Over-parameterised, uncertain 'mathematical marionettes' - How can we best use catchment water quality models? An example of an 80-year catchment-scale nutrient balance

The Integrated Catchment Model of Nitrogen (INCA-N) was applied to the River Lambourn, a Chalk river-system in southern England. The model's abilities to simulate the long-term trend and seasonal patterns in observed stream water nitrate concentrations from 1920 to 2003 were tested. This is the first time a semi-distributed, daily time-step model has been applied to simulate such a long time period and then used to calculate detailed catchment nutrient budgets which span the conversion of pasture to arable during the late 1930s and 1940s. Thus, this work goes beyond source apportionment and looks to demonstrate how such simulations can be used to assess the state of the catchment and develop an understanding of system behaviour. The mass-balance results from 1921, 1922, 1991, 2001 and 2002 are presented and those for 1991 are compared to other modelled and literature values of loads associated with nitrogen soil processes and export. The variations highlighted the problem of comparing modelled fluxes with point measurements but proved useful for identifying the most poorly understood inputs and processes thereby providing an assessment of input data and model structural uncertainty. The modelled terrestrial and instream mass-balances also highlight the importance of the hydrological conditions in pollutant transport. Between 1922 and 2002, increased inputs of nitrogen from fertiliser, livestock and deposition have altered the nitrogen balance with a shift from possible reduction in soil fertility but little environmental impact in 1922, to a situation of nitrogen accumulation in the soil, groundwater and instream biota in 2002. In 1922 and 2002 it was estimated that approximately 2 and 18 kg N ha(-1) yr(-1) respectively were exported from the land to the stream. The utility of the approach and further considerations for the best use of models are discussed. (C) 2008 Elsevier B.V. All rights reserved.

Evaluating a new LISFLOOD-FP formulation with data from the summer 2007 floods in Tewkesbury, UK

Two-dimensional flood inundation modelling is a widely used tool to aid flood risk management. In urban areas, where asset value and population density are greatest, the model spatial resolution required to represent flows through a typical street network (i.e. < 10m) often results in impractical computational cost at the whole city scale. Explicit diffusive storage cell models become very inefficient at such high resolutions, relative to shallow water models, because the stable time step in such schemes scales as a quadratic of resolution. This paper presents the calibration and evaluation of a recently developed new formulation of the LISFLOOD-FP model, where stability is controlled by the Courant–Freidrichs–Levy condition for the shallow water equations, such that, the stable time step instead scales linearly with resolution. The case study used is based on observations during the summer 2007 floods in Tewkesbury, UK. Aerial photography is available for model evaluation on three separate days from the 24th to the 31st of July. The model covered a 3.6 km by 2 km domain and was calibrated using gauge data from high flows during the previous month. The new formulation was benchmarked against the original version of the model at 20 m and 40 m resolutions, demonstrating equally accurate performance given the available validation data but at 67x faster computation time. The July event was then simulated at the 2 m resolution of the available airborne LiDAR DEM. This resulted in a significantly more accurate simulation of the drying dynamics compared to that simulated by the coarse resolution models, although estimates of peak inundation depth were similar.

An assessment of the fine sediment dynamics in an upland river system: INCA-Sed modifications and implications for fisheries

There is a need for better links between hydrology and ecology, specifically between landscapes and riverscapes to understand how processes and factors controlling the transport and storage of environmental pollution have affected or will affect the freshwater biota. Here we show how the INCA modelling framework, specifically INCA-Sed (the Integrated Catchments model for Sediments) can be used to link sediment delivery from the landscape to sediment changes in-stream. INCA-Sed is a dynamic, process-based, daily time step model. The first complete description of the equations used in the INCA-Sed software (version 1.9.11) is presented. This is followed by an application of INCA-Sed made to the River Lugg (1077 km2) in Wales. Excess suspended sediment can negatively affect salmonid health. The Lugg has a large and potentially threatened population of both Atlantic salmon (Salmo salar) and Brown Trout (Salmo trutta). With the exception of the extreme sediment transport processes, the model satisfactorily simulated both the hydrology and the sediment dynamics in the catchment. Model results indicate that diffuse soil loss is the most important sediment generation process in the catchment. In the River Lugg, the mean annual Guideline Standard for suspended sediment concentration, proposed by UKTAG, of 25 mg l− 1 is only slightly exceeded during the simulation period (1995–2000), indicating only minimal effect on the Atlantic salmon population. However, the daily time step simulation of INCA-Sed also allows the investigation of the critical spawning period. It shows that the sediment may have a significant negative effect on the fish population in years with high sediment runoff. It is proposed that the fine settled particles probably do not affect the salmonid egg incubation process, though suspended particles may damage the gills of fish and make the area unfavourable for spawning if the conditions do not improve.

Translating climate forecasts into agricultural terms: advances and challenges

Seasonal climate prediction offers the potential to anticipate variations in crop production early enough to adjust critical decisions. Until recently, interest in exploiting seasonal forecasts from dynamic climate models (e.g. general circulation models, GCMs) for applications that involve crop simulation models has been hampered by the difference in spatial and temporal scale of GCMs and crop models, and by the dynamic, nonlinear relationship between meteorological variables and crop response. Although GCMs simulate the atmosphere on a sub-daily time step, their coarse spatial resolution and resulting distortion of day-to-day variability limits the use of their daily output. Crop models have used daily GCM output with some success by either calibrating simulated yields or correcting the daily rainfall output of the GCM to approximate the statistical properties of historic observations. Stochastic weather generators are used to disaggregate seasonal forecasts either by adjusting input parameters in a manner that captures the predictable components of climate, or by constraining synthetic weather sequences to match predicted values. Predicting crop yields, simulated with historic weather data, as a statistical function of seasonal climatic predictors, eliminates the need for daily weather data conditioned on the forecast, but must often address poor statistical properties of the crop-climate relationship. Most of the work on using crop simulation with seasonal climate forecasts has employed historic analogs based on categorical ENSO indices. Other methods based on classification of predictors or weather types can provide daily weather inputs to crop models conditioned on forecasts. Advances in climate-based crop forecasting in the coming decade are likely to include more robust evaluation of the methods reviewed here, dynamically embedding crop models within climate models to account for crop influence on regional climate, enhanced use of remote sensing, and research in the emerging area of 'weather within climate'.

Translating climate forecasts into agricultural terms: advances and challenges

Seasonal climate prediction offers the potential to anticipate variations in crop production early enough to adjust critical decisions. Until recently, interest in exploiting seasonal forecasts from dynamic climate models (e.g. general circulation models, GCMs) for applications that involve crop simulation models has been hampered by the difference in spatial and temporal scale of GCMs and crop models, and by the dynamic, nonlinear relationship between meteorological variables and crop response. Although GCMs simulate the atmosphere on a sub-daily time step, their coarse spatial resolution and resulting distortion of day-to-day variability limits the use of their daily output. Crop models have used daily GCM output with some success by either calibrating simulated yields or correcting the daily rainfall output of the GCM to approximate the statistical properties of historic observations. Stochastic weather generators are used to disaggregate seasonal forecasts either by adjusting input parameters in a manner that captures the predictable components of climate, or by constraining synthetic weather sequences to match predicted values. Predicting crop yields, simulated with historic weather data, as a statistical function of seasonal climatic predictors, eliminates the need for daily weather data conditioned on the forecast, but must often address poor statistical properties of the crop-climate relationship. Most of the work on using crop simulation with seasonal climate forecasts has employed historic analogs based on categorical ENSO indices. Other methods based on classification of predictors or weather types can provide daily weather inputs to crop models conditioned on forecasts. Advances in climate-based crop forecasting in the coming decade are likely to include more robust evaluation of the methods reviewed here, dynamically embedding crop models within climate models to account for crop influence on regional climate, enhanced use of remote sensing, and research in the emerging area of 'weather within climate'.

A simple relationship between volcanic sulfate aerosol optical depth and surface temperature change simulated in an atmosphere-ocean general circulation model.

In this study we quantify the relationship between the aerosol optical depth increase from a volcanic eruption and the severity of the subsequent surface temperature decrease. This investigation is made by simulating 10 different sizes of eruption in a global circulation model (GCM) by changing stratospheric sulfate aerosol optical depth at each time step. The sizes of the simulated eruptions range from Pinatubo‐sized up to the magnitude of supervolcanic eruptions around 100 times the size of Pinatubo. From these simulations we find that there is a smooth monotonic relationship between the global mean maximum aerosol optical depth anomaly and the global mean temperature anomaly and we derive a simple mathematical expression which fits this relationship well. We also construct similar relationships between global mean aerosol optical depth and the temperature anomaly at every individual model grid box to produce global maps of best‐fit coefficients and fit residuals. These maps are used with caution to find the eruption size at which a local temperature anomaly is clearly distinct from the local natural variability and to approximate the temperature anomalies which the model may simulate following a Tambora‐sized eruption. To our knowledge, this is the first study which quantifies the relationship between aerosol optical depth and resulting temperature anomalies in a simple way, using the wealth of data that is available from GCM simulations.

Parallel pipelined histogram architectures

Proposed is a unique cell histogram architecture which will process k data items in parallel to compute 2q histogram bins per time step. An array of m/2q cells computes an m-bin histogram with a speed-up factor of k; k ⩾ 2 makes it faster than current dual-ported memory implementations. Furthermore, simple mechanisms for conflict-free storing of the histogram bins into an external memory array are discussed.

Boundary integral methods for singularly perturbed boundary value problems

In this paper we consider boundary integral methods applied to boundary value problems for the positive definite Helmholtz-type problem -DeltaU + alpha U-2 = 0 in a bounded or unbounded domain, with the parameter alpha real and possibly large. Applications arise in the implementation of space-time boundary integral methods for the heat equation, where alpha is proportional to 1/root deltat, and deltat is the time step. The corresponding layer potentials arising from this problem depend nonlinearly on the parameter alpha and have kernels which become highly peaked as alpha --> infinity, causing standard discretization schemes to fail. We propose a new collocation method with a robust convergence rate as alpha --> infinity. Numerical experiments on a model problem verify the theoretical results.

Ensemble data assimilation in the presence of cloud

In numerical weather prediction (NWP) data assimilation (DA) methods are used to combine available observations with numerical model estimates. This is done by minimising measures of error on both observations and model estimates with more weight given to data that can be more trusted. For any DA method an estimate of the initial forecast error covariance matrix is required. For convective scale data assimilation, however, the properties of the error covariances are not well understood. An effective way to investigate covariance properties in the presence of convection is to use an ensemble-based method for which an estimate of the error covariance is readily available at each time step. In this work, we investigate the performance of the ensemble square root filter (EnSRF) in the presence of cloud growth applied to an idealised 1D convective column model of the atmosphere. We show that the EnSRF performs well in capturing cloud growth, but the ensemble does not cope well with discontinuities introduced into the system by parameterised rain. The state estimates lose accuracy, and more importantly the ensemble is unable to capture the spread (variance) of the estimates correctly. We also find, counter-intuitively, that by reducing the spatial frequency of observations and/or the accuracy of the observations, the ensemble is able to capture the states and their variability successfully across all regimes.

Comment on “A modified leapfrog scheme for shallow water equations” by Wen-Yih Sun and Oliver M.T. Sun

A recent paper published in this journal considers the numerical integration of the shallow-water equations using the leapfrog time-stepping scheme [Sun Wen-Yih, Sun Oliver MT. A modified leapfrog scheme for shallow water equations. Comput Fluids 2011;52:69–72]. The authors of that paper propose using the time-averaged height in the numerical calculation of the pressure-gradient force, instead of the instantaneous height at the middle time step. The authors show that this modification doubles the maximum Courant number (and hence the maximum time step) at which the integrations are stable, doubling the computational efficiency. Unfortunately, the pressure-averaging technique proposed by the authors is not original. It was devised and published by Shuman [5] and has been widely used in the atmosphere and ocean modelling community for over 40 years.

An experiment in the Assimilation of Data in Dynamical Analysis

A system for continuous data assimilation is presented and discussed. To simulate the dynamical development a channel version of a balanced barotropic model is used and geopotential (height) data are assimilated into the models computations as data become available. In the first experiment the updating is performed every 24th, 12th and 6th hours with a given network. The stations are distributed at random in 4 groups in order to simulate 4 areas with different density of stations. Optimum interpolation is performed for the difference between the forecast and the valid observations. The RMS-error of the analyses is reduced in time, and the error being smaller the more frequent the updating is performed. The updating every 6th hour yields an error in the analysis less than the RMS-error of the observation. In a second experiment the updating is performed by data from a moving satellite with a side-scan capability of about 15°. If the satellite data are analysed at every time step before they are introduced into the system the error of the analysis is reduced to a value below the RMS-error of the observation already after 24 hours and yields as a whole a better result than updating from a fixed network. If the satellite data are introduced without any modification the error of the analysis is reduced much slower and it takes about 4 days to reach a comparable result to the one where the data have been analysed.

The surface urban energy and water balance scheme (SUEWS): evaluation in Los Angeles and Vancouver

An urban energy and water balance model is presented which uses a small number of commonly measured meteorological variables and information about the surface cover. Rates of evaporation-interception for a single layer with multiple surface types (paved, buildings, coniferous trees and/or shrubs, deciduous trees and/or shrubs, irrigated grass, non-irrigated grass and water) are calculated. Below each surface type, except water, there is a single soil layer. At each time step the moisture state of each surface is calculated. Horizontal water movements at the surface and in the soil are incorporated. Particular attention is given to the surface conductance used to model evaporation and its parameters. The model is tested against direct flux measurements carried out over a number of years in Vancouver, Canada and Los Angeles, USA. At all measurement sites the model is able to simulate the net all-wave radiation and turbulent sensible and latent heat well (RMSE = 25–47 W m−2, 30–64 and 20–56 W m−2, respectively). The model reproduces the diurnal cycle of the turbulent fluxes but typically underestimates latent heat flux and overestimates sensible heat flux in the day time. The model tracks measured surface wetness and simulates the variations in soil moisture content. It is able to respond correctly to short-term events as well as annual changes. The largest uncertainty relates to the determination of surface conductance. The model has the potential be used for multiple applications; for example, to predict effects of regulation on urban water use, landscaping and planning scenarios, or to assess climate mitigation strategies.

An easily implemented agro-hydrological procedure with dynamic root simulation for water transfer in the crop-soil system: validation and application

Models for water transfer in the crop-soil system are key components of agro-hydrological models for irrigation, fertilizer and pesticide practices. Many of the hydrological models for water transfer in the crop-soil system are either too approximate due to oversimplified algorithms or employ complex numerical schemes. In this paper we developed a simple and sufficiently accurate algorithm which can be easily adopted in agro-hydrological models for the simulation of water dynamics. We used a dual crop coefficient approach proposed by the FAO for estimating potential evaporation and transpiration, and a dynamic model for calculating relative root length distribution on a daily basis. In a small time step of 0.001 d, we implemented algorithms separately for actual evaporation, root water uptake and soil water content redistribution by decoupling these processes. The Richards equation describing soil water movement was solved using an integration strategy over the soil layers instead of complex numerical schemes. This drastically simplified the procedures of modeling soil water and led to much shorter computer codes. The validity of the proposed model was tested against data from field experiments on two contrasting soils cropped with wheat. Good agreement was achieved between measurement and simulation of soil water content in various depths collected at intervals during crop growth. This indicates that the model is satisfactory in simulating water transfer in the crop-soil system, and therefore can reliably be adopted in agro-hydrological models. Finally we demonstrated how the developed model could be used to study the effect of changes in the environment such as lowering the groundwater table caused by the construction of a motorway on crop transpiration. (c) 2009 Elsevier B.V. All rights reserved.

An exploration of the equivalent weights particle filter

Particle filters are fully non-linear data assimilation techniques that aim to represent the probability distribution of the model state given the observations (the posterior) by a number of particles. In high-dimensional geophysical applications the number of particles required by the sequential importance resampling (SIR) particle filter in order to capture the high probability region of the posterior, is too large to make them usable. However particle filters can be formulated using proposal densities, which gives greater freedom in how particles are sampled and allows for a much smaller number of particles. Here a particle filter is presented which uses the proposal density to ensure that all particles end up in the high probability region of the posterior probability density function. This gives rise to the possibility of non-linear data assimilation in large dimensional systems. The particle filter formulation is compared to the optimal proposal density particle filter and the implicit particle filter, both of which also utilise a proposal density. We show that when observations are available every time step, both schemes will be degenerate when the number of independent observations is large, unlike the new scheme. The sensitivity of the new scheme to its parameter values is explored theoretically and demonstrated using the Lorenz (1963) model.

Unsteady flow simulation of a vertical axis augmented wind turbine: a two-dimensional study

As the integration of vertical axis wind turbines in the built environment is a promising alternative to horizontal axis wind turbines, a 2D computational investigation of an augmented wind turbine is proposed and analysed. In the initial CFD analysis, three parameters are carefully investigated: mesh resolution; turbulence model; and time step size. It appears that the mesh resolution and the turbulence model affect result accuracy; while the time step size examined, for the unsteady nature of the flow, has small impact on the numerical results. In the CFD validation of the open rotor with secondary data, the numerical results are in good agreement in terms of shape. It is, however, observed a discrepancy factor of 2 between numerical and experimental data. Successively, the introduction of an omnidirectional stator around the wind turbine increases the power and torque coefficients by around 30–35% when compared to the open case; but attention needs to be given to the orientation of the stator blades for optimum performance. It is found that the power and torque coefficients of the augmented wind turbine are independent of the incident wind speed considered.