TDMM (Time-Dependent Memory Method) is a linear algorithm for determining, in REAL-TIME, select time-dependent statistical properties of a random, nonstationary signal (Treviño and Andreas, 2000). Here, the signal is intermittent turbulence associated with the passage of a density current in the stable boundary layer; particulars of the data are found in Sun et al. (2001). The time-dependent properties we consider are the variance of vertical velocity and the integral scale. TDMM introduces a new time scale, called the MEMORY, which is different from the traditional scales used in turbulence analysis, yet, in some sense, is "natural" to turbulence correlations. TDMM produces auto-correlations which have time-dependent integral scales, a feature not found using traditional averaging (Comte-Bellot and Corrsin, 1971; Sreenivasan et al., 1978). This accrues because random perturbations are not averaged over the same-size window as the recorded signal itself. Using the MEMORY as the fundamental scale permits us to define the "optimal" time-dependent window [t-?T,t], where t is the PRESENT and ?T=?T(t)>0 is the window width over which the signal should be averaged. Finding the optimal averaging window avoids invoking a larger (or smaller) than necessary window for time averaging and permits realistic assessment of nonstationary features. By "optimal" we mean that ?T(t) is large enough to include all behavior relevant to the auto-correlation and yet not so long as to include changes with time in its lag behavior due to nonstationarity. In other words, TDMM shows how to properly average to compute meaningful statistics in nonstationary conditions. As time evolves, TDMM deploys forward and updates the values determined, providing the user with a real-time assessment of the time-dependent statistical characteristics of the turbulence. Fidelity in turbulence analysis requires answering two questions. The first is: how much of the past (and only the past) influences the present? The second is: how long is "long enough" to average when estimating statistics? The collective answers are called averaging time-scales. For turbulence, these are dynamic, vary randomly with time, and define optimal segmentation of the turbulence time series. The prevailing belief is that the USER provides the answers and that both questions have the same answer. Since turbulence, though, is a phenomenon governed by its own physical laws, the premise of TDMM is that the TURBULENCE provides the answers. This precludes the possibility that the user creates a reality in conflict with the turbulence. Specifically, that the user's answers may not be compatible with the turbulence and will likely both be the same. TDMM is a decision-making algorithm that adapts to stationary or nonstationary turbulence. If the turbulence is stationary, TDMM produces statistics that are constant in time. If the signal is nonstationary, TDMM produces statistics that vary with time. From the user, TDMM requires only the ACCURACY of the measurements and the SAMPLING RATE.

Comte-Bellot, G. and Corrsin, S.: 1971, ‘Simple Eulerian Time Correlation of Full- and Narrow-band Velocity Signals in Grid-Generated "Isotropic" Turbulence’, J. Fluid Mech. 48, 273-337. Sreenivasan, K. R., Chambers, A. J., and Antonia, R. A.: 1978, 'Accuracy of Moments of Velocity and Scalar Fluctuations in the Atmospheric Surface Layer', Boundary-Layer Meteorol. 14, 341-359 Sun, J. and sixteen others: 2001, ‘Intermittent Turbulence Associated with a Density Current Passage in the Stable Boundary Layer’, Boundary-Layer Meteorol. (in press). Treviño, G. and Andreas, E. L.: 2000, ‘Averaging Intervals for Spectral Analysis of Nonstationary Turbulence’, Boundary-Layer Meteor. 95, 231-247.