Drift Uncertainty Research Articles

Search for evidence of trend slow-down in the long-term TOMS/SBUV total ozone data record: the importance of instrument drift uncertainty

Abstract. We have developed a merged ozone data set (MOD) for the period October 1978 through June 2006 combining total ozone measurements (Version 8 retrieval) from the TOMS (Nimbus 7, Earth Probe) and SBUV/SBUV2 (Nimbus 7, NOAA 9/11/16) series of satellite instruments. We use the MOD data set to search for evidence of ozone recovery in response to the observed leveling off of chlorine and bromine compounds in the stratosphere. A crucial step in any time series analysis is the evaluation of uncertainties. In addition to the standard statistical time series uncertainties, we evaluate the possible instrument drift uncertainty for the MOD data set. We combine these two sources of uncertainty and apply them to a cumulative sum of residuals (CUSUM) analysis for trend slow-down. For the extra-polar mean between 60° S and 60° N, the apparent slow-down in trend is found to be clearly significant if instrument uncertainties are ignored. When instrument uncertainties are added, the slow-down becomes marginally significant at the 2σ level. For the mid-latitudes of the northern hemisphere (30° to 60° N) the trend slow-down is highly significant at the 2σ level, while in the southern hemisphere the trend slow-down has yet to meet the 2σ significance criterion. The rate of change of chlorine/bromine compounds is similar in both hemispheres, and we expect the ozone response to be similar in both hemispheres as well. The asymmetry in the trend slow-down between hemispheres likely reflects the influence of dynamical variability, and thus a clearly statistically significant response of total ozone to the leveling off of chlorine and bromine in the stratosphere is not yet indicated.

Stabilization of Uncertain Nonholonomic Systems via Time-Varying Sliding Mode Control

This note addresses the robust stabilization problem for a general class of nonholonomic systems in the presence of drift uncertainties. The control approach developed is based on the combined applications of the sliding mode control technique and nonlinear time-varying systems theory. First, some properties of nonlinear time-varying systems are introduced for the purpose of designing sliding mode controller. An explicit time-varying feedback form is provided to guarantee the existence and uniqueness of periodic time-varying solution for the corresponding linear periodic partial differential equation. Second, an explicit discontinuous feedback control law is presented to guarantee the existence of sliding mode. The first integrals obtained by the previous periodic partial differential equation are then directly used to determine the switching function. The uniform asymptotic stability of the closed loop system is proved via the invariance principle of nonlinear time-varying systems. Finally, an example is given to illustrate the proposed approach.

Comparison of Canadian daily ice charts with surface observations off Newfoundland, winter 1992

Abstract Forecast ice drift rates and thicknesses displayed on daily ice charts and forecast winds for the Canadian east coast are compared to on‐ice observations made during the second Canadian Atlantic Storm Program (CASP II) of March 1992. Observed and 24‐hour forecasts of daily ice drift rates were weakly correlated even though long‐term means closely matched observations. Daily drift rates have an RMS error of 13 cm s‐1 relative to a 15 cm s‐1 mean in addition to an RMS direction error of 50 degrees. Contributions towards daily drift uncertainties were: the estimation of winds, unmodelled physics of ocean and ice cover processes; and the inconsistency in the methods used by the ice forecaster. Correlation coefficients between forecast winds and on‐ice observed winds decreased from 0.8 at 0‐hour to 0.7 for the 30‐hour forecast. Similar results were found between ice drift rates from forecast winds. Histograms of ice thicknesses observed along narrow swaths using a helicopter‐towed electromagnetic sensor compared well with undeformed ice thicknesses representing large areas on ice charts, with differences mainly caused by difference in ice type representation and by co‐registering the two data sets.