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Historical in situ ocean temperature profile measurements are important for a wide range of ocean and climate research activities. A large proportion of the profile observations have been recorded using expendable bathythermographs (XBTs), and required bias corrections for use in climate change studies. It is generally accepted that the bias, and therefore bias correction, depends on the type of XBT used. However, poor historical metadata collection practices mean the XBT probe type information is often missing, for 59% of profiles between 1967 and 2000, limiting the development of reliable bias corrections. We develop a process of estimating missing instrument type metadata (the combination of both model and manufacturer) systematically, constructing a machine learning pipeline based on thorough data exploration to inform these choices. The predicted instrument type, where missing, will facilitate improved XBT bias corrections. The new approach improves the accuracy of the XBT type classification compared to previous approaches from a recall value of 0.75–0.94. We also develop an approach to account for the uncertainty associated with metadata assignments using ensembles of decision trees, which could feed into an ensemble approach to creating ocean temperature datasets. We describe the challenges arising from the nature of the dataset in applying standard machine learning techniques to the problem. We have implemented this in a portable, reproducible way using standard data science tools, with a view to these techniques being applied to other similar problems in climate science.

Day-to-day variations in surface air temperature affect society in many ways, but daily surface air temperature measurements are not available everywhere. Therefore, a global daily picture cannot be achieved with measurements made in situ alone and needs to incorporate estimates from satellite retrievals. This article presents the science developed in the EU Horizon 2020–funded EUSTACE project (2015–19, www.eustaceproject.org) to produce global and European multidecadal ensembles of daily analyses of surface air temperature complementary to those from dynamical reanalyses, integrating different ground-based and satellite-borne data types. Relationships between surface air temperature measurements and satellite-based estimates of surface skin temperature over all surfaces of Earth (land, ocean, ice, and lakes) are quantified. Information contained in the satellite retrievals then helps to estimate air temperature and create global fields in the past, using statistical models of how surface air temperature varies in a connected way from place to place; this needs efficient statistical analysis methods to cope with the considerable data volumes. Daily fields are presented as ensembles to enable propagation of uncertainties through applications. Estimated temperatures and their uncertainties are evaluated against independent measurements and other surface temperature datasets. Achievements in the EUSTACE project have also included fundamental preparatory work useful to others, for example, gathering user requirements, identifying inhomogeneities in daily surface air temperature measurement series from weather stations, carefully quantifying uncertainties in satellite skin and air temperature estimates, exploring the interaction between air temperature and lakes, developing statistical models relevant to non-Gaussian variables, and methods for efficient computation.

The empirical finding that market movements in stock prices may be correlated with the order flow of other stocks has led to the notion of "cross-impact" and has prompted the development of multivariate models of market impact. These models are parametrized by a matrix of impact coefficients whose off-diagonal elements are meant to capture how trades in one asset influence the price of other assets, leading to a large number of 'cross-impact' parameters which may not be identified solely based on the covariance of returns with order flow. Moreover, empirical evidence suggests that these cross-impact terms are unstable and change sign randomly over time, which poses a problem for their interpretation and use. We reexamine this empirical evidence from a causal standpoint and offer a simpler explanation for the observed correlation between the returns of an asset and the order flow imbalance of other assets, in terms of common components in order flow across stocks which may naturally arise from multi-asset trading strategies. We provide empirical evidence from order flow and price changes of NASDAQ-100 stocks to support this explanation. Our results show the main determinants of impact to be idiosyncratic order flow imbalance as well as a market order flow factor common across stocks. Additional ‘cross-impact’ terms account for less than 1% of market impact. This leads to a parsimonious approach for causal modelling of multi-asset impact, which does not require introducing any concept of "cross-impact".

We perform an empirical investigation of 'market impact' of trades using a large dataset of transactions executed by institutional investors in the US equity market. We find that price variations during trade execution are mainly driven by the aggregate order flow imbalance rather than the direction or size of individual trades. We find the main determinants of the amplitude of these price variations to be market volatility and trade duration. By contrast, trade size and execution speed, as measured by the participation rate, are found to have little or no influence on 'market impact' for orderly trade executions. Conditional on trade duration, trade size is found to have little influence on price variations during execution. We find evidence for a square-root dependence of price changes on duration rather than trade size and propose a simple explanation for this dependence in terms of the well-known square-root scaling of volatility as a function of duration. Our explanation is consistent with previous empirical studies on market impact and provides a simple rationale for the ubiquity of the 'square-root law' in these studies. We also examine the role of the participation rate in determining 'market impact': using evidence from large VWAP trades with high participation rates, we show that, conditional on duration, even large changes in participation rate have negligible influence on market impact, contradicting the assumption, common in optimal execution models, that impact increases with the participation rate. In fact, we provide evidence for the opposite effect: for a given trade size, the slower the execution, the higher the amplitude of price variations during the trade. Our findings highlight the need to revisit some common models of market impact and their use in the design of optimal execution, and suggest that it is more meaningful to focus on the modelling of aggregate order flow dynamics and the management of portfolio volatility during execution rather than the optimisation of 'impact' at a trade-by-trade level.

The non-perturbative computation of the energy-momentum tensor can be used to study the scaling behaviour of strongly coupled quantum field theories. The Wilson flow is an essential tool to find a meaningful formulation of the energy-momentum tensor on the lattice. We extend recent studies of the renormalisation of the energy-momentum tensor in four-dimensional gauge theory to the case of a three-dimensional scalar theory to investigate its intrinsic structure and numerical feasibility on a more basic level. In this paper, we discuss translation Ward identities, introduce the Wilson flow for scalar theory, and present our results for the renormalisation constants of the scalar energy-momentum tensor., Comment: Talk presented at the 34th International Symposium on Lattice Field Theory (Lattice 2016) by Susanne Ehret