Introduction

During 2000, the Economist (2001) reported that at least 6 of the top 12 loss of life events and 9 of the top 12 insured property losses were associated with hydrologic events. Late in 1999, an estimated 50,000 lives were lost associated with heavy rain along the northern coast of Venezuela. The quality and quantity of potable water is also important (Pielke and Guenni, 1999). As reported in the Economist (May 29, 1999, p. 102), while 90% of the world's population has enough water at present, by 2050 more than 40% of the population is estimated as facing a water shortage. The access to safe water is even more serious. In the same article the Economist reports that only about 30% of the rural residents of Brazil currently have access to safe water. Vorosmarty et al. (2000) demonstrate that population growth is the much larger threat to global water resources than any of the current generation projections of future climate. Understanding and quantifying the past, present, and future water availability at the global, regional, and local scales are scientifically, socially, and politically important aspects in balancing water supply and water demand.

Predictability of water resources at any scale 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. Figure 1 illustrates the suite of environmental stresses that can threaten water resources. 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. This was a major factor in the

Handbook of Weather, Climate, and Water: Atmospheric Chemistry, Hydrology, and Societal Impacts, Edited by Thomas D. Potter and Bradley R. Colman. ISBN 0-471-21489-2 © 2003 John Wiley & Sons, Inc.

588 STOCHASTIC CHARACTERISTICS AND MODELING OF HYDROCUMATIC PROCESSES

large loss of life in the 1999 flood in Venezuela. Assessing the sensitivity of hydro-logic processes to landscape change and vegetation dynamics represents one component of Figure 1. To illustrate the procedure to quantitatively assess sensitivity, Figure 2 shows the change in the total model simulated 210-day (during 1989) precipitation over the central United States (Eastman et al., 2001) associated with: (a) the conversion of the current landscape back to its natural form, (b) the radiative effect of doubled atmospheric carbon dioxide, and (c) the biological effect on vegetation of doubled atmospheric carbon dioxide. A coupled atmospheric-vegetation-soil dynamics model was used. The larger scale atmospheric forcing, however, remains identical for the three experiments and is derived from observed National Center for Environmental Prediction analyses (Kalnay et al., 1996).

This analysis shows the surprising result that both landscape change and the biological effect of carbon dioxide can exert a major effect on precipitation. With landscape change, the natural vegetation in the central United States had larger transpiration associated with greater vegetation coverage, particularly tall grass prairie in the eastern portion of the model domain. The increased transpiration cooled the daytime summer atmosphere, thereby preferentially permitting fewer rain showers in the model. Similarly, the enrichment of the atmosphere with carbon dioxide facilitated greater vegetation growth, such that cooling the daytime

Predictability requires:

- the adequate quantitative understanding ot these Interactions

- thai the feecJbacks are not substantially nonlinear.

Figure 1 Use of ecological vulnerability/susceptioility in environmental assessment. (Adapted from Pielke and Guenni, 1999.)

Predictability requires:

- the adequate quantitative understanding ot these Interactions

- thai the feecJbacks are not substantially nonlinear.

Figure 1 Use of ecological vulnerability/susceptioility in environmental assessment. (Adapted from Pielke and Guenni, 1999.)

Figure 2 (see color insert) RAMS/GEMTM coupled model results—the seasonal domain-averaged (central Great Plains) for 210 days during the growing season, contributions to maximum daily temperature, minimum daily temperature, precipitation, and leaf area index due to F1 = natural vegetation, f2 = 2XC02 radiation, and f3 = 2xC02 biology. (Adapted from Eastman et ai, 2001). See ftp site for color image.

Figure 2 (see color insert) RAMS/GEMTM coupled model results—the seasonal domain-averaged (central Great Plains) for 210 days during the growing season, contributions to maximum daily temperature, minimum daily temperature, precipitation, and leaf area index due to F1 = natural vegetation, f2 = 2XC02 radiation, and f3 = 2xC02 biology. (Adapted from Eastman et ai, 2001). See ftp site for color image.

atmosphere was also increased for this case. Such experiments illustrate a procedure to assess the sensitivity of hydrologic processes (precipitation in the above example) to environmental change. By assessing the sensitivity of a hydrologic process to the spectrum of environmental stressors, the largest sensitivities can be determined. With this information, social scientists and policy scientists can determine where to most effectively use resources to mitigate or adapt to the environmental threats (Sarewitz et ai., 2000).

This brief introduction 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 cffect of extremes such as Hoods 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, snow pack, stream flow, infiltration, soil moisture, sea surface temperature, etc. The rest of this chapter focuses on the characterization and modeling of such processes by using stochastic methods. It is essentially an introduction and overv iew to two major separate chapters dealing specifically and more in depth with simulation (Salas et al., 2002) and forecasting (Valdes ct aL 2002) of hydroclimatic processes particularly precipitation and streamflow.

2 GENERAL CHARACTERISTICS OF HYDROCLIMATIC PROCESSES

Mathematical models are generally used for stochastic simulation and forecasting of hydroclimatic processes. The stochastic characterization of the underlying processes is important in constructing such models. In general, the stochastic characteristics of hydroclimatic processes such as precipitation and runoff depend on the type of data at hand. Data may be available on a continuous time scale or at discrete points in time. For instance, most hydrologic series of practical interest are discrete time series defined on hourly, daily, weekly, monthly, bimonthly, quarterly, and annual time intervals. The term seasonal time series is often used for series with time intervals that are fractions of a year (usually a month or multiples of a month). Likewise, hourly, daily, weekly, monthly, and seasonal series are often called periodic-stochastic series. Hydroclimatic time series may consist of a single time series (univariate series) or multiple time series (multivariate series).

Hydroclimatic time series are generally autocorrelated. Autocorrelation in some series such as streamflow usually arises from the effect of surface, soil, and groundwater storages that cause the water to remain in the system through subsequent time periods (Salas, 1993). For instance, basins with significant surface storage in the form of lakes, swamps, or glaciers, produce streamflow series that are autocorrelated. Likewise, subsurface storage, especially groundwater storage produces significant autocorrelation in the streamflow series derived from groundwater outflow. Conversely, annual precipitation and annual maximum flows (flood peaks) are usually uncorrelated. Sometimes significant autocorrelation may be the result of trends and/or shifts in the series (Salas and Boes, 1980; Eltahir, 1989). In addition, multiple hydroclimatic series may be cross-correlated. For example, the precipitation series at two nearby sites, or the streamflow series of two nearby gaging stations in a river basin are expected to be cross-correlated because the sites are subject to similar climatic and hydrologic events. As the sites considered become farther apart, their cross-correlation decreases. However, because of the effect of some large-scale atmospheric-oceanic phenomena such as El Nino Southern Oscillation (ENSO), significant cross-correlation between sea surface temperature (SST) and streamflow between sites thousands of miles apart can be found (Eltahir, 1996). Furthermore, one would expect a significant cross-correlation between a streamflow time series and the corresponding areal average precipitation series over the same basin.

Hydroclimatic time series are intermittent when the variable under consideration takes on nonzero and zero values throughout the length of the record. For instance, the precipitation that is observed in a recording rain gage is an intermittent time series. Likewise, hourly, daily, and weekly rainfall are typically intermittent time series, while monthly and annual rainfall are usually nonintermittent. However, in semiarid and arid regions even monthly and annual precipitation and monthly and annual runoff may be intermittent as well.

Traditionally, certain annual hydroclimatic series have been considered to be stationary, although this assumption may be incorrect as a result of large-scale climatic variability, natural disruptions such as a volcanic eruption, and anthropogenic changes such as the effect of reservoir construction on downstream flow, and the effect of landscape changes on some components of the hydrologic cycle. On the other hand, hydroclimatic series defined at time intervals smaller than a year, such as months, generally exhibit distinct seasonal (periodic) patterns due to the annual revolution of Earth around the sun, which produces the annual cycle in most hydro-climatic processes. Some series of interest to hydrology and water resources, such as daily urban water use, may also exhibit a weekly pattern due to variations of demands within a week. Likewise, hourly time series may have a distinct diurnal pattern due to the variations of demands within a day. Summer hourly rainfall series or certain water quality constituents related to temperature may also exhibit distinct diurnal patterns due to the daily rotation of Earth that causes variations of net radiation within the day (Obeysekera et al, 1987; Katz and Parlange, 1995). Seasonal patterns of hydroclimatic series translate into statistical characteristics that vary within the year (or within a week or a day as the case may be) such as seasonal or periodic variations in the mean, variance, covariance, and skewness. Removing the seasonality in the mean and in the variance has been generally accomplished by the so-called seasonal standardization. This procedure is often referred to in the literature as deseasonalization. Unfortunately, this term is a misnomer since it may imply that the residual series is free of seasonality. However, seasonality may still be present in the covariance structure as is generally the case for seasonal streamflow series (Salas, 1993).

Hydroclimatic time series may exhibit trends, shifts or jumps, seasonality, autocorrelation, and non-normality. These attributes of hydroclimatic time series are referred to as components (Salas, 1993). In general, natural and human-induced factors may produce gradual and instantaneous trends and shifts (jumps) in hydroclimatic series. For example, a large forest fire in a river basin can immediately affect the runoff, producing a shift in the runoff series, whereas a gradual killing of a forest (e.g., by an insect infestation that takes years for its population to build up) can result in gradual changes or trends in the runoff series. A large volcanic explosion such as the one at Mount St. Helens in 1980 or a large landslide can produce sudden changes in the sediment transport series of a stream. Trends in non-point-source water quality series may be the result of long-term changes in agricultural practices and agricultural land development. Likewise, shifts in certain water quality constituents may be caused by agricultural activities such as sudden changes in the use of certain types of pesticides. Changes in land use and the development of reservoirs and diversion structures may also cause trends and shifts in streamflow series. The current concern about global warming and large-scale climatic variability, such as shifts in the intertropical convergence zone (ICZ) and the effects of large-scale oscillations such as ENSO and the Pacific Decadal Oscillation (PDO), is making hydroclimatol-ogists more aware of the occurrence of trends and shifts in hydroclimatic time series. Figure 3 illustrates the observed swings or shifts of the time series of standardized deviations of annual rainfall for Central and West Sahel areas during the period 1950-1998 (Landsea et al, 1999). Concerns regarding the effects of such types of sudden shifts observed in some hydroclimatic time series on water resources, the environment, and society have been expressed and documented in the literature (e.g., Kerr, 1992; Taylor, 1999). Statistical techniques are available for detecting, c I--1—"---1

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