Physically consistent responses of the global atmospheric hydrological cycle in models and observations

Robust and physically understandable responses of the global atmospheric water cycle to a warming climate are presented. By considering interannual responses to changes in surface temperature (T), observations and AMIP5 simulations agree on an increase in column integrated water vapor at the rate 7 %/K (in line with the Clausius­Clapeyron equation) and of precipitation at the rate 2-­3 %/K (in line with energetic constraints). Using simple and complex climate models, we demonstrate that radiative forcing by greenhouse gases is currently suppressing global precipitation (P) at ~ -0.15 %/decade. Along with natural variability, this can explain why observed trends in global P over the period 1988-2008 are close to zero. Regional responses in the global water cycle are strongly constrained by changes in moisture fluxes. Model simulations show an increased moisture flux into the tropical wet region at 900 hPa and an enhanced outflow (of smaller magnitude) at around 600 hPa with warming. Moisture transport explains an increase in P in the wet tropical regions and small or negative changes in the dry regions of the subtropics in CMIP5 simulations of a warming climate. For AMIP5 simulations and satellite observations, the heaviest 5-day rainfall totals increase in intensity at ~15 %/K over the ocean with reductions at all percentiles over land. The climate change response in CMIP5 simulations shows consistent increases in P over ocean and land for the highest intensities, close to the Clausius-Clapeyron scaling of 7 %/K, while P declines for the lowest percentiles, indicating that interannual variability over land may not be a good proxy for climate change. The local changes in precipitation and its extremes are highly dependent upon small shifts in the large-scale atmospheric circulation and regional feedbacks.

Estimation of optimal gravity wave parameters for climate models using data assimilation

There is a current need to constrain the parameters of gravity wave drag (GWD) schemes in climate models using observational information instead of tuning them subjectively. In this work, an inverse technique is developed using data assimilation principles to estimate gravity wave parameters. Because mostGWDschemes assume instantaneous vertical propagation of gravity waves within a column, observations in a single column can be used to formulate a one-dimensional assimilation problem to estimate the unknown parameters. We define a cost function that measures the differences between the unresolved drag inferred from observations (referred to here as the ‘observed’ GWD) and the GWD calculated with a parametrisation scheme. The geometry of the cost function presents some difficulties, including multiple minima and ill-conditioning because of the non-independence of the gravity wave parameters. To overcome these difficulties we propose a genetic algorithm to minimize the cost function, which provides a robust parameter estimation over a broad range of prescribed ‘true’ parameters. When real experiments using an independent estimate of the ‘observed’ GWD are performed, physically unrealistic values of the parameters can result due to the non-independence of the parameters. However, by constraining one of the parameters to lie within a physically realistic range, this degeneracy is broken and the other parameters are also found to lie within physically realistic ranges. This argues for the essential physical self-consistency of the gravity wave scheme. A much better fit to the observed GWD at high latitudes is obtained when the parameters are allowed to vary with latitude. However, a close fit can be obtained either in the upper or the lower part of the profiles, but not in both at the same time. This result is a consequence of assuming an isotropic launch spectrum. The changes of sign in theGWDfound in the tropical lower stratosphere, which are associated with part of the quasi-biennial oscillation forcing, cannot be captured by the parametrisation with optimal parameters.

A comprehensive benchmarking system for evaluating global vegetation models.

We present a benchmark system for global vegetation models. This system provides a quantitative evaluation of multiple simulated vegetation properties, including primary production; seasonal net ecosystem production; vegetation cover, composition and 5 height; fire regime; and runoff. The benchmarks are derived from remotely sensed gridded datasets and site-based observations. The datasets allow comparisons of annual average conditions and seasonal and inter-annual variability, and they allow the impact of spatial and temporal biases in means and variability to be assessed separately. Specifically designed metrics quantify model performance for each process, 10 and are compared to scores based on the temporal or spatial mean value of the observations and a “random” model produced by bootstrap resampling of the observations. The benchmark system is applied to three models: a simple light-use efficiency and water-balance model (the Simple Diagnostic Biosphere Model: SDBM), and the Lund-Potsdam-Jena (LPJ) and Land Processes and eXchanges (LPX) dynamic global 15 vegetation models (DGVMs). SDBM reproduces observed CO2 seasonal cycles, but its simulation of independent measurements of net primary production (NPP) is too high. The two DGVMs show little difference for most benchmarks (including the interannual variability in the growth rate and seasonal cycle of atmospheric CO2), but LPX represents burnt fraction demonstrably more accurately. Benchmarking also identified 20 several weaknesses common to both DGVMs. The benchmarking system provides a quantitative approach for evaluating how adequately processes are represented in a model, identifying errors and biases, tracking improvements in performance through model development, and discriminating among models. Adoption of such a system would do much to improve confidence in terrestrial model predictions of climate change 25 impacts and feedbacks.

Interface dynamics in planar neural field models

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from the understanding of visual hallucinations to the generation of electroencephalographic signals. Typical patterns include localized solutions in the form of traveling spots, as well as intricate labyrinthine structures. These patterns are naturally defined by the interface between low and high states of neural activity. Here we derive the equations of motion for such interfaces and show, for a Heaviside firing rate, that the normal velocity of an interface is given in terms of a non-local Biot-Savart type interaction over the boundaries of the high activity regions. This exact, but dimensionally reduced, system of equations is solved numerically and shown to be in excellent agreement with the full nonlinear integral equation defining the neural field. We develop a linear stability analysis for the interface dynamics that allows us to understand the mechanisms of pattern formation that arise from instabilities of spots, rings, stripes and fronts. We further show how to analyze neural field models with linear adaptation currents, and determine the conditions for the dynamic instability of spots that can give rise to breathers and traveling waves.

Climate determinism revisited: multiple equilibria in a complex climate model

Multiple equilibria in a coupled ocean–atmosphere–sea ice general circulation model (GCM) of an aquaplanet with many degrees of freedom are studied. Three different stable states are found for exactly the same set of parameters and external forcings: a cold state in which a polar sea ice cap extends into the midlatitudes; a warm state, which is ice free; and a completely sea ice–covered “snowball” state. Although low-order energy balance models of the climate are known to exhibit intransitivity (i.e., more than one climate state for a given set of governing equations), the results reported here are the first to demonstrate that this is a property of a complex coupled climate model with a consistent set of equations representing the 3D dynamics of the ocean and atmosphere. The coupled model notably includes atmospheric synoptic systems, large-scale circulation of the ocean, a fully active hydrological cycle, sea ice, and a seasonal cycle. There are no flux adjustments, with the system being solely forced by incoming solar radiation at the top of the atmosphere. It is demonstrated that the multiple equilibria owe their existence to the presence of meridional structure in ocean heat transport: namely, a large heat transport out of the tropics and a relatively weak high-latitude transport. The associated large midlatitude convergence of ocean heat transport leads to a preferred latitude at which the sea ice edge can rest. The mechanism operates in two very different ocean circulation regimes, suggesting that the stabilization of the large ice cap could be a robust feature of the climate system. Finally, the role of ocean heat convergence in permitting multiple equilibria is further explored in simpler models: an atmospheric GCM coupled to a slab mixed layer ocean and an energy balance model

Developing a reliable strategy to infer the effective soil hydraulic properties from field evaporation experiments for agro-hydrological models

The Richards equation has been widely used for simulating soil water movement. However, the take-up of agro-hydrological models using the basic theory of soil water flow for optimizing irrigation, fertilizer and pesticide practices is still low. This is partly due to the difficulties in obtaining accurate values for soil hydraulic properties at a field scale. Here, we use an inverse technique to deduce the effective soil hydraulic properties, based on measuring the changes in the distribution of soil water with depth in a fallow field over a long period, subject to natural rainfall and evaporation using a robust micro Genetic Algorithm. A new optimized function was constructed from the soil water contents at different depths, and the soil water at field capacity. The deduced soil water retention curve was approximately parallel but higher than that derived from published pedo-tranfer functions for a given soil pressure head. The water contents calculated from the deduced soil hydraulic properties were in good agreement with the measured values. The reliability of the deduced soil hydraulic properties was tested in reproducing data measured from an independent experiment on the same soil cropped with leek. The calculation of root water uptake took account for both soil water potential and root density distribution. Results show that the predictions of soil water contents at various depths agree fairly well with the measurements, indicating that the inverse analysis is an effective and reliable approach to estimate soil hydraulic properties, and thus permits the simulation of soil water dynamics in both cropped and fallow soils in the field accurately. (C) 2009 Elsevier B.V. All rights reserved.

Concurrent recordings of bladder afferents from multiple nerves using a microfabricated PDMS microchannel electrode array

In this paper we present a compliant neural interface designed to record bladder afferent activity. We developed the implant's microfabrication process using multiple layers of silicone rubber and thin metal so that a gold microelectrode array is embedded within four parallel polydimethylsiloxane (PDMS) microchannels (5 mm long, 100 μm wide, 100 μm deep). Electrode impedance at 1 kHz was optimized using a reactive ion etching (RIE) step, which increased the porosity of the electrode surface. The electrodes did not deteriorate after a 3 month immersion in phosphate buffered saline (PBS) at 37 °C. Due to the unique microscopic topography of the metal film on PDMS, the electrodes are extremely compliant and can withstand handling during implantation (twisting and bending) without electrical failure. The device was transplanted acutely to anaesthetized rats, and strands of the dorsal branch of roots L6 and S1 were surgically teased and inserted in three microchannels under saline immersion to allow for simultaneous in vivo recordings in an acute setting. We utilized a tripole electrode configuration to maintain background noise low and improve the signal to noise ratio. The device could distinguish two types of afferent nerve activity related to increasing bladder filling and contraction. To our knowledge, this is the first report of multichannel recordings of bladder afferent activity.

Is the Helmholtz equation really sign-indefinite?

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique at wavenumbers that correspond to eigenvalues of the Laplacian, and thus the variational problem cannot be sign-definite. However, even in cases where the solution is unique for all wavenumbers, the standard variational formulations of the Helmholtz equation are still indefinite when the wavenumber is large. This indefiniteness has implications for both the analysis and the practical implementation of finite element methods. In this paper we introduce new sign-definite (also called coercive or elliptic) formulations of the Helmholtz equation posed in either the interior of a star-shaped domain with impedance boundary conditions, or the exterior of a star-shaped domain with Dirichlet boundary conditions. Like the standard variational formulations, these new formulations arise just by multiplying the Helmholtz equation by particular test functions and integrating by parts.

Available potential energy density for a multicomponent Boussinesq fluid with arbitrary nonlinear equation of state

In this paper, the concept of available potential energy (APE) density is extended to a multicomponent Boussinesq fluid with a nonlinear equation of state. As shown by previous studies, the APE density is naturally interpreted as the work against buoyancy forces that a parcel needs to perform to move from a notional reference position at which its buoyancy vanishes to its actual position; because buoyancy can be defined relative to an arbitrary reference state, so can APE density. The concept of APE density is therefore best viewed as defining a class of locally defined energy quantities, each tied to a different reference state, rather than as a single energy variable. An important result, for which a new proof is given, is that the volume integrated APE density always exceeds Lorenz’s globally defined APE, except when the reference state coincides with Lorenz’s adiabatically re-arranged reference state of minimum potential energy. A parcel reference position is systematically defined as a level of neutral buoyancy (LNB): depending on the nature of the fluid and on how the reference state is defined, a parcel may have one, none, or multiple LNB within the fluid. Multiple LNB are only possible for a multicomponent fluid whose density depends on pressure. When no LNB exists within the fluid, a parcel reference position is assigned at the minimum or maximum geopotential height. The class of APE densities thus defined admits local and global balance equations, which all exhibit a conversion with kinetic energy, a production term by boundary buoyancy fluxes, and a dissipation term by internal diffusive effects. Different reference states alter the partition between APE production and dissipation, but neither affect the net conversion between kinetic energy and APE, nor the difference between APE production and dissipation. We argue that the possibility of constructing APE-like budgets based on reference states other than Lorenz’s reference state is more important than has been previously assumed, and we illustrate the feasibility of doing so in the context of an idealised and realistic oceanic example, using as reference states one with constant density and another one defined as the horizontal mean density field; in the latter case, the resulting APE density is found to be a reasonable approximation of the APE density constructed from Lorenz’s reference state, while being computationally cheaper.

An urban parameterization for a global climate model. Part I: Formulation and evaluation for two cities

Urbanization, the expansion of built-up areas, is an important yet less-studied aspect of land use/land cover change in climate science. To date, most global climate models used to evaluate effects of land use/land cover change on climate do not include an urban parameterization. Here, the authors describe the formulation and evaluation of a parameterization of urban areas that is incorporated into the Community Land Model, the land surface component of the Community Climate System Model. The model is designed to be simple enough to be compatible with structural and computational constraints of a land surface model coupled to a global climate model yet complex enough to explore physically based processes known to be important in determining urban climatology. The city representation is based upon the “urban canyon” concept, which consists of roofs, sunlit and shaded walls, and canyon floor. The canyon floor is divided into pervious (e.g., residential lawns, parks) and impervious (e.g., roads, parking lots, sidewalks) fractions. Trapping of longwave radiation by canyon surfaces and solar radiation absorption and reflection is determined by accounting for multiple reflections. Separate energy balances and surface temperatures are determined for each canyon facet. A one-dimensional heat conduction equation is solved numerically for a 10-layer column to determine conduction fluxes into and out of canyon surfaces. Model performance is evaluated against measured fluxes and temperatures from two urban sites. Results indicate the model does a reasonable job of simulating the energy balance of cities.

Forecasting US output growth using leading indicators: an appraisal using MIDAS models

We evaluate the predictive power of leading indicators for output growth at horizons up to 1 year. We use the MIDAS regression approach as this allows us to combine multiple individual leading indicators in a parsimonious way and to directly exploit the information content of the monthly series to predict quarterly output growth. When we use real-time vintage data, the indicators are found to have significant predictive ability, and this is further enhanced by the use of monthly data on the quarter at the time the forecast is made

Real-time forecasting of inflation and output growth with autoregressive models in the presence of data revisions

We examine how the accuracy of real-time forecasts from models that include autoregressive terms can be improved by estimating the models on ‘lightly revised’ data instead of using data from the latest-available vintage. The benefits of estimating autoregressive models on lightly revised data are related to the nature of the data revision process and the underlying process for the true values. Empirically, we find improvements in root mean square forecasting error of 2–4% when forecasting output growth and inflation with univariate models, and of 8% with multivariate models. We show that multiple-vintage models, which explicitly model data revisions, require large estimation samples to deliver competitive forecasts. Copyright © 2012 John Wiley & Sons, Ltd.

Influence of mass diffusion in sea ice dynamical models

The mixing of floes of different thickness caused by repeated deformation of the ice cover is modeled as diffusion, and the mass balance equation for sea ice accounting for mass diffusion is developed. The effect of deformational diffusion on the ice thickness balance is shown to reach 1% of the divergence effect, which describes ridging and lead formation. This means that with the same accuracy the mass balance equation can be written in terms of mean velocity rather than mean mass-weighted velocity, which one should correctly use for a multicomponent fluid such as sea ice with components identified by floe thickness. Mixing (diffusion) of sea ice also occurs because of turbulent variations in wind and ocean drags that are unresolved in models. Estimates of the importance of turbulent mass diffusion on the dynamic redistribution of ice thickness are determined using empirical data for the turbulent diffusivity. For long-time-scale prediction (≫5 days), where unresolved atmospheric motion may have a length scale on the order of the Arctic basin and the time scale is larger than the synoptic time scale of atmospheric events, turbulent mass diffusion can exceed 10% of the divergence effect. However, for short-time-scale prediction, for example, 5 days, the unresolved scales are on the order of 100 km, and turbulent diffusion is about 0.1% of the divergence effect. Because inertial effects are small in the dynamics of the sea ice pack, diffusive momentum transfer can be disregarded.

A comprehensive benchmarking system for evaluating global vegetation models

We present a benchmark system for global vegetation models. This system provides a quantitative evaluation of multiple simulated vegetation properties, including primary production; seasonal net ecosystem production; vegetation cover; composition and height; fire regime; and runoff. The benchmarks are derived from remotely sensed gridded datasets and site-based observations. The datasets allow comparisons of annual average conditions and seasonal and inter-annual variability, and they allow the impact of spatial and temporal biases in means and variability to be assessed separately. Specifically designed metrics quantify model performance for each process, and are compared to scores based on the temporal or spatial mean value of the observations and a "random" model produced by bootstrap resampling of the observations. The benchmark system is applied to three models: a simple light-use efficiency and water-balance model (the Simple Diagnostic Biosphere Model: SDBM), the Lund-Potsdam-Jena (LPJ) and Land Processes and eXchanges (LPX) dynamic global vegetation models (DGVMs). In general, the SDBM performs better than either of the DGVMs. It reproduces independent measurements of net primary production (NPP) but underestimates the amplitude of the observed CO2 seasonal cycle. The two DGVMs show little difference for most benchmarks (including the inter-annual variability in the growth rate and seasonal cycle of atmospheric CO2), but LPX represents burnt fraction demonstrably more accurately. Benchmarking also identified several weaknesses common to both DGVMs. The benchmarking system provides a quantitative approach for evaluating how adequately processes are represented in a model, identifying errors and biases, tracking improvements in performance through model development, and discriminating among models. Adoption of such a system would do much to improve confidence in terrestrial model predictions of climate change impacts and feedbacks.

Instantaneous gelation in Smoluchowski’s coagulation equation revisited

We study the solutions of the Smoluchowski coagulation equation with a regularization term which removes clusters from the system when their mass exceeds a specified cutoff size, M. We focus primarily on collision kernels which would exhibit an instantaneous gelation transition in the absence of any regularization. Numerical simulations demonstrate that for such kernels with monodisperse initial data, the regularized gelation time decreasesas M increases, consistent with the expectation that the gelation time is zero in the unregularized system. This decrease appears to be a logarithmically slow function of M, indicating that instantaneously gelling kernels may still be justifiable as physical models despite the fact that they are highly singular in the absence of a cutoff. We also study the case when a source of monomers is introduced in the regularized system. In this case a stationary state is reached. We present a complete analytic description of this regularized stationary state for the model kernel, K(m1,m2)=max{m1,m2}ν, which gels instantaneously when M→∞ if ν>1. The stationary cluster size distribution decays as a stretched exponential for small cluster sizes and crosses over to a power law decay with exponent ν for large cluster sizes. The total particle density in the stationary state slowly vanishes as [(ν−1)logM]−1/2 when M→∞. The approach to the stationary state is nontrivial: Oscillations about the stationary state emerge from the interplay between the monomer injection and the cutoff, M, which decay very slowly when M is large. A quantitative analysis of these oscillations is provided for the addition model which describes the situation in which clusters can only grow by absorbing monomers.