Scientific Investigations Report 2010–5201

U.S. Department of the Interior

U.S. Geological Survey

Empirical Models of Wind Conditions on 

Upper Klamath Lake, Oregon

Prepared in cooperation with the Bureau of Reclamation 
Cover: Photograph of U.S. Geological Survey meteorologic station near Howard Bay in 

Upper Klamath Lake. (Photograph taken by Kristofor Kannarr, U.S. Geological Survey, 2010.)
Empirical Models of Wind Conditions on 

Upper Klamath Lake, Oregon

By Norman L. Buccola and Tamara M. Wood

Prepared in cooperation with the Bureau of Reclamation

Scientific-Investigations Report 2010–5201

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, 

natural hazards, and the environment, visit http://www.usgs.gov or call 1-888-ASK-USGS

For an overview of USGS information products, including maps, imagery, and publications, 

visit http://www.usgs.gov/pubprod

To order this and other USGS information products, visit http://store.usgs.gov

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Buccola, N.L., and Wood, T.M., 2010, Empirical models of wind conditions on Upper Klamath Lake, Oregon: U.S. 

Geological Survey Scientific-Investigations Report 2010–5201, 26 p.
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope ..............................................................................................................................3

Data Description ............................................................................................................................................4

Statistical Methods and Model Algorithms...............................................................................................4

Gap-Filling Wind Models .....................................................................................................................5

Historical Wind Models .......................................................................................................................7

Results of Gap-Filling Wind Models .........................................................................................................10

Results of Historical Wind Models ..........................................................................................................19

Summary and Conclusions.........................................................................................................................23

Acknowledgments ......................................................................................................................................23

References Cited..........................................................................................................................................23

Figures

Figure 1. Map of Upper Klamath Lake, Oregon, showing the location of sites used 

in this report ................................................................................. 2

Figure 2. Flow chart showing steps in the construction of gap-filling models for 

wind time series on Upper Klamath Lake, Oregon .................................... 5

Figure 3. Graph showing examples of the original east-west components of the 

wind vector at site MDN on Upper Klamath Lake, Oregon, with the lowand high-frequency components obtained with preprocessing method 1 and 

the eigenvector smoothed version obtained with preprocessing method 2 ......... 6

Figure 4. Bar graphs showing wind direction at the mouth of the Williamson River 

(WMR) and Klamath Falls Airport (KLMT) near Upper Klamath Lake, Oregon ...... 8

Figure 5. Flow chart showing steps in the construction of the historical wind models 

for Upper Klamath Lake, Oregon ......................................................... 9

Figure 6. Graphs showing simulated and observed east-west and north-south 

components of the wind vector at site MDL on Upper Klamath Lake, Oregon ...... 14

Figure 7. Graphs showing simulated and observed east-west and north-south 

components of the wind vector at site MDN on Upper Klamath Lake, Oregon ...... 15

Figure 8. Graphs showing observed and simulated currents at site ADCP1, Upper 

Klamath Lake, Oregon, August 2006 ...................................................... 17

Figure 9. Graphs showing simulated tracer concentration and residuals at sites 

GBE and NBI, Upper Klamath Lake, August 2006 ....................................... 18

Figure 10. Graphs showing comparison of calibration and validation years for 

MARS_HIST2 and ANN _HIST2 wind models, Upper Klamath Lake, Oregon ...... 20

Figure 11. Graph showing observed and reconstructed wind data at WMR on 

Upper Klamath Lake, Oregon, aggregated on a weekly basis, 2005–09............... 21

Figure 12. Graph showing reconstructed wind data at WMR on Upper Klamath Lake, 

Oregon, aggregated on a weekly basis, 2004–05 ....................................... 22
iv

Tables

Table 1. Nondefault parameter values used in ANN and MARS wind models for 

Upper Klamath Lake, Oregon............................................................... 10

Table 2. Time series that were used as input to the gap-filling models for wind 

component vectors at sites MDN and MDL on Upper Klamath Lake, Oregon ...... 11

Table 3. Goodness-of-fit statistics for the Upper Klamath Lake, Oregon, gap-filling 

wind models during the calibration (May 12–September 29, 2007) and 

validation periods (May 12–September 30, 2006) ....................................... 13

Table 4. Upper Klamath Lake UnTRIM model goodness-of-fit velocity statistics at 

site ADCP1, Upper Klamath Lake, Oregon ................................................ 16

Table 5. Daily time series used in the historical wind models of Upper Klamath Lake, 

Oregon ....................................................................................... 19

Table 6. Goodness-of-fit statistics for the historical wind models of site WMR during 

the calibration and validation period...................................................... 19

Conversion Factors, Datums, and Abbreviations and 

Acronyms

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

meter (m) 33.28 foot (ft) 

kilometer (km) 0.621 mile (mi) 

Velocity

centimeter per second (cm/s) 0.3937 inch per second (in/s)

meter per second (m/s) 33.28 foot per second (ft/s) 

meter per second (m/s) 2.2369 mile per hour (mi/h) 

Datums

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Elevation, as used in this report, refers to distance above the Upper Klamath Lake Vertical 

Datum (UKLVD), which is used by the Bureau of Reclamation for reporting the elevation of Upper 

Klamath Lake.
v

ADCP acoustic Doppler current profiler

AgriMet Pacific Northwest Cooperative Agricultural Weather Network

ANN Artificial Neural Networks

BIAS Bias or Mean error

HIST Historical Model

MARS Multivariate Adaptive Regressive Splines

NASH Nash-Sutcliffe error 

NCDC National Climatic Data Center

NOPPM Un-filtered data

PPM1 Pre-processing (filtering) method 1

PPM2 Pre-processing (filtering) method 2

USGS U.S. Geological Survey

Conversion Factors, Datums, and Abbreviations and 

Acronyms—Continued

Abbreviations and Acronyms
vi

This page intentionally left blank.
Empirical Models of Wind Conditions on Upper Klamath 

Lake, Oregon

By Norman L. Buccola and Tamara M. Wood

Abstract

Upper Klamath Lake is a large (230 square kilometers), 

shallow (mean depth 2.8 meters at full pool) lake in southern 

Oregon. Lake circulation patterns are driven largely by wind, 

and the resulting currents affect the water quality and ecology 

of the lake. To support hydrodynamic modeling of the lake 

and statistical investigations of the relation between wind and 

lake water-quality measurements, the U.S. Geological Survey 

has monitored wind conditions along the lakeshore and at 

floating raft sites in the middle of the lake since 2005. In order 

to make the existing wind archive more useful, this report 

summarizes the development of empirical wind models that 

serve two purposes: (1) to fill short (on the order of hours or 

days) wind data gaps at raft sites in the middle of the lake, and 

(2) to reconstruct, on a daily basis, over periods of months to 

years, historical wind conditions at U.S. Geological Survey 

sites prior to 2005. Empirical wind models based on Artificial 

Neural Network (ANN) and Multivariate-Adaptive Regressive 

Splines (MARS) algorithms were compared. ANNs were 

better suited to simulating the 10-minute wind data that are 

the dependent variables of the gap-filling models, but the 

simpler MARS algorithm may be adequate to accurately 

simulate the daily wind data that are the dependent variables 

of the historical wind models. To further test the accuracy of 

the gap-filling models, the resulting simulated winds were 

used to force the hydrodynamic model of the lake, and the 

resulting simulated currents were compared to measurements 

from an acoustic Doppler current profiler. The error statistics 

indicated that the simulation of currents was degraded as 

compared to when the model was forced with observed winds, 

but probably is adequate for short gaps in the data of a few 

days or less. Transport seems to be less affected by the use of 

the simulated winds in place of observed winds. The simulated 

tracer concentration was similar between model results when 

simulated winds were used to force the model, and when 

observed winds were used to force the model, and differences 

between the two results did not accumulate over time. 

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. 
2 Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon

Figure 1. Upper Klamath Lake, Oregon, showing the location of sites used in this report. 

Norman_basemap 01

er

iv R

Hawks

Lake Sevenmile Canal

West Canal

Upper

Klamath

Marsh Modoc Point Main Canal

Whiteline

Reservoir

Swan

Lake

Round Lake

Lake Ewauna

Lost River

Nuss

Lake

Spring

Lake

Wood

River

Marsh

nos mailli W

Ball

Bay

Shoalwater Bay

Meadow

Lake

John C Boyle

Reservoir

Agency Straits

Upper

Wocus

Marsh

Caledonia

Marsh

Hank's 

Marsh

Link

River

Moss

Agency

Lake

Pelican

Bay

Klamath

Creek

Lake

Howard

Bay

Aspen

Lake

C Nannie r Ch

e

er

gu

ry Creek

Spra

Rock Creek

Eagle

r ev Ri

sknaB

hsi F

Varney

Creek

Clover Creek

Spencer

Creek

revi Rdoo W

keer C

k

t

e

s

er

oL

C

ut o Tr

derson

An Creek Rattlesnake

Point.

Hagelstein

County Park

Modoc Rim

Ball

Point

97

Bare

Island

97

140

140

70

62

Klamath 

Falls

Plum Valley

Ridge

Modoc

Point

Link

River 

Dam

Coon

Point

122°10' 122° 121°50' 121°40'

42°

30'

42°

20'

42°

10'

VER

RI HTA MALK

0 2 4 6 8 10 Miles

0 2 4 6 8 10 Kilometers

EXPLANATION

Meteorological station

Water quality station

Elevation, in feet

4143.3

4110

MDN-MET

BLB-MET

MDL-MET

HDB-MET

SSHR-MET

AGKO

WMR-MET

GBE

ADCP1

NBI

KFLO

KLMT

OREGON

Study

Area
Introduction 3

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. 
4 Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon

Data Description

Wind measurements used in the gap-filling model were 

collected at six USGS meteorological sites—MDL, MDN, 

BLB, HDB, SSHR, WMR—as well as two nearby AgriMet 

sites (Bureau of Reclamation, 1997)—AGKO and KFLO 

(fig. 1). Meteorological instrumentation at sites MDL and 

MDN was mounted on floating rafts on the lake during the 

summer (approximately May through September); data were 

collected at the other sites continuously through the year. 

Construction associated with the breaching of levees around 

the Williamson River Delta dictated that the site near the 

mouth of the Williamson River be relocated twice during the 

period covered by this report. Site WMR was relocated to 

WME in May 2007, and WME was in turn relocated to WRW 

in April 2008. Data from WMR, WME, and WRW were used 

interchangeably in this report due to their close proximity; 

references to WMR wind data should be interpreted to mean 

data from the Williamson River Delta site, which was at 

one of these three locations, depending on the time period. 

During the periods used for calibration and validation of the 

gap-filling model, USGS data were measured at 10-minute 

intervals. AgriMet data were collected at 15-minute intervals, 

and for the purposes of the gap-filling wind model, were 

interpolated linearly (after a conversion to north-south and 

east-west components) to match the 10-minute intervals of the 

USGS data. The air temperature used in the gap-filling model 

was measured at site WMR and was collected at 10-minute 

intervals. 

Datasets used in the historical wind model included the 

wind measured at the AgriMet sites AGKO and KFLO (daily 

mean speed and direction), as well as global solar radiation 

(cumulative daily), relative humidity (daily mean), and air 

temperature (daily mean) measured at AGKO. These variables 

were downloaded from the AgriMet website as daily values 

(Bureau of Reclamation, 1997). The daily mean wind speed 

and direction was then converted to east-west and northsouth components, when appropriate, and depending on 

the model type. An additional dataset used in the historical 

model is the data collected since 1959 at the Klamath Falls 

Airport (KLMT) by the National Oceanic and Atmospheric 

Administration and distributed via the Internet by the NCDC 

(National Oceanic and Atmospheric Administration, no date). 

The KLMT site (fig. 1) is only about 2 km from the KFLO 

site, but the sensors at the AgriMet sites are at 2 m above the 

ground, whereas the sensors at the KLMT sites are at 10 m 

above the ground. Daily means of the wind components, air 

temperature, dew point temperature, sky cover, and altimetric 

pressure were calculated from the original NCDC data, 

which were collected at irregular intervals over the day, but 

generally at hourly temporal resolution. Daily means of sky 

cover were calculated after converting categorical values to 

numerical values as follows (adapted from ASOS user’s guide 

[National Weather Service, 1998]): clear sky=0, scattered 

clouds=0.31, broken clouds=0.75, overcast sky=0.83, partial 

obscuration=0.92, and obscuration=1.0.

Statistical Methods and Model 

Algorithms

Two statistical modeling algorithms were used and 

compared in both the gap-filling and historical models: 

Artificial Neural Networks (ANN) and Multivariate Adaptive 

Regressive Splines (MARS). ANNs provide a flexible 

method of relating input and output variables through an 

interconnected mesh of nonlinear transfer functions. The 

R-package nnet provided the feed-forward, single-hiddenlayer ANN that was used in this work (Venables and Ripley, 

2002). Nondefault parameters used in the nnet algorithm 

were size (number of units in the hidden layer) and decay

(weight decay). The number of units in the hidden layer (size

parameter) generally determines the complexity of the neuralnetwork model and is relative to the complexity of the dataset 

that is being used to train or calibrate the model. The weight 

decay (decay parameter) is dependent on the size parameter, 

such that the former will not have much effect until the latter 

is of a sufficient value. Therefore, the minimum number of 

hidden-layer units (size) was determined first, as it primarily 

determined the complexity of the ANN. After size was 

determined, the optimum decay value was determined while 

holding size constant. The best model results were achieved 

through an optimization process in which size and decay were 

adjusted by trial-and-error iteratively until model-fit statistics 

from the calibration and validation time periods matched as 

closely as possible. The goal of this optimization process was 

to obtain parameter values, which resulted in models that 

could accurately simulate a wide range of wind conditions.

MARS is a multiple-regression technique that allows 

for nonlinearity between the dependent and independent 

variables described by a discrete change in slope between 

linear segments. MARS can achieve a closer fit to measured 

data using a larger number of input variables than leastsquares regression while still utilizing recursive linearregression techniques (Friedman, 1991). The R-package earth

incorporates the MARS algorithms and has the ability to 

sort through a large initial set of input variables by removing 

input variables stepwise from this initial model framework 

until the most statistically effective subset of variables is 

left, resulting in a model that is not overfit (Milborrow, 

2009). The nondefault parameter in the earth package that 

was manipulated for this work was nk, which is one of the 

criteria used to limit the number of input variables that are 

used to predict the dependent variable in the MARS model 

construction process. The value of nk was set to the smallest 

possible value (thereby limiting the complexity of the model) 

that did not show a substantial degradation in performance 

over a more complex model (one with a higher nk value). This 

iterative process was guided by minimizing the difference 

between fit statistics calculated over the calibration and 

validation time periods. 
Statistical Methods and Model Algorithms 5

Gap-Filling Wind Models

The dependent variables of the gap-filling models 

numbered four: the east-west and north-south components 

of the wind at two sites, MDN and MDL. The independent 

(explanatory) variables were the east-west and north-south 

components of the wind at six sites (HDB, BLB, WMR, 

SSHR, AGKO, KFLO), and air temperature at one site 

(WMR, fig. 1). Each time series was passed to both ANN 

and MARS models in three ways—with no preprocessing 

(NOPPM) and with two types of preprocessing with different 

degrees of smoothing. These two methods are denoted as 

preprocessing method 1 (PPM1), in which the original data 

were decomposed into low- and high-frequency components, 

and preprocessing method 2 (PPM2), in which an eigenvector 

filter was used to smooth the data (fig. 2).

The first preprocessing method (PPM1) consisted of 

decomposing each measured wind time series into low- and 

high-frequency components. The low-frequency component 

was a 24-hour moving average of the original data. The 

high-frequency component was obtained by subtracting 

the low-frequency component from the original data. This 

high‐frequency component was smoothed using a 3-hour 

moving average. The low- and high-frequency components 

were passed to separate models that were used to simulate 

the low- and high-frequency components of the dependent 

variables with both ANN and MARS. Low-frequency model 

output was added to the list of possible inputs that were used 

in the high-frequency models. The final output time series was 

obtained by adding the two simulated components together 

(fig. 3). 

Projection of wind speed and direction onto north-south and east-west components

Low freq. component High freq. component

Lags

ANN/MARS

Low/high frequency

decomposition (PPM1) 

Eigenvector

filtering (PPM2) 

Recombine components

Calculate goodness-offit statistics

Calculate goodness-offit statistics

Lags

Interpolate 10-minute data

from hourly or 15-minute data

Lags

ANN/MARS

ANN/MARS

3-hour moving average

Scale variables

Scale

variables 

No Preprocessing

(NOPPM)

Calculate goodness-offit statistics

Lags

ANN/MARS

Scale

variables 

Scale variables

Rescale output Rescale output Rescale output

Figure 2. Steps in the construction of gap-filling models for wind time series on Upper Klamath Lake, Oregon.
6 Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon

The second method of preprocessing the input data made 

use of an eigenvector filter, essentially performing a principal 

component analysis on the original time series and lagged 

copies of the time series. The function decevf in the R-package 

pastecs was used to perform this calculation (Ibañez and 

others, 2009). The parameter lag, in this filtering algorithm, 

was set to 4 hours after a trial-and-error optimization process. 

The goal of this filter optimization was to smooth each time 

series while minimizing the loss of important high-frequency 

fluctuations. The time series was then reconstructed using 

only the two most important eigenvectors, resulting in a 

smoothed version of the original time series. The preprocessed 

time series was then passed to both ANN and MARS models 

(fig. 2). 

In order to incorporate the large-scale spatial features 

of the wind over the lake, time series of estimates of the 

two‐dimensional divergence (the amount of spreading of 

the wind vectors) and curl (the amount of rotation of the 

wind vectors) of the wind were calculated and used as 

two additional inputs to the wind models. Based on a twodimensional representation (at ground level) of the wind 

at sites WME (the northernmost lake sites) and SSHR (the 

southernmost lake sites), the divergence (div) and curl (curl) 

of the wind field W (x,y) were calculated at each observation 

time as follows:

tac10-0520_fig03

−10

−6

−4

−2

0

2

4

6

8

10

Observed

Preprocessing (filtering) method 1 low−frequency component

Preprocessing (filtering) method 1 high−frequency component

Sum of preprocessing method 1 components

DAY IN AUGUST 2006

EAST−WEST MDN VELOCITY, IN METERS PER SECOND

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

−10

−6

−8

−8

−4

−2

0

2

4

6

8

10

Observed

Preprocessing (filtering) method 2

Figure 3. Examples of the original east-west components of the wind vector at site MDN on Upper Klamath 

Lake, Oregon, with the low- and high-frequency components obtained with preprocessing method 1 and the 

eigenvector smoothed version obtained with preprocessing method 2.
Statistical Methods and Model Algorithms 7

 ( WME SSHR ) WME SSHR ( ) ( ) u u v v div W W x y

− − = ∇ • ≈ +

∆ ∆ , (1)

and

( WME SSHR ) WME SSHR

WME

WME

SSHR

SSHR

( ) ( ) ,

where

and

are the east-west and north-south 

components, respectively, of the wind

vector at WME,

and

are the east-west and north-south

components, r

u u v v curl W W

y x

u

v

u

v

− − = ∇ × ≈ − ∆ ∆

espectively, of the wind

 vector at SSHR,

is the longitudinal distance between the two

sites, 

is the latitudinal distance between the two

sites,

 is the dot product, and

is the cross-product of the tw

x

y

∆

∆

•

× o vectors shown.

(2)

The final preprocessing step was to scale the magnitude 

of each time series to the interval [0,1]. This assured that the 

range of all model inputs was the same, and in the case of the 

ANN model, that the range matched the range of the internal 

ANN output units (Venables and Ripley, 2002). Model inputs 

were scaled linearly using a method adopted from Rajee and 

others (2009):

( min( )) , (max( ) min( ))

where

is the original time series, 

is the scaled time series,

max( ) is the maximum of the time series, and

min( ) is the minimum of the time series.

s

s

x x

x

x x

x

x

x

x

− = − (3)

This scaling was repeated for each time series; thus, the values 

of min(x) and max(x) were unique to each time series, and 

furthermore, were calculated for the calibration dataset and 

used unchanged in the validation dataset. The output of all 

models was postprocessed using equation 4: 

(max( ) min( ) min( ), )

where

is the output time series.

o s

o

x x x x x

x

= − + (4)

In addition to preprocessing, lags were applied to each 

input variable to create additional model inputs that were 

mathematically independent. All variables were lagged by 

-6, +6, +12, or +24 hours, where a positive lag indicates that 

the time series was shifted forward in time and a negative lag 

indicates that it was shifted backward in time. All gap-filling 

models were calibrated using data from May 12, 2007, to 

September 29, 2007, and validated with data from May 12, 

2006, to September 30, 2006. These dates bracketed the period 

when the rafts were located at sites MDN and MDL. 

Historical Wind Models

Two methods were used to simulate a daily wind record 

over a long period of time. The first method, denoted HIST1, 

used as a dependent variable the daily mean wind speed at 

WMR (fig. 1). For HIST1, the daily mean wind direction at 

the Klamath Falls Airport (KLMT), with a constant rotation, 

was used as a proxy for the wind direction at WMR. (For 

this purpose, the daily mean wind direction is defined as 

the direction of the vector whose orthogonal components 

are the daily mean of the east-west and north-south wind 

components.) The rotation of +5 degrees was determined from 

the distribution of the difference between the daily mean wind 

direction at WMR and KLMT over the calibration time period 

(fig. 4). The independent (explanatory) variables for this 

method were the daily mean wind speed, relative humidity, air 

temperature, and daily cumulative solar radiation measured at 

AGKO and KFLO, as well as the daily mean wind speed, sky 

cover, dew point temperature, air temperature, and altimetric 

pressure at KLMT. 

The second method, denoted HIST2, used as dependent 

variables the daily mean of the east-west and north-south 

components of the wind at WMR and simulated each 

component separately (fig. 5). The independent variables 

for HIST2 were the daily mean east-west and north-south 

components of the wind, daily cumulative solar radiation, 

daily mean relative humidity, and daily mean air temperature 

measured at AGKO and KFLO, as well as, the daily mean 

east-west and north-south components of the wind, sky cover, 

dew point temperature, air temperature, and altimetric pressure 

at KLMT. 

Both historical wind models were calibrated using 

data from 2006 through 2007 and validated using data from 

2008 through 2009. Preprocessing for HIST1 and HIST2 

methods consisted of scaling each input variable to [0,1], as 

was done for the gap-filling models. The scaled time series 

were then passed to both MARS and ANN models (eq. 3). 

Postprocessing consisted of rescaling the output using 

equation 4.
8 Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon

tac10-0520_fig04

10 50 90 130 170 210 250 290 330

WIND DIRECTION, IN DEGREES

FREQUENCY

0

100

200

300

KLMT 2005−09

WMR 2005−09

WIND DIRECTION DIFFERENCE, KMLT−WME, IN DEGREES

−30 −20 −10 0 10 20 30

0

20

40

60

80

PEAK FREQUENCY = 5 DEGREES

A.

B.

Figure 4. Wind direction at the mouth of the Williamson River (WMR) and Klamath Falls Airport (KLMT) near 

Upper Klamath Lake, Oregon (see fig. 1 for site locations): (A) daily mean wind direction at sites WMR and 

KLMT during 2005–09; (B) difference between the daily mean wind direction at KLMT and WMR during 

2005–09. The daily mean wind direction is defined as the direction of the vector whose orthogonal 

components are the daily mean of the east-west and north-south wind components.
Statistical Methods and Model Algorithms 9

tac10-0520_fig05

Daily mean meteorologic data

HIST1 HIST2

Vector

transformation 

USGS WMR

wind direction

approximated by

NCDC KLMT 

Model USGS WMR N-S

and W-E wind vectors

with ANN/MARS 

Transform back to

speed/direction 

USGS WMR

wind speed

modeled

with ANN/MARS 

Scale inputs

Scale inputs

Rescale output

Rescale output

Figure 5. Steps in the construction of the historical wind models for Upper Klamath Lake, Oregon.
10 Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon

Results of Gap-Filling Wind Models

The MARS algorithm was used to determine which 

explanatory variables were the most significant (based on 

optimized values of nk, table 1) and should be kept in each 

model. These selected variables were then used as inputs to 

both the ANN and MARS models. The optimized, nondefault 

values of parameters size and decay for the ANN models are 

provided in table 1. 

A different set of the most significant explanatory 

variables was determined for each dependent variable and 

for each of the preprocessing methods used (table 2). Some 

features of the different sets are consistent with the geographic 

context. For example, site BLB is in the sets of explanatory 

variables for MDN models more than in the sets for MDL 

models. Similarly, site SSHR is in the sets of variables for 

MDL models more than in the sets for MDN models. These 

results reflect the closer proximity of BLB to MDN and 

SSHR to MDL. In general, the sets of variables in table 2 are 

notable for the number and variety of variables that contribute 

significantly to the models. The set for each dependent 

variable contains data from all sites around the lake, as well as 

the east-west and north-south components. 

Goodness-of-fit statistics for the MARS models 

(MARS_PPM1, MARS_PPM2, and MARS_NOPPM) and 

the neural network models (ANN_PPM1, ANN_PPM2, and 

ANN_NOPPM) are shown in table 3. The Nash-Sutcliffe error 

(Weglarczyk, 1998), defined as 2 NASH 1 MSE / o = − s , where 

MSE is the mean-squared-error of the computed values, an

2

os is the variance of the observed values. NASH is a measure 

of the error between the simulated and observed time series 

normalized by the variability in the original time series, and 

approaches 1 as the mean-squared-error approaches zero. 

In general, NASH values greater than zero indicate a model 

fit that is more valuable than simply using the mean of the 

measured data. Likewise, NASH values less than zero indicate 

that a more accurate model could be achieved by using 

the mean of the measured data. The mean error, defined as 

BIAS = − m m c o (where mc = mean of simulated values and 

mo = mean of observed values), was calculated as a measure of 

the relative skewness of model results. 

During calibration, ANN and MARS models resulted 

in similar fit statistics, whereas the validation period resulted 

in better statistical fits (indicated by higher NASH values 

and lower absolute BIAS values) for ANN models than for 

MARS models (table 3). The difference between validation 

and calibration of NASH values ranged from -0.07 to 0.05 for 

all ANN models, and from -0.26 to 0.06 for MARS models, 

indicating that ANN models resulted in a more consistent 

fit between validation and calibration periods than MARS 

models. This trend was most evident in the north-south 

MDL component MARS models during validation, where 

all three MARS models resulted in higher BIAS values than 

the north‐south MDL ANN models. Overall, NASH values 

were higher (indicating more accurate fits) for models of the 

MDL north-south component than for the MDL east-west 

component, but the opposite was true for the models of the 

MDN north-south and east-west components. At site MDL, 

the north-south component was larger in magnitude than 

the east-west component, and at site MDN, the east-west 

component was larger in magnitude than the north-south 

component (figs. 6 and 7). Thus, the models generally do 

a better job of fitting the dominant component of the wind 

vector at both sites. Among all models, peak winds generally 

were underpredicted. Comparisons of the three most accurate 

models are shown in figures 6 and 7. Of these three models, 

peak winds tended to be simulated more accurately by the 

ANN_NOPPM model at both MDN and MDL, which captures 

the high-frequency signal better than the other models. 

Possibly indicative of this ability to model the high-frequency 

signal, the NOPPM models had a greater number of significant 

inputs and greater input variable diversity than the PPM1 and 

PPM2 models (table 2). 

Table 1. Nondefault parameter values used in ANN and MARS wind models for Upper Klamath Lake, Oregon.

[Abbreviations: PPM1, preprocessing (filtering) method 1; PPM2, preprocessing (filtering) method 2; NOPPM, unfiltered data; n-s, north-south wind 

component; e-w, east-west wind component; ws, wind speed]

Model 

algorithm

R

function 

name

Parameter 

name

Gap-filling model preprocessing method Historic model method

PPM1 PPM2 NOPPM

HIST1 HIST2

MDN MDL MDN MDL MDN MDL

n-s e-w n-s e-w n-s e-w n-s e-w n-s e-w n-s e-w ws n-s e-w

MARS earth nk 24 32 8 16 16

ANN nnet

size 1 1 1 1 2 1 4 1 3 3 5 1 2 2 1

decay 1.0E-02 1.0E-03 1.0E-02 1.0E-04 1.0E-04 1.0E-03 1.0E-03 1.0E-02 1.0E-02
Results of Gap-Filling Wind Models 11

Table 2. Time series that were used as input to the gap-filling models for wind component vectors at sites MDN and MDL on Upper Klamath Lake, Oregon.[Abbreviations: PPM1, preprocessing (filtering) method 1; PPM2, preprocessing (filtering) method 2; NOPPM, unfiltered data; n-s, north-south wind component; e-w, east-west wind component; air, air temperature; div, wind divergence; curl, wind curl; lfmod, low frequency model output]

Order of

 importance as 

determined by 

MARS

north-south wind component at MDN east-west wind component at MDN north-south wind component at MDL east-west wind component at MDL

Site Type of data Time shift (hours) Site Type of data Time shift (hours) Site Type of data Time shift (hours) Site Type of data Time shift (hours)

Dependent variables chosen for PPM1 low-frequency models

1 WMR n-s WMR e-w HDB n-s HDB n-s

2 HDB e-w +6 BLB e-w AGKO n-s WMR e-w

3 BLB n-s HDB n-s BLB n-s +6 KFLO e-w4 BLB e-w WMR,SSHR div -6 WMR air +24 HDB e-w +6

5 AGKO e-w +24 WMR,SSHR curl HDB n-s +6 HDB e-w +24

6 WMR air -6 WMR,SSHR curl +6 WMR n-s -6 WMR air +24

7 WMR,SSHR div -6 BLB n-s -6 WMR,SSHR div AGKO n-s

8 WMR,SSHR curl WMR n-s +24 WMR e-w +24 SSHR n-s +12

9 HDB n-s AGKO n-s +12 WMR,SSHR curl +24 HDB n-s +12

10 SSHR n-s +12 AGKO e-w +24 SSHR n-s -6 WMR,SSHR curl -6

11 HDB e-w +6 BLB n-s -6

Dependent variables chosen for PPM1 high-frequency models

1 WMR n-s WMR e-w AGKO n-s WMR e-w

2 BLB n-s WMR air -6 WMR air +6 HDB e-w

3 BLB e-w WMR air HDB n-s HDB n-s4 WMR e-w +6 BLB e-w WMR e-w KFLO e-w -6

5 WMR air +24 WMR n-s WMR air WMR air +6

6 HDB n-s BLB e-w +6 WMR n-s WMR air

7 KFLO n-s BLB n-s BLB e-w +12 AGKO e-w8 KFLO e-w KFLO e-w BLB n-s +6 AGKO n-s +6

9 WMR e-w WMR,SSHR div +24 SSHR e-w +12 MDL-lfmod n-s +6

10 WMR e-w -6 KFLO e-w +6 BLB n-s -6 KFLO e-w +6

11 HDB n-s KFLO n-s +6
12 Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon Table 2. Time series that were used as input to the gap-filling models for wind component vectors at sites MDN and MDL on Upper Klamath Lake, Oregon.—Continued

[Abbreviations: PPM1, preprocessing (filtering) method 1; PPM2, preprocessing (filtering) method 2; NOPPM, unfiltered data; n-s, north-south wind component; e-w, east-west wind component; air, air temperature; div, wind divergence; curl, wind curl; lfmod, low frequency model output]

Order of

 importance as 

determined by 

MARS

north-south wind component at MDN east-west wind component at MDN north-south wind component at MDL east-west wind component at MDL

Site Type of data Time shift (hours) Site Type of data Time shift (hours) Site Type of data Time shift (hours) Site Type of data Time shift (hours)

Dependent variables chosen for PPM2 models

1 WMR n-s WMR e-w AGKO n-s HDB e-w

2 BLB n-s WMR air HDB n-s HDB n-s3 BLB e-w WMR air +6 BLB n-s +6 WMR e-w4 WMR e-w BLB e-w WMR n-s KFLO e-w +6

5 HDB n-s -6 BLB n-s WMR,SSHR div BLB n-s +126 WMR e-w +6 WMR n-s AGKO n-s -6 SSHR n-s -6

7 KFLO e-w AGKO e-w +6 AGKO e-w AGKO e-w

8 KFLO n-s AGKO e-w WMR e-w WMR air -6

9 HDB n-s WMR,SSHR div +24 AGKO n-s +12 KFLO n-s +12

10 WMR e-w -6 WMR air -6 AGKO e-w +6

11 HDB e-w KFLO e-w +12 AGKO n-s +24

Dependent variables chosen for NOPPM models

1 WMR n-s WMR e-w HDB n-s HDB e-w

2 BLB n-s BLB e-w AGKO n-s WMR e-w

3 BLB e-w WMR air WMR n-s HDB n-s

4 HDB n-s -6 WMR air +6 WMR air +6 KFLO e-w +6

5 WMR e-w AGKO e-w WMR,SSHR div AGKO e-w

6 WMR e-w +6 WMR n-s WMR air WMR air

7 HDB n-s BLB n-s HDB n-s +6 WMR air +6

8 WMR e-w -6 AGKO e-w +6 AGKO n-s +6 SSHR e-w

9 KFLO e-w SSHR n-s SSHR e-w AGKO n-s +24

10 KFLO n-s AGKO n-s SSHR n-s -6 KFLO n-s +12

11 HDB e-w WMR air -6 AGKO n-s +12 AGKO e-w +6

12 AGKO e-w WMR,SSHR div +24 WMR e-w SSHR n-s -6

13 WMR air +24 KFLO e-w KFLO n-s +12 BLB e-w

14 AGKO n-s -6 WMR air +12 BLB e-w +6 KFLO e-w +1215 HDB n-s +12 KFLO e-w
Results of Gap-Filling Wind Models 13

Table 3. Goodness-of-fit statistics for the Upper Klamath Lake, Oregon, gap-filling wind models during the 

calibration (May 12–September 29, 2007) and validation periods (May 12–September 30, 2006).

[NASH and BIAS are the Nash-Sutcliffe error and bias error respectively, between the simulated and observed time series. NASH 

values are unit-less, BIAS values are in meters per second. Abbreviations: PPM1, preprocessing (filtering) method 1; PPM2, 

preprocessing (filtering) method 2; NOPPM, unfiltered data; n-s, north-south wind component; e-w, east-west wind component] 

Model

NASH BIAS

MDN MDL MDN MDL

n-s e-w n-s e-w n-s e-w n-s e-w

Calibration

ANN_PPM1 0.44 0.83 0.70 0.68 0.00 0.00 0.00 0.00

ANN_PPM2 .48 .83 .73 .67 .00 .00 .01 .01

ANN_NOPPM .49 .84 .75 .67 .00 .00 .01 .01

MARS_PPM1 .51 .84 .74 .69 .00 .00 .00 .00

MARS_PPM2 .49 .84 .72 .68 .00 .00 .00 .01

MARS_NOPPM .47 .82 .70 .67 .00 .00 .00 .01

 Validation

ANN_PPM1 0.49 0.78 0.75 0.62 0.17 0.09 -0.01 -0.12

ANN_PPM2 .53 .79 .70 .60 .25 .04 .04 -.06

ANN_NOPPM .53 .78 .76 .61 .16 .09 .02 -.04

MARS_PPM1 .25 .76 .70 .58 .04 -.10 .27 -.02

MARS_PPM2 .51 .78 .67 .61 .17 -.01 .28 -.07

MARS_NOPPM .53 .76 .73 .51 .17 .07 .13 -.12

Validation-calibration

ANN_PPM1 0.05 -0.05 0.05 -0.06 0.18 0.09 -0.02 -0.12

ANN_PPM2 .05 -.04 -.03 -.07 .24 .04 .03 -.07

ANN_NOPPM .04 -.06 .00 -.06 .16 .09 .01 -.05

MARS_PPM1 -.26 -.08 -.04 -.12 .04 -.10 .27 -.03

MARS_PPM2 .01 -.06 -.05 -.07 .17 -.01 .27 -.08

MARS_NOPPM .06 -.06 .03 -.16 .17 .07 .13 -.13
14 Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon

tac10-0520_fig06

NORTH−SOUTH VELOCITY, IN METERS PER SECOND −10 −2−4−6−86420 Observed Artificial neural networks - preprocessing (filtering) model 1 Artificial neural networks - preprocessing (filtering) model 2 Artificial neural networks - no preprocessing model

MDL GAP−FILLING MODEL COMPARISON

DAY IN AUGUST 2006

EAST−WEST VELOCITY, IN METERS PER SECOND

7 8 9 10 11 12 13 14 15 16 17 18 19 20

−2−4−6−8

86420

Figure 6. Simulated and observed east-west and north-south components of the wind vector at site MDL on Upper Klamath Lake, Oregon.
Results of Gap-Filling Wind Models 15tac10-0520_fig07

NORTH−SOUTH VELOCITY, IN METERS PER SECOND −2−4−6−8

420

ObservedArtificial neural networks - preprocessing (filtering) model 1Artificial neural networks - preprocessing (filtering) model 2Artificial neural networks - no preprocessing model

MDN GAP−FILLING MODEL COMPARISON

DAY IN AUGUST 2006

EAST−WEST VELOCITY, IN METERS PER SECOND

7 8 9 10 11 12 13 14 15 16 17 18 19 20

−2−4−6

8642

0

10

Figure 7. Simulated and observed east-west and north-south components of the wind vector at site MDN on Upper Klamath Lake, Oregon.
16 Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon

One objective of the gap-filling models is to generate 

wind data at the raft sites on the lake for use in a spatial 

interpolation that incorporates data from these sites as well 

as sites on the shoreline into a spatially variable wind field 

to drive the hydrodynamic model. A measure of how well 

the gap-filling models meet this objective is how well the 

hydrodynamic model, using the wind forcing created using 

the simulated winds over the lake, is able to simulate observed 

water currents. The most accurate gap-filling models (ANN 

models) were used to simulate the winds at sites MDN and 

MDL from mid-July through August 2006. These simulated 

winds were then used in combination with the measured 

winds at the other four sites around the lake to create a 

spatially variable wind. The three-dimensional UnTRIM 

hydrodynamic model of the lake, which is described in Wood 

and others (2008), was then used to simulate water currents 

and water temperature with this new wind forcing. The period 

July 26–August 31, 2006, was selected because this was the 

period selected previously for model validation (Wood and 

others, 2008). Goodness-of-fit statistics for currents simulated 

using only observed winds and observed winds at shoreline 

sites in combination with winds simulated with the gap-filling 

models were compared to site ADCP1 (table 4, fig. 1), where 

measurements from an Acoustic Doppler Current Profiler 

(ADCP) were available (Gartner and others, 2007). 

The root-mean-square error and particularly the bias 

as measured by the mean error increased substantially with 

the use of the simulated winds at MDN and MDL. From the 

comparison of the simulated currents (fig. 8), it seems that the 

increased error largely is attributable to weaker peak currents 

resulting from the model forced with simulated winds. This 

is true on a daily basis, but particularly is noticeable during 

times of high velocities. Simulated currents derived from 

observed winds also underpredicted measured currents, but the 

error is greater when the simulated winds are used to force the 

hydrodynamic model. The increase in the mean error (bias) 

when the best ANN wind model is used to simulate the winds 

is 0.7 cm/s, and the increase in the root-mean-squared error 

is about 1.2 cm/s. In general, the gap-filling models seem to 

be adequate to fill data gaps over short periods of time (a few 

days or less). Given the increase in the error statistics, the use 

of the gap-filling models over periods of many days should be 

evaluated in the context of the problem being addressed. 

The accurate simulation of the water currents in the lake 

is important in part because the transport of water-quality 

constituents and passively drifting larval fish is determined 

by the water currents. Errors in the simulation of currents 

will propagate into errors in the simulation of transport. 

A numerical tracer was used to assess the difference in 

simulated transport resulting from the use of the simulated 

winds instead of the observed winds at the two raft sites. The 

numerical tracer was initialized to zero at the beginning of the 

simulation. The only source of the tracer during the simulation 

was the Williamson River, where the tracer was put into the 

lake at a concentration of 10 (units are arbitrary). The time 

evolution of the concentration of the tracer at two sites in the 

lake, in Goose Bay (GBE) and north of Buck Island (NBI; 

fig. 1), is shown in figure 9. Overall, the tracers derived from 

simulated winds closely matched those derived from observed 

winds. Specifically, the mean absolute difference over the 

47-day simulation between the concentration of the tracer as 

simulated using only observed winds and the concentration 

of the tracer as simulated using simulated winds at the raft 

sites was 0.052, 0.031, and 0.047 (units are arbitrary) at site 

GBE for ANN_NOPPM, ANN_PPM1, and ANN_PPM2, 

respectively. At site NBI, the mean absolute difference was 

0.022, 0.023, and 0.011 for ANN_NOPPM, ANN_PPM1, 

and ANN_PPM2, respectively. Equally as important as the 

mean absolute difference is the lack of error propagation in 

the simulated tracers through time. That is, small differences 

occurring earlier in the tracer concentration time series do not 

compound and result in much larger differences later in the 

simulation. 

Table 4. Upper Klamath Lake UnTRIM model goodness-of-fit 

velocity statistics at site ADCP1, Upper Klamath Lake, Oregon.

[The time period for the calculation is July 26–August 31, 2006. Data are 

in centimeters per second. Abbreviations: NOPPM, unfiltered data; PPM1, 

preprocessing (filtering) method 1; PPM2, preprocessing (filtering) method 2]

Type of wind Mean error Root-meansquare error 

Winds as observed 2.3 3.9

ANN_NOPPM 3.0 5.1

ANN_PPM1 3.2 5.3

ANN_PPM2 3.4 5.5
Results of Gap-Filling Wind Models 17

tac10-0520_fig08

6 8 10 12 14 16

0

10

20

30

40

50

WATER CURRENT SPEED, IN 

CENTIMETERS PER SECOND

0

100

200

300

400

500

WATER CURRENT DIRECTION

-15

-10

-5

0

5

10

15

ERROR IN EAST-WEST COMPONENT,

IN CENTIMETERS PER SECOND

-15

-10

-5

0

5

10

15

ERROR IN NORTH-SOUTH COMPONENT,

IN CENTIMETERS PER SECOND

Observed

Simulated with observed winds

Artificial neural networks - no preprocessing model

Artificial neural networks - preprocessing (filtering) model 1

Artificial neural networks - preprocessing (filtering) model 2

DAY IN AUGUST 2006

Figure 8. Observed and simulated currents at site ADCP1, Upper Klamath Lake, Oregon, August 2006.
18 Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon

0-0520_fig09

0

2

4

6

8

10

CONCENTRATION

07-14 07-24 08-03 08-13 08-23 09-02

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

-2

-1

0

1

2

3

4

DIFFERENCE IN CONCENTRATION

0

1

2

3

4

GBE

NBI

GBE

NBI

Simulated with observed winds

Artificial neural networks - no preprocessing model

Artificial neural networks - preprocessing (filtered) model 1

Artificial neural networks - preprocessing (filtered) model 2

EXPLANATION

MONTH AND DAY IN 2006

Figure 9. Simulated tracer concentration and residuals at sites GBE and NBI, Upper Klamath Lake, 

August 2006.
Results of Historical Wind Models 19

Results of Historical Wind Models 

Similar to the gap-filling models, the MARS algorithm 

was used to select the most significant explanatory variables 

for the ANN and the MARS historical wind models. These 

selected variables are shown in table 5. The model of the 

north-south wind component at WMR selected a greater 

diversity and larger number of input variables than that 

selected for the model of the east-west component—notably, 

relative humidity at AGKO and sky cover at KLMT were 

added. Solar radiation was selected by the MARS algorithm 

as a significant variable for all three dependent variables in the 

historical models (table 5).

Using the same statistical measures as above, the 

historical wind models are compared in table 6. For all 

models, NASH values ranged from 0.63 to 0.87 while BIAS 

values ranged from -0.24 to 0.11 m/s. HIST2 models had 

higher NASH values and lower BIAS values than HIST1 

values, indicating a better statistical fit to measured data. Thus, 

the historical wind models that use the individual components 

of the wind as dependent variables (both ANN and MARS 

models) perform better than the historical wind models that 

use wind speed only as the dependent variable. Figure 10

displays the close fit to measured data that simulated HIST2 

models obtained. As was the case for the gap-filling models, 

peak winds are the most difficult for the models to simulate 

consistently, and the models for the dominant (north-south) 

component of the wind perform better. 

Winds reconstructed with the ANN_HIST2 model and 

measured wind at WMR during the calibration and validation 

period were aggregated on a weekly basis in order to visualize 

wind patterns for multiple years simultaneously (fig. 11). To 

create these “vector-bar” plots, the mean daily north-south 

wind components and east-west wind components were first 

converted to wind speed and direction. Next, the daily mean 

wind direction occurring each day was compartmentalized into 

eight directional bins. The maximum wind speed occurring 

in the most populated direction bin was used to determine 

the height of each bar. The mean of the wind-direction values 

associated with maximum wind-speed values determined 

the direction of the arrows. The maximum wind speeds 

and associated wind direction were used because they are 

assumed to be most environmentally significant for Upper 

Klamath Lake. The seasonal reconstructed winds generally 

matched the seasonal change in measured winds at WMR 

(red and black “vector-bars”). A closer agreement generally 

was observed during summer, when the winds are weaker. In 

cases where simulated wind direction differed from measured 

wind direction, the difference was infrequently more than 

45 degrees. 

To demonstrate the use of the ANN_HIST2 model 

to reconstruct a long-term record, the model was used to 

reconstruct the daily wind record at WMR from January 1, 

2004, through June 12, 2005, prior to the time when data 

were collected at this site (fig. 12). This approach has the 

potential to expand the length of the wind record at WMR or 

other sites around the lake backward in time to at least 2000 

(when collection of the AgriMet data began) for the purpose of 

statistical investigation of the relation between wind and water 

quality in the lake. 

Table 5. Daily time series used in the historical wind models of 

Upper Klamath Lake, Oregon.

[Abbreviations: n-s, north-south wind component; e-w, east-west wind 

component; ws, wind speed; rh, relative humidity; sc, sky cover; sr, solar 

radiation]

Order of 

importance as 

determined by 

MARS

HIST1 HIST2

Wind speed at 

WMR

Northsouth wind 

component at 

WMR

East-west wind 

component at 

WMR

Site 

Type 

of 

data

 Site 

Type 

of 

data

 Site 

Type of 

data

1 AGKO ws KLMT n-s KLMT e-w

2 KLMT ws AGKO n-s AGKO e-w

3 AGKO sr AGKO sr KLMT n-s

4 KFLO n-s AGKO n-s

5 AGKO rh AGKO sr

6 KLMT sc

7 KLMT e-w

Table 6. Goodness-of-fit statistics for the historical wind 

models of site WMR during the calibration and validation period.

[NASH and BIAS are the Nash-Sutcliffe error and mean error, respectively, 

between the simulated and observed time series. NASH values are unit-less. 

BIAS values are in meters per second. Abbreviations: n-s, north-south wind 

component; e-w, east-west wind component]

Model

NASH BIAS

Calibration Validation Calibration Validation

n-s e-w n-s e-w n-s e-w n-s e-w

MARS_HIST1 0.84 0.63 0.81 0.70 0.10 -0.16 0.06 -0.24

MARS_HIST2 .87 .78 .87 .73 .00 .00 .05 -.17

ANN_HIST1 .84 .63 .82 .69 .11 -.15 .07 -.23

ANN_HIST2 .87 .73 .87 .74 .00 .00 .07 .16
20 Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon

tac10-0520_fig10

CALIBRATION

NORTH−SOUTH VELOCITY,

IN METERS PER SECOND −2

−4−6

86420

VALIDATION

MONTH IN 2007

EAST−WEST VELOCITY,

IN METERS PER SECOND

4 5 6 7 8 9 10

−2

86420

MONTH IN 2008

4 5 6 7 8 9 10

ObservedMultivariate adaptive regressive splines - historical wind model 2Artificial neural networks - historical wind model 2

Figure 10. Comparison of calibration and validation years for MARS_HIST2 and ANN _HIST2 wind models, Upper Klamath Lake, Oregon.
Results of Historical Wind Models 21 tac10-0520_fig11

WIND SPEED, IN METERS PER SECOND

06−19 07−03 07−17 07−31 08−14 08−28 09−11 09−25 10−09 10−23 11−06 11−20 12−04 12−18

9630

2005

01−01 01−15 01−29 02−12 02−26 03−12 03−26 04−09 04−23 05−07 05−21 06−04 06−18 07−02 07−16 07−30 08−13 08−27 09−10 09−24 10−08 10−22 11−05 11−19 12−03 12−17 12−31

9630

2006

01−07 01−21 02−04 02−18 03−04 03−18 04−01 04−15 04−29 05−13 05−27 06−10 06−24 07−08 07−22 08−05 08−19 09−02 09−16 09−30 10−14 10−28 11−11 11−25 12−09 12−23 12−31

9630

2007

01−06 01−20 02−03 02−17 03−02 03−16 03−30 04−13 04−27 05−11 05−25 06−08 06−22 07−06 07−20 08−03 08−17 08−31 09−14 09−28 10−12 10−26 11−09 11−23 12−07 12−21

9630

2008

01−04 01−18 02−01 02−15 03−01 03−15 03−29 04−12 04−26 05−10 05−24 06−07 06−21 07−05 07−19 08−02 08−13

9630

2009

N

E

S

W

DIRECTION

MEASUREDRECONSTRUCTED

EXPLANATION

Figure 11. Observed and reconstructed wind data at WMR on Upper Klamath Lake, Oregon, aggregated on a weekly basis, 2005–09. Wind data were reconstructed 

using ANN_HIST2. Arrowheads indicate wind direction.
22 Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon

tac10-0520_fig12

01−04 01−18 02−01 02−15 02−29 03−14 03−28 04−11 04−25 05−09 05−23 06−06 06−20 07−04 07−18 08−01 08−15 08−29 09−12 09−26 10−10 10−24 11−07 11−21 12−05 12−19

9630

2004

WIND SPEED, IN METERS PER SECOND

01−02 01−16 01−30 02−13 02−27 03−13 03−27 04−10 04−24 05−08 05−22 06−05

9630

2005

N

E

S

W

DIRECTION

RECONSTRUCTED

EXPLANATION

Figure 12. Reconstructed wind data at WMR on Upper Klamath Lake, Oregon, aggregated on a weekly basis, 2004–05. Wind data were reconstructed using ANN_

HIST2. Arrowhead indicates wind direction. 
References Cited 23

Summary and Conclusions

Nonlinear empirical models were developed using 

artificial neural networks (ANN) and multivariate adaptive 

regressive splines (MARS) to simulate wind data on Upper 

Klamath Lake. Both types of models were able to successfully 

simulate the wind on Upper Klamath Lake based on wind and 

other meteorological variables measured nearby. By using 

the MARS method of selecting model input variables prior 

to using the ANN, some insight into the dependence of wind 

on various meteorological variables at other land-based sites 

around the lake was gained. The most successful models were 

dependent on a diverse set of input variables measured at 

several sites around the lake.

MARS and ANN were used successfully to simulate 

wind data at two floating raft sites on Upper Klamath Lake. 

Both methods were able to capture most of the variability in 

the 10-minute wind time series. Two different preprocessing 

methods to smooth the input variables were investigated, 

but the preprocessing did not improve the performance of 

the models greatly, and the extra step of smoothing the data 

may not be necessary. Gap-filling models based on ANN 

performed moderately better than those based on MARS. 

Although the ANN approach does not directly reveal the 

nature of dependencies between input and output variables as 

well as the MARS approach, the greater accuracy achieved 

with the ANN approach may justify the added opacity. The set 

of explanatory variables that contributed to the “best” models 

as determined by the MARS algorithm included wind from 

all sites around the lake, as well as wind divergence and curl, 

and air temperature. The best models for the raft sites included 

both east-west and north-south wind components from other 

land-based sites and comprised from 11 to 15 independent 

variables.

The winds simulated with the ANN gap-filling models 

were used in the spatially variable wind forcing for the 

hydrodynamic model of Upper Klamath Lake. The error 

statistics for the simulated currents, when the simulated winds 

were used to force the model, were comparable to those for 

the currents that were simulated when only observed winds 

were used to force the model. It can be concluded that this 

technique is adequate for filling gaps of several days in the 

wind data collected from the rafts on the lake. A numerical 

tracer experiment indicated that the errors in transport 

that result when simulated winds are used to drive the 

hydrodynamic model probably are small, particularly when 

averaged over periods of several days or more. 

The ANN and MARS were used to accurately reconstruct 

wind data at the Williamson River Delta site WMR on a daily 

timestep over several years. Both ANN and MARS historical 

models performed similarly. The datasets long enough to 

be useful as input to these models were more limited than 

those available for input to the gap-filling model. Significant 

explanatory variables selected by the MARS algorithm 

included wind, solar radiation, and relative humidity at 

AgriMet sites (AGKO and KFLO), as well as wind and sky 

cover at the Klamath Falls Airport site (KMLT). The most 

successful historical wind model simulated the north-south 

and east-west components separately. The accuracy was 

higher for this historical wind model than for the gap-filling 

model, and indicates the potential to simulate the wind on 

a daily timestep going backward in time at least to the year 

2000, when the AgriMet data were first collected. Given the 

long data record at KMLT, there is a potential to develop an 

historical wind model based only on data collected at that site 

to reconstruct the wind at sites around UKL back to 1959, but 

that is beyond the scope of the current work and the accuracy 

of such a model has not been investigated for this report.

Acknowledgments 

This work was funded by the Bureau of Reclamation 

(Interagency Agreement 08AA200098) and the U.S. 

Geological Survey.

References Cited

Bureau of Reclamation, 1997, AgriMet Weather Data—Pacific 

Northwest cooperative agricultural weather network: 

Bureau of Reclamation, accessed July 2, 2010, at http://

www.usbr.gov/pn/agrimet/wxdata.html.

Cannon, A.J., and Whitfield, P.H., 2001, Modeling transient 

pH depressions in coastal streams of British Columbia using 

neural networks: Journal of the American Water Resources 

Association, v. 37, issue 1, p. 73–89.

Conrads, P.A., and Roehl, E.A., 1999, Comparing physicsbased and neural network models for simulating salinity, 

temperature, and dissolved oxygen in a complex, tidally 

affected river basin: Proceedings of the 1999 South Carolina 

Environmental Conference, Myrtle Beach, S.C., March 

15–16, 1999. (Also available at http://smig.usgs.gov/

features_0399/nnm1.html/.)
24 Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon

Conrads, P.A., Roehl, E.A., Daamen, R.C., and Kitchens, 

W.M., 2006, Simulation of water levels and salinity in the 

rivers and tidal marshes in the vicinity of the Savannah 

National Wildlife Refuge, Coastal South Carolina and 

Georgia: U.S. Geological Survey, Scientific Investigations 

Report 2006-5187, 134 p. (Also available at http://pubs.

usgs.gov/sir/2006/5187/.)

Conrads, P.A., and Roehl, E.A., Jr., 2007, Analysis of 

salinity intrusion in the Waccamaw River and the 

Atlantic Intracoastal Waterway near Myrtle Beach, South 

Carolina, 1995–2002: U.S. Geological Survey Scientific 

Investigations Report 2007-5110, 41 p. (Also available at 

http://pubs.usgs.gov/sir/2007/5110/.)

Friedman, J.H., 1991, Multivariate Adaptive Regressive 

Splines: Annals of Statistics, v. 19, no. 1, p. 1-67, accessed 

September 7, 2010, at http://projecteuclid.org/DPubS?s

ervice=UI&version=1.0&verb=Display&handle=euclid.

aos/1176347963/.

Gartner, J.W., Wellman, R.E., Wood, T.M., and Cheng, R.T., 

2007, Water velocity and suspended solids measurements by 

in-situ instruments in Upper Klamath Lake, Oregon: U.S. 

Geological Survey Open-File Report 2007-1279, 136 p. 

(Also available at http://pubs.usgs.gov/of/2007/1279/.)

Hoilman, G.R., Lindenberg, M.K., and Wood, T.M., 2008, 

Water quality conditions in Upper Klamath and Agency 

Lakes, Oregon, 2005: U.S. Geological Survey Scientific 

Investigations Report 2008–5026, 44 p. (Also available at 

http://pubs.usgs.gov/sir/2008/5026/.) 

Ibanez, Frederic, Grosjean, Philippe, and Etienne, 

Michele, 2009, Pastecs—Package for analysis of spacetime ecological series, R package version 1.3–10, 

accessed May 13, 2010, at http://CRAN.R-project.org/

package=pastecs.

Kann, Jacob, and Welch, E.B., 2005, Wind control on water 

quality in shallow, hypereutrophic Upper Klamath Lake, 

Oregon: Lake and Reservoir Management, v. 21, no. 2, 

p. 149–158.

Kretzschmar, Ralf, Eckert, Pierre, Cattani, Daniel, and 

Eggiman, Fritz, 2004, Neural network classifiers for local 

wind prediction: Journal of Applied Meteorology, v. 43, 

p. 727–738. 

Kulkarni, M.A., Patil, Sunil, Rama, G.V., and Sen, P.N., 2008, 

Wind speed prediction using statistical regression and 

neural network: Journal of Earth System Science, v. 117, 

no. 4, p. 457–463. 

Laenen, Antonius, and LeTourneau, A.P., 1996, Upper 

Klamath basin nutrient-loading study—Estimate of windinduced resuspension of bed sediment during periods of 

low lake elevation: U.S. Geological Survey Open-File 

Report 95-414, 11 p.

Lindenberg, M.K., Hoilman, G.R., and Wood, T.M., 2009, 

Water quality conditions in Upper Klamath and Agency 

Lakes, Oregon, 2006: U.S. Geological Survey Scientific 

Investigations Report 2008-5201, 54 p. (Also available at 

http://pubs.usgs.gov/sir/2008/5201/.)

Milborrow, Stephen, 2009, “Earth—Multivariate adaptive 

regression spline models” R package version 2.3-5 (derived 

from mda:mars by Trevor Hastie and Robert Tibshirani), 

accessed August 24, 2009, at http://cran.r-project.org/web/

packages/earth/index.html.

National Oceanic and Atmospheric Administration, [n.d.], 

NNDC climate data online: National Oceanic and 

Atmospheric Administration, accessed April 16, 2010, at 

http://www7.ncdc.noaa.gov/CDO/cdo.

National Weather Service, 1998, Automated surface observing 

system (ASOS), user’s guide: Silver Springs, Md., National 

Oceanic and Atmospheric Administration, National Weather 

Service, 56 p., accessed August 2, 2010, at http://www.nws.

noaa.gov/asos/aum-toc.pdf.

Rajaee, Taher, Mirbagheri, S.A., Zounemat-Kermani, 

Mohammad, Nourani, Vahid, 2009, Daily suspended 

sediment concentration simulation using ANN and neurofuzzy models: Science of the Total Environment, v. 407, 

issue 17, p. 4916–4927.

Risley, J.C., Roehl, E.A., and Conrads, P.A., 2003, Estimating 

water temperatures in small streams in western Oregon 

using neural network models: U.S. Geological Survey 

Water-Resources Investigations Report 02-4218, 59 p. 

(Available at http://pubs.usgs.gov/wri/wri024218/.)

Rounds, S.A., 2002, Development of a neural network model 

for dissolved oxygen in the Tualatin River, Oregon, in 

Proceedings of the Second Federal Interagency Hydrologic 

Modeling Conference, Las Vegas, Nevada, July 29–August 

1, 2002: Subcommittee on Hydrology of the Interagency 

Advisory Committee on Water Information, 13 p., accessed 

July 6, 2010, at http://or.water.usgs.gov/tualatin/ann_

proceedings.pdf.

Shamseldin, A.Y., 1997, Application of a neural network 

technique to rainfall-runoff modeling: Journal of Hydrology, 

v. 199, p. 272–294.
References Cited 25

Venables, W.N., and Ripley, B.D., 2002, Modern applied 

statistics with S, 4th ed.: Springer-Verlag, New York, 495 p.

Weglarczyk, Stanislaw, 1998, The interdependence and 

applicability of some statistical quality measures for 

hydrological models: Journal of Hydrology, v. 206, 

p. 98–103.

Wood, T.M., Hoilman, G.R., and Lindenberg, M.K., 2006, 

Water-quality conditions in Upper Klamath Lake, Oregon, 

2002–04: U.S. Geological Survey Scientific Investigations 

Report 2006-5209, 52 p. (Also available at http://pubs.usgs.

gov/sir/2006/5209/.)

Wood, T.M., 2009, Preliminary study of the effect of the 

proposed Long Lake Valley Project operation on the 

transport of larval suckers in Upper Klamath Lake, Oregon: 

U.S. Geological Survey Open-File Report 2009-1060, 24 p. 

(Also available at http://pubs.usgs.gov/of/2009/1060/.)

Wood, T.M., Cheng, R.T., Gartner, J.W., Hoilman, G.R., 

Lindenberg, M.K., and Wellman, R.E., 2008, Modeling 

hydrodynamics and heat transport in Upper Klamath Lake, 

Oregon, and implications for water quality: U.S. Geological 

Survey Scientific Investigations Report 2008–5076, 48 p. 

(Also available at http://pubs.usgs.gov/sir/2008/5076/.) 
26 Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon

This page intentionally left blank.
Publishing support provided by the U.S. Geological Survey

Publishing Network, Tacoma Publishing Service Center

For more information concerning the research in this report, contact the

 Director, Oregon Water Science Center

U.S. Geological Survey

2130 SW 5th Avenue

Portland, Oregon 97201

http://or.water.usgs.gov
Buccola and Wood— Empirical Models of Wind Conditions on Upper Klamath Lake, Oregon—Scientific Investigations Report 2010–5201