# Daily Temperature as a function of time

1. Oct 7, 2012

### zzinfinity

Hi,
I trying to loosely express temperature during the day as a function of time. Essentially what I want is to be able to take the average high and low temperature for say May 15th, and use those 2 data points to extrapolate a function that gives the temperature as a function of the minute.
Looking at daily temperature graphs, it appears to loosely follow the form of a sign wave. So lets say I knew my high temperature was 10 degrees and my low was -10 degrees. How accurate would it be to say.

Temp(t)= -10Cos(pi*t/720) where t is the number of minutes after the the coldest time of the night.

Is this in any way an accurate representation. Is there a better way to do this with only a little bit of climate data?

Thanks.

2. Oct 7, 2012

### Andre

Even if it was, maybe only when the day and night cycle is 12-12 hours, the higher the lattitude, the more problems you're likely running into

Weather stations routinely produce hourly data, which can be averaged to compile algorithms like that or google diurnal temperatures.

Last edited: Oct 7, 2012
3. Oct 8, 2012

A sine wave is a good rough approximation, but if you're looking for something more accurate, then you have to take other factors into account than time and min/max temperature.

Here's a graphical hourly forecast for Melbourne, Florida, near their weather forecast office. Any NWS site should allow you to view a similar graphical hourly forecast.
http://forecast.weather.gov/MapClic...51412429&unit=0&lg=english&FcstType=graphical

If you view this any time in the near future from when I posted it, you'll see that this time of year, South Florida has a relatively sharp incline to the near-max from 9am to 1pm, and then gently rounding off to the maximum around 3pm. This is due to the formation of coastal showers and thunderstorms forming along the sea breeze boundaries. From the maximum, it's then a slow linear decline from there to the diurnal minimum.

Some factors I can think of that would alter the pattern from a pure sine wave include:

Geographically-specific repeating weather patterns - I've seen coastal areas in California that have a regular morning fog that "burns off" by a certain time, followed by a jump in surface level air temps. Along the Great Lakes, "lake effect" weather patterns can help slow rapid night-time heat loss in the winter. Coastal storms during South Florida's rainy season certainly alter the temperature curve in the late afternoons as mentioned above.

Albedo - Areas dominated by pavement will absorb heat more than a snow-covered field. The latent heat may later moderate night time temperature loss, particularly around big cities. Albedo varies by season in Northerly climates.

If patterns for the above factors are known, you may be able to more accurately approximate the curve for a specific area.

Last edited: Oct 8, 2012