Effect of property variation and modelling on convection in a fluid overlying a porous layer

An accurate computational analysis is presented for the onset of thermal convection in a two‐layer system which is comprised of a saturated layer of porous material described by Darcy's law, over which lies a layer of the same saturating fluid. The two‐layer system is heated from below and the upper (fluid) surface is allowed to be fixed or stress free. The onset of convection may have a bi‐modal nature in which convection may be dominated by the porous medium or by the fluid depending on the depths of the relative layers, but this is strongly controlled by material parameters. The effect of variation of relevant fluid and porous material properties is investigated in detail, as is the effect of the interface boundary condition between the fluid and the porous medium. Copyright © 2001 John Wiley & Sons, Ltd.     

High resolution velocity analysis of ocean bottom seismometer data by theτ-p method

A method of high resolution seismic velocity analysis for ocean bottom seismometer (OBS) records is applied to the study of the shallow oceanic crust, especially sedimentary and basement layers. This method is based on the direct-p mapping and the-sum inversion. We use data obtained from a 1989 airgun-OBS experiment in the northern Yamato Basin, Japan Sea and derive P- and S-wave velocity functions that can be compared with the seismic reflection profiles. Using split-spread profile records, we obtain interface dips and true interval velocities from the OBS data. These results show good agreement with the reflection profile records, the acoustic velocities of core samples, and sonic log profiles. We also present a method for estimating errors in the derived velocity functions by calculating covariance of the derived layers' thicknesses. The estimated depth errors are about 150 m at shallow depths, which is close to the seismic wavelength used. The high resolution of this method relies on accurate determination of shot positions by GPS, spatially dense seismic observations, and the use of unsaturated reflected waves arriving after the direct water wave that are observed on low-gain component records.     

An Assessment of Changes in Winter Cold and Warm Spells over Canada

The recent Third Assessment Report (TAR) of the Intergovernmental Panel onClimate Change (IPCC) indicated that observed 20th century changes in severalclimatic extremes are qualitatively consistent with those expected due to increasedgreenhouse gases. However, a lack of adequate data and analyses make conclusiveevidence of changing extremes somewhat difficult, particularly, in a global sense.In Canada, extreme temperature events, especially those during winter, can havemany adverse environmental and economic impacts. In light of the aforementionedIPCC report, the main focus of this analysis is to examine observed trends andvariability in the frequency, duration, and intensity of winter (Jan–Feb–Mar) cold and warm spells over Canada during the second half of the 20th century.Cold spell trends display substantial spatial variability across the country. From1950–1998, western Canada has experienced decreases in the frequency, duration, and intensity of cold spells, while in the east, distinct increases in the frequency and duration have occurred. These increases are likely associated with morefrequent occurrences of the positive phase of the North Atlantic Oscillation (NAO)during the last several decades. With regard to winter warm spells, significantincreases in both the frequency and duration of these episodes were observedacross most of Canada. One exception was found in the extreme northeasternregions, where warm spells are becoming shorter and less frequent. The resultsof this study are discussed within the context of climate warming expectations.     

The distribution of Spearman’s rho trend statistic for persistent hydrologic data

Abstract

Spearman’s rho, a distribution-free statistic, has been suggested in the literature for testing the significance of trend in time series data. Although the use of the test based on Spearman’s rho (also known as the Daniels test) is less widespread than that based on Kendall’s tau (the Mann-Kendall test), the two tests have been shown in the literature to be equivalent for time series with independent observations. The distribution of the Mann-Kendall trend statistic for persistent data has been previously addressed in the literature. In this paper, the distribution of Spearman’s rho as a trend test statistic for persistent data is studied. Following the same procedures used for Kendall’s tau in earlier work, an exact expression for the variance of Spearman’s rho for persistent data with multivariate Gaussian dependence is derived, and a method for calculating the exact full distribution of rho for small sample sizes is also outlined. Approximations for moderate and large sample sizes are also discussed. A case study of testing the significance of trends in a group of world river flow station data using both Kendall’s tau and Spearman’s rho is presented. Both the theoretical results and those of the case study confirm the equivalence of trend testing based on Spearman’s rho and Kendall’s tau for persistent hydrologic data.

Editor Z. W. Kundzewicz; Associate editor S. Grimaldi     

The distribution of Kendall's tau for testing the significance of cross-correlation in persistent data

Abstract

Kendall's tau (τ) has been widely used as a distribution-free measure of cross-correlation between two variables. It has been previously shown that persistence in the two involved variables results in the inflation of the variance of τ. In this paper, the full null distribution of Kendall's τ for persistent data with multivariate Gaussian dependence is derived, and an approximation to the full distribution is proposed. The effect of the deviation from the multivariate Gaussian dependence model on the distribution of τ is also investigated. As a demonstration, the temporal consistency and field significance of the cross-correlation between the North Hemisphere (NH) temperature time series in the period 1850–1995 and a set of 784 NH tree-ring width (TRW) proxies in addition to 105 NH tree-ring maximum latewood density (MXD) proxies are studied. When persistence is ignored, the original Mann-Kendall test gives temporally inconsistent results between the early half (1850–1922) and the late half (1923–1995) of the record. These temporal inconsistencies are largely eliminated when persistence is accounted for, indicating the spuriousness of a large portion of the identified cross-correlations. Furthermore, the use of the modified test in combination with a field significance test that is robust to spatial correlation indicates the absence of field significant cross-correlation in both halves of the record. These results have serious implications for the use of tree-ring data as temperature proxies, and emphasize the importance of utilizing the correct distribution of Kendall's τ in order to avoid the overestimation of the significance of cross-correlation between data that exhibit significant persistence.

Citation Hamed, K. H. (2011) The distribution of Kendall's tau for testing the significance of cross-correlation in persistent data. Hydrol. Sci. J. 56(5), 841–853.     

Analysis of groundwater level trend in Jakham River Basin of Southern Rajasthan

Groundwater accounts for about half of the water use for irrigation in India.The fluctuation pattern of the groundwater level is examined by observing rainfall replenishment and monitoring wells.The southern part of Rajasthan has experienced abrupt changes in rainfall and has been highly dependent on groundwater over decades.This study presents the impact of over-dependence on groundwater usage for irrigation and other purposes,spatially and temporally.Hence,the objective of this study is to examine the groundwater level trend by using statistical analysis and geospatial technique.Rainfall factor was also studied in groundwater level fluctuation during 2009-2019.To analyze the influence of each well during recharge or withdrawal of groundwater,thiessien polygonswere generated from them.In the Jakham River basin,75 wells have been identified for water level trend study using the Mann-Kendall statistical test.The statistics of trend analysis show that 15%wells are experiencing water level decline in pre-monsoon,while very low percentage of wells have such trend during post-monsoon season.The average rate of water level decline is 0.245 m/a in pre-monsoon and 0.05 m/a in post-monsoon.The aquifer recharge potential is also decreasing by year.it is expected that such type of studies will help the policy makers to adopt advanced management practices to ensure sustainable groundwater resource management.     

A dependence modelling study of extreme rainfall in Madeira Island

The dependence between variables plays a central role in multivariate extremes. In this paper, spatial dependence of Madeira Island's rainfall data is addressed within an extreme value copula approach through an analysis of maximum annual data. The impact of altitude, slope orientation, distance between rain gauge stations and distance from the stations to the sea are investigated for two different periods of time. The results obtained highlight the influence of the island's complex topography on the spatial distribution of extreme rainfall in Madeira Island.     

Analyzing reproduction of correlations in Monte Carlo simulations: application to mine project valuation

Monte Carlo (MC) simulations are extensively used to assess risk in mining ventures; however, the correlation between the inputs used to build the models is often overlooked. We observed how value-at-risk (VaR) of a mining venture was affected by running MC simulations, using two different input correlation methods: Spearman's rank correlation and copulas using Kendall's tau. The goal was to compare different correlation approaches on risk analysis associated with uncertain parameters of mining ventures and uncover which one would yield the most accurate result. Three case studies were carried out to compare correlation structures. Modelling the input variable correlations was better achieved using copulas since they were able to capture a wider range of correlations that did not make any linearity assumptions. In the case study based on MC simulations, the impact of the input correlation choice on the VaR was rather severe with an approximate 9% difference between the results obtained with Spearman's correlations and the Normal copula correlations.