A mathematical model for assessing the influence of stocking rate on the incidence of droughts and for estimating the optimal stocking rates¹

Extract from M.Sc. (Agric) thesis submitted by the senior author to the University of the Orange Free State.

Abstract

The Putu 11 simulation model was used to simulate veld production for each of 47 years, using weather input data and soil properties of a site at Glen. Grassland drought was defined as that condition encountered when 100 kg/ha or less standing dry matter was simulated. Model simulations of monthly DM production at five selected stocking rates were used for determining the dates of occurrence and duration of the droughts. Simulated drought duration was found to be linearly related to stocking rate. Theoretically, no droughts were identified at stocking rates less than 6,25 ha/LSU. A simple economic analysis of the results indicated that the gross profits were optimised at a rate of 5,78 ha/LSU. The use of mathematical models for drought analysing and classification was successfully demonstrated.

Uittreksel

Die Putu 11 simulasiemodel is gebruik vir die simulering van veldproduksie vir ‘n periode van 47 Jaar met klimaatdata as inset by gegewe grondeienskappe in die Glen omgewing. ‘n Droogte is gedefinieer as ‘n toestand waar die gesimuleerde staande droë materiaal ‘n massa van 100 kg/ha of minder bereik. Model simulasies van maandelikse droëmateriaal produksies by vyf geselekteerde veeladings is gebruik vir die bepaling van die daturas van voorkoms en lengte van droogtes. Die gesimuleerde duur van droogtes is verwant aan veelading. Dit is gevind dat daar teoreties nie droogtes sal voorkom by veeladings ligter as 6,25 ha/GVE nie. ‘n Eenvoudige ekonomiese ontleding is op die resultate gedoen en daar is gevind dat bruto wins ‘n optimum bereik het by ‘n veelading van 5,78 ha/GVE. Die gebruik van wiskundige modelle vir die ontleding en klassifisering van droogte is bewys.

Additional index words:

• Drought indices
• Palmer index
• Putu 11

Notes

Extract from M.Sc. (Agric) thesis submitted by the senior author to the University of the Orange Free State.

Present address: P.O. Box 3250, Pretoria, 0001.