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.     

Influence of surface and vegetation characteristics on C-band radar measurements for soil moisture content

Soil moisture estimation using microwave remote sensing faces challenges of the segregation of influences mainly from roughness and vegetation. Under static surface conditions, it was found that Radarsat C-band SAR shows reasonably good correlation and sensitivity with changing soil moisture. Dynamic surface and vegetation conditions are supposed to result in a substantial reduction in radar sensitivity to soil moisture. A C-band scatterometer system (5.2 GHz) with a multi-polarization and multi-angular configuration was used 12 times to sense the soil moisture over a tall vegetated grass field. A score of vegetation and soil parameters were recorded on every occasion of the experiment. Three radar backscattering models Viz., Integral Equation Model (IEM), an empirical model and a volume scattering model, have been used to predict the backscattering phenomena. The volume scattering model, using the Distorted Born Approximation, is found to predict the backscattering phenomena reasonably well. But the surface scattering models are expectedly found to be inadequate for the purpose. The temporal variation of soil moisture does show good empirical relationship with the observed radar backscattering. But as the vegetation biomass increases, the radar shows higher sensitivity to the vegetation parameters compared to surface characteristics. A sensitivity analysis of the volume scattering model for all the parameters also reveals that the radar is more sensitive to plant parameters under high biomass conditions, particularly vegetation water content, but the sensitivity to surface characteristics, particularly to soil moisture, is also appreciable.     

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.     

Distribution of Indus born mica along Gulf of Kachchh coast: Implications in understanding current dynamics

Indus is one of the major sources of sediments to the Gulf of Kachchh. Yet only its <63 micron fraction is studied in detail with regards to the offshore current dynamics. Hence here we present our study on characteristic signature of the Indus sediment load (i.e. mica minerals) in >63 micron size fraction along the coast of Gulf of Kachchh. The spatial distribution of mica minerals along the Gulf of Kachchh coast was studied which showed in general decreasing trend as we move along the northern and southern coast of the Gulf of Kachchh but, an increase in amount near the southern mouth at Okha. The study shows that the earlier proposed tidal barrier is ineffective in restricting movement of mica across the mouth of the gulf due to its characteristic transport mechanism. Also the presence of mudflats along the gulf of Kachchh coast plays a vital role as sediment receptors in the active sediment transport processes and mica minerals prove to be a promising simple tracer in studying the Indus born sediments in the region.     

Computing the Sensitivity Kernels for 2.5-D Seismic Waveform Inversion in Heterogeneous,Anisotropic Media

2.5-D modeling and inversion techniques are much closer to reality than the simple and traditional 2-D seismic wave modeling and inversion. The sensitivity kernels required in full waveform seismic tomographic inversion are the Fréchet derivatives of the displacement vector with respect to the independent anisotropic model parameters of the subsurface. They give the sensitivity of the seismograms to changes in the model parameters. This paper applies two methods, called ‘the perturbation method’ and ‘the matrix method’, to derive the sensitivity kernels for 2.5-D seismic waveform inversion. We show that the two methods yield the same explicit expressions for the Fréchet derivatives using a constant-block model parameterization, and are available for both the line-source (2-D) and the point-source (2.5-D) cases. The method involves two Green’s function vectors and their gradients, as well as the derivatives of the elastic modulus tensor with respect to the independent model parameters. The two Green’s function vectors are the responses of the displacement vector to the two directed unit vectors located at the source and geophone positions, respectively; they can be generally obtained by numerical methods. The gradients of the Green’s function vectors may be approximated in the same manner as the differential computations in the forward modeling. The derivatives of the elastic modulus tensor with respect to the independent model parameters can be obtained analytically, dependent on the class of medium anisotropy. Explicit expressions are given for two special cases—isotropic and tilted transversely isotropic (TTI) media. Numerical examples are given for the latter case, which involves five independent elastic moduli (or Thomsen parameters) plus one angle defining the symmetry axis.     

Classifying zones of suitability for manual drilling using textural and hydraulic parameters of shallow aquifers: a case study in northwestern Senegal

A method is proposed that uses analysis of borehole stratigraphic logs for the characterization of shallow aquifers and for the assessment of areas suitable for manual drilling. The model is based on available borehole-log parameters: depth to hard rock, depth to water, thickness of laterite and hydraulic transmissivity of the shallow aquifer. The model is applied to a study area in northwestern Senegal. A dataset of boreholes logs has been processed using a software package (TANGAFRIC) developed during the research. After a manual procedure to assign a standard category describing the lithological characteristics, the next step is the automated extraction of different textural parameters and the estimation of hydraulic conductivity using reference values available in the literature. The hydraulic conductivity values estimated from stratigraphic data have been partially validated, by comparing them with measured values from a series of pumping tests carried out in large-diameter wells. The results show that this method is able to produce a reliable interpretation of the shallow hydrogeological context using information generally available in the region. The research contributes to improving the identification of areas where conditions are suitable for manual drilling. This is achieved by applying the described method, based on a structured and semi-quantitative approach, to classify the zones of suitability for given manual drilling techniques using data available in most African countries. Ultimately, this work will support proposed international programs aimed at promoting low-cost water supply in Africa and enhancing access to safe drinking water for the population.     

Space Weather: Physics,Effects and Predictability

The time varying conditions in the near-Earth space environment that may affect space-borne or ground-based technological systems and may endanger human health or life are referred to as space weather. Space weather effects arise from the dynamic and highly variable conditions in the geospace environment starting from explosive events on the Sun (solar flares), Coronal Mass Ejections near the Sun in the interplanetary medium, and various energetic effects in the magnetosphere–ionosphere–atmosphere system. As the utilization of space has become part of our everyday lives, and as our lives have become increasingly dependent on technological systems vulnerable to the space weather influences, the understanding and prediction of hazards posed by these active solar events have grown in importance. In this paper, we review the processes of the Sun–Earth interactions, the dynamic conditions within the magnetosphere, and the predictability of space weather effects on radio waves, satellites and ground-based technological systems today.