Gaussian quadrature 4D-VAR

A new incremental four-dimensional variational (4D-Var) data assimilation algorithm is introduced. The algorithm does not require the computationally expensive integrations with the nonlinear model in the outer loops. Nonlinearity is accounted for by modifying the linearization trajectory of the observation operator based on integrations with the tangent linear (TL) model. This allows us to update the linearization trajectory of the observation operator in the inner loops at negligible computational cost. As a result the distinction between inner and outer loops is no longer necessary. The key idea on which the proposed 4D-Var method is based is that by using Gaussian quadrature it is possible to get an exact correspondence between the nonlinear time evolution of perturbations and the time evolution in the TL model. It is shown that J-point Gaussian quadrature can be used to derive the exact adjoint-based observation impact equations and furthermore that it is straightforward to account for the effect of multiple outer loops in these equations if the proposed 4D-Var method is used. The method is illustrated using a three-level quasi-geostrophic model and the Lorenz (1996) model.

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).

The large-scale circulation change at the end of the Baiu season in Japan as seen in ERA40 data

The time evolution of the circulation change at the end of the Baiu season is investigated using ERA40 data. An end-day is defined for each of the 23 years based on the 850 hPa θe value at 40˚Nin the 130-140˚E sector exceeding 330 K. Daily time series of variables are composited with respect to this day. These composite time-series exhibit a clearer and more rapid change in the precipitation and the large-scale circulation over the whole East Asia region than those performed using calendar days. The precipitation change includes the abrupt end of the Baiu rain, the northward shift of tropical convection perhaps starting a few days before this, and the start of the heavier rain at higher latitudes. The northward migration of lower tropospheric warm, moist tropical air, a general feature of the seasonal march in the region, is fast over the continent and slow over the ocean. By mid to late July the cooler air over the Sea of Japan is surrounded on 3 sides by the tropical air. It is suggestive that the large-scale stage has been set for a jump to the post-Baiu state, i.e., for the end of the Baiu season. Two likely triggers for the actual change emerge from the analysis. The first is the northward movement of tropical convection into the Philippine region. The second is an equivalent barotropic Rossby wave-train, that over a 10-day period develops downstream across Eurasia. It appears likely that in most years one or both mechanisms can be important in triggering the actual end of the Baiu season.

The Asian summer monsoon: an intercomparison of CMIP5 vs. CMIP3 simulations of the late 20th century

The boreal summer Asian monsoon has been evaluated in 25 Coupled Model Intercomparison Project-5 (CMIP5) and 22 CMIP3 GCM simulations of the late 20th Century. Diagnostics and skill metrics have been calculated to assess the time-mean, climatological annual cycle, interannual variability, and intraseasonal variability. Progress has been made in modeling these aspects of the monsoon, though there is no single model that best represents all of these aspects of the monsoon. The CMIP5 multi-model mean (MMM) is more skillful than the CMIP3 MMM for all diagnostics in terms of the skill of simulating pattern correlations with respect to observations. Additionally, for rainfall/convection the MMM outperforms the individual models for the time mean, the interannual variability of the East Asian monsoon, and intraseasonal variability. The pattern correlation of the time (pentad) of monsoon peak and withdrawal is better simulated than that of monsoon onset. The onset of the monsoon over India is typically too late in the models. The extension of the monsoon over eastern China, Korea, and Japan is underestimated, while it is overestimated over the subtropical western/central Pacific Ocean. The anti-correlation between anomalies of all-India rainfall and Niño-3.4 sea surface temperature is overly strong in CMIP3 and typically too weak in CMIP5. For both the ENSO-monsoon teleconnection and the East Asian zonal wind-rainfall teleconnection, the MMM interannual rainfall anomalies are weak compared to observations. Though simulation of intraseasonal variability remains problematic, several models show improved skill at representing the northward propagation of convection and the development of the tilted band of convection that extends from India to the equatorial west Pacific. The MMM also well represents the space-time evolution of intraseasonal outgoing longwave radiation anomalies. Caution is necessary when using GPCP and CMAP rainfall to validate (1) the time-mean rainfall, as there are systematic differences over ocean and land between these two data sets, and (2) the timing of monsoon withdrawal over India, where the smooth southward progression seen in India Meteorological Department data is better realized in CMAP data compared to GPCP data.

A spatio-temporal structure-based approach to drought characterisation

Drought characterisation is an intrinsically spatio-temporal problem. A limitation of previous approaches to characterisation is that they discard much of the spatio-temporal information by reducing events to a lower-order subspace. To address this, an explicit 3-dimensional (longitude, latitude, time) structure-based method is described in which drought events are defined by a spatially and temporarily coherent set of points displaying standardised precipitation below a given threshold. Geometric methods can then be used to measure similarity between individual drought structures. Groupings of these similarities provide an alternative to traditional methods for extracting recurrent space-time signals from geophysical data. The explicit consideration of structure encourages the construction of summary statistics which relate to the event geometry. Example measures considered are the event volume, centroid, and aspect ratio. The utility of a 3-dimensional approach is demonstrated by application to the analysis of European droughts (15 °W to 35°E, and 35 °N to 70°N) for the period 1901–2006. Large-scale structure is found to be abundant with 75 events identified lasting for more than 3 months and spanning at least 0.5 × 106 km2. Near-complete dissimilarity is seen between the individual drought structures, and little or no regularity is found in the time evolution of even the most spatially similar drought events. The spatial distribution of the event centroids and the time evolution of the geographic cross-sectional areas strongly suggest that large area, sustained droughts result from the combination of multiple small area (∼106 km2) short duration (∼3 months) events. The small events are not found to occur independently in space. This leads to the hypothesis that local water feedbacks play an important role in the aggregation process.

Quantification of chemical and physical processes influencing ozone during long-range transport using a trajectory ensemble

During long-range transport, many distinct processes – including photochemistry, deposition, emissions and mixing – contribute to the transformation of air mass composition. Partitioning the effects of different processes can be useful when considering the sensitivity of chemical transformation to, for example, a changing environment or anthropogenic influence. However, transformation is not observed directly, since mixing ratios are measured, and models must be used to relate changes to processes. Here, four cases from the ITCT-Lagrangian 2004 experiment are studied. In each case, aircraft intercepted a distinct air mass several times during transport over the North Atlantic, providing a unique dataset and quantifying the net changes in composition from all processes. A new framework is presented to deconstruct the change in O3 mixing ratio (Δ O3) into its component processes, which were not measured directly, taking into account the uncertainty in measurements, initial air mass variability and its time evolution. The results show that the net chemical processing (Δ O3chem) over the whole simulation is greater than net physical processing (Δ O3phys) in all cases. This is in part explained by cancellation effects associated with mixing. In contrast, each case is in a regime of either net photochemical destruction (lower tropospheric transport) or production (an upper tropospheric biomass burning case). However, physical processes influence O3 indirectly through addition or removal of precursor gases, so that changes to physical parameters in a model can have a larger effect on Δ O3chem than Δ O3phys. Despite its smaller magnitude, the physical processing distinguishes the lower tropospheric export cases, since the net photochemical O3 change is −5 ppbv per day in all three cases. Processing is quantified using a Lagrangian photochemical model with a novel method for simulating mixing through an ensemble of trajectories and a background profile that evolves with them. The model is able to simulate the magnitude and variability of the observations (of O3, CO, NOy and some hydrocarbons) and is consistent with the time-average OH following air-masses inferred from hydrocarbon measurements alone (by Arnold et al., 2007). Therefore, it is a useful new method to simulate air mass evolution and variability, and its sensitivity to process parameters.

Extreme wind storms over Europe in present and future climate: a cluster analysis approach

Boreal winter wind storm situations over Central Europe are investigated by means of an objective cluster analysis. Surface data from the NCEP-Reanalysis and ECHAM4/OPYC3-climate change GHG simulation (IS92a) are considered. To achieve an optimum separation of clusters of extreme storm conditions, 55 clusters of weather patterns are differentiated. To reduce the computational effort, a PCA is initially performed, leading to a data reduction of about 98 %. The clustering itself was computed on 3-day periods constructed with the first six PCs using "k-means" clustering algorithm. The applied method enables an evaluation of the time evolution of the synoptic developments. The climate change signal is constructed by a projection of the GCM simulation on the EOFs attained from the NCEP-Reanalysis. Consequently, the same clusters are obtained and frequency distributions can be compared. For Central Europe, four primary storm clusters are identified. These clusters feature almost 72 % of the historical extreme storms events and add only to 5 % of the total relative frequency. Moreover, they show a statistically significant signature in the associated wind fields over Europe. An increased frequency of Central European storm clusters is detected with enhanced GHG conditions, associated with an enhancement of the pressure gradient over Central Europe. Consequently, more intense wind events over Central Europe are expected. The presented algorithm will be highly valuable for the analysis of huge data amounts as is required for e.g. multi-model ensemble analysis, particularly because of the enormous data reduction.

The global distribution of phytoplankton size spectrum and size classes from their light-absorption spectra derived from satellite data

The absorption spectra of phytoplankton in the visible domain hold implicit information on the phytoplankton community structure. Here we use this information to retrieve quantitative information on phytoplankton size structure by developing a novel method to compute the exponent of an assumed power-law for their particle-size spectrum. This quantity, in combination with total chlorophyll-a concentration, can be used to estimate the fractional concentration of chlorophyll in any arbitrarily-defined size class of phytoplankton. We further define and derive expressions for two distinct measures of cell size of mixed populations, namely, the average spherical diameter of a bio-optically equivalent homogeneous population of cells of equal size, and the average equivalent spherical diameter of a population of cells that follow a power-law particle-size distribution. The method relies on measurements of two quantities of a phytoplankton sample: the concentration of chlorophyll-a, which is an operational index of phytoplankton biomass, and the total absorption coefficient of phytoplankton in the red peak of visible spectrum at 676 nm. A sensitivity analysis confirms that the relative errors in the estimates of the exponent of particle size spectra are reasonably low. The exponents of phytoplankton size spectra, estimated for a large set of in situ data from a variety of oceanic environments (~ 2400 samples), are within a reasonable range; and the estimated fractions of chlorophyll in pico-, nano- and micro-phytoplankton are generally consistent with those obtained by an independent, indirect method based on diagnostic pigments determined using high-performance liquid chromatography. The estimates of cell size for in situ samples dominated by different phytoplankton types (diatoms, prymnesiophytes, Prochlorococcus, other cyanobacteria and green algae) yield nominal sizes consistent with the taxonomic classification. To estimate the same quantities from satellite-derived ocean-colour data, we combine our method with algorithms for obtaining inherent optical properties from remote sensing. The spatial distribution of the size-spectrum exponent and the chlorophyll fractions of pico-, nano- and micro-phytoplankton estimated from satellite remote sensing are in agreement with the current understanding of the biogeography of phytoplankton functional types in the global oceans. This study contributes to our understanding of the distribution and time evolution of phytoplankton size structure in the global oceans.

Sequential variations of phytoplankton growth and mortality in an NPZ model: a remote-sensing-based assessment

Radiometric data in the visible domain acquired by satellite remote sensing have proven to be powerful for monitoring the states of the ocean, both physical and biological. With the help of these data it is possible to understand certain variations in biological responses of marine phytoplankton on ecological time scales. Here, we implement a sequential data-assimilation technique to estimate from a conventional nutrient–phytoplankton–zooplankton (NPZ) model the time variations of observed and unobserved variables. In addition, we estimate the time evolution of two biological parameters, namely, the specific growth rate and specific mortality of phytoplankton. Our study demonstrates that: (i) the series of time-varying estimates of specific growth rate obtained by sequential data assimilation improves the fitting of the NPZ model to the satellite-derived time series: the model trajectories are closer to the observations than those obtained by implementing static values of the parameter; (ii) the estimates of unobserved variables, i.e., nutrient and zooplankton, obtained from an NPZ model by implementation of a pre-defined parameter evolution can be different from those obtained on applying the sequences of parameters estimated by assimilation; and (iii) the maximum estimated specific growth rate of phytoplankton in the study area is more sensitive to the sea-surface temperature than would be predicted by temperature-dependent functions reported previously. The overall results of the study are potentially useful for enhancing our understanding of the biological response of phytoplankton in a changing environment.

A GCSS model intercomparison for a tropical squall line observed during toga-coare. II: Intercomparison of single-column models and a cloud-resolving model

This paper presents single-column model (SCM) simulations of a tropical squall-line case observed during the Coupled Ocean-Atmosphere Response Experiment of the Tropical Ocean/Global Atmosphere Programme. This case-study was part of an international model intercomparison project organized by Working Group 4 ‘Precipitating Convective Cloud Systems’ of the GEWEX (Global Energy and Water-cycle Experiment) Cloud System Study. Eight SCM groups using different deep-convection parametrizations participated in this project. The SCMs were forced by temperature and moisture tendencies that had been computed from a reference cloud-resolving model (CRM) simulation using open boundary conditions. The comparison of the SCM results with the reference CRM simulation provided insight into the ability of current convection and cloud schemes to represent organized convection. The CRM results enabled a detailed evaluation of the SCMs in terms of the thermodynamic structure and the convective mass flux of the system, the latter being closely related to the surface convective precipitation. It is shown that the SCMs could reproduce reasonably well the time evolution of the surface convective and stratiform precipitation, the convective mass flux, and the thermodynamic structure of the squall-line system. The thermodynamic structure simulated by the SCMs depended on how the models partitioned the precipitation between convective and stratiform. However, structural differences persisted in the thermodynamic profiles simulated by the SCMs and the CRM. These differences could be attributed to the fact that the total mass flux used to compute the SCM forcing differed from the convective mass flux. The SCMs could not adequately represent these organized mesoscale circulations and the microphysicallradiative forcing associated with the stratiform region. This issue is generally known as the ‘scale-interaction’ problem that can only be properly addressed in fully three-dimensional simulations. Sensitivity simulations run by several groups showed that the time evolution of the surface convective precipitation was considerably smoothed when the convective closure was based on convective available potential energy instead of moisture convergence. Finally, additional SCM simulations without using a convection parametrization indicated that the impact of a convection parametrization in forced SCM runs was more visible in the moisture profiles than in the temperature profiles because convective transport was particularly important in the moisture budget.

Analytical solutions of a minimal model of species migration in a bounded domain

A minimal model of species migration is presented which takes the form of a parabolic equation with boundary conditions and initial data. Solutions to the differential problem are obtained that can be used to describe the small- and large-time evolution of a species distribution within a bounded domain. These expressions are compared with the results of numerical simulations and are found to be satisfactory within appropriate temporal regimes. The solutions presented can be used to describe existing observations of nematode distributions, can be used as the basis for further work on nematode migration, and may also be interpreted more generally.

SPARC Data Initiative: Comparison of water vapor climatologies from international satellite limb sounders

Within the SPARC Data Initiative, the first comprehensive assessment of the quality of 13 water vapor products from 11 limb-viewing satellite instruments (LIMS, SAGE II, UARS-MLS, HALOE, POAM III, SMR, SAGE III, MIPAS, SCIAMACHY, ACE-FTS, and Aura-MLS) obtained within the time period 1978-2010 has been performed. Each instrument's water vapor profile measurements were compiled into monthly zonal mean time series on a common latitude-pressure grid. These time series serve as basis for the "climatological" validation approach used within the project. The evaluations include comparisons of monthly or annual zonal mean cross sections and seasonal cycles in the tropical and extratropical upper troposphere and lower stratosphere averaged over one or more years, comparisons of interannual variability, and a study of the time evolution of physical features in water vapor such as the tropical tape recorder and polar vortex dehydration. Our knowledge of the atmospheric mean state in water vapor is best in the lower and middle stratosphere of the tropics and midlatitudes, with a relative uncertainty of. 2-6% (as quantified by the standard deviation of the instruments' multiannual means). The uncertainty increases toward the polar regions (+/- 10-15%), the mesosphere (+/- 15%), and the upper troposphere/lower stratosphere below 100 hPa (+/- 30-50%), where sampling issues add uncertainty due to large gradients and high natural variability in water vapor. The minimum found in multiannual (1998-2008) mean water vapor in the tropical lower stratosphere is 3.5 ppmv (+/- 14%), with slightly larger uncertainties for monthly mean values. The frequently used HALOE water vapor data set shows consistently lower values than most other data sets throughout the atmosphere, with increasing deviations from the multi-instrument mean below 100 hPa in both the tropics and extratropics. The knowledge gained from these comparisons and regarding the quality of the individual data sets in different regions of the atmosphere will help to improve model-measurement comparisons (e.g., for diagnostics such as the tropical tape recorder or seasonal cycles), data merging activities, and studies of climate variability.

An anatomy of the cooling of the North Atlantic Ocean in the 1960s and 1970s

In the 1960s and early 1970s sea surface temperatures in the North Atlantic Ocean cooled rapidly. There is still considerable uncertainty about the causes of this event, although various mechanisms have been proposed. In this observational study it is demonstrated that the cooling proceeded in several distinct stages. Cool anomalies initially appeared in the mid-1960s in the Nordic Seas and Gulf Stream Extension, before spreading to cover most of the Subpolar Gyre. Subsequently, cool anomalies spread into the tropical North Atlantic before retreating, in the late 1970s, back to the Subpolar Gyre. There is strong evidence that changes in atmospheric circulation, linked to a southward shift of the Atlantic ITCZ, played an important role in the event, particularly in the period 1972-76. Theories for the cooling event must account for its distinctive space-time evolution. Our analysis suggests that the most likely drivers were: 1) The “Great Salinity Anomaly” of the late 1960s; 2) An earlier warming of the subpolar North Atlantic, which may have led to a slow-down in the Atlantic Meridional Overturning Circulation; 3) An increase in anthropogenic sulphur dioxide emissions. Determining the relative importance of these factors is a key area for future work.

Impacts of 20th century aerosol emissions on the South Asian monsoon in the CMIP5 models

Comparison of single-forcing varieties of 20th century historical experiments in a subset of models from the Fifth Coupled Model Intercomparison Project (CMIP5) reveals that South Asian summer monsoon rainfall increases towards the present day in Greenhouse Gas (GHG)-only experiments with respect to pre-industrial levels, while it decreases in anthropogenic aerosol-only experiments. Comparison of these single-forcing experiments with the all-forcings historical experiment suggests aerosol emissions have dominated South Asian monsoon rainfall trends in recent decades, especially during the 1950s to 1970s. The variations in South Asian monsoon rainfall in these experiments follows approximately the time evolution of inter-hemispheric temperature gradient over the same period, suggesting a contribution from the large-scale background state relating to the asymmetric distribution of aerosol emissions about the equator. By examining the 24 available all-forcings historical experiments, we show that models including aerosol indirect effects dominate the negative rainfall trend. Indeed, models including only the direct radiative effect of aerosol show an increase in monsoon rainfall, consistent with the dominance of increasing greenhouse gas emissions and planetary warming on monsoon rainfall in those models. For South Asia, reduced rainfall in the models with indirect effects is related to decreased evaporation at the land surface rather than from anomalies in horizontal moisture flux, suggesting the impact of indirect effects on local aerosol emissions. This is confirmed by examination of aerosol loading and cloud droplet number trends over the South Asia region. Thus, while remote aerosols and their asymmetric distribution about the equator play a role in setting the inter-hemispheric temperature distribution on which the South Asian monsoon, as one of the global monsoons, operates, the addition of indirect aerosol effects acting on very local aerosol emissions also plays a role in declining monsoon rainfall. The disparity between the response of monsoon rainfall to increasing aerosol emissions in models containing direct aerosol effects only and those also containing indirect effects needs to be urgently investigated since the suggested future decline in Asian anthropogenic aerosol emissions inherent to the representative concentration pathways (RCPs) used for future climate projection may turn out to be optimistic. In addition, both groups of models show declining rainfall over China, also relating to local aerosol mechanisms. We hypothesize that aerosol emissions over China are large enough, in the CMIP5 models, to cause declining monsoon rainfall even in the absence of indirect aerosol effects. The same is not true for India.

A traceable physical calibration of the vertical advection-diffusion equation for modelling ocean heat uptake

The classic vertical advection-diffusion (VAD) balance is a central concept in studying the ocean heat budget, in particular in simple climate models (SCMs). Here we present a new framework to calibrate the parameters of the VAD equation to the vertical ocean heat balance of two fully-coupled climate models that is traceable to the models’ circulation as well as to vertical mixing and diffusion processes. Based on temperature diagnostics, we derive an effective vertical velocity w∗ and turbulent diffusivity k∗ for each individual physical process. In steady-state, we find that the residual vertical velocity and diffusivity change sign in mid-depth, highlighting the different regional contributions of isopycnal and diapycnal diffusion in balancing the models’ residual advection and vertical mixing. We quantify the impacts of the time-evolution of the effective quantities under a transient 1%CO2 simulation and make the link to the parameters of currently employed SCMs.