# day length calculations

Timothy Martin timm at u.washington.edu
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) -
3.15*(L^4)*(10^-7)

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
74:139-154.

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 u.washington.edu
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 citrus.ucr.edu
>
>

```