Modelling the spatial variability of snow water equivalent at the catchment scale

International audienceThe spatial distribution of snow water equivalent (SWE) is modelled as a two parameter gamma distribution. The parameters of the distribution are dynamical in that they are functions of the number of accumulation and melting events and the temporal correlation of accumulation and melting events. The estimated spatial variability is compared to snow course observations from the alpine catchments Norefjell and Aursunden in Southern Norway. A fixed snow course at Norefjell was measured 26 times during the snow season and showed that the spatial coefficient of variation change during the snow season with a decreasing trend from the start of the accumulation period and a sharp increase in the melting period. The gamma distribution with dynamical parameters reproduced the observed spatial statistical features of SWE well both at Norefjell and Aursunden. Also the shape of simulated spatial distribution of SWE agreed well with the observed at Norefjell. The temporal correlation tends to be positive for both accumulation and melting events. However, at the start of melting, a better fit between modelled and observed spatial standard deviation of SWE is obtained by using negative correlation between SWE and melt

Dynamical properties of the spatial distribution of snow

International audienceA simulation exercise has been performed to study the temporal development of snow covered area and the spatial distribution of snow-water equivalent (SWE). Special consideration has been paid to how the properties of the spatial statistical distribution of SWE change as a response to accumulation and ablation events. A distributed rainfall-runoff model at resolution 1 x 1 km2 has been run with time series of precipitation and temperature fields of the same spatial resolution derived from the atmospheric model HIRLAM. The precipitation fields are disaggregated and the temperature fields are interpolated. Time series of the spatial distribution of snow-water equivalent and snow-covered area for three seasons for a catchment in Norway is generated. The catchment is of size 3085 km2 and two rectangular sub-areas of 484 km2 are located within the larger catchment. The results show that the shape of the spatial distribution of SWE for all three areas changes during winter. The distribution is very skewed at the start of the accumulation season but then the skew decreases and, as the ablation season sets in, the spatial distribution again becomes more skewed with a maximum near the end of the ablation season. For one of the sub-areas, a consistently more skewed distribution of SWE is found, related to higher variability in precipitation. This indicates that observed differences in the spatial distribution of snow between alpine and forested areas can result from differences in the spatial variability of precipitation. The results obtained from the simulation exercise are consistent with modelling the spatial distribution of SWE as summations of a gamma distributed variable. Keywords: Snow, SWE, spatial distribution, simulated hydrometeorological field

A stochastic event-based approach for flood estimation in catchments with mixed rainfall and snowmelt flood regimes

The estimation of extreme floods is associated with high uncertainty, in part due to the limited length of streamflow records. Traditionally, statistical flood frequency analysis and an event-based model (PQRUT) using a single design storm have been applied in Norway. We here propose a stochastic PQRUT model, as an extension of the standard application of the event-based PQRUT model, by considering different combinations of initial conditions, rainfall and snowmelt, from which a distribution of flood peaks can be constructed. The stochastic PQRUT was applied for 20 small- and medium-sized catchments in Norway and the results give good fits to observed peak-over-threshold (POT) series. A sensitivity analysis of the method indicates (a) that the soil saturation level is less important than the rainfall input and the parameters of the PQRUT model for flood peaks with return periods higher than 100 years and (b) that excluding the snow routine can change the seasonality of the flood peaks. Estimates for the 100- and 1000-year return level based on the stochastic PQRUT model are compared with results for (a) statistical frequency analysis and (b) a standard implementation of the event-based PQRUT method. The differences in flood estimates between the stochastic PQRUT and the statistical flood frequency analysis are within 50&thinsp;% in most catchments. However, the differences between the stochastic PQRUT and the standard implementation of the PQRUT model are much higher, especially in catchments with a snowmelt flood regime.</p

The what and where of adding channel noise to the Hodgkin-Huxley equations

One of the most celebrated successes in computational biology is the Hodgkin-Huxley framework for modeling electrically active cells. This framework, expressed through a set of differential equations, synthesizes the impact of ionic currents on a cell's voltage -- and the highly nonlinear impact of that voltage back on the currents themselves -- into the rapid push and pull of the action potential. Latter studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic Hodgkin-Huxley equations. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly Matlab simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950) and http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl

Twenty-three unsolved problems in hydrology (UPH) – a community perspective

This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through on-line media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focussed on process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come

The spatial variability of snow water equivalent

International audienceThe spatial distribution of snow water equivalent (SWE) is modelled as a two parameter gamma distribution. The parameters of the distribution are dynamical in that they are functions of the number of accumulation and ablation events and the temporal correlation of accumulation and ablation events. The estimated spatial variability is compared to snow course observations from the alpine catchments Norefjell and Aursunden in Southern Norway. A fixed snow course at Norefjell was measured 26 times during the snow season, which showed that the spatial coefficient of variation change during the snow season with a decreasing trend from the start of the accumulation period and a sharp increase in the ablation period. The gamma distribution with dynamical parameters reproduced the observed spatial statistical features of SWE well both at Norefjell and Aursunden. Also the shape of simulated spatial distribution of SWE agreed well with the observed at Norefjell. The temporal correlation tends to be positive for both accumulation and ablation events. However, at the start of ablation, a better fit between modelled and observed spatial standard deviation of SWE is obtained by using negative correlation between SWE and melt

Dynamical properties of the spatial distribution of snow

A simulation exercise has been performed to study the temporal development of snow covered area and the spatial distribution of snow-water equivalent (SWE). Special consideration has been paid to how the properties of the spatial statistical distribution of SWE change as a response to accumulation and ablation events. A distributed rainfall-runoff model at resolution 1 x 1 km2 has been run with time series of precipitation and temperature fields of the same spatial resolution derived from the atmospheric model HIRLAM. The precipitation fields are disaggregated and the temperature fields are interpolated. Time series of the spatial distribution of snow-water equivalent and snow-covered area for three seasons for a catchment in Norway is generated. The catchment is of size 3085 km2 and two rectangular sub-areas of 484 km2 are located within the larger catchment. The results show that the shape of the spatial distribution of SWE for all three areas changes during winter. The distribution is very skewed at the start of the accumulation season but then the skew decreases and, as the ablation season sets in, the spatial distribution again becomes more skewed with a maximum near the end of the ablation season. For one of the sub-areas, a consistently more skewed distribution of SWE is found, related to higher variability in precipitation. This indicates that observed differences in the spatial distribution of snow between alpine and forested areas can result from differences in the spatial variability of precipitation. The results obtained from the simulation exercise are consistent with modelling the spatial distribution of SWE as summations of a gamma distributed variable. Keywords: Snow, SWE, spatial distribution, simulated hydrometeorological field

Hydrologic effects of land and water management in North America and Asia: 1700&ndash;1992

The hydrologic effects of land use changes, dams, and irrigation in North America and Asia over the past 300 years are studied using a macroscale hydrologic model. The simulation results indicate that the expansion of croplands over the last three centuries has resulted in 2.5 and 6 percent increases in annual runoff volumes for North America and Asia, respectively, and that these increases in runoff to some extent have been compensated by increased evapotranspiration caused by irrigation practices. Averaged over the year and the continental scale, the accumulated anthropogenic impacts on surface water fluxes are hence relatively minor. However, for some regions within the continents human activities have altered hydrologic regimes profoundly. Reservoir operations and irrigation practices in the western part of USA and Mexico have resulted in a 25 percent decrease in runoff in June, and a 9 percent decrease in annual runoff volumes reaching the Pacific Ocean. In the area in South East Asia draining to the Pacific Ocean, land use changes have caused an increase in runoff volumes throughout the year, and the average annual increase in runoff is 12 percent

Twenty-three unsolved problems in hydrology (UPH) – a community perspective

This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through online media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focused on the process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come