On variational data assimilation in continuous time

Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a continuous time generalization of what is known as weakly constrained four-dimensional variational assimilation (4D-Var) in the geosciences. The technique allows to assimilate trajectories in the case of partial observations and in the presence of model error. Several mathematical aspects of the approach are studied. Computationally, it amounts to solving a two-point boundary value problem. For imperfect models, the trade-off between small dynamical error (i.e. the trajectory obeys the model dynamics) and small observational error (i.e. the trajectory closely follows the observations) is investigated. This trade-off turns out to be trivial if the model is perfect. However, even in this situation, allowing for minute deviations from the perfect model is shown to have positive effects, namely to regularize the problem. The presented formalism is dynamical in character. No statistical assumptions on dynamical or observational noise are imposed.

Overview of observations from the RADAGAST experiment in Niamey, Niger: 2. Radiative fluxes and divergences

Broadband shortwave and longwave radiative fluxes observed both at the surface and from space during the Radiative Atmospheric Divergence using ARM Mobile Facility, GERB data and AMMA Stations (RADAGAST) experiment in Niamey, Niger, in 2006 are presented. The surface fluxes were measured by the Atmospheric Radiation Measurement (ARM) Program Mobile Facility (AMF) at Niamey airport, while the fluxes at the top of the atmosphere (TOA) are from the Geostationary Earth Radiation Budget (GERB) instrument on the Meteosat-8 satellite. The data are analyzed as daily averages, in order to minimize sampling differences between the surface and top of atmosphere instruments, while retaining the synoptic and seasonal changes that are the main focus of this study. A cloud mask is used to identify days with cloud versus those with predominantly clear skies. The influence of temperature, water vapor, aerosols, and clouds is investigated. Aerosols are ubiquitous throughout the year and have a significant impact on both the shortwave and longwave fluxes. The large and systematic seasonal changes in temperature and column integrated water vapor (CWV) through the dry and wet seasons are found to exert strong influences on the longwave fluxes. These influences are often in opposition to each other, because the highest temperatures occur at the end of the dry season when the CWV is lowest, while in the wet season the lowest temperatures are associated with the highest values of CWV. Apart from aerosols, the shortwave fluxes are also affected by clouds and by the seasonal changes in CWV. The fluxes are combined to provide estimates of the divergence of radiation across the atmosphere throughout 2006. The longwave divergence shows a relatively small variation through the year, because of a partial compensation between the seasonal variations in the outgoing longwave radiation (OLR) and surface net longwave radiation. A simple model of the greenhouse effect is used to interpret this result in terms of the dependence of the normalized greenhouse effect at the TOA and of the effective emissivity of the atmosphere at the surface on the CWV. It is shown that, as the CWV increases, the atmosphere loses longwave energy to the surface with about the same increasing efficiency with which it traps the OLR. When combined with the changes in temperature, this maintains the atmospheric longwave divergence within the narrow range that is observed. The shortwave divergence is mainly determined by the CWV and aerosol loadings and the effect of clouds is much smaller than on the component fluxes.

Forecast impact of targeted observations: sensitivity to observation error and proximity to steep orography

For a targeted observations case, the dependence of the size of the forecast impact on the targeted dropsonde observation error in the data assimilation is assessed. The targeted observations were made in the lee of Greenland; the dependence of the impact on the proximity of the observations to the Greenland coast is also investigated. Experiments were conducted using the Met Office Unified Model (MetUM), over a limited-area domain at 24-km grid spacing, with a four-dimensional variational data assimilation (4D-Var) scheme. Reducing the operational dropsonde observation errors by one-half increases the maximum forecast improvement from 5% to 7%–10%, measured in terms of total energy. However, the largest impact is seen by replacing two dropsondes on the Greenland coast with two farther from the steep orography; this increases the maximum forecast improvement from 5% to 18% for an 18-h forecast (using operational observation errors). Forecast degradation caused by two dropsonde observations on the Greenland coast is shown to arise from spreading of data by the background errors up the steep slope of Greenland. Removing boundary layer data from these dropsondes reduces the forecast degradation, but it is only a partial solution to this problem. Although only from one case study, these results suggest that observations positioned within a correlation length scale of steep orography may degrade the forecast through the anomalous upslope spreading of analysis increments along terrain-following model levels.

The distribution of the ring current: Cluster observations

Extending previous studies, a full-circle investigation of the ring current has been made using Cluster 4-spacecraft observations near perigee, at times when the Cluster array had relatively small separations and nearly regular tetrahedral configurations, and when the Dst index was greater than −30 nT (non-storm conditions). These observations result in direct estimations of the near equatorial current density at all magnetic local times (MLT) for the first time and with sufficient accuracy, for the following observations. The results confirm that the ring current flows westward and show that the in situ average measured current density (sampled in the radial range accessed by Cluster 4–4.5RE) is asymmetric in MLT, ranging from 9 to 27 nAm−2. The direction of current is shown to be very well ordered for the whole range of MLT. Both of these results are in line with previous studies on partial ring extent. The magnitude of the current density, however, reveals a distinct asymmetry: growing from 10 to 27 nAm−2 as azimuth reduces from about 12:00MLT to 03:00 and falling from 20 to 10 nAm−2 less steadily as azimuth reduces from 24:00 to 12:00MLT. This result has not been reported before and we suggest it could reflect a number of effects. Firstly, we argue it is consistent with the operation of region-2 field aligned-currents (FACs), which are expected to flow upward into the ring current around 09:00MLT and downward out of the ring current around 14:00MLT. Secondly, we note that it is also consistent with a possible asymmetry in the radial distribution profile of current density (resulting in higher peak at 4– 4.5RE). We note that part of the enhanced current could reflect an increase in the mean AE activity (during the periods in which Cluster samples those MLT).

Arctic ozone depletion in 2002–2003 measured by ASUR and comparison with POAM observations

We present ozone loss estimated from airborne measurements taken during January–February and March in the Arctic winter 2002/2003. The first half of the winter was characterized by unusually cold temperatures and the second half by a major stratospheric sudden warming around 15–18 January 2003. The potential vorticity maps show a vortex split in the lower stratosphere during the major warming (MW) in late January and during the minor warming in mid-February due to wave 1 amplification. However, the warming can be termed as a vortex displacement event as there was no vortex split during the MW period at 10 hPa. Very low temperatures, large areas of polar stratospheric clouds (PSCs), and high chlorine activation triggered significant ozone loss in the early winter, as the vortex moved to the midlatitude regions. The ozone depletion derived from the ASUR measurements sampled inside the vortex, in conjunction with the Mimosa-Chim model tracer, shows a maximum of 1.3 ± 0.2 ppmv at 450–500 K by late March. The partial column loss derived from the ASUR ozone profiles reaches up to 61 ± 4 DU in 400–550 K in the same period. The evolution of ozone and ozone loss assessed from the ASUR measurements is in very good agreement with POAM observations. The reduction in ozone estimated from the POAM measurements shows a similar maximum of 1.3 ± 0.2 ppmv at 400–500 K or 63 ± 4 DU in 400–550 K in late March. Our study reveals that the Arctic winter 2002/2003 was unique as it had three minor warmings and a MW, yet showed large loss in ozone. No such feature was observed in any other Arctic winter in the 1989–2010 period. In addition, an unusually large ozone loss in December, around 0.5 ± 0.2 ppmv at 450–500 K or 12 ± 1 DU in 400–550 K, was estimated for the first time in the Arctic. A careful and detailed diagnosis with all available published results for this winter exhibits an average ozone loss of 1.5 ± 0.3 ppmv at 450–500 K or 65 ± 5 DU in 400–550 K by the end of March, which exactly matches the ozone depletion derived from the ASUR, POAM and model data. The early ozone loss together with considerable loss afterwards put the warm Arctic winter 2002/2003 amongst the moderately cold winters in terms of the significance of the ozone loss.

Interaction among non-toxic phytoplankton, toxic phytoplankton and zooplankton: inferences from field observations

We explore the mutual dependencies and interactions among different groups of species of the plankton population, based on an analysis of the long-term field observations carried out by our group in the North–West coast of the Bay of Bengal. The plankton community is structured into three groups of species, namely, non-toxic phytoplankton (NTP), toxic phytoplankton (TPP) and zooplankton. To find the pair-wise dependencies among the three groups of plankton, Pearson and partial correlation coefficients are calculated. To explore the simultaneous interaction among all the three groups, a time series analysis is performed. Following an Expectation Maximization (E-M) algorithm, those data points which are missing due to irregularities in sampling are estimated, and with the completed data set a Vector Auto-Regressive (VAR) model is analyzed. The overall analysis demonstrates that toxin-producing phytoplankton play two distinct roles: the inhibition on consumption of toxic substances reduces the abundance of zooplankton, and the toxic materials released by TPP significantly compensate for the competitive disadvantages among phytoplankton species. Our study suggests that the presence of TPP might be a possible cause for the generation of a complex interaction among the large number of phytoplankton and zooplankton species that might be responsible for the prolonged coexistence of the plankton species in a fluctuating biomass.