Polynomial and rational approximation for electronic structure calculations

Atomic-scale simulation of matter has become an important research tool in physics, chemistry, material science and biology as it allows for insights which neither theoretical nor experimental investigation can provide. The most accurate of these simulations are based on the laws of quantum mechanics, in which case the main computational bottleneck becomes the evaluation of functions f(H) of a sparse matrix H (the Hamiltonian). One way to evaluate such matrix functions is through polynomial and rational approximation, the theory of which is reviewed in Chapter 2 of this thesis. It is well known that rational functions can approximate the relevant functions with much lower degrees than polynomials, but they are more challenging to use in practice since they require fast algorithms for evaluating rational functions r(H) of a matrix argument H. Such an algorithm has recently been proposed in the form of the Pole Expansion and Selected Inversion (PEXSI) scheme, which evaluates r(H) by writing r(x) = P k ck x−zk in partial-fraction-decomposed form and then employing advanced sparse factorisation techniques to evaluate only a small subset of the entries of the resolvents (H − z) −1 . This scheme scales better than cubically in the matrix dimension, but it is not a linear scaling algorithm in general. We overcome this limitation in Chapter 3 by devising a modified, linear-scaling PEXSI algorithm which exploits that most of the fill-in entries in the triangular factorisations computed by the PEXSI algorithm are negligibly small. Finally, Chapter 4 presents a novel algorithm for computing electric conductivities which requires evaluating a bivariate matrix function f(H, H). We show that the Chebyshev coefficients ck1k2 of the relevant function f(x1, x2) concentrate along the diagonal k1 ∼ k2 and that this allows us to approximate f(x1, x2) much more efficiently than one would expect based on a straightforward tensor-product extension of the one-dimensional arguments

The CrowdWater game: A playful way to improve the accuracy of crowdsourced water level class data

Data quality control is important for any data collection program, especially in citizen science projects, where it is more likely that errors occur due to the human factor. Ideally, data quality control in citizen science projects is also crowdsourced so that it can handle large amounts of data. Here we present the CrowdWater game as a gamified method to check crowdsourced water level class data that are submitted by citizen scientists through the CrowdWater app. The app uses a virtual staff gauge approach, which means that a digital scale is added to the first picture taken at a site and this scale is used for water level class observations at different times. In the game, participants classify water levels based on the comparison of the new picture with the picture containing the virtual staff gauge. By March 2019, 153 people had played the CrowdWater game and 841 pictures were classified. The average water level for the game votes for the classified pictures was compared to the water level class submitted through the app to determine whether the game can improve the quality of the data submitted through the app. For about 70% of the classified pictures, the water level class was the same for the CrowdWater app and game. For a quarter of the classified pictures, there was disagreement between the value submitted through the app and the average game vote. Expert judgement suggests that for three quarters of these cases, the game based average value was correct. The initial results indicate that the CrowdWater game helps to identify erroneous water level class observations from the CrowdWater app and provides a useful approach for crowdsourced data quality control. This study thus demonstrates the potential of gamified approaches for data quality control in citizen science projects

Accuracy of crowdsourced streamflow and stream level class estimates

Streamflow data are important for river management and the calibration of hydrological models. However, such data are only available for gauged catchments. Citizen science offers an alternative data source, and can be used to estimate streamflow at ungauged sites. We evaluated the accuracy of crowdsourced streamflow estimates for 10 streams in Switzerland by asking citizens to estimate streamflow either directly, or based on the estimated width, depth and velocity of the stream. Additionally, we asked them to estimate the stream level class by comparing the current stream level with a picture that included a virtual staff gauge. To compare the different estimates, the stream level class estimates were converted into streamflow. The results indicate that stream level classes were estimated more accurately than streamflow, and more accurately represented high and low flow conditions. Based on this result, we suggest that citizen science projects focus on stream level class estimates instead of streamflow estimates

Value of crowd‐based water level class observations for hydrological model calibration

While hydrological models generally rely on continuous streamflow data for calibration, previous studies have shown that a few measurements can be sufficient to constrain model parameters. Other studies have shown that continuous water level or water level class (WL‐class) data can be informative for model calibration. In this study, we combined these approaches and explored the potential value of a limited number of WL‐class observations for calibration of a bucket‐type runoff model (HBV) for four catchments in Switzerland. We generated synthetic data to represent citizen science data and examined the effects of the temporal resolution of the observations, the numbers of WL‐classes, and the magnitude of the errors in the WL‐class data on the model validation performance. Our results indicate that on average one observation per week for a one‐year period can significantly improve model performance compared to the situation without any streamflow data. Furthermore, the validation performance for model parameters calibrated with WL‐class observations was similar to the performance of the calibration with precise water level measurements. The number of WL‐classes did not influence the validation performance noticeably when at least four WL‐classes were used. The impact of typical errors for citizen‐science‐based estimates of WL‐classes on the model performance was small. These results are encouraging for citizen science projects where citizens observe water levels for otherwise ungauged streams using virtual or physical staff gauges

Climate change impacts on future snow, ice and rain runoff in a Swiss mountain catchment using multi-dataset calibration

Study region The hydropower reservoir of Gigerwald is located in the alpine valley Calfeisental in eastern Switzerland. The lake is fed by runoff from rain, snow melt and ice melt from a few small glaciers, as well as by water collected in a neighbouring valley. Study focus Water resources in the Alps are projected to undergo substantial changes in the coming decades. It is therefore essential to explore climate change impacts in catchments with hydropower facilities. We present a multi-dataset calibration (MDC) using discharge, snowcover data and glacier mass balances for an ensemble of hydrological simulations performed using the Hydrologiska Byråns Vattenbalansavdelning (HBV)-light model. The objective is to predict the future changes in hydrological processes in the catchment and to assess the benefits of a MDC compared to a traditional calibration to discharge only. New hydrological insights for the region We found that the annual runoff dynamics will undergo significant changes with more runoff in winter and less in summer by shifting parts of the summer melt runoff to an earlier peak in spring. We furthermore found that the MDC reduces the uncertainty in the projections of glacial runoff and leads to a different distribution of runoff throughout the year than if calibrated to discharge only. We therefore argue that MDC leads to more consistent model results by representing the runoff generation processes more realistically.J. Seibert and M. Vis provided important support regarding the application of the HBV-light model. We furthermore want to thank Kirsti Hakala for providing valuable comments on the selection of climate models. We also acknowledge the Kraftwerke Sarganserland AG for the discharge data, MeteoSwiss for the gridded weather datasets and the EU-funded FP6 Integrated Project ENSEMBLES for the climate projections. Comments by two anonymous reviewers helped to improve the manuscript."Peer Reviewed

Light-driven molecular motors embedded in covalent organic frameworks

The incorporation of molecular machines into the backbone of porous framework structures will facilitate nano actuation, enhanced molecular transport, and other out-of-equilibrium host-guest phenomena in well-defined 3D solid materials. In this work, we detail the synthesis of a diamine-based light-driven molecular motor and its incorporation into a series of imine-based polymers and covalent organic frameworks (COF). We study structural and dynamic properties of the molecular building blocks and derived self-assembled solids with a series of spectroscopic, diffraction, and theoretical methods. Using an acid-catalyzed synthesis approach, we are able to obtain the first crystalline 2D COF with stacked hexagonal layers that contains 20 mol% molecular motors. The COF features a specific pore volume and surface area of up to 0.45 cm(3) g(-1) and 604 m(2) g(-1), respectively. Given the molecular structure and bulkiness of the diamine motor, we study the supramolecular assembly of the COF layers and detail stacking disorders between adjacent layers. We finally probe the motor dynamics with in situ spectroscopic techniques revealing current limitations in the analysis of these new materials and derive important analysis and design criteria as well as synthetic access to new generations of motorized porous framework materials

Virtual Staff Gauges for Crowd-Based Stream Level Observations

Hydrological observations are crucial for decision making for a wide range of water resource challenges. Citizen science is a potentially useful approach to complement existing observation networks to obtain this data. Previous projects, such as CrowdHydrology, have demonstrated that it is possible to engage the public in contributing hydrological observations. However, hydrological citizen science projects related to streamflow have, so far, been based on the use of different kinds of instruments or installations; in the case of stream level observations, this is usually a staff gauge. While it may be relatively easy to install a staff gauge at a few river sites, the need for a physical installation makes it difficult to scale this type of citizen science approach to a larger number of sites because these gauges cannot be installed everywhere or by everyone. Here, we present a smartphone app that allows collection of stream level information at any place without any physical installation as an alternative approach. The approach is similar to geocaching, with the difference that instead of finding treasure-hunting sites, hydrological measurement sites can be generated by anyone and at any location and these sites can be found by the initiator or other citizen scientists to add another observation at another time. The app is based on a virtual staff gauge approach, where a picture of a staff gauge is digitally inserted into a photo of a stream bank or a bridge pillar, and the stream level during a subsequent field visit to that site is compared to the staff gauge on the first picture. The first experiences with the use of the app by citizen scientists were largely encouraging but also highlight a few challenges and possible improvements

In situ monitoring and mechanism of the mechanochemical formation of a microporous MOF-74 framework

Mechanochemistry provides a rapid, efficient route to metal-organic framework Zn-MOF-74 directly from a metal oxide and without bulk solvent. In situ synchrotron X-ray diffraction monitoring of the reaction course reveals two new phases and an unusual step-wise process in which a close-packed intermediate reacts to form the open framework. The reaction can be performed on a gram scale to yield a highly porous material after activation