Transactions of the ASABE Vol. 52(4): 1213-1221 2009 American Society of Agricultural and Biological Engineers ISSN 0001-2351 1213 TECHNICAL NOTE: PREDICTING WIND‐DRIVEN W AVES IN SMALL RESERVOIRS Y. Ozeren, D. G. Wren ABSTRACT. The earthen levees commonly used to form irrigation reservoirs are subjected to significant embankment erosion due to wind‐generated waves. The design of bank protection measures relies on adequate prediction of wave characteristics based on wind conditions and fetch length. Current formulations are based primarily on winds and waves in large water bodies and do not provide an optimal fit to waves in small water bodies such as irrigation ponds. Based on wind and wave data collected in an irrigation reservoir near Carlisle, Arkansas, the coefficients in a commonly used equation for wind wave prediction were improved for use in irrigation reservoirs. Details of the development of the new coefficients as well as data collection procedures are presented here. With the new empirical coefficients, the RMS error is 0.01 m for energy‐based significant wave height and 0.06 s for peak wave period. Keywords. Erosion protection, Levee protection, Wave prediction, Wind measurement. rrigation reservoirs are used to store water during winter months so that it can be used to irrigate crops during the growing season. Of the approximately 700 miles of earthen levees currently being used for irrigation ponds in the U.S., at least 50% experience significant damage due to wind‐driven waves (Carman, 2003). Efforts to mitigate this damage require estimates of the size of waves that will impact the levees (Ozeren et al., 2008). Techniques developed for larger water bodies have been found to be inadequate for predicting wind‐driven waves in irrigation reservoirs (Vincent et al., 2002). The energy transferred to the water surface by wind generates a range of wave heights and periods that increase as the waves travel across the available fetch length. The process of wave generation by wind can be explained by combining the resonance model developed by Phillips (1957) and the shear flow model developed by Miles (1957). Pressure fluctuations within the wind field disturb the still water and cause water surface undulations. These pressure fluctuations moving in the direction of the wind resonate with the free wave speed and amplify the undulations. As the size of these undulations increases, they begin to affect the pressure distribution within the wind field, resulting in a pressure difference between two wave crests. The net force created by the higher pressure on the windward face of the wave results in wave growth. Another explanation for the energy transfer between wind and waves was developed by Longuet‐Higgins (1969). As the wave heights increase, shorter waves steepen and break on the crests of faster traveling, longer waves. Therefore, as the speed, fetch, or Submitted for review in October 2008 as manuscript number SW 7755; approved for publication by the Soil & Water Division of ASABE in July 2009. The authors are Yavuz Ozeren, Research Associate, Department of Biology, University of Mississippi, University, Mississippi; and Daniel G. Wren, Hydraulic Engineer, USDA‐ARS National Sedimentation Labo- ratory, Oxford, Mississippi. Corresponding author: Daniel G. Wren, P.O. Box 1157, Oxford, MS 38655; phone: 662‐232‐2329; fax: 662‐281‐5706; e‐mail:ĂDaniel.Wren@ars.usda.gov. duration of the wind increases, wave height and period also increase. If the wind blows with a constant speed and direction over a certain fetch for sufficient time for the waves to travel the entire fetch length, then the wave characteristics will only depend on the fetch length and wind speed. This is known as the fetch‐limited condition, and it is assumed that steady‐ state wave conditions are achieved for that fetch (Vincent et al., 2002). If the wind duration is less than the required time for the waves to travel the fetch, then the wave conditions will be time dependent, and such wave conditions are described as duration‐limited. The duration‐limited condition is based on the assumption that wind speed increases suddenly in an area far from the boundaries, a condition that is rarely met. Wind blowing for an unlimited duration over an unlimited distance will have a limiting fetch length beyond which the waves do not continue to grow. This limiting condition is called a fully developed sea, and the rate of energy input to the waves from the wind is balanced with dissipation by wave breaking and turbulence (Sorensen, 1993). Due to the complexity of the physical phenomena, most methods for wave prediction are based on semi‐empirical relations. The methods have been modified as wind and wave data were accumulated over time, resulting in better predictions. The significant wave method (SMB method) was developed by Sverdrup and Munk (1947) and improved by Bretschneider (1952). The SMB method combines a simple energy growth concept with empirical calibrations using field data. Natural waves can be characterized by their frequency spectrum, which provides a measure of the energy at each frequency. Therefore, recent researchers seek to predict the wave energy spectrum given wind conditions (Sorensen, 1993). The simple empirical models of wave prediction assume uniform and steady wind conditions and neglect depth variations and shallow water processes. Discrete spectral and parametric methods of wave prediction have been developed to better represent the physical processes by coupling energy conservation principals with air‐water and water‐bed interaction processes. These models require numerical solution of complex equations with I