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NASA NTRS1996

Intercomparison, Visualization, and Analysis Testbed System for EOS Global Assimilated Datasets and Satellite Data

The Space Science and Engineering Center (SSEC) of the University of Wisconsin - Madison had two primary goals for NASA grant NAG5-2906. (1) Collaborate with scientists at NASA Goddard Space Flight Center (GSFC) to integrate SSEC's Vis5D software into NASA's Interactive Image Spread Sheet (IISS). Vis5D provides environmental modelers with interactive three-dimensional visualization of their model output. Integration of Vis5D with the IISS would give 3-D graphics capability to the iiss. (2) Make improvements in Vis5D as required by scientists at the NASA Data Assimilation Office (DAO). We were successful in both of these goals. Furthermore, the generic approach taken to achieving the first goal has enabled Vis5D to be integrated into many other software systems.

Source record↗

NASA NTRS2002

Sensitivity Studies for Assimilated Ozone Profiles

An ozone data assimilation system at the NASA/Goddard Data Assimilation Office (DAO) produces three-dimensional global ozone fields. They are obtained by assimilating ozone retrieved from the Solar Backscatter UltraViolet/2 (SBUV/2) instrument and the Earth Probe Total Ozone Mapping Spectrometer (EP TOMS) measurements into an off-line parameterized chemistry and transport model. In this talk we focus on the quality of lower stratospheric assimilated ozone profiles. Ozone in the lower stratosphere plays a key role in the forcing of climate. A biased ozone field in this region will adversely impact calculations of the stratosphere-troposphere exchange and, when used as a first guess in retrievals, the values determined from satellite observations. The SBUV/2 ozone data have a coarse vertical resolution with increased uncertainty below the ozone maximum, and TOMS provides only total ozone columns. Thus, the assimilated ozone profiles in the lower stratosphere are only weakly constrained by the incoming SBUV and TOMS data. Consequently, the assimilated ozone distribution should be sensitive to changes in inputs to the statistical analysis scheme. We investigate the sensitivity of assimilated ozone profiles to changes in a variety of system inputs: TOMS and SBUV/2 data selection, forecast and observations error covariance models, inclusion or omission of a parameterized chemistry model, and different versions of DAO assimilated wind fields used to drive the transport model. Comparisons of assimilated ozone fields with independent observations, primarily ozone sondes, are used to determine the impact of each of these changes.

Stajner, Ivanka↗

NASA NTRS1989

The use of assimilated stratospheric data in constituent transport calculations

A stratospheric assimilation system has been developed, which generates wind data that is consistent with the geopotential height (and temperature) field and the primitive equations in the general circulation model. This paper reports the first known calculations to use data from an assimilation to calculate constituent transport in the stratosphere. Nitric acid (NHO3) during the Limb IR Monitor of the Stratosphere (Gille et al., 1984) period is studied. The high-latitude time variance of the HNO3 is accurately captured. These studies suggest that data from an assimilation process offers tremendous potential for studying stratospheric dynamics, constituent transport, and chemistry.

Rood, Richard B.↗

NASA NTRS1999

Improving Assimilated Global Data Sets using TMI Rainfall and Columnar Moisture Observations

A global analysis that optimally combine observations from diverse sources with physical models of atmospheric and land processes can provide a comprehensive description of the climate systems. Currently, such data products contain significant errors in primary hydrological fields such as precipitation and evaporation, especially in the tropics. In this study, we show that assimilating precipitation and total precipitable water (TPW) retrievals derived from the TRMM Microwave Imager (TMI) improves not only the hydrological cycle but also key climate parameters such as clouds, radiation, and the large-scale circulation produced by the Goddard Earth Observing System (GEOS) data assimilation system (DAS). In particular, assimilating TMI rain improves clouds and radiation in areas of active convection, as well as the latent heating distribution and the large-scale motion field in the tropics, while assimilating TMI TPW heating distribution and the large-scale motion field in the tropics, while assimilating TMI TPW retrievals leads to reduced moisture biases and improved radiative fluxes in clear-sky regions. The improved analysis also improves short-range forecasts in the tropics. Ensemble forecasts initialized with the GEOS analysis incorporating TMI rain rates and TPW yield smaller biases in tropical precipitation forecasts beyond 1 day and better 500 hPa geopotential height forecasts up to 5 days. Results of this study demonstrate the potential of using high-quality space-borne rainfall and moisture observations to improve the quality of assimilated global data for climate analysis and weather forecasting applications

Hou, Arthur Y.↗

NASA NTRS2003

Impact of Flow-Dependent Error Correlations and Tropospheric Chemistry on Assimilated Ozone

The presentation compares different versions of a global three-dimensional ozone data assimilation system developed at NASA's Data Assimilation Office. The Solar Backscatter Ultraviolet/2 (SBUV/2) total and partial ozone column retrievals are the sole data assimilated in all of the experiments presented. We study the impact of changing the forecast error covariance model from a version assuming static correlations with a one that captures a short-term Lagrangian evolution of those correlations. This is further combined with a study of the impact of neglecting the tropospheric ozone production, loss and dry deposition rates, which are obtained from the Harvard GEOS-CHEM model. We compare statistical characteristics of the assimilated data and the results of validation against independent observations, obtained from WMO balloon-borne sondes and the Polar Ozone and Aerosol Measurement (POAM) III instrument. Experiments show that allowing forecast error correlations to evolve with the flow results in positive impact on assimilated ozone within the regions where data were not assimilated, particularly at high latitudes in both hemispheres. On the other hand, the main sensitivity to tropospheric chemistry is in the Tropics and sub-Tropics. The best agreement between the assimilated ozone and the in-situ sonde data is in the experiment using both flow-dependent error covariances and tropospheric chemistry.

Wargan, K.↗

NASA NTRS2019

Progress Toward Implementation of Coupled Ocean/Atmosphere in Unified Forward Operator (UFO)

The (Sea-Ice Ocean and Coupled Assimilation) SOCA project focuses on meshing atmospheric and marine data assimilation efforts to create innovative data assimilation systems. One of the main goals ofSOCA is to make use of surface-sensitive radiances to constrain sea-ice and upper ocean fields (e.g., salinity, temperature, sea-ice fraction, sea-ice temperature, etc.). the focus of this research is to build first elements toward an ocean/sea-ice/atmosphere coupled data assimilation capability, with a focus on supporting and developing the assimilation of observations sensitive to multiple sub-domains. We Setup the existing Joint Effort for Data assimilation Integration (JEDI) coupled UFO (CRTM related) for surface sensitive microwave radiances (SST and SSS) focusing on Global Precipitation Measurement (GPM) Imager (GMI) and Soil Moisture Active Passive (SMAP).

Ebrahimi, Hamideh↗

NASA NTRS2013

Assimilation of Quality Controlled AIRS Temperature Profiles using the NCEP GFS

We have previously conducted a number of data assimilation experiments using AIRS Version-5 quality controlled temperature profiles as a step toward finding an optimum balance of spatial coverage and sounding accuracy with regard to improving forecast skill. The data assimilation and forecast system we used was the Goddard Earth Observing System Model , Version-5 (GEOS-5) Data Assimilation System (DAS), which represents a combination of the NASA GEOS-5 forecast model with the National Centers for Environmental Prediction (NCEP) operational Grid Point Statistical Interpolation (GSI) global analysis scheme. All analyses and forecasts were run at a 0.5deg x 0.625deg spatial resolution. Data assimilation experiments were conducted in four different seasons, each in a different year. Three different sets of data assimilation experiments were run during each time period: Control; AIRS T(p); and AIRS Radiance. In the "Control" analysis, all the data used operationally by NCEP was assimilated, but no AIRS data was assimilated. Radiances from the Aqua AMSU-A instrument were also assimilated operationally by NCEP and are included in the "Control". The AIRS Radiance assimilation adds AIRS observed radiance observations for a select set of channels to the data set being assimilated, as done operationally by NCEP. In the AIRS T(p) assimilation, all information used in the Control was assimilated as well as Quality Controlled AIRS Version-5 temperature profiles, i.e., AIRS T(p) information was substituted for AIRS radiance information. The AIRS Version-5 temperature profiles were presented to the GSI analysis as rawinsonde profiles, assimilated down to a case-by-case appropriate pressure level p(sub best) determined using the Quality Control procedure. Version-5 also determines case-by-case, level-by-level error estimates of the temperature profiles, which were used as the uncertainty of each temperature measurement. These experiments using GEOS-5 have shown that forecasts resulting from analyses using the AIRS T(p) assimilation system were superior to those from the Radiance assimilation system, both with regard to global 7 day forecast skill and also the ability to predict storm tracks and intensity.

Susskind, Joel↗

NASA NTRS2010

Use of Quality Controlled AIRS Temperature Soundings to Improve Forecast Skill

AIRS was launched on EOS Aqua on May 4, 2002, together with AMSU-A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. The primary products of AIRS/AMSU-A are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. Also included are the clear column radiances used to derive these products which are representative of the radiances AIRS would have seen if there were no clouds in the field of view. All products also have error estimates. The sounding goals of AIRS are to produce 1 km tropospheric layer mean temperatures with an rms error of 1K, and layer precipitable water with an rms error of 20 percent, in cases with up to 90 percent effective cloud cover. The products are designed for data assimilation purposes for the improvement of numerical weather prediction, as well as for the study of climate and meteorological processes. With regard to data assimilation, one can use either the products themselves or the clear column radiances from which the products were derived. The AIRS Version 5 retrieval algorithm is now being used operationally at the Goddard DISC in the routine generation of geophysical parameters derived from AIRS/AMSU data. A major innovation in Version 5 is the ability to generate case-by-case level-by-level error estimates for retrieved quantities and clear column radiances, and the use of these error estimates for Quality Control. The temperature profile error estimates are used to determine a case-by-case characteristic pressure pbest, down to which the profile is considered acceptable for data assimilation purposes. The characteristic pressure p(sub best) is determined by comparing the case dependent error estimate (delta)T(p) to the threshold values (Delta)T(p). The AIRS Version 5 data set provides error estimates of T(p) at all levels, and also profile dependent values of pbest based on use of a Standard profile dependent threshold (Delta)T(p). These Standard thresholds were designed as a compromise between optimal use for data assimilation purposes, which requires highest accuracy (tighter Quality Control), and climate purposes, which requires more spatial coverage (looser Quality Control). Subsequent research using Version 5 sounding and error estimates showed that tighter Quality Control performs better for data assimilation proposes, while looser Quality Control better spatial coverage) performs better for climate purposes. We conducted a number of data assimilation experiments using the NASA GEOS-5 Data Assimilation System as a step toward finding an optimum balance of spatial coverage and sounding accuracy with regard to improving forecast skill. The model was run at a horizontal resolution of 0.5 degree latitude x 0.67 degree longitude with 72 vertical levels. These experiments were run during four different seasons, each using a different year. The AIRS temperature profiles were presented to the GEOS-5 analysis as rawinsonde profiles, and the profile error estimates (delta)T(p) were used as the uncertainty for each measurement in the data assimilation process.

Susskind, Joel↗

NASA NTRS1999

Reconstruction of the 1997/1998 El Nino from TOPEX/POSEIDON and TOGA/TAO Data Using a Massively Parallel Pacific-Ocean Model and Ensemble Kalman Filter

Two massively parallel data assimilation systems in which the model forecast-error covariances are estimated from the distribution of an ensemble of model integrations are applied to the assimilation of 97-98 TOPEX/POSEIDON altimetry and TOGA/TAO temperature data into a Pacific basin version the NASA Seasonal to Interannual Prediction Project (NSIPP)ls quasi-isopycnal ocean general circulation model. in the first system, ensemble of model runs forced by an ensemble of atmospheric model simulations is used to calculate asymptotic error statistics. The data assimilation then occurs in the reduced phase space spanned by the corresponding leading empirical orthogonal functions. The second system is an ensemble Kalman filter in which new error statistics are computed during each assimilation cycle from the time-dependent ensemble distribution. The data assimilation experiments are conducted on NSIPP's 512-processor CRAY T3E. The two data assimilation systems are validated by withholding part of the data and quantifying the extent to which the withheld information can be inferred from the assimilation of the remaining data. The pros and cons of each system are discussed.

Keppenne, C. L.↗

NASA NTRS2022

Assessment of Retrieved GMI Emissivity Over Land, Snow, and Sea Ice in the GEOS System

Directly assimilating microwave radiances over land, snow and sea ice remains a significant challenge for data assimilation systems. These data assimilation systems are critical to the success of global numerical weather prediction systems including the Global Earth Observing System-Atmospheric Data Assimilation System (GEOS-ADAS). Extending more surface sensitive microwave channels over land, snow and ice could provide a needed source of data for Numerical Weather Prediction particularly in the Planetary Boundary Layer (PBL). Unfortunately, the accuracy of emissivity models currently available within the GEOS-ADAS along with other data assimilation systems are insufficient to simulate and assimilate radiances. Recently, Munchak et al. (2020) published a 5-year climatological database for retrieved microwave emissivity from the GPM Microwave Imager (GMI) aboard the Global Precipitation Mission (GPM). In this work the database is utilized by modifying the GEOS-ADAS to use this emissivity database in place of the default emissivity value available in the Community Radiative Transfer Model (CRTM), which is the fast radiative transfer model used by the GEOS-ADAS. As a first step, the GEOS-ADAS is run in a so-called “stand-alone” mode to simulate radiances from GMI using the default CRTM emissivity, and replacing the default CRTM emissivity models with values from Munchak et al, 2020. The simulated observations using Munchak et al., 2020 agree more closely with observations from GMI. These results are presented along with a discussion of the implication for GMI observations within the GEOS-ADAS.

GPM↗

NASA NTRSDate not supplied

An Update on the Hydrological Land Surface Data and Services at NASA GES DISC

"The NASA Goddard Earth Sciences Data and Information Services Center (GES DISC) is one of twelve NASA Earth Observing System data centers that document, process, archive and distribute data from Earth science missions and related projects. The GES DISC hosts many hydrological land surface data products including North American Land Data Assimilation System (NLDAS), Global Land Data Assimilation System (GLDAS), the Famine Early Warning Systems Network (FEWS NET) Land Data Assimilation System (FLDAS), and assimilated-Gravity Recovery and Climate Experiment (GRACE). The Land Surface Model (LSM) products contain model output, including heat fluxes, rain, snow, soil temperature, soil moisture and runoff; and observational forcing data, including surface pressure, temperature, precipitation, downward shortwave and longwave radiation, humidity, and wind. The temporal resolution of the hydrology data at the GES DISC ranges from hourly to monthly and the spatial resolution 0.1 degree to 1.0 degree. The variability of Earth’s water and energy cycles can be characterized with these spatially and temporally consistent, and quality controlled hydrological land surface data. These data could support ongoing modeling activities, and help improve our understanding of land-surface-atmosphere interactions and their impact on climate. Over the years, new data is added, and older data is reprocessed and updated. This presentation provides a summary table of the hydrological data and discusses recent updates to the data and data services at the GES DISC. New data products include (1) GRACE Global Version 3.0 drought indicators and (2) FLDAS monthly global and Central Asia daily data. Reprocessed and updated products include (1) NLDAS Version 2.0 and (2) GRACE United States Version 4.0 drought indicators. Lastly, this presentation will discuss the opportunities for accessing some of our hydrology data from the cloud. As the hydrology land surface data is moved to the cloud, users can expect faster service for longer time series, notably the hydrology data rods time series service."

Ashley Heath↗

NASA NTRS2003

Local and Remote Sources of Precipitation during the 1993 Midwestern United States Flood

During June and July of 1993, devastating and persistent rainfall caused substantial damage in the Midwest United States primarily focused on the Mississippi River Basin. Above noma1 springtime rains primed the region for flooding. The resulting wet soil was thought to be a major source of water for the heavy summer precipitation. On the other hand, northward moisture transport was extremely intense during the summer. In this study, we have implemented passive tracers to diagnose the geographic source of water for precipitation, called Water Vapor Tracers (WVT), into the NASA Data Assimilation Office (DAO) Data Assimilation System (DAS). The WVT diagnostics can produce detailed budgets of the geographical sources of water that precipitates in any region, and they consider physical and dynamical tendencies at the model time step. The 1993 summer has been reanalyzed with the new WVT diagnostics to better understand the local and remote source of water for precipitation during the flood. Because the DAS also uses observations of water in the atmospheric hydrologic budget, we will also evaluate the impact of the observations on the local and remote sources of water in the DAS.

Bosilovich, Michael↗

NASA NTRS2008

Using Sensor Web Processes and Protocols to Assimilate Satellite Data into a Forecast Model

The goal of the Sensor Management Applied Research Technologies (SMART) On-Demand Modeling project is to develop and demonstrate the readiness of the Open Geospatial Consortium (OGC) Sensor Web Enablement (SWE) capabilities to integrate both space-based Earth observations and forecast model output into new data acquisition and assimilation strategies. The project is developing sensor web-enabled processing plans to assimilate Atmospheric Infrared Sounding (AIRS) satellite temperature and moisture retrievals into a regional Weather Research and Forecast (WRF) model over the southeastern United States.

Goodman, H. Michael↗

NASA NTRS2003

Analysis and Forecast of Two Storms Characterized by Extreme Deepening Rates

Between 25 and 27 December 1999 two very intense cyclones, named Lothar and Martin, swept across northern and western France causing substantial life and property loss. In this work, the finite volume general circulation model and data assimilation system (fvDAS) developed at the Data Assimilation Office of the NASA Goddard Space and Flight Center is being used to investigate these storms. In the first part of this article the dynamics of the storms is analyzed, and some important mechanisms are unveiled. The second part describes a set of eleven data assimilation experiments to study the impact of different data types on the automated analyses. Cloud-track winds provided by EUMETSAT and surface winds from QuikSCAT are being used. These data are assimilated with a range of different parameter settings of the forecast error covariance model. The results show that generally the additional wind data set have positive impacts on the analyses: particularly, the analysis of Lothar can be slightly improved by using the Eumetsat winds, and the analysis of Martin can be strongly improved by using the full-resolution QuikSCAT winds with a more localized influence. The third part of this article is focused on the forecast of Lothar which is very well predicted in the 1-5 day range by the fvDAS system.

Reale, Oreste↗

NASA NTRSDate not supplied

Implementing JEDI into NASA GMAO’s Real Time Production Suite

NASA’s Global Modeling and Assimilation Office (GMAO) has prepared their first production system involving the Joint Effort for Data assimilation Integration (JEDI) framework. In this system the central analysis, that drives the deterministic forecast, will be provided using JEDI. This talk outlines the phased approach to implementing JEDI into production that GMAO has designed, and how this approach will allow for a careful analysis of the system against the existing data assimilation framework (GSI). In the first phase of implementation the existing data assimilation system will perform certain actions that are still under development in JEDI. These include thinning the observations and producing satellite bias correction coefficients. JEDI is hooked up to the existing workflow so a single line switch can activate whether the existing or JEDI-based analysis is cycled. Outside of the monumental effort to construct JEDI that is ongoing at the Joint Center for Satellite Data Assimilation (JCSDA), GMAO have undertaken two areas of considerable effort. The talk will describe these efforts and highlight the main challenges that have been encountered. The first area of work is to implement the background error model from the existing data assimilation system into JEDI. The second is to validate the observing system in JEDI against the one in GSI, which has involved several new features being added to the observation operators in JEDI. While the longer-term plans involve trying to improve on the GSI in these two areas, GMAO is keen to have JEDI start from a trusted baseline. This is also key to implementing JEDI quickly so other priorities, such as increasing the number of model levels, can be easily worked on in parallel. GMAO is actively working on a framework to shepherd in the next generation coupled data assimilation system and model. As JEDI is implemented for the first time the plan is to ambitiously cycle through implementations, frequently bringing JEDI features to production. Details of these plans will be given in the talk and we will highlight key implementation and product milestones that we hope to achieve, as well as touch on the development environment that we will use to support frequent refreshing of the production system.

JEDI↗

NASA NTRS1999

Massively Parallel Assimilation of TOGA/TAO and Topex/Poseidon Measurements into a Quasi Isopycnal Ocean General Circulation Model Using an Ensemble Kalman Filter

A massively parallel ensemble Kalman filter (EnKF)is used to assimilate temperature data from the TOGA/TAO array and altimetry from TOPEX/POSEIDON into a Pacific basin version of the NASA Seasonal to Interannual Prediction Project (NSIPP)ls quasi-isopycnal ocean general circulation model. The EnKF is an approximate Kalman filter in which the error-covariance propagation step is modeled by the integration of multiple instances of a numerical model. An estimate of the true error covariances is then inferred from the distribution of the ensemble of model state vectors. This inplementation of the filter takes advantage of the inherent parallelism in the EnKF algorithm by running all the model instances concurrently. The Kalman filter update step also occurs in parallel by having each processor process the observations that occur in the region of physical space for which it is responsible. The massively parallel data assimilation system is validated by withholding some of the data and then quantifying the extent to which the withheld information can be inferred from the assimilation of the remaining data. The distributions of the forecast and analysis error covariances predicted by the ENKF are also examined.

Keppenne, Christian L.↗

NASA NTRS1999

Improving Reanalyses Using TRMM and SSM/I-Derived Precipitation and Total Precipitable Water Observations

Global reanalyses currently contain significant errors in the primary fields of the hydrological cycle such as precipitation, evaporation, moisture, and the related cloud fields, especially in the tropics. The Data Assimilation Office (DAO) at the NASA Goddard Space Flight Center has been exploring the use of rainfall and total precipitable water (TPW) observations from the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) and the Special Sensor Microwave/ Imager (SSM/I) instruments to improve these fields in reanalyses. The DAO has developed a "1+1"D procedure to assimilate 6-hr averaged rainfall and TPW into the Goddard Earth Observing System (GEOS) Data Assimilation System (DAS). The algorithm is based on a 6-hr time integration of a column version of the GEOS DAS. The "1+1" designation refers to one spatial dimension plus one temporal dimension. The scheme minimizes the least-square differences between the satellite-retrieved rain rates and those produced by the column model over the 6-hr analysis window. The control variables are analysis increments of moisture within the Incremental Analysis Update (IAU) framework of the GEOS DAS. This 1+1D scheme, in its generalization to four dimensions, is related to the standard 4D variational assimilation but differs in its choice of the control variable. Instead of estimating the initial condition at the beginning of the assimilation cycle, it estimates the constant IAU forcing applied over a 6-hr assimilation cycle. In doing so, it imposes the forecast model as a weak constraint in a manner similar to the variational continuous assimilation techniques. We present results from an experiment in which the observed rain rate and TPW are assumed to be "perfect". They show that assimilating the TMI and SSM/I-derived surface precipitation and TPW observations improves not only the precipitation and moisture fields but also key climate parameters directly linked to convective activities such as clouds, the outgoing longwave radiation, and the large-scale circulation in the tropics. In particular, assimilating these data types reduce the state-dependent systematic errors in the assimilated products. The improved analysis also leads to a better short-range forecast, but the impact is modest compared with improvements in the time-averaged fields. These results suggest that, in the presence of biases and other errors of the forecast model, it is possible to improve the time-averaged "climate content" in the assimilated data without comparable improvements in the short-range forecast skill. Results of this experiment provide a useful benchmark for evaluating error covariance models for optimal use of these data types.

Hou, Arthur Y.↗

NASA NTRS2002

The Retrospective Iterated Analysis Scheme for Nonlinear Chaotic Dynamics

Atmospheric data assimilation is the name scientists give to the techniques of blending atmospheric observations with atmospheric model results to obtain an accurate idea of what the atmosphere looks like at any given time. Because two pieces of information are used, observations and model results, the outcomes of data assimilation procedure should be better than what one would get by using one of these two pieces of information alone. There is a number of different mathematical techniques that fall under the data assimilation jargon. In theory most these techniques accomplish about the same thing. In practice, however, slight differences in the approaches amount to faster algorithms in some cases, more economical algorithms in other cases, and even give better overall results in yet some other cases because of practical uncertainties not accounted for by theory. Therefore, the key is to find the most adequate data assimilation procedure for the problem in hand. In our Data Assimilation group we have been doing extensive research to try and find just such data assimilation procedure. One promising possibility is what we call retrospective iterated analysis (RIA) scheme. This procedure has recently been implemented and studied in the context of a very large data assimilation system built to help predict and study weather and climate. Although the results from that study suggest that the RIA scheme produces quite reasonable results, a complete evaluation of the scheme is very difficult due to the complexity of that problem. The present work steps back a little bit and studies the behavior of the RIA scheme in the context of a small problem. The problem is small enough to allow full assessment of the quality of the RIA scheme, but it still has some of the complexity found in nature, namely, its chaotic-type behavior. We find that the RIA performs very well for this small but still complex problem which is a result that seconds the results of our early studies.

Todling, Ricardo↗