Current Research in Hydrology and Water Resources Under Professor Jose D. Salas


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Current Research in Hydrology and Water Resources

Under Professor
Jose D. Salas

Basic and applied research in many aspects of hydrology and water resources have been carried
out under the lead of Professor Jose D. Salas at Colorado State University sinc
e the 1970’s. A
large number of graduate students both at the M.S. and Ph.D. levels as well as Post
Fellows and Visiting Professors and Scientists have been involved in such an effort. Current
research interest and activities include the follo

Drought Analysis, Prediction, and Management

Flood Prediction, Forecasting and Control

Stochastic Analysis, Modeling, and Simulation of Hydrological Processes

Hydroclimatic Variability

Spatial Analysis of Hydrological Processes

l Hydrology

Watershed and River Basin Modeling

The abstracts listed below give an example or our research activities in the various areas as
referred to above.

Return Period and Risk of Hydrologic Events: 1. Mathematical Formulation.

Bonifacio Ferná
ndez and José D. Salas

ASCE Journal of Hydrologic Engineering, Vol.4, No. 4, October 1999, pp.

. The estimation of return periods of hydrological events and the corresponding risks of
failure of hydraulic structures that are associated wi
th such events are important aspects in many
water resources studies. For simple hydrologic events such as those related to independent
annual floods, both the return period and the risk of failure can be readily calculated. However,
no general applicabl
e methods are available for estimation of return periods, risk of failure, and
reliability of service in cases of more complex hydrological events such as those related to
dependent annual flows and droughts. In this article, the definitions commonly emp
loyed for
return period and risk of failure are re
examined and a general procedure for their estimation are
presented which may be applicable to a wide range of hydrological events related to floods,
droughts, minimum flows, aquifer levels, and reservoir
levels and outflows. Part 2 of this article
includes numerical examples and applications.

Return Period and Risk of Hydrologic Events: 2. Applications.

Bonifacio Fernández and José D. Salas

ASCE Journal of Hydrologic Engineering, Vol.4, No. 4, October 1
999, pp.

A mathematical formulation to estimate return periods and risks of failure of complex
hydrologic events such as those arising from dependent floods and droughts have been examined
in the first part of this paper (Fernandez and
Salas, 1999, this issue). Specifically, some
relationships and algorithms for computing return periods and associated risks for runs arising
from independent and dependent events assuming that dependence is represented by a two
Markov chain have bee
n proposed. The applicability of these procedures are illustrated herein
considering several types of hydrological events with emphasis on those where dependence is
important. First, meteorological droughts based on annual precipitation are considered as

examples of events consisting of runs in independent trials. Then, minimum streamflows and


maximum annual lake outflows are included as examples of dependent events assuming that
dependence is represented by a simple Markov chain. Likewise, hydrological

droughts based on
annual streamflow series are considered. In addition, the estimation of return period and risk are
illustrated by data generation.

Uncertainty Analysis of Reservoir Sedimentation

Jose D. Salas and Hyun
Suk Shin

ASCE Journal

of Hydrologic Engineering, Vol.5, No. 2, April 2000, pp. 145


Significant advances have been made in understanding reservoir sedimentation, but
predicting the accumulation of sediment in a reservoir is still a complex problem. In estimatin
reservoir sedimentation and accumulation, a number of uncertainties arise. These are related to,
quantity of streamflow, sediment load, sediment particle size and specific weight, trap efficiency,
and reservoir operation. Monte Carlo Simulation (MCS) a
nd Latin Hypercube Sampling (LHS) are
used herein to quantify the uncertainty of annual reservoir sedimentation and accumulated reservoir
sedimentation through time. In addition, sensitivity analysis is performed to examine the
importance of various facto
rs on the uncertainty of annual reservoir sedimentation. The proposed
procedures have been applied to the Kenny Reservoir at the White River Basin in Colorado. The
uncertainty of annual reservoir sedimentation and the effect of each uncertain factor take
individually and
in combinations, on the uncertainty of accumulated reservoir sedimentation
through time have been examined. The results show that annual streamflow and sediment load are
the most important factors determining the variability of annual
reservoir sedimentation and
accumulation. In the Kenny Reservoir, the uncertainty expressed by the coefficient of variation can
be on the order of 65 % for annual reservoir sedimentation and 39 % for accumulated reservoir
sedimentation volume.

Return Per
iod and Risk of Droughts for Dependent Hydrologic Processes

hua Chung and Jose D. Salas

ASCE Journal of Hydrologic Engineering, Vol.5, No. 3,

2000, pp.

: The occurrence probabilities, return periods, and risks of drought events a
re estimated
for dependent hydrologic processes. Traditionally, Markovian models have been used for
modeling hydrologic processes having short
term time dependence. However, they are
inadequate for processes exhibiting longer time dependence. In this pa
per, low order DARMA
models are used for modeling the variability of wet and dry years. Specifically we center our
attention on the occurrence of drought events particularly their duration by using the concept of
runs. The probability distribution of dro
ught occurrence, expected values and variances of first
arrival and interarrival times of drought events and the associated risks are derived. The derived
equations and algorithms are verified by Monte Carlo simulation experiments. The applicability
of t
he proposed methods is demonstrated by using annual streamflow data of the South Platte
River in Colorado, North America and the Niger River in Africa. It is concluded that the
proposed methods are quite useful for modeling drought events assuming that lo
w order
DARMA models can describe wet and dry years.

Regional Drought Analysis Based on Neural Networks

Suk Shin and Jose D. Salas

ASCE Journal of Hydrologic Engineering, Vol.5, No. 2, April 2000, pp.145


The main objective of the res
earch reported herein has been to develop an approach to
analyze and quantify the spatial and temporal patterns of meteorological droughts based on annual


precipitation data. By using a non
parametric spatial analysis neural network algorithm, the
zed and standardized precipitation data is classified into certain degrees of drought severity
(for example, extreme drought, severe drought, mild drought, and non
drought) based on a number
of truncation levels corresponding to specified quantiles of the
standard normal distribution (the
15%, 35%, and 50% quantiles were used here for illustration). Then posterior probabilities of
drought severity at any given point in the region are determined and the point is assigned a Bayesian
Drought Severity Index de
pending on whether the maximum posterior probability correspond to
either extreme
, severe
, mild
, or non
drought. This index may be useful for constructing drought
severity maps that display the spatial variability of drought severity for the whole regi
on on a yearly
basis. Furthermore, the severity of the drought event for the region as a whole and the sequence and
duration of drought episodes through time can be determined. The proposed regional drought
analysis approach was applied
to analyze and qu
antify regional droughts for the southwestern

region of Colorado.

The results were useful for deriving maps of precipitation fields for the
entire region, maps of posterior probability of drought severity, and maps of drought severity
indices. They were
useful for visualizing the spatial pattern of droughts and for deriving other
drought properties such as duration. The results obtained suggest that the proposed approach is a
viable tool for analyzing and synthesizing droughts on a regional basis.

mflow Forecasting Based on Artificial Neural Networks

J. D. Salas, M. Markus and A.S. Tokar

Chapter 4 in
Artificial Neural Networks in Hydrology
, G. Rao and A.R. Rao (Editors),
Kluwer Academic Publishers, London.


An alternative approach to flow
forecasting has been developed in recent years based
on Artificial Neural Networks (ANNs). The functioning of the human brain and nervous system
has inspired the method. ANNs are capable of determining relationships between inputs and
outputs of a physic
al system by a network of interconnecting nodes that adjust their connecting
weights (parameters) based on training samples, and discover the rules governing the association
between the inputs and outputs. From a modeling point of view, a disadvantage of
networks is that the inner mechanisms of the process are not easily discovered. While an
examination of the coefficients of stochastic models can reveal useful information about the
series under study (and thus about the system itself), there are n
o established techniques to obtain
comparable information from the weights of a neural network model. Nevertheless, ANNs have
been shown to be very effective for many practical problems in a number of disciplines such as
in medical sciences, electrical an
d mechanical engineering, control theory, and water science and
engineering. The purpose of this chapter is to illustrate some basic concepts and applications of
ANNs to streamflow forecasting. There has been a rapidly growing interest among water
sts to apply neural networks in water resources. ANNs have been applied in wastewater
analysis to forecast sludge bulking (Capodaglio et al., 1991); forecasting water quality such as
salinity (Dandy and Maier, 1993); forecasting daily water demands (Zhang

et al., 1993); flow
forecasting (Zhu and Fujita, 1993, Lachtermacher and Fuller, 1993); snowmelt
forecasting (Markus et al., 1995); unit hydrograph estimation (Hjelmfelt et al., 1993); modeling
daily rainfall
runoff processes (Hsu et al., 1995; Sha
mseldin, 1997; Tokar and Johnson, 1999);
assessment of stream ecological and hydrological responses to climate change (Poff et al., 1996);
rainfall forecasting (French et al., 1992); sediment transport prediction (Trent et al., 1993a); pier
scour estimatio
n (Trent et al., 1993b); and groundwater remediation (Roger et al., 1994; Rizzo
and Dougherty, 1994). In this chapter we provide procedures for building artificial neural
networks for streamflow forecasting. An elementary example and two cases studies ar






and Environmental

ased on



Suk Shin and Jose D. Salas

Chapter 13 in
Artificial Neural Networks in Hydrology
, G. Rao and A.R. Rao (Editors),
Kluwer Academic Publishers, London.

The analysis and modeling of the spatial variability associated with geophysical data
such as hydrological and environmental data, has been of concern to geophysicists for many
decades. For instance, the spatial characterization of rainfall, th
e variability of parameters
describing groundwater flow such as transmissivity and hydraulic conductivity, the variation of
water quality properties in a lake or reservoir,

the spatial distribution of acid rainfall, and
spatial variability of drought

are only a few examples.

The analysis of spatial data can be made
by using traditional methods such as Thiessen polygons and linear interpolation based on
distance between sites. Likewise,

Geostatistical methods such as Kriging have been commonly
d for spatial analysis of hydrological, meteorological,


as soil properties rainfall; groundwater flow and contamination and regional droughts. In spite
of the variety of applications of Kriging for geophysical spatial da

some drawbacks of this
method have been apparent.

Artificial Neural Networks (ANNs) are alternative computational
approaches that are based on theories of the massive interconnection with neurons or nodes and
parallel processing. They have been sugge
sted for solving scientific and engineering problems
such as pattern recognition and classification, chaotic time series analysis, and time series
forecasting. The developments and applications of ANNs for geophysical data have increased
rapidly and publi
shed literature in the last few years relate to problems on river flow prediction
activated sludge prediction, daily water demand prediction, determination of aquifer parameters,
groundwater reclamation , rainfall
runoff process, and spatial analysis
of s
oil properties
. In this
, we

an optimal nonparametric estimator for spatial variables that do not require
stationarity and normality of the variables, and derive the (nonparametric) variance and skewnes

estimators, which are useful for d
etermining the precision of estimation at any arbitrary point.
Furthermore, we estimate the posterior probability that any location belongs to a given class
(among some predefined classes of the spatial variable of interest) and also a Bayesian classifier

that is useful for defining class boundaries over the region. We also discuss the implementation
of a non
parametric spatial analysis neural network (SANN) algorithm and illustrate its
applicability for spatial analysis and classification of precipitatio
n for South Korea and
groundwater contamination for Arizona, USA.

Relating Autocorrelations and Crossing Rates of Continuous and Discrete
Valued Hydrologic Processes

Jose D. Salas, Chen
hua Chung, and Bonifacio Fernandez L

ASCE Journal of Hydrologic Engin
eering, Vol.6, No. 2, Mar/Apr. 2001, pp.


The return period and risk of extreme droughts can be derived from hydrologic series of
wet and dry years. If

denotes a continuous valued hydrologic series such as annual streamflows,

a seri
es of wet and dry years,

, can be obtained by clipping


such that






. A method is presented for relating the autocorrelation functions


. In addition, the relationships between the crossing rate



derived. The method assumes that the underlying hydrologic series is stationary and normally
distributed. The applicability of the methods and derived relationships has been examined and
tested by using annual streamflow series at several sites and by simulation experiments based on


low order ARMA and DARMA models. The analysis of 23 series of a
nnual flows reveals that
the derived relationship between


are applicable and reliable. The same
conclusion is reached when simulated samples from the ARMA(1,1) model are utilized. In
addition, it has be
en shown that the autocorrelation function

obtained (by using the
derived relationship) from

of a low order ARMA model, can be fitted by a low order
DARMA model. The significance of the relationships between

the referred autocorrelation
functions has been documented in terms of estimating certain drought properties. It has been
shown that significant differences can be obtained for estimating the return periods and risks of
certain droughts events if the samp
le autocorrelations

are used instead of the derived

. Furthermore, it has been shown that the derived relationships between




ly quite well for annual streamflows.

Regional Flood Frequency Analysis Based on a Weibull Model: 1. Estimation
and Asymptotic Variances

Haeng Heo, Duane C. Boes, and Jose D. Salas.

Journal of Hydrology, 242 (2001), pp.


Parameter es
timation in a regional flood frequency setting, based on a Weibull model,
is revisited. A two
parameter Weibull distribution at each site, with common shape parameter
over sites that is rationalized by a flood index assumption, and with independence in sp
ace and
time, is assumed. The estimation techniques of method of moments and method of probability
weighted moments are studied by proposing a family of estimators for each technique and
deriving the asymptotic variance of each estimator. Then a single e
stimator and its asymptotic
variance for each technique, suggested by trying to minimize the asymptotic variance over the
family of estimators, is obtained. These asymptotic variances are compared to the Cramer
lower bound, which is known to be the as
ymptotic variance of the maximum likelihood
estimator. A companion paper considers the application of this model and these estimation
techniques to a real data set. It includes a simulation study designed to indicate the sample size
required for compatib
ility of the asymptotic results to fixed sample sizes.

Regional Flood Frequency Analysis Based on a Weibull Model: 2. Simulations
and Applications

Haeng Heo, Jose D. Salas, and Duane C. Boes.

Journal of Hydrology, 242 (2001), pp.


gional flood frequency analysis based on an index flood assumption and a two
parameter Weibull distribution has been studied and simulation experiments were performed to
compare the sample properties of quantile estimates based on the maximum likelihood (M
moments (MOM), and probability weighted moments (PWM) methods, and to determine the
applicability of the asymptotic variances of quantile estimators obtained for each method for
finite samples. Results of these experiments showed biases and mean squar
e errors vary with
sample size, number of sites, nonexceedance probability, shape parameter, and estimation
method. The ratio of the asymptotic variance (Avar) and the mean square error has been
examined to see how well Avar represents the variability of
quantile estimators for finite
samples. In general, asymptotic formulas are quite good even for samples of size 25. The
proposed regional model and estimation procedures are illustrated by analyzing some actual
flood data from Illinois and Wisconsin.


imation of Confidence Intervals of Quantiles for the Weibull Distribution

Haeng Heo,
J.H., Kim,

and Jose D. Salas

Jour. of Stochastic Environmental Research and Risk Assessment,

15(4), 284
309, 2001.

: Estimation of confidence limits and inter
vals for the two

and three
Weibull distributions are presented based on the methods of moment (MOM), probability
weighted moments (PWM), and maximum likelihood (ML). The asymptotic variances of the
MOM, PWM, and ML quantile estimators are deriv
ed as a function of the sample size, return
period, and parameters. Such variances can be used for estimating the confidence limits and
confidence intervals of the population quantiles. Except for the two
parameter Weibull model,
the formulas obtained do

not have simple forms but can be evaluated numerically. Simulation
experiments were performed to verify the applicability of the derived confidence intervals of
quantiles. The results show that overall, the ML method for estimating the confidence limits

performs better than the other two methods in terms of bias and mean square error. This is
specially so for

0.5 even for small sample sizes (e.g.
=10). However, the drawback of the
ML method for determining the c
onfidence limits is that it requires that the shape parameter be
bigger than 2. The Weibull model based on the MOM, ML, and PWM estimation methods was
applied to fit the distribution of annual 7
day low flows and 6
hour maximum annual rainfall
data. The
results showed that the differences in the estimated quantiles based on the three
methods are not large, generally are less than 10%. However, the differences between the
confidence limits and confidence intervals obtained by the three estimation methods
may be
more significant. For instance, for the 7
day low flows the ratio between the estimated
confidence interval to the estimated quantile based on ML is about 17% for T

2 while it is
about 30% for estimation based on MOM and PWM meth
ods. In addition, the analysis of the
rainfall data using the three
parameter Weibull showed that while ML parameters can be
estimated, the corresponding confidence limits and intervals could not be found because the
shape parameter was smaller than 2.

Population Index Flood Method for Regional Frequency Analysis

OliG. B. Sveinsson, Duane C. Boes, and Jose D. Salas

Water Resources Research, Vol.
37(11), 2733

. Regional frequency analyses based on index flood procedures have been used

the hydrologic community since 1960. It appears that when the index flood method was first
suggested the index
flood was taken to be the at
site population mean, which in turn, in the last
two or three decades, has been estimated by the at
site sam
ple mean. The objectives of this
paper are to investigate the consequences of replacing a population characteristic with its sample
counterpart and to propose an analytically correct regional model dubbed as the population index
flood (PIF) method. In th
is method the homogeneity of the region is embedded in the structure
of the parameter space of the underlying distribution model. Simulation experiments are
conducted to test the proposed PIF method based on the General Extreme Value (GEV)
distribution wit
h parameters estimated using the method of maximum likelihood (MLE) and the
method of probability weighted moments (PWM). Furthermore, in the simulation experiments
the PIF method is compared with the Hosking and Wallis regional estimation scheme (HW
me). Comparing among all index flood methods investigated herein, the PIF method with
parameters estimated using MLE provides the best overall results for the 0.95 and the 0.99
quantiles in terms of both bias and root mean square error for moderate to suf
ficiently large
sample sizes, but for the 0.995 quantile the HW
scheme seems to perform best for the
investigated sample sizes.


Regional Frequency Analysis of Extreme Precipitation in Northeastern
Colorado and Fort Collins Flood of 1997

OliG. B. Sveinsson,

Jose D. Salas, and Duane C. Boes

ASCE Jour. Hydrologic Engineering, Vol. 7(1), 49
63, 2002.

Regional frequency analysis based on the index flood method has been utilized to
analyze short duration annual maximum precipitation (AMP) for Northeaste
rn Colorado. An
extraordinary storm and flood that occurred in the City of Fort Collins, Colorado, in July 1997
prompted the study. The main objective of the study was to develop regional frequency curves
that may be useful for that part of Colorado. In ad
dition, we wanted to answer the question
whether the City’s design criteria for storm drainage as of 1997 was adequate, and to determine
to what degree the referred storm was indeed an extraordinary storm. We utilized up
technology that has been wi
dely popularized in literature, with some minor modifications. We
conclude that the regional growth curves developed may be useful for the subregions specified.
However, they should be used with caution for sites located near the boundaries of subregions
lose to the Colorado Front Range. This has become evident in determining the precipitation
quantiles for Fort Collins, for which it was necessary to further narrow down the subregions.
The study also showed that the city’s storm drainage design criteria w
ere underestimated.
the 1997 2 and 3 h storms appear to be 100 yr1 events, while the return period of
the 6 h storm may have been of the order of 400 years. While the study provided us with some
practical answers, it nevertheless also brought
a number of questions concerning the assumptions
underlying the index flood approach and several steps regarding the definition of regions and
testing criteria thereof. These are discussed at length in the final section of the paper.

Modeling the Dynamic
s of Long Term Variability of Hydroclimatic Processes

OliG. B. Sveinsson, Jose D. Salas, Duane C. Boes, and Roger A. Pielke Sr.

Journal of Hydrometeorology, AMS, accepted, 2002


The stochastic analysis, modeling, and simulation of climatic and hyd
processes such as precipitation, streamflow, and sea surface temperature have usually been based
on assumed stationarity or randomness of the process under consideration. However, empirical
evidence of many hydroclimatic data shows temporal variabi
lity involving trends, oscillatory
behavior, and sudden shifts. While many studies have been made for detecting and testing the
statistical significance of these special characteristics, the probabilistic framework for modeling
the temporal dynamics of suc
h processes appears to be lacking. In this paper we propose a family
of stochastic models that can be used to capture the dynamics of abrupt shifts in hydroclimatic
time series. The applicability of such shifting mean models are illustrated by using time s
data of annual PDO indices and annual streamflows of the Niger River.

The 2002 Version of SAMS: Stochastic Analysis Modeling and Simulation

Jose D. Salas, Oli G. Sveinsson, William L. Lane, and Donald K. Frevert

Second Federal Interagency Hydrolo
gic Modeling Conference, July 28

August 1, 2002,
Las Vegas, Nevada

. The 2002 version of the Stochastic Analysis, Modeling and Simulation (SAMS)
package provides enhanced technical capabilities from the earlier versions of the program. The
hical user interface and the mechanisms for handling the data have been entirely rewritten in
MS Visual C++. As a result the 2002 version of SAMS is easier to use and easier to update and


maintain. The package consists of many menu option windows that fo
cus on three primary
application modules

Statistical Analysis of Data, Fitting of a Stochastic Model (including
parameter estimation and testing), and Generating Synthetic Series. SAMS has the capability of
analyzing single site and multisite annual and

seasonal data such as monthly and weekly.
Results can be presented in graphical and tabular forms and, if desired, saved to an output file.
Some illustrations are made to demonstrate the improved technical capabilities of the program
using flow data of
the Colorado River system.

Stochastic Analysis Modeling and Simulation (SAMS 2000)

Jose D. Salas, William L. Lane, and Donald K. Frevert

Chapter 21 in
Mathematical Models of Small Watershed Hydrology and Applications
, edited
by V.P. Singh and D.K. Frev
ert, Water Resources Publications, LLC, Littleton, Colorado,
pp. 749

. Stochastic simulation of water resources time series in general and hydrologic time
series in particular has been widely used for several decades for various problems relate
d to
planning and management of water resources systems. Typical examples are determining the
capacity of a reservoir, evaluating the reliability of a reservoir of a given capacity, verifying the
adequacy of a water resources management strategy under var
ious potential hydrologic
scenarios, and evaluating the performance of an irrigation system under uncertain irrigation
water deliveries. Stochastic simulation of hydrologic time series such as streamflow is typically
based on mathematical models. For thi
s purpose a number of stochastic models and software
packages have been suggested in literature. Examples of specific oriented software for
hydrologic time series simulation are HEC
4 (U.S Army Corps of Engineers, 1971), LAST (Lane
and Frevert, 1990), and

SPIGOT (Grygier and Stedinger, 1990). The U. S. Bureau of
Reclamation (USBR) developed the LAST package during 1977
1979. Originally, it was
designed to run on a mainframe computer (Lane, 1979) but later it was modified for use on
personal computers (La
ne and Frevert, 1990). While various additions and modifications have
been made to LAST over the past 20 years, the package has not kept pace with either advances in
time series modeling or advances in computer technology. The US Bureau of reclamation an
Colorado State University developed the software Stochastic Analysis Modeling and Simulation
(SAMS). The purpose of this chapter is to provide a summarized description of SAMS
The chapter includes some examples.

Stochastic Characteristics an
d Modeling of Hydroclimatic Processes

José D. Salas and Roger Pielke Sr.

Chapter 32 in
Handbook of Weather, Climate, and Water
, edited by T.D. Potter and B.
Colman, John Wiley & Sons, 2002, p. 585

. Predictability of water resources at any s
cale requires a good understanding of
atmospheric, oceans, and land surface processes and their interactions. In addition, land and
oceanic biospheric processes play an important role in the global environment. As population
increases in a watershed, for

example, increased clearing of trees and shrubs, as well as
habitation within gulleys and ravines, can increase the vulnerability of the local population to
flash flooding. The chapter highlights the importance of the interrelationships and interactions
among the various forcing functions of the environment particularly as they relate to water
resources availability and the effect of extremes such as floods and droughts on the environment


and on society, and vice versa. Estimating those interactions and
effects hinges on the proper
characterization of the underlying hydroclimatic processes involved such as air temperature,
precipitation, humidity, snowpack, streamflow, infiltration, soil moisture, sea surface
temperature, etc. The rest of this article fo
cuses on the characterization and modeling of such
processes by using stochastic methods. It is essentially an introduction and overview to two
major separate articles dealing specifically and more in depth with simulation (Salas et al., 2002)
and forecas
ting (Valdes et al., 2002) of hydroclimatic processes particularly precipitation and

Stochastic Simulation of Precipitation and Streamflow Processes

José D. Salas, Jorge A. Ramírez, Paolo Burlando, and Roger Pielke Sr.

Chapter 33 in
ook of Weather, Climate, and Water
, edited by T.D. Potter and B.
Colman, John Wiley & Sons, 2002

. Stochastic simulation of hydroclimatic processes such as precipitation and streamflow
have become standard tools for analyzing many water related p
roblems. Simulation signifies
"mimicking" the behavior of the underlying process so that realistic representations of it can be
made. For this purpose a number of empirical, mathematically/physically based,
mathematically/stochastically based, analog/physi
cally based, and physical/laboratory
based models and approaches have been proposed and developed in the literature. This article
emphasizes simulation based on stochastic and probabilistic techniques. Also, the emphasis will
be on precipitation and

streamflow processes, although many of the methods and models
included herein are equally applicable for other hydroclimatic processes as well such as
evapotranspiration, soil moisture, surface and groundwater levels, and sea surface temperature.
tic simulation enables one to obtain equally likely sequences of hydroclimatic processes
that may occur in the future. They are useful for many water resources problems such as: (a)
estimating the design capacity of a reservoir system under uncertain stre
amflows, (b) evaluating
the performance of a water resources system in meeting projected water demands under
uncertain system’s inputs, (c) estimating drought properties, such as drought length and
magnitude based on simulated streamflows at key points in
the water supply system under
consideration, (d) deriving the distribution of the underlying output variable of a groundwater
flow equation (e.g. the hydraulic head), given the distribution of the parameters (e.g. the
hydraulic conductivity) and boundary c
onditions, (e) establishing the uncertainty in travel time
and spread of pollutants in porous media as a function of the uncertainty in the parameters of the
groundwater contamination transport model, and (f) analyzing the impacts of large
scale climate
riability and global climate change on water supply availability and the ensuing planning and
operation of water resources projects.

Stochastic Forecasting of Precipitation and Streamflow Processes

Juan B. Valdés, Paolo Burlando, and José D. Salas

r 34 in
Handbook of Weather, Climate, and Water
, edited by T.D. Potter and B.
Colman, John Wiley & Sons, 2002.

. Over the past two decades, considerable research has been carried out in hydrology
on developing mathematical tools and approaches for


and long
term precipitation and
streamflow forecasting. The forecasts may be concerned with flood warning, flood control,
water quality control, navigation, energy production, and irrigation. In short, forecasting is


generally used for operationa
l and management purposes while simulation is used for design and
planning purposes.

Forecasting of hydrological processes is an important tool for many water
resources management and operational problems.
Forecasting has been developed using similar
roaches as for simulation, although many models and techniques are unique either for
simulation or forecasting. This article emphasizes forecasting based on stochastic and
probabilistic techniques. Also, the emphasis will be on precipitation and streamfl
ow processes,
although many of the methods and models included herein are equally applicable for other
hydroclimatic processes as well such as evapotranspiration, soil moisture, surface and
groundwater levels, and sea surface temperature. The article incl
udes short

and long
forecasting techniques of precipitation and streamflows such as Kalman, regression models,
autoregressive integrated moving average (ARIMA) models, ARMAX models, transfer function
noise (TFN) models, and models based in artificial

neural networks (ANN).

Long Range Forecasting of the Nile River Flows Using Climatic Forcing

Ahmed K. Eldaw, Jose D. Salas, Luis A.Garcia

Journal of Applied Meteorology, AMS, submitted, 2002

Correlation analysis is used to determine the li
near relationship between the Nile River
flows and leading climatic indicators such as SST and precipitation in an effort to establish a basis
for quantitative long
term streamflow prediction. The analysis of the lead
lag correlations between
the Blue Nile

River flows during the “flood season” July
October (JASO) and SSTs led to the
identification of a number of regions in the oceans that are significantly correlated and suggests
that the SSTs may be useful for predicting the Blue Nile flows. The significan
t correlation regions
between SST in the Pacific and Blue Nile JASO flows evolve through time in a manner that are
consistent with the ENSO development, i.e., the evolution of the ENSO signal in the Pacific Ocean
is reflected in the evolution of the referr
ed cross
correlation field. In addition, the Blue Nile River
JASO flows is significantly correlated with the previous year August
November Guinea
precipitation which suggests that the Guinea precipitation is another potential predictor of the Blue
Nile Ri
ver flows with 11 months of lead
time. Furthermore, models based on Multiple Linear
Regression (MLR) and Principal Component Analysis (PCA) are used to forecast the Blue Nile
flows based on SST in the three oceans and the previous year Guinea precipitation
. The models
based on PCA showed significant improvement in forecast accuracy over MLR models developed
in terms of the original variables. The predictability is shown to be the highest for forecasts made
in the preceding season and decreases as the lead
time increases. The R
s for validation based on
PCA models vary in the range 84% to 59% for forecast lead times of 4 to 16 months, respectively.
Further analysis using only SST predictors for the period 1913
1989 indicates that the
predictability of the B
lue Nile River JASO flows is more affected by the variability of SSTs in the
Pacific Ocean than by those of the other oceans. The conclusion is that long range forecasting of
the Blue Nile River flows with lead times over one year is possible with a high
degree of explained
variance by using SST in a few regions in the Pacific Ocean and the previous year Guinea

Uncertainty of Quantile Estimators Using the Population Index Flood Method

OliG. B. Sveinsson, Jose D. Salas, and Duane C. Boes

ater Resources Research, submitted

. The population index flood (PIF) method is a recent analytical model for regional

frequency analysis. In this paper explicit equations based on Fisher's information are derived for


estimating the standard

error of at
site quantile estimators for two regional population index
flood methods utilizing the generalized extreme value distribution with maximum likelihood
Simulation experiments for different sized regions and different values of the s
parameter show that the suggested methods for estimating the standard error of at
site quantile
estimators give values close to the actual or true values. In addition, similar simulation
experiments are also used to test the accuracy of a newly sugges
ted procedure for estimating the
standard errors of at
site quantile estimators for the Hosking and Wallis regional index flood
method. The results of the simulations indicate that these estimated standard errors can in some
cases be very unreliable. In ge
neral this study shows that the PIF models are a useful addition to
existing regional frequency analysis models, and that their analytic structure, which is not
present in other regional models, have important theoretical and practical implications.

elations and Crossing Rates of Periodic
Stochastic Hydrologic Processes

Jose D. Salas, Chen
hua. Chung, and Antonino Cancelliere

ASCE Jour. Hydrologic Engineering, submitted, 2002.


Discrete valued binary series resulting from clipping a conti
nuous valued
hydrological series at a certain threshold level are useful for analyzing and modeling a variety of
hydrological processes such as the occurrences of wet and dry days, deficit and surplus series,
and water quality series exceeding or not excee
ding a certain allowable level. In addition, binary
time series are useful for risk analysis of hydrologic events, such as those related to the
occurrence of extreme low flows and droughts. A method that relates the correlation functions
of a periodic co
ntinuous valued series and the corresponding clipped periodic binary series is
proposed. The method is used to derive the parameters of a discrete PDAR(1) process as a
function of the of the parameters of the underlying continuous valued PAR(1) process.
Furthermore, the relationship between the periodic crossing rates of a discrete binary series and
the autocorrelation function of the continuous valued series is derived. The proposed
relationships have been tested using data of monthly streamflow series
for several streams as
well as simulation experiments based on the PAR(1) and DPAR(1) models. The results indicate
the validity of the derived relationships and their applicability for analyzing and modeling
stochastic hydrological series.

iction of Extreme Events for Hydrologic Processes that Exhibit Abrupt
Shifting Patterns

OliG. B. Sveinsson, Jose D. Salas, and Duane C. Boes

ASCE Jour. Hydrologic Engineering, submitted, 2002.

We propose a probabilistic framework for modeling ex
treme events such as annual
maximum precipitation for a given storm duration, annual maximum floods, and annual low
flows. The model assumes that the underlying data sequence exhibits abrupt changes or shifts in
the mean, and the data are skewed and autoc
orrelated. Thus, the stochastic model is assumed to
shift abruptly from one stationary state to another one around a long
term mean. The proposed
modeling framework is based upon the previously suggested shifting mean (SM) models
developed by Sveinsson
et al. (2002), where the process was autocorrelated but the marginal
distribution was normally distributed and as a result the model skewness was zero. The main
objective of the research reported herein has been to further extend the referred SM models to

incorporate skewed marginal distributions so that they can be applicable for frequency analysis


of extreme events. For this purpose, two SM models and alternative estimation procedures were
developed particularly using the general extreme value, Pearson
III, and Gumbel distributions.
The proposed models utilizing skewed distributions have been successfully applied for
determining extreme quantiles of the quarter
monthly maximum annual outflows of Lake
Ontario and the 7
day annual low flows for the Parana

River in Argentina.

Shifting Mean Plus Persistence Model for Simulating the Great Lakes Net
Basin Supplies

OliG. B. Sveinsson, Jose D. Salas, Vincent Fortin

ASCE Jour. Hydrologic Engineering, submitted, 2002.

. In current shifting mean model
s the autocorrelation structure is assumed to arise from

the combination of sudden shifts in the mean level of the process under consideration and the
time between such shifts. The objective of this study is to add direct persistence feature to the

shifting mean models. This is done by assuming that the underlying process can be
represented by a shifting mean AR(1) model. In this study the applicability of the proposed
model for simulating the annual net basin supplies (NBS) of the Great Lakes syste
m is analyzed.
The NBS of lakes Erie, Ontario, and St. Clair are autocorrelated and show sudden shifting
behavior, and thus are successfully modeled by the proposed models. On the other hand, the
NBS of the other lakes, Michigan
Huron and Superior, do not
show signs of sudden shifts and do
not appear to be autocorrelated.

Multivariate Shifting Mean Plus Persistence Model for Simulating the Great
Lakes Net Basin Supplies

OliG. B. Sveinsson and Jose D. Salas

ASCE Jour. Hydrologic Engineering, submitted, 200


The focus of this paper is to develop a multivariate model to model the net basin
supplies (NBS) of the Great Lakes. Not all NBS series show similar behavior. For example, a
feature that is apparent in some but not all NBS series is a sudden
shifting pattern. In this paper
we expand previous studies of univariate shifting mean models to develop contemporaneous
shifting mean models. These multivariate models are further mixed with CARMA models in
such a way, that the lag zero correlation in spa
ce is conserved between the underlying processes
of the different models. The full contemporaneous shifting mean CARMA models are
successfully applied for modeling jointly the whole Great Lakes system, preserving the spatial
correlation at lag zero betwee
n different lakes, and preserving other important statistical
characteristics of the individual lakes.