Uncertainty in the determination of soil hydraulic parameters and its influence on the performance of two hydrological models of different complexity

Data of soil hydraulic properties forms often a limiting factor in unsaturated zone modelling, especially at the larger scales. Investigations for the hydraulic characterization of soils are time-consuming and costly, and the accuracy of the results obtained by the different methodologies is still debated. However, we may wonder how the uncertainty in soil hydraulic parameters relates to the uncertainty of the selected modelling approach. We performed an intensive monitoring study during the cropping season of a 10 ha maize field in Northern Italy. The data were used to: i) compare different methods for determining soil hydraulic parameters and ii) evaluate the effect of the uncertainty in these parameters on different variables (i.e. evapotranspiration, average water content in the root zone, flux at the bottom boundary of the root zone) simulated by two hydrological models of different complexity: SWAP, a widely used model of soil moisture dynamics in unsaturated soils based on Richards equation, and ALHyMUS, a conceptual model of the same dynamics based on a reservoir cascade scheme. We employed five direct and indirect methods to determine soil hydraulic parameters for each horizon of the experimental profile. Two methods were based on a parameter optimization of: a) laboratory measured retention and hydraulic conductivity data and b) field measured retention and hydraulic conductivity data. The remaining three methods were based on the application of widely used Pedo-Transfer Functions: c) Rawls and Brakensiek, d) HYPRES, and e) ROSETTA. Simulations were performed using meteorological, irrigation and crop data measured at the experimental site during the period June – October 2006. Results showed a wide range of soil hydraulic parameter values generated with the different methods, especially for the saturated hydraulic conductivity Ksat and the shape parameter a of the van Genuchten curve. This is reflected in a variability of the modeling results which is, as expected, different for each model and each variable analysed. The variability of the simulated water content in the root zone and of the bottom flux for different soil hydraulic parameter sets is found to be often larger than the difference between modeling results of the two models using the same soil hydraulic parameter set. Also we found that a good agreement in simulated soil moisture patterns may occur even if evapotranspiration and percolation fluxes are significantly different. Therefore multiple output variables should be considered to test the performances of methods and model

Quantum algorithm for the Boolean hidden shift problem

The hidden shift problem is a natural place to look for new separations between classical and quantum models of computation. One advantage of this problem is its flexibility, since it can be defined for a whole range of functions and a whole range of underlying groups. In a way, this distinguishes it from the hidden subgroup problem where more stringent requirements about the existence of a periodic subgroup have to be made. And yet, the hidden shift problem proves to be rich enough to capture interesting features of problems of algebraic, geometric, and combinatorial flavor. We present a quantum algorithm to identify the hidden shift for any Boolean function. Using Fourier analysis for Boolean functions we relate the time and query complexity of the algorithm to an intrinsic property of the function, namely its minimum influence. We show that for randomly chosen functions the time complexity of the algorithm is polynomial. Based on this we show an average case exponential separation between classical and quantum time complexity. A perhaps interesting aspect of this work is that, while the extremal case of the Boolean hidden shift problem over so-called bent functions can be reduced to a hidden subgroup problem over an abelian group, the more general case studied here does not seem to allow such a reduction.Comment: 10 pages, 1 figur

Comment on τ\tau decay puzzle

We analize the current data on $\tau$-lepton decays and show that they are consistent with the Standard ModelComment: 5 pages, 1 figure (available from de authors), Latex, preprint IFT-P.022/9

Optimal quantum circuits for general phase estimation

We address the problem of estimating the phase phi given N copies of the phase rotation gate u(phi). We consider, for the first time, the optimization of the general case where the circuit consists of an arbitrary input state, followed by any arrangement of the N phase rotations interspersed with arbitrary quantum operations, and ending with a POVM. Using the polynomial method, we show that, in all cases where the measure of quality of the estimate phi' for phi depends only on the difference phi'-phi, the optimal scheme has a very simple fixed form. This implies that an optimal general phase estimation procedure can be found by just optimizing the amplitudes of the initial state.Comment: 4 pages, 3 figure

Neutrix Calculus and Finite Quantum Field Theory

In general, quantum field theories (QFT) require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series. We apply neutrix calculus, developed in connection with asymptotic series and divergent integrals, to QFT,obtaining finite renormalizations. While none of the physically measurable results in renormalizable QFT is changed, quantum gravity is rendered more manageable in the neutrix framework.Comment: 10 pages; LaTeX; version to appear in J. Phys. A: Math. Gen. as a Letter to the Edito

The quality of student dialogue in citizenship education

This study investigates the relationship between the quality of student dialogue and students’ ability to justify their viewpoints on a moral issue. A curriculum unit for dialogic citizenship education was developed and implemented in the 8th grade of secondary education. In the final lesson, students discussed a moral issue and then wrote an essay on it. The results show that students who made more value-related utterances during the discussion also referred more often and more explicitly in their individually written essays to moral values. This study indicates that the quality of the content of students’ dialogue is important for their ability to substantiate their opinion on moral issues with value-laden argumentation. Approaches to citizenship education in which dialogue is a central element should, therefore, pay specific attention to the validation of ideas in student dialogue

Gravity induced over a smooth soliton

I consider gravity induced over a smooth (finite thickness) soliton. Graviton kinetic term is coupled to bulk scalar that develops solitonic vacuum expectation value. Couplings of Kaluza-Klein modes to soliton-localized matter are suppressed, giving rise to crossover distance $r_c=M_{P}^2/M_{*}^3$ between 4D and 5D behavior. This system can be viewed as a finite thickness brane regularization of the model of Dvali, Gabadadze and Porrati.Comment: 12 pages, 2 figure

The Power of Brane-Induced Gravity

We study the role of the brane-induced graviton kinetic term in theories with large extra dimensions. In five dimensions we construct a model with a TeV-scale fundamental Planck mass and a {\it flat} extra dimension the size of which can be astronomically large. 4D gravity on the brane is mediated by a massless zero-mode, whereas the couplings of the heavy Kaluza-Klein modes to ordinary matter are suppressed. The model can manifest itself through the predicted deviations from Einstein theory in long distance precision measurements of the planetary orbits. The bulk states can be a rather exotic form of dark matter, which at sub-solar distances interact via strong 5D gravitational force. We show that the induced term changes dramatically the phenomenology of sub-millimeter extra dimensions. For instance, high-energy constraints from star cooling or cosmology can be substantially relaxed.Comment: 24 pages, 4 eps figures; v2 typos corrected; v3 1 ref. added; PRD versio

On SIC-POVMs in Prime Dimensions

The generalized Pauli group and its normalizer, the Clifford group, have a rich mathematical structure which is relevant to the problem of constructing symmetric informationally complete POVMs (SIC-POVMs). To date, almost every known SIC-POVM fiducial vector is an eigenstate of a "canonical" unitary in the Clifford group. I show that every canonical unitary in prime dimensions p > 3 lies in the same conjugacy class of the Clifford group and give a class representative for all such dimensions. It follows that if even one such SIC-POVM fiducial vector is an eigenvector of such a unitary, then all of them are (for a given such dimension). I also conjecture that in all dimensions d, the number of conjugacy classes is bounded above by 3 and depends only on d mod 9, and I support this claim with computer computations in all dimensions < 48.Comment: 6 pages, no figures. v3 Refs added, improved discussion of previous work. Ref to a proof of the main conjecture also adde

The added value of high-resolution above coarse-resolution remote sensing images in crop yield forecasting: A case study in the Egyptian Nile Delta

Crop growth models play a major role in sustaining the world-wide food security. These models are used to simulate crop growth during the growing season, and the final crop yield at the end of the growing season, given the farmers’ management practices. At a more strategic level, these crop growth models play an important role to decision makers to take timely decisions regarding food import and/or export strategies. The simulation accuracy of crop growth models relies on the quality of the input data. Since crop yield forecasting applications are often applied over large areas that rely on a spatially distributed crop growth model, the uncertainty in the spatial variation of the input data increases. Remote sensing images are often used in crop growth models because remote sensing images provide spatially distributed input data to these models. These images are available in numerous spatial resolutions, where coarse resolution images are often freely available compared to the more expensive high-resolution images. Therefore, the objective of the current study was to evaluate the added value of high-resolution satellite imagery above coarse-resolution satellite imagery in crop yield forecasting