Under the Weather: Uncertainty and weather forecasting in a chaotic system

Most of us, if not all of us, have seen a forecast graphic similar to the one pictured below. Temperatures are shown as specific numbers, such as 72° or 69°. This is called a “deterministic” forecast, which is a forecast that doesn’t show any uncertainty. While people tend to like this approach to forecasting, it can be problematic.

In my first article, I mentioned that there is uncertainty in every forecast, whether small or large—but I didn’t dive into why that uncertainty exists, or how we can deal with it.

A lot of this uncertainty stems from something called “chaos” and “chaos theory.” The American Meteorological Society defines “chaos” as the “property describing a dynamical system that exhibits erratic behavior in the sense that very small changes in the initial state of the system rapidly lead to large and apparently unpredictable changes in the later state.” In other words, in a chaotic system, the tiniest change in the initial condition can lead to significant and unpredictable differences later.

A commonly used example of a chaotic system is a double pendulum. To see an example of such a device, please take a couple minutes to watch this video:

In this simulation, you can see how the slight change in the starting positions of the double pendulums leads to significant and unpredictable differences.

Our atmosphere is also a chaotic system, which makes forecasting a bit more of a challenge, especially long-range forecasts.

Weather forecast models are all initialized with a set of initial conditions, which could be data from a satellite or surface observations. This data is used in a set of complex differential equations (shown below), which are then solved in order to obtain future conditions. This is what the models are doing behind the scenes.

However, because our atmosphere is a chaotic system, the tiniest change in the initial conditions could lead to a drastically different result down the road. Plus, the initial conditions and observations we have are not perfect. Thus, it can sometimes be hard to get an accurate deterministic forecast (i.e. a specific number in a temperature, for example), especially beyond a couple weeks or so. In fact, we essentially lose all forecast skill beyond two weeks due to the chaotic nature of our atmosphere.

Another problem with deterministic forecasts is that I’ve noticed people tend to get too caught up in the specific values. I’ve had people tell me “I heard it’s supposed to be 73 degrees” or whatever number. But the temperature could fall in a range of values due to uncertainty! This is why, in my forecast graphics, I show temperatures as “low-70s” or “mid-60s.” This better portrays uncertainty and prevents people from getting too caught up on an exact number. Besides, who is going to notice the difference in temperature if it’s 72 rather than 73?

While deterministic forecasts do have some value, as you can see, there are issues. So, what is the alternative? The alternative is probabilistic forecasts, which helps to deal with uncertainty and the chance that a specific event will occur. An extremely practical and useful way to do this is with ensemble forecasts.

This is essentially a bunch of different model forecasts, but each member of the ensemble starts with a slightly different initial condition. In doing this, we get a range of possibilities for potential outcomes. We can then determine the probability and likelihood of an outcome based on how many members predict it. In addition, we can take an average of all the outcomes; in general, the ensemble mean/average is more skillful than each of the members by themselves.

Below is an example of an ensemble, showing the 24-hour total amount of precipitation for Paine Field in Everett.

This is the GFS ensemble, with 30 total members. Each of these members were initialized with a slightly different initial condition, and as you can see, each of them ends up different. When I look at an ensemble like this, I notice a couple things. First, all the members show no rain through the middle of next week. This is a pretty good indication that we should be dry through then. Next, most of the members show that we have a chance of rain toward the end of next week and into the weekend. However, this is still quite a bit in the future, so this could change. At this point, all it does is it gives me something to keep an eye on in future model runs. The green bars in the bottom panel show the average of the 30 different solutions. This is generally where I look for a good idea of how much rain could happen, as opposed to each of the members separately.

Below is another example, with temperatures instead of rain. Most of the members agree on temperatures through next week, but after that, notice how they begin to vary. There is a lot more variation. This is a prime example of chaos. However, we can notice the general temperature trends, such as they look to be going lower, which is to be expected as we get closer to winter.

One thing to note is that although ensembles tend to be more skillful, they still are not perfect. Sometimes they can forecast an uncommon event too frequently, or they don’t forecast a specific event enough. Regardless, we still have to deal with our chaotic atmosphere; but forecasts have improved so much in recent decades, and improvement should continue.

There is so much that I could write about regarding this topic. It is complex. In future articles, I will likely show ensemble graphics, as I prefer these over the deterministic ones, so I hope this gives everyone a basic understanding of what they are and how to use them. If you have any additional questions, let me know below, and I will try my best to answer them!

Now here’s a look at your weekend forecast:


Right now, the only “action” we have weather-wise is the return of smoke into the area. Thankfully, it is expected to stay in the upper atmosphere (i.e. aloft), which means that even though we can tell it’s smoky through the tint of the sun or moon and the haziness, it shouldn’t impact our air quality significantly. This smoke is expected to decrease starting Saturday, so fingers crossed! Other than that, we are expecting dry conditions and comfortable temperatures. We could see some isolated patches of fog in the mornings, but if that happens, it’s expected to clear up, making for a nice few days! Enjoy it! I’ll just be over here waiting for the rain to come back.

— By Kelsie Knowles

Kelsie Knowles is a meteorologist and recent University of Washington graduate who lives in north Lynnwood. After writing weather blogs as a KOMO News intern, she discovered a passion for writing about weather. You can learn more in her blog www.wxnoggin.com and you can also follow her on Twitter at @kels_wx3.



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