Introduction

The importance of wind in determining circulation patterns and water quality in Upper Klamath Lake has been well established (Laenen and LeTourneau, 1996; Kann and Welch, 2005; Wood and others, 2006; Holiman and others, 2008; Wood and others, 2008). The collection of wind data at or near the lake is, therefore, a critical contribution to studies of the lake’s ecosystem and water quality. These studies address problems as diverse as (1) the occurrence of low dissolved-oxygen events (Kann and Welch, 2005; Wood and others, 2006), (2) the dependence of cyanobacterial vertical distribution on water-column stratification (J.W. Gartner, U.S Geological Survey, unpub. data, 2010), (3) the transport through the Williamson River Delta as a function of lake elevation, and wind speed and direction (T.M. Wood, U.S. Geological Survey, unpub. data, 2010), and (4) the transport of young larval suckers through the Williamson River Delta (Wood, 2009).

In 2005, as part of a cooperative study with the Bureau of Reclamation to determine water circulation patterns and heat transport in Upper Klamath Lake, several meteorological sites were established on the shoreline of Upper Klamath Lake and at two sites on rafts on the lake (fig. 1), to accurately describe the spatial variation of the wind over the surface of the lake. Wind data collected during the summers of 2005 and 2006 were used successfully as a forcing function in a hydrodynamic model of Upper Klamath Lake developed by Wood and others (2008). However, the collection of wind data since 2005 has been limited by the fact that the raft sites are in place only during the late spring through early fall months, May through September.

The ability to predict or, in the case of looking back in time, to “reconstruct” wind speed and direction at a site, would be useful for two reasons. First, the data needed to drive the hydrodynamic model are unavailable outside of May through September, which limits some applications of the model. For example, one application is to predict the passive transport of larval suckers through the Williamson River Delta and the lake. Larval suckers drift down the Williamson River in early spring, in some years prior to the availability of wind data at the two raft sites on the lake. Therefore, the ability to simulate early spring conditions at those sites a few days or weeks prior to the deployment of the rafts would make the hydrodynamic model more useful. In addition, there are occasional gaps in the wind records from May through October due to equipment failures that are too long to fill by simple interpolation. In these cases, reconstruction of the wind data is needed over a relatively short period of days or a few weeks, but at a high temporal resolution (at least hourly) to provide an accurate forcing function for the hydrodynamic model. The second reason that reconstructing the wind data at a site close to the lake would be useful is that it has the potential to extend the data record backward in time, prior to 2005, based on longer datasets collected elsewhere. This could provide several more years of overlap between wind data and water quality or other datasets for statistical analysis (for example, the Klamath Tribes water-quality monitoring began in 1986).

This study, done in cooperation with the Bureau of Reclamation, evaluated the accuracy of two multivariate, nonlinear, empirical methods for reconstructing the wind conditions at the raft sites on Upper Klamath Lake based on meteorological data collected at sites on the shoreline of the lake and at other locations in the basin. These two methods were Multivariate Adaptive Regressive Splines (MARS), a variation of linear regression, and Artificial Neural Networks (ANNs). MARS is a nonparametric technique that describes nonlinear dependencies on independent variables with piecewise linear segments of differing slope (Friedman, 1991). The change in slope occurs at a “knot” value that is part of the solution to the problem. Because the form of individual terms is linear, the dependencies of MARS models are simpler to understand and visualize than are those of the ANN models. The MARS models are built in two passes. On the forward pass, terms are added until the maximum specified number of terms is reached. On the backward pass, all existing terms are considered at each step and the least important term is removed, based on a generalized cross-validation comparison, which is a means of weighing goodness-of-fit against additional model complexity (Milborrow, 2009). With this recursive procedure, MARS selects the independent variables that constitute the best model.

Artificial Neural Networks have been used successfully in environmental studies to predict wind (Kretzschmar and others, 2004; Kulkarni and others, 2008), storm runoff (Shamseldin, 1997), and water-quality parameters, such as dissolved oxygen (Rounds, 2002), water temperature (Risley and others 2003), salinity (Conrads and Roehl, 1999; Conrads and others, 2006; Conrads and Roehl, 2007), sediment concentration (Rajaee and others, 2009), and pH (Cannon and Whitfield, 2001). ANNs rely on discerning and then “learning” the relations among variables based on many realizations of past events covering a large range in conditions, and therefore benefit from the large amount of data provided by the long records of hourly measurements collected at meteorological sites. Both ANN and MARS methods, being empirical in nature, allow data of varying types (for example, wind, air temperature, relative humidity, or solar radiation) to be tested as important explanatory variables without knowledge of a specific deterministic equation to describe the relation between dependent and independent variables, and do not require that the relations be linear. As such, these models are well suited to the current problem of reconstructing the wind data at a single site based on wind and other meteorological data collected nearby. The logical assumption is that the datasets are related, but the exact nature and physical description of that relation are unavailable.

Two sets of models were built for this study, and each set included the MARS and the ANN approach to the problem. The first set of models, used for reconstructing short periods of 10-minute wind data at the raft sites, is designated as the “gap-filling” models. The second set of models, used to reconstruct longer periods of daily wind data, is designated as the “historical” models.

Purpose and Scope

This report presents the results of efforts to demonstrate the feasibility of models based on MARS and ANN to simulate the wind at two raft sites on Upper Klamath Lake and document their accuracy, using as input the meteorological variables measured at six other sites, four U.S. Geological Survey (USGS) sites on the shoreline of the lake, and two AgriMet sites located away from the shoreline. These models simulate the wind over periods of a few days to a week or more on a 10-minute basis to match the temporal resolution of the observations and are appropriate only for filling gaps in the data since 2005, when intensive collection of meteorological data around the shoreline of the lake began.

Second, this report presents the results of efforts to assess the feasibility and document the accuracy of models, based on MARS and ANN, to simulate the historical wind record at a single site on the lake shoreline on a daily basis. These models could be used to reconstruct the wind record at any lake site since 2000, using data from the long-term Pacific Northwest Cooperative Agricultural Weather Network (AgriMet) and the National Climatic Data Center (NCDC) sites located from 8.0 to 11.5 km from the shoreline of Upper Klamath Lake.

First posted October 27, 2010