Resolution of sharp fronts in the presence of model error in variational data assimilation

We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong constraint 4DVar (L2-norm)method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.

The du2J mouse model of ataxia and absence epilepsy has deficient cannabinoid CB1 receptor-mediated signalling

Key point summary • Cerebellar ataxias are progressive debilitating diseases with no known treatment and are associated with defective motor function and, in particular, abnormalities to Purkinje cells. • Mutant mice with deficits in Ca2+ channel auxiliary α2δ-2 subunits are used as models of cerebellar ataxia. • Our data in the du2J mouse model shows an association between the ataxic phenotype exhibited by homozygous du2J/du2J mice and increased irregularity of Purkinje cell firing. • We show that both heterozygous +/du2J and homozygous du2J/du2J mice completely lack the strong presynaptic modulation of neuronal firing by cannabinoid CB1 receptors which is exhibited by litter-matched control mice. • These results show that the du2J ataxia model is associated with deficits in CB1 receptor signalling in the cerebellar cortex, putatively linked with compromised Ca2+ channel activity due to reduced α2δ-2 subunit expression. Knowledge of such deficits may help design therapeutic agents to combat ataxias. Abstract Cerebellar ataxias are a group of progressive, debilitating diseases often associated with abnormal Purkinje cell (PC) firing and/or degeneration. Many animal models of cerebellar ataxia display abnormalities in Ca2+ channel function. The ‘ducky’ du2J mouse model of ataxia and absence epilepsy represents a clean knock-out of the auxiliary Ca2+ channel subunit, α2δ-2, and has been associated with deficient Ca2+ channel function in the cerebellar cortex. Here, we investigate effects of du2J mutation on PC layer (PCL) and granule cell (GC) layer (GCL) neuronal spiking activity and, also, inhibitory neurotransmission at interneurone-Purkinje cell(IN-PC) synapses. Increased neuronal firing irregularity was seen in the PCL and, to a less marked extent, in the GCL in du2J/du2J, but not +/du2J, mice; these data suggest that the ataxic phenotype is associated with lack of precision of PC firing, that may also impinge on GC activity and requires expression of two du2J alleles to manifest fully. du2J mutation had no clear effect on spontaneous inhibitory postsynaptic current (sIPSC) frequency at IN-PC synapses, but was associated with increased sIPSC amplitudes. du2J mutation ablated cannabinoid CB1 receptor (CB1R)-mediated modulation of spontaneous neuronal spike firing and CB1Rmediated presynaptic inhibition of synaptic transmission at IN-PC synapses in both +/du2J and du2J/du2J mutants; effects that occurred in the absence of changes in CB1R expression. These results demonstrate that the du2J ataxia model is associated with deficient CB1R signalling in the cerebellar cortex, putatively linked with compromised Ca2+ channel activity and the ataxic phenotype.

Sensitivity of a hydraulic model to changes in channel erosion during extreme flooding

Recent research into flood modelling has primarily concentrated on the simulation of inundation flow without considering the influences of channel morphology. River channels are often represented by a simplified geometry that is implicitly assumed to remain unchanged during flood simulations. However, field evidence demonstrates that significant morphological changes can occur during floods to mobilise the boundary sediments. Despite this, the effect of channel morphology on model results has been largely unexplored. To address this issue, the impact of channel cross-section geometry and channel long-profile variability on flood dynamics is examined using an ensemble of a 1D-2D hydraulic model (LISFLOOD-FP) of the 1:2102 year recurrence interval floods in Cockermouth, UK, within an uncertainty framework. A series of hypothetical scenarios of channel morphology were constructed based on a simple velocity based model of critical entrainment. A Monte-Carlo simulation framework was used to quantify the effects of channel morphology together with variations in the channel and floodplain roughness coefficients, grain size characteristics, and critical shear stress on measures of flood inundation. The results showed that the bed elevation modifications generated by the simplistic equations reflected a good approximation of the observed patterns of spatial erosion despite its overestimation of erosion depths. The effect of uncertainty on channel long-profile variability only affected the local flood dynamics and did not significantly affect the friction sensitivity and flood inundation mapping. The results imply that hydraulic models generally do not need to account for within event morphodynamic changes of the type and magnitude modelled, as these have a negligible impact that is smaller than other uncertainties, e.g. boundary conditions. Instead morphodynamic change needs to happen over a series of events to become large enough to change the hydrodynamics of floods in supply limited gravel-bed rivers like the one used in this research.

Broad range of 2050 warming from an observationally constrained large climate model ensemble

Incomplete understanding of three aspects of the climate system—equilibrium climate sensitivity, rate of ocean heat uptake and historical aerosol forcing—and the physical processes underlying them lead to uncertainties in our assessment of the global-mean temperature evolution in the twenty-first century1,2. Explorations of these uncertainties have so far relied on scaling approaches3,4, large ensembles of simplified climate models1,2, or small ensembles of complex coupled atmosphere–ocean general circulation models5,6 which under-represent uncertainties in key climate system properties derived from independent sources7–9. Here we present results from a multi-thousand-member perturbed-physics ensemble of transient coupled atmosphere–ocean general circulation model simulations. We find that model versions that reproduce observed surface temperature changes over the past 50 years show global-mean temperature increases of 1.4–3 K by 2050, relative to 1961–1990, under a mid-range forcing scenario. This range of warming is broadly consistent with the expert assessment provided by the Intergovernmental Panel on Climate Change Fourth Assessment Report10, but extends towards larger warming than observed in ensemblesof-opportunity5 typically used for climate impact assessments. From our simulations, we conclude that warming by the middle of the twenty-first century that is stronger than earlier estimates is consistent with recent observed temperature changes and a mid-range ‘no mitigation’ scenario for greenhouse-gas emissions.

Anticipatory engineering: anticipation in sensory-motor systems of human

In visual tracking experiments, distributions of the relative phase be-tween target and tracer showed positive relative phase indicating that the tracer precedes the target position. We found a mode transition from the reactive to anticipatory mode. The proposed integrated model provides a framework to understand the antici-patory behaviour of human, focusing on the integration of visual and soma-tosensory information. The time delays in visual processing and somatosensory feedback are explicitly treated in the simultaneous differential equations. The anticipatory behaviour observed in the visual tracking experiments can be ex-plained by the feedforward term of target velocity, internal dynamics, and time delay in somatosensory feedback.

Using the Technology Acceptance Model to explore community dwelling older adults’ perceptions of a 3D interior design application to facilitate pre-discharge home adaptations

Background In the UK occupational therapy pre-discharge home visits are routinely carried out as a means of facilitating safe transfer from the hospital to home. Whilst they are an integral part of practice, there is little evidence to demonstrate they have a positive outcome on the discharge process. Current issues for patients are around the speed of home visits and the lack of shared decision making in the process, resulting in less than 50 % of the specialist equipment installed actually being used by patients on follow-up. To improve practice there is an urgent need to examine other ways of conducting home visits to facilitate safe discharge. We believe that Computerised 3D Interior Design Applications (CIDAs) could be a means to support more efficient, effective and collaborative practice. A previous study explored practitioners perceptions of using CIDAs; however it is important to ascertain older adult’s views about the usability of technology and to compare findings. This study explores the perceptions of community dwelling older adults with regards to adopting and using CIDAs as an assistive tool for the home adaptations process. Methods Ten community dwelling older adults participated in individual interactive task-focused usability sessions with a customised CIDA, utilising the think-aloud protocol and individual semi-structured interviews. Template analysis was used to carry out both deductive and inductive analysis of the think-aloud and interview data. Initially, a deductive stance was adopted, using the three pre-determined high-level themes of the technology acceptance model (TAM): Perceived Usefulness (PU), Perceived Ease of Use (PEOU), Actual Use (AU). Inductive template analysis was then carried out on the data within these themes, from which a number of sub-thmes emerged. Results Regarding PU, participants believed CIDAs served as a useful visual tool and saw clear potential to facilitate shared understanding and partnership in care delivery. For PEOU, participants were able to create 3D home environments however a number of usability issues must still be addressed. The AU theme revealed the most likely usage scenario would be collaborative involving both patient and practitioner, as many participants did not feel confident or see sufficient value in using the application autonomously. Conclusions This research found that older adults perceived that CIDAs were likely to serve as a valuable tool which facilitates and enhances levels of patient/practitioner collaboration and empowerment. Older adults also suggested a redesign of the interface so that less sophisticated dexterity and motor functions are required. However, older adults were not confident, or did not see sufficient value in using the application autonomously. Future research is needed to further customise the CIDA software, in line with the outcomes of this study, and to explore the potential of collaborative application patient/practitioner-based deployment.

A moving point approach to model shallow ice sheets: a study case with radially-symmetrical ice sheets

Predicting the evolution of ice sheets requires numerical models able to accurately track the migration of ice sheet continental margins or grounding lines. We introduce a physically based moving point approach for the flow of ice sheets based on the conservation of local masses. This allows the ice sheet margins to be tracked explicitly and the waiting time behaviours to be modelled efficiently. A finite difference moving point scheme is derived and applied in a simplified context (continental radially-symmetrical shallow ice approximation). The scheme, which is inexpensive, is validated by comparing the results with moving-margin exact solutions and steady states. In both cases the scheme is able to track the position of the ice sheet margin with high precision.

Diagnosing observation error correlations for Doppler radar radial winds in the Met Office UKV model using observation-minus-background and observation-minus-analysis statistics

With the development of convection-permitting numerical weather prediction the efficient use of high resolution observations in data assimilation is becoming increasingly important. The operational assimilation of these observations, such as Dopplerradar radial winds, is now common, though to avoid violating the assumption of un- correlated observation errors the observation density is severely reduced. To improve the quantity of observations used and the impact that they have on the forecast will require the introduction of the full, potentially correlated, error statistics. In this work, observation error statistics are calculated for the Doppler radar radial winds that are assimilated into the Met Office high resolution UK model using a diagnostic that makes use of statistical averages of observation-minus-background and observation-minus-analysis residuals. This is the first in-depth study using the diagnostic to estimate both horizontal and along-beam correlated observation errors. By considering the new results obtained it is found that the Doppler radar radial wind error standard deviations are similar to those used operationally and increase as the observation height increases. Surprisingly the estimated observation error correlation length scales are longer than the operational thinning distance. They are dependent on both the height of the observation and on the distance of the observation away from the radar. Further tests show that the long correlations cannot be attributed to the use of superobservations or the background error covariance matrix used in the assimilation. The large horizontal correlation length scales are, however, in part, a result of using a simplified observation operator.

Mid-holocene and last glacial maximum climate simulations with the IPSL model-part I: comparing IPSLCM5A to IPSLCM4

The climates of the mid-Holocene (MH), 6,000 years ago, and of the Last Glacial Maximum (LGM), 21,000 years ago, have extensively been simulated, in particular in the framework of the Palaeoclimate Modelling Intercomparion Project. These periods are well documented by paleo-records, which can be used for evaluating model results for climates different from the present one. Here, we present new simulations of the MH and the LGM climates obtained with the IPSL_CM5A model and compare them to our previous results obtained with the IPSL_CM4 model. Compared to IPSL_CM4, IPSL_CM5A includes two new features: the interactive representation of the plant phenology and marine biogeochemistry. But one of the most important differences between these models is the latitudinal resolution and vertical domain of their atmospheric component, which have been improved in IPSL_CM5A and results in a better representation of the mid-latitude jet-streams. The Asian monsoon’s representation is also substantially improved. The global average mean annual temperature simulated for the pre-industrial (PI) period is colder in IPSL_CM5A than in IPSL_CM4 but their climate sensitivity to a CO2 doubling is similar. Here we show that these differences in the simulated PI climate have an impact on the simulated MH and LGM climatic anomalies. The larger cooling response to LGM boundary conditions in IPSL_CM5A appears to be mainly due to differences between the PMIP3 and PMIP2 boundary conditions, as shown by a short wave radiative forcing/feedback analysis based on a simplified perturbation method. It is found that the sensitivity computed from the LGM climate is lower than that computed from 2 × CO2 simulations, confirming previous studies based on different models. For the MH, the Asian monsoon, stronger in the IPSL_CM5A PI simulation, is also more sensitive to the insolation changes. The African monsoon is also further amplified in IPSL_CM5A due to the impact of the interactive phenology. Finally the changes in variability for both models and for MH and LGM are presented taking the example of the El-Niño Southern Oscillation (ENSO), which is very different in the PI simulations. ENSO variability is damped in both model versions at the MH, whereas inconsistent responses are found between the two versions for the LGM. Part 2 of this paper examines whether these differences between IPSL_CM4 and IPSL_CM5A can be distinguished when comparing those results to palaeo-climatic reconstructions and investigates new approaches for model-data comparisons made possible by the inclusion of new components in IPSL_CM5A.

A moving-point approach to model shallow ice sheets: a study case with radially symmetrical ice sheets

Predicting the evolution of ice sheets requires numerical models able to accurately track the migration of ice sheet continental margins or grounding lines. We introduce a physically based moving-point approach for the flow of ice sheets based on the conservation of local masses. This allows the ice sheet margins to be tracked explicitly. Our approach is also well suited to capture waiting-time behaviour efficiently. A finite-difference moving-point scheme is derived and applied in a simplified context (continental radially symmetrical shallow ice approximation). The scheme, which is inexpensive, is verified by comparing the results with steady states obtained from an analytic solution and with exact moving-margin transient solutions. In both cases the scheme is able to track the position of the ice sheet margin with high accuracy.

Evaluation of a polynya flux model by means of thermal infrared satellite estimates

We test the ability of a two-dimensional flux model to simulate polynya events with narrow open-water zones by comparing model results to ice-thickness and ice-production estimates derived from thermal infrared Moderate Resolution Imaging Spectroradiometer (MODIS) observations in conjunction with an atmospheric dataset. Given a polynya boundary and an atmospheric dataset, the model correctly reproduces the shape of an 11 day long event, using only a few simple conservation laws. Ice production is slightly overestimated by the model, owing to an underestimated ice thickness. We achieved best model results with the consolidation thickness parameterization developed by Biggs and others (2000). Observed regional discrepancies between model and satellite estimates might be a consequence of the missing representation of the dynamic of the thin-ice thickening (e.g. rafting). We conclude that this simplified polynya model is a valuable tool for studying polynya dynamics and estimating associated fluxes of single polynya events.