||Click on either map for an enlargement, or on a box on the map below to see the corresponding figure.
The San Francisco Bay and Delta is a dynamic tide-affected system. Understanding the transport and fate of water, salt, suspended sediment, organic carbon, toxic substances, and non-mobile and feeble swimming organisms within such a system is challenging. Yet, it is a necessary first step toward understanding how the Bay/Delta's ecosystem works and, ultimately, how to best manage (and rehabilitate) the system.
Eulerian vs. Lagrangian frames of reference
There are two fundamental ways of thinking about and measuring transport processes, each with its advantages and disadvantages. The first, and usually more intuitive approach, is to put sensors in the water at a given location to concurrently measure the water speed (currents) and the concentration of any constituent of interest (water, salt, toxics, biota, etc.). From a combination of these measurements, one can (in theory) estimate the transport of any constituent, or flux, past a given point (assuming sufficient spatial and temporal coverage). Making measurements at fixed locations follows what oceanographers call an Eulerian point of view. Long time series (from months to years) can be collected using Eulerian techniques, particularly using today's measurement technologies. Eulerian data, therefore, has the advantage of being used to study the effects of processes that operate on tidal to yearly timescales. The problem with Eulerian measurements, however, is that the quantity of interest - transport - is fundamentally Lagrangian, which is the term oceanographers use for the second, often less intuitive way of thinking about and measuring transport processes.
The Lagrangian point of view or way of thinking follows the water mass. Therefore, the drifter measurements presented in this poster are Lagrangian measurements. Lagrangian measurements not only show the ultimate fate of a given water mass (and the ultimate fate of stuff in the water: salt, biota, etc.) over a specified time period, but Lagrangian measurements also reveal the transport pathways. In a system with flows and geometry as complicated as one finds in the Bay and Delta, the ultimate transport pathways are not always obvious (depending on location and the Delta inflows) and may not be well predicted by Eulerian measurements or Eulerian presentations of numerical model results (particularly during low Delta outflow periods).
The distinctions between Eulerian and Lagrangian concepts are often difficult, yet understanding the differences is fundamental to understanding the mechanisms that control the transport and fate of anything in the Bay/Delta system. To aid in understanding, it may be useful to think of Eulerian measures in terms of a benthic (e.g. clams) world view and Lagrangian measures in terms of a pelagic (e.g. fish) world view. Swimming behavior aside, the environment that a fish, suspended in the water column, experiences over a tidal cycle is very different from what a clam, fixed to the bottom, experiences over the same time frame. Figures 4a, 4b, and 5b provide examples of how far a given water mass travels in a 1/2 tidal cycle (6.0, 7.5, and 6.0 mi, respectively), underscoring the difference between the two different reference frames. Inferring transport from Eulerian measurements is analogous to asking the clam to predict what will happen to the fish! No matter how smart the clam (or how precise the measurements), in many cases the clam (or the scientist) will simply not have enough information - sitting at a fixed site on the estuary bed - to predict what will happen to a fish (transport) suspended in the water column.
Even though Lagrangian measurements provide a direct measure of the transport and fate of a given water mass, Lagrangian measurements are difficult to make for extended periods (> day). The results one obtains greatly depends on the precise location and time a given water mass is "tagged" with a drifter or dye. For example, the paths taken by the three sets of drifters released in the reserve fleet channel near the Benicia Bridge (Figure 4b) rapidly diverge to a final separation of 3.0 mi, even though their initial separation was only 100 yards. Therefore, great care must be taken in the placement of drifters, in the timing of drifter release, and in the interpretation of the relatively short-lived experiments drifter studies represent (hours compared to months for Eulerian measurements).
The USGS employs both Eulerian and Lagrangian methods to understand transport in the Bay and Delta. Many of the Lagrangian measurements made by the USGS in the fall of 1998 and winter 1999 are presented in this series of web pages.