 at the central site. The mean width of the simulation envelope at the peripheral site is 0.34 kPa (the mean width of the 90% prediction intervals is 0.21 kPa). Despite this rather narrow width, the simulation envelope is far too conservative, with the observed pressure being outside the envelope only 17 times as opposed to the expected value of 168 if the intervals were calibrated. Furthermore, the upper envelope is particularly conservative, as the observed pressure is one of the highest 30 ranks only 0.56% of the time as opposed to 30% of the time for a calibrated interval. This asymmetry in the upper and lower envelopes should be expected, given the fact that  the predicted values forZ(x) are higher on average than the observedZ(x). Since the prediction errors at different times may be strongly correlated, this apparent substantial miscalibration is not necessarily a sign of a problem with the methodology. For example, if we consider the ranks at each time point of the 100 series (the observed series plus the 99 simulated series), then 19 of these series are at no time the minimum or maximum of the 100 series. Thus, being outside the simulation envelope only 17 times is not at all unusual. This overconservativeness is not caused by too much variability in the simulated values ofZ, since if we setZ to the same value in all 99 simulated series (given by the elevation-adjusted kriging predictor under the pure nugget model), then the observed series is the minimum or maximum at 10 time points, whereas 14 of the 99 simulated series are never the minimum or maximum.
5. Discussion. This work only considers prediction of a single meteorological quantity at two locations. Extending the approach to a large number of locations and/or to predicting area averages introduces no new conceptual challenges, although the computational burden would increase. However, the assumption of no coherence at temporal frequencies higher than hourly is unreasonable at sufficiently small spatial scales, so that conditional simulations at high spatial resolution under the fitted model here would have high frequency fluctuations with too much spatial variability at nearby locations. To examine the scope of this problem, I carried out conditional simulations at two locations, the peripheral prediction site and a location 1 km north of this site (and assumed to be at the same elevation). Over the 99 simulations, the average variance of the differences between the simulated values at the two sites was 0.0030, which is about 14% of the same quantity when comparing the simulations at the peripheral and central prediction sites. This average variance corresponds to a standard deviation of 0.054 kPa, which is not that much bigger than the overall uncertainty in the measurements of 0.035 kPa.
Nevertheless, if one wanted to do something about even these quite small local fluctuations in pressure, one could change the model to allow spatial dependencies at higher frequencies. For example, consider setting ω 0 = π (so that δ is only forced to be 0 at ±π), thus adding a knot at π for δ, θ and β, but otherwise leaving all of the other knot locations given in the appendix unchanged. The lack of spatial independence at higher frequencies does slow down the computations relative to the model with ω 0 = π/6, but they are still manageable. The loglikelihood then increases by about 73 with the addition of the three parameters, even though the fitted coherences at the hourly frequency, which were forced to be 0 in the smaller model, have quite small values: between 0.0079 and 0.068 for all pairs of monitoring sites. Unfortunately, making this change does not, in fact, create strong coherences at high frequencies and small spatial scales because the estimated value for β is less than −1.88 for all frequencies higher than the hourly, putting an upper bound of around 0.132 on coherences in this frequency range no matter how close two locations are. Thus, it would appear that we would need to remove or somehow constrain the spatial nugget effect at higher frequencies in order to get the strong coherences we would want at short spatial scales. Removing the spatial nugget entirely seriously degrades the fit at lower frequencies. Replacing the spatial nugget term in the first line of (1) by, for example, π −π S 0 (ω)C 0 (|x|)e iωt dω, where C 0 is a valid, continuous, isotropic correlation function that is identically 0 at all distances greater than the shortest distance between the 11 monitoring sites, would not have any effect on the likelihood function but would allow coherences to tend to 1 as distances tend to 0. However, the data provide no information about the choice of C 0, so such a solution would be highly arbitrary. A better solution would be to collect data for some period of time at a small but tightly spaced set of sites as part of one of the SGP Field Campaigns that are carried out in the region (see www.arm.gov/sites/sgp.stm).
Extending this work to the multivariate setting is a greater challenge. Specifically, it is not obvious how to extend the model in Stein (2005) to the multivariate setting in a way that allows for realistic dependencies across quantity, space and time. Although some recent works such as Haas (2002) and Tzala and Best (2008) consider statistical modeling of multivariate space-time processes, these works focus on much longer time scales and it is not clear the models and methods they propose are suitable for capturing the dynamics affecting high-frequency meteorological data. Another challenge in statistically modeling winds and temperatures is that there are clear diurnal cycles in the dependence structure that may not be removable by such simple schemes as rescaling the data depending on the hour of the day. Therefore, it may be necessary to use space-time multivariate models that are only cyclostationary in time [Hurd and Miamee (2007)] rather than stationary.
Finally, let us return to the issue raised in the Introduction of making use of further meteorological information. In particular, such information might be of considerable value in handling the bursts of high volatility. Specifically, to the extent that rapid changes in pressure are due to the passage of weather fronts and the space-time evolution of these fronts can be mapped using, for example, upper level winds, one could try to model the volatility at a particular place and time in terms of a distance to the nearest front and the strength of that front rather than, as I did here, assuming the volatility does not depend on spatial location.Favourite 5 books read in 2017
This year I set myself the challenge to read 30 books. It was ultimately a bad idea. 30 books is roughly one book every 12 days which while certainly possible, just wasn’t practical for me. You see, I go through phases. A couple of months of doing nothing but reading, followed by a few months of doing, well, nothing. Things get in the way: podcasts stack up, work gets hectic and I find focusing on the page of words in front of me too difficult. As a result, I’ve read quite a few short books, for no other reason than I needed to catch up to stay on track. That’s not the point of reading.
Don’t get me wrong: some of those short books have been fantastic: the shortest made it into this list. It’s less a problem that I read short ones, but more of an issue that I entirely ignored anything over 300 pages, regardless of how good it may be. 2018 won’t include a similar goal. My intention for 2018 will be to read more, rather than read more, if that translates? Quality over quantity, every time.
Anyway, my short attention span aside, I‘ve enjoyed some absolutely incredible stories this year, from brand new authors to legends of their craft. From technology CEOs to political journalists and theoretical physicists. They have all captivated me, taught me, and through their words made me think, laugh and cry.
When breath becomes air, by Paul Kalanithi
This is one of the greatest books I have ever read, though I find it difficult to fully explain why, so I’ll let Paul himself try:
What makes life meaningful enough to go on living?
I can’t begin to imagine being in the position of having to genuinely try and answer that question. Waking up in perpetual pain looking for the reasons to actually get dressed. This book is his answer and in my opinion, it’s perfect.
Conclave, by Robert Harris
I’ve lived through two conclaves and in both cases watched the white smoke rise, saw the new pope greet St. Peter’s Square, and assume that there wasn’t much to the formal procedure that occurred within the Sistine Chapel cum clave.
While of course being a work a fiction, Robert Harris’ Conclave provides a peak behind that locked door and exposes what we should’ve expected: that politics, friendships and discord are all high on the menu, just as they would be during any election to a position of supreme power.
Hit Refresh, by Satya Nadella
It’s not often that a sitting CEO of a multinational company writes a book about being the CEO of a multinational company, but Satya isn’t necessary a typical CEO.
Leading Microsoft at a time when the competition is incredibly advanced, technology continues to move at an intense speed and the world still sees you as the Windows company, Satya must surely have everything to do. As a consultant at a Microsoft Partner using their products on a daily basis, I get to see first-hand just how the culture is changing, how Microsoft is betting big on the future while expanding their reach to all devices and operating systems.
It showed me that you must always have respect for your competitor, but don’t be in awe.
Satya deserves the credit for a lot of this. Driving