The sigma coordinate is inherited from the original code. [EFDC+] Everything else on this page including Sigma-Zed and its three configurations, and re-layering as the bed evolves was developed by DSI and exists only in EFDC+.

How you divide the water column determines whether your model reproduces stratification correctly, and in stratified systems stratification governs almost everything else. It sets where the thermocline forms, how long it persists, whether dissolved oxygen at depth is replenished or drawn down, and how far a salt wedge travels upstream.

The difficulty is that a stretched vertical coordinate follows the bed. Where bathymetry drops away steeply, layers tilt with it and computing a horizontal gradient means differencing between two points at different elevations. That introduces a well-documented error in the horizontal pressure gradient (Mellor et al., 1994), along with matching errors in concentration and velocity gradients. The error is generally significant only where bathymetry varies steeply — but that describes most deep reservoirs, many lakes, and any estuary with a dredged navigation channel.

The sigma coordinate approach is a topographically conformal system used widely across three-dimensional hydrodynamic models. It divides every water column into the same number of layers, regardless of depth.

This resolves shallow and deep regions equally well and equally efficiently at the same time, and it suits waterbodies with complicated geometry and large changes in bottom elevation. It is the conventional EFDC approach and is adequate for a large range of applications.

Its limitation is the pressure gradient error described above. There is also a class of applications, for example, a deep navigation channel in an otherwise shallow estuary is the standard, where you would rather use physical z layering in one part of the domain and sigma layering in another. SIG gives you no way to do that.

[EFDC+] The Sigma-Zed approach was developed by DSI (Craig et al., 2014) to address both problems. SGZ allows the number of layers to vary across the model domain based on water depth, so each cell can carry a different layer count. Shallow cells get fewer layers; deep cells get more.

What makes this work numerically is face matching: the z coordinate varies at each cell face so that active layers line up with those in the adjacent cell. This is the fundamental difference between SGZ and the generalized vertical coordinate (GVC) approach available in the legacy code, and it is what keeps horizontal gradients well-behaved across a depth transition.

The payoff is direct. Horizontal pressure gradient error is substantially reduced, density stratification is represented far more realistically, and the model runs faster. In SGZ the total number of vertical layers can be very large, yet computational time is shorter than a similarly configured SIG model, because shallow cells no longer carry layers they don’t need. Sigma-Zed is now the recommended standard approach in EFDC+.

The difference is visible in a single profile. The two figures below show the same waterbody, the same cell, and the same date, modelled once with sigma layering and once with Sigma-Zed.

Specified Bottom: You set the number of layers in each horizontal cell directly. This gives the most control where you know exactly where resolution matters.

Uniform Layering: Layer bottoms are aligned horizontally across the domain, so a given layer sits at the same elevation everywhere it exists. This produces the closest behavior to a traditional z grid while retaining a surface-following top layer.

Specified Thickness from Top new in EEMS 12.1: [EFDC+] Rather than defining layers as relative splits of the water column, you specify actual layer thicknesses in meters. Layers are built downward from the surface, with the bottom of each aligned horizontally. Combined with a specified maximum depth for the domain, this lets you say directly that you want half-meter resolution through the surface mixed layer and coarser layers beneath, the kind of control a Z grid gives you, without giving up a surface-following coordinate.

[EFDC+] When sediment transport is simulated with bed morphology active, erosion and deposition change water depths as the run proceeds, and the depth ratios that set each cell’s layer count change with them. EFDC+ can therefore re-layer the domain as the bed evolves, updating bottom layer indices across the grid. This is an optional capability, enabled when your application needs it.

Learn more about Sigma-Zed and see examples of how it has been applied to waterbodies in North America such as Lake Washington and Lake Mead here.