day length calculations

Timothy Martin timm at
Fri Sep 8 12:06:21 EST 1995

I happened across a daylength model in Zhang and Lemeur (1995).  They 
cite Jackson et al. (1983) as the original source of the model.

The number of daylight hours (N) is calculated as (using ^ to designate 
an exponent; 10^2 = 10 squared, and with lots of parentheses 
to avoid ambiguity):

N = 0.945*(a + b*sin^2(pi*(D+10)/365))

a is the shortest daylight period of the year and b is the number of 
hours that must be added to a to obtain the longest day of the year.  
D is the day of the year.  a and b are calculated as:

a = 12.0 - 5.69*L*(10^-2) - 2.02*(L^2)*(10^-4) + 8.25*(L^3)*(10^-6) - 

b = 0.123*L - 3.10*(L^2)*(10^-4) + 8*(L^3)*(10^-7) + 4.99*(L^4)*(10^-7)

where L is the latitude in degrees.

Zhang and Lemeur. 1995. Evaluation of daily evapotranspiration estimates 
from instantaneous measurements. Agricultural and Forest Meteorology 

Jackson et al. 1983. Estimation of daily evapotranspiration from on 
time-of-day measurements. Agricultural Water Management 7:351-362.

Hope this helps.

Tim Martin
timm at
College of Forest Resources
Box 352100
University of Washington
Seattle, WA  98195-2100

On 8 Sep 1995, amanda braley wrote:

> Does anybody know of or have a basic (or similar) computer model that
> will calculate the hours of daylight at any given latitude? I'm 
> working on a photoperiod project for which knowing the weekly 
> average hours of daylight at the various latitudes from which the 
> stock plants were collected would be usefull.  I have a table of 
> sunrise and sunset times, from which I could painstakingly calculate 
> the hours of daylight myself, but I was hoping somebody might have been
> clever enough to write a little model to do this for me.
> Sincerely,
> Amanda Braley
> Staff Research Associate
> University of California
> Riverside, CA 92521
> braley at

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