The K Method for Estimating Earthquake Activity Parameters and Effect of the Boundary Uncertainty of the Source Region:Discussion on the Seismic Zoning Method

Two aspects of a new method,which can be used for seismic zoning,are introduced in this paper.On the one hand,the approach to estimate b value and annual activity rate proposed by Kijko and Sellevoll needs to use the earthquake catalogue.The existing earthquake catalogue contains both historical and recent instrumental data sets and it is inadequate to use only one part.Combining the large number of historical events with recent complete records and taking the magnitude uncertainty into account,Kijko’s method gives the maximum likelihood estimation of b value and annual activity rate,which might be more realistic.On the other hand,this method considers the source zone boundary uncertainty in seismic hazard analysis,which means the earthquake activity rate across a boundary of a source zone changes smoothly instead of abruptly and avoids too large a gradient in the calculated results.

Spatial distribution of δ2H and δ18O values in the hydrologic cycle of the Nile Basin

Existing δ2H and δ18O values for precipitation and surface water in the Nile Basin were used to analyze precipitation inputs and the influence of evaporation on the isotopic signal of the Nile River and its tributaries. The goal of the data analysis was to better understand basin processes that influence seasonal streamflow for the source waters of the Nile River, because climate and hydrologic models have continued to produce high uncertainty in the prediction of precipitation and streamflow in the Nile Basin. An evaluation of differences in precipitation δ2H and δ18O values through linear regression and distribution analysis indicate variation by region and season in the isotopic signal of precipitation across the Nile Basin. The White Nile Basin receives precipitation with a more depleted isotopic signal compared to the Blue Nile Basin. The hot temperatures of the Sahelian spring produce a greater evaporation signal in the precipitation isotope distribution compared to precipitation in the Sahara/Mediterranean region, which can be influenced by storms moving in from the Mediterranean Sea. The larger evaporative effect is reversed for the two regions in summer because of the cooling of the Sahel from inflow of Indian Ocean monsoon moisture that predominantly influences the climate of the Blue Nile Basin. The regional precipitation isotopic signals convey to each region＇s streamflow, which is further modified by additional evaporation according to the local climate. Isotope ratios for White Nile streamflow are significantly altered by evaporation in the Sudd, but this isotopic signal is minimized for streamflow in the Nile River during the winter, spring and summer seasons because of the flow dominance of the Blue Nile. During fall, the contribution from the White Nile may exceed that of the Blue Nile, and the heavier isotopic signal of the White Nile becomes apparent. The variation in climatic conditions of the Nile River Basin provides a means of identifying mechanistic processes through changes in isotope ratios of hydrogen and oxygen, which have utility for separating precipitation origin and the effect of evaporation during seasonal periods. The existing isotope record for precipitation and streamflow in the Nile Basin can be used to evaluate predicted streamflow in the Nile River from a changing climate that is expected to induce further changes in precipitation patterns across the Nile Basin.

Regional moment-independent sensitivity analysis with its applications in engineering

Traditional Global Sensitivity Analysis（GSA） focuses on ranking inputs according to their contributions to the output uncertainty.However,information about how the specific regions inside an input affect the output is beyond the traditional GSA techniques.To fully address this issue,in this work,two regional moment-independent importance measures,Regional Importance Measure based on Probability Density Function（RIMPDF） and Regional Importance Measure based on Cumulative Distribution Function（RIMCDF）,are introduced to find out the contributions of specific regions of an input to the whole output distribution.The two regional importance measures prove to be reasonable supplements of the traditional GSA techniques.The ideas of RIMPDF and RIMCDF are applied in two engineering examples to demonstrate that the regional moment-independent importance analysis can add more information concerning the contributions of model inputs.

Probability density functions of quantum mechanical observable uncertainties

We study the uncertainties of quantum mechanical observables, quantified by the standard deviation(square root of variance) in Haar-distributed random pure states. We derive analytically the probability density functions(PDFs) of the uncertainties of arbitrary qubit observables.Based on these PDFs, the uncertainty regions of the observables are characterized by the support of the PDFs. The state-independent uncertainty relations are then transformed into the optimization problems over uncertainty regions, which opens a new vista for studying stateindependent uncertainty relations. Our results may be generalized to multiple observable cases in higher dimensional spaces.

Effects of the Physical Process Ensemble Technique on Simulation of Summer Precipitation over China

The effects of the physical process ensemble technique on simulation of summer precipitation over China have been studied by using a p-σregional climate model with 9 vertical levels（pσ-RCM9）.The results show that there are obvious differences among simulations of summer precipitation over China from different individual ensemble members.The simulated precipitation over China is sensitive to different cumulus convection,radiative transfer,and land surface process parameterizations.These differences lead to large uncertainties in the simulation results.The standard deviation of the simulated summer precipitation departure percentage over West China is larger than that over East China,signifying that the simulated precipitation over East China has higher reliability and consistency than that over West China.The Talagr and diagram shows that the ensemble system has reasonable dispersion in the simulated summer mean precipitation over East China.The summer ensemble mean precipitation over East China evaluated by various indices is better than most single simulations.The physical process ensemble technique reduces the uncertainties of the model physics in precipitation and improves the simulation results as a whole.Further, adopting the optimized ensemble mean method can obviously improve the performance of the pσ-RCM9 model in simulation of summer precipitation over East China.