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NASA NTRS2011

Ten Years of Cloud Properties from MODIS: Global Statistics and Use in Climate Model Evaluation

The NASA Moderate Resolution Imaging Spectroradiometer (MODIS), launched onboard the Terra and Aqua spacecrafts, began Earth observations on February 24, 2000 and June 24,2002, respectively. Among the algorithms developed and applied to this sensor, a suite of cloud products includes cloud masking/detection, cloud-top properties (temperature, pressure), and optical properties (optical thickness, effective particle radius, water path, and thermodynamic phase). All cloud algorithms underwent numerous changes and enhancements between for the latest Collection 5 production version; this process continues with the current Collection 6 development. We will show example MODIS Collection 5 cloud climatologies derived from global spatial . and temporal aggregations provided in the archived gridded Level-3 MODIS atmosphere team product (product names MOD08 and MYD08 for MODIS Terra and Aqua, respectively). Data sets in this Level-3 product include scalar statistics as well as 1- and 2-D histograms of many cloud properties, allowing for higher order information and correlation studies. In addition to these statistics, we will show trends and statistical significance in annual and seasonal means for a variety of the MODIS cloud properties, as well as the time required for detection given assumed trends. To assist in climate model evaluation, we have developed a MODIS cloud simulator with an accompanying netCDF file containing subsetted monthly Level-3 statistical data sets that correspond to the simulator output. Correlations of cloud properties with ENSO offer the potential to evaluate model cloud sensitivity; initial results will be discussed.

Platnick, Steven E.↗
NASA NTRS2012

P69 Using the NASA-Unified WRF to Assess the Impacts of Real-Time Vegetation on Simulations of Severe Weather

Since June 2010, the NASA Short-term Prediction Research and Transition (SPoRT; Goodman et al. 2004; Darden et al. 2010; Stano et al. 2012; Fuell et al. 2012) Center has been generating a real-time Normalized Difference Vegetation Index (NDVI) and corresponding Green Vegetation Fraction (GVF) composite based on reflectances from NASA s Moderate Resolution Imaging Spectroradiometer (MODIS) instrument. This dataset is generated at 0.01 resolution across the Continental United States (CONUS), and updated daily. The goal of producing such a vegetation dataset is to improve over the default climatological GVF dataset in land surface and numerical weather prediction models, in order to have better simulations of heat and moisture exchange between the land surface and the planetary boundary layer. Details on the SPoRT/MODIS vegetation composite algorithm are presented in Case et al. (2011). Vegetation indices such as GVF and Leaf Area Index (LAI) are used by land surface models (LSMs) to represent the horizontal and vertical density of plant vegetation (Gutman and Ignatov 1998), in order to calculate transpiration, interception and radiative shading. Both of these indices are related to the NDVI; however, there is an inherent ambiguity in determining GVF and LAI simultaneously from NDVI, as described in Gutman and Ignatov (1998). One practice is to specify the LAI while allowing the GVF to vary both spatially and temporally, as is done in the Noah LSM (Chen and Dudhia 2001; Ek et al. 2003). Operational versions of Noah within several of the National Centers for Environmental Prediction (NCEP) global and regional modeling systems hold the LAI fixed, while the GVF varies according to a global monthly climatology. This GVF climatology was derived from NDVI data on the NOAA Advanced Very High Resolution Radiometer (AVHRR) polar orbiting satellite, using information from 1985 to 1991 (Gutman and Ignatov 1998; Jiang et al. 2010). Representing data at the mid-point of every month, the climatological dataset is on a grid with 0.144 (~16 km) spatial resolution and is distributed with the community WRF model (Ek et al. 2003; Jiang et al. 2010; Skamarock et al. 2008).

Case, Jonathan L.↗
NASA NTRS2018

NASA SPoRT JPSS PG Activities in Alaska

SPoRT (NASA's Short-term Prediction Research and Transition Center) has collaboratively worked with Alaska WFOs (Weather Forecast Offices) to introduce RGB (Red/Green/Blue false color image) imagery to prepare for NOAA-20 (National Oceanic and Atmospheric Administration, JPSS (Joint Polar Satellite System) series-20 satellite) VIIRS (Visible Infrared Imaging Radiometer Suite) and improve forecasting aviation-related hazards. Last R2O/O2R (Research-to-Operations/Operations-to-Research) steps include incorporating NOAA-20 VIIRS in RGB suite and fully transitioning client-side RGB processing to GINA (Geographic Information Network of Alaska) and Alaska Region. Alaska Region WFOs have been part of the successful R2O/O2R story to assess the use of NESDIS (National Environmental Satellite, Data, and Information Service) Snowfall Rate product in operations. SPoRT introduced passive microwave rain rate and IMERG (Integrated Multi-satellitE Retrievals for GPM (Global Precipitation Measurement)) (IMERG) to Alaska WFOs for use in radar-void areas and assessing flooding potential. SPoRT has been part of the multi-organization collaborative effort to introduce Gridded NUCAPS (NOAA Unique CrIS/ATMS (Crosstrack Infrared Sounder/Advanced Technology Microwave Sounder) Processing System) to the Anchorage CWSU (Center Weather Service Unit) to assess Cold Air Aloft events, [and as part of NOAA's PG (Product Generation) effort].

Berndt, Emily↗
NASA NTRS1980

A cloud cover model based on satellite data

A model for worldwide cloud cover using a satellite data set containing infrared radiation measurements is proposed. The satellite data set containing day IR, night IR and incoming and absorbed solar radiation measurements on a 2.5 degree latitude-longitude grid covering a 45 month period was converted to estimates of cloud cover. The global area was then classified into homogeneous cloud cover regions for each of the four seasons. It is noted that the developed maps can be of use to the practicing climatologist who can obtain a considerable amount of cloud cover information without recourse to large volumes of data.

Somerville, P. N.↗
NASA NTRS1984

User's guide for SBUV/TOMS ozone derivative products

A series of products are available derived from the total-ozone and ozone vertical profile results for the Solar Backscattered Ultraviolet/Total-Ozone Mapping Spectrometer (SBUV/TOMS) Nimbus-7 operation. Products available are (1) orbital height-latitude cross sections of the SBUV profile data, (2) daily global total ozone contours in polar coordinates, (3) daily averages of total ozone in global 5x5 degree latitude-longitude grid, (4) daily, monthly and quarterly averages of total ozone and profile data in 10 degree latitude zones, (5) tabular presentation of zonal means, (6) daily global total ozone and profile contours in polar coordinates. The ""Derivative Products User's Guide'' describes each of these products in detail, including their derivation and presentation format. Information is provided on how to order the tapes and microfilm from the National Space Science Data Center.

Fleig, A. J.↗
NASA NTRS2003

High Performance Parallel Methods for Space Weather Simulations

This is the final report of our NASA AISRP grant entitled 'High Performance Parallel Methods for Space Weather Simulations'. The main thrust of the proposal was to achieve significant progress towards new high-performance methods which would greatly accelerate global MHD simulations and eventually make it possible to develop first-principles based space weather simulations which run much faster than real time. We are pleased to report that with the help of this award we made major progress in this direction and developed the first parallel implicit global MHD code with adaptive mesh refinement. The main limitation of all earlier global space physics MHD codes was the explicit time stepping algorithm. Explicit time steps are limited by the Courant-Friedrichs-Lewy (CFL) condition, which essentially ensures that no information travels more than a cell size during a time step. This condition represents a non-linear penalty for highly resolved calculations, since finer grid resolution (and consequently smaller computational cells) not only results in more computational cells, but also in smaller time steps.

Hunter, Paul↗
NASA NTRS2005

NASA GES DISC On-line Visualization and Analysis System for Gridded Remote Sensing Data

The ability to use data stored in the current NASA Earth Observing System (EOS) archives for studying regional or global phenomena is highly dependent on having a detailed understanding of the data's internal structure and physical implementation. Gaining this understanding and applying it to data reduction is a time-consuming task that must be undertaken before the core investigation can begin. This is an especially difficult challenge when science objectives require users to deal with large multi-sensor data sets that are usually of different formats, structures, and resolutions. The NASA Goddard Earth Sciences Data and Information Services Center (GES DISC) has taken a major step towards meeting this challenge by developing an infrastructure with a Web interface that allows users to perform interactive analysis online without downloading any data, the GES-DISC Interactive Online Visualization and Analysis Infrastructure or "Giovanni." Giovanni provides interactive, online, analysis tools for data users to facilitate their research. There have been several instances of this interface created to serve TRMM users, Aerosol scientists, Ocean Color and Agriculture applications users. The first generation of these tools support gridded data only. The user selects geophysical parameters, area of interest, time period; and the system generates an output on screen in a matter of seconds. The currently available output options are: Area plot averaged or accumulated over any available data period for any rectangular area; Time plot time series averaged over any rectangular area; Hovmoller plots image view of any longitude-time and latitude-time cross sections; ASCII output for all plot types; Image animation for area plot. Another analysis suite deals with parameter intercomparison: scatter plots, temporal correlation maps, GIs-compatible outputs, etc. This allow user to focus on data content (i.e. science parameters) and eliminate the need for expensive learning, development and processing tasks that are redundantly incurred by an archive's user community. The current implementation utilizes the GrADS-DODS Server (GDS), and provides subsetting and analysis services across the Internet for any GrADS-readable dataset. The subsetting capability allows users to retrieve a specified temporal and/or spatial subdomain from a large dataset, eliminating the need to download everything simply to access a small relevant portion of a dataset. The analysis capability allows users to retrieve the results of an operation applied to one or more datasets on the server. We use this approach to read pre-processed binary files and/or to read and extract the needed parts directly from HDF or HDF-EOS files. These subsets then serve as inputs into GrADS analysis scripts. It can be used in a wide variety of Earth science applications: climate and weather events study and monitoring; modeling. It can be easily configured for new applications.

Leptoukh, Gregory G.↗
NASA NTRS2000

BOREAS RSS-10 TOMS Circumpolar One-Degree PAR Images

The Boreal Ecosystem-Atmosphere Study (BOREAS) Remote Sensing Science (RSS)-10 team investigated the magnitude of daily, seasonal, and yearly variations of Photosynthetically Active Radiation (PAR) from ground and satellite observations. This data set contains satellite estimates of surface-incident PAR (400-700 nm, MJ/sq m) at one-degree spatial resolution. The spatial coverage is circumpolar from latitudes of 41 to 66 degrees north. The temporal coverage is from May through September for years 1979 through 1989. Eleven-year statistics are also provided: (1) mean, (2) standard deviation, and (3) coefficient of variation for 1979-89. The PAR estimates were derived from the global gridded ultraviolet reflectivity data product (average of 360, 380 nm) from the Nimbus-7 Total Ozone Mapping Spectrometer (TOMS). Image mask data are provided for identifying the boreal forest zone, and ocean/land and snow/ice-covered areas. The data are available as binary image format data files. The PAR data are available from the Earth Observing System Data and Information System (EOSDIS) Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC). The data files are available on a CD-ROM (see document number 20010000884).

Dye, Dennis G.↗
NASA NTRS2015

Improving the Timeliness of Winter Wheat Production Forecast in the United States of America, Ukraine and China Using MODIS Data and NCAR Growing Degree Day Information

Wheat is themost important cereal crop traded on international markets and winter wheat constitutes approximately 80% of global wheat production. Thus, accurate and timely production forecasts are critical for making informed agricultural policies and investments, as well as increasing market efficiency and stability. Becker-Reshef et al. (2010) developed an empirical generalized model for forecasting winter wheat production. Their approach combined BRDF-corrected daily surface reflectance from Moderate resolution Imaging Spectroradiometer (MODIS) Climate Modeling Grid (CMG) with detailed official crop statistics and crop typemasks. It is based on the relationship between the Normalized Difference Vegetation Index (NDVI) at the peak of the growing season, percent wheat within the CMG pixel (area within the CMG pixel occupied by wheat), and the final yields. This method predicts the yield approximately one month to six weeks prior to harvest. In this study, we include Growing Degree Day (GDD) information extracted from NCEP/NCAR reanalysis data in order to improve the winter wheat production forecast by increasing the timeliness of the forecasts while conserving the accuracy of the original model. We apply this modified model to three major wheat-producing countries: the Unites States (US), Ukraine and China from 2001 to 2012. We show that a reliable forecast can be made between one month to a month and a half prior to the peak NDVI (meaning two months to two and a half months prior to harvest), while conserving an accuracy of 10% in the production forecast.

Production↗
NASA NTRS2004

Distributive On-line Processing, Visualization and Analysis System for Gridded Remote Sensing Data

The ability to use data stored in the current Earth Observing System (EOS) archives for studying regional or global phenomena is highly dependent on having a detailed understanding of the data's internal structure and physical implementation. Gaining this understanding and applying it to data reduction is a time- consuming task that must be undertaken before the core investigation can begin. This is an especially difficult challenge when science objectives require users to deal with large multi-sensor data sets that are usually of different formats, structures, and resolutions, for example, when preparing data for input into modeling systems. The NASA Goddard Earth Sciences Data and Information Services Center (GES DISC) has taken a major step towards meeting this challenge by developing an infrastructure with a Web interface that allows users to perform interactive analysis online without downloading any data, the GES-DISC Interactive Online Visualization and Analysis Infrastructure or "Giovanni." Giovanni provides interactive, online, analysis tools for data users to facilitate their research. There have been several instances of this interface created to serve TRMM users, Aerosol scientists, Ocean Color and Agriculture applications users. The first generation of these tools support gridded data only. The user selects geophysical parameters, area of interest, time period; and the system generates an output on screen in a matter of seconds. The currently available output options are: Area plot averaged or accumulated over any available data period for any rectangular area; Time plot time series averaged over any rectangular area; Time plots image view of any longitude-time and latitude-time cross sections; ASCII output for all plot types; Image animation for area plot. In the future, we will add correlation plots, GIS-compatible outputs, etc. This allow user to focus on data content (i.e. science parameters) and eliminate the need for expensive learning, development and processing tasks that are redundantly incurred by an archive's user community. The current implementation utilizes the GrADS-DODS Server (GDS), a stable, secure data server that provides subsetting and analysis services across the Internet for any GrADS-readable dataset. The subsetting capability allows users to retrieve a specified temporal and/or spatial subdomain from a large dataset, eliminating the need to download everything simply to access a small relevant portion of a dataset. The analysis capability allows users to retrieve the results of an operation applied to one or more datasets on the server. In our case, we use this approach to read pre-processed binary files and/or to read and extract the needed parts from HDF or HDF-EOS files. These subsets then serve as inputs into GrADS processing and analysis scripts. It can be used in a wide variety of Earth science applications: climate and weather events study and monitoring; modeling. It can be easily configured for new applications.

Leptoukh, G.↗
NASA NTRS2019

Citizen Science Twitter Data Management for Earth Science Applications

Social media data can provide useful real-time and historical information relating to the natural world, but managing this data poses challenges. Scientists at GES DISC are exploring the potential of Twitter data to augment precipitation data from the Global Precipitation Measurement (GPM) mission. However, the format of Twitter data is unconventional in the context of NASA data centers, resulting in frustration for scientists who need to work with the data. This study investigated procedures and standards needed to properly manage Twitter data to make them compatible with these data centers. After comparing databases, the study found that the MongoDB database was best suited for the storage of raw Twitter data due to its flexibility, ability to be accessed by multiple users, and querying functionality. The study used the Python package Zarr to transform processed Twitter data into a gridded format similar to that of satellite data. Each Tweet was mapped onto a time-space grid; each grid location contained information about Tweet attributes and precipitation. The study developed a pipeline for downloading, storing, and gridding Twitter data and transformed Twitter data into an understandable format for users of NASA satellite data.

Li, Rachel↗
NASA NTRS2006

Introduction to MODIS Cloud Products

The Earth's radiative energy balance and hydrological cycle are fundamentally coupled with the distribution and properties of clouds. Therefore, the ability to remotely infer cloud properties and their variation in space and time is crucial for establishing climatologies as a reference for validation of present-day climate models and in assessing future climate change. Remote cloud observations also provide data sets useful for testing and improving cloud model physics, and for assimilation into numerical weather prediction models. The MODerate Resolution Imaging Spectroradiometer (MODIS) imagers on the Terra and Aqua Earth Observing System (EOS) platforms provide the capability for globally retrieving these properties using passive solar reflectance and infrared techniques. In addition to providing measurements similar to those offered on a suite of historical operational weather platforms such as the Advanced Very High Resolution Radiometer (AVHRR), the High-resolution Infrared Radiation Sounder (HIRS), and the Geostationary Operational Environmental Satellite (GOES), MODIS provides additional spectral and/or spatial resolution in key atmospheric bands, along with on-board calibration, to expand the capability for global cloud property retrievals. The core MODIS operational cloud products include cloud top pressure, thermodynamic phase, optical thickness, particle size, and water path, and are derived globally at spatial resolutions of either 1- or 5-km (referred to as Level-2 or pixel-level products). In addition, the MODIS atmosphere team (collectively providing cloud, aerosol, and clear sky products) produces a combined gridded product (referred to as Level-3) aggregated to a 1 equal-angle grid, available for daily, eight-day, and monthly time periods. The wealth of information available from these products provides critical information for climate studies as well as the continuation and improved understanding of existing satellite-based cloud climatologies derived from heritage instruments. This chapter provides an overview of the MODIS Level-2 and -3 operational cloud products.

Baum, Bryan A.↗
NASA NTRS2012

Preliminary Results of a U.S. Deep South Warm Season Deep Convective Initiation Modeling Experiment using NASA SPoRT Initialization Datasets for Operational National Weather Service Local Model Runs

The initiation of deep convection during the warm season is a forecast challenge in the relative high instability and low wind shear environment of the U.S. Deep South. Despite improved knowledge of the character of well known mesoscale features such as local sea-, bay- and land-breezes, observations show the evolution of these features fall well short in fully describing the location of first initiates. A joint collaborative modeling effort among the NWS offices in Mobile, AL, and Houston, TX, and NASA s Short-term Prediction Research and Transition (SPoRT) Center was undertaken during the 2012 warm season to examine the impact of certain NASA produced products on the Weather Research and Forecasting Environmental Modeling System. The NASA products were: a 4-km Land Information System data, a 1-km sea surface temperature analysis, and a 4-km greenness vegetation fraction analysis. Similar domains were established over the southeast Texas and Alabama coastlines, each with a 9 km outer grid spacing and a 3 km inner nest spacing. The model was run at each NWS office once per day out to 24 hours from 0600 UTC, using the NCEP Global Forecast System for initial and boundary conditions. Control runs without the NASA products were made at the NASA SPoRT Center. The NCAR Model Evaluation Tools verification package was used to evaluate both the forecast timing and location of the first initiates, with a focus on the impacts of the NASA products on the model forecasts. Select case studies will be presented to highlight the influence of the products.

Medlin, Jeffrey M.↗
NASA NTRS2018

Comparisons of Two Spatial Implementations of a Crop Model Using Remotely Sensed Observations over Southeastern United States

Global food security is one of the most pressing issues of the current century, particularly for developing nations. Agricultural simulation models can be a key component in testing new technologies, seeds and cultivars etc. However, inaccurate input information, model related errors and the mode of implementation can also add to model uncertainties. In this study, the crop model is implemented in two separate fashions: a)gridded (GriDSSAT model) and b) using random spatial ensembles (RHEAS model). This is done in the Southeastern US to evaluate and understand the modelperformance over a region data availabilities. Once the model performance is assessed, multiple satellite based earth observation parameters such as soil moisture, vegetation index etc. can be assimilated into crop models to reduce input and model related uncertainties particularly in data limited regions. In this study, the National Agricultural Statistical Services (NASS) reported yield data at county levels are used for comparison andvalidation purposes. The GriDSSAT model estimation of corn yields in comparison with the reported NASS yields showed an overall RMSD of nearly 3720 (kg/ha) whereas RMSD for the RHEAS model implementation was 3550 (kg/ha). Overall the GriDSSAT model had negative bias of nearly 2400 kg/ha (except for 2013) while RHEAS had a slight positive bias of 400 kg/ha (approx.).

SERVIR↗
NASA NTRS2012

Preliminary Results of a U.S. Deep South Modeling Experiment Using NASA SPoRT Initialization Datasets for Operational National Weather Service Local Model Runs

A joint collaborative modeling effort among the NWS offices in Mobile, AL, and Houston, TX, and NASA Short-term Prediction Research and Transition (SPoRT) Center began during the 2011-2012 cold season, and continued into the 2012 warm season. The focus was on two frequent U.S. Deep South forecast challenges: the initiation of deep convection during the warm season; and heavy precipitation during the cold season. We wanted to examine the impact of certain NASA produced products on the Weather Research and Forecasting Environmental Modeling System in improving the model representation of mesoscale boundaries such as the local sea-, bay- and land-breezes (which often leads to warm season convective initiation); and improving the model representation of slow moving, or quasi-stationary frontal boundaries (which focus cold season storm cell training and heavy precipitation). The NASA products were: the 4-km Land Information System, a 1-km sea surface temperature analysis, and a 4-km greenness vegetation fraction analysis. Similar domains were established over the southeast Texas and Alabama coastlines, each with an outer grid with a 9 km spacing and an inner nest with a 3 km grid spacing. The model was run at each NWS office once per day out to 24 hours from 0600 UTC, using the NCEP Global Forecast System for initial and boundary conditions. Control runs without the NASA products were made at the NASA SPoRT Center. The NCAR Model Evaluation Tools verification package was used to evaluate both the positive and negative impacts of the NASA products on the model forecasts. Select case studies will be presented to highlight the influence of the products.

Wood, Lance↗
NASA NTRS1992

A global mean sea surface based upon GEOS 3 and Seasat altimeter data

A mean sea surface relative to the International Union of Geodesy 1980 Geodetic Reference System reference ellipsoid has been derived from Seasat and GEOS 3 altimeter measurements. This surface, called MSS-9012, has been computed on a grid of 1/8 deg resolution. The surface covers the global ocean between 70 deg N and 72 deg S. Comparisons are made between MSS-9012 and ocean bathymetry. The eastern extent of the Chain Fracture Zone in the Gulf of Guinea is more apparent in the altimetry than in the bathymetry data, as are many other features. The combination of data from the two satellites has successfully retrieved more information about the sea surface than was previously possible using only Seasat data.

Marsh, J. G.↗
NASA NTRS2008

A Goddard Multi-Scale Modeling System with Unified Physics

Numerical cloud resolving models (CRMs), which are based the non-hydrostatic equations of motion, have been extensively applied to cloud-scale and mesoscale processes during the past four decades. Recent GEWEX Cloud System Study (GCSS) model comparison projects have indicated that CRMs agree with observations in simulating various types of clouds and cloud systems from different geographic locations. Cloud resolving models now provide statistical information useful for developing more realistic physically based parameterizations for climate models and numerical weather prediction models. It is also expected that Numerical Weather Prediction (NWP) and regional scale model can be run in grid size similar to cloud resolving model through nesting technique. Current and future NASA satellite programs can provide cloud, precipitation, aerosol and other data at very fine spatial and temporal scales. It requires a coupled global circulation model (GCM) and cloud-scale model (termed a szrper-parameterization or multi-scale modeling -framework, MMF) to use these satellite data to improve the understanding of the physical processes that are responsible for the variation in global and regional climate and hydrological systems. The use of a GCM will enable global coverage, and the use of a CRM will allow for better and more sophisticated physical parameterization. NASA satellite and field campaign can provide initial conditions as well as validation through utilizing the Earth Satellite simulators. At Goddard, we have developed a multi-scale modeling system with unified physics. The modeling system consists a coupled GCM-CRM (or MMF); a state-of-the-art weather research forecast model (WRF) and a cloud-resolving model (Goddard Cumulus Ensemble model). In these models, the same microphysical schemes (2ICE, several 3ICE), radiation (including explicitly calculated cloud optical properties), and surface models are applied. In addition, a comprehensive unified Earth Satellite simulator has been developed at GSFC, which is designed to fully utilize the multi-scale modeling system. A brief review of the multi-scale modeling system with unified physics/simulator and examples is presented in this article.

Tao, W.K.↗
NASA NTRS1992

Artificial intelligence approach to planning the robotic assembly of large tetrahedral truss structures

An assembly planner for tetrahedral truss structures is presented. To overcome the difficulties due to the large number of parts, the planner exploits the simplicity and uniformity of the shapes of the parts and the regularity of their interconnection. The planning automation is based on the computational formalism known as production system. The global data base consists of a hexagonal grid representation of the truss structure. This representation captures the regularity of tetrahedral truss structures and their multiple hierarchies. It maps into quadratic grids and can be implemented in a computer by using a two-dimensional array data structure. By maintaining the multiple hierarchies explicitly in the model, the choice of a particular hierarchy is only made when needed, thus allowing a more informed decision. Furthermore, testing the preconditions of the production rules is simple because the patterned way in which the struts are interconnected is incorporated into the topology of the hexagonal grid. A directed graph representation of assembly sequences allows the use of both graph search and backtracking control strategies.

Homemdemello, Luiz S.↗