Calibration of uncertain flood inundation models using remotely sensed water levels

A traditional method of validating the performance of a flood model when remotely sensed data of the flood extent are available is to compare the predicted flood extent to that observed. The performance measure employed often uses areal pattern-matching to assess the degree to which the two extents overlap. Recently, remote sensing of flood extents using synthetic aperture radar (SAR) and airborne scanning laser altimetry (LIDAR) has made more straightforward the synoptic measurement of water surface elevations along flood waterlines, and this has emphasised the possibility of using alternative performance measures based on height. This paper considers the advantages that can accrue from using a performance measure based on waterline elevations rather than one based on areal patterns of wet and dry pixels. The two measures were compared for their ability to estimate flood inundation uncertainty maps from a set of model runs carried out to span the acceptable model parameter range in a GLUE-based analysis. A 1 in 5-year flood on the Thames in 1992 was used as a test event. As is typical for UK floods, only a single SAR image of observed flood extent was available for model calibration and validation. A simple implementation of a two-dimensional flood model (LISFLOOD-FP) was used to generate model flood extents for comparison with that observed. The performance measure based on height differences of corresponding points along the observed and modelled waterlines was found to be significantly more sensitive to the channel friction parameter than the measure based on areal patterns of flood extent. The former was able to restrict the parameter range of acceptable model runs and hence reduce the number of runs necessary to generate an inundation uncertainty map. A result of this was that there was less uncertainty in the final flood risk map. The uncertainty analysis included the effects of uncertainties in the observed flood extent as well as in model parameters. The height-based measure was found to be more sensitive when increased heighting accuracy was achieved by requiring that observed waterline heights varied slowly along the reach. The technique allows for the decomposition of the reach into sections, with different effective channel friction parameters used in different sections, which in this case resulted in lower r.m.s. height differences between observed and modelled waterlines than those achieved by runs using a single friction parameter for the whole reach. However, a validation of the modelled inundation uncertainty using the calibration event showed a significant difference between the uncertainty map and the observed flood extent. While this was true for both measures, the difference was especially significant for the height-based one. This is likely to be due to the conceptually simple flood inundation model and the coarse application resolution employed in this case. The increased sensitivity of the height-based measure may lead to an increased onus being placed on the model developer in the production of a valid model

The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains

Semi-analytical expressions for the momentum flux associated with orographic internal gravity waves, and closed analytical expressions for its divergence, are derived for inviscid, stationary, hydrostatic, directionally-sheared flow over mountains with an elliptical horizontal cross-section. These calculations, obtained using linear theory conjugated with a third-order WKB approximation, are valid for relatively slowly-varying, but otherwise generic wind profiles, and given in a form that is straightforward to implement in drag parametrization schemes. When normalized by the surface drag in the absence of shear, a quantity that is calculated routinely in existing drag parametrizations, the momentum flux becomes independent of the detailed shape of the orography. Unlike linear theory in the Ri → ∞ limit, the present calculations account for shear-induced amplification or reduction of the surface drag, and partial absorption of the wave momentum flux at critical levels. Profiles of the normalized momentum fluxes obtained using this model and a linear numerical model without the WKB approximation are evaluated and compared for two idealized wind profiles with directional shear, for different Richardson numbers (Ri). Agreement is found to be excellent for the first wind profile (where one of the wind components varies linearly) down to Ri = 0.5, while not so satisfactory, but still showing a large improvement relative to the Ri → ∞ limit, for the second wind profile (where the wind turns with height at a constant rate keeping a constant magnitude). These results are complementary, in the Ri > O(1) parameter range, to Broad’s generalization of the Eliassen–Palm theorem to 3D flow. They should contribute to improve drag parametrizations used in global weather and climate prediction models.

Impact of non-hydrostatic effects and trapped lee waves on mountain wave drag in directionally sheared flow

The orographic gravity wave drag produced in flow over an axisymmetric mountain when both vertical wind shear and non-hydrostatic effects are important was calculated using a semi-analytical two-layer linear model, including unidirectional or directional constant wind shear in a layer near the surface, above which the wind is constant. The drag behaviour is determined by partial wave reflection at the shear discontinuity, wave absorption at critical levels (both of which exist in hydrostatic flow), and total wave reflection at levels where the waves become evanescent (an intrinsically non-hydrostatic effect), which produces resonant trapped lee wave modes. As a result of constructive or destructive wave interference, the drag oscillates with the thickness of the constant-shear layer and the Richardson number within it (Ri), generally decreasing at low Ri and when the flow is strongly non-hydrostatic. Critical level absorption, which increases with the angle spanned by the wind velocity in the constant-shear layer, shields the surface from reflected waves, keeping the drag closer to its hydrostatic limit. While, for the parameter range considered here, the drag seldom exceeds this limit, a substantial drag fraction may be produced by trapped lee waves, particularly when the flow is strongly non-hydrostatic, the lower layer is thick and Ri is relatively high. In directionally sheared flows with Ri = O(1), the drag may be misaligned with the surface wind in a direction opposite to the shear, a behaviour which is totally due to non-trapped waves. The trapped lee wave drag, whose reaction force on the atmosphere is felt at low levels, may therefore have a distinctly different direction from the drag associated with vertically propagating waves, which acts on the atmosphere at higher levels.

The evolution of the sun’s open magnetic flux: II. full solar cycle simulations

In this paper the origin and evolution of the Sun’s open magnetic flux is considered by conducting magnetic flux transport simulations over many solar cycles. The simulations include the effects of differential rotation, meridional flow and supergranular diffusion on the radial magnetic field at the surface of the Sun as new magnetic bipoles emerge and are transported poleward. In each cycle the emergence of roughly 2100 bipoles is considered. The net open flux produced by the surface distribution is calculated by constructing potential coronal fields with a source surface from the surface distribution at regular intervals. In the simulations the net open magnetic flux closely follows the total dipole component at the source surface and evolves independently from the surface flux. The behaviour of the open flux is highly dependent on meridional flow and many observed features are reproduced by the model. However, when meridional flow is present at observed values the maximum value of the open flux occurs at cycle minimum when the polar caps it helps produce are the strongest. This is inconsistent with observations by Lockwood, Stamper and Wild (1999) and Wang, Sheeley, and Lean (2000) who find the open flux peaking 1–2 years after cycle maximum. Only in unrealistic simulations where meridional flow is much smaller than diffusion does a maximum in open flux consistent with observations occur. It is therefore deduced that there is no realistic parameter range of the flux transport variables that can produce the correct magnitude variation in open flux under the present approximations. As a result the present standard model does not contain the correct physics to describe the evolution of the Sun’s open magnetic flux over an entire solar cycle. Future possible improvements in modeling are suggested.

A multiwave range test for obstacle reconstructions with unknown physical properties

We develop a new multiwave version of the range test for shape reconstruction in inverse scattering theory. The range test [R. Potthast, et al., A ‘range test’ for determining scatterers with unknown physical properties, Inverse Problems 19(3) (2003) 533–547] has originally been proposed to obtain knowledge about an unknown scatterer when the far field pattern for only one plane wave is given. Here, we extend the method to the case of multiple waves and show that the full shape of the unknown scatterer can be reconstructed. We further will clarify the relation between the range test methods, the potential method [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Inverse Problems (Oberwolfach, 1986), Internationale Schriftenreihe zur Numerischen Mathematik, vol. 77, Birkhäuser, Basel, 1986, pp. 93–102] and the singular sources method [R. Potthast, Point sources and multipoles in inverse scattering theory, Habilitation Thesis, Göttingen, 1999]. In particular, we propose a new version of the Kirsch–Kress method using the range test and a new approach to the singular sources method based on the range test and potential method. Numerical examples of reconstructions for all four methods are provided.

Quantification of chemical and physical processes influencing ozone during long-range transport using a trajectory ensemble

During long-range transport, many distinct processes – including photochemistry, deposition, emissions and mixing – contribute to the transformation of air mass composition. Partitioning the effects of different processes can be useful when considering the sensitivity of chemical transformation to, for example, a changing environment or anthropogenic influence. However, transformation is not observed directly, since mixing ratios are measured, and models must be used to relate changes to processes. Here, four cases from the ITCT-Lagrangian 2004 experiment are studied. In each case, aircraft intercepted a distinct air mass several times during transport over the North Atlantic, providing a unique dataset and quantifying the net changes in composition from all processes. A new framework is presented to deconstruct the change in O3 mixing ratio (Δ O3) into its component processes, which were not measured directly, taking into account the uncertainty in measurements, initial air mass variability and its time evolution. The results show that the net chemical processing (Δ O3chem) over the whole simulation is greater than net physical processing (Δ O3phys) in all cases. This is in part explained by cancellation effects associated with mixing. In contrast, each case is in a regime of either net photochemical destruction (lower tropospheric transport) or production (an upper tropospheric biomass burning case). However, physical processes influence O3 indirectly through addition or removal of precursor gases, so that changes to physical parameters in a model can have a larger effect on Δ O3chem than Δ O3phys. Despite its smaller magnitude, the physical processing distinguishes the lower tropospheric export cases, since the net photochemical O3 change is −5 ppbv per day in all three cases. Processing is quantified using a Lagrangian photochemical model with a novel method for simulating mixing through an ensemble of trajectories and a background profile that evolves with them. The model is able to simulate the magnitude and variability of the observations (of O3, CO, NOy and some hydrocarbons) and is consistent with the time-average OH following air-masses inferred from hydrocarbon measurements alone (by Arnold et al., 2007). Therefore, it is a useful new method to simulate air mass evolution and variability, and its sensitivity to process parameters.

Vertical structure and physical processes of the Madden-Julian oscillation: Biases and uncertainties at short range

An analysis of diabatic heating and moistening processes from 12-36 hour lead time forecasts from 12 Global Circulation Models are presented as part of the "Vertical structure and physical processes of the Madden-Julian Oscillation (MJO)" project. A lead time of 12-36 hours is chosen to constrain the large scale dynamics and thermodynamics to be close to observations while avoiding being too close to the initial spin-up for the models as they adjust to being driven from the YOTC analysis. A comparison of the vertical velocity and rainfall with the observations and YOTC analysis suggests that the phases of convection associated with the MJO are constrained in most models at this lead time although the rainfall in the suppressed phase is typically overestimated. Although the large scale dynamics is reasonably constrained, moistening and heating profiles have large inter-model spread. In particular, there are large spreads in convective heating and moistening at mid-levels during the transition to active convection. Radiative heating and cloud parameters have the largest relative spread across models at upper levels during the active phase. A detailed analysis of time step behaviour shows that some models show strong intermittency in rainfall and differences in the precipitation and dynamics relationship between models. The wealth of model outputs archived during this project is a very valuable resource for model developers beyond the study of the MJO. In addition, the findings of this study can inform the design of process model experiments, and inform the priorities for field experiments and future observing systems.

Seasonal variations of the physical and optical characteristics of Saharan Dust: results from the Dust outflow and Deposition to the Ocean (DODO) experiment

North African dust is important for climate through its direct radiative effect on solar and terrestrial radiation and its role in the biogeochemical system. The Dust Outflow and Deposition to the Ocean project (DODO) aimed to characterize the physical and optical properties of airborne North African dust in two seasons and to use these observations to constrain model simulations, with the ultimate aim of being able to quantify the deposition of iron to the North Atlantic Ocean. The in situ properties of dust from airborne campaigns measured during February and August 2006, based at Dakar, Senegal, are presented here. Average values of the single scattering albedo (0.99, 0.98), mass specific extinction (0.85 m^2 g^-1 , 1.14 m^2 g^-1 ), asymmetry parameter (0.68, 0.68), and refractive index (1.53--0.0005i,1.53--0.0014i) for the accumulation mode were found to differ by varying degrees between the dry and wet season, respectively. It is hypothesized that these differences are due to different source regions and transport processes which also differ between the DODO campaigns. Elemental ratios of Ca/Al were found to differ between the dry and wet season (1.1 and 0.5, respectively). Differences in vertical profiles are found between seasons and between land and ocean locations and reflect the different dynamics of the seasons. Using measurements of the coarse mode size distribution and illustrative Mie calculations, the optical properties are found to be very sensitive to the presence and amount of coarse mode of mineral dust, and the importance of accurate measurements of the coarse mode of dust is highlighted.

Crop yield reduction in the tropics under climate change: Processes and uncertainties

Many modelling studies examine the impacts of climate change on crop yield, but few explore either the underlying bio-physical processes, or the uncertainty inherent in the parameterisation of crop growth and development. We used a perturbed-parameter crop modelling method together with a regional climate model (PRECIS) driven by the 2071-2100 SRES A2 emissions scenario in order to examine processes and uncertainties in yield simulation. Crop simulations used the groundnut (i.e. peanut; Arachis hypogaea L.) version of the General Large-Area Model for annual crops (GLAM). Two sets of GLAM simulations were carried out: control simulations and fixed-duration simulations, where the impact of mean temperature on crop development rate was removed. Model results were compared to sensitivity tests using two other crop models of differing levels of complexity: CROPGRO, and the groundnut model of Hammer et al. [Hammer, G.L., Sinclair, T.R., Boote, K.J., Wright, G.C., Meinke, H., and Bell, M.J., 1995, A peanut simulation model: I. Model development and testing. Agron. J. 87, 1085-1093]. GLAM simulations were particularly sensitive to two processes. First, elevated vapour pressure deficit (VPD) consistently reduced yield. The same result was seen in some simulations using both other crop models. Second, GLAM crop duration was longer, and yield greater, when the optimal temperature for the rate of development was exceeded. Yield increases were also seen in one other crop model. Overall, the models differed in their response to super-optimal temperatures, and that difference increased with mean temperature; percentage changes in yield between current and future climates were as diverse as -50% and over +30% for the same input data. The first process has been observed in many crop experiments, whilst the second has not. Thus, we conclude that there is a need for: (i) more process-based modelling studies of the impact of VPD on assimilation, and (ii) more experimental studies at super-optimal temperatures. Using the GLAM results, central values and uncertainty ranges were projected for mean 2071-2100 crop yields in India. In the fixed-duration simulations, ensemble mean yields mostly rose by 10-30%. The full ensemble range was greater than this mean change (20-60% over most of India). In the control simulations, yield stimulation by elevated CO2 was more than offset by other processes-principally accelerated crop development rates at elevated, but sub-optimal, mean temperatures. Hence, the quantification of uncertainty can facilitate relatively robust indications of the likely sign of crop yield changes in future climates. (C) 2007 Elsevier B.V. All rights reserved.

Parameter sensitivity and predictive uncertainty in a new water quality model, Q(2)

A new dynamic model of water quality, Q(2), has recently been developed, capable of simulating large branched river systems. This paper describes the application of a generalized sensitivity analysis (GSA) to Q(2) for single reaches of the River Thames in southern England. Focusing on the simulation of dissolved oxygen (DO) (since this may be regarded as a proxy for the overall health of a river); the GSA is used to identify key parameters controlling model behavior and provide a probabilistic procedure for model calibration. It is shown that, in the River Thames at least, it is more important to obtain high quality forcing functions than to obtain improved parameter estimates once approximate values have been estimated. Furthermore, there is a need to ensure reasonable simulation of a range of water quality determinands, since a focus only on DO increases predictive uncertainty in the DO simulations. The Q(2) model has been applied here to the River Thames, but it has a broad utility for evaluating other systems in Europe and around the world.

The quasi-nondispersive regimes of long extratropical baroclinic rossby waves over (slowly varying) topography

Actual energy paths of long, extratropical baroclinic Rossby waves in the ocean are difficult to describe simply because they depend on the meridional-wavenumber-to-zonal-wavenumber ratio tau, a quantity that is difficult to estimate both observationally and theoretically. This paper shows, however, that this dependence is actually weak over any interval in which the zonal phase speed varies approximately linearly with tau, in which case the propagation becomes quasi-nondispersive (QND) and describable at leading order in terms of environmental conditions (i.e., topography and stratification) alone. As an example, the purely topographic case is shown to possess three main kinds of QND ray paths. The first is a topographic regime in which the rays follow approximately the contours f/h(alpha c) = a constant (alpha(c) is a near constant fixed by the strength of the stratification, f is the Coriolis parameter, and h is the ocean depth). The second and third are, respectively, "fast" and "slow" westward regimes little affected by topography and associated with the first and second bottom-pressure-compensated normal modes studied in previous work by Tailleux and McWilliams. Idealized examples show that actual rays can often be reproduced with reasonable accuracy by replacing the actual dispersion relation by its QND approximation. The topographic regime provides an upper bound ( in general a large overestimate) of the maximum latitudinal excursions of actual rays. The method presented in this paper is interesting for enabling an optimal classification of purely azimuthally dispersive wave systems into simpler idealized QND wave regimes, which helps to rationalize previous empirical findings that the ray paths of long Rossby waves in the presence of mean flow and topography often seem to be independent of the wavenumber orientation. Two important side results are to establish that the baroclinic string function regime of Tyler and K se is only valid over a tiny range of the topographic parameter and that long baroclinic Rossby waves propagating over topography do not obey any two-dimensional potential vorticity conservation principle. Given the importance of the latter principle in geophysical fluid dynamics, the lack of it in this case makes the concept of the QND regimes all the more important, for they are probably the only alternative to provide a simple and economical description of general purely azimuthally dispersive wave systems.

Stratospheric water vapour and high climate sensitivity in a version of the HadSM3 climate model

It has been shown previously that one member of the Met Office Hadley Centre single-parameter perturbed physics ensemble – the so-called "low entrainment parameter" member – has a much higher climate sensitivity than other individual parameter perturbations. Here we show that the concentration of stratospheric water vapour in this member is over three times higher than observations, and, more importantly for climate sensitivity, increases significantly when climate warms. The large surface temperature response of this ensemble member is more consistent with stratospheric humidity change, rather than upper tropospheric clouds as has been previously suggested. The direct relationship between the bias in the control state (elevated stratospheric humidity) and the cause of the high climate sensitivity (a further increase in stratospheric humidity) lends further doubt as to the realism of this particular integration. This, together with other evidence, lowers the likelihood that the climate system's physical sensitivity is significantly higher than the likely upper range quoted in the Intergovernmental Panel on Climate Change's Fourth Assessment Report.

Quantification of physical and biological uncertainty in the simulation of the yield of a tropical crop using present-day and doubled CO2 climates

The impacts of climate change on crop productivity are often assessed using simulations from a numerical climate model as an input to a crop simulation model. The precision of these predictions reflects the uncertainty in both models. We examined how uncertainty in a climate (HadAM3) and crop General Large-Area Model (GLAM) for annual crops model affects the mean and standard deviation of crop yield simulations in present and doubled carbon dioxide (CO2) climates by perturbation of parameters in each model. The climate sensitivity parameter (lambda, the equilibrium response of global mean surface temperature to doubled CO2) was used to define the control climate. Observed 1966-1989 mean yields of groundnut (Arachis hypogaea L.) in India were simulated well by the crop model using the control climate and climates with values of lambda near the control value. The simulations were used to measure the contribution to uncertainty of key crop and climate model parameters. The standard deviation of yield was more affected by perturbation of climate parameters than crop model parameters in both the present-day and doubled CO2 climates. Climate uncertainty was higher in the doubled CO2 climate than in the present-day climate. Crop transpiration efficiency was key to crop model uncertainty in both present-day and doubled CO2 climates. The response of crop development to mean temperature contributed little uncertainty in the present-day simulations but was among the largest contributors under doubled CO2. The ensemble methods used here to quantify physical and biological uncertainty offer a method to improve model estimates of the impacts of climate change.

Chemical, physical and electrical properties of aged dodecylbenzene 2: thermal ageing of single isomers in air

The linear isomer of dodecylbenzene (DDB), 1-phenyldodecane, was aged at temperatures of 105 and 135 degrees C in air and the resultant products were analyzed using a range of analytical techniques. On ageing, the 1-phenyldodecane darkened, the acid number, dielectric loss and water content increased and significant oxidation peaks were detected in the infrared spectrum. When aged in the presence of copper, a characteristic peak at 680 nm was also detected by UV/visible spectroscopy but, compared with previous studies of a cable-grade DDB, the strength of this peak was much increased and no appreciable precipitate formation occurred. At the same time, very high values of dielectric loss were recorded. On ageing in the absence of copper, an unusually strong infrared carbonyl band was seen, which correlates well with the detection of dodecanophenone by gas chromatography / mass spectrometry and nuclear magnetic resonance spectroscopy. It was therefore concluded that the ageing process proceeds via the initial production of aromatic ketones, which may then be further oxidized to carboxylic acids. In the presence of copper, these oxidation products are present in lower quantities, most of these oxidation products being combined with the copper present in the oil to give copper carboxylates. The behavior is described in terms of a complex autoxidation mechanism, in which copper acts as both an oxidizing and a reducing agent, depending on its oxidation state and, in particular, promotes elimination via the oxidation of intermediate alkyl radical species to carbocations.

Gas-solid reactions of single crystals: a study of the reaction of bromine with single crystals of trans-cinnamic acid and a range of its derivatives by infrared and Raman microspectroscopy

Single crystals of trans-cinnamic acid and of a range of derivatives of this compound containing halogen substituents on the aromatic ring have been reacted with 165 Torr pressure of bromine vapour in a sealed desiccator at 20 degrees C for 1 week. Infrared and Raman microspectroscopic examination of the crystals shows that bromination of the aliphatic double bond, but not of the aromatic ring, has occurred. It is demonstrated also that the reaction is truly gas-solid in nature. A time-dependent study of these reactions shows that they do not follow a smooth diffusion-controlled pathway. Rather the reactions appear to be inhomogeneous and to occur at defects within the crystal. The reaction products are seen to flake from the surface of the crystal. It is shown, therefore, that these are not single crystal to single crystal transitions, as have been observed previously for the photodimerisation of trans-cinnamic acid and several of its derivatives. It is shown that there are no by-products of the reaction and that finely ground samples react to form the same products as single crystals.