The GPS Toolbox

The GPS Toolbox is dedicated to highlighting algorithms utilized by GPS engineers and scientists. If you have an interesting algorithm you would like to share with our readers or if you have a topic you would like to see covered in a future column, contact us at gps-toolbox@ngs.noaa.gov. To comment on the algorithms presented here, or to leave a request for an algorithm you may be looking for, visit our Web site (http://www.ngs.noaa.gov/gps-toolbox). ? 2000 John Wiley & Sons, Inc.     

Determination of failure probabilities of flood defence systems with improved dynamic bounds method

In this paper, we describe the computational framework of a novel method for solving the challenging problem of probabilistic finite elements. The method is called Improved Dynamic Bounds (IDB) and was developed recently to improve the efficiency of the dynamic bounds. The IDB is used in finite element numerical models to calculate time-dependent failure analyses of structures. In applications, the IDB can speed up the overall simulation process by several orders of magnitude. In applications controlled by two influential variables (e.g, two-dimensional problem), the computational efficiency is improved by a factor of 769 according to Rajabalinejad (2009). Applications of IDB indicate the method is most efficient for problems where the number of influential variables are limited. This is often the case for geotechnical and coastal flood defence systems. The IDB method is applied in this paper to the 17th Street Flood Wall, a component of the flood defence system (levee infra-structure) that failed during the Hurricane Katrina, to calculate the failure probability of an I-wall.     

Variation in Coronal Activity from Solar Cycle 24 Minimum to Maximum Using Three-Dimensional Reconstructions of the Coronal Electron Density from STEREO/COR1

Three-dimensional electron density distributions in the solar corona are reconstructed for 100 Carrington rotations (CR 2054?–?2153) during 2007/03?–?2014/08 using the spherically symmetric method from polarized white-light observations with the inner coronagraph (COR1) onboard the twin Solar Terrestrial Relations Observatory (STEREO). These three-dimensional electron density distributions are validated by comparison with similar density models derived using other methods such as tomography and a magnetohydrodynamics (MHD) model as well as using data from the Solar and Heliospheric Observatory (SOHO)/Large Angle and Spectrometric Coronagraph (LASCO)-C2. Uncertainties in the estimated total mass of the global corona are analyzed based on differences between the density distributions for COR1-A and -B. Long-term variations of coronal activity in terms of the global and hemispheric average electron densities (equivalent to the total coronal mass) reveal a hemispheric asymmetry during the rising phase of Solar Cycle 24, with the northern hemisphere leading the southern hemisphere by a phase shift of 7?–?9 months. Using 14 CR (\(\approx13\)-month) running averages, the amplitudes of the variation in average electron density between Cycle 24 maximum and Cycle 23/24 minimum (called the modulation factors) are found to be in the range of 1.6?–?4.3. These modulation factors are latitudinally dependent, being largest in polar regions and smallest in the equatorial region. These modulation factors also show a hemispheric asymmetry: they are somewhat larger in the southern hemisphere. The wavelet analysis shows that the short-term quasi-periodic oscillations during the rising and maximum phases of Cycle 24 have a dominant period of 7?–?8 months. In addition, it is found that the radial distribution of the mean electron density for streamers at Cycle 24 maximum is only slightly larger (by \(\approx30\%\)) than at cycle minimum.     

Evidence for the occurrence of hydrogeochemical processes in the groundwater of Khoy plain,northwestern Iran,using ionic ratios and geochemical modeling

Rapid population growth, industrialization, and agricultural expansion in the Khoy area (northwestern Iran) have led to its dependence on groundwater and degradation of groundwater quality. This study attempts to decipher the major processes and factors that degrade the groundwater quality of the Khoy plain. For this purpose, 54 groundwater samples from unconfined and confined aquifers of the plain were collected in July 2017 and analyzed for major cations and anions (Na, K, Ca, Mg, HCO₃, SO_4, and Cl), minor ions (NO₃ and F), and Al. Magnesium and bicarbonate were identified as the dominant cation and anion, respectively. Several ionic ratios and geochemical modeling using PHREEQC indicated that the most important hydrogeochemical processes to affect groundwater quality in the plain were weathering and dissolution of evaporitic and silicate minerals, mixing, and ion exchange. There were smaller effects from evaporation and anthropogenic factors (e.g., industries). Results showed that the high salinity of the groundwater in the northeast area of the plain was due to the high solubility of the evaporitic minerals, e.g., halite and gypsum. Reverse ion exchange and the contribution of mineral dissolution were more significant than ion exchange in the northeastern part of the plain. Elevated salinity of the groundwater in the southeast was attributed mostly to reverse ion exchange and somewhat to evaporation.     

Past,present and future vegetation-cloud feedbacks in the Amazon Basin

To begin exploring the underlying mechanisms that couple vegetation to cloud formation processes, we derive the lifting condensation level (LCL) to estimate cumulus cloud base height. Using a fully coupled land–ocean–atmosphere general circulation model (HadCM3LC), we investigate Amazonian forest feedbacks on cloud formation over three geological periods; modern-day (a.d. 1970–1990), the last glacial maximum (LGM; 21 kya), and under a future climate scenario (IS92a; a.d. 2070–2090). Results indicate that for both past and future climate scenarios, LCL is higher relative to modern-day. Statistical analyses indicate that the 800 m increase in LCL during the LGM is related primarily to the drier atmosphere promoted by lower tropical sea surface temperatures. In contrast, the predicted 1,000 m increase in LCL in the future scenario is the result of a large increase in surface temperature and reduced vegetation cover.     

Investigation of the evolution of coronal bright points and magnetic field topology

Our investigation has been carried using the instruments onboard the Solar Dynamics Observatory (SDO) providing a high resolution of images (AIA photographs and HMI magnetograms). We have investigated the structure and magnetic evolution of several coronal bright points and small scale N-S polarity magnetic fluxes closely associated with them. We also compare the evolution of the magnetic polarities of elementary isolated sources of positive and negative fluxes (magnetic bipoles) and coronal bright points. Tiny (“elementary”) coronal bright points have been detected. A standard coronal bright point is shown to be a group of “elementary” coronal bright points that flare up sequentially. Our investigation shows that a change in the magnetic fluxes of opposite polarities is observed before the flare of a coronal bright point. We show that not all cases of the formation of coronal bright points are described by the magnetic reconnection model. This result has not been considered previously and has not been pointed out by other authors.     

Martian water vapor: Mars Express PFS/LW observations

We present the seasonal and geographical variations of the martian water vapor monitored from the Planetary Fourier Spectrometer Long Wavelength Channel aboard the Mars Express spacecraft. Our dataset covers one martian year (end of Mars Year 26, Mars Year 27), but the seasonal coverage is far from complete. The seasonal and latitudinal behavior of the water vapor is globally consistent with previous datasets, Viking Orbiter Mars Atmospheric Water Detectors (MAWD) and Mars Global Surveyor Thermal Emission Spectrometer (MGS/TES), and with simultaneous results obtained from other Mars Express instruments, OMEGA and SPICAM. However, our absolute water columns are lower and higher by a factor of 1.5 than the values obtained by TES and SPICAM, respectively. In particular, we retrieve a Northern midsummer maximum of 60 pr-μm, lower than the 100-pr-μm observed by TES. The geographical distribution of water exhibits two local maxima at low latitudes, located over Tharsis and Arabia. Global Climate Model (GCM) simulations suggest that these local enhancements are controlled by atmospheric dynamics. During Northern spring, we observe a bulge of water vapor over the seasonal polar cap edge, consistent with the northward transport of water from the retreating seasonal cap to the permanent polar cap. In terms of vertical distribution, we find that the water volume mixing ratio over the large volcanos remains constant with the surface altitude within a factor of two. However, on the whole dataset we find that the water column, normalized to a fixed pressure, is anti-correlated with the surface pressure, indicating a vertical distribution intermediate between control by atmospheric saturation and confinement to a surface layer. This anti-correlation is not reproduced by GCM simulations of the water cycle, which do not include exchange between atmospheric and subsurface water. This situation suggests a possible role for regolith-atmosphere exchange in the martian water cycle.