Per Gloersen

A confidence limit for the empirical mode decomposition and Hilbert spectral analysis

The confidence limit is a standard measure of the accuracy of the result in any statistical analysis. Most of the confidence limits are derived as follows. The data are first divided into subsections and then, under the ergodic assumption, the temporal mean is substituted for the ensemble mean. Next, the confidence limit is defined as a range of standard deviations from this mean. However, such a confidence limit is valid only for linear and stationary processes. Furthermore, in order for the ergodic assumption to be valid, the subsections have to be statistically independent. For non‐stationary and nonlinear processes, such an analysis is no longer valid. The confidence limit of the method here termed EMD/HSA (for empirical mode decomposition/Hilbert spectral analysis) is introduced by using various adjustable stopping criteria in the sifting processes of the EMD step to generate a sample set of intrinsic mode functions (IMFs). The EMD technique acts as a pre‐processor for HSA on the original data, producing a set of components (IMFs) from the original data that equal the original data when added back together. Each IMF represents a scale in the data, from smallest to largest. The ensemble mean and standard deviation of the IMF sample sets obtained with different stopping criteria are calculated, and these form a simple random sample set. The confidence limit for EMD/HSA is then defined as a range of standard deviations from the ensemble mean. Without evoking the ergodic assumption, subdivision of the data stream into short sections is unnecessary; hence, the results and the confidence limit retain the full‐frequency resolution of the full dataset. This new confidence limit can be applied to the analysis of nonlinear and non‐stationary processes by these new techniques. Data from length‐of‐day measurements and a particularly violent recent earthquake are used to demonstrate how the confidence limit is obtained and applied. By providing a confidence limit for this new approach, a stable range of stopping criteria for the decomposition or sifting phase (EMD) has been established, making the results of the final processing with HSA, and the entire EMD/HSA method, more definitive.

Arctic sea ice extents, areas, and trends, 1978-1996

Satellite passive-microwave data for November 1978 through December 1996 reveal marked seasonal, regional, and interannual variabilities, with an overall decreasing trend of −34,300±3700 km2/yr (−2.8%/decade) in Arctic sea ice extents over the 18.2-year period. Decreases occur in all seasons and on a yearly average basis, although they are largest in spring and smallest in autumn. Regionally, the Kara and Barents Seas have the largest decreases, at −15,200±1900 km2/yr (−10.5%/decade), followed by the Seas of Okhotsk and Japan, the Arctic Ocean, Greenland Sea, Hudson Bay, and Canadian Archipelago. The yearly average trends for the total, the Kara and Barents Seas, and the Seas of Okhotsk and Japan all have high statistical significance, with the null hypothesis of a 0 slope being rejected at a 99% confidence level. Regions showing increasing yearly average ice extents are Baffin Bay/Labrador Sea, the Gulf of St. Lawrence, and the Bering Sea, with only the increases in the Gulf of St. Lawrence being statistically significant at the 99% level. Hemispheric results for sea ice areas exhibit the same −2.8%/decade decrease as for ice extents and hence a lower absolute decrease (−29,500±3800 km2/yr), with the ice-free area within the ice pack correspondingly decreasing at −4800±1600 km2/yr. Confidence levels for the trends in ice areas and ice-free water areas exceed 99% and 95%, respectively. Nonetheless, interannual variability is high, and, for instance, the Arctic Ocean ice extents have a positive trend 1990–1996, in spite of their negative trend for the time period as a whole.

Passive Microwave Algorithms for Sea Ice Concentration: A Comparison of Two Techniques

Abstract The most comprehensive large-scale characterization of the global sea ice cover so far has been provided by satellite passive microwave data. Accurate retrieval of ice concentrations from these data is important because of the sensitivity of surface flux (e.g., heat, salt, and water) calculations to small changes in the amount of open water (leads and polynyas) within the polar ice packs. Two algorithms that have been used for deriving ice concentrations from multichannel data are compared. One is the NASA Team algorithm and the other is the Bootstrap algorithm, both of which were developed at NASAs Goddard Space Flight Center. The two algorithms use different channel combinations, reference brightness temperatures, weather filters, and techniques. Analyses are made to evaluate the sensitivity of algorithm results to variations of emissivity and temperature with space and time. To assess the difference in the performance of the two algorithms, analyses were performed with data from both hemispheres and for all seasons. The results show only small differences in the central Arctic in winter but larger disagreements in the seasonal regions and in summer. In some areas in the Antarctic, the Bootstrap technique shows ice concentrations higher than those of the Team algorithm by as much as 25%; whereas, in other areas, it shows ice concentrations lower by as much as 30%. The differences in the results are caused by temperature effects, emissivity effects, and tie point differences. The Team and the Bootstrap results were compared with available Landsat, advanced very high resolution radiometer (AVHRR) and synthetic aperture radar (SAR) data. AVHRR, Landsat, and SAR data sets all yield higher concentrations than the passive microwave algorithms. Inconsistencies among results suggest the need for further validation studies.

Deriving long‐term time series of sea ice cover from satellite passive‐microwave multisensor data sets

We have generated consistent sea ice extent and area data records spanning 18.2 years from passive-microwave radiances obtained with the Nimbus 7 scanning multichannel microwave radiometer and with the Defense Meteorological Satellite Program F8, F11, and F13 special sensor microwave/imagers. The goal in the creation of these data was to produce a long-term, consistent set of sea ice extents and areas that provides the means for reliably determining sea ice variability over the 18.2-year period and also serves as a baseline for future measurements. We describe the method used to match the sea ice extents and areas from these four multichannel sensors and summarize the problems encountered when working with radiances from sensors having different frequencies, different footprint sizes, different visit times, and different calibrations. A major obstacle to adjusting for these differences is the lack of a complete year of overlapping data from sequential sensors. Nonetheless, our procedure reduced ice extent differences during periods of sensor overlap to less than 0.05% and ice area differences to 0.6% or less.

A scanning multichannel microwave radiometer for Nimbus-G and SeaSat-A

A scanning multichannel microwave radiometer (SMMR) has been designed for the Nimbus-G spacecraft and incorporated also into the SeaSat-A payload for the primary purpose of determining sea surface temperatures and wind stress on a nearly all-weather basis. Observations of microwave polarization components will be made at wavelengths of 0.8, 1.4, 1.7, 2.8, and 4.6 cm over a swath 822 km wide below the Nimbus-G and 595 km wide below the SeaSat-A spacecraft. The smallest spatial resolution cell is about 20 km at a wavelength of 0.8 cm, and proportionately larger at the other wavelengths. Using algorithms based on a combination of experimental data and physical models for converting the observed brightness temperatures, the indicated accuracies of the results (excluding conditions of significant rainfall) are within 1 K for sea surface temperature and 2 m/s for surface wind speeds, over a range from 0-50 m/s.

Passive microwave images of the polar regions and research applications

Passive microwave images of the polar regions, first produced after the launch of the Nimbus-5 Electrically Scanning Microwave Radiometer (ESMR)in December 1972, have become a valuable new source of polar information. Some of the potential applications of this new capability were anticipated. Of these, the sensing of sea ice through clouds and the polar night is probably the most important application for polar research and for operations on the polar seas. Other applications, such as the measurement of certain near-surfaceice sheet parameters, have been formulated more recently. Measurement of various ocean surface parameters is expected from the forthcoming multifrequency microwave observations. Undoubtedly additional uses of passive microwave datawill be conceived and developed. Two remarkable aspects of satellite-borne microwave radiometers are the complete spatial detail obtained by the scanning sensors and the temporal detail provided by continual coverage. For example, the observations of detailed microwave emission patterns over the Antarctic ice sheet should yield information that could not be obtained by surface or even aircraft measurements. Sequences of images produced at three-day intervalsreveal short-term ice sheet and sea ice phenomena that would otherwise be missed.

Time-dependence of sea-ice concentration and multiyear ice fraction in the Arctic Basin

The time variation of the sea-ice concentration and multiyear ice fraction within the pack ice in the Arctic Basin is examined, using microwave images of sea ice recently acquired by the Nimbus-5 spacecraft and the NASA CV-990 airborne laboratory. The images used for these studies were constructed from data acquired from the Electrically Scanned Microwave Radiometer (ESMR) which records radiation from earth and its atmosphere at a wavelength of 1.55 cm. Data are analyzed for four seasons during 1973–1975 to illustrate some basic differences in the properties of the sea ice during those times. Spacecraft data are compared with corresponding NASA CV-990 airborne laboratory data obtained over wide areas in the Arctic Basin during the Main Arctic Ice Dynamics Joint Experiment (1975) to illustrate the applicability of passive-microwave remote sensing for monitoring the time dependence of sea-ice concentration (divergence). These observations indicate significant variations in the sea-ice concentration in the spring, late fall and early winter. In addition, deep in the interior of the Arctic polar sea-ice pack, heretofore unobserved large areas, several hundred kilometers in extent, of sea-ice concentrations as low as 50% are indicated.

Spatial distribution of trends and seasonally in the hemispheric sea ice covers: 1978–1996

We extend earlier analyses of a 8.8-year sea ice data set that described the local seasonal variations and trends in each of the hemispheric sea ice covers to the recently merged 18.2-year sea ice record from four satellite instruments. The seasonal cycle characteristics remain essentially the same as for the shorter time series, but the local trends are markedly different, in some cases reversing sign. The sign reversal reflects the lack of a consistent long-term trend and could be the result of localized long-term oscillations in the hemispheric sea ice covers. By combining the separate hemispheric sea ice records into a global one, we have shown that there are statistically significant net decreases in the sea ice coverage on a global scale. The change in the global sea ice extent is −0.01 ± 0.003 × 106 km2 per decade. The decrease in the areal coverage of the sea ice is only slightly smaller, so that the difference in the two, the ice-free areas within the packs, has no statistically significant change.

Comparison of interannual intrinsic modes in hemispheric sea ice covers and other geophysical parameters

Recent papers have described 18-year trends and interannual oscillations in the Arctic and Antarctic sea ice extents, areas, and enclosed open water areas based on newly formulated 18.2-year ice concentration time series. They were obtained by fine-tuning the sea ice algorithm tie points individually for each of the four sensors used to acquire the data. In this paper, these analyses are extended to an examination of the intrinsic modes of these time series, obtained by means of empirical mode decomposition, which handles both nonstationary and nonlinear data as found in these time series, unlike filtering techniques based on Fourier analysis. Our analysis centers on periodicities greater than one year. Quasi-biennial and quasi-quadrennial oscillations similar to those observed earlier with a multitaper-filtered Fourier analysis technique were also observed. The intrinsic modes described feature frequency as well as amplitude modulation within their respective frequency bands. The slowest varying mode in the Antarctic sea ice cover has slightly less than a full period during this 18.2-year time period, but the change in sign of its curvature hints at a modal period of about 19 years, with important implications for the trend analyses published earlier.

Reestablishing the circumpolar wave in sea ice around Antarctica from one winter to the next

Remarkable correlation exists between warm water, poleward winds over the ocean, and low sea ice concentrations and extents over the winter sea ice pack around Antarctica, even to the point of continuing paterns across the ice-sea boundary. Since the wind stress associated with poleward wind is expected to compact the ice during sea ice edge retraction, we conclude that the memory of the Antarctic circumpolar wave in the sea ice pack is carried from one austral winter to the next by the neighboring water temperatures since the sea ice pack retracts nearly to Antarctica in austral summer.