Lawrence E. Flynn

Factoring: a method for scheduling parallel loops

~lw advantage of , capability of rallel machines, application programs must contain sufficient parallelism, and this parallelism must be effectively scheduled on multiple processors. Loops without dependences among their iterations are a rich source of parallelism in scientific code. Restructuring compilers for sequential programs have been particularly successful in determining when loop iterations are independent and can be executed in parallel. Because of the prevalence of parallel loops, optimal parallel-loop scheduling has received considerable attention in both academic and industrial communities. The fundamental trade-off in scheduling parallel-loop iterations is that of maintaining balanced processor workloads vs. minimizing scheduling overhead. Consider, for example, a loop with N iterations that contain an IF statement. Depending on whether the body of the IF statement is executed, an iteration has LONG or SHORT execution time. If we naively schedule the iterations on P processors in chunks of N/P iterations, a strategy called static chunking (SC), a chunk of one processor may consist of iterations that are all LONG, while a chunk of another processor may consist of iterations that are all SHORT. Hence, different processors may finish at widely different times. Since the loop finishing time is equal to the latest finishing time of any of the processors executing the loop, the overall finishing time may be greater than optimal with SC. Alternatively, if we (also naively) schedule the iterations one at a time, a strategy called self-scheduling (SS), then there will be N scheduling operations. With SS, a processor obtains a new iteration whenever it becomes idle, so the processors finish at nearly the same time and the workload is balanced. Because of the scheduling overhead , however, the overall finishing time may be greater than optimal. The characteristics of the iterations determine which scheme performs better. For instance, variable-length, coarse-grained iterations favor SS, while constant-length, fine-grained iterations favor SC. Even when iterations do not contain conditional statements, their running times are likely to be variable because of interference from their environment (other iterations, the operating system, and other programs). The scheduling schemes just discussed are extremes; between the two lie schemes that attempt to minimize the cumulative contribution of uneven processor finishing times and of scheduling overhead. Such schemes schedule iterations in chunks of sizes greater than one but less than N/P, where size is the number of iterations in the chunk. Both fixed-size and variable-size chunk-ing schemes have been proposed. In …

Record Low Global Ozone in 1992

The 1992 global average total ozone, measured by the Total Ozone Mapping Spectrometer (TOMS) on the Nimbus-7 satellite, was 2 to 3 percent lower than any earlier year observed by TOMS (1979 to 1991). Ozone amounts were low in a wide range of latitudes in both the Northern and Southern hemispheres, and the largest decreases were in the regions from 10�S to 20�S and 100N to 60�N. Global ozone in 1992 is at least 1.5 percent lower than would be predicted by a statistical model that includes a linear trend and accounts for solar cycle variation and the quasi-biennial oscillation. These results are confirmed by comparisons with data from other ozone monitoring instruments: the SBUV/2 instrument on the NOAA-11 satellite, the TOMS instrument on the Russian Meteor-3 satellite, the World Standard Dobson Instrument 83, and a collection of 22 ground-based Dobson instruments.

Algorithm for the estimation of vertical ozone profiles from the backscattered ultraviolet technique

An implementation of the optimal estimation scheme to obtain vertical ozone profiles from satellite measurements of backscattered solar ultraviolet (buv) radiation is described. This algorithm (Version 6.0) has been used to produce a 15-year data set of global ozone profiles from Nimbus 7 SBUV, NOAA 11 SBUV/2, and Space Shuttle SSBUV instruments. A detailed discussion of the information content of the measurement is presented. Using high vertical resolution ozone profiles from the SAGE II experiment as “truth” profiles, it is shown that the buv technique can capture short-term variabilities of ozone in 5-km vertical layers, between 0.3 mbar and 100 mbar, with a precision of 5–15%. However, outside the 1–20 mbar range, buv-derived results are heavily influenced by a priori assumptions. To minimize this influence, it is recommended that the studies of long-term trends using buv data be restricted to 1–20 mbar range. Outside this range, only the column amounts of ozone between 20 mbar and surface, and above 1 mbar, can be considered relatively free of a priori assumptions.

Long-term ozone trends derived from the 16-year combined Nimbus 7/Meteor 3 TOMS Version 7 record

Ozone measurements from the Nimbus 7 TOMS instrument, which operated from November 1978 through early May 1993, have been extended through December 1994 using data from the TOMS instrument on-board the Russian Meteor 3 satellite. Both TOMS data records have recently been recalibrated, and then reprocessed using the Version 7 retrieval algorithm. Long-term trend estimates obtained from a multiple regression analysis show ozone losses in the extended data record similar to those reported in previous studies using Version 6 TOMS and SBUV data, and ground-based Dobson data. Ozone continues to decline through the end of 1994, with the most significant ozone losses occurring in the high southern latitudes during October (−20% per decade) and in the northern mid- to high-latitudes during March/April (−6 to −8% per decade). There is no significant ozone trend in the tropics. Annual-average trends derived from the Nimbus 7 Version 7 data are 0–2.5% per decade less negative than those derived over the same time period using Version 6 data.

Ozone trends deduced from combined Nimbus 7 SBUV and NOAA 11 SBUV/2 data

The long-term time series of global ozone from the Nimbus-7 SBUV (Nov. 1978–June 1990) are extended through June 1994 by using measurements from the NOAA-11 SBUV/2. The data sets are merged based upon comparisons during the 18-month overlap period in which both instruments were operational. During this period, the average offset between the two time series is less than 2% in total ozone, and less than 6% in Umkehr layers 1–10. A linear-regression trend model is applied to the extended time series to calculate updated trends as a function of latitude and altitude. Trends through June 1994 are 1.5-2% per decade less negative than through June 1990 in the tropical middle stratosphere (35–40 km) and in the upper stratosphere (45–50 km) at mid-latitudes. In the lower stratosphere, the trends are nearly 1.5% per decade more negative in the southern hemisphere tropical regions to 25°S, but remain relatively unchanged elsewhere. The seasonal structure of the total ozone trends is similar to past trend study results, but the magnitude of the seasonal trend can vary by 2% per decade depending on the length of the time series. Both TOMS (through April 1993) and SBUV total ozone time series show small negative trends in the equatorial region, though they are not statistically significant at the 2-σ level.

Factoring: a practical and robust method for scheduling parallel loops

No abstract available

The mid‐latitude total ozone trends in the northern hemisphere

The total column ozone trends derived from satellite measurements at northern mid-latitudes during winter and spring seasons appear to be significantly larger than predicted by recent 2-D photochemical models. Analyses of 13 to 14 years of the Nimbus-7 TOMS total ozone measurements suggest that satellite-derived trends during winter and spring months are influenced by interannual variability associated with dynamical perturbations in the atmosphere. Such perturbations cause large longitudinal spread in total ozone trends at mid-latitudes. For example, the decadal trends in column ozone during February over the 10° latitude band centered at 40° N vary from about −9% to about −4% with error bars of 4 to 6% at the 2σ level. During the same month the zonally averaged trend is about −6±3%. The trends in certain geographical regions or locations, such as the Mediterranean region (35° to 45°N, 0° to 30°E) and Athens, Greece (38°N, 24°E), track the seasonal trends derived from the zonally-averaged data. Given the large uncertainties of the regional and local trends, such similarities may be fortuitous. By using the lower stratospheric and tropospheric temperatures as indices of dynamical variability in the ozone trend analysis, the total ozone trends are reduced by 1 to 3% per decade. For the winter months (December, January and February), the midlatitude trends (zonally averaged) are respectively −3.7±2.5 and −5.1±2.8 % per decade with and without using the lower stratospheric temperature as an index of dynamical variability.

Comparison of SBUV and SAGE II ozone profiles: Implications for ozone trends

Solar backscattered ultraviolet (SBUV) ozone profiles have been compared with Stratospheric Aerosol and Gas Experiment (SAGE) II profiles over the period October 1984 through June 1990, when data are available from both instruments. SBUV measurements were selected to closely match the SAGE II latitude/longitude measurement pattern. There are significant differences between the SAGE II sunrise and the sunset zonal mean ozone profiles in the equatorial zone, particularly in the upper stratosphere, that may be connected with extreme SAGE II solar azimuth angles for tropical sunrise measurements. Calculation of the average sunset bias between SBUV and SAGE II ozone profiles shows that allowing for diurnal variation in Umkehr layer 10, SBUV and SAGE II agree to within +/- 5% for the entire stratosphere in the northern midlatitude zone. The worst agreement is seen at southern midlatitudes near the ozone peak (disagreements of +/- 10%), apparently the result of the SBUV ozone profile peaking at a lower altitude than SAGE. The integrated ozone columns (cumulative above 15 km) agree very well, to within +/- 2.3% in all zones for both sunset and sunrise measurements. A comparison of the time dependence of SBUV and SAGE II shows that there was less than +/- 5% relative drift over the 5.5 years for all altitudes except below 25 km, where the SBUV vertical resolution is poor. The best agreement with SAGE is seen in the integrated column ozone (cumulative above 15 km), where SAGE II has a 1% negative trend relative to SBUV over the comparison period. There is a persistent disagreement of the two instruments in Umkehr layers 9 and 10 of +/- 4% over the 5.5-year comparison period. In the equatorial zone this disagreement may be caused in part by a large positive trend (0.8 K per year) in the National Meteorologica Center temperatures used to convert the SAGE II measurement of ozone density versus altitude to a pressure scale for comparison with SBUV. In the middle stratosphere (30-40 km), SBUV shows a 2-4% negative drift relative to SAGE II. If the actual ozone trends are considered, SBUV and SAGE II agree in showing little ozone change (less than 2%) between 1984 and 1990, except in layer 3 where SAGE II measures a large ozone decrease. But over 11 years, SBUV measured a 7% per decade ozone decrease between 40 and 50 km, decreasing in magnitude at lower altitudes, in good agreement with 11-year trends derived from the average of 5 Umkehr stations.

Validation of Ozone Monitoring Instrument level 1b data products

[1] The validation of the collection 2 level 1b radiance and irradiance data measured with the Ozone Monitoring Instrument (OMI) on NASA’s Earth Observing System (EOS) Aura satellite is investigated and described. A number of improvements from collection 2 data to collection 3 data are identified and presented. It is shown that with these improvements in the calibration and in the data processing the accuracy of the geophysically calibrated level 1b radiance and irradiance is improved in the collection 3 data. It is shown that the OMI level 1b irradiance product can be reproduced from a high-resolution solar reference spectrum convolved with the OMI spectral slit functions within 3% for the Fraunhofer structure and within 0.5% for the offset. The agreement of the OMI level 1b irradiance data product with other available literature irradiance spectra is within 4%. The viewing angle dependence of the irradiance and the irradiance goniometry are discussed, and improvements in the collection 3 data are described. The in-orbit radiometric degradation since launch is shown to be smaller than 0.5% above 310 nm and increases to about 1.2% at 270 nm. It is shown how the viewing angle dependence of the radiance is improved in the collection 3 data. The calculation of the surface albedo from OMI measurement data is discussed, and first results are presented. The OMI surface albedo values are compared to literature values from the Total Ozone Mapping Spectrometer (TOMS) and the Global Ozone Monitoring Experiment (GOME). Finally, improvements in the spectral and spatial stray light corrections from collection 2 data to collection 3 data are presented and discussed.

Achieving satellite instrument calibration for climate change

For the most part, satellite observations of climate are not presently sufficiently accurate to establish a climate record that is indisputable and hence capable of determining whether and at what rate the climate is changing. Furthermore, they are insufficient for establishing a baseline for testing long-term trend predictions of climate models. Satellite observations do provide a clear picture of the relatively large signals associated with interannual climate variations such as El Nino-Southern Oscillation (ENSO), and they have also been used to diagnose gross inadequacies of climate models, such as their cloud generation schemes. However, satellite contributions to measuring long-term change have been limited and, at times, controversial, as in the case of differing atmospheric temperature trends derived from the U.S. National Oceanic and Atmospheric Administrations (NOAA) microwave radiometers.