There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

Adaptive immunity depends on T-cell exit from the thymus and T and B cells travelling between secondary lymphoid organs to survey for antigens. After activation in lymphoid organs, T cells must again return to circulation to reach sites of infection; however, the mechanisms regulating lymphoid organ exit are unknown. An immunosuppressant drug, FTY720, inhibits lymphocyte emigration from lymphoid organs, and phosphorylated FTY720 binds and activates four of the five known sphingosine-1-phosphate (S1P) receptors1,2,3,4. However, the role of S1P receptors in normal immune cell trafficking is unclear. Here we show that in mice whose haematopoietic cells lack a single S1P receptor (S1P1; also known as Edg1) there are no T cells in the periphery because mature T cells are unable to exit the thymus. Although B cells are present in peripheral lymphoid organs, they are severely deficient in blood and lymph. Adoptive cell transfer experiments establish an intrinsic requirement for S1P1 in T and B cells for lymphoid organ egress. Furthermore, S1P1-dependent chemotactic responsiveness is strongly upregulated in T-cell development before exit from the thymus, whereas S1P1 is downregulated during peripheral lymphocyte activation, and this is associated with retention in lymphoid organs. We find that FTY720 treatment downregulates S1P1, creating a temporary pharmacological S1P1-null state in lymphocytes, providing an explanation for the mechanism of FTY720-induced lymphocyte sequestration. These findings establish that S1P1 is essential for lymphocyte recirculation and that it regulates egress from both thymus and peripheral lymphoid organs.

Lymphocyte egress from thymus and peripheral lymphoid organs is dependent on S1P receptor 1

[1] A new 2° resolution global climatology of the mixed layer depth (MLD) based on individual profiles is constructed. Previous global climatologies have been based on temperature or density-gridded climatologies. The criterion selected is a threshold value of temperature or density from a near-surface value at 10 m depth (ΔT = 0.2°C or Δσθ = 0.03 kg m−3). A validation of the temperature criterion on moored time series data shows that the method is successful at following the base of the mixed layer. In particular, the first spring restratification is better captured than with a more commonly used larger criteria. In addition, we show that for a given 0.2°C criterion, the MLD estimated from averaged profiles results in a shallow bias of 25% compared to the MLD estimated from individual profiles. A new global seasonal estimation of barrier layer thickness is also provided. An interesting result is the prevalence in mid- and high-latitude winter hemispheres of vertically density-compensated layers, creating an isopycnal but not mixed layer. Consequently, we propose an optimal estimate of MLD based on both temperature and density data. An independent validation of the maximum annual MLD with oxygen data shows that this oxygen estimate may be biased in regions of Ekman pumping or strong biological activity. Significant differences are shown compared to previous climatologies. The timing of the seasonal cycle of the mixed layer is shifted earlier in the year, and the maximum MLD captures finer structures and is shallower. These results are discussed in light of the different approaches and the choice of criterion.

/pdf/mixed-layer-depth-over-the-global-ocean-an-examination-of-3xkoso12fd.pdf

Mixed layer depth over the global ocean: An examination of profile data and a profile-based climatology

The potential for sea ice-albedo feedback to give rise to nonlinear climate change in the Arctic Ocean – defined as a nonlinear relationship between polar and global temperature change or, equivalently, a time-varying polar amplification – is explored in IPCC AR4 climate models. Five models supplying SRES A1B ensembles for the 21 st century are examined and very linear relationships are found between polar and global temperatures (indicating linear Arctic Ocean climate change), and between polar temperature and albedo (the potential source of nonlinearity). Two of the climate models have Arctic Ocean simulations that become annually sea ice-free under the stronger CO 2 increase to quadrupling forcing. Both of these runs show increases in polar amplification at polar temperatures above-5 o C and one exhibits heat budget changes that are consistent with the small ice cap instability of simple energy balance models. Both models show linear warming up to a polar temperature of-5 o C, well above the disappearance of their September ice covers at about-9 o C. Below-5 o C, surface albedo decreases smoothly as reductions move, progressively, to earlier parts of the sunlit period. Atmospheric heat transport exerts a strong cooling effect during the transition to annually ice-free conditions. Specialized experiments with atmosphere and coupled models show that the main damping mechanism for sea ice region surface temperature is reduced upward heat flux through the adjacent ice-free oceans resulting in reduced atmospheric heat transport into the region.

Geophysical fluid dynamics.

[1] A composite time series (1993–2000) of sea surface height anomaly from several satellites is used to identify eddies in the South China Sea (SCS). The eddy lifetime, radius, strength, and straight-line travel distance are estimated. Altogether 58 anticyclonic eddies and 28 cyclonic eddies are identified for this period. They are grouped into four geographical zones according to known eddy generation mechanisms, and their statistics are discussed accordingly. Our geographical classification is a useful first step in gaining an overview of their generation.

/pdf/mesoscale-eddies-in-the-south-china-sea-observed-with-eogqaltsnm.pdf

Mesoscale eddies in the South China Sea observed with altimeter data

https://faculty.nps.edu/pcchu/web_paper/jcp/CCD.pdf

A Three-Point Combined Compact Difference Scheme

Economic order quantity of deteriorating items under permissible delay in payments

The seasonal ocean circulation and the seasonal thermal structure in the South China Sea (SCS) were studied numerically using the Princeton Ocean Model (POM) with 20-km horizontal resolution and 23 sigma levels conforming to a realistic bottom topography. A 16-month control run was performed using climatological monthly mean wind stresses, restoring-type surface salt and heat, and observational oceanic inflow/outflow at the open boundaries. The seasonally averaged effects of isolated forcing terms are presented and analyzed from the following experiments: 1) nonlinear dynamic effects removed, 2) wind effects removed, and 3) open boundary inflow/outflow set to zero. This procedure allowed analysis of the contribution of individual parameters to the general hydrology and specific features of the SCS: for example, coastal jets, mesoscale topographic gyres, and countercurrents. The results show that the POM model has the capability of simulating seasonal variations of the SCS circulation and thermoha...

Dynamical Mechanisms for the South China Sea Seasonal Circulation and Thermohaline Variabilities

The seasonal ocean circulation and the seasonal thermal structure in the South China Sea (SCS) were studied numerically using the Princeton Ocean Model (POM) with 20-km horizontal resolution and 23 sigma levels conforming to a realistic bottom topography. A 16-month control run was performed using climatological monthly mean wind stresses, restoring-type surface salt and heat, and observational oceanic inflow/outflow at the open boundaries. The seasonally averaged effects of isolated forcing terms are presented and analyzed from the following experiments: 1) nonlinear dynamic effects removed, 2) wind effects removed, and 3) open boundary inflow/outflow set to zero. This procedure allowed analysis of the contribution of individual parameters to the general hydrology and specific features of the SCS: for example, coastal jets, mesoscale topographic gyres, and countercurrents. The results show that the POM model has the capability of simulating seasonal variations of the SCS circulation and thermohaline structure. The simulated SCS surface circulation is generally anticyclonic (cyclonic) during the summer (winter) monsoon period with a strong western boundary current, a mean maximum speed of 0.5 m s21 (0.95 m s21), a mean volume transport of 5.5 Sv (10.6 Sv) (Sv [ 106 m3 s21), and extending to a depth of around 200 m (500 m). During summer, the western boundary current splits and partially leaves the coast; the bifurcation point is at 148N in May and shifts south to 108N in July. A mesoscale eddy on the Sunda shelf (Natuna Island eddy) was also simulated. This eddy is cyclonic (anticyclonic) with maximum swirl velocity of 0.6 m s21 at the peak of the winter (summer) monsoon. The simulated thermohaline structure for summer and winter are nearly horizontal from east to west except at the coastal regions. Coastal upwelling and downwelling are also simulated: localized lifting (descending) of the isotherms and isohalines during summer (winter) at the west boundary. The simulation is reasonable when compared to the observations. Sensitivity experiments were designed to investigate the driving mechanisms. Nonlinearity is shown to be important to the transport of baroclinic eddy features, but otherwise insignificant. Transport from lateral boundaries is of considerable importance to summer circulation and thermal structure, with lesser effect on winter monsoon hydrology. In general, seasonal circulation patterns and upwelling phenomena are determined and forced by the wind, while the lateral boundary forcing plays a secondary role in determining the magnitude of the circulation velocities.

/pdf/notes-and-correspondence-dynamical-mechanisms-for-the-south-2y2bteyx5p.pdf

Peter C. Chu

Papers

Mesoscale eddies in the South China Sea observed with altimeter data

A Three-Point Combined Compact Difference Scheme

Economic order quantity of deteriorating items under permissible delay in payments

Dynamical Mechanisms for the South China Sea Seasonal Circulation and Thermohaline Variabilities

NOTES AND CORRESPONDENCE Dynamical Mechanisms for the South China Sea Seasonal Circulation and Thermohaline Variabilities