Physics-based modelling for remote sensing of snow

Remote sensing is the only practicable means to observe snow at large scales. Measurements from passive microwave instruments have been used to derive snow climatology since the late 1970’s, but the algorithms used were limited by the computational power of the era. Simplifications such as the assumption of constant snow properties enabled snow mass to be retrieved from the microwave measurements, but large errors arise from those assumptions, which are still used today. A better approach is to perform retrievals within a data assimilation framework, where a physically-based model of the snow properties can be used to produce the best estimate of the snow cover, in conjunction with multi-sensor observations such as the grain size, surface temperature, and microwave radiation. We have developed an existing snow model, SNOBAL, to incorporate mass and energy transfer of the soil, and to simulate the growth of the snow grains. An evaluation of this model is presented and techniques for the development of new retrieval systems are discussed.

Grey-box radial basis function modelling

A fundamental principle in data modelling is to incorporate available a priori information regarding the underlying data generating mechanism into the modelling process. We adopt this principle and consider grey-box radial basis function (RBF) modelling capable of incorporating prior knowledge. Specifically, we show how to explicitly incorporate the two types of prior knowledge: (i) the underlying data generating mechanism exhibits known symmetric property, and (ii) the underlying process obeys a set of given boundary value constraints. The class of efficient orthogonal least squares regression algorithms can readily be applied without any modification to construct parsimonious grey-box RBF models with enhanced generalisation capability.

Modelling and control of Hammerstein system using B-spline approximation and the inverse of De Boor algorithm

In this article a simple and effective controller design is introduced for the Hammerstein systems that are identified based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The controller is composed by computing the inverse of the B-spline approximated nonlinear static function, and a linear pole assignment controller. The contribution of this article is the inverse of De Boor algorithm that computes the inverse efficiently. Mathematical analysis is provided to prove the convergence of the proposed algorithm. Numerical examples are utilised to demonstrate the efficacy of the proposed approach.

Issues in the assimilation of the sources of a trace gas by inverse modelling

The problem of reconstructing the (otherwise unknown) source and sink field of a tracer in a fluid is studied by developing and testing a simple tracer transport model of a single-level global atmosphere and a dynamic data assimilation system. The source/sink field (taken to be constant over a 10-day assimilation window) and initial tracer field are analysed together by assimilating imperfect tracer observations over the window. Experiments show that useful information about the source/sink field may be determined from relatively few observations when the initial tracer field is known very accurately a-priori, even when a-priori source/sink information is biased (the source/sink a-priori is set to zero). In this case each observation provides information about the source/sink field at positions upstream and the assimilation of many observations together can reasonably determine the location and strength of a test source.

A three-regime model of speculative behaviour: modelling the evolution of the S&P 500 composite index

We examine whether a three-regime model that allows for dormant, explosive and collapsing speculative behaviour can explain the dynamics of the S&P 500. We extend existing models of speculative behaviour by including a third regime that allows a bubble to grow at a steady rate, and propose abnormal volume as an indicator of the probable time of bubble collapse. We also examine the financial usefulness of the three-regime model by studying a trading rule formed using inferences from it, whose use leads to higher Sharpe ratios and end of period wealth than from employing existing models or a buy-and-hold strategy.

Integration of remote sensing and GIS for modelling flash floods in Wadi Hudain catchment, Egypt

This paper presents a new approach to modelling flash floods in dryland catchments by integrating remote sensing and digital elevation model (DEM) data in a geographical information system (GIS). The spectral reflectance of channels affected by recent flash floods exhibit a marked increase, due to the deposition of fine sediments in these channels as the flood recedes. This allows the parts of a catchment that have been affected by a recent flood event to be discriminated from unaffected parts, using a time series of Landsat images. Using images of the Wadi Hudain catchment in southern Egypt, the hillslope areas contributing flow were inferred for different flood events. The SRTM3 DEM was used to derive flow direction, flow length, active channel cross-sectional areas and slope. The Manning Equation was used to estimate the channel flow velocities, and hence the time-area zones of the catchment. A channel reach that was active during a 1985 runoff event, that does not receive any tributary flow, was used to estimate a transmission loss rate of 7·5 mm h−1, given the maximum peak discharge estimate. Runoff patterns resulting from different flood events are quite variable; however the southern part of the catchment appears to have experienced more floods during the period of study (1984–2000), perhaps because the bedrock hillslopes in this area are more effective at runoff production than other parts of the catchment which are underlain by unconsolidated Quaternary sands and gravels. Due to high transmission loss, runoff generated within the upper reaches is rarely delivered to the alluvial fan and Shalateen city situated at the catchment outlet. The synthetic GIS-based time area zones, on their own, cannot be relied on to model the hydrographs reliably; physical parameters, such as rainfall intensity, distribution, and transmission loss, must also be considered.

Measurements and modelling of airflows in houses using passive sampling and HAM software

Passive samplers have been predominantly used to monitor environmental conditions in single volumes. However, measurements using a calibrated passive sampler- Solid Phase Microextraction (SPME) fibre, in three houses with cold pitched roof, successfully demonstrated the potential of the SPME fibre as a device for monitoring air movement in two volumes. The roofs monitored were pitched at 15° - 30° with insulation thickness varying between 200-300 mm on the ceiling. For effective analysis, two constant sources of volatile organic compounds were diffused steadily in the house. Emission rates and air movement from the house to the roof was predicted using developed algorithms. The airflow rates which were calibrated against conventional tracer gas techniques were introduced into a HAM software package to predict the effects of air movement on other varying parameters. On average it was shown from the in situ measurements that about 20-30% of air entering the three houses left through gaps and cracks in the ceiling into the roof. Although these field measurements focus on the airflows, it is associated with energy benefits such that; if these flows are reduced then significantly energy losses would also be reduced (as modelled) consequently improving the energy efficiency of the house. Other results illustrated that condensation formation risks were dependent on the airtightness of the building envelopes including configurations of their roof constructions.