Modelling radar-rainfall estimation uncertainties using elliptical and Archimedean copulas with different marginal distributions

Abstract

Given that radar-based rainfall has been broadly applied in hydrological studies, quantitative modelling of its uncertainty is critically important, as the error of input rainfall is the main source of error in hydrological modelling. Using an ensemble of rainfall estimates is an elegant solution to characterize the uncertainty of radar-based rainfall and its spatial and temporal variability. This paper has fully formulated an ensemble generator for radar precipitation estimation based on the copula method. Each ensemble member is a probable realization that represents the unknown true rainfall field based on the distribution of radar rainfall (RR) error and its spatial error structure. An uncertainty model consisting of a deterministic component and a random error factor is presented based on the distribution of gauge rainfall conditioned on the radar rainfall (GR|RR). Two kinds of copulas (elliptical and Archimedean copulas) are introduced to generate random errors, which are imposed by the deterministic component. The elliptical copulas (e.g. Gaussian and t-copula) generate the random errors based on the multivariate distribution, typically of decomposition of the error correlation matrix using the LU decomposition algorithm. The Archimedean copulas (e.g. Clayton and Gumbel) utilize the conditional dependence between different radar pixels to obtain random errors. Based on those, a case application is carried out in the Brue catchment located in southwest England. The results show that the simulated uncertainty bands of rainfall encompass most of the reference raingauge measurements with good agreement between the simulated and observed spatial dependences. This indicates that the proposed scheme is a statistically reliable method in ensemble radar rainfall generation and is a useful tool for describing radar rainfall uncertainty.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi     

Viewing Angle Effect on the Remote Sensing Monitoring of Wheat and Rice Crops

Abstract

Bidirectional reflectance characteristics of a wheat and a rice canopy were studied using radiometric measurements over the two canopies with an Exotech Radiometer Model 100AX. For both rice and wheat, the measurements exhibited significant variations in reflectance amplitude for varying viewing zenith angles and their values decreased from backward to forward scattering direction. Reflectance obtained its maximum value in the backscatter direction for the viewing angle that corresponds approximately to the solar zenith angle at the time of measurements. Canopy background condition (irrigated or non‐irrigated) was an important determining factor of canopy reflectance particularly in the near‐infrared region of the solar spectrum. Furthermore, bidirectional response characteristics of a vegetation canopy were influenced by the amount of vegetation cover.     

Non-standard structure formation scenarios

Observations on galactic scales seem to be in contradiction with recent high resolution N-body simulations. This so-called cold dark matter (CDM) crisis has been addressed in several ways, ranging from a change in fundamental physics by introducing self-interacting cold dark matter particles to a tuning of complex astrophysical processes such as global and/or local feedback. All these efforts attempt to soften density profiles and reduce the abundance of satellites in simulated galaxy halos. In this contribution we are exploring the differences between a Warm Dark Matter model and a CDM model where the power on a certain scale is reduced by introducing a narrow negative feature (`dip'). This dip is placed in a way so as to mimic the loss of power in the WDM model: both models have the same integrated power out to the scale where the power of the Dip model rises to the level of the unperturbed CDM spectrum again. Using N-body simulations we show that that the new Dip model appears to be a viable alternative to WDM while being based on different physics: where WDM requires the introduction of a new particle species the Dip stems from anon-standard inflationary period. If we are looking for an alternative to the currently challenged standard ΛCDM structure formation scenario, neither the ΛWDM nor the new Dip model can be ruled out with respect to the analysis presented in this contribution. They both make very similar predictions and the degeneracy between them can only be broken with observations yet to come. This revised version was published online in August 2006 with corrections to the Cover Date.     

Warm dark matter versus bumpy power spectra

In this paper we explore the differences between a warm dark matter (WDM) model and a cold dark matter (CDM) model where the power on a certain scale is reduced by introducing a narrow negative feature ('dip'). This dip is placed in a way so as to mimic the loss of power in the WDM model: both models have the same integrated power out to the scale where the power of the dip model rises to the level of the unperturbed CDM spectrum again.
Using N -body simulations we show that some of the large-scale clustering patterns of this new model follow more closely the usual CDM scenario while simultaneously suppressing small-scale structures (within galactic haloes) even more efficiently than WDM. The analysis in the paper shows that the new Dip model appears to be a viable alternative to WDM, but it is based on different physics. Where WDM requires the introduction of a new particle species, the Dip model is based on a non-standard inflationary period. If we are looking for an alternative to the currently challenged standard ΛCDM structure formation scenario, neither the ΛWDM nor the new Dip model can be ruled out based on the analysis presented in this paper. They both make very similar predictions and the degeneracy between them can only be broken with observations yet to come.     

A combined experimental study of vivianite and As (V) reactivity in the pH range 2–11

Four different sets of experiments were completed in order to constrain vivianite [Fe₃(PO₄)₂ · 8H₂O] reactivity under conditions pertinent to As(V)-bearing groundwater systems. Firstly, titration experiments were undertaken in the pH range 4-9 to determine the zero point of charge (ZPC) of vivianite; showing that the ZPC lies at a pH of approximately 5.3. Secondly, the steady state dissolution rates of vivianite far from equilibrium were measured in aqueous solutions in the pH range 2–10 at 18.5 ^°C (±3 °C) using a fluidized bed reactor. The rate of vivianite dissolution, R, is given by     

Radon distributions in the Hail Region of Northern Saudi Arabia

Indoor radon measurements were carried out in a total of 420 dwellings and 17 schools in Hail region of Saudi Arabia, using NTDs based radon dosimeters. The duration of the measurements was one year, from April 2008 to April 2009. The indoor radon concentrations varied from 4 to 513 Bq/m³ with an overall average of 45 Bq/m³ for all surveyed dwellings. These passive measurements were confirmed by the active measurements. The anomalous concentrations above 200 Bq/m³ were observed in 13 dwellings, representing 3.1 % of the total surveyed dwellings. In Inbowan village alone, it was found that 7.6 % of the dwellings have indoor radon concentration above 200 Bq/m³. The highest average indoor radon concentration of 64 Bq/m³ was found in Inbowan village while the lowest average of 24 Bq/m³ was found in Majasah village. The city of Hail showed an average indoor radon concentration of 49 Bq/m³. The average indoor radon concentration in one area located at the edge of the Aja Mountain in Hail city was 111 Bq/m³. The elevated indoor radon concentrations in many dwellings in the Hail region, prompted us to measure outdoor ground radon in such locations using gas monitor. It was found that radon concentrations at a depth of 0.5 m varied significantly from place to place ranging from 1.2 to 177 kBq/m³. The outdoor radon concentrations are generally correlated with the indoor radon measurements. Radon exhalations from construction materials and soil samples from the Hail region were also measured. It was found that radon exhalations from soil samples are higher than that of construction materials by a factor of at least 3 and reaching up to 11. These results indicate that soil is the main source of indoor radon. Geological interpretations of the results are also given.     

Optimization of chlorination boosters in drinking water distribution network for Al-Khobar City in Saudi Arabia

Water quality management in distribution networks is directly related to spatial distribution of chlorine boosters and its dosages. Water chlorination is essential to reduce the effects of bacterial and other microbiological contaminants. A higher dosage of chlorine generates harmful by-products in addition to changes in drinking water’s taste and odor. The optimization of chlorine dosage is necessary to decrease the microbial contaminants that affect water quality. Once the chlorine threshold is determined for microbial contaminant, it will help decision makers suggest optimal values. These decisions can rely on the estimated water quality index (WQI). WQI is an index to evaluate water quality and can be linked to adequate residual chlorine with optimal booster dosage, numbers, and locations in water distribution network (WDN). The city of Al-Khobar, Saudi Arabia’s WDN was selected to validate the application of this study. Based on geographic location, the city Al-Khobar water network was divided into five zones. The initial temporal and spatial analysis pointed out poor water quality zones. EPANET, a modeling and simulating software, was applied to evaluate the WQI. Those EPANET results were then integrated with an optimization model. The optimization model suggested new chlorine booster locations to improve water quality in the city of Al-Khobar water distribution network.     

Spatiotemporal trends of temperature extremes in Bangladesh under changing climate using multi-statistical techniques

Theoretical and Applied Climatology - The rise in the frequency and magnitude of extreme temperature phenomena across the globe has led to the recurrent incidence of global climate hazards, which...