Optimal Service-Based Competition with Heterogeneous Suppliers

We investigate how a competition can be designed to maximize expected profit for a buyer who wishes to allocate demand among a diverse set of suppliers when his profit is dependent on the supplier’s service levels. The candidate suppliers are heterogeneous in their capacities and cost structures, and compete for shares of the buyer’s demand based on their promised service levels. To characterize the optimal competition, we first identify a family of allocation functions that are service maximizing, meaning they can intensify the competition to a point where each supplier provides its maximum feasible service level and the outcome of the competition is a predefined set of demand shares. We show that using a service maximizing allocation function is a necessary condition for solving the buyer’s problem. We then characterize the optimal demand allocation set and, when they are endogenous, the optimal procurement prices. When both demand allocation and procurement prices can be chosen by the buyer, we find that the competition also maximizes supply chain profit. Through a set of numerical examples, we show that the benefit of using this optimal competition design, including its specified demand allocation function and suggested procurement prices, can be significant

cDrake CPIES Data Report November 2007 to December 2011

The goal of cDrake is to quantify the transport and understand the dynamic balances of the Antarctic Circumpolar Current (ACC) in Drake Passage. For this purpose, a transport line spanning all of Drake Passage and a local dynamics array of CPIES were deployed for a period of four years. A CPIES comprises an inverted echo sounder equipped with a bottom pressure gauge and a current meter tethered 50 m above the bottom. In addition to the CPIESs, three current meter moorings were deployed along the continental margins for the initial two years of the field program. Subsequently, a current meter comparison mooring was deployed in a region of strong bottom currents for a period of one year. Conductivity-temperature-depth and lowered acoustic Doppler current profiler measurements were taken at each CPIES site. Shipboard acoustic Doppler current profiler measured the velocity structure along the cruise track. In this report, the CPIES data collected during the field experiment are presented. The collection, processing and calibration of the CPIES are described

Cascadia Pilot Experiment Data Report

This report documents the processing of data collected from an line of inverted echo sounders equipped with bottom pressure gauges and current meters (CPIES) deployed offshore of Oregon in the Cascadia subduction zone region from April to November 2017. The line consisted of four URI-model CPIES across the continental slope, spanning water depths from 2900 m to 1300 m. From offshore to onshore, the sites were designated O1, O1.5, O2 and O3. The instrument spacing telescoped toward the coast from 3.5 km to 7 km to 9 km. CTDs were taken at each site on the deployment and recovery cruises. Additionally, two Sonardyne-model PIES (lacking the integrated current meter) were colocated at the deepest and shallowest sites (O1 and O3) for comparison tests. An Aanderaa Seaguard current meter was moored in August 2017 at site O2 because the status of CPIES current meter at that location was uncertain

PIES and CPIES Data Processing Manual

The Inverted Echo Sounder (IES) is an ocean bottom-moored instrument that measures the vertical acoustic travel time (VATT) round-trip from the seafloor to the sea surface and back. The VATT varies principally due to changes in the temperature profile of the water column, making the IES well-suited for monitoring changes in temperature structure and dynamic height (baroclinic signal). Currently, the Model 6.2, a combined IES, data-logger, and acoustic release, with measurements of bottom pressure and temperature (PIES) and optional measurements of current speed and direction (CPIES, with attached Aanderaa Doppler current sensor) is produced at URI/GSO. Data are processed in situ and are available (optional) remotely by an acoustic telemetry link. In addition to the IES-measured baroclinic signals, barotropic near-bottom pressure variations may be measured with the optional pressure sensor. A report was written in 1991 describing IES data processing [Fields et al., 1991]. Since that report, significant improvements have been made to both IES hardware and software, warranting an update of the IES data processing. The report by Kennelly et al. [2007] documents the standard processing steps contained in IESpkg 3, which has been used since the early 2000s, for IES/PIES/CPIES Models 6.1 and 6.2 at URI/GSO. More recently, IESpkg 4 was developed to allow more flexibility in the processing steps and data outputs, and to process the Fast PIES versions that sample 96 travel times each hour. This report documents the processing steps in IESpkg 4 and it repeats as much of the original text of Kennelly et al. [2007] as is still applicable. A separate document, Inverted Echo Sounder User\u27s Manual, IES Model 6.2, describes the IES hardware and instrument configuratio

An Intercomparison of Four Models of Current Meter in High Current Conditions in Drake Passage

Seven current meters representing four models were placed for an 11 month deployment on a stiffly buoyed mooring to intercompare their velocity measurements: two VMCMs, two Aanderaa RCM11s, two Aanderaa SEAGUARDSs, and a Nortek Aquadopp. The current meters were placed 6 m apart from each other at about 4000 m depth in an area of Drake Passage expected to have strong near-bottom currents, that were nearly independent of depth. Two high-current events occurred in bursts of semi-diurnal pulses lasting several days, one with peak speeds up to 67 cm/s and the other above 35 cm/s. The current speed measurements all agreed within about 5% when vector-averaged over simultaneous time intervals: the full time interval (198 days) when all instruments were working, and the two high-speed events lasting 21 days and 7 days. The VMCMs, chosen as the reference measurements, were found to measure the median of the mean-current magnitudes. The RCM11 and SEAGUARD current speeds had a nearly 1:1 relationship with the median. They agreed within 2% at higher speeds (35-70 cm/s), whereas in lower speed ranges (0-35 cm/s) the vector-averaged speeds for the RCM11s and SEAGUARDS were, respectively, 4-5% lower and 3-5% higher than the median. The Aquadopp current speeds were about 7% higher than the VMCMs over the range (0-40 cm/s) encountered through their shorter common time period

Estimates of Eddy Heat Flux Crossing the Antarctic Circumpolar Current from Observations in Drake Passage

The 4-yr measurements by current- and pressure-recording inverted echo sounders in Drake Passage produced statistically stable eddy heat flux estimates. Horizontal currents in the Antarctic Circumpolar Current (ACC) turn with depth when a depth-independent geostrophic current crosses the upper baroclinic zone. The dynamically important divergent component of eddy heat flux is calculated. Whereas full eddy heat fluxes differ greatly in magnitude and direction at neighboring locations within the local dynamics array (LDA), the divergent eddy heat fluxes are poleward almost everywhere. Case studies illustrate baroclinic instability events that cause meanders to grow rapidly. In the southern passage, where eddy variability is weak, heat fluxes are weak and not statistically significant. Vertical profiles of heat flux are surface intensified with ~50% above 1000 m and uniformly distributed with depth below. Summing poleward transient eddy heat transport across the LDA of −0.010 ± 0.005 PW with the stationary meander contribution of −0.004 ± 0.001 PW yields −0.013 ± 0.005 PW. A comparison metric, −0.4 PW, represents the total oceanic heat loss to the atmosphere south of 60°S. Summed along the circumpolar ACC path, if the LDA heat flux occurred at six “hot spots” spanning similar or longer path segments, this could account for 20%–70% of the metric, that is, up to −0.28 PW. The balance of ocean poleward heat transport along the remaining ACC path should come from weak eddy heat fluxes plus mean cross-front temperature transports. Alternatively, the metric −0.4 PW, having large uncertainty, may be high

Mapping Circulation in the Kuroshio Extension with an Array of Current and Pressure Recording Inverted Echo Sounders

The Kuroshio Extension System Study (KESS) aimed to quantify processes governing the variability of and the interaction between the Kuroshio Extension and the recirculation gyre. To meet this goal, a suite of instrumentation, including 43 inverted echo sounders equipped with bottom pressure gauges and current meters [current and pressure recording inverted echo sounders (CPIES)], was deployed. The array was centered on the first quasi-stationary meander crest and trough east of Japan, which is also the region of highest eddy kinetic energy. KESS was the first experiment to deploy a large quantity of these new CPIES instruments, and it was unique in that the instruments were deployed in water depths (5300–6400 m) close to their limit of operation. A comprehensive narrative of the methodology to produce mesoscale-resolving four-dimensional circulation fields of temperature, specific volume anomaly, and velocity from the KESS CPIES array is provided. In addition, an improved technique for removing pressure drift is introduced. Methodology and error estimates were verified with several independent datasets. Temperature error was lowest on the equatorward side of the Kuroshio Extension core and decreased with depth (1.5°C at 300 m, 0.3°C at 600 m, and \u3c0.1°C below 1200 m). Velocity errors were highest in regions of strong eddy kinetic energy, within and south of the jet core. Near the surface, the error in geostrophic velocity between adjacent CPIES was typically 10 cm s−1, decreasing downward to 6 cm s−1 at 500-m depth and 5 cm s−1 below 800 m. The rms differences from pointwise current measurements are nearly twice as large as the geostrophic errors, because the pointwise velocities include submesoscale and ageostrophic contributions

Generation of high-frequency topographic Rossby waves in the Gulf of Mexico

The Loop Current Eddy (LCE) separation cycle energizes deep circulation in the eastern Gulf of Mexico, transferring energy from the surface intensified Loop Current (LC) to the typically quiescent lower layers. To document the generation and radiation of deep energy during this cycle, an array of 24 current and pressure recording inverted echo sounders (CPIES) is deployed in the region 89°W to 86°W, 25°N to 27.5°N with the intent to capture circulation near bathymetric features thought to be important for current-topographic interactions: Campeche Bank, Mississippi Fan, and West Florida Shelf. During the nearly two-year deployment, June 2019 to May 2021, three LCE separation events are observed, during which energy injected into the deep Gulf organizes into two distinct frequency bands (1/100 – 1/20 days–1 and 1/20 – 1/10 days–1). High-frequency variability dominates the array’s northwest corner in the vicinity of the Mississippi Fan. Wave properties are consistent with topographic Rossby Waves (TRWs) with wavelengths of 150 – 300 km. Their generation coincides with each LCE separation and is attributed to an upper-lower layer resonant coupling between surface meanders and the sloping topography of the Mississippi Fan. TRWs captured by the CPIES array will likely intensify as wavelengths shorten in steeper topography along propagation pathways towards the Sigsbee Escarpment, generating hazardous currents with the potential to disrupt oil and gas operations in the region