A bivariate pareto model for drought

Univariate Pareto distributions have been so widely used in hydrology. It seems however that bivariate or multivariate Pareto distributions have not yet found applications in hydrology, especially with respect to drought. In this note, a drought application is described by assuming a bivariate Pareto model for the joint distribution drought durations and drought severity in the State of Nebraska. Based on this model, exact distributions are derived for the inter arrival time, magnitude and the proportion of droughts. Estimates of 2, 5, 10, 20, 50 and 100 year return periods are derived for the three variables, drought duration, drought severity and the pairwise combinations: (drought duration, drought severity), (inter arrival time of drought, proportion of drought) and (drought duration, drought magnitude). These return period estimates could have an important role in hydrology, for example, with respect to measures of vegetation water stress for plants in water-controlled ecosystems.     

GPS,Galileo, QZSS and IRNSS differential ISBs: estimation and application

Knowledge of inter-system biases (ISBs) is essential to combine observations of multiple global and regional navigation satellite systems (GNSS/RNSS) in an optimal way. Earlier studies based on GPS, Galileo, BDS and QZSS have demonstrated that the performance of multi-GNSS real-time kinematic positioning is improved when the differential ISBs (DISBs) corresponding to signals of different constellations but transmitted at identical frequencies can be calibrated, such that only one common pivot satellite is sufficient for inter-system ambiguity resolution at that particular frequency. Recently, many new GNSS satellites have been launched. At the beginning of 2016, there were 12 Galileo IOV/FOC satellites and 12 GPS Block IIF satellites in orbit, while the Indian Regional Navigation Satellite System (IRNSS) had five satellites launched of which four are operational. More launches are scheduled for the coming years. As a continuation of the earlier studies, we analyze the magnitude and stability of the DISBs corresponding to these new satellites. For IRNSS this article presents for the first time DISBs with respect to the L5/E5a signals of GPS, Galileo and QZSS for a mixed-receiver baseline. It is furthermore demonstrated that single-frequency (L5/E5a) ambiguity resolution is tremendously improved when the multi-GNSS observations are all differenced with respect to a common pivot satellite, compared to classical differencing for which a pivot satellite is selected for each constellation.     

Anisotropy in a natural soft clayey silt

Undisturbed specimens of a soft clayey silt have been taken vertically, horizontally and at 45° to the vertical at the base of a trench and submitted to consolidation and undrained triaxial compression and extension tests in the laboratory. Undrained shear strengths and compressibilities are found to be strongly dependent on sample orientation, but the effective stress strength parameters are shown to be much more influenced by stress path than sample orientation. The pore-pressure response vs axial strain is shown to be unaffected by sample orientation. Most of the anisotropic effects are shown to be eliminated by successively consolidating the specimens under isotropic pressure increments and re-testing in undrained shear. Some of the evidence from the experimental programme indicates that tension resisting bonds act between the grains of the soil specimens.     

Letter to the Editor

Many shortcomings in the recent paper by Muraleedharan, Rao, Kurup, Unnikrishnan Nair and Sinha [Coastal Engineering, 2007, in press] are pointed out.     

Ratio of generalized random variables with application

The generalized Pareto distribution is one of the popular models in the environmental sciences. Scientists in these areas are often interested in comparing the values of an environmental variable under two different conditions, locations, etc. This would require the study of the ratio X/(X+Y) where X and Y are independent generalized Pareto random variables. In this note, the exact distribution of X/(X+Y) is derived, which turns out to involve the Gauss hypergeometric function. An application of this result is provided to assess the relative extremity of rainfall for 14 locations in Florida. Some computer programs for use in the applications are also provided.     

Extremes of Daily Rainfall in West Central Florida

Annual maxima of daily rainfall data dating from 1901 to 2003 are modeled for fourteen locations in West Central Florida. The generalized extreme value (GEV) distribution is fitted to data from each location. The location parameter of the GEV is formulated as a function of time to adequately describe the extremes of rainfall and to predict their future behavior. We find evidence of non-stationarity in the form of trends for eight of the fourteen locations considered. We quantify the change in extreme rainfall for each location and provide return levels for the years 2010, 2020, 2050 and 2100. We also derive estimates of return levels for daily rainfall and provide a classification of the fourteen locations based on the degree of severity of these estimates. This paper provides the first application of extreme value distributions to rainfall data specifically from Florida.     

Mapping joint hurricane wind and surge hazards for Charleston,South Carolina

Combined effects of hurricane wind and surge can pose significant threats to coastal cities. Although current design codes consider the joint occurrence of wind and surge, information on site-specific joint distributions of hurricane wind and surge along the US Coast is still sparse and limited. In this study, joint hazard maps for combined hurricane wind and surge for Charleston, South Carolina (SC), were developed. A stochastic Markov chain hurricane simulation program was utilized to generate 50,000 years of full-track hurricane events. The surface wind speeds and surge heights from individual hurricanes were computed using the Georgiou’s wind field model and the Sea, Lake and Overland Surges from Hurricanes (SLOSH) model, respectively. To validate the accuracy of the SLOSH model, the simulated surge levels were compared to the surge levels calculated by another state-of-the-art storm surge model, ADCIRC (Advanced Circulation), and the actual observed water elevations from historical hurricane events. Good agreements were found between the simulated and observed water elevations. The model surface wind speeds were also compared with the design wind speeds in ASCE 7-10 and were found to agree well with the design values. Using the peak wind speeds and maximum surge heights, the joint hazard surfaces and the joint hazard maps for Charleston, SC, were developed. As part of this study, an interactive computer program, which can be used to obtain the joint wind speed and surge height distributions for any location in terms of latitude and longitude in Charleston area, was created. These joint hazard surfaces and hazard maps can be used in a multi-hazard design or risk assessment framework to consider the combined effects of hurricane wind and surge.     

Fully coupled finite element model for dynamics of partially saturated soils

Understanding the response of partially saturated earth structures under various static and dynamic loads is important for the design and construction of economical and safe geotechnical engineering structures. In this study, the numerical approach is used to understand the dynamics of partially saturated soils. The mathematical equations governing the dynamics of partially saturated soils are derived based on the theory of mixtures and implemented within a finite element framework. The stress–strain behavior of the soil is represented by an elasto-plastic constitutive model for unsaturated soil based on bounding surface concept and the moisture-suction behavior is modeled using van Genuchten model. Fully coupled finite element simulations are performed to study the response of partially saturated soil embankment under earthquake loading and validated with centrifuge test results available in the literature. The predicted displacement responses are in good agreement with the measured responses. The pore water pressure, pore air pressure, matric suction, the degree of saturation in various elements and the response of the embankment under different initial moisture content are also discussed.     

A truncated inverted beta distribution with application to air pollution data

The inverted beta distributions are popular models for hydrology. However, they suffer from the fact that they do not possess finite moments of all orders. In this note, a truncated version of the inverted beta distribution is introduced, which possesses finite moments of all orders and could therefore be a better model for hydrological data with a finite upper bound. Explicit expressions for the moments of the truncated distribution and its estimation procedure are derived. An application is provided to ozone level data from New York.