Making Grass Greener

Water shortage is an ongoing problem. This spring, California mandated a 25% reduction in response to their drought. Atlanta nearly ran out of water during a 2007-2008 drought. Cities throughout the southwest including Phoenix, Las Vegas, and Los Angeles have begun paying residents to convert grass lawns to native plants.

When sprinklers operate on a fixed schedule, there is a chance they run during or near a rain event. Your team is tasked with developing an algorithm which will control sprinkler operation based on weather data and constructing a model  to estimate water needs for a lawn which can be personalized based on the lawn’s characteristics. Combining these, you will analyze the impact of need-based lawn care.

(1)    Develop an algorithm to control when the sprinklers turn on based on weather data and the water demand of a given lawn. Assume the system controlling the sprinklers has access to current and forecast weather data. Your algorithm should adjust according to the watering needs of the lawn.

(2)    Develop a mathematical model to determine how much water is required to maintain lawn health. Consider different varieties including tall fescue, Kentucky bluegrass, and buffalo grass. Other factors you may wish to consider include regional temperature, humidity, and sunshine/shade. Once your model is constructed, use it to estimate water requirements for a lawn in Seattle WA, Phoenix AZ, Cleveland OH, and Atlanta GA.

(3)    Using historical precipitation data from June and July 2014 as a case study, compare water usage in the four cities from part (2) in the following scenarios:

  • Sprinklers are set on a timer, unchanged through the growing season. The timer is set to provide enough water to keep the lawn healthy through typical regional hot and dry periods.
  • Sprinklers operate using your algorithm from part (1).
  • The lawn is removed and replaced with native landscape plants.

Based on your estimates, make a recommendation for appropriate lawn management in each of the four cities.

Daily weather data:

Monthly average data:

Problem submitted by Paul Taylor, an associate professor in the department of mathematics at Shippensburg University, Pennsylvania.