Impacts of increasing the aerosol complexity in the Met Office global numerical weather prediction model.

The inclusion of the direct and indirect radiative effects of aerosols in high-resolution global numerical weather prediction (NWP) models is being increasingly recognised as important for the improved accuracy of short-range weather forecasts. In this study the impacts of increasing the aerosol complexity in the global NWP configuration of the Met Office Unified Model (MetUM) are investigated. A hierarchy of aerosol representations are evaluated including three-dimensional monthly mean speciated aerosol climatologies, fully prognostic aerosols modelled using the CLASSIC aerosol scheme and finally, initialised aerosols using assimilated aerosol fields from the GEMS project. The prognostic aerosol schemes are better able to predict the temporal and spatial variation of atmospheric aerosol optical depth, which is particularly important in cases of large sporadic aerosol events such as large dust storms or forest fires. Including the direct effect of aerosols improves model biases in outgoing long-wave radiation over West Africa due to a better representation of dust. However, uncertainties in dust optical properties propagate to its direct effect and the subsequent model response. Inclusion of the indirect aerosol effects improves surface radiation biases at the North Slope of Alaska ARM site due to lower cloud amounts in high-latitude clean-air regions. This leads to improved temperature and height forecasts in this region. Impacts on the global mean model precipitation and large-scale circulation fields were found to be generally small in the short-range forecasts. However, the indirect aerosol effect leads to a strengthening of the low-level monsoon flow over the Arabian Sea and Bay of Bengal and an increase in precipitation over Southeast Asia. Regional impacts on the African Easterly Jet (AEJ) are also presented with the large dust loading in the aerosol climatology enhancing of the heat low over West Africa and weakening the AEJ. This study highlights the importance of including a more realistic treatment of aerosol–cloud interactions in global NWP models and the potential for improved global environmental prediction systems through the incorporation of more complex aerosol schemes.

Stochastic climate theory and modeling

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as subgrid-scale parameterizations (SSPs) as well as for model error representation, uncertainty quantification, data assimilation, and ensemble prediction. The need to use stochastic approaches in weather and climate models arises because we still cannot resolve all necessary processes and scales in comprehensive numerical weather and climate prediction models. In many practical applications one is mainly interested in the largest and potentially predictable scales and not necessarily in the small and fast scales. For instance, reduced order models can simulate and predict large-scale modes. Statistical mechanics and dynamical systems theory suggest that in reduced order models the impact of unresolved degrees of freedom can be represented by suitable combinations of deterministic and stochastic components and non-Markovian (memory) terms. Stochastic approaches in numerical weather and climate prediction models also lead to the reduction of model biases. Hence, there is a clear need for systematic stochastic approaches in weather and climate modeling. In this review, we present evidence for stochastic effects in laboratory experiments. Then we provide an overview of stochastic climate theory from an applied mathematics perspective. We also survey the current use of stochastic methods in comprehensive weather and climate prediction models and show that stochastic parameterizations have the potential to remedy many of the current biases in these comprehensive models.

Field-aligned plasma flow in the quiet, mid-latitude ionosphere deduced from topside soundings

A method for quantifying diffusive flows of O+ ions in the topside ionosphere from satellite soundings is described. A departure from diffusive equilibrium alters the shape of the plasma scale-height profile near the F2-peak where ion-neutral frictional drag is large. The effect enables the evaluation of , the field-aligned flux of O+ ions relative to the neutral oxygen atom gas, using MSIS model values for the neutral thermospheric densities and temperature. Upward flow values are accurate to within about 10%, the largest sources of error being the MSIS prediction for the concentration of oxygen atoms and the plasma temperature gradient deduced from the sounding. Downward flux values are only determined to within 20%. From 60,000 topside soundings, taken at the minimum and rising phase of the solar cycle, a total of 1098 mean scale-height profiles are identified for which no storm sudden commencement had occurred in the previous 12 days and for which Kp was less than 2o, each mean profile being an average of about six soundings. A statistical study ofdeduced from these profiles shows the diurnal cycle of O+ flow in the quiet, topside ionosphere at mid-latitudes and its seasonal variations. The differences betweenand ion flux observations from incoherent scatter radars are considered using the meridional thermospheric winds predicted by a global, three-dimensional model. The mean interhemispheric flow from summer to winter is compared with predictions by a numerical model of the protonospheric coupling of conjugate ionospheres for up to 6 days following a geomagnetic storm. The observed mean (of order 3 × 1016 ions day−1 along a flux tube of area 1 m2 at 1000 km) is larger than predicted for day 6 and the suggested explanation is a decrease in upward flows from the winter, daytime ionosphere between the sixth and twelfth days.

A single-column model ensemble approach applied to the TWP-ICE experiment

Single-column models (SCM) are useful test beds for investigating the parameterization schemes of numerical weather prediction and climate models. The usefulness of SCM simulations are limited, however, by the accuracy of the best estimate large-scale observations prescribed. Errors estimating the observations will result in uncertainty in modeled simulations. One method to address the modeled uncertainty is to simulate an ensemble where the ensemble members span observational uncertainty. This study first derives an ensemble of large-scale data for the Tropical Warm Pool International Cloud Experiment (TWP-ICE) based on an estimate of a possible source of error in the best estimate product. These data are then used to carry out simulations with 11 SCM and two cloud-resolving models (CRM). Best estimate simulations are also performed. All models show that moisture-related variables are close to observations and there are limited differences between the best estimate and ensemble mean values. The models, however, show different sensitivities to changes in the forcing particularly when weakly forced. The ensemble simulations highlight important differences in the surface evaporation term of the moisture budget between the SCM and CRM. Differences are also apparent between the models in the ensemble mean vertical structure of cloud variables, while for each model, cloud properties are relatively insensitive to forcing. The ensemble is further used to investigate cloud variables and precipitation and identifies differences between CRM and SCM particularly for relationships involving ice. This study highlights the additional analysis that can be performed using ensemble simulations and hence enables a more complete model investigation compared to using the more traditional single best estimate simulation only.

Sparse density estimation on the multinomial manifold

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model. Since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold, we use the well-known Riemannian trust-region (RTR) algorithm for solving this problem. The first- and second-order Riemannian geometry of the multinomial manifold are derived and utilized in the RTR algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimators.

Estimation of Gaussian process regression model using probability distance measures

A new class of parameter estimation algorithms is introduced for Gaussian process regression (GPR) models. It is shown that the integration of the GPR model with probability distance measures of (i) the integrated square error and (ii) Kullback–Leibler (K–L) divergence are analytically tractable. An efficient coordinate descent algorithm is proposed to iteratively estimate the kernel width using golden section search which includes a fast gradient descent algorithm as an inner loop to estimate the noise variance. Numerical examples are included to demonstrate the effectiveness of the new identification approaches.

On-line Gaussian mixture density estimator for adaptive minimum bit-error-rate beamforming receivers

We develop an on-line Gaussian mixture density estimator (OGMDE) in the complex-valued domain to facilitate adaptive minimum bit-error-rate (MBER) beamforming receiver for multiple antenna based space-division multiple access systems. Specifically, the novel OGMDE is proposed to adaptively model the probability density function of the beamformer’s output by tracking the incoming data sample by sample. With the aid of the proposed OGMDE, our adaptive beamformer is capable of updating the beamformer’s weights sample by sample to directly minimize the achievable bit error rate (BER). We show that this OGMDE based MBER beamformer outperforms the existing on-line MBER beamformer, known as the least BER beamformer, in terms of both the convergence speed and the achievable BER.

Low complexity equalization of HCM systems with DPFFT demodulation over doubly-selective channels

To mitigate the inter-carrier interference (ICI) of doubly-selective (DS) fading channels, we consider a hybrid carrier modulation (HCM) system employing the discrete partial fast Fourier transform (DPFFT) demodulation and the banded minimum mean square error (MMSE) equalization in this letter. We first provide the discrete form of partial FFT demodulation, then apply the banded MMSE equalization to suppress the residual interference at the receiver. The proposed algorithm has been demonstrated, via numerical simulations, to be its superior over the single carrier modulation (SCM) system and circularly prefixed orthogonal frequency division multiplexing (OFDM) system over a typical DS channel. Moreover, it represents a good trade-off between computational complexity and performance.

The error of representation: basic understanding

Representation error arises from the inability of the forecast model to accurately simulate the climatology of the truth. We present a rigorous framework for understanding this kind of error of representation. This framework shows that the lack of an inverse in the relationship between the true climatology (true attractor) and the forecast climatology (forecast attractor) leads to the error of representation. A new gain matrix for the data assimilation problem is derived that illustrates the proper approaches one may take to perform Bayesian data assimilation when the observations are of states on one attractor but the forecast model resides on another. This new data assimilation algorithm is the optimal scheme for the situation where the distributions on the true attractor and the forecast attractors are separately Gaussian and there exists a linear map between them. The results of this theory are illustrated in a simple Gaussian multivariate model.

Two fast radiative transfer methods to improve the temporal sampling of clouds in numerical weather prediction and climate models

The high computational cost of calculating the radiative heating rates in numerical weather prediction (NWP) and climate models requires that calculations are made infrequently, leading to poor sampling of the fast-changing cloud field and a poor representation of the feedback that would occur. This paper presents two related schemes for improving the temporal sampling of the cloud field. Firstly, the ‘split time-stepping’ scheme takes advantage of the independent nature of the monochromatic calculations of the ‘correlated-k’ method to split the calculation into gaseous absorption terms that are highly dependent on changes in cloud (the optically thin terms) and those that are not (optically thick). The small number of optically thin terms can then be calculated more often to capture changes in the grey absorption and scattering associated with cloud droplets and ice crystals. Secondly, the ‘incremental time-stepping’ scheme uses a simple radiative transfer calculation using only one or two monochromatic calculations representing the optically thin part of the atmospheric spectrum. These are found to be sufficient to represent the heating rate increments caused by changes in the cloud field, which can then be added to the last full calculation of the radiation code. We test these schemes in an operational forecast model configuration and find a significant improvement is achieved, for a small computational cost, over the current scheme employed at the Met Office. The ‘incremental time-stepping’ scheme is recommended for operational use, along with a new scheme to correct the surface fluxes for the change in solar zenith angle between radiation calculations.

Imbalanced land-surface water budgets in a numerical weather prediction system

There has been a significant increase in the skill and resolution of numerical weather prediction models (NWPs) in recent decades, extending the time scales of useful weather predictions. The land-surface models (LSMs) of NWPs are often employed in hydrological applications, which raises the question of how hydrologically representative LSMs really are. In this paper, precipitation (P), evaporation (E) and runoff (R) from the European Centre for Medium-Range Weather Forecasts (ECMWF) global models were evaluated against observational products. The forecasts differ substantially from observed data for key hydrological variables. In addition, imbalanced surface water budgets, mostly caused by data assimilation, were found on both global (P-E) and basin scales (P-E-R), with the latter being more important. Modeled surface fluxes should be used with care in hydrological applications and further improvement in LSMs in terms of process descriptions, resolution and estimation of uncertainties is needed to accurately describe the land-surface water budgets.

A route to systematic error in forecasts of Rossby waves

Recent work has shown that both the amplitude of upper-level Rossby waves and the tropopause sharpness decrease with forecast lead time for several days in some operational weather forecast systems. In this contribution, the evolution of error growth in a case study of this forecast error type is diagnosed through analysis of operational forecasts and hindcast simulations. Potential vorticity (PV) on the 320-K isentropic surface is used to diagnose Rossby waves. The Rossby-wave forecast error in the operational ECMWF high-resolution forecast is shown to be associated with errors in the forecast of a warm conveyor belt (WCB) through trajectory analysis and an error metric for WCB outflows. The WCB forecast error is characterised by an overestimation of WCB amplitude, a location of the WCB outflow regions that is too far to the southeast, and a resulting underestimation of the magnitude of the negative PV anomaly in the outflow. Essentially the same forecast error development also occurred in all members of the ECMWF Ensemble Prediction System and the Met Office MOGREPS-15 suggesting that in this case model error made an important contribution to the development of forecast error in addition to initial condition error. Exploiting this forecast error robustness, a comparison was performed between the realised flow evolution, proxied by a sequence of short-range simulations, and a contemporaneous forecast. Both the proxy to the realised flow and the contemporaneous forecast a were produced with the Met Office Unified Model enhanced with tracers of diabatic processes modifying potential temperature and PV. Clear differences were found in the way potential temperature and PV are modified in the WCB between proxy and forecast. These results demonstrate that differences in potential temperature and PV modification in the WCB can be responsible for forecast errors in Rossby waves.

A Posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws

In this work we construct reliable a posteriori estimates for some semi- (spatially) discrete discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the relative entropy stability framework, which leads to error control in the case of smooth solutions. The methodology we use is quite general and allows for a posteriori control of discontinuous Galerkin schemes with standard flux choices which appear in the approximation of conservation laws. In addition to the analysis, we conduct some numerical benchmarking to test the robustness of the resultant estimator.

Two-way CSI-assisted AF relaying with HPA nonlinearity

In this paper, we investigate half-duplex two-way dual-hop channel state information (CSI)-assisted amplify-and-forward (AF) relaying in the presence of high-power amplifier (HPA) nonlinearity at relays. The expression for the end-to-end signal-to-noise ratio (SNR) is derived as per the modified system model by taking into account the interference caused by relaying scheme and HPA nonlinearity. The system performance of the considered relaying network is evaluated in terms of average symbol error probability (SEP) in Nakagami-$m$ fading channels, by making use of the moment-generating function (MGF) approach. Numerical results are provided and show the effects of several parameters, such as quadrature amplitude modulation (QAM) order, number of relays, HPA parameters, and Nakagami parameter, on performance.