Improving Gas Demand Forecast During Extreme Cold Events

This thesis explores techniques by which the accuracy of gas demand forecasts can be improved during extreme cold events. Extreme cold events in natural gas demand data are associated with large forecast error, which represents high business risk to gas distribution utilities. This work begins by showing patterns associated with extreme cold events observed in natural gas demand data. We present a temporal pattern identification algorithm that identifies extreme cold events in the data. Using a combination of phase space reconstruction and a nearest neighbor classifier, we identify events with dynamics similar to those of an observed extreme event. Results obtained show that our identification algorithm (RPS-kNN) is able to successfully identify extreme cold events in natural gas demand data. Upon identifying the extreme cold events in the data, we attempt to learn the residuals of the gas demand forecast estimated by a base-line model during extreme cold events. The base-line model overforecasts days before and underforecasts days after the coldest day in an extreme cold event due to an unusual response in gas demand to extreme low temperatures. We present an adjustment model architecture that learns the pattern of the forecast residuals and predicts future values of the residuals. The forecasted residuals are used to adjust the initial base model’s estimate to derive a new estimate of the daily gas demand. Results show that the adjustment model only improves the forecast in some instances. Next, we present another technique to improve the accuracy of gas demand forecast during extreme cold events. We begin by introducing the Prior Day Weather Sensitivity (PDWS), an indicator that quantifies the impact of prior day temperature on daily gas demand. By investigating the complex relationship between prior day temperature and daily gas demand, we derived a PDWS function that suggests PDWS varies by temperature and temperature changes. We show that by accounting for this PDWS function in a gas demand model, we obtain a gas model with better predictive power. We present results that show improved accuracy for most unusual day types

How rare is the Bullet Cluster (in a Λ\LambdaCDM universe)?

The Bullet Cluster (1E0657-56) is well-known as providing visual evidence of dark matter but it is potentially incompatible with the standard $\Lambda$CDM cosmology due to the high relative velocity of the two colliding clusters. Previous studies have focussed on the probability of such a high relative velocity amongst selected candidate systems. This notion of `probability' is however difficult to interpret and can lead to paradoxical results. Instead, we consider the expected number of Bullet-like systems on the sky up to a specified redshift, which allows for direct comparison with observations. Using a Hubble volume N-body simulation with high resolution we investigate how the number of such systems depends on the masses of the halo pairs, their separation, and collisional angle. This enables us to extract an approximate formula for the expected number of halo-halo collisions given specific collisional parameters. We use extreme value statistics to analyse the tail of the pairwise velocity distribution and demonstrate that it is fatter than the previously assumed Gaussian form. We estimate that the number of dark matter halo pairs as or more extreme than 1E0657-56 in mass, separation and relative velocity is $1.3^{+2.0}_{-0.6}$ up to redshift $z=0.3$. However requiring the halos to have collided and passed through each other as is observed decreases this number to only 0.1. The discovery of more such systems would thus indeed present a challenge to the standard cosmology.Comment: v2, 14 pages, 10 figures. Revised in response to Referee's queries - in particular the expected number of Bullet-like systems drops by an order of magnitude when the halos are required to have collided and passed through each other. Accepted by JCA