Variational data assimilation for parameter estimation: application to a simple morphodynamic model

Data assimilation is a sophisticated mathematical technique for combining observational data with model predictions to produce state and parameter estimates that most accurately approximate the current and future states of the true system. The technique is commonly used in atmospheric and oceanic modelling, combining empirical observations with model predictions to produce more accurate and well-calibrated forecasts. Here, we consider a novel application within a coastal environment and describe how the method can also be used to deliver improved estimates of uncertain morphodynamic model parameters. This is achieved using a technique known as state augmentation. Earlier applications of state augmentation have typically employed the 4D-Var, Kalman filter or ensemble Kalman filter assimilation schemes. Our new method is based on a computationally inexpensive 3D-Var scheme, where the specification of the error covariance matrices is crucial for success. A simple 1D model of bed-form propagation is used to demonstrate the method. The scheme is capable of recovering near-perfect parameter values and, therefore, improves the capability of our model to predict future bathymetry. Such positive results suggest the potential for application to more complex morphodynamic models.

Characteristics of Langmuir Turbulence in the Ocean Mixed Layer

This study uses large-eddy simulation (LES) to investigate the characteristics of Langmuir turbulence through the turbulent kinetic energy (TKE) budget. Based on an analysis of the TKE budget a velocity scale for Langmuir turbulence is proposed. The velocity scale depends on both the friction velocity and the surface Stokes drift associated with the wave field. The scaling leads to unique profiles of nondimensional dissipation rate and velocity component variances when the Stokes drift of the wave field is sufficiently large compared to the surface friction velocity. The existence of such a scaling shows that Langmuir turbulence can be considered as a turbulence regime in its own right, rather than a modification of shear-driven turbulence. Comparisons are made between the LES results and observations, but the lack of information concerning the wave field means these are mainly restricted to comparing profile shapes. The shapes of the LES profiles are consistent with observed profiles. The dissipation length scale for Langmuir turbulence is found to be similar to the dissipation length scale in the shear-driven boundary layer. Beyond this it is not possible to test the proposed scaling directly using available data. Entrainment at the base of the mixed layer is shown to be significantly enhanced over that due to normal shear turbulence.

Surface wave processes in air-sea interaction

We review briefly recent progress on understanding the role of surface waves on the marine atmospheric boundary layer and the ocean mixed layer and give a global perspective on these processes by analysing ERA-40 data. Ocean surface waves interact with the marine atmospheric boundary layer in two broad regimes: (i) the conventional wind-driven wave regime, when fast winds blow over slower moving waves, and (ii) a wave-driven wind regime when long wavelength swell propagates under low winds, and generates a wave-driven jet in the lower part of the marine boundary layer. Analysis of ERA-40 data indicates that the wave-driven wind regime is as prevalent as the conventional wind-driven regime. Ocean surface waves also change profoundly mixing in the ocean mixed layer through generation of Langmuir circulation. Results from large-eddy simulation are used here to develop a scaling for the resulting Langmuir turbulence, which is a necessary step in developing a parametrization of the process. ERA-40 data is then used to show that the Langmuir regime is the predominant regime over much of the global ocean, providing a compelling motivation for parameterising this process in ocean general circulation models.

The relationship between diffuse spectral reflectance of the soil and its cation exchange capacity is scale-dependent

Diffuse reflectance spectroscopy (DRS) is increasingly being used to predict numerous soil physical, chemical and biochemical properties. However, soil properties and processes vary at different scales and, as a result, relationships between soil properties often depend on scale. In this paper we report on how the relationship between one such property, cation exchange capacity (CEC), and the DRS of the soil depends on spatial scale. We show this by means of a nested analysis of covariance of soils sampled on a balanced nested design in a 16 km × 16 km area in eastern England. We used principal components analysis on the DRS to obtain a reduced number of variables while retaining key variation. The first principal component accounted for 99.8% of the total variance, the second for 0.14%. Nested analysis of the variation in the CEC and the two principal components showed that the substantial variance components are at the > 2000-m scale. This is probably the result of differences in soil composition due to parent material. We then developed a model to predict CEC from the DRS and used partial least squares (PLS) regression do to so. Leave-one-out cross-validation results suggested a reasonable predictive capability (R2 = 0.71 and RMSE = 0.048 molc kg− 1). However, the results from the independent validation were not as good, with R2 = 0.27, RMSE = 0.056 molc kg− 1 and an overall correlation of 0.52. This would indicate that DRS may not be useful for predictions of CEC. When we applied the analysis of covariance between predicted and observed we found significant scale-dependent correlations at scales of 50 and 500 m (0.82 and 0.73 respectively). DRS measurements can therefore be useful to predict CEC if predictions are required, for example, at the field scale (50 m). This study illustrates that the relationship between DRS and soil properties is scale-dependent and that this scale dependency has important consequences for prediction of soil properties from DRS data

A new set of orthogonal patterns in weather and climate: Optimally interpolated patterns.

A new spectral-based approach is presented to find orthogonal patterns from gridded weather/climate data. The method is based on optimizing the interpolation error variance. The optimally interpolated patterns (OIP) are then given by the eigenvectors of the interpolation error covariance matrix, obtained using the cross-spectral matrix. The formulation of the approach is presented, and the application to low-dimension stochastic toy models and to various reanalyses datasets is performed. In particular, it is found that the lowest-frequency patterns correspond to largest eigenvalues, that is, variances, of the interpolation error matrix. The approach has been applied to the Northern Hemispheric (NH) and tropical sea level pressure (SLP) and to the Indian Ocean sea surface temperature (SST). Two main OIP patterns are found for the NH SLP representing respectively the North Atlantic Oscillation and the North Pacific pattern. The leading tropical SLP OIP represents the Southern Oscillation. For the Indian Ocean SST, the leading OIP pattern shows a tripole-like structure having one sign over the eastern and north- and southwestern parts and an opposite sign in the remaining parts of the basin. The pattern is also found to have a high lagged correlation with the Niño-3 index with 6-months lag.

U.K. HiGEM: The New U.K. High-Resolution Global Environment Model—Model Description and Basic Evaluation

This article describes the development and evaluation of the U.K.’s new High-Resolution Global Environmental Model (HiGEM), which is based on the latest climate configuration of the Met Office Unified Model, known as the Hadley Centre Global Environmental Model, version 1 (HadGEM1). In HiGEM, the horizontal resolution has been increased to 0.83° latitude × 1.25° longitude for the atmosphere, and 1/3° × 1/3° globally for the ocean. Multidecadal integrations of HiGEM, and the lower-resolution HadGEM, are used to explore the impact of resolution on the fidelity of climate simulations. Generally, SST errors are reduced in HiGEM. Cold SST errors associated with the path of the North Atlantic drift improve, and warm SST errors are reduced in upwelling stratocumulus regions where the simulation of low-level cloud is better at higher resolution. The ocean model in HiGEM allows ocean eddies to be partially resolved, which dramatically improves the representation of sea surface height variability. In the Southern Ocean, most of the heat transports in HiGEM is achieved by resolved eddy motions, which replaces the parameterized eddy heat transport in the lower-resolution model. HiGEM is also able to more realistically simulate small-scale features in the wind stress curl around islands and oceanic SST fronts, which may have implications for oceanic upwelling and ocean biology. Higher resolution in both the atmosphere and the ocean allows coupling to occur on small spatial scales. In particular, the small-scale interaction recently seen in satellite imagery between the atmosphere and tropical instability waves in the tropical Pacific Ocean is realistically captured in HiGEM. Tropical instability waves play a role in improving the simulation of the mean state of the tropical Pacific, which has important implications for climate variability. In particular, all aspects of the simulation of ENSO (spatial patterns, the time scales at which ENSO occurs, and global teleconnections) are much improved in HiGEM.

Comparing sampling needs for variograms of soil properties computed by the method of moments and residual maximum likelihood

It has been generally accepted that the method of moments (MoM) variogram, which has been widely applied in soil science, requires about 100 sites at an appropriate interval apart to describe the variation adequately. This sample size is often larger than can be afforded for soil surveys of agricultural fields or contaminated sites. Furthermore, it might be a much larger sample size than is needed where the scale of variation is large. A possible alternative in such situations is the residual maximum likelihood (REML) variogram because fewer data appear to be required. The REML method is parametric and is considered reliable where there is trend in the data because it is based on generalized increments that filter trend out and only the covariance parameters are estimated. Previous research has suggested that fewer data are needed to compute a reliable variogram using a maximum likelihood approach such as REML, however, the results can vary according to the nature of the spatial variation. There remain issues to examine: how many fewer data can be used, how should the sampling sites be distributed over the site of interest, and how do different degrees of spatial variation affect the data requirements? The soil of four field sites of different size, physiography, parent material and soil type was sampled intensively, and MoM and REML variograms were calculated for clay content. The data were then sub-sampled to give different sample sizes and distributions of sites and the variograms were computed again. The model parameters for the sets of variograms for each site were used for cross-validation. Predictions based on REML variograms were generally more accurate than those from MoM variograms with fewer than 100 sampling sites. A sample size of around 50 sites at an appropriate distance apart, possibly determined from variograms of ancillary data, appears adequate to compute REML variograms for kriging soil properties for precision agriculture and contaminated sites. (C) 2007 Elsevier B.V. All rights reserved.

Do High-Frequency Eddies Contribute to Low-Frequency Teleconnection Tendencies?*

An isentropic potential vorticity (PV) budget analysis is employed to examine the role of synoptic transients, advection, and nonconservative processes as forcings for the evolution of the low-frequency PV anomalies locally and those associated with the North Atlantic Oscillation (NAO) and the Pacific–North American (PNA) pattern. Specifically, the rate of change of the low-frequency PV is expressed as a sum of tendencies due to divergence of eddy transport, advection by the low-frequency flow (hereafter referred to as advection), and the residual nonconservative processes. The balance between the variances and covariances of these terms is illustrated using a novel vector representation. It is shown that for most locations, as well as for the PNA pattern, the PV variability is dominantly driven by advection. The eddy forcing explains a small amount of the tendency variance. For the NAO, the role of synoptic eddy fluxes is found to be stronger, explaining on average 15% of the NAO tendency variance. Previous studies have not assessed quantitively how the various forcings balance the tendency. Thus, such studies may have overestimated the role of eddy fluxes for the evolution of teleconnections by examining, for example, composites and regressions that indicate maintenance, rather than evolution driven by the eddies. The authors confirm this contrasting view by showing that during persistent blocking (negative NAO) episodes the eddy driving is relatively stronger.

The role of eddies in driving the tropospheric response to stratospheric heating perturbations

A simplified general circulation model has been used to investigate the chain of causality whereby changes in tropospheric circulation and temperature are produced in response to stratospheric heating perturbations. Spinup ensemble experiments have been performed to examine the evolution of the tropospheric circulation in response to such perturbations. The primary aim of these experiments is to investigate the possible mechanisms whereby a tropospheric response to changing solar activity over the 11-yr solar cycle could be produced in response to heating of the equatorial lower stratosphere. This study therefore focuses on a stratospheric heating perturbation in which the heating is largest in the tropics. For comparison, experiments are also performed in which the stratosphere is heated uniformly at all latitudes and in which it is heated preferentially in the polar region. Thus, the mechanisms discussed have a wider relevance for the impact of stratospheric perturbations on the troposphere. The results demonstrate the importance of changing eddy momentum fluxes in driving the tropospheric response. This is confirmed by the lack of a similar response in a zonally symmetric model with fixed eddy forcing. Furthermore, it is apparent that feedback between the tropospheric eddy fluxes and tropospheric circulation changes is required to produce the full model response. The quasigeostrophic index of refraction is used to diagnose the cause of the changes in eddy behavior. It is demonstrated that the latitudinal extent of stratospheric heating is important in determining the direction of displacement of the tropospheric jet and storm track.

Formation and circulation of the cold intermediate layer in the Gulf of Saint Lawrence

[ 1] The local heat content and formation rate of the cold intermediate layer (CIL) in the Gulf of Saint Lawrence are examined using a combination of new in situ wintertime observations and a three-dimensional numerical model. The field observations consist of five moorings located throughout the gulf over the period of November 2002 to June 2003. The observations demonstrate a substantially deeper surface mixed layer in the central and northeast gulf than in regions downstream of the buoyant surface outflow from the Saint Lawrence Estuary. The mixed-layer depth in the estuary remains shallow (< 60 m) throughout winter, with the arrival of a layer of near-freezing waters between 40 and 100 m depth in April. An eddy-permitting ice-ocean model with realistic forcing is used to hindcast the period of observation. The model simulates well the seasonal evolution of mixed-layer depth and CIL heat content. Although the greatest heat losses occur in the northeast, the most significant change in CIL heat content over winter occurs in the Anticosti Trough. The observed renewal of CIL in the estuary in spring is captured by the model. The simulation highlights the role of the northwest gulf, and in particular, the separation of the Gaspe Current, in controlling the exchange of CIL between the estuary and the gulf. In order to isolate the effects of inflow through the Strait of Belle Isle on the CIL heat content, we examine a sensitivity experiment in which the strait is closed. This simulation shows that the inflow has a less important effect on the CIL than was suggested by previous studies.

Fast approximate calculation of multiply scattered lidar returns

An efficient method is described for the approximate calculation of the intensity of multiply scattered lidar returns. It divides the outgoing photons into three populations, representing those that have experienced zero, one, and more than one forward-scattering event. Each population is parameterized at each range gate by its total energy, its spatial variance, the variance of photon direction, and the covariance, of photon direction and position. The result is that for an N-point profile the calculation is O(N-2) efficient and implicitly includes up to N-order scattering, making it ideal for use in iterative retrieval algorithms for which speed is crucial. In contrast, models that explicitly consider each scattering order separately are at best O(N-m/m!) efficient for m-order scattering and often cannot be performed to more than the third or fourth order in retrieval algorithms. For typical cloud profiles and a wide range of lidar fields of view, the new algorithm is as accurate as an explicit calculation truncated at the fifth or sixth order but faster by several orders of magnitude. (C) 2006 Optical Society of America.

The cumulus-capped boundary layer. I: Modelling transports in the cloud layer

Scalar-flux budgets have been obtained from large-eddy simulations (LESs) of the cumulus-capped boundary layer. Parametrizations of the terms in the budgets are discussed, and two parametrizations for the transport term in the cloud layer are proposed. It is shown that these lead to two models for scalar transports by shallow cumulus convection. One is equivalent to the subsidence detrainment form of convective tendencies obtained from mass-flux parametrizations of cumulus convection. The second is a flux-gradient relationship that is similar in form to the non-local parametrizations of turbulent transports in the dry-convective boundary layer. Using the fluxes of liquid-water potential temperature and total water content from the LES, it is shown that both models are reasonable diagnostic relations between fluxes and the vertical gradients of the mean fields. The LESs used in this study are for steady-state convection and it is possible to treat the fluxes of conserved thermodynamic variables as independent, and ignore the effects of condensation. It is argued that a parametrization of cumulus transports in a model of the cumulus-capped boundary layer should also include an explicit representation of condensation. A simple parametrization of the liquid-water flux in terms of conserved variables is also derived.

The physical properties of the atmosphere in the new Hadley Centre Global Environmental Model (HadGEM1). Part II: Aspects of variability and regional climate

The performance of the atmospheric component of the new Hadley Centre Global Environmental Model (HadGEM1) is assessed in terms of its ability to represent a selection of key aspects of variability in the Tropics and extratropics. These include midlatitude storm tracks and blocking activity, synoptic variability over Europe, and the North Atlantic Oscillation together with tropical convection, the Madden-Julian oscillation, and the Asian summer monsoon. Comparisons with the previous model, the Third Hadley Centre Coupled Ocean-Atmosphere GCM (HadCM3), demonstrate that there has been a considerable increase in the transient eddy kinetic energy (EKE), bringing HadGEM1 into closer agreement with current reanalyses. This increase in EKE results from the increased horizontal resolution and, in combination with the improved physical parameterizations, leads to improvements in the representation of Northern Hemisphere storm tracks and blocking. The simulation of synoptic weather regimes over Europe is also greatly improved compared to HadCM3, again due to both increased resolution and other model developments. The variability of convection in the equatorial region is generally stronger and closer to observations than in HadCM3. There is, however, still limited convective variance coincident with several of the observed equatorial wave modes. Simulation of the Madden-Julian oscillation is improved in HadGEM1: both the activity and interannual variability are increased and the eastward propagation, although slower than observed, is much better simulated. While some aspects of the climatology of the Asian summer monsoon are improved in HadGEM1, the upper-level winds are too weak and the simulation of precipitation deteriorates. The dominant modes of monsoon interannual variability are similar in the two models, although in HadCM3 this is linked to SST forcing, while in HadGEM1 internal variability dominates. Overall, analysis of the phenomena considered here indicates that HadGEM1 performs well and, in many important respects, improves upon HadCM3. Together with the improved representation of the mean climate, this improvement in the simulation of atmospheric variability suggests that HadGEM1 provides a sound basis for future studies of climate and climate change.

A new perspective on blocking

It is argued that the essential aspect of atmospheric blocking may be seen in the wave breaking of potential temperature (θ) on a potential vorticity (PV) surface, which may be identified with the tropopause, and the consequent reversal of the usual meridional temperature gradient of θ. A new dynamical blocking index is constructed using a meridional θ difference on a PV surface. Unlike in previous studies, the central blocking latitude about which this difference is constructed is allowed to vary with longitude. At each longitude it is determined by the latitude at which the climatological high-pass transient eddy kinetic energy is a maximum. Based on the blocking index, at each longitude local instantaneous blocking, large-scale blocking, and blocking episodes are defined. For longitudinal sectors, sector blocking and sector blocking episodes are also defined. The 5-yr annual climatologies of the three longitudinally defined blocking event frequencies and the seasonal climatologies of blocking episode frequency are shown. The climatologies all pick out the eastern North Atlantic–Europe and eastern North Pacific–western North America regions. There is evidence that Pacific blocking shifts into the western central Pacific in the summer. Sector blocking episodes of 4 days or more are shown to exhibit different persistence characteristics to shorter events, showing that blocking is not just the long timescale tail end of a distribution. The PV–θ index results for the annual average location of Pacific blocking agree with synoptic studies but disagree with modern quantitative height field–based studies. It is considered that the index used here is to be preferred anyway because of its dynamical basis. However, the longitudinal discrepancy is found to be associated with the use in the height field index studies of a central blocking latitude that is independent of longitude. In particular, the use in the North Pacific of a latitude that is suitable for the eastern North Atlantic leads to spurious categorization of blocking there. Furthermore, the PV–θ index is better able to detect Ω blocking than conventional height field indices.

Where do winds drive the Antarctic Circumpolar Current?

The strength of the Antarctic Circumpolar Current (ACC) is believed to depend on the westerly wind stress blowing over the Southern Ocean, although the exact relationship between winds and circumpolar transport is yet to be determined. Here we show, based on theoretical arguments and a hierarchy of numerical modeling experiments, that the global pycnocline depth and the baroclinic ACC transport are set by an integral measure of the wind stress over the path of the ACC, taking into account its northward deflection. Our results assume that the mesoscale eddy diffusivity is independent of the mean flow; while the relationship between wind stress and ACC transport will be more complicated in an eddy-saturated regime, our conclusion that the ACC is driven by winds over the circumpolar streamlines is likely to be robust.