# Vortex Lattice UXO Mobility Model for Reef-Type Range Environments

## Dr. Gerald D'Spain | Scripps Institution of Oceanography

## MR-201003

## Objectives of the Demonstration

This project leveraged previous ESTCP investments in the development of an unexploded ordnance (UXO) Mobility Model (MM) to assess probable UXO fate and transport at the Waianae dump site, HI and at the Vieques Islands, PR firing and bombing exercise ranges (with focus on the South Impact Area). The objective of this work was to develop modifications to the UXO MM software to implement reef geomorphology in the model grid building scheme. This feature allows the model to predict UXO migration and burial in a reef environment without relying on dense LIDAR bathymetric grids that limit the model’s computational domain, thereby increasing its computational efficiency in complex reef environments. This refinement uses geomorphic control cells consisting of a reef platform bounded by awa channels. An assemblage of these cells creates a digital representation of the fringing reef system around Vieques Island.

## Technology Description

The reef platform micro-bathymetry was constructed from spatial Fourier transforms of the LIDAR data using the reef platform at the Pacific Missile Range Facility (PMRF), Kauai as a geomorphic proxy of other island reef systems. The Fourier transforms allow the billions of discrete LIDAR data points to be compressed into a workable number of Fourier coefficients that represent the roughness details of the reef platforms of the awa control cells. With these discrete control cells, the vortex lattice algorithms can rapidly calculate ambient flow features such as bathymetric divergence over a UXO field. A discrete arrangement of these awa control cells allows numerically stable computations of erosion and transport of large UXO fields over reefs that surround an entire island.

This new awa cell computational approach using synthetic micro-bathymetry of reef platform roughness was validated in hindcast against the PMRF database from UXO field experiments using the same predictive skill measures detailed by the Naval Facilities Engineering Service Center (NFESC) as part of ESTCP project
MR-200417. Two approaches to assessing the skill of the awa cell predictions of the magnitude of migration and burial of UXO surrogates at PMRF were assessed. In the first approach, probability density functions (PDF’s) of migration and burial magnitudes predicted by the awa cell model were constructed and compared with the probability density functions assembled from the observed outcomes of the experiment. Because the experimental outcomes involve small ensemble statistics, this project merged the results of all 24 surrogates from the inshore and offshore test sites into a single set of probability density functions. In the second approach, a predictive skill factor *R* was computed from the mean squared error between the awa cell prediction and measured outcomes for migration distance, *ξ*, and burial depth, *h*. The peak, spread, and shape of the predicted and measured probability density functions of migration were quite similar to each other. The upgraded awa-cell MM predicted a mean migration distance of 1.25 m as compared to a measured mean migration of 1.45 m from the ensemble of 24 UXO surrogates. For the extremes, the measured and modeled minimum migration distance was 0 m, occurring at the offshore site, while the predicted maximum migration distance was 3.0 m as compared to a measured maximum migration of 4.0 m occurring at the inshore cluster of 12 UXO surrogates. In the predicted and observed outcomes, migration almost exclusively occurred along the major axis of the awa channel. The peak of the measured burial probability distribution, its spread, and shape all closely resemble the modeled distribution. The upgraded awa-cell MM predicted a mean burial depth of 17.5 cm as compared to a measured mean burial depth of 20.5 cm from the ensemble of 24 UXO surrogates. For the extremes, the measured and modeled minimum burial depths were on the order of 8 cm occurring at the offshore site, while the model predictions indicated a maximum burial depth of 50.0 cm as compared to a measured maximum burial depth of 40.0 cm occurring at the inshore cluster of 12 UXO surrogates.

The skill factor, *R _{ξ}*, for the awa-model at PMRF was

*R*

_{ξ}_{ }= 0.88 for migration and

*R*= 0.90 for burial. For modeling of coastal processes and mine burial prediction in particular, a skill factor in excess of 0.8 was considered to be a good result. The predictive skill factors achieved by upgraded awa-cell MM at PMRF using the synthetic micro-bathymetry are comparable to the predictive skill previously achieved using the high resolution LIDAR data directly on a relatively smaller area of reef. Alternatively, the accuracy of predictions from upgraded awa-cell MM based the Fourier reconstructed reef platform roughness (mode-2) versus the earlier approach using the high resolution LIDAR bathymetry can be quantified by the coefficient of determination, r

_{h}^{2}. The numerically efficient Fourier-based mode-2 can replicate the mode-3 simulations of migration (based on high resolution LIDAR inputs) with r

^{2}= 0.93, and the burial predictions within r

^{2}= 0.86. Because the upgraded awa-cell MM can do better than R > 0.8 or r

^{2}> 0.8, it performs with an accuracy comparable to the present ESTCP certified MM, while the cost savings derived from its reduced input rigor makes it attractive for remediation planning. The upgraded MM is able to achieve this comparable performance at significantly greater numerical efficiency and stability, allowing it to model the fate and transport of significantly greater numbers of UXO over larger UXO fields. Whereas the earlier generation MM code modeled fate and transport of only 24 UXO surrogates, the upgraded awa-cell MM is capable of modeling the simultaneous migration and burial of as many as 500 UXO.

## Demonstration Results

After validating software revisions using the ESTCP-funded field data at PMRF, this work tested and proved the hypothesis (through long-term, extreme-event simulations at Vieques Island) that the UXO eventually concentrate in the reef awa channels. Here, UXO were amenable to recovery by conventional sand dredging methods, while presenting a persistent danger of becoming transported to the beach during storms if not recovered. Concentration of UXO in the awa channels over time resulted from higher mobility on the reef platform due to two primary mechanisms: 1) higher ambient wave-induced velocity over the locally shallower reef platform, and 2) reduced rolling resistance of UXO on the hard substrate of the reef platform. However, lithification effects acting to cement UXO in place on the reef platform were not explicitly treated by the model physics.

## Implementation Issues

The UXO sorting mechanism that was demonstrated at biogenic reef environments has important cost savings and remediation planning implications. It is generally infeasible to search 100% of a known underwater UXO field with 100% probability of detection using present platform and sensor technology. Therefore, it is advantageous and cost-effective to integrate these numerical models at the outset of a survey with detection systems to guide those assets into the most problematic areas of a given underwater UXO field. By using the upgraded UXO MM to develop an initial Wide Area Assessment (WAA), that subdivides a UXO field into stable and unstable areas, one can avoid wasting deployment of detection resources in areas where UXO populations are either depleted by sorting, or remain permanently entombed beneath a stable seabed.

Predictive fate and transport models can be used to conduct an analysis of the risk and cost impact of UXO at a coastal site. Given an area of UXO locations and the required input data, the model output can be used to clearly define: a) areas outside of human contact and b) areas where UXO are fully stabilized and pose little risk to humans. Further consideration of the risks presented by the UXO can lead range management to make recommendations for site remediation and assessment of the hazard presented to humans and wildlife. Substantial benefits to remediation planners can be obtained from using these models to:

- Determine and minimize the scope of any required remediation efforts, minimize survey and removal efforts, and thus realize potential savings of millions of dollars.
- Ensure that any remediation effort covers enough distance that UXO will not move back into areas of concern (to avoid recurring cleanup efforts).
- Aid in planning the sampling survey by predicting: a) the conditions under which the most UXO would be unburied (visible) and b) the effective half-life of the survey data. This predictive capability enables survey and/or remediation efforts to be scheduled with respect to making a determination of how long UXO will remain where they are found. Often, considerable mobilization time is required for UXO clearance efforts. Post survey model predictions can provide guidance to remediation planners of the effects of intervening storms on already located UXO positions during the period between UXO surveys and site mobilization of clearance assets.
- Provide an inexpensive, rapidly implemented method of demonstrating good-faith effort to assess risk to public health from UXO.

The long-term goal is to include the UXO mobility and burial model output in forthcoming risk evaluation models specifically configured to support munitions response programs. The operational costs of using the UXO MM vary from $100,000 for a Mode 1 “desktop” analysis to approximately $1,000,000 for a detailed Mode 3 analysis of a large site, which would include bathymetric surveys, UXO distribution baseline surveys, etc. The primary cost driver at any level of analysis is the acquisition of site environmental data (i.e., waves, currents, seafloor sediments, and initial UXO distributions), and the conversion of those data into input files that are consistent with the UXO MM code formats.

## Products

## Points of Contact

### Principal Investigator

Dr. Gerald D'Spain

Scripps Institution of Oceanography

Phone: 858-534-5517