basin. The capability of the Eta model to reproduce the drought events that occurred between the years 2011 and 2016 was compared against the Climate Prediction Center Morphing (CMORPH) precipitation data. Two sets of 60-day simulations were produced: one started in September (SO) and the other in January (JF) of each year. These months were chosen to evaluate the model’s capability to reproduce the onset and the middle of the rainy seasons in central Brazil, where the upper Sao Francisco River is located. The SO simulations reproduced the observed spatial distribution of precipitation but underestimated the amounts. Precipitation errors exhibited large variability across the subbasins. The JF simulations also reproduced the observed precipitation distribution but overestimated it in the upper and lower subbasins. The JF simulations better captured the interannual variability in precipitation. The 60-day simulations were discretized into six 10-day accumulations to assess the intramonthly variability. They showed that the simulations captured the onset of the rainy season and the small periods of rainy months that occurred in these severe drought years. This research is a critical step to indicate subbasins where the model simulation needs to be improved and provide initial information to support water allocation in the region.

Statistical inference for mixed jump processes by Markov switching model with application to identify seismicity levels

Describing the non-stationarity of mixed stochastic jump processes presents a formidable challenge. This study employs a mixed compound Poisson process by Markov switching model (CPMSM) to address the issue of overdispersed data of random jumps. The Poisson rate is governed by a continuous-time Markov chain in this model. By assuming independence of the compound Poisson process and jump sizes, we present a generalized algorithm to estimate the parameters of CPMSM and try to predict the future behavior of this stochastic system. To investigate the potential application of this model and the accuracy of our algorithm, we provide a numerical simulation example in the context of the auto insurance payout scenario. The results suggest that CPMSM is an effective method of describing jump behavior controlled by random counts with mode switching via a Markov chain. Furthermore, we demonstrate a specific application of this model in identifying seismicity levels of Greek earthquake data and identify four hidden states. Finally, we compare its fitting effectiveness with the ETAS model using two public earthquake datasets in Japan and Iran.

A neural encoder for earthquake rate forecasting

Forecasting the timing of earthquakes is a long-standing challenge. Moreover, it is still debated how to formulate this problem in a useful manner, or to compare the predictive power of different models. Here, we develop a versatile neural encoder of earthquake catalogs, and apply it to the fundamental problem of earthquake rate prediction, in the spatio-temporal point process framework. The epidemic type aftershock sequence model (ETAS) effectively learns a small number of parameters to constrain the assumed functional forms for the space and time correlations of earthquake sequences (e.g., Omori-Utsu law). Here we introduce learned spatial and temporal embeddings for point process earthquake forecasting models that capture complex correlation structures. We demonstrate the generality of this neural representation as compared with ETAS model using train-test data splits and how it enables the incorporation additional geophysical information. In rate prediction tasks, the generalized model shows >4% improvement in information gain per earthquake and the simultaneous learning of anisotropic spatial structures analogous to fault traces. The trained network can be also used to perform short-term prediction tasks, showing similar improvement while providing a 1000-fold reduction in run-time.

Impacts of increasing greenhouse gas concentrations and deforestation on extreme rainfall events in the Amazon basin: A multi‐model ensemble‐based study

AbstractThe main objective of this study was to evaluate the effects of increasing greenhouse gases (GHGs) and total deforestation of the Amazon on extreme rainfall events in the Amazon basin. In order to quantify these impacts, numerical experiments were performed with the Eta regional climate model forced from initial and boundary conditions from the BESM, HadGEM2‐ES, and MIROC5 earth system models. In the experiment related to the increase in GHGs, numerical simulations were performed according to the IPCC RCP8.5 scenario. The effect of deforestation was quantified via an experiment in which the forest in the Amazon basin was replaced by areas of degraded pasture in the Eta model. For the analyses of the changes in extreme rainfall events, the multi‐model ensemble technique was used. The results were evaluated in terms of anomalies relative to the sensitivity and control experiments. In the results, it was observed that in an RCP8.5‐type GHG emission scenario there is a statistically significant increase in the maximum number of consecutive days without rain, a reduction in the maximum number of consecutive rainy days, reduction in total annual precipitation, and reduction in maximum annual precipitation accumulated over one and 5 days, respectively. The results for the scenario with increased GHGs and large‐scale deforestation in the Amazon basin are similar to the RCP8.5 scenario, but the intensity of changes in climate indices is significantly greater. It was also verified that the changes in the climatic indices are strongly associated with alterations in the energy balances at the surface and, consequently, in the large‐scale circulation. In general, it can be highlighted that the climate in the Amazon region is strongly dependent on the presence of the forest.

An assessment of the present hydroclimatic regime of the Madeira River basin using climate and hydrological models

ABSTRACT Southwestern Amazonia has low spatial coverage of hydro-meteorological data, making climate and hydrological models essential tools. Thus, it is necessary to evaluate these models to verify their suitability for future climate change assessments. We evaluate the ability of a regional climate model (Eta) forced with three Earth system models and a large-scale hydrological model (MGB) to represent hydroclimatic variables for the current climate in the Madeira River basin. Different hydro-meteorological databases are used to evaluate the systematic errors of the coupled model system. The simulation results show that the Eta model underestimates (overestimates) precipitation over the basin during the rainy (dry) season. The hydrological processes simulated by the MGB are considered satisfactory, although the model has some limitations with respect to the timing of floods and their removal in different discharge regimes.

Cut-cell Eta Model: History and Challenges Overcome

Incentive for writing a limited area weather prediction model stemmed from the author’s several years stay at the University of California in Los Angeles, at the end of the sixties. Exposed to what he refers to as the Akio Arakawa approach, having had an idea for a scheme that was an improvement to what Arakawa was using, and being aware of the importance of topography for the weather of the country he was to continue his career in, led in 1973 to his first limited area 3D code, the forerunner of what was to become the Eta model. Refinements and enhancements introduced by the author in subsequent years and of the collaborator he acquired, Zaviša Janjić, resulted in the code that when installed at the then U.S. National Meteorological Center, attracted attention. Hallmarks of the model were Mesinger’s eta vertical coordinate, and Janjić’s transformation of the Arakawa horizontal advection scheme to the model’s semi-staggered B/E grid. In 1993 the Eta became the primary regional forecasting model of the U.S. Weather Bureau, and in 1998 its precipitation accuracy of 24-48 h forecasts became higher across all intensity thresholds than that of its predecessor, the Nested Grid Model (NGM) for its 00-24 h forecasts. Lately, the Eta is extensively used also as a regional climate model (RCM), mostly over the South American domain, and in near-real time as a tool for the North American Regional Reanalysis (NARR), run by the U.S. National Centers for Environmental Prediction/Climate Prediction Center. Several later unique numerical refinements of the Eta addressing problems noticed are summarized in a “before and after” fashion, and results are mentioned of its ensemble skill compared to that of its highly acclaimed driver European Centre for Medium-Range Weather Forecasts (ECMWF) model.

Regional climate modeling in the Amazon basin to evaluate fire risk

ABSTRACT Studies regarding deforestation, the hydrological cycle, climate change and fire weather can benefit from the detailed simulations provided by regional climate models (RCM). While much attention has been given to fire activity in the Amazon, few studies have used RCM runs to assess fire risk and variables associated to fire occurrence. We evaluated precipitation, temperature and a fire risk index from the ensemble of Eta model simulations coupled with three different global climate models for the Amazon basin. The RCM runs were compared to reanalysis data for the dry season from 1979 to 2005. The maximum and 2-m temperature fields were underestimated over the entire region, but showed a statistically significant spatial correlation with the reference data. Precipitation was overestimated over the Amazon, in accordance with the major sources of moisture analyzed. The Keetch-Byram drought index (KBDI) was not significantly affected by the bias found in temperature and precipitation, and the ensemble improved relative to the individual member simulations. KBDI estimations performed better with the ensemble of the three evaluated members, however the Eta model showed some limitations. The validation of modeled fire risk could benefit from the use of satellite hotspot data. Furthermore, the KBDI can also be used in the assessment of how climate change interacts with fire activity in the Amazon region.

Magnitude distribution and clustering properties of the 3-D seismicity in Central Apennines (Italy)

SUMMARYIn this paper we deal with statistical features of earthquakes, seeking possible correlations between the Gutenberg–Richter magnitude distribution and the short-term clustering in an area of the Central Apennines, Italy, where significant seismicity with earthquakes exceeding magnitude 6.0 has been repeatedly observed from 1990 to the present. For this purpose, a recently developed version of the ETAS model, incorporating a 3-D spatial triggering kernel, has been adopted. Our analysis has been carried out representing the b-value and the probability of independence of events on six vertical cross-sections suitably related to the seismic structures that are considered responsible of the seismicity observed in the study area. The results of the statistical analysis of the seismicity in the study area have shown a clear distinction between the western normal low-angle fault system, characterized by eastward dip and the eastern normal fault systems, with westward dip. In the former (Etrurian Fault System; EFS) we found seismicity with a high b-value and high probability of independence, that is a scarce capacity of producing clusters and strong aftershock sequences. The eastern fault systems of our study area are distinguishable in two main distinct systems, which generated two strong seismic sequences in 1997 and 2016–2017. In the former (Colfiorito) sequence the seismicity showed a very low b-value and a modest probability of independence, while in the latter (Central Italy) sequence the b-value was significantly higher and the probability of independence had extremely low values (manifesting a high level of clustering). The much higher b-value of the EFS than the other extensional sources could be caused by its peculiar seismotectonic role of discontinuity at the base of the normal active faulting, and its reduced capacity of accumulating stress. This circumstance may be interpreted by a difference in the rheological properties of these fault systems, possibly also in relation to their present status in the earthquake cycle and the presence of strong aftershock sequences.

Mid-Holocene climate simulations over Brazil using the Eta regional paleoclimate model

Paleoclimate simulations are generally performed using coarse global climate models. However, validation of these simulations using a local dataset may be penalized by the coarse grid of the global models. Using a regional climate model, which benefits from the use of higher resolution in a limited area and specific period of time, may help improve the validation of the simulations and help to understand the climate of the past. The objective of this study is to evaluate the Mid-Holocene (MH) simulations for Brazil at 20 km spatial resolution using the regional Eta Model. The simulations are produced by nesting the Eta Model to the National Institute for Space Research (INPE) Global Spectral Atmospheric Model at T062 resolution and 28 vertical levels. Both global and regional models used the same orbital parameters to produce the Milankovic Cycles based on the Berger parameterization. The models adopted the typical carbon dioxide values for the present time and the MH. Downscaling simulations were performed with the Eta Model, resulting in simulations of 2 periods of time, the Eta 0k (present) and the Eta 6k (MH), each 10 years long. The evaluation compares these simulations against proxy data and other paleoclimate model simulations for the region. The difference between the two simulations, 6k and 0k, provides the changes between the two climatic periods. The Eta simulations indicate that the climate during MH was more humid over Northeast Brazil; this agrees partially with paleoclimate data in eastern Northeast Brazil. The Amazon region simulations were mostly drier during MH, in agreement with the paleoclimate data. A weaker convergence of winds in the MH, with winds blowing from the Amazon toward Southeast Brazil, affected the formation and the positioning of the South Atlantic Convergence Zone. Consequently, the associated moisture transport toward the Southeast was smaller; this reduced precipitation in the Brazilian southeastern, central-west, and southern regions, which agrees with the proxy data. The Eta Model simulated a cooler climate for the MH over the Northeast, Central, Southeast, and South Brazil. However, this simulated temperature showed less agreement against proxy data. The Amazon region was slightly warmer, and other transition regions showed no climate change. Overall, the results show that this modified version of the Eta Model is suitable for paleoclimate studies and provides added value over the driver model.

Climate change projections and impacts on the eucalyptus plantation around the Doce River basin, in Minas Gerais, Brazil

The goal of this work is to assess the precipitation and temperature trends in climate change projections in the state of Minas Gerais in Brazil, with emphasis on the Doce River basin, using high resolution climate projections suitable for the scale of the basin. Tailored impact assessment of climate change on eucalyptus plantation in terms of thermal and water stress is provided for the basin. We analyzed the downscaling of climate change projections produced by the Eta regional model at 20-km nested to three global models, CanESM2-ES, HadGEM2-ES and MIROC5, and at 5-km resolutions nested to HadGEM2-ES. In historical period, the temperature and precipitation patterns are reproduced by the Eta model. The 5-km Eta simulations provides more spatial detail of the maximum precipitation near the regions of high topography, although in these areas, precipitation is overestimated with respect to the WorldClim data. All projections agree with a warmer climate in the basin until 2070. Precipitation projections indicate a decrease in future periods. The analysis of extreme temperature indices shows an increase in warm days and warm nights and a decrease in cold days and in cold nights until 2070. Future projections indicate trends of reduction in annual rainfall and increase in consecutive dry days. Regarding the eucalyptus, future productivity may be at risk, as most locations will meet more frequently the water stress conditions. Six locations may meet both thermal and water stress conditions and become unsuitable for eucalyptus plantation if only climate factors are considered.