Yes. That’s right. Weather Logistics uses a dusty climate change calculator developed in its current form during spring 2003. But dusty need not mean redundant, as the old adage states: simple and ingenious often go hand-in-hand. During the year 2000 a simple demonstration of the climate calculator was produced using my Sharp EL-9400 calculator to emulate the seasonal cycle in temperatures in Nottingham. The instructions asked for a day … a month … the user then waited a second … and as if by magic the average temperature was output. Result!

Whilst the chosen town of Nottingham may not seem like an extraordinary place in terms of weather – it proved a keystone for creating climate data for 18 other major towns and cities in the United Kingdom from Aberdeen (Scotland) to Tenby (Wales). The climate calculator describe here is therefore particularly successful for representing the Central England Temperature (CET) that forms a basis of historical climate records.

Original calculation of climate

Later versions of the model demonstrated how to account for the more rapid trend in the land-surface temperatures during the spring compared to autumn, which caused a large offset during the equinoxes. This involved a little mathematical trick: To avoid chaotic output, only wave-functions that could exactly fit into the bounds of a year (365.25 days) were used. Two functions were then combined – the main function, a single phase oscillation (wavefunction 1) and a secondary “wavefunction 2″ (two complete periods per year). The latter function effectively lowers the autumn temperatures and raises the spring temperatures to within 0.5°C (0.9°F) of the official climate averages. The function generating approach is similar to the mathematical methods of a Fourier Series.

The more modern and published climate calculator 2003 was developed as an undergraduate student at the University of Reading – in Microsoft(TM) Office 1997-2003. It was fully integrated with the internet and has been operating without adaptation for 10 years – with no depletion in output quality. Climate calculations were validated against and produce results that are consistent with the 30 year 1961-1990 climatology averages of the Met Office Hadley Centre for Climate Change Prediction and Research. The first mathematical beauty of the formulas is their front-to-end decoding – with no logic gates. This makes calculators of the average temperature conditions very rapid – with embedded code that is now processed with much improved speed upon the age of broadband internet and computer processing power.

Spreadsheet calculations of climate

Another feature of the calculator is its extensibility within the UK. There is a single master formula (Eq 1 below) to compute for all regions. Finally, the third “trade secret” is its piggy-backing of an existing operating feature of all computers: time. Almost every computer has a date-code, which was converted into a number and is then used as the single dependent variable in the formula. All software updates and scheduled activities such as calendars and emails are based on this datecode. Time functionality gives the user the impression that the climate calculations are dynamic, whilst the code was generated and capable of operation before birth of dynamic html code. Environment based calculations are in essence like DNA that behave differently in a chemical soup in a prescribed part of the body. Likewise, the climate calculator is decoded by the internet search engine into a different output depending on the time that the computer makes the calculations.

Eq 1. Part 1 wavefunction ((dT/2)*SIN( ((360/365.25) *(DATE-22.746)-87.982)*PI())/180)+(T_max-dT/2))+ …

Part 2 wavefunction 2 ( ((dT/2)/7.75)*SIN(( (2*(360/365.25)) *(DATE-160)-87.982)*PI())/180)-0.61)

Here PI()=3.1415…, DATE is the Microsoft(TM) Excel numerical date-code that is automatically updated, T_max / T_min are the maximum and minimum monthly temperature in degrees in Celsius respectively. dT indicates the seasonal difference between the maximum and minimum monthly daytime (or nighttime) temperature, July and January in the case of my calculations for the UK.

Climate applications. The climate calculator has formed the basis of seasonal weather forecasts undertaken at Weather Logistics UK from August 2010 to November 2011 – a statistical based scheme that indicated the deviation from average upper air-stream and air temperature conditions several months in advance. Furthermore, the calculator was used to rapidly compute the demand for heating energy to fuel households. In an educational sense, the calculator is an easy way to get communities involved in climate change. Feel free to have a play with my open source code and the calculator.

To examine Chaos Theory – which describes how small perturbations in initial conditions produce seemingly random outcomes – you could adjust the value in part 1. For example by changing (Eq 1) to 364.25 and part 2 (Eq 1) to 366.0, you could explore that effect this change impedes on the climate – model difference over say 100 years time!

Teasing Patterns of Predictability from Chaos … Why Future Forecasting Products Call upon the Trained Eye of the Observer

We all recall the BBQ Summer of 2010! Perhaps you were busy searching for shorts and swimming costumes in April as the shops loaded in their summer gear. At this point in time Britain’s sun shone brightly, but we’ve now learned through recent experience that present weather patterns need not be obliged to stay. It all looked promising as many of us decided to take our recession busting domestic holidays. At-least that was until the until the extreme rainfall and rainy deluges hit home, with us all believing strongly that the summer would surely take a drier turn? It most certainly didn’t. As August drew to a rather soggy close, it left many of us paddling in muddy fields. For those less fortunate, waterlines marked the inside of their living quarters whilst they packed their essentials in preparation for a lengthy stay next door!

In a period of outrage the public become angry and confused. Surely weather forecasters had made a mistake, or their model had been playing up?

Whilst the model may have been right, chaos also says that it was almost certainly wrong.

Predictability in a Chaotic Climate System

Chaos theory states that small perturbations in the initial conditions can be amplified into much larger uncertainties at some point in the future. It is a mathematical definition for the outcome that arises when a number of non-perfect observations of at-least one predictor are different from reality. These uncertainties combine together in a manner that produces a set of strikingly different or almost unconstrained set of possible events at some unknown point in the future. Multiple futures are determined in weather forecasting either by running different ensemble member models or by the use of the same model with marginally perturbed inputs / observations. Chaos is distinct from randomness, in the sense that chaos exhibits patterns of behaviour that seem to repeat themselves (e.g. fractal behaviour). It is worth noting that most recurrent patterns themselves are unpredictable, perhaps only existing for a unique recipe of pre-defined starting conditions. In the physical sciences, Meteorology included, it is the very nature of small imbalances between more than one quasi-stable outcome that allows chaos to arise (and is also part of its definition).

In the world of atmospheric dynamics, we often picture an idealised world where a high altitude ribbon of fast moving fluid circumnavigates a band of the Earth. You may have guessed that this is known as a jet stream. Whilst this ribbon of air fluctuates (oscillates north and south) often wildly in its path, we are pretty confident that at any point in the future Britain’s jet stream will steer low pressure systems eastward. The two basic states that we could identify are high and low pressure conditions – which we could assign a probability of 50:50, as we see no reason to believe that a particular state would be preferred (more stable) were it not for knowledge of our climate, atmospheric physics and through dynamical modelling. Statistics wins over chaos, as we can provide non-definite answers to problems that are based on historical records of outcomes.

The forecast model produced and applied by Weather Logistics UK perturbs a climate mean, so it is constrained to the known events of the past. The model has performed well over recent years, although in the future regional climate changes and shifting weather patterns add further complexity in defining an average baseline.

It is convenient to liken climatology and climate statistics to studying answers to test papers before sitting a high-school examination: barring the examiner, nobody knows the questions, but we could feasibly have insight through studying all the possible answers. Certain types of questions are almost sure to appear, yet that is not certain it is based on past experience of papers. In atmospheric science climate shifts add particular headache, as unusual weather patterns introduce an extra field of uncertainty – just like student’s anxieties over the examination board changing their syllabus.

Why Blocking Patterns Introduce Certainty to a Chaotic System

Blocking patterns appear to prefer particular locations than others, which means they are recurrent features that will continue to produce a similar set of outcomes. A dynamic and freely moving jet stream and low pressure systems provides us much less certainty – whilst blocking patterns slow down the fluctuations into a longer time-frame allowing us to base a seasonal forecast system on a fixed or frozen state of affairs. All the time the blocking “sticks put” we can use this glued climatic state to conduct our analysis.

Can Blocking High Pressure Systems be easily Monitored?

A free flowing system produces an more predictable climatic state (close to the historical statistical average), with global temperature patterns governed by large scale variability such as the Pacific and Atlantic Oscillations that are somewhat teleconnected. In contrast, blocking high pressure systems produce detectable extreme conditions such as prolonged drought, flooding, high and low temperatures (outside the expected thresholds). Their residence period in a preferred location can impose detectable anomalies in the sea surface temperatures, such as the hot waters off the Eastern states that invigorated the recent super-storm Sandy.

Climate Signals and Indicators to Monitor Blocking Intensity

Sea surface temperature anomalies are a big indicator of blocking patterns, since high pressures exhibit quasi-stationary behaviour that lasts sufficiently long to leave a noticeable signature upon the region where they are situated. In particular, high pressure conditions allow thermal energy from the atmosphere and surface to escape more freely to space, whilst increasing the absorbed solar radiation. Depending on the latitude and surface reflectivity and emissivity, this can either induce a small regional warm or cold bias from the surface temperature climatology record. An additional forcing is exerted by the dynamic transport of moisture and heat poleward at the impact zone with a westerly jet stream. On the downstream side cooler and drier polar air is drawn equator-ward causing some surface wind-driven cooling at lower latitudes. Additionally, blocking high pressure systems drive the surface currents of ocean gyres, either slowing or accelerating the flow of oceanic water. In the North Atlantic Ocean this can force a temporary slow-down of the Atlantic Meridional Oscillation (which is dependent on the high pressure blocking location – i.e. it is latitude and longitude position critical)*.

The Impact of Blocking Patterns on Extreme Weather Events

Blocking patterns have been causing havoc across the world. In America they have attributed to the extreme northerly trajectory of Hurricane Sandy (as mentioned above) that made landfall in the Eastern states during October 2012 amongst several other weather phenomenon. The Eurasian continent has fallen victim to the Russian droughts and the European heatwave of 2003, whilst over Asian the monsoon rains have been deflected further north into the less familiar territory of Pakistan. This has resulted in widespread flooding. Closer to home, blocking high pressure systems occur most frequently around central England, as we are situated directly in the path of a polar jet stream. With droughts in early 2012, followed by an abrupt shift to wetter weather, our seasons are becoming somewhat topsy-turvy.

Overview

Blocking patterns provide a key that can turn our otherwise turn our troublesome and otherwise chaotic British weather observations into successful seasonal to decadal predictions. What’s more this is best achieved through alternative modelling techniques, as the driving mechanisms for blocking patterns and their representations in Numerical Weather Prediction models are currently inadequate.

*Please consult our jet stream blocking coding system for the British Isles, any questions can be sent via email (forecasts@weatherlogistics.com) or on my Twitter page (@cjnankervis) where I regularly tweet my long range weather predictions.

Christopher Nankervis BSc (Hons) Met

Specialist in Earth Observation, Climate Physics

Project Manager @ Weather Logistics UK