Can a simple mathematical model be used to characterize monthly, yearly, and longer cloud patterns over a particular site? If so, can the model parameters be used to differentiate one location from another?
Understanding the behavior of clouds is a critical to understanding Earth's climate.
Because clouds are more reflective than most land surfaces (ice, snow, and possibly some bright deserts are the
exceptions),
they are a major contributor to the planetary albedo as viewed from space. Planetary albedo determines how
much of the solar radiation incident on Earth is reflected and how much is absorbed.
Changes in the type and amount of clouds,
and their distribution around the globe can modify climate. Or, conversely, changes in cloud patterns caused
by a variety of processes can themselves be a cause of cimate change — either amplifying or diminishing
the effects of those processes.
Cloud cover at a particular location is determined primarily by seasonal climatology and weather. Total cloud amounts often have seasonal variability modified by weather-driven "noise." The weather effect may be large or small relative to seasonal effects, depending on the local climatology. In addition, the yearly average cloud amount may change with time, either in a random fashion because of weather or as a result of longer-term trends associated with a changing climate. Trends in total cloud cover and cloud type are strongly related to climate changes. Changes in cloud amount and type can both influence and be influenced by changes in climate, as a result of feedback mechanisms which are important but not yet well understood.
Cloud data are available from the MyNASAData website:
https://mynasadata.larc.nasa.gov/las/getUI.do
Monthly average cloud coverage data from NASA's International Satellite Cloud Climatology Project (ISCCP) project are available from January, 1994, through June, 2008. (The time range of data available through MyNASAData
depends on the status of projects providing the data as well as the effort required to put satellite-derived data into an easily accessible format.) The display below was generated by requesting time series data around 40°N, 75°W. The MyNASAData website automatically generates a grah, using the nearest available ISCCP grid point. Clicking on the "Show Values" tab will bring up a listing of the data used to generate the graph, which can then be saved as a text file and imported into Excel.
What observations can one make about these data? First of all, there is obviously a strong seasonal component. Maximum cloud coverage occurs around January-February and minimum coverage occurs in early fall. "On top" of the seasonal cycle there is a considerable amount of "noise" related to weather.
For periodic behavior like this, a sine or cosine curve is often a reasonable place to start with a model. The graph below shows a sine curve with a period of 12 months fitted to the ISCCP data. This model assumes:
• an offset from month 0 (December), because the maximum cloudiness doesn't occur at month 0
• an annual mean that is the same from year to year
• an amplitude for deviations from the annual mean.
There are mathematical tools that can be used to do a "least squares" fit for this model, but in Excel it is easy just to try values for these three parameters, calculate the sum of the squares for all months,
sum of squares = Σ[(data - model)2]
and change the values until the sum of squares is minimum. (This process takes only a few minutes!) For these data, the resulting values are shown in this screen capture from the Excel file:
Of course, this model still doesn't look like the real data because there is no weather-generated noise imposed on the sine curve.
This noise can be modeled by adding normally distributed values to the sine model value for any given month. In Excel, the appropriate way to generate normally distributed numbers is with this formula:
sine model + [cell containing a "noise amplitude" value, A]*SQRT(-2*LN(RAND()))*SIN(2*PI()*RAND())
where A is selected by trial and error. The graph below shows the model plus normally distributed random noise,
with A=5. The values don't match the actual data of course, but their behavior is very similar to the real data. (Perhaps the value of A could be a little larger?)
There are other cloud products on MyNASAData, too, including subsets of total cloud cover from ISCCP and similar data from other satellites. These might provide interesting opportunities for comparisons among various satellite products.
The sine model used here will not work for all locations. Some places have much different seasonal patterns, for example, where there are monsoons and pronounced "rainy" and "dry" seasons.
It is a considerable assumption to use the same yearly average cloud cover over several years as has been done for the model illustrated above.
For some sites this might be not at all justified and, in any case, such an assumption makes it impossible to look for trends, even though the relatively short time periods represented in MyNASAData are not long enough to draw any meaningful conclusions about whether there are long-term changes in cloud patterns.
There are many links to information about clouds and Earth's climate on NASA's Earth Observatory website.
Also, you can find more information on websites for the The CALIPSO Project, the ISCCP Project, and the Surface Radiation Budget Project