Evaluating the Quality of Ground-Based Microwave Radiometer Measurements and Retrievals Using Detrended Fluctuation and Spectral Analysis Methods

Abstract

Time series both of microwave radiometer brightness temperature measurements at 23.8 and 31.4 GHz and of retrievals of water vapor and liquid water path from these brightness temperatures are evaluated using the detrended fluctuation analysis method. As quantified by the parameter α, this method (i) enables identification of the time scales over which noise dominates the time series and (ii) characterizes the temporal range of correlations in the time series. The more common spectral analysis method is also used to assess the data and its results are compared with those from detrended fluctuation analysis method. The assumption that measurements should have certain scaling properties allows the quality of the measurements to be characterized. The additional assumption that the scaling properties of the measurements of an atmospheric quantity are preserved in a useful retrieval provides a means for evaluating the retrieval itself. Applying these two assumptions to microwave radiometer measurements and retrievals demonstrates three points. First, the retrieved water vapor path during cloudy-sky periods can be dominated by noise on shorter than 30 min time scales (α-exponent = 0.1) and exhibits no scaling behavior at longer time scales. However, correlations in the brightness temperatures and liquid water path retrievals are found to be consistent with a power-law behavior for time scales up to 3 hr with an α-exponent equal to approximately 0.3, as in other geophysical phenomena. Second, clear-sky, moist atmospheres show the expected scaling for both measurements and retrievals of the water vapor path. Third, during clear-sky, dry atmospheric days, instrument noise from the 31.4 GHz channel compromises the quality of the water vapor path retrieval. The detrended fluctuation analysis method is thus proposed as means for assessing the quality of both the instrument data and the retrieved parameters obtained from these data.

Generalized Hurst exponent and multifractal function of original and translated texts mapped into frequency and length time series

“…It is said that the variable is multifractal if those moments exhibit a power-law dependence in the resolution parameter. On the other hand, geometrical approaches [37][38][39][40][41][42] try to assess a local power-law dependency on the resolution parameter for the same intensive variables at every particular point. The geometrical approach is informative about the spatial localization of self-similar (fractal) structures, but leads to some difficulty when having to justify the retrieval of scaling exponents.…”

Time correlations and 1/f behavior in backscattering radar reflectivity measurements from cirrus cloud ice fluctuations

“…New techniques have been recently developed that can systematically eliminate trends in the data and thus reveal some intrinsic dynamical properties such as fluctuation correlations that are very often masked by nonstationarities. There have been indeed a large number of studies on long-range power law correlations in time series [Kantz and Schreiber, 1997;Brockwell and Davis, 1998;Malamud and Turcotte, 1999;Schreiber, 1999] in many research fields such as biology [Stanley et al, 1993;Hausdorff et al, 1997;Ivanov et al, 1996Ivanov et al, , 1999Mercik et al, 2000;Ashkenazy et al, 2001], finance [Mantegna and Stanley, 1995;Vandewalle and Ausloos, 1997;Ausloos and Ivanova, 1999;Ausloos, 2001] meteorology and climatology [Koscielny- Bunde et al, 1993Bunde et al, , 1998Davis et al, 1996;Ivanova et al, 2000Ivanova et al, , 2002Ausloos and Ivanova, 2001;Bunde et al, 2001;Peters et al, 2002]. Some of us have already examined long-range time correlations in nonstationary atmospheric signals of the liquid water path [Ivanova et al, 2000] and water vapor path [Ivanova et al, 2002] in stratus clouds, as well as in large-scale meteorological signals like the Southern Oscillation Index [Ausloos and Ivanova, 2001].…”

A Calibration Scheme for Microwave Radiometers Using Tipping Curves and Kalman Filtering

“…In [21], a method is proposed for a detailed evaluation of the quality of ground-based radiometer data, where the authors make use of the DFA method [10]. In order to apply the DFA technique, a time series y(t) of length N is divided into N/τ nonoverlapping periods, each containing τ values.…”