Simulating rainfall time-series: how to account for statistical variability at multiple scales?

Daily rainfall is a complex signal exhibiting alternation of dry and wet states, seasonal fluctuations and an irregular behavior at multiple scales that cannot be preserved by stationary stochastic simulation models. In this paper, we try to investigate some of the strategies devoted to preserve these features by comparing two recent algorithms for stochastic rainfall simulation: the first one is the modified Markov model, belonging to the family of Markov-chain based techniques, which introduces non-stationarity in the chain parameters to preserve the long-term behavior of rainfall. The second technique is direct sampling, based on multiple-point statistics, which aims at simulating a complex statistical structure by reproducing the same data patterns found in a training data set. The two techniques are compared by first simulating a synthetic daily rainfall time-series showing a highly irregular alternation of two regimes and then a real rainfall data set. This comparison allows analyzing the efficiency of different elements characterizing the two techniques, such as the application of a variable time dependence, the adaptive kernel smoothing or the use of low-frequency rainfall covariates. The results suggest, under different data availability scenarios, which of these elements are more appropriate to represent the rainfall amount probability distribution at different scales, the annual seasonality, the dry-wet temporal pattern, and the persistence of the rainfall events.     

Deformational and crystallization history of the Precambrian rocks in north-central Aravalli Mountain,Rajasthan, India

Large-scale structures, textures and mineral assemblages in the Precambrian rocks of the Banded Gneissic Complex and the overlying Delhi Group in north-central Aravalli Mountain reveal a complex deformational-crystallization history. In the basement Gneissic Complex at least three deformational events, D₀, D₁ and D₂, and two separate episodes of metamorphism, M₁ and M₂, are recognized. The supracrustal Delhi Rocks display only two phases of deformation, D₁ and D₂, associated with a single protracted period of metamorphism, M₂.The first phase of deformation (D₁) of the Delhi orogeny (1650-900 m.y.) produced large isoclinal folds that are overturned towards the southeast and have gentle plunges in NE and SW directions. The second phase of deformation (D₂) gave rise to tight open folds on the limbs and axial-plane surfaces of the D₁ folds. These folds generally plunge towards the N and NNW at 30°–80°. In the Basement Complex one more deformation (D₀) of the Pre-Delhi orogeny (> 2000 m.y.) is recorded by the presence of reclined and recumbent folds with W to WNW trending fold axes. The D₀ folds were superimposed by D₁ and D₂ folds during the Delhi orogeny.The three deformational events have been correlated with the crystallization periods of minerals in the rocks and a setting in time is established for this part of the Aravalli range.     

A geospatial analysis of Samudra Tapu and Gepang Gath glacial lakes in the Chandra Basin,Western Himalaya

Geospatial studies carried out in two major proglacial lakes of Samudra Tapu and Gepang Gath (Chandra Basin, Western Himalaya) showed substantial expansion in their area and volume over the last four decades (1971–2014). The linear and areal expansions for the lakes Samudra Tapu and Gepang Gath were 1889, 1509 m and 1, 0.6 km², respectively. The results show that increased melting of the feeder glaciers over this period is major contributor to expand the volumes approximately 20 times of both the lakes Samudra Tapu and Gepang Gath. This expansion of lakes volume of Samudra Tapu and Gepang Gath from 3.4 × 10⁶ to 67.7 × 10⁶ and 1.5 × 10⁶ to 27.5 × 10⁶ m³, respectively, is quite significance in terms of hazards generated from glacial lake outburst floods (GLOF). This kind of climate change induced increase in the rate of glacial melting is a cause of concern, as the Himalaya Mountains may turn out to be vulnerable to natural hazards like GLOF.     

Reflection and transmission ofSH waves in an initially stressed medium consisting of a sandy layer lying over a fluid-saturated porous solid

Biot's theory is employed to study the reflection and transmission ofSH waves in a sandy layer lying over a fluid-saturated porous solid half-space. The entire medium is considered under constant initial stress. Effects of sandiness, initial stress, anelasticity and viscosity of the interstitial fluid on the partitioning of energy are studied. In the presence of initial stress the incident wave starts attenuating when incider beyond a certain angle (depending upon the amount of initial stress), even if the medium is perfectly clastic. Anelasticity of the solid layer results in the dissipation of energy during transmission. The direction of attenuation vector of incident wave affects the dissipation energy to a large extent. Effect on partitioning of energy reverse at incidence after the critical angle. A complete account of energy returmed back to the underlying half-space and that which is dissipated in the overlying layer has been discussed analytically as well as numerically.     

Drought parameters in relation to truncation levels

Drought parameters, namely the longest duration, largest severity and the intensity have been calculated in relation to the truncation levels ranging from 0 to −0\5 in the standardized domain for the normal, gamma and log‐normal probability distribution functions (PDFs) of the drought variables. The drought variables taken in the investigation are the annual rainfall and runoff time‐series evolving randomly and obeying the Markovian dependence. The analysis showed that the assumption of independence of the drought duration and intensity works well in deriving the expression for drought severity at various truncation levels. An estimate of drought intensity has been realized from the concept of the truncated normal distribution of the standardized form of the time‐series of drought variables in the normalized domain. Furthermore the non‐normality and the dependence in the time‐series have a significant effect on the drought parameters at the truncation levels under consideration. Copyright © 2000 John Wiley & Sons, Ltd.     

Dissociation constants of protonated cysteine species in seawater media

The dissociation constants (pK₁, pK₂ and pK₃) for cysteine have been measured in seawater as a function of temperature (5 to 45 °C) and salinity (S = 5 to 35). The seawater values were lower than the values in NaCl at the same ionic strength. In an attempt to understand these differences, we have made measurements of the constants in Na–Mg–Cl solutions at 25 °C. The measured values have been compared to those calculated from the Pitzer ionic interaction model. The lower values of pK₃ in the Na–Mg–Cl solutions have been attributed to the formation of Mg²⁺ complexes with Cys²⁻ anions

Mg²⁺ + Cys²⁻ = MgCys

The stability constants have been fitted to

after corrections are made for the interaction of Mg²⁺ with H⁺.The pK₁ seawater measurements indicate that H₃Cys⁺ interacts with SO₄²⁻. The Pitzer parameters β⁰(H₃CysSO₄), β¹(H₃CysSO₄) and C(H₃CysSO₄) have been determined for this interaction. The formation of CaCys as well as MgCys are needed to account for the values of pK₂ and pK₃ in seawater.The consideration of the formation of MgCys and CaCys in seawater yields model calculated values of pK₁, pK₂ and pK₃ that agree with the measured values to within the experimental error of the measurements. This study shows that it is important to consider all of the ionic interactions in natural waters when examining the dissociation of organic acids.     

Trend analysis of rainfall time series for Sindh river basin in India

The main goal of this paper is to estimate a set of optimal seasonal, daily, and hourly values of atmospheric turbidity and surface radiative parameters Ångström’s turbidity coefficient (β), Ångström’s wavelength exponent (α), aerosol single scattering albedo (ω_o), forward scatterance (F_c) and average surface albedo (ρ_g), using the Brute Force multidimensional minimization method to minimize the difference between measured and simulated solar irradiance components, expressed as cost functions. In order to simulate the components of short-wave solar irradiance (direct, diffuse and global) for clear sky conditions, incidents on a horizontal surface in the Metropolitan Area of Rio de Janeiro (MARJ), Brazil (22° 51′ 27″ S, 43° 13′ 58″ W), we use two parameterized broadband solar irradiance models, called CPCR2 and Iqbal C, based on synoptic information. The meteorological variables such as precipitable water (u_w) and ozone concentration (u_o) required by the broadband solar models were obtained from moderate-resolution imaging spectroradiometer (MODIS) sensor on Terra and Aqua NASA platforms. For the implementation and validation processes, we use global and diffuse solar irradiance data measured by the radiometric platform of LabMiM, located in the north area of the MARJ. The data were measured between the years 2010 and 2012 at 1-min intervals. The performance of solar irradiance models using optimal parameters was evaluated with several quantitative statistical indicators and a subset of measured solar irradiance data. Some daily results for Ångström’s wavelength exponent α were compared with Ångström’s parameter (440–870 nm) values obtained by aerosol robotic network (AERONET) for 11 days, showing an acceptable level of agreement. Results for Ångström’s turbidity coefficient β, associated with the amount of aerosols in the atmosphere, show a seasonal pattern according with increased precipitation during summer months (December–February) in the MARJ.