Complete families of linearly non-degenerate rational curves

We prove that a complete family of linearly non-degenerate rational curves of degree $e > 2$ in $\mathbb{P}^n$ has at most $n-1$ moduli. For $e = 2$ we prove that such a family has at most $n$ moduli. It is unknown whether or not this is the best possible result. The general method involves exhibiting a map from the base of a family $X$ to the Grassmaninian of $e$-planes in $\mathbb{P}^n$ and analyzing the resulting map on cohomology.Comment: 14 page

Solar Spectral Irradiance Changes During Cycle 24

We use solar spectra obtained by the Ozone Monitoring Instrument (OMI) on board the Aura satellite to detect and follow long-term (years) and short-term (weeks) changes in the solar spectral irradiance (SSI) in the 265-500 nm spectral range. During solar Cycle 24, in the relatively line-free regions the SSI changed by approximately 0.6% +/- 0.2% around 265 nm. These changes gradually diminish to 0.15% +/- 0.20% at 500 nm. All strong spectral lines and blends, with the notable exception of the upper Balmer lines, vary in unison with the solar "continuum." Besides the lines with strong chromospheric components, the most involved species include Fe I blends and all prominent CH, NH, and CN spectral bands. Following the general trend seen in the solar "continuum," the variability of spectral lines also decreases toward longer wavelengths. The long-term solar cycle SSI changes are closely, to within the quoted 0.1%-0.2% uncertainties, matched by the appropriately adjusted short-term SSI variations derived from the 27 day rotational modulation cycles. This further strengthens and broadens the prevailing notion about the general scalability of the UV SSI variability to the emissivity changes in the Mg II 280 nm doublet on timescales from weeks to years. We also detect subtle deviations from this general rule: the prominent spectral lines and blends at lambda approximately or greater than 350 nm show slightly more pronounced 27 day SSI changes when compared to the long-term (years) trends. We merge the solar data from Cycle 21 with the current Cycle 24 OMI and GOME-2 observations and provide normalized SSI variations for the 170-795 nm spectral region

Improvement of Stratospheric Aerosol Extinction Retrieval from OMPS/LP Using a New Aerosol Model

The Ozone Mapping and Profiler Suite Limb Profiler (OMPS/LP) has been flying on the Suomi National Polar-orbiting Partnership (S-NPP) satellite since October 2011. It is designed to produce ozone and aerosol vertical profiles at 2km vertical resolution over the entire sunlit globe. Aerosol extinction profiles are computed with Mie theory using radiances measured at 675nm. The operational Version 1.0 (V1.0) aerosol extinction retrieval algorithm assumes a bimodal lognormal aerosol size distribution (ASD) whose parameters were derived by combining an in situ measurement of aerosol microphysics with the Stratospheric Aerosol and Gas Experiment (SAGE II) aerosol extinction climatology. Internal analysis indicates that this bimodal lognormal ASD does not sufficiently explain the spectral dependence of LP-measured radiances. In this paper we describe the derivation of an improved aerosol size distribution, designated Version 1.5 (V1.5), for the LP retrieval algorithm. The new ASD uses a gamma function distribution that is derived from Community Aerosol and Radiation Model for Atmospheres (CARMA)-calculated results. A cumulative distribution fit derived from the gamma function ASD gives better agreement with CARMA results at small particle radii than bimodal or unimodal functions. The new ASD also explains the spectral dependence of LP-measured radiances better than the V1.0 ASD. We find that the impact of our choice of ASD on the retrieved extinctions varies strongly with the underlying reflectivity of the scene. Initial comparisons with collocated extinction profiles retrieved at 676nm from the SAGE III instrument on the International Space Station (ISS) show a significant improvement in agreement for the LP V1.5 retrievals. Zonal mean extinction profiles agree to within 10% between 19 and 29km, and regression fits of collocated samples show improved correlation and reduced scatter compared to the V1.0 product. This improved agreement will motivate development of more sophisticated ASDs from CARMA results that incorporate latitude, altitude and seasonal variations in aerosol properties

How Does the Sun's Spectrum Vary?

Recent observations made by the Spectral Irradiance Monitor (SIM) on the Solar Radiation and Climate Experiment (SORCE) spacecraft suggest that the Sun's visible and infrared spectral irradiance increased from 2004 to 2008, even as the total solar irradiance measured simultaneously by SORCE's Total Irradiance Monitor (TIM) decreased. As well, solar ultraviolet (UV) irradiance decreased 3 to 10 times more than expected from prior observations and model calculations of the known effects of sunspot and facular solar features. Analysis of the SIM spectral irradiance observations during the solar minimum epoch of 2008, when solar activity was essentially invariant, exposes trends in the SIM observations relative to both total solar irradiance and solar activity that are unlikely solar in origin. We suggest that the SIM's radically different solar variability characterization is a consequence of undetected instrument sensitivity drifts, not true solar spectrum changes. It is thus doubtful that simulations of climate and atmospheric change using SIM measurements are indicative of real behavior in the Earth's climate and atmosphere

Long-term variation of Saturn H2 emission

The goal of this research effort was to analyze the long-term IUE database of Saturn images for the possible presence of diffuse H2 emissions, using techniques originally developed for analysis of Jupiter images. The poor S/N ratio in many of the Saturn images proved to be a significant limitation to the possible detection of H2 emission. The creation of a satisfactory background atmosphere model was also limited by difficulties in reproducing the observed C2H2 band structure at long wavelengths. The results currently available suggest that diffuse H2 emission is present on Saturn on some occasions. However, the IUE data are not able to indicate whether H2 emission is present at all times with a magnitude proportional to solar activity, as was shown for Jupiter

Solar UV Variations During the Decline of Cycle 23

Characterization of temporal and spectral variations in solar ultraviolet irradiance over a solar cycle is essential for understanding the forcing of Earth's atmosphere and climate. Satellite measurements of solar UV variability for solar cycles 21, 22, and 23 show consistent solar cycle irradiance changes at key wavelengths (e.g. 205 nm, 250 nm) within instrumental uncertainties. All historical data sets also show the same relative spectral dependence for both short-term (rotational) and long-term (solar cycle) variations. Empirical solar irradiance models also produce long-term solar UV variations that agree well with observational data. Recent UV irradiance data from the Solar Radiation and Climate Experiment (SORCE) Spectral Irradiance Monitor (SIM) and Solar Stellar Irradiance Comparison Experiment (SOLSTICE) instruments covering the declining phase of Cycle 23 present a different picture oflong-term solar variations from previous results. Time series of SIM and SOLSTICE spectral irradiance data between 2003 and 2007 show solar variations that greatly exceed both previous measurements and predicted irradiance changes over this period, and the spectral dependence of the SIM and SOLSTICE variations during these years do not show features expected from solar physics theory. The use of SORCE irradiance variations in atmospheric models yields substantially different middle atmosphere ozone responses in both magnitude and vertical structure. However, short-term solar variability derived from SIM and SOLSTICE UV irradiance data is consistent with concurrent solar UV measurements from other instruments, as well as previous results, suggesting no change in solar physics. Our analysis of short-term solar variability is much less sensitive to residual instrument response changes than the observations of long-term variations. The SORCE long-term UV results can be explained by under-correction of instrument response changes during the first few years of measurements, rather than requiring an unexpected change in the physical behavior of the Sun

Identification of Solar Cycle 23 Minimum from Solar UV Measurements: NOAA-9 and NOAA-11 SBUV/2, UARS SUSIM, UARS Solstice

The purpose of this report is to present results from the study of solar cycles from solar UV measurements from March 1985 to May 1997. The study determined solar minimum date from daily spectral irradiance data sensitive to noise and the means through which long-term calibration was obtained. In this study magnesium II time series was determined from NOAA-9, and UARS (Upper Atmosphere Research Satellite) SUMIM and SOLSTICE satellites

SBUV/2 Long-Term Measurements of Solar Spectral Variability

The NOAA-11 SBUV/2 spectral solar data have been corrected for long-term instrument changes to produce a 5.5 year data record during solar cycle 22 (December 1988 - October 1994). Residual drifts in the data at long wavelengths are +/- 1% or less. At 200-205 nm, where solar variations drive stratospheric photochemistry, these data indicate long-term solar changes of 5-7% from the maximum of Cycle 22 in April 1991 through the end of the NOAA-11 data record. Comparisons of NOAA-11 data with UARS SUSIM and SOLSTICE for the period October 1991 - October 1994, when all 3 instruments were operating simultaneously, show that the observed long-term variations in 200-205 nm irradiance agree to within 2%. This result is consistent with predictions from the Mg-2 proxy index. The SBUV/2 instruments represent a valuable resource for long-term solar UV activity studies because of their overlapping data records. In addition to the NOAA-11 data presented here, the NOAA-9 SBUV/2 instrument began taking data in March 1985 and is still operating, providing a complete record of Cycle 22 behavior from a single instrument. Three additional SBUV/2 instruments are scheduled to be launched between 1997 and 2003, which should permit full coverage of solar cycle 23

Changes in photochemically significant solar UV spectral irradiance as estimated by the composite Mg II index and scale factors

Quantitative assessment of the impact of solar ultraviolet irradiance variations on stratospheric ozone abundances currently requires the use of proxy indicators. The Mg II core-to-wing index has been developed as an indicator of solar UV activity between 175-400 nm that is independent of most instrument artifacts, and measures solar variability on both rotational and solar cycle time scales. Linear regression fits have been used to merge the individual Mg II index data sets from the Nimbus-7, NOAA-9, and NOAA-11 instruments onto a single reference scale. The change in 27-dayrunning average of the composite Mg II index from solar maximum to solar minimum is approximately 8 percent for solar cycle 21, and approximately 9 percent for solar cycle 22 through January 1992. Scaling factors based on the short-term variations in the Mg II index and solar irradiance data sets have been developed to estimate solar variability at mid-UV and near-UV wavelengths. Near 205 nm, where solar irradiance variations are important for stratospheric photo-chemistry and dynamics, the estimated change in irradiance during solar cycle 22 is approximately 10 percent using the composite Mg II index and scale factors

Influence of Short-Term Solar UV Variability on the Determination of Solar Cycle Minimum

Smoothing solar UV data on rotational timescale (approx. 27 days) improves identification of solar minimum. Smoothing intervals which are not multiples of rotational period (e.g. 35 days) can leave measurable residual signal. No evidence found for periodic behavior on intermediate (50-250 days) time scales during Cycle 22, based on data from three solar UV instruments