The explicit consideration of model error in data assimilation is increasing. While this improves the realism of the situation (i.e. models have deficiencies), it also increases the complexity of the problem. Two common situations are often explored: independent model errors every time step (easy to study in theory) and fixed model errors (easy to implement in practice). We present the solution for an (ensemble) Kalman smoother in the presence of auto-correlated model error with a general (non-zero and non-infinite) memory. Moreover, we study the consequences of using a wrongly guessed memory in the data assimilation which is different from the true memory of the system.
We also provide some insight into the situations when model error with different time-scales may arise. We provide a simple analysis for a linear two-scale problem with a fast and a slow component. We show how the interactions can lead to three elements in the slow scale: direct, memory and noise (simple and complex). We discuss how these elements are addressed in sequential DA and provide some ideas of how to improve this treatment.

Abstract: The volume of catchment discharge that reaches a stream via the overland flow path is critical for water quality prediction, because it is via this pathway that most particulate pollutants are generated and transported to the stream channel, via surface erosion processes. When it rains, spatial variation in the soil infiltration rate leads to the formation and reabsorption of rivulets on the surface, and local topography determines the coalescence of rivulets.

We consider the question of how coalescence facilitates overland flow using a highly abstracted version of the problem, in which the drainage pattern is represented by a Galton-Watson tree. We show that as the rate of rainfall increases there is a distinct phase-change: when there is no stream coalescence the critical point occurs when the rainfall rate equals the infiltration rate, but when we allow coalescence the critical point occurs when the rainfall rate is less than the infiltration rate, and increasing the amount of coalescence increases the total expected runoff.

Prof Jones profile:

I am an applied mathematician with a background in data analytics, optimisation and simulation. Many of my projects involve assembling data from divers sources, using it to build simulation models, then using those models to inform management decisions. Previous collaborators include the Australian Department of Agriculture, Fisheries and Forestry (planning for the Post Entry Quarantine facility, a national infrastructure project); the Australian Office of Transport Security (improving security procedures in Australian airports); Rate Valuation Services (a financial services company);  McLaran International (the racing team); Merlin Power Systems (a feasibility study for an emergency response scheme for power generators in the UK); and National Air Traffic Systems (responsible for air traffic control in the UK).

My work makes use of a wide range of computational, analytical and mathematical techniques. I have taught graduate courses in machine learning and data mining, and I am the principal author of a best-selling text book on programming and simulation using the language R. Much of my current research concerns complex spatio-temporal environmental data, in particular problems of water runoff in catchment areas.

TITLE
Stochastically Generated Skew: Implications for Forecast Probabilities

ABSTRACT

The salient non-Gaussian features of observed climatological distributions are captured by so-called stochastically generated skewed (SGS) distributions that include Gaussian distributions as special cases. SGS distributions are associated with damped linear Markov processes perturbed by asymmetric stochastic noise and as such represent the simplest physically based prototypes of the observed distributions. As is true in most dynamical systems, an ensemble-mean forecast based on this process is generally not the most likely forecast, and the forecast uncertainty depends on the initial conditions, even when the initial conditions are perfect. Further, the heavy tails associated with SGS distributions have large ramifications for prediction of extremes. In this talk, I will discuss these and other annoyances.

The presentations will take place at the University of Reading on October 17th 2018, the agenda can be see here

We welcome applications from students with a very strong track record and a degree in Mathematics, Statistics, Engineering, Physics or related discipline. The project will involve the development of Statistical Methodology and a significant amount of Computing, so experience in scientific computation is highly desirable. The project will also involve theoretical investigations so good grasp of concepts from Analysis and Probability will be very useful.

The student will be part of the MPECDT programme, which is joint between the Universities of Reading and Imperial College London. This programme comprises an MRes in the first year followed by a PhD for three years. The student will be based primarily at Imperial College London but will also spend some time at the National Physical Laboratory (located in Teddington, South West London), as well as participating in MPECDT events at the University of Reading.

How to apply:

Applications should be lodged via the MPECDT applications procedure, indicating that the candidate wishes to be considered for the NPL joint project. The deadline for applications is 31 January 2017, and interviews will be held on 22 February.

Project Description:

Background:

Air pollution in cities is a major health problem. Regulations require that air quality is monitored and large scale sensor networks are being used to provide point measurements of pollutants. New data analytics is required to convert these point measurements to aggregate measures of air quality that enable cities to monitor air quality and assess the effectiveness of interventions.

Project:

This project will develop methodology for performing improved statistical inference on environmental modelling applications. These applications require the use of a large number of sensors that collect data frequently and are distributed over a large region in space. This motivates the use of space time varying stochastic dynamical models to model environmental quantities such as air quality, pollution level and temperature. Naturally one is interested in fitting these models to real data collected in practice. In addition, one is also interested on improving on the statistical inference using appropriate temporally-resolved observations, optimal spatial sensor placement or automatic calibration of sensor biases. From a statistical perspective, these problems can be formulated using a Bayesian framework that combine posterior inference with optimal design. Performing Bayesian inference or optimal design for these models is analytically intractable so one needs to rely on simulation-based numerical methods. We will be looking at computational methods that are principled but intensive and, given the additional challenge related to the high dimensionality of the models and data, exploit the structure of the underlying statistical model at hand to design effective algorithms that can be used in practice. This means that popular methods such as Sequential Monte Carlo (SMC) or Markov Chain Monte Carlo (MCMC) need to be carefully extended to accommodate the particular models in the application.

For further information on the project please contact Professor Alistair Forbes (alistair.forbes@npl.co.uk) and Dr Nikolas Kantas  (n.kantas@imperial.ac.uk).