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Seasonal snowpack is an important predictor of the water resources available in the following spring and early-summer melt season. Total basin snow water equivalent (SWE) estimation usually requires a form of statistical analysis that is implicitly built upon the Gaussian framework. However, it is important to characterize the non-Gaussian properties of snow distribution for accurate large-scale SWE estimation based on remotely sensed or sparse ground-based observations. This study quantified non-Gaussianity using sample negentropy; the Kullback–Leibler divergence from the Gaussian distribution for field-observed snow depth data from the North Slope, Alaska; and three representative SWE distributions in the western USA from the Airborne Snow Observatory (ASO). Snowdrifts around lakeshore cliffs and deep gullies can bring moderate non-Gaussianity in the open, lowland tundra of North Slope, Alaska, while the ASO dataset suggests that subalpine forests may effectively suppress the non-Gaussianity of snow distribution. Thus, non-Gaussianity is found in areas with partial snow cover and wind-induced snowdrifts around topographic breaks on slopes and on other steep terrain features. The snowpacks may be considered weakly Gaussian in coastal regions with open tundra in Alaska and alpine and subalpine terrains in the western USA if the land is completely covered by snow. The wind-induced snowdrift effect can potentially be partitioned from the observed snow spatial distribution guided by its Gaussianity.

One of the main objectives of the scientific enterprise is the development of well-performing yet parsimonious models for all natural phenomena and systems. In the 21st century, scientists usually represent their models, hypotheses, and experimental observations using digital computers. Measuring performance and parsimony of computer models is therefore a key theoretical and practical challenge for 21st century science. “Performance” here refers to a model's ability to reduce predictive uncertainty about an object of interest. “Parsimony” (or complexity) comprises two aspects: descriptive complexity – the size of the model itself which can be measured by the disk space it occupies – and computational complexity – the model's effort to provide output. Descriptive complexity is related to inference quality and generality; computational complexity is often a practical and economic concern for limited computing resources. In this context, this paper has two distinct but related goals. The first is to propose a practical method of measuring computational complexity by utility software “Strace”, which counts the total number of memory visits while running a model on a computer. The second goal is to propose the “bit by bit” method, which combines measuring computational complexity by “Strace” and measuring model performance by information loss relative to observations, both in bit. For demonstration, we apply the “bit by bit” method to watershed models representing a wide diversity of modelling strategies (artificial neural network, auto-regressive, process-based, and others). We demonstrate that computational complexity as measured by “Strace” is sensitive to all aspects of a model, such as the size of the model itself, the input data it reads, its numerical scheme, and time stepping. We further demonstrate that for each model, the bit counts for computational complexity exceed those for performance by several orders of magnitude and that the differences among the models for both computational complexity and performance can be explained by their setup and are in accordance with expectations. We conclude that measuring computational complexity by “Strace” is practical, and it is also general in the sense that it can be applied to any model that can be run on a digital computer. We further conclude that the “bit by bit” approach is general in the sense that it measures two key aspects of a model in the single unit of bit. We suggest that it can be enhanced by additionally measuring a model's descriptive complexity – also in bit.

The current work addresses one of the key building blocks towards an improved understanding of flood processes and associated changes in flood characteristics and regimes in Europe: the development of a comprehensive, extensive European flood database. The presented work results from ongoing cross-border research collaborations initiated with data collection and joint interpretation in mind. A detailed account of the current state, characteristics and spatial and temporal coverage of the European Flood Database, is presented. At this stage, the hydrological data collection is still growing and consists at this time of annual maximum and daily mean discharge series, from over 7000 hydrometric stations of various data series lengths. Moreover, the database currently comprises data from over 50 different data sources. The time series have been obtained from different national and regional data sources in a collaborative effort of a joint European flood research agreement based on the exchange of data, models and expertise, and from existing international data collections and open source websites. These ongoing efforts are contributing to advancing the understanding of regional flood processes beyond individual country boundaries and to a more coherent flood research in Europe.

The dynamical evolution of the flood response to landscape-climate feedbacks is evaluated in a joint nonlinear statistical-dynamical approach. For that purpose, a spatiotemporal sensitivity analysis is conducted on hydrological data from 1976–2008 over 804 catchments throughout Austria, and a general, data-independent nonlinear dynamical model is built linking floods with climate (via precipitation), landscape (via elevation) and their feedbacks. These involve nonlinear scale interactions, with landform evolution processes taking place at the millennial scale (slow dynamics), and climate adjusting in years to decades (fast dynamics). The results show that floods are more responsive to spatial (regional) than to temporal (decadal) variability. Catchments from dry lowlands and high wetlands exhibit similarity between the spatial and temporal sensitivities (spatiotemporal symmetry) and low landscape-climate codependence, suggesting they are not coevolving significantly. However, intermediate regions show differences between those sensitivities (symmetry breaks) and higher landscape-climate codependence, suggesting undergoing coevolution. The break of symmetry is an emergent behaviour from nonlinear feedbacks within the system. A new coevolution index is introduced relating spatiotemporal symmetry with relative characteristic celerities, which need to be taken into account in hydrological space-time trading. Coevolution is expressed here by the interplay between slow and fast dynamics, represented respectively by spatial and temporal characteristics. The dynamical model captures emerging features of the flood dynamics and nonlinear landscape-climate feedbacks, supporting the nonlinear statistical assessment of spatiotemporally asymmetric flood change. Moreover, it enables the dynamical estimation of flood changes in space and time from the given knowledge at different spatiotemporal conditions. This study ultimately brings to light emerging signatures of change in floods arising from nonlinear slow-fast feedbacks in the landscape-climate dynamics, and contributes towards a better understanding of spatiotemporal flood changes and underlying nonlinearly interacting drivers.

Non-Gaussian multivariate probability distributions, derived from climate and geofluid statistics, allow for nonlinear correlations between linearly uncorrelated components, due to joint Shannon negentropies. Triadic statistical dependence under pair-wise (total or partial) independence is thus possible. Synergy or interaction information among triads is estimated. We formulate an optimization method of triads in the space of orthogonal rotations of normalized principal components, relying on the maximization of third-order cross-cumulants. Its application to a minimal one-dimensional, periodic, advective model leads to enhanced triads that occur between oscillating components of circular or locally confined wave trains satisfying the triadic wave resonance condition.

There is growing concern that flooding is becoming more frequent and severe in Europe. A better understanding of flood regime changes and their drivers is therefore needed. The paper reviews the current knowledge on flood regime changes in European rivers that has traditionally been obtained through two alternative research approaches. The first approach is the data-based detection of changes in observed flood events. Current methods are reviewed together with their challenges and opportunities. For example, observation biases, the merging of different data sources and accounting for nonlinear drivers and responses. The second approach consists of modelled scenarios of future floods. Challenges and opportunities associated with flood change scenarios are discussed such as fully accounting for uncertainties in the modelling cascade and feedbacks. To make progress in flood change research, we suggest that a synthesis of these two approaches is needed. This can be achieved by focusing on long duration records and flood-rich and flood-poor periods rather than on short duration flood trends only, by formally attributing causes of observed flood changes, by validating scenarios against observed flood regime dynamics, and by developing low-dimensional models of flood changes and feedbacks. The paper finishes with a call for a joint European flood change research network.

The June 2013 flood in the Upper Danube Basin was one of the largest floods in the past two centuries. An atmospheric blocking situation produced precipitation exceeding 300 mm over four days at the northern rim of the Alps. The high precipitation, along with high antecedent soil moisture, gave rise to extreme flood discharges in a number of tributaries including the Tiroler Ache, Saalach, Salzach and Inn. Runoff coefficients ranged from 0.2 in the Bavarian lowlands to 0.6 in the Alpine areas in Austria. Snowfall at high altitudes (above about 1600 m a.s.l.) reduced the runoff volume produced. Precipitation was distributed over two blocks separated by a few hours, which resulted in a single peak, long-duration flood wave at the Inn and Danube. At the confluence of the Bavarian Danube and the Inn, the small time lag between the two flood waves exacerbated the downstream flood at the Danube. Because of the long duration and less inundation, there was less flood peak attenuation along the Austrian Danube reach than for the August 2002 flood. Maximum flood discharges of the Danube at Vienna were about 11 000 m3 s−1, as compared to 10 300, 9600 and 10 500 m3 s−1 in 2002, 1954 and 1899, respectively. This paper reviews the meteorological and hydrological characteristics of the event as compared to the 2002, 1954 and 1899 floods, and discusses the implications for hydrological research and flood risk management.