Lag is the time between the peak flow and the centroid of rainfall. Lag time defines the shape of your hydrograph when using unit hydrograph methods. The time of concentration is used generally with rational method type analysis. However, when you are routing hydrographs you need to describe the shape of the hydrograph and water mass.
Ray Linsley's (Hydrology For Engineers) has a pretty good description.
I think the specific definitions varies for different models.
In general, I think of time-of-concentratin as a characteristic of a basin that results in attenuation of runoff generated from the basin's surfaces. Lag time can be used to refer to the difference in the time that it takes for runoff from different basins to reach the same point. But lag time can also be used to talk about peak flow attenuation compared to either another basin or the timing of the peak rainfall intensity.
Here is some more detailed background on the "time of concentration" based on some research I've been doing recently.
Several methods, specifically the Santa Barbara Urban Hydrograph and TR-20, use the Attenuation-Kinematic (Att-Kin) routing procedure (or a slight variatin thereof) that was developed by SCS and is documented for TR-20 (1981). This hydrologic routing procedure treats a basin like a long uniform channel, and runoff generated is routed through the channel using basic inflow & outflow relations.
The relationship between inflow and outflow in a specific basin is represented by a "storage coefficient". By definition, if you plot the storage in the basin versus the discharge rate, the instantaneous slope of the line is the storage coefficient, K. Going back to the idea of the long uniform channel, it can be shown that:
Storage = depth * width * length
Discharge = velocity * width * depth
Defining velocity = length/(travel time) yields:
storage coefficient K = length/velocity = travel time = called time of concentration in standard engineering practice
I won't bore you with the rest of the derivation and application of the routing equations, but you end up with an expression where the basin discharge for a timestep is a function of the previous inflows & discharge, the model timestep, and the travel time.
Changes to the time of concentration in the Santa Barbara model affect the timing of the peak flows, but it is not linear (e.g. increasing the Tc by 15 min does not necessarily delay the peak by 15 min).
Reference: Hydrology Technical Note 2 by SCS, Chapter 1 "The Modified Att-Kin ROuting Model" download from:
