# What are the odds on a white Christmas this year?

By Ian Roulstone - Head of Department of Mathematics, University of Surrey

If you’re dreaming of a white Christmas you might look to the bookies to check the odds. Despite reports that this will be the coldest winter since 1963, with less than a week to go the odds of a flurry in London on the big day were hovering around 7/2, one of the lowest chances of snow for several years.

But perhaps mathematicians know better. When it comes to forecasting the likelihood of a snow blizzard, our weather presenters know what to say – predicting the odds of snow falling during the week ahead is relatively easy. However, predicting if there will be enough snow for festive frolicking with snowmen, sledging and snowball fights is much harder. We can tell if snow will fall, but not how much, which is arguably the most important Christmas weather question of all.

Weather forecasting is based on computer modelling, but surprisingly these models do not actually predict snow. A single variable is used to predict whether water will visit as liquid, vapour or ice so other information, such as air temperature is needed to stack the odds of snow.

Computer models are able to forecast the amount of water produced when air rises above the height at which water vapour begins to condense. Known as the Quantitative Precipitation Forecast (QPF), when it comes to snow prediction this is an important variable. But there are many sensitive factors that can affect the odds in favour of rain, or make it very difficult to distinguish between different types of snow, from a disappointing slush to our traditional fluffy festive flurry.

If temperatures are low enough, rain will fall as snow. And then forecasters need a way to translate the QPF into an equivalent snowfall. We use a ratio of about 1 to 10 to calculate how much snow will be produced from an amount of rainwater. If the QPF predicts one inch of rain, we’d be admiring a pretty good ten-inch covering of snow!

## Snow joke

Sounds simple? Think again. As with so many things in life, it’s not all about quantity, but quality; the quality of the snow that is.

This magic 1:10 rain to snow ratio can vary depending on whether the snow is “wet” or “dry.” Dry snow is composed of those small powdery flakes that make for great skiing; it is less dense and contains less water. It forms when there is very little moisture available. Under these circumstances, the rain to snow ratio can be considerably higher, quite often 1 to 20!

London in 2009 - Image Credit: John Curnow/WikimediaCommons

Then there is “wet” snow. This is the heavier, moisture-packed variety that can quickly turn into ankle-twisting ice patches. Here, there is abundant moisture, and the snowflakes are bigger and wetter. The typical ratio becomes 1 to 5.

To know if we’ll be getting the “right” kind of Christmas flurry, we therefore need to have very accurate forecasts of moisture levels in the atmosphere, plus an understanding of the variation of temperature with altitude.

## Blizzard of numbers

Our forecast models describe a snapshot of the weather at a given moment using vast arrays of numbers to describe the atmosphere. This array of numbers takes into account a host of basic variables such as moisture and temperature.

Calculating how these many millions of “weather pixels” will interact and adapt requires superfast computation and large amounts of memory. This resource-heavy computational model leads to inevitable limitations when predicting snowfall. So there is a trade-off between the geographical coverage of the models and the detail that we can expect from them.

It simply requires too much computer power to accurately predict snow (and importantly, what kind of snow) across the country. This trade-off is critical when it comes to calculating reliable QPFs, and therefore working out the chances of a proper white Christmas.

Forecasters often turn to the lessons learned at college – dew points, temperature soundings from meteorological balloon ascents and real-time reports from weather stations to assess the impact of a snow storm. So whether you turn to the bookies, TV weather presenters or even us mathematicians, getting an expert to predict snow – one of our most loved, and occasionally loathed, weather features – is a really tough call. But in any case it always depends on number crunching and the power of mathematics.

News form the weather robot

We may be able to capture the beauty of a perfect snow-covered Christmas day with high-resolution digital cameras, but capturing the mystery behind snowfall in our sophisticated weather prediction models is much more challenging.

Whether you should take a flutter on a flurry this year comes down to “seat of the pants” knowledge, a little hopeful wishing and, sometimes, a sprinkling of Christmas magic.

Source: The Conversation