A joint state and parameter estimation scheme for nonlinear dynamical systems

We present a novel algorithm for concurrent model state and parameter estimation in nonlinear dynamical systems. The new scheme uses ideas from three dimensional variational data assimilation (3D-Var) and the extended Kalman filter (EKF) together with the technique of state augmentation to estimate uncertain model parameters alongside the model state variables in a sequential filtering system. The method is relatively simple to implement and computationally inexpensive to run for large systems with relatively few parameters. We demonstrate the efficacy of the method via a series of identical twin experiments with three simple dynamical system models. The scheme is able to recover the parameter values to a good level of accuracy, even when observational data are noisy. We expect this new technique to be easily transferable to much larger models.

The sensitivity of convective aggregation to diabatic processes in idealized radiative-convective equilibrium simulations

Idealized explicit convection simulations of the Met Office Unified Model exhibit spontaneous self-aggregation in radiative-convective equilibrium, as seen in other models in previous studies. This self-aggregation is linked to feedbacks between radiation, surface fluxes, and convection, and the organization is intimately related to the evolution of the column water vapor field. Analysis of the budget of the spatial variance of column-integrated frozen moist static energy (MSE), following Wing and Emanuel [2014], reveals that the direct radiative feedback (including significant cloud longwave effects) is dominant in both the initial development of self-aggregation and the maintenance of an aggregated state. A low-level circulation at intermediate stages of aggregation does appear to transport MSE from drier to moister regions, but this circulation is mostly balanced by other advective effects of opposite sign and is forced by horizontal anomalies of convective heating (not radiation). Sensitivity studies with either fixed prescribed radiative cooling, fixed prescribed surface fluxes, or both do not show full self-aggregation from homogeneous initial conditions, though fixed surface fluxes do not disaggregate an initialized aggregated state. A sensitivity study in which rain evaporation is turned off shows more rapid self-aggregation, while a run with this change plus fixed radiative cooling still shows strong self-aggregation, supporting a “moisture memory” effect found in Muller and Bony [2015]. Interestingly, self-aggregation occurs even in simulations with sea surface temperatures (SSTs) of 295 K and 290 K, with direct radiative feedbacks dominating the budget of MSE variance, in contrast to results in some previous studies.

Characterisation of convective regimes over the British Isles

Convection-permitting modelling has led to a step change in forecasting convective events. However, convection occurs within different regimes which exhibit different forecast behaviour. A convective adjustment timescale can be used to distinguish between these regimes and examine their associated predictability. The convective adjustment timescale is calculated from radiosonde ascents and found to be consistent with that derived from convection-permitting model forecasts. The model-derived convective adjustment timescale is then examined for three summers in the British Isles to determine characteristics of the convective regimes for this maritime region. Convection in the British Isles is predominantly in convective quasi-equilibrium with 85%of convection having a timescale less than or equal to three hours. This percentage varies spatially with more non-equilibriumevents occurring in the south and southwest. The convective adjustment timescale exhibits a diurnal cycle over land. The nonequilibrium regime occurs more frequently at mid-range wind speeds and with winds from southerly to westerly sectors. Most non-equilibrium convective events in the British Isles are initiated near large coastal orographic gradients or on the European continent. Thus, the convective adjustment timescale is greatest when the location being examined is immediately downstream of large orographic gradients and decreases with distance from the convective initiation region. The dominance of convective quasiequilibrium conditions over the British Isles argues for the use of large-member ensembles in probabilistic forecasts for this region.

Interactions between wind-blown snow redistribution and melt ponds in a coupled ocean–sea ice model

Introducing a parameterization of the interactions between wind-driven snow depth changes and melt pond evolution allows us to improve large scale models. In this paper we have implemented an explicit melt pond scheme and, for the first time, a wind dependant snow redistribution model and new snow thermophysics into a coupled ocean–sea ice model. The comparison of long-term mean statistics of melt pond fractions against observations demonstrates realistic melt pond cover on average over Arctic sea ice, but a clear underestimation of the pond coverage on the multi-year ice (MYI) of the western Arctic Ocean. The latter shortcoming originates from the concealing effect of persistent snow on forming ponds, impeding their growth. Analyzing a second simulation with intensified snow drift enables the identification of two distinct modes of sensitivity in the melt pond formation process. First, the larger proportion of wind-transported snow that is lost in leads directly curtails the late spring snow volume on sea ice and facilitates the early development of melt ponds on MYI. In contrast, a combination of higher air temperatures and thinner snow prior to the onset of melting sometimes make the snow cover switch to a regime where it melts entirely and rapidly. In the latter situation, seemingly more frequent on first-year ice (FYI), a smaller snow volume directly relates to a reduced melt pond cover. Notwithstanding, changes in snow and water accumulation on seasonal sea ice is naturally limited, which lessens the impacts of wind-blown snow redistribution on FYI, as compared to those on MYI. At the basin scale, the overall increased melt pond cover results in decreased ice volume via the ice-albedo feedback in summer, which is experienced almost exclusively by MYI.

On the parameterization of turbulent surface fluxes over heterogeneous sea ice surfaces

Turbulent surface fluxes of momentum and sensible and latent heat as well as surface temperature, air temperature, air humidity, and wind speed were measured by the German Falcon research aircraft over the marginal ice zone (MIZ) of the northern Baltic Sea and the Fram Strait. Applying the bulk formulas and the stability functions to the measurements, the roughness lengths for momentum z0, sensible heat zT, and latent heat zq were calculated. As mean values over a wide range of sea ice conditions, we obtain z0 = 5 � 10�4 m, zT = 1 � 10�8 m, and zq = 1 � 10�7 m. These correspond to the following mean values (± standard deviations) of neutral transfer coefficients reduced to 10 m height, CDN10 = (1.9 ± 0.8) � 10�3, CHN10 = (0.9 ± 0.3) � 10�3, and CEN10 = (1.0 ± 0.2) � 10�3. An average ratio of z0/zT � 104 was observed over the range of 10�6 m < z0 < 10�2 m and differs from previously published results over compact sea ice (10�1 < z0/zT < 103). Other observational results over heterogeneous sea ice do not exist. However, our z0/zT ratio approximately agrees with observations over heterogeneous land surfaces. Flux parameterizations based on commonly used roughness lengths ratios (z0 = zT = zq) overestimate the surface heat fluxes compared to our measurements by more than 100%.

The COnvective Precipitation Experiment (COPE): investigating the origins of heavy precipitation in the southwestern UK

A recent field campaign in southwest England used numerical modeling integrated with aircraft and radar observations to investigate the dynamic and microphysical interactions that can result in heavy convective precipitation. The COnvective Precipitation Experiment (COPE) was a joint UK-US field campaign held during the summer of 2013 in the southwest peninsula of England, designed to study convective clouds that produce heavy rain leading to flash floods. The clouds form along convergence lines that develop regularly due to the topography. Major flash floods have occurred in the past, most famously at Boscastle in 2004. It has been suggested that much of the rain was produced by warm rain processes, similar to some flash floods that have occurred in the US. The overarching goal of COPE is to improve quantitative convective precipitation forecasting by understanding the interactions of the cloud microphysics and dynamics and thereby to improve NWP model skill for forecasts of flash floods. Two research aircraft, the University of Wyoming King Air and the UK BAe 146, obtained detailed in situ and remote sensing measurements in, around, and below storms on several days. A new fast-scanning X-band dual-polarization Doppler radar made 360-deg volume scans over 10 elevation angles approximately every 5 minutes, and was augmented by two UK Met Office C-band radars and the Chilbolton S-band radar. Detailed aerosol measurements were made on the aircraft and on the ground. This paper: (i) provides an overview of the COPE field campaign and the resulting dataset; (ii) presents examples of heavy convective rainfall in clouds containing ice and also in relatively shallow clouds through the warm rain process alone; and (iii) explains how COPE data will be used to improve high-resolution NWP models for operational use.

Proper evaluation of the external convective heat transfer for the thermal analysis of cool roofs

Cool materials are characterized by high solar reflectance and high thermal emittance; when applied to the external surface of a roof, they make it possible to limit the amount of solar irradiance absorbed by the roof, and to increase the rate of heat flux emitted by irradiation to the environment, especially during nighttime. However, a roof also releases heat by convection on its external surface; this mechanism is not negligible, and an incorrect evaluation of its entity might introduce significant inaccuracy in the assessment of the thermal performance of a cool roof, in terms of surface temperature and rate of heat flux transferred to the indoors. This issue is particularly relevant in numerical simulations, which are essential in the design stage, therefore it deserves adequate attention. In the present paper, a review of the most common algorithms used for the calculation of the convective heat transfer coefficient due to wind on horizontal building surfaces is presented. Then, with reference to a case study in Italy, the simulated results are compared to the outcomes of a measurement campaign. Hence, the most appropriate algorithms for the convective coefficient are identified, and the errors deriving by an incorrect selection of this coefficient are discussed.

A new method for the characterisation and verification of local spatial predictability for convective scale ensembles

The use of kilometre-scale ensembles in operational forecasting provides new challenges for forecast interpretation and evaluation to account for uncertainty on the convective scale. A new neighbourhood based method is presented for evaluating and characterising the local predictability variations from convective scale ensembles. Spatial scales over which ensemble forecasts agree (agreement scales, S^A) are calculated at each grid point ij, providing a map of the spatial agreement between forecasts. By comparing the average agreement scale obtained from ensemble member pairs (S^A(mm)_ij), with that between members and radar observations (S^A(mo)_ij), this approach allows the location-dependent spatial spread-skill relationship of the ensemble to be assessed. The properties of the agreement scales are demonstrated using an idealised experiment. To demonstrate the methods in an operational context the S^A(mm)_ij and S^A(mo)_ij are calculated for six convective cases run with the Met Office UK Ensemble Prediction System. The S^A(mm)_ij highlight predictability differences between cases, which can be linked to physical processes. Maps of S^A(mm)_ij are found to summarise the spatial predictability in a compact and physically meaningful manner that is useful for forecasting and for model interpretation. Comparison of S^A(mm)_ij and S^A(mo)_ij demonstrates the case-by-case and temporal variability of the spatial spread-skill, which can again be linked to physical processes.

Intercomparison of methods of coupling between convection and large-scale circulation. 2: Comparison over non-uniform surface conditions

As part of an international intercomparison project, the weak temperature gradient (WTG) and damped gravity wave (DGW) methods are used to parameterize large-scale dynamics in a set of cloud-resolving models (CRMs) and single column models (SCMs). The WTG or DGW method is implemented using a configuration that couples a model to a reference state defined with profiles obtained from the same model in radiative-convective equilibrium. We investigated the sensitivity of each model to changes in SST, given a fixed reference state. We performed a systematic comparison of the WTG and DGW methods in different models, and a systematic comparison of the behavior of those models using the WTG method and the DGW method. The sensitivity to the SST depends on both the large-scale parameterization method and the choice of the cloud model. In general, SCMs display a wider range of behaviors than CRMs. All CRMs using either the WTG or DGW method show an increase of precipitation with SST, while SCMs show sensitivities which are not always monotonic. CRMs using either the WTG or DGW method show a similar relationship between mean precipitation rate and column-relative humidity, while SCMs exhibit a much wider range of behaviors. DGW simulations produce large-scale velocity profiles which are smoother and less top-heavy compared to those produced by the WTG simulations. These large-scale parameterization methods provide a useful tool to identify the impact of parameterization differences on model behavior in the presence of two-way feedback between convection and the large-scale circulation.

Improved information about the vertical location and extent of monolayer clouds from POLDER3 measurements in the oxygen A-band

This paper describes new advances in the exploitation of oxygen A-band measurements from POLDER3 sensor onboard PARASOL, satellite platform within the A-Train. These developments result from not only an account of the dependence of POLDER oxygen parameters to cloud optical thickness τ and to the scene's geometrical conditions but also, and more importantly, from the finer understanding of the sensitivity of these parameters to cloud vertical extent. This sensitivity is made possible thanks to the multidirectional character of POLDER measurements. In the case of monolayer clouds that represent most of cloudy conditions, new oxygen parameters are obtained and calibrated from POLDER3 data colocalized with the measurements of the two active sensors of the A-Train: CALIOP/CALIPSO and CPR/CloudSat. From a parameterization that is (μs, τ) dependent, with μs the cosine of the solar zenith angle, a cloud top oxygen pressure (CTOP) and a cloud middle oxygen pressure (CMOP) are obtained, which are estimates of actual cloud top and middle pressures (CTP and CMP). Performances of CTOP and CMOP are presented by class of clouds following the ISCCP classification. In 2008, the coefficient of the correlation between CMOP and CMP is 0.81 for cirrostratus, 0.79 for stratocumulus, 0.75 for deep convective clouds. The coefficient of the correlation between CTOP and CTP is 0.75, 0.73, and 0.79 for the same cloud types. The score obtained by CTOP, defined as the confidence in the retrieval for a particular range of inferred value and for a given error, is higher than the one of MODIS CTP estimate. Scores of CTOP are the highest for bin value of CTP superior in numbers. For liquid (ice) clouds and an error of 30 hPa (50 hPa), the score of CTOP reaches 50% (70%). From the difference between CTOP and CMOP, a first estimate of the cloud vertical extent h is possible. A second estimate of h comes from the correlation between the angular standard deviation of POLDER oxygen pressure σPO2 and the cloud vertical extent. This correlation is studied in detail in the case of liquid clouds. It is shown to be spatially and temporally robust, except for clouds above land during winter months. The analysis of the correlation's dependence on the scene's characteristics leads to a parameterization providing h from σPO2. For liquid water clouds above ocean in 2008, the mean difference between the actual cloud vertical extent and the one retrieved from σPO2 (from the pressure difference) is 5 m (−12 m). The standard deviation of the mean difference is close to 1000 m for the two methods. POLDER estimates of the cloud geometrical thickness obtain a global score of 50% confidence for a relative error of 20% (40%) of the estimate for ice (liquid) clouds over ocean. These results need to be validated outside of the CALIPSO/CloudSat track.

Pension scheme redesign and wealth redistribution between the members and sponsor: the USS rule change in October 2011

The redesign of defined benefit pension schemes usually results in a substantial redistribution of wealth between age cohorts of members, pensioners, and the sponsor. This is the first study to quantify the redistributive effects of a rule change by a real world scheme (the Universities Superannuation Scheme, USS) where the sponsor underwrites the pension promise. In October 2011 USS closed its final salary scheme to new members, opened a career average revalued earnings (CARE) section, and moved to ‘cap and share’ contribution rates. We find that the pre-October 2011 scheme was not viable in the long run, while the post-October 2011 scheme is probably viable in the long run, but faces medium term problems. In October 2011 future members of USS lost 65% of their pension wealth (or roughly £100,000 per head), equivalent to a reduction of roughly 11% in their total compensation, while those aged over 57 years lost almost nothing. The riskiness of the pension wealth of future members increased by a third, while the riskiness of the present value of the sponsor’s future contributions reduced by 10%. Finally, the sponsor’s wealth increased by about £32.5 billion, equivalent to a reduction of 26% in their pension costs.

Sensitivity of resolved and parameterized surface drag to changes in resolution and parameterization

The relative contribution of resolved and parameterized surface drag towards balancing the atmospheric angular momentum flux convergence (AMFC), and their sensitivity to horizontal resolution and parameterization, are investigated in an atmospheric model. This sensitivity can be difficult to elucidate in free-running climate models, in which the AMFC varies with changing climatologies and, as a result, the relative contributions of surface terms balancing the AMFC also vary. While the sensitivity question has previously been addressed using short-range forecasts, we demonstrate that a nudging framework is an effective method for constraining the AMFC. The Met Office Unified Model is integrated at three horizontal resolutions ranging from 130 km (N96) to 25 km (N512) while relaxing the model’s wind and temperature fields towards the ERAinterim reanalysis within the altitude regions of maximum AMFC. This method is validated against short range forecasts and good agreement is found. These experiments are then used to assess the fidelity of the exchange between parameterized and resolved orographic torques with changes in horizontal resolution. Although the parameterized orographic torque reduces substantially with increasing horizontal resolution, there is little change in resolved orographic torque over 20N to 50N. The tendencies produced by the nudging routine indicate that the additional drag at lower horizontal resolution is excessive. When parameterized orographic blocking is removed at the coarsest of these resolutions, there is a lack of compensation, and even compensation of the opposite sense, by the boundary layer and resolved torques which is particularly pronounced over 20N to 50N. This study demonstrates that there is strong sensitivity in the behaviour of the resolved and parameterized surface drag over this region.

Surface Urban Energy and Water Balance Scheme (SUEWS): development and evaluation at two UK sites

The Surface Urban Energy and Water Balance Scheme (SUEWS) is evaluated at two locations in the UK: a dense urban site in the centre of London and a residential suburban site in Swindon. Eddy covariance observations of the turbulent fluxes are used to assess model performance over a twoyear period (2011-2013). The distinct characteristics of the sites mean their surface energy exchanges differ considerably. The model suggests the largest differences can be attributed to surface cover (notably the proportion of vegetated versus impervious area) and the additional energy supplied by human activities. SUEWS performs better in summer than winter, and better at the suburban site than the dense urban site. One reason for this is the bias towards suburban summer field campaigns in observational data used to parameterise this (and other) model(s). The suitability of model parameters (such as albedo, energy use and water use) for the UK sites is considered and, where appropriate, alternative values are suggested. An alternative parameterisation for the surface conductance is implemented, which permits greater soil moisture deficits before evaporation is restricted at non-irrigated sites. Accounting for seasonal variation in the estimation of storage heat flux is necessary to obtain realistic wintertime fluxes.

Mobile sink based fault diagnosis scheme for wireless sensor networks

Network diagnosis in Wireless Sensor Networks (WSNs) is a difficult task due to their improvisational nature, invisibility of internal running status, and particularly since the network structure can frequently change due to link failure. To solve this problem, we propose a Mobile Sink (MS) based distributed fault diagnosis algorithm for WSNs. An MS, or mobile fault detector is usually a mobile robot or vehicle equipped with a wireless transceiver that performs the task of a mobile base station while also diagnosing the hardware and software status of deployed network sensors. Our MS mobile fault detector moves through the network area polling each static sensor node to diagnose the hardware and software status of nearby sensor nodes using only single hop communication. Therefore, the fault detection accuracy and functionality of the network is significantly increased. In order to maintain an excellent Quality of Service (QoS), we employ an optimal fault diagnosis tour planning algorithm. In addition to saving energy and time, the tour planning algorithm excludes faulty sensor nodes from the next diagnosis tour. We demonstrate the effectiveness of the proposed algorithms through simulation and real life experimental results.

Modeling study of the aspect ratio influence on urban canopy energy fluxes with a modified wall-canyon energy budget scheme

The influence of the aspect ratio (building height/street canyon width) and the mean building height of cities on local energy fluxes and temperatures is studied by means of an Urban Canopy Model (UCM) coupled with a one-dimensional second-order turbulence closure model. The UCM presented is similar to the Town Energy Balance (TEB) model in most of its features but differs in a few important aspects. In particular, the street canyon walls are treated separately which leads to a different budget of radiation within the street canyon walls. The UCM has been calibrated using observations of incoming global and diffuse solar radiation, incoming long-wave radiation and air temperature at a site in So Paulo, Brazil. Sensitivity studies with various aspect ratios have been performed to assess their impact on urban temperatures and energy fluxes at the top of the canopy layer. In these simulations, it is assumed that the anthropogenic heat flux and latent heat fluxes are negligible. Results show that the simulated net radiation and sensible heat fluxes at the top of the canopy decrease and the stored heat increases as the aspect ratio increases. The simulated air temperature follows the behavior of the sensible heat flux. (C) 2010 Elsevier Ltd. All rights reserved.