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1 15 Universities Council on Water Resources Issue 140, Pages 15-23, September 2008 Incorporating Complexity and Uncertainty in Planning Models for Engineering: Economic Analysis within the U.S. Army Corps of Engineers Mark B. Gravens 1, Keith D. Hofseth 2, Richard M. Males 3, David A. Moser 4, and Cory M. Rogers 5 USACE Research & Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS 1 ; USACE Navigation Economic Technologies, Alexandria, VA 2 ; RMM Technical Services, Cincinnati, OH 3 ; USACE, Alexandria, VA 4 ; CDM, Carbondale, IL 5 Established by Congress in 1802, the U.S. Army Corps of Engineers (USACE) has both military and civil responsibilities. Among its responsibilities for civil works, the Corps investigates, develops, and maintains the nation s water and related environmental resources, including navigation, shore protection, and flood control projects. In so doing, the Corps must deal with natural and man-made systems on a scale ranging from small watersheds and localized problems to the Mississippi River Basin. The Corps is charged with analyzing and understanding the systems for which it has stewardship responsibility, and has developed a planning process that attempts to display the benefits and costs of implementation of various project alternatives, and compare those benefits and costs with the do-nothing or without project alternative. A fundamental question that is to be answered when the Corps undertakes a study of a proposed project is Is it worth it? That is, do the benefits to the nation of implementing a project exceed the costs? The calculation of benefits and costs is done over a period of time, typically 50 years. When planning is viewed in this framework, it is clear that, in order to estimate benefits and costs, assumptions must be made regarding natural phenomena and human behaviors into the future. How many hurricanes will take place in the project area? How severe will they be? What will people do to their houses in the face of repeated flooding? Will they rebuild to a safer construction standard? If a port channel is deepened to allow larger vessels to service a port, how will this affect traffic at other ports? If a lock is persistently out of service, at what point will shippers choose to use other modes of transportation (rail, truck)? What we have, then, is the need for analysis of a natural-engineering-economic-behavioral system that is clearly beyond complete predictive capability. Unlike systems that are largely manmade, where failure rates can be estimated and reliability established in an analytical sense, the long periods of time of a life cycle, the limited knowledge and data available to predict the natural system behavior, and the difficulty of predicting human behavioral responses, all combine to create an analysis problem that we know we cannot solve; we can only estimate. That is, we understand that the true complexity of the problem is beyond our capabilities to analyze, and that simplifications must be made if we are to approach answering the Is it worth it? question. In the face of this evolving understanding of the problem, the Corps has elected, as noted above, to adopt a life cycle approach, coupled with the incorporation of risk and uncertainty as a fundamental component of the analysis process (Moser 1996). What does this mean? It means that the Corps recognizes that any historical record of natural events can be considered as a single sample from a large possible population of such records. It means that there is an understanding that data are inherently uncertain, and are often best characterized as distributions rather than point

2 Gravens, Hofseth, Males, Moser, and Rogers 16 estimates. It means that the future will not be like the past, and that the selection of any single future is not a good basis for analyzing the benefits of a particular project. Because investments are made in the near term, at a specific (and largely fixed) scale, they will produce different outputs (in terms of actual damages prevented) depending upon the future conditions that will occur. A low-cost shore protection project may work perfectly acceptably under one possible future sequence of storms under which few hurricanes hit the area, but lead to large economic losses (and possible loss of human life) under another sequence of storms of more severe weather impact. Thus, most importantly, it means that decision-making must take into account the variability and uncertainty in project outputs, and that analysts must be able to provide estimates of that variability and uncertainty in an understandable, meaningful fashion. This understanding of complexity and uncertainty presents significant challenges to both analysts and decision-makers, who are not typically accustomed to working in such a framework. Modeling and the Corps Planning Process The specific approach to analysis of proposed Corps projects has evolved over many years, and is still evolving. While often the subject of criticism, the Corps planning process is, in general, much more highly developed than many other public planning processes in that it explicitly requires accounting for costs and benefits, and for analysis of both with- and without-project alternatives. Planning efforts are extensively and formally documented. Corps planning is increasingly done in close partnership (and cost-sharing) with local agencies, with extensive public involvement. Computer modeling has long been a basic tool within the planning process. A number of entities within the Corps have contributed to this effort. The Institute for Water Resources (IWR) is one such entity within the USACE. IWR s specialty is in integrated water resources management, focusing on planning analysis and hydrologic engineering, and on the collection, management, and dissemination of civil works and navigation information, including the Nation s waterborne commerce data. The Hydrologic Engineering Center (HEC) in Davis, California, is a world leader in development of computer models for surface water hydrology, river hydraulics and sediment transport, hydrologic statistics and risk analysis, reservoir system analysis, planning analysis, and real-time water control management. The Engineer Research and Development Center Coastal and Hydraulic Lab in Vicksburg, MS, is internationally known for physical and mathematical models of river and coastal systems. The USACE Planning Center of Expertise for inland navigation, located in Huntington, WV, primarily focuses on economic evaluation and plan formulation for studies of individual locks and inland waterway systems, as well as engineering reliability analysis for navigation structures, and has developed numerous mathematical models that are widely used in Corps studies. All of these groups have attempted to respond to the need for analytical tools used within Corps studies by developing computer models and databases with varying emphases on aspects of engineering, riverine and coastal hydrology, economics, and decision-making aids. These centers of expertise are continually improving their products as technology, understanding, and the needs of the Corps planning process change. At the same time, individual Corps districts have also developed analytical tools used for specific projects. Development and application of computer models is thus a normal and expected part of most Corps planning processes. It should be noted that, because of the highly specific and structured nature of Corps analyses, there is a tendency within the Corps to use models developed specifically in the context of the Corps planning process, rather than applying models developed elsewhere. In the light of critiques leveled in recent years at the Corps development, application, and use of analytical models, the Corps has undertaken a Planning Models Improvement Program (PMIP) and model certification initiative, to insure that models used by Corps agencies meet the highest technical standards and suitability for use for their intended purpose. The intent is to have a toolbox of certified models that Corps agencies can use with the assurance that they are the proper fit for the problem at hand.

3 Incorporating Complexity and Uncertainty in Planning Models for Engineering 17 Because computer models are frequently central to Corps planning efforts, and these planning efforts are increasingly subject to scrutiny from a wide variety of sources, the concepts of transparent and glass box (as opposed to black box) models have become important. The basic idea is that it should be clear to users and reviewers of models exactly what data are being used by the model, and how the models function. This requires a rather different approach to model development and use than has been common in the past. Analytical Frameworks There are two basic approaches to dealing with problems that are framed as life cycle problems with uncertainty. Frequency-based analysis attempts to describe the nature of future events as a set of values or curves of magnitude vs. probability (or return period) more extreme events are expected to have lower probabilities of occurrence. Once the curves are developed (a significant task in itself), they can be used to develop similar frequency estimates of impacts. A common example is flood damage analysis, in which a flood stage frequency curve providing the probabilities of different flood stages is combined with a stage-damage curve, giving the damage associated with any particular flood level, to derive a curve of probability of damages. When employing the frequency-based approach, a life cycle analysis is represented by a sequence of snap shots as the curves exogenously shift due to land use changes or changed hydrology. Frequency-based analysis has the advantage of being relatively easy to implement, but has less flexibility in terms of representation of complex dynamic processes, and tends to conflate together a number of phenomena and processes. An alternative method is that of Monte Carlo simulation (MCS), in which the processes and mechanisms of the system under study are represented as a computer model, with inputs that vary based on probability distributions. An advantage to MCS is the high level of detail that can be represented, the congruence of model entities with real-world entities, and the capability of including a variety of dynamic responses. MCS models also lend themselves to visualization quite well. Disadvantages include the extensive time that may be needed to develop the simulation, potentially large data requirements, difficulty of verification and calibration, huge amounts of data that can be generated, and the possible need for long runs of multiple iterations for convergence. The Corps has adopted both frameworks in its development of analytical models. The remainder of this paper, however, examines some of the MCS models that have been developed in recent years or are currently under development, in the arenas of inland navigation, shore protection, and port and harbor analysis. The emphasis in this discussion is not so much on the details of a specific model, rather it is on the nature of the model development process as related to the underlying issues of complexity and uncertainty. Model Development Process A model development process that has evolved in recent years is particularly useful for complex planning models. This process starts with the preparation of a design document, a statement of the key problems and issues that are to be resolved, and the proposed methods of resolving them. The development of design documents is not common in many model development efforts, but has proven to be an excellent tool for creating a common terminology and understanding, defining key issues, stating and managing expectations, allowing a number of participants to get involved, and providing a vehicle for peer review, all at an early stage of the process. At least initially, these design documents are typically not a blueprint for software design, but rather an explication of the problem and a proposed framework for modeling the problem. Assumptions are made explicitly clear and recommendations on how to proceed are offered up for the entire development team to comment on. The development team is generally a multi-disciplinary group, consisting of modelers, experts in the problem domain, software developers and eventual end-users of the subject model. The design document is passed among the entire team in iterative fashion, evolving its complexity and the team s understanding until the team is satisfied and ready to proceed with early stage model development. Once the design document has been developed

4 18 Gravens, Hofseth, Males, Moser, and Rogers and approved, the next steps involve: preparation of a proof-of-concept model or tinkertoy, a simplified working version that is used to explore and solve basic issues of data structures, model algorithms, and sample outputs; development of a prototype, a first-cut model that contains the essential components of the model (user interface, data structure, computational engine, outputs), which is then successively refined in a process called spiral development; and 3. application and continued refinement of the model in a test bed application, i.e. as part of a real world planning problem (not simply using test data). The test bed approach insures that the model is tied closely to Corps needs, and, by virtue of being part of a planning effort, the model inputs, outputs, and behavior are given close scrutiny. Following successful test bed application, the model may be modified further, training materials developed, and the model then becomes ready for certification and wider application, both within the Corps and externally. Within this overall process, a number of model architecture and technology features have proven to be very useful in supporting the development of complex simulation models. The use of object-oriented approaches allows for sharing of components between models, for example, random number generators and statistical tools. A data-driven framework stores all relevant problem-definition data in databases (typically Microsoft Access (tm)), so that models are readily transportable to different problems, and are not custom-written for each problem. An overall architecture (Figure 1) with a database, computational kernel, user interface, and withinsimulation and post-processing visualization and animation, provides a logical and physical separation of the major model components. This loose coupling of components allows for independent development of various elements of the model as well as numerous points at which data and processes can be verified, through animation and generation of detailed output files. This supports the transparency goal of model development, and is essential for model debugging and verification. In addition, the database clearly identifies the required input, and generated output data. Inland Navigation The U.S. inland navigation system consists of nearly 12,000 miles of commercially navigable User Interface Run Computational Engine (Monte Carlo Simulation Kernel) Within - Simulation Animation Output Data Files Reports Graphics Database Post- Processing Animation Figure 1. Typical model architecture.

5 Incorporating Complexity and Uncertainty in Planning Models for Engineering 19 inland and coastal waterways, on which over 1,000 million short tons of commodities moved in There are 212 lock sites owned or operated by the Corps, with an average age of 55 years (USACE, 2005). Due to the age of the locks and the importance of the waterway system to commerce, recreation, water supply, flood control, and the environment, the Corps must continually make decisions on expenditures for operation, maintenance, rehabilitation, and other improvements to locks and channels. Because expenditures for these improvements can be quite large, a careful analysis is required. Benefits of lock and channel improvements are measured primarily in terms of transportation cost savings such as the value of reduction of delay to shippers on the waterway. Delays occur primarily at locks, which may be undersized for the current traffic, and when there are outages, either scheduled for maintenance or unscheduled due to unforeseen problems. Originally, the problem was analyzed at single locks, but it was soon recognized that improvements at a single lock may not lead to overall system improvements because the congestion will just move to the next lock upstream or downstream. Thus, a system-wide analysis is required. The system boundaries, however, are not limited to the waterway. Shippers have options in terms of transportation modes that they select waterway, truck, rail, truck-to-rail, and truck-to-waterway. Waterway shipping would appear to have a natural price advantage for large bulk, low value per weight commodities. Truck transportation is the most costly per ton-mile, but is economical for expensive time-sensitive commodities, and can avoid transfer costs. Rail transport lies in between the two, and extensive studies have been carried out on shipper response and price elasticity in terms of the transportation mode that is chosen. The complexity of the analysis is thus characterized by: 1. a large multi-modal transportation system (waterway plus alternative routes); difficulty in estimating the nature of origin to destination waterway traffic (due to the manner in which data are collected); uncertainty as to the reliability of locks, and the associated consequences of inadequate performance; and 4. problems in characterizing shipper response to anticipated transit times and reliability, in terms of timing of shipments and modal choice. The Corps had developed and applied a number of previous Monte Carlo simulation models that address inland navigation issues, including the Waterway Analysis Model (WAM), NavSym (Institute for Water Resources 1999), the Life Cycle Lock Model (LCLM) (Institute for Water Resources 1999), as well as the Ohio River Navigation Improvements Model (ORNIM) (Curlee 2004). These models dealt with some, but not all, of the issues noted above. The Corps, in recognition of the complexity of the problems associated with navigation economics, initiated the Navigation Economics Technologies (NETS) research program in 2002 (USACE 2006, Hofseth 2006) to develop basic data, theoretical constructs, and analytical tools and models to assist in waterway studies (both inland and coastal ports). As a portion of this effort, an initiative was developed to create a new inland waterway navigation model, the Navigation System Simulation (NaSS) that would deal with the issues noted above. The design and development of NaSS is following the previously described model development process. The NaSS design document (Males 2006) was prepared as a collaborative effort of those who had been involved in development and application of the previous navigation models, and was externally reviewed by other experts in the field. All pertinent documents, including review comments, are posted on the NETS website ( cfm). At present (October 2006), the model is in the prototype stage of development. Shore Protection The U.S. Army Corps of Engineers has major responsibility for construction of shoreline protection projects in coastal areas of the U.S. These projects typically involve beach nourishment, i.e. the routine placement of sand on the beach to reconfigure the berm and dune,

6 20 Gravens, Hofseth, Males, Moser, and Rogers providing more protection to inland structures in case of storms. The Corps can only construct such projects where they are economically justified that is where the benefits exceed the costs. A proper economic analysis must take into account the probabilistic nature of storm-associated damage to structures. This damage is a function of structure location and character, storm intensity, storm timing, and the degree of protection that is provided by the natural or constructed beach. Thus, the analysis requires a combination of meteorology, coastal engineering, and economic analyses. Previous models developed and applied within the Corps used either a frequency-based analysis, with an essentially static representation of the shoreline and land development, or a simulation model with limited capability for representation of shoreline response to differing populations of storms. The current model, called Beach-fx, has been in development since November of 2001 under the auspices of the Engineer Research and Development Center and the Institute for Water Resources. The model development process described previously was strongly influenced by Beach-fx development efforts, which were characterized by extensive meetings with Corps field personnel and outside experts during all stages of the development process, and the use of an inter-disciplinary project development team (coastal engineers, economists, and computer scientists). Beach-fx is a Monte Carlo simulation model that combines storm information, shoreline response information, and property information to estimate damage based on erosion, flooding, and wave impact to arrive at the desired estimates of benefits and costs. The model improves on previous models in this arena by being strongly based on representation of coastal engineering processes, incorporating the impact of multiple storms, and with better representation of uncertainty. The model is currently in the test bed stage of development, in cooperation with the Mobile District of the Corps of Engineers, where it is being used in a study of shore protection for 26 miles of beaches in Walton County, Florida. BeachFx uses a variety of animation and visualization techniques, including 3-dimensional animation, in which the user can fly over the beach as it changes in response to storms and management. Obviously, one of the key issues in such a model is the treatment of uncertainty in the meteorological driving forces the intensity and timing of storms. Beach-fx requires, as input, a set of plausible storms for the area. These storms are assigned to seasons, with annual probabilities of occurrence associated with each season. Within a life cycle, a synthetic sequence of storms is generated, by first determining the number of storms in a given season (through a Poisson distribution), and then selecting storms from the database, in a process of bootstrap sampling with replacement. The timing of storms within a season is assigned randomly within the season, with a provision to keep storms separated by a user-specified amount; for example, no storms should occur within one week of each other. One of the realizations from the test bed application is that planners often wish to verify the model behavior with a specific storm, or raise questions such as What would happen if Hurricane Katrina hit the area? Beach-fx thus also allows the user to set a particular sequence of storms, either in addition to, or instead of, the synthetically generated sequence. There are many arguments as to why Hurricane Katrina (or a hurricane of similar force) is not likely to hit the Walton County beaches (no hurricane of category 3 or beyond has made a direct impact on this portion of the coast during the period of record). However, allowing the user to specify such a situation is consistent with the data-driven philosophy that places the justification of this assumption on the data assignment. Another area of inherent complexity and uncertainty in shore protection projects is determining the without project condition. As will be recalled, Corps analysis requires a comparison of the with-project condition with what would take place in the absence of the Corps project. For coastal communities, this may involve State, local, or private property owner actions, including pro-vision of emergency nourishment and armoring of structures where permitted by law. The prediction of this behavior is a difficult proposition at best. Due to the nature of the Corps economic analysis, the less action taken in the absence of a Federal project, the more advantageous the project itself becomes from an economic point of view, because damages in the without project condition are greater.

7 Incorporating Complexity and Uncertainty in Planning Models for Engineering 21 Consequently, a project that averts those higher damages is more attractive from a benefit-cost point of view. Because Corps projects are done in cooperation with local communities, it is in the interest of the community to understate the actions that would take place in the absence of the Federal project, but actual state/local activity is hard to estimate. As is usual in situations like this, scenario analysis is the preferred approach, allowing for examination of different views of the without project condition. For example, within Beach-fx, different levels of emergency nourishment can be set, reflecting alternate possible local responses. Port and Harbor Analysis Port improvements under the auspices of the Corps of Engineers typically take the form of channel widening and deepening, and provision of moorings or anchorage sites. These improvements fulfill the goals of reducing delay at the port due to congestion in channels and turning basins, and in allowing larger and/or more heavily loaded vessels to use the port. Reduction of congestion at a port can be measured in terms of vessel time spent at the port in the with- and without-project condition. Individual ports do not, however, stand alone they are part of a worldwide system of ocean commerce. Improvements at one port may have system effects, changing vessel transit patterns that may be constrained by a single depth-limiting port. Improvements to one port may also result in a shift of traffic from another port, but according to the procedures for economic analysis of the Corps, the shift of traffic may be counted as a regional economic benefit, but not as a national economic benefit unless overall efficiency can be shown to be improved. Simulating the entire system of oceangoing commerce to determine the feasibility of a channel dredging project at a single port is beyond current data and modeling capability. The Corps is approaching the general problem incrementally, through the development of a navigation analysis tool suite, under the general framework of the NETS initiative described above. Elements of this tool suite include HarborSym, a Monte Carlo simulation model of vessel movement at a single port (Moser et al. 2004), tools and models for statistical port traffic analysis and synthetic simulation of vessel arrivals (Hofseth et al. 2006), and 3-D animation and visualization (Rogers 2006). The HarborSym model takes as input a description of a port as a tree-structured network of reaches, docks, turning areas, and moorings; a set of vessel arrivals; and information on transit rules in each reach (based on vessel draft and size), all stored in a relational database. The model then routes vessels to the dock and out again, observing the transit rules. An essential feature of the model is the animation and visualization capability that allows users to see how vessels move through the system. This visualization has proven important for verification of the routing algorithms. Two types of visualization are provided: withinsimulation animation, in which the vessels are displayed schematically while the simulation is running, and post-processing animation, in which a more realistic 3-dimensional view of movement is available on top of a base map. Both animations allow the user to query the status of an individual vessel. These animations are important from a user confidence point of view, as well as for marketing the model. HarborSym has proceeded from the test bed stage of development to a fielded model, with associated training materials, and has been or is being applied in a number of Corps studies. Other aspects of the navigation analysis tool suite are still in prototype stages of development. Summary and Conclusions The U.S. Army Corps of Engineers does planning in a public arena, and is continually attempting to improve its approaches. Problems examined are inherently complex, uncertain, and multidisciplinary. The Corps has elected to pursue the development of Monte Carlo simulation models as a key strategy for performing the needed analyses. These models are developed as glass box models, with clear descriptions of the design decisions that have been made within the model development process, an open, iterative, and collaborative process of development, an architecture that clearly separates out data from processing, and extensive detailed outputs including animation. The approach has proven useful, and will continue

8 22 Gravens, Hofseth, Males, Moser, and Rogers to be used. These models produce outputs that are reflective of the uncertainty framework in which they are built the results are in the form of a distribution, rather than a single point. That is, the answers are not It will cost $50,000,000, but rather Here is the range and distribution of costs and benefits. This approach is a huge leap from previous methods, and it is not clear that the decision-making framework is ready to deal with probabilistic information of this nature. It is simpler to make decisions when there is a single measurable criterion, such as average net benefits. It is much more difficult to choose when variability comes into play this explicitly introduces the idea of risk and uncertainty into the decision-making process. The Corps has recognized this issue (Males 2002), but there is as yet little experience of real-world decision-making that is informed by the types of outputs that the new generation of models can provide. It is this arena, the display of uncertainty information to decisionmakers, and the enabling of decision methods in this framework, that requires further exploration if the state of the art of technical analysis is to be reflected in good decisions for society. Acknowledgements The work described here has been supported by the Institute for Water Resources, Alexandria, VA, and the Engineering Research and Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS of the U.S. Army Corps of Engineers. Much of the work was done in conjunction with Corps Districts, in particular the Mobile, Galveston, and Jacksonville Districts. Mark Lisney of the Institute for Water Resources serves as the project manager for the NaSS inland navigation model. Author Bios and Contact Information Mark B. Gravens is a Research Hydraulic Engineer specializing in coastal engineering and beach modeling at the USAE Research & Development Center, Coastal and Hydraulics Laboratory, Vicksburg, MS, Mark. B.Gravens@erdc.usace.army.mil. Keith D. Hofseth has served as a Corps economist for over 21 years; conducting studies in flood control, deep draft navigation, inland navigation and hydropower. He co-authored the first guidance for major rehabilitation analysis and was a pioneer in bringing risk and uncertainty into the Corp s planning process. He served as Chief Economist in the Alaska district and currently is the Technical Director of the Navigation Economic Technologies research program at the Institute for Water Resources. Keith.D.Hofseth@IWR01.USACE.army.mil. Richard M. Males, is an independent consultant trained in civil engineering and water resources, who has worked on the development of planning and decisionmaking models for the Corps for over 20 years. He can be contacted at RMM Technical Services, Inc., 3319 Eastside Avenue, Cincinnati, OH males@iac. net. David A. Moser has been an economist with the Corps of Engineers for 21 years, and currently serves as the Chief Economist of the Corps and Senior Team Leader Economics at the Institute for Water Resources where he conducts research in economic methods related to benefit-cost analysis and risk analysis methods for water resources. David.A.Moser@usace.army.mil. Cory M. Rogers is a computer scientist specializing in the development of software applications to solve complex decision making problems. He has worked extensively on development teams for Corps planning models for the past 10 years. Mr. Rogers has expertise in database design, Graphical User Interface (GUI) development, simulation modeling, decision support systems and software architecture. He can be contacted at CDM, 1050 North Reed Station Road, Carbondale, IL rogerscm@cdm.com. References Curlee, T. R., I. K. Busch, M. R. Hilliard, G. Oladosu, F. Southworth, D. P. Vogt The Economic Foundations of the Ohio River Navigation Investment Model (ORNIM). Transportation Research Record No Water Transport 1871: Available at: science_technology/technical%20articles/ornim_ Foundations%20_RR.pdf#search=%22ornim%20cor ps%20navigation%20ohio%20river%22. Hofseth, K The Institute For Water Resource s Navigation Economic Technologies (NETS) Research Program. Proceedings, 31 st PIANC Congress, Estoril, Portugal. Hofseth, K., S. Heisey, R. Males, and C. Rogers Development of Commodity-Driven Vessel Movements for Economic Analysis of Port Improvements. Proceedings, 31 st PIANC Congress, Estoril, Portugal.

9 Incorporating Complexity and Uncertainty in Planning Models for Engineering 23 Institute for Water Resources Tools for Risk Based Economic Analysis. IWR Report 99-R-2. U.S. Army Corps of Engineers, Institute for Water Resources, Alexandria, VA. Available at: army.mil/inside/products/pub/iwrreports/99r02.pdf. Males, R. M Beyond expected value: Making decisions under risk and uncertainty. IWR Report 02-R-4. Institute of Water Resources, U.S. Army Corps of Engineers. Alexandria, VA. Available at: iwrreports/02r4bey_exp_val.pdf. Males, R. M Navigation System Simulation (NaSS) Design Document. IWR Report 06-NETS- R-06, Institute for Water Resources, USACE, Ft. Belvoir, VA. Available at: army.mil/docs/navsyssim/06-nets-r-06.pdf. Moser, D., K. Hofseth, S. Heisey, R. Males, and C. Rogers HarborSym: A Data-Driven Monte Carlo Simulation Model of Vessel Movement in Harbors. Proceedings of HMS2004. Rio De Janeiro, Brazil. Moser, D. A The Use of Risk Analysis by the U.S. Army Corps of Engineers. Water Resources Update, 103: Rogers, C., W. Woelbeling, R. Males, K. Hofseth, and S. Heisey HSAM: An Interactive, Immersive Animation of Deep-draft Maritime Traffic Simulations. Proceedings, 31 st PIANC Congress, Estoril, Portugal. U.S. Army Corps of Engineers, The U.S. Waterway System Transportation Facts, Navigation Data Center USACE. Available at: usace.army.mil/ndc/factcard/fc05/factcard.pdf. U.S. Army Corps of Engineers, Navigation Economics Technologies Program, Available at: