An alternative method for non-negative estimation of variance components

A typical problem of estimation principles of variance and covariance components is that they do not produce positive variances in general. This caveat is due, in particular, to a variety of reasons: (1) a badly chosen set of initial variance components, namely initial value problem (IVP), (2) low redundancy in functional model, (3) an improper stochastic model, and (4) data’s possibility of containing outliers. Accordingly, a lot of effort has been made in order to design non-negative estimates of variance components. However, the desires on non-negative and unbiased estimation can seldom be met simultaneously. Likewise, in order to search for a practical non-negative estimator, one has to give up the condition on unbiasedness, which implies that the estimator will be biased. On the other hand, unlike the variance components, the covariance components can be negative, so the methods for obtaining non-negative estimates of variance components are not applicable. This study presents an alternative method to non-negative estimation of variance components such that non-negativity of the variance components is automatically supported. The idea is based upon the use of the functions whose range is the set of all positive real numbers, namely positive-valued functions (PVFs), for unknown variance components in stochastic model instead of using variance components themselves. Using the PVF could eliminate the effect of IVP on the estimation process. This concept is reparameterized on the restricted maximum likelihood with no effect on the unbiasedness of the scheme. The numerical results show the successful estimation of non-negativity estimation of variance components (as positive values) as well as covariance components (as negative or positive values).     

Surface deformation analysis of dense GPS networks based on intrinsic geometry: deterministic and stochastic aspects

In this contribution, the regularized Earth’s surface is considered as a graded 2D surface, namely a curved surface, embedded in a Euclidean space . Thus, the deformation of the surface could be completely specified by the change of the metric and curvature tensors, namely strain tensor and tensor of change of curvature (TCC). The curvature tensor, however, is responsible for the detection of vertical displacements on the surface. Dealing with eigenspace components, e.g., principal components and principal directions of 2D symmetric random tensors of second order is of central importance in this study. Namely, we introduce an eigenspace analysis or a principal component analysis of strain tensor and TCC. However, due to the intricate relations between elements of tensors on one side and eigenspace components on other side, we will convert these relations to simple equations, by simultaneous diagonalization. This will provide simple synthesis equations of eigenspace components (e.g., applicable in stochastic aspects). The last part of this research is devoted to stochastic aspects of deformation analysis. In the presence of errors in measuring a random displacement field (under the normal distribution assumption of displacement field), the stochastic behaviors of eigenspace components of strain tensor and TCC are discussed. It is applied by a numerical example with the crustal deformation field, through the Pacific Northwest Geodetic Array permanent solutions in period January 1999 to January 2004, in Cascadia Subduction Zone. Due to the earthquake which occurred on 28 February 2001 in Puget Sound (M _w > 6.8), we performed computations in two steps: the coseismic effect and the postseismic effect of this event. A comparison of patterns of eigenspace components of deformation tensors (corresponding the seismic events) reflects that: among the estimated eigenspace components, near the earthquake region, the eigenvalues have significant variations, but eigendirections have insignificant variations.     

The study of environmental effects of chemical fertilizers and domestic sewage on water quality of Taft region, Central Iran

One of the important indicators to show the quality of water for drinking and irrigation is nitrate values in water and soil. Nitrate enters surface water and groundwater through degradation and decomposition of human and animal wastes, industrial productions, and agricultural runoff. The present paper focuses on the concentration of nitrite (NO₂ ^?1) and nitrate (NO₃ ^?1) of the groundwater in Taft region, Central Iran. Sixty-one samples of the region’s aqueducts, wells, and springs were collected in September 2008 and May 2009 and analyzed by ICP-MS method. However, distribution maps of nitrate and nitrite and their frequency diagram in the pertinent samples have been generated. Then, they were compared to the US Environmental Protection Agency (EPA) and WHO international standards. The mean of nitrate content measured in the samples was 18.52 mg/l, maximum was 115 mg/l which is higher than the EPA standard (i.e., 10 mg/l), and the mean of nitrite content was about 0.06 mg/l. According to the distribution maps, concentration of these anions is high in the downstream of settlements and farmlands of Taft region. With respect to the penetration of agricultural wastes, flooding irrigation, thin layer of alluvium, sandy texture, and the amount of fertilizer consumed in the region, and also absence of any natural source for these anions and absence of the major industrial activities in the region to produce sewage, it seems that nitrate and nitrite originated from the agricultural sewage and human waste. As the content of nitrate in drinking water in the region is higher than WHO and EPA standards, so there is the risk of methemoglobinemia disease in infants. In addition, nitrate content within the stomach and lungs interacts with amine and nitrosamines are made up which are potentially the initial cause of all cancers in human.     

Active and online prediction of BOD5 in river systems using reduced-order support vector machine

Due to the limitations of hardware sensors for online measurement of the water quality parameters such as 5-day biochemical oxygen demand (BOD₅), the recent research efforts have focused on the software sensors for the rapid prediction of such parameters. The main objective in this research is to develop a reduced-order support vector machine (ROSVM) model based on the proper orthogonal decomposition to solve the time-consuming problem of the BOD₅ measurements. The performance of the newly developed methodology is tested on the Sefidrood River Basin, Iran. Subsequently, the predicted values of BOD₅, resulted from the selected developed ROSVM model, are compared with the results of support vector machine (SVM) model. According to the obtained results, selected ROSVM model seems to be more accurate, showing Person correlation coefficient (R) and root mean square error (RMSE) equal to 0.97 and 6.94, respectively. Further, the investigations based on developed discrepancy ratio (DDR) statistic for selection of the optimum model between the best accurate ROSVM and SVM models are carried out. Results of DDR statistic indicated superior performance of the selected ROSVM model comparing to the SVM technique for online prediction of BOD₅ in the Sefidrood River.     

Stochastic modeling of Iranian earthquakes and estimation of ground motion for future earthquakes in Greater Tehran

Strong-motion data from eight significant well-documented earthquakes in Iran have been simulated using a stochastic modeling technique for finite faults proposed by Beresnev and Atkinson [Bull Seismol Soc Am 87 (1997) 67–84; Seism Res Lett 69 (1998) 27–32]. The database consists of 61 three-component records from eight earthquakes of magnitude ranging from M 6.3 to M 7.4, recorded at hypocentral distances up to 200 km. The model predictions are in good agreement with available Iranian strong-motion data as evidenced by near-zero average of differences between logarithms of the observed and predicted values for all frequencies. The strength factor, sfact, a quantity that controls the high-frequency radiation from the source is determined, on an event-by-event basis, by fitting simulated to observed response spectra.     

Multivariate statistical analysis of deformation tensors: independent vs. correlated tensor observations

In the presence of errors in measuring a random displacement field (under the normal distribution assumption of displacement field), stochastic behaviors of principal components of deformation tensors (strain tensor and tensor of change of curvature (TCC)), based on the intrinsic assumption of geometrical modeling of surface deformation analysis, are discussed. We divided the contents into two parts: In the first, we considered independent random vectors of repeated tensor measurements. In the second step, we considered correlations among repeated measurements. Then, covariance components between tensor elements by Helmert estimator, based on prior information of variance components, are estimated. As a case study, both assumptions are applied to the estimation of principal components of deformation rate tensor observations in Zagros region (Western Iran). The results of numerical analysis showed that greatest shortening is accommodated in oblique orientation (NS) with respect to the Main Recent Fault (MRF), northwest part of North Zagros, Central Iran block and MRF, respectively. Most of the extensions occurred in the east part of the belt. The pattern of eigenspace components of TCC shows highest positive values across the NW region, nearly in orthogonal direction to the MRF and Main Zagros Fault (MZF). The pattern has insignificant values in the Central Zagros. It takes the significant negative values across the SW part, especially along the SPF and Persian Gulf shore. The effect of non-independent observations on the estimation of eigenspace components of deformation tensors (strain tensor and TCC) shows that the estimation of covariance components has influence on the confidence intervals of eigenspace components, especially in seismically active regions of the belt (along the Persian Gulf shore, NW of the belt and region between the Central Iran block and MRF). The results demonstrate the importance of considering the correlation structure among the observations on statistical behavior of principal components of deformation tensors in seismically active regions.     

Regional analysis of streamflow drought: a case study in southwestern Iran

Droughts are complex natural hazards that, to a varying degree, affect some parts of the world every year. The range of drought impacts is related to drought occurring in different stages of the hydrological cycle and usually different types of droughts such as meteorological, agricultural, hydrological, and socio-economical are the most distinguished types. Hydrological drought includes streamflow and groundwater droughts. In this paper, streamflow drought was analyzed using the method of truncation level (at 70 % level) by daily discharges at 54 stations in southwestern Iran. Frequency analysis was carried out for annual maximum series of drought deficit volume and duration. 35 factors such as physiographic, climatic, geologic and vegetation were studied to carry out the regional analysis. According to conclusions of factor analysis, the six most effective factors include watershed area, the sum rain from December to February, the percentage of area with NDVI <0.1, the percentage of convex area, drainage density and the minimum of watershed elevation, explained 89.2 % of variance. The homogenous regions were determined by cluster analysis and discriminate function analysis. The suitable multivariate regression models were ascertained and evaluated for hydrological drought deficit volume with 2 years return period. The significance level of models was 0.01. The conclusion showed that the watershed area is the most effective factor that has a high correlation with drought deficit volume. Moreover, drought duration was not a suitable index for regional analysis.