AbstractThe Army Corps of Engineers for decades has used two primary metrics to prioritize maintenance activities for coastal navigation projects: cargo tonnage at the project associated port and the controlling depth in the navigation channel relative to the project design depth. These metrics are generated through normal business practices and provide some insight into the relative importance (tonnage) of the port and the condition (controlling depth) of the channel. They have been incorporated into a risk-based framework that drives funds toward locations where project conditions have declined and the consequences of failure are high. With the maturation of a suite of technology programs, the U.S. Army Corps of Engineers (USACE) has an emerging capability to hindcast the underkeel clearance of vessels that transited through maintained waterways at the reach level. This study demonstrates an underkeel clearance-based assessment of shipping through the Southwest Pass of the Mississippi River over the span of three years by combining marine vessel automatic identification system data, tidal predictions, channel bathymetric surveys, and records of vessel sailing draft from entrances and clearances to domestic ports. The Southwest Pass is prone to rapid and widespread sedimentation and has received in excess of $100M annually for maintenance dredging in the last decade. Mobilizing dredges to this area in response to emergent sedimentation scenarios has proved disruptive to other dredging projects on the Gulf and Atlantic coasts, all of which rely on a finite fleet of dredges to maintain our Nation’s navigable waterways. Underkeel clearance-based performance is assessed at varying timescales in context of operational parameters such as draft restrictions limiting the size of vessels authorized to transit through the channel. Assessment of the spatial distribution of vessel traffic with respect to channel shoaling is also made.IntroductionTwo compelling and competing incentives have faced vessel operators since the advent of maritime shipping. On the one hand, maximizing vessel load increases the value of individual transits. On the other hand, maximizing clearance below the keel increases the likelihood of safe transit. Parker and Huff (1998) discussed these competing drivers, the elements that contribute to total water depth and the tools available to ships’ masters in managing underkeel clearance (UKC). Over time, economic drivers have consistently acted to cause ships to increase in size. In parallel, ports and connecting waterways have by necessity gotten deeper and wider.Throughout the coevolution of vessels and waterway infrastructure, unobstructed transits have been achieved by assuming static clearance requirements in design or employing them in operation (PIANC 2014; Ruggeri et al. 2016; Curtis 2018). The trend in the literature is toward navigation channel designs with relatively smaller cross-sectional area to vessel cross-sectional area by replacing conservative deterministic methods with more sophisticated probabilistic methods. This trend continues with examples where channel design has been optimized on the basis of managing UKC (Parker and Huff 1998; Curtis 2018; Mahar 2018). The result is more efficient deployment of construction capital or improved cargo throughput, facilitated by improvements in vessel control and communication technologies.Despite active research in infrastructure design (Curtis 2018; Harkin et al. 2018) and vessel operation (Parker and Huff 1998; Ruggeri et al. 2016), relatively little attention has been paid to the UKC implications in waterways during the maintenance lifecycle phase. For the most part, entities charged with maintaining maritime infrastructure have opted to maintain navigation channels to design limits if possible. When maintaining full project dimensions is not possible, for example, due to fiscal constraints, smaller dimensions may be maintained—particularly if they still provide for cost-effective marine transportation for the local port interests. This incurs risk that tends to either make vessel loading less profitable or keel strike more likely, although these effects are variable by project (Curtis 2018).This effort aims to develop a model of UKC measurement from archival data that can be scaled to match the 40,233-km (25,000 mi) coastal navigation channel portfolio managed by the U.S. Army Corps of Engineers (USACE). A UKC model will enable the USACE to deploy a more targeted and precise regimen for prioritizing dredging outlays that ensures adequate vessel clearances, thereby freeing significant resources to be repurposed to maximize vessel safety across the portfolio.BackgroundThe USACE is a public agency charged with designing and maintaining coastal and inland waterways to facilitate the safe passage of marine vessels. The agency spends approximately $1B annually to maintain constructed waterways that connect open oceans to marine terminals with design depths greater than 4.6 m (15 ft), primarily through dredging. It prioritizes the selection of maintenance projects, to include timing and dredging depth, based on total annual tonnage moved through each waterway using a risk-based approach described in annual budget guidance (USACE 2020b). Recent efforts have focused on a more rigorous approach to optimizing project selection and dredge fleet scheduling (Loney et al. 2020).At present, the optimization model considers the annualized tonnage and value of cargo moved over maintained waterways as well as the draft at which cargo is moved. Data are derived from the Waterborne Commerce Statistics and analyzed using the nonreleasable database known as the Channel Portfolio Tool (CPT; Mitchell 2009, 2012). Annualized sediment accumulation rates and dredging operation costs are considered in the Corps Shoaling Analysis Tool (CSAT), which is part of the optimization model (Dunkin and Mitchell 2015). The connectivity of projects is considered to prevent unnecessary dredging in situations where connected projects have differing limiting depths (Mitchell et al. 2013; Loney et al. 2020). The sophisticated optimization model has brought mathematical rigor to the formerly ad hoc prioritization scheme.The CSAT component of the optimization model relies on historical bathymetric surveys to estimate sediment accumulation rates. Given a planning duration, this shoaling rate is applied to individual channels to extrapolate the volume of sediment that will accumulate. The shoaled volume is converted to a channel depth forecast from which available depth losses may be estimated (Dunkin and Mitchell 2015; Loney et al. 2020). It may be inferred that channel depth losses will impact cargo throughput due to resulting limitations on vessel draft. For instance, Rosati et al. (2013) described the linear relationship between vessel draft and the corresponding vessel loading in terms of tonnage.As project depths are most commonly measured from the mean lower low water (MLLW) tidal datum, additional channel depth can be gained or lost from time-varying contributors to total water depth that include tidal variation and long-term trends in the local sea level. Within the USACE portfolio, tidal variation ranges from approximately 0.3 m (1 ft) in the Gulf of Mexico to nearly 9.1 m (30 ft) in Alaska on a subdaily timescale. Linear sea level trend projections for 2050, measured over decadal timescales, also vary between rising approximately 0.5 m (1.6 ft) in the Gulf of Mexico and falling by 0.5 m (1.6 ft) in Alaska (VIMS 2020).Sediment transfer that changes bathymetric elevation can vary on the order of meters gained or lost over monthly or shorter timescales (USACE 2020a). In addition to temporal variability, the spatial distribution of sediment accumulation varies between projects and within the channels of any particular project. Since channel dimensions are typically multiples of vessel dimensions (PIANC 2014), it is possible for localized reductions in channel depth to occur without corresponding adverse impacts to vessel transits, even during low water. For instance, vessels may simply navigate around accumulated sediment in a sufficiently wide channel or wait for favorable tide conditions to sail over it. Comparing the spatial distribution of sedimentation with regard to vessel swept path will enable an improved understanding of how channels may accumulate sediment without impacting marine traffic.For these reasons, it is worthwhile to model past vessel transits with regard to spatiotemporal variations in bathymetric elevation and water surface. Such an approach was historically impractical due to the size of the USACE portfolio, the number of transiting vessels, and the cost to measure individual vessel movements. However, the maturation of the marine vessel automatic identification system (AIS) has resulted in a spatiotemporal record of vessels moving on waterways globally. The USACE has demonstrated that this data source is useful for monitoring waterway activity (Young and Scully 2018; Scully et al. 2020). Scully and Mitchell (2017) also demonstrated that AIS data may be used to develop a model that quantifies the reliability of individual projects based on UKC criteria. UKC based on AIS provides a targeted metric that captures the extent to which individual waterway users take advantage of the service provided directly by the USACE (Frittelli 2011).The present effort provides two novel and complimentary contributions. First, a method to relate the spatial distribution of vessel traffic with regard to sediment accumulated in a defined navigation channel is presented. It can be assumed that sediment accumulated above authorized project depth and within the swept path of vessels presents a risk of keel strike. The magnitude of overlap in these footprints serves as a proxy measure of shoal interference without incurring the vertical measurement uncertainty necessary to compute UKC. Second, a method is proposed to estimate the UKC of historical vessel transits. This method provides a measure of depth below keel regardless of whether sediment has accumulated above authorized project depths. Observed minimum UKC values can be interpreted to understand user preferences regarding safety margins. Both methods use publicly available data sources spanning several years in a high-performance computing environment. The utility of these methods to assist waterway managers is demonstrated in the Southwest Pass of the Mississippi River, where dredging expenditures have exceeded $60M annually since 2015.DataSeveral data sources are aggregated to facilitate this assessment for the study period January 1, 2015–December 31, 2017. This period was chosen as it represented the longest, most recent span of overlapping data in the area of interest at the time the study began. The navigation channel framework divides the footprint of navigation channels maintained by the USACE into a collection of geospatial polygons. These geospatial polygons serve as the common reference system to align all spatial data (Libeau 2007) for a given project and channel reach. Bathymetric survey practice varies across USACE projects in terms of spatial measurement density, temporal frequency, and reference geodesy. Survey coverage may range from a single measurement per tens of square meters to several measurements per square meter. Collection frequency ranges from daily to annual surveys. It is assumed that the USACE survey frequency at all projects is appropriate to reflect the underlying morphodynamic behavior of the channel bed. Most surveys are collected in the state plane geodetic system of the state within which the project is located, although some states may use several state plane references (e.g., Texas and Hawaii have five each and Alaska has nine). Hydrographic survey information depicting channel bed elevation was obtained from the USACE eHydro database (USACE 2020a). This enterprise system stores channel bathymetric elevation measurements for each channel segment polygon as collections of scattered points in the original state plane coordinate system and vertical reference datum. The data representing bathymetric elevation in Southwest Pass consumes 94 GB of disk space, while the national coverage data set consumes 600 GB. The vertical elevation accuracy of these surveys is estimated to be ±0.076–±0.609 m (Byrnes et al. 2002). These survey data were converted from native state plane geodesy to Universal Transverse Mercator (UTM) coordinates in meters and a consistent vertical reference datum of MLLW, also in meters.The scattered points for each survey were spatially interpolated onto a 5 × 5 m rectilinear grid spanning the corresponding channel polygon. Each individual survey does not necessarily cover the full channel footprint, and no spatial extrapolation is performed in this step. If no survey point is proximate (within 5 m) to the corresponding rectilinear grid point, the grid point is left blank during the spatial interpolation. To facilitate rapid matching with the vessel data, it was desired to generate estimated elevation data at each point in the 5 × 5 m rectilinear grid at a daily interval. In this configuration, the appropriate elevation data can be matched to the vessel position report via simple time indexing given the day of the vessel transit. For each point in the 5 × 5 m rectilinear grid, the elevation data are subsequently interpolated through time to generate a daily record of the elevation at each survey point. The end product is a daily 5 × 5 m rectilinear grid of estimated elevations for each channel footprint (channel polygon).Archival vessel traffic information for the study period was obtained from the Marine Cadastre AIS data set (BOEM and NOAA 2018). This data set stores AIS data from the NAIS system (USCG 2020) in a regular 1-min interval across the United States. There are 930 GB of Marine Cadastre data for the January 1, 2015–December 31, 2017 study period. The Marine Cadastre data for Southwest Pass for the same time period are 2.2 GB. The Marine Cadastre data set is stored as a dynamic portion, which includes time-stamped vessel position, heading, course, and speed over ground, which are generated by shipboard GPS units. The maritime mobile service identity links the dynamic portion to the static portion, which contains additional particulars reported by the vessel including vessel type, length, beam, and draft. Among large commercial vessels, with which this study is principally concerned, the length and beam of the vessels stored in AIS are generally considered to change infrequently and to be more reliable than draft (Harati-Mokhtari et al. 2007; Calder and Schwehr 2009; Robards et al. 2016). Vessel length and beam are used in combination with vessel heading information to resolve the approximate footprint of the vessel in transit (Dunkin et al. 2018). If the vessel length, beam, and/or heading are unknown, the default values are 10, 10 m, and 0°, respectively. These default values do not reflect the actual dimensions of typical deep drafting vessels but do ensure that only portions of the channel that the vessel transited over with reasonable certainty are utilized in the analysis (i.e., those points close to the position of the AIS transceiver).The vessel draft stored in AIS is static and does not take into account factors such as water density and vessel loading that may cause the observed draft to vary with time and location; therefore, it is considered to be less accurate than is desired for the purpose of this study. Instead, the draft reported by the vessel to the U.S. Customs and Border Patrol nearest in time to the vessel’s transit through the study area is found using the Foreign Vessel Entrances and Clearances record (IWR 2018) by indexing with the timestamp of the vessel position reports. This is assumed to better represent the sailing draft as failing to comply with mandated reporting can incur civil or criminal penalties under 19 CFR Part 4. If the vessel draft cannot be found in the Foreign Vessel Entrances and Clearances record, then the vessel draft recorded in AIS is retained and flagged in the data.In a similar fashion, the timestamp of the vessel position report is used to index the record of water level predictions (E) available through the NOAA COOPS system (NOAA 2020). Which station’s water level data are used to estimate UKC depends on the physical distance between the centroid of each channel framework polygon and the station. The water level predictions at each station are used in lieu of the measured water level to avoid erroneous interpolation across large gaps in the measured water level record. This choice is a concession to the comprehensiveness of the prediction data set compared to the measurement data set as this methodology is scaled up to cover the national channel portfolio. Given that neither voyage planners nor vessels in transit would have access to the measured data set, this concession is assumed to be reasonable. The availability of more accurate information that includes hydrometeorological components to vessel operators in real time will result in differences between actual and estimated water levels and, therefore, UKC values. However, it is further assumed that these differences will be random and normally distributed so as not to bias estimates generated with the methodology presented. Water surface elevation (WSE) predictions are recorded as meters positive above MLLW at a time interval of 6 min.MethodsThe minimum information required to estimate the total water depth includes the elevation of the water surface and the bathymetric elevation at the location of interest. Based on the conventions described in the “Data” section, the total water depth at every point on the grid is calculated as the sum of the WSE and the depth to the channel bed estimated from the survey data, z, (both relative to MLLW), h = E + z. The data representing the total water depth used in this approach are comparable to the minimum publicly available information from predictive tide stations and nautical charts that would be useful to voyage planners, as described by Parker and Huff (1998). Gross UKC, which this study calculates at every vessel position report in each reach, can be calculated by subtracting the vessel draft, T, from the available water depth (PIANC 2014), UKC = h − T. Fig. 1 pictorially represents the relationship between UKC, WSE (h), and survey-estimated depth (z). For every vessel position report, the total water depth used in this calculation represents the depth where 75% of observations below the resolved vessel footprint are deeper. The height of accumulated sediment (shoaling), zs, is estimated entirely from the interpolated survey data and is calculated for each grid point as the channel authorized depth (za) minus the survey depth (z), zs = za − z. This parameter is only calculated where the authorized depth exceeds the survey depth.Several metrics are provided to quantify the interaction of vessels in transit with sediment accumulated within the channel framework. Channel area is simply the sum of area for all cells (ncells) in a particular channel segment (dx × dy × ncells)—dx and dy are 5 m in this study. Cells in the channel raster are encoded as shoaled if the survey depth is less than the authorized channel depth. The channel shoaled area at any time step is the sum of all shoaled cells (nshoals), multiplied by the cell area (25 m2–269.1 ft2). The channel shoal volume at any time step is calculated by taking the sum of the differences between authorized channel depth (za) and surveyed channel depth for shoaled cells, multiplied by the cell area (dx×dy×∑n=1nshoals[za−zn]).For every vessel position in a given time step, cells are tagged as under vessel if a vessel’s footprint passes over the cell’s centroid. The total area under vessels on a given day is computed as the sum of all cells beneath a vessel footprint (nvcells), multiplied by the cell area. The shoaled area under vessels is calculated as the set intersect of channel shoaled cells with under vessel cells, multiplied by the cell area. Finally, the volume of sediment under vessels is estimated as the channel shoaled volume of the set intersect of shoaled cells and under vessel cells. Fig. 2 represents the channel cell tagging strategy.Additional descriptions of the vessels’ channel use and the interaction between vessels and shoals may be derived from the aforementioned area and volume quantities. The ratio of area under vessels to channel area for any timestep gives a measure of the physical dimensions of a vessel’s swept path with regard to the channel dimensions. The ratio of shoaled area to channel area for any timestep gives a measure of the extent of channel shoaling. The ratio of shoaled area under vessels to channel shoaled area for any timestep gives a measure of the physical dimensions of a vessel’s swept path with regard to the shoaled area of the channel. The ratio of shoaled volume under vessels to channel shoaled volume for any timestep gives a measure of the volume of accumulated sediment within the swept path of transiting vessels.Case StudyThe Mississippi River watershed is the third largest in the world, draining 3.2 × 106 km2 (1.3 × 106 mi2). This area accounts for 41% of the contiguous United States. The Southwest Pass of the Mississippi River (Fig. 3) is a critical component of the U.S. marine transportation system. It provides access to 23,000 km (14,500 mi) of navigable inland waterways on the Mississippi River and its tributaries (USACE 2018a). The channel framework seaward of Venice, Louisiana consists of 12 polygons that cover 1,341 ha (843 ac) and range in size from 69 ha (171 ac) to 127 ha (314 ac). All 12 Southwest Pass channel polygons considered in this study are wholly contained within UTM Zone16R. Southwest Pass is maintained to a depth of 14.8 m (48.5 ft) relative to MLLW (USACE 2018a).An average of 296 hydrographic surveys were conducted for each channel reach during the study period, ranging from 36 (monthly) surveys for the least-frequently surveyed channel reach to 541 surveys for the most-surveyed reach. The longest period of time between subsequent surveys is 1 month for the 12 Southwest Pass channel reaches in this study.The specific NOAA COOPS tide gage predictions utilized in this analysis are Pilots Station East, SW Pass, LA (Station ID: 8760922) and Pilottown, LA (Station ID: 8760721)—the two stations located within Southwest Pass in the vicinity of the 12 Southwest Pass channel polygons. For this study, the greatest possible horizontal distance between observed vessel position and NOAA COOPS station is 17 km. The mean absolute errors of the water level prediction to the measurements for SID: 8760922 and SID: 8760721 are 0.16 and 0.14 m, respectively, for the time period presented. Table 1 shows the tide gage used for each specific reach.Table 1. NOAA tide gages assigned to each reachTable 1. NOAA tide gages assigned to each reachGage No.SWP_02SWP_03SWP_04SWP_05SWP_06SWP_07SWP_08SWP_09SWP_10SWP_11SWP_12SWP_138760721XXXXXXX—————8760922———————XXXXXThe Bar Pilots operating in Southwest Pass regularly impose vessel draft restrictions in response to rapid and widespread sedimentation that occurs within this 51.5 km (32 mi) stretch of river that extends from Venice, LA to the Gulf of Mexico (Louisiana Maritime Association 2021). The record of draft restrictions in Southwest Pass, including beginning/end dates and maximum allowed draft, were obtained from the USACE New Orleans District. The most severe restriction in place between 2011 and 2020 prohibited vessels with drafts greater than 10.7 m (35 ft) from transiting through Southwest Pass. Based on this information, the results presented for this analysis are restricted to vessels with drafts greater than or equal to 9.1 m (30 ft).In total, 2.5 million unique vessel position reports were observed. A total of 586 million available depth calculations, 588 million accumulated sediment calculations, and 2.5 million UKC calculations were made. In total, 89% of vessels were matched in the Foreign Vessel Entrances and Clearances record. Of those vessels with both a Foreign Vessel Entrances and Clearances draft and an AIS recorded draft, the Foreign Entrances and Clearances draft was an average of 0.09 m larger for the vessels observed to transit Southwest Pass during the study period. Additionally, the vessel horizontal dimensions were known for 96% of the vessel transits observed in Southwest Pass during the study period. Fig. 4 shows the distribution of UKC measurements at each vessel position report for vessels in draft bins of 9.1 m (30 ft)–12.2 m (40 ft), 12.2 m (40 ft), 13.7 m (45 ft), and greater than 13.7 m (45 ft). Of these vessel position reports, 0.045% were calculated to have less than the PIANC (2014) recommended 0.6 m (2 ft) manoeuvrability margin (MM). PIANC (2014) defines MM as the time-averaged clearance under a ship and states “A minimum value of 5% of draught or 0.6 m, whichever is greater, has been found to provide adequate MM for most ship sizes, types, and channels.”Fig. 5 shows the composite relationship between kilotonnes of cargo and vessel draft for vessels with drafts greater than 9.1 m (30 ft) (USACE 2018b). These vessels could plausibly be impacted by accumulated sediment with or without draft restriction in place. It is assumed that shallower drafting vessels are unlikely to be impacted by the draft restrictions or sediment accumulation observed during the study period. This relationship is not deterministic for individual vessels. Instead, it provides a statistical basis for quantifying the amount of cargo that must be removed to accommodate a corresponding reduction in draft of the average vessel importing or exporting cargo through Southwest Pass. A 1-m (3.3-ft) reduction in vessel draft results in an average of 11.6 fewer kilotonnes (12,800 tons) per vessel transit in Southwest Pass.Vessels drafting over 9.1 m moved 84% of cargo tonnage and made 29% of total trips for this period (USACE 2018b). The largest ships, drafting 13.7 m (45 ft) or greater, tend to move a disproportionately large amount of cargo compared to smaller ships (6% of total tonnage, 1% of total trips) (USACE 2018b). Thus, there is an incentive to provide sufficient depth to accommodate the largest vessels. Vessel operators may delay, divert, lighter, or lightload cargo to mitigate for draft reductions (Rosati et al. 2013).To avoid the economic impacts of draft restrictions in Southwest Pass, the USACE spent over $60M per year in fiscal years 2015–2017. The dredging cost and volume removed are shown in Table 2. Mobilizing dredges to this area in response to emergent sedimentation scenarios has proved disruptive to other dredging projects on the Gulf and Atlantic coasts, all of which rely on a finite fleet of dredges to maintain our Nation’s navigable waterways (GovTrack 2020).Table 2. Dredging effort and cargo performance metrics for Southwest PassTable 2. Dredging effort and cargo performance metrics for Southwest Pass
Fiscal yearDollars ($M)aDredged volume (million m3)aCargo throughput (megatonnes)b201566142162016651622120176217236SWP_12 demonstrated the greatest percentage of area shoaled relative to the channel area of any channel, as shown in Fig. 6. The peak shoaled portion of channel area for this time series was 61 ha (151 ac), approximately 89% of the total reach area. The greatest gross shoaled area occurred in SWP_05 at 84 ha (208 ac), accounting for 72% of that channel’s total area. SWP_12 had the greatest shoaled volume of any reach, 7.5 × 105 m3 (9.8 × 105 yd3). Timeseries plots are represented throughout this work for the sake of readability. Table 3 summarizes the channel areas and the maximum observed shoaling within each reach. The median of the largest observed shoaled area of the studied channel reaches was 48% of total channel area.Table 3. Channel area, shoaled area, and shoaled volume, by reachTable 3. Channel area, shoaled area, and shoaled volume, by reach
Channel framework IDChannel area (ha)Maximum observed shoaled area (ha)Maximum observed shoaled volume (105 m3)SWP_0211230.1SWP_0310470.2SWP_04113623.3SWP_05117846.8SWP_06107412.6SWP_07112543.7SWP_08109504.0SWP_09109534.4SWP_10109674.4SWP_11108675.2SWP_1268617.5SWP_1362272.1Of the maximum shoaling observed in SWP_12, 62.7% of shoaled area and 49.6% of shoaled volume occur under vessels. Fig. 7 shows the time series of seven-day averaged minimum UKC for SWP_12, both for vessels transiting over shoaled areas and the entire channel. In this reach, the smallest observed 7-day average minimum UKC over shoals and over the entire channel was 0.6 m (2 ft), shown in the upper panel time series. This occurred during a period of draft restriction in February 2016, which coincided with the period of peak shoaling. It is notable that the observed minimum clearance matches PIANC (2014) guidance. The lower panel time series in Fig. 7 shows that the drafts of vessels incurring minimum UKC in the unrestricted period of late 2016 and early 2017 were larger than those incurring the globally minimum UKC in February 2016. However, for the majority of the study period, the minimum observed UKC occurred in areas that were not shoaled. An interpretation of this time series is that the deepest drafting vessels, which should be expected to govern UKC, tend to navigate through areas lacking accumulated sediment. Conversely, vessels with drafts insufficient to contact the channel bottom freely navigate over shoaled areas with UKC that exceed those of larger vessels in unshoaled areas. The converging over entire channel and over shoals lines indicate periods when the spatial distributions of sediment accumulation and vessel swept path interact such that shoaling directly impacts maximum vessel draft. Table 4 indicates shoaling and UKC metrics computed for each reach.Table 4. Shoaling and UKC metrics by reachTable 4. Shoaling and UKC metrics by reachChannel framework IDMaximum observed daily vessel countMaximum % shoaled area under vesselsMaximum % shoaled volume under vesselsMin. UKC (m) entire channelMin. UKC (m) over shoalsSWP_022284. is frequently discussed in terms of vessel draft. Fig. 8 shows the ratio of UKC to vessel draft for SWP_12. The PIANC (2014) concept of MM is also relevant here because it relates to the necessary clearance below a transiting vessel to allow adequate maneuverability. Managing navigation channels for a variety of users implies maintaining at least 5% UKC as a percentage of vessel draft or 0.6 m UKC for the deepest transiting vessels per PIANC guidance. Fig. 8 shows that, with few exceptions, vessels transiting SWP_12 had UKC greater than or equal to 10% of vessel draft over the entire channel and significantly more over shoals.Fig. 9 shows an enlarged view of the 2016 segment of SWP_12 shown in Fig. 7. At the time of minimum UKC, there is convergence in the draft of vessels traveling over shoaled and unshoaled areas. It can be interpreted from Figs. 7 and 9 that for a brief period in the winter of 2016, sediment accumulation migrated into the path of the deepest drafting vessels. During the 2016 draft restriction, the average maximum daily draft was 12.8 m (42.0 ft). The average maximum daily draft following the restriction period was 13.3 m (43.6 ft). Thus, the impact to vessel draft resulting from the restriction represents a reduction of 0.5 m, or 3.8%, of the postrestriction mean draft. The corresponding impact of cargo reduction during the draft restriction is estimated as 11.6 kt/m/t × 0.5 m = 5.8 kt per transit. A conservative estimate of 14.7 MT of disrupted tonnage due to conditions during the draft restriction can be made by multiplying the 5.8 kt per transit value by 2,542 observed transits during this period. Some vessels transiting during the restriction had drafts less than the maximum draft allowed during the restriction; therefore, the actual disrupted tonnage is likely smaller.The minimum depth observed during this study was 5.8 m (19 ft) below MLLW in SWP_12 on June 8, 2017. This represents 9 m (29.5 ft) of sediment accumulation. Fig. 10(a) indicates that this shoal formed at the corner of a slight bend in the channel. Fig. 10(b) shows the extent to which vessel footprints overlap with channel shoals during the June 8, 2017 shoaling conditions. Most vessels appear to navigate in the center portion of the channel, while shallow channel conditions tend to form first on the channel margins. This pattern of shoaling at the channel margins and vessel traffic near the channel centerline is common in the twelve reaches presented in this study.Fig. 11 shows the time series of the seven-day moving average of UKC available to vessels incurring minimum UKC in SWP_12 over the full-depth channel (a) and over shoals (b) in terms of vessel draft and available depth. The difference in height between the black available depth bars and the grey draft bars indicates the observed seven-day moving average of minimum UKC. It makes two points clear. First, the total available depth varies daily as a function of WSE and bathymetric elevation, but severely limited depth conditions (e.g., below 13.7 m [45 ft]) are infrequent. Second, there is more variability in the population of observed vessel drafts, such that minimum UKC events tend to be caused by deeper-drafting vessels not shallower water depth conditions, particularly during periods of unrestricted draft. This remains true over shoaled areas, although vessel drafts tend to be relatively smaller over shoals than over the entire channel.The shoaled area and shoaled volumes below vessels are summarized in Table 5 by vessel draft at 9.1 m (30 ft), 12.2 m (40 ft), and 13.7 m (45 ft) increments. The maximum number of vessels within the respective draft bins observed in a day is also provided by reach. This table indicates that vessels drafting 13.7 m (45 ft) or more are rare, with no more than two daily transits observed on any given day over the study period. The shoaled channel area and accumulated sediment volume below these vessels are correspondingly small. Examining SWP_12 again, Table 3 indicates 61 ha (151 ac) of shoaled area and 7.5 × 105 m3 (9.8 × 105 yd3) of shoaled volume were observed. Of that, 1.5 ha (3.7 ac) of shoaled area and 0.08 × 105 m3 (0.10 × 105 yd3) of shoaled volume occurred below the largest vessels.Table 5. Vessel counts, area, and volume shoaled below vessels of drafts greater than those indicated, by reachTable 5. Vessel counts, area, and volume shoaled below vessels of drafts greater than those indicated, by reachReachObservation9.1 M (30 ft)12.2 m (40 ft)13.7 m (45 ft)SWP_02Max. daily vessel count2262Shoal area below vessels (ha) volume below vessels (105 m3) daily vessel count2162Shoal area below vessels (ha) volume below vessels (105 m3) daily vessel count2262Shoal area below vessels (ha) volume below vessels (105 m3)1.770.440.09SWP_05Max. daily vessel count2362Shoal area below vessels (ha) volume below vessels (105 m3)3.140.790.10SWP_06Max. daily vessel count2362Shoal area below vessels (ha) volume below vessels (105 m3)0.820.080.02SWP_07Max. daily vessel count2362Shoal area below vessels (ha) volume below vessels (105 m3) daily vessel count2262Shoal area below vessels (ha) volume below vessels (105 m3)0.800.190.06SWP_09Max. daily vessel count2262Shoal area below vessels (ha) volume below vessels (105 m3) daily vessel count2362Shoal area below vessels (ha) volume below vessels (105 m3)0.850.310.04SWP_11Max. daily vessel count2362Shoal area below vessels (ha)33.310.51.9Shoal volume below vessels (105 m3)1.770.340.06SWP_12Max. daily vessel count2262Shoal area below vessels (ha) volume below vessels (105 m3)3.740.950.08SWP_13Max. daily vessel count2062Shoal area below vessels (ha) volume below vessels (105 m3)0.360.050.01Fig. 12 casts the observed UKC for all 17,729 vessel transits in SWP_12 in terms of vessel draft. Vessels reporting less than the PIANC recommended 5% minimum MM totaled 0.23% of observed transits. PIANC (2014) also recommends a channel design upper range of 15% of vessel draft UKC in quiescent waterways and up to 40% of draft as UKC in wave-exposed waterways. SWP_12 and SWP_13 are exposed to waves. In total, 47% of observed transits in reach SWP_12 exceeded the most conservative UKC recommendation as a result of relatively small vessel draft as opposed to limited channel depth.DiscussionThe results in the case of the Southwest Pass of the Mississippi River demonstrate that the smallest 7-day average minimum observed UKC was 0.6 m (2 ft). However, this occurred in both shoaled and unshoaled areas. Table 4 demonstrates that UKC over shoals was at times the smallest observed in the channel reach but often larger than that observed over unshoaled areas of the navigation channel. It can be inferred that under certain conditions, vessel operators will transit large ships with thin safety margins over full-depth portions of the channel. However, such small clearances were rare. Frequently, much more clearance was available—typically controlled by the draft of the transiting vessel more than water level or bathymetric elevation. Vessel operators are either managing vessels to obtain optimal clearance, or vessels are sized such that UKC will be limited only in extreme shoaling cases. Thus, in addition to measuring channel performance, the UKC metric provides a measure of individual operator preference, and the extent to which users take advantage of the service USACE provides through dredging.By definition, channel depth lost to sediment accumulation plays a role in limiting the size of vessels moving through maintained waterways. However, vessels passing over shoals in Southwest Pass tended to have more, not less, UKC. This was mostly due to the overall shallower draft of vessels passing over shoals. The exception to this tendency was when accumulated sediment migrated into the path of the deepest drafting vessels, which tend to prefer the center of the navigation channel.Table 2 provides the necessary information to make dredging effectiveness comparisons in terms of price per m3 of sediment removed, or tonne of cargo throughput. Dredging activities in Southwest Pass equated to $4.74 per m3 removed in FY16 versus $4.06 per m3 for FY 17. The cost of dredging was $0.29 per tonne of recorded throughput in FY16 versus $0.26 per tonne in FY17. Either metric indicates that FY16 and FY17 were comparable, although FY17 was more efficient that FY16. Introducing vessel position information offers another comparative lens. If the shoaled area in the swept path of vessels per day is summed, 14.2 × 103 ha-days of shoaling were observed in FY16 compared to 7.4 × 103 ha-days in FY17. Thus, the cost was approximately $4,600 per ha-day of vessel-encountered shoaling in FY16 versus $8,900 per ha-day in FY17. Sediment removed from the swept path of vessels cost approximately 89% more in FY17 than FY16.The results of this analysis show that accumulated sediment in the swept path of the largest vessels is relatively small compared to both the volume occurring within the entire channel, and the swept path of all vessels. It is also evident that the spatiotemporal distribution of sediment and vessels influences the cost of sediment removed from vessel swept path. A natural management question emerges: What level of maintenance is appropriate for a navigation channel where most operators are observed not to take full advantage of the depth provided?The answer to this question is not trivial. On the one hand, single digit percentage reductions in the dredging budget at Southwest Pass would result in millions of dollars that could be reapplied to other projects where maintenance spending might be more impactful. On the other hand, reducing dredging efforts in Southwest Pass would incur some risk of disruption to the deepest drafting vessels. These risks could be mitigated by revising the dredging strategy, e.g., dredging those areas most frequently transited by the deepest drafting vessels. However, this question cannot be answered in a vacuum. It is necessary to make a comparison between the performance of all waterways managed within the portfolio, which is beyond the scope of the present effort.A comparator between competing reaches and projects to augment the existing optimization model would account for both the volume of vessel traffic and the frequency that observed UKC approaches a meaningful threshold. An example ranking scheme for individual channels based on PIANC (2014) might consider the total number of vessel transits observed in a reach with UKC of 15% or less (40% or less for wave-exposed reaches) of vessel draft. A simple summation across each reach included in competing work packages could be used to rank them.PIANC (2014) also suggests the consideration of other hyperlocal factors. For instance, each pilotage association has its own operating guidelines pertaining to UKC. Certain vessel types, such as LNG tankers, may require additional clearance compared to general cargo vessels. The risks associated with different bottom types, ranging from rock to fluid mud, must also be considered. As complex as these considerations may be, they are all spatially linked through the channel framework and can thus be meaningfully compiled.Conclusions and Future WorkThis study demonstrates a method for estimating the gross UKC of vessels that transited waterways managed by the USACE. It leverages open-source data sets generated by a cohort of federal agencies concerned with water resources in the Unites States. The method provides a direct measure of a critical operational concern for vessel masters, unlike the tonnage, vessel draft, or channel depth metrics currently in use.This method is not without limitations. The estimate of UKC presented in this study does not capture hydrodynamic phenomena, like squat, vessel motion, wave activity, or water density, that influence vessel operation. Atmospheric phenomena like barometric pressure and wind effects are likewise omitted. Vessel models are primitively resolved, and lack the specificity of vessel models used by others (Ruggeri et al. 2016). The study area is the most frequently surveyed waterway in the USACE portfolio, and therefore scaling up to include less frequently surveyed waterways may incur additional uncertainty in bathymetric elevation. Despite these limitations, this paper demonstrates the feasibility of an UKC assessment through fusion of available data sets that cover the full scope of the USACE coastal navigation channel portfolio and highlights the insights that may be gleaned with comparing observed vessel footprint to shoaled channel area.In the future, this methodology will be extended to include the complete USACE coastal navigation channel portfolio. Additional effort will be focused on determining what channel performance metric best incorporates vessel clearance into the project selection optimization model being developed by the USACE.AcknowledgmentsThis work was funded by the Coastal Inlets Research Program of the U.S. Army Corps of Engineers. 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