Source: ENVIRONMENTAL MONITORING HANDBOOK P ● A ● R ● T ● WATER Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website WATER Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website Source: ENVIRONMENTAL MONITORING HANDBOOK CHAPTER WATER QUALITY GUIDELINES Barry T Hart INTRODUCTION Most countries now have water resources management policies aimed at achieving sustainable use of their water resources by protecting and enhancing their quality while maintaining economic and social development Achieving this objective requires that the needs and wants of the community for each water resource are defined and that these resources are protected from degradation These community needs generally are called the environmental values (or beneficial uses) of the water body and can include water for drinking, swimming, fishing, recreation, agricultural food production, and/or ecosystem protection Water quality guidelines (or criteria) are the scientific and technical information used to provide an objective means for judging the quality needed to maintain a particular environmental value Knowledge-based management decisions made on the basis of this scientific knowledge are far more preferable than those resulting from pressure by narrowly focused lobby groups A number of water quality guideline compilations are now available (e.g., USEPA, 1986a; CCREM, 1991; ANZECC, 1992) With few exceptions, these are broadly similar in their approach and in the threshold values they recommend However, the recently released Australian and New Zealand water quality guidelines mark a radical departure from the conventionally derived water quality guidelines (ANZECC/ARMCANZ, 2000a) The key elements of these new guidelines are that they are risk-based, focus on ecological issues rather than single indicators, provide information for an increased number of ecosystem types, and require more site-specific information This chapter seeks to define the information and knowledge required by water managers and environmental protection agencies in deciding whether a particular water body has good or bad water quality The important role of water quality guidelines in the water resources management process is covered first The types of water quality guidelines are then discussed, focusing first on the human uses of water (e.g., drinking, recreation, and irrigation) The main part of the chapter relates to guidelines for aquatic ecosystem protection USE OF GUIDELINES IN THE SUSTAINABLE MANAGEMENT OF WATER RESOURCES The sustainable use of a water resource involves managing both the quantity and quality of the resource This chapter will focus mainly on water quality aspects and only briefly cover other aspects of water resources management A later section contains a short discussion of flow and habitat considerations 1.3 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website WATER QUALITY GUIDELINES 1.4 WATER Before considering in detail the water resource management process and the role of water quality guidelines in this process, a number of important and highly relevant considerations are highlighted ● ● ● ● ● Water environments are naturally quite variable systems, particularly in flow and ecosystem types Therefore, any process that seeks to manage a water resource adequately must be responsive, flexible, and adaptable (Walters, 1986) A key objective of modern water management is to maintain the ecological integrity of the resource However, the knowledge base and mechanisms to underpin this new ecosystem-based management approach are poorly developed (Boon et al., 1992; Sparks, 1995; Hart et al., 1999) It is now generally well recognized that most water bodies are closely linked to their catchment and that activities within the catchment can influence the quality of such water bodies (lake, reservoir, river, or estuary) Thus integrated catchment and waterways management is essential if the quality of particular water resources is to be maintained in the future Water resource management must address community needs and wishes, and to achieve this, the community must be involved in the management process Technical and scientific information is essential but not sufficient for the successful management of rivers Water management involves difficult trade-off decisions often between incompatible objectives, such as ecosystem protection and additional water for irrigation It is vital that the decision-making process is as transparent as possible if such decisions are to be accepted by the community Figure 1.1 shows the main steps involved in the water resource management process (Hart et al., 1999) These are discussed briefly below Knowing the system A good scientific and technical understanding of the aquatic system is essential if it is to be managed effectively In particular, information is needed about the condition of the catchment, the water resource itself, the present water quality and stressors* likely to degrade the quality, and uses of the water resource Management goals Clearly, it is essential in any management process to decide why the system is being managed At the highest level, the goal of managing a natural resource is to improve community well-being through sustainable use and protection of the natural environment Effective management of a nation’s water and aquatic resources is crucial to the continued viability of society Environmental values (or beneficial uses) Identification of the community needs and wishes for the water resource (e.g., agricultural water supply, swimming, fishing, and protection of the ecosystem) provides the first step in defining the environmental values of a particular water body The major environmental values considered in most guideline documents are ● ● ● ● ● Ecosystem protection Drinking water supply Recreational water use Agricultural water use (e.g., irrigation, stock watering, aquaculture) Water for industry *Stressors are the physical, chemical, or biologic factors that can cause an adverse effect on an aquatic ecosystem Toxic stressors include heavy metals and toxic organic compounds, salinity, and pH Nontoxic stressors include nutrients, turbidity and suspended particulate matter, organic matter, flow, and habitat Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website WATER QUALITY GUIDELINES WATER QUALITY GUIDELINES 1.5 FIGURE 1.1 Water resources management framework (Modified from Hart et al., 1999.) Since these uses may change with time, the water quality management process must be sufficiently adaptive to allow the goals to change in step with community values There is no simple method for determining management goals The process must be interactive and should involve at least the community, resource managers, and researchers Objectives or targets Each environmental value requires a certain level of water quality to be maintained The water quality to sustain environmental values may be defined by establishing water quality objectives that become the goals for management action This is a complex process that depends on such factors as feasibility and costs of achieving the desired water quality and the lost opportunity costs to the community if these environmental goals are not reached The objectives usually aim either ● ● To protect waterway values (e.g., those which not allow waste discharge, no sand extraction, and those which apply restrictions on catchment activities) or To restore waterway values (e.g., works programs to prevent existing erosion of banks, stabilize beds, revegetate banks, and restore catchment buffer strips) Key indicators of quality These water quality objectives are established in terms of key indicators of quality that provide a means of identifying and measuring change in the environmental values They can include physical, chemical, radiologic, microbial, or biological measures of water quality Broadly, three types of indicators of environmental quality exist: ● Indicators that are normally present in the water and can be monitored usefully for a change in concentration, quantity, or quality (e.g., salinity and nutrient and heavy metal concentrations) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website WATER QUALITY GUIDELINES 1.6 WATER ● ● Indicators that are not normally present but which if detected in certain concentrations or quantities can be used to identify a change (e.g., concentrations of pesticides and other toxic organic compounds) Indicators that are normally present but the absence of which reflects a change Guidelines These provide an objective means for judging the quality needed to maintain a particular environmental value Normally they are described in terms of the key indicators of quality (but see page 1.12 for a new way to define water quality guidelines) Management actions Water quality objectives defined by the preceding process will require actions to maintain and/or attain the desired quality and therefore achieve the environmental values identified by the community Programs or strategies that might be developed to achieve these objectives could include control of waste discharges, water quality protection, catchment revegetation, nutrient reduction, river rehabilitation, resnagging of a river, and the provision of adequate environmental flows Performance assessment There is now increased pressure on water management agencies to assess their performance and report the results publicly This requires that an effective monitoring program is put in place and that there is an appropriate feedback mechanism to confirm that the various management goals are being met or that they need to be revised (ANZECC/ARMCANZ, 2000b) In the past, performance has been judged on the basis of whether threshold physicochemical indicator (e.g., dissolved oxygen, nutrients, pH, heavy metals) concentrations are achieved or not In situations where protection of the ecosystem is the goal, monitoring of the biota is a more direct indicator of whether the goal has been achieved than measuring a physicochemical surrogate For more details on indicators of ecosystem health, see Loeb and Spacie (1994), Davis and Simon (1995), Norris et al (1995), and Wright et al (2000) Research The ecological understanding of most aquatic environments is inadequate, this being particularly so for rivers and streams (Boon et al., 1992; Cullen et al., 1996; Lake, 2000) Obtaining the required information will demand sustained and focused long-term ecological research on these ecosystems Where possible, these studies should be multidisciplinary and catchment-based and done as collaborative partnerships between researchers and managers WATER QUALITY GUIDELINES FOR HUMAN USES Guidelines have been established for all the major uses of water In this section we cover those relating to human uses: drinking water, agricultural water (including aquaculture), and water for recreational and aesthetic uses Guidelines for ecosystem protection are covered in later Sections Drinking Water Drinking water should be safe to use and aesthetically pleasing The quality of drinking water is focused primarily on the protection of human health, and for this reason, drinking water guidelines mostly have been established by health authorities, e.g., the World Health Organization (WHO, 1984) and the Australian National Health and Medical Research Council (NH&MRC/ARMCANZ, 1996) These authorities list guideline values for a wide range of indicators, including Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website WATER QUALITY GUIDELINES WATER QUALITY GUIDELINES ● ● ● ● 1.7 Microorganisms (e.g., pathogenic bacteria, viruses, toxic algae) Inorganic chemicals (e.g., nitrates, heavy metals) Organic chemicals (e.g., toxic organic compounds, pesticides, disinfection by-products) Radioactive materials These guideline values apply at the point of use, normally the home tap However, the more progressive water authorities are increasingly seeking to manage the total supply system—the streams and rivers in the catchment, storage and service reservoirs, treatment and disinfection facilities, service mains, and consumer plumbing and appliances Agricultural Water Guidelines generally are provided for three broad agricultural uses of water: irrigation, stock watering, and aquaculture Irrigation In most developed countries of the world and in an increasing number of developing countries, irrigation uses a substantial proportion of the available water resource (UNEP, 2001) For example, approximately 70 percent (approximately 12,000 gigaliters) of Australia’s developed water is used for irrigation compared with 21 percent for urban and industrial purposes and percent for rural water supply (NLWA, 2001) Guidelines for irrigation water quality generally focus on the physical, chemical, and microbiological factors that may affect crop growth or the soil environment Trigger values or thresholds are provided for ● ● ● ● Microbiological indicators (e.g., human and animal pathogens, plant pathogens) Salinity and sodicity (these can affect both plant growth and soil structure) Inorganic contaminants (e.g., chloride, sodium, heavy metals) Organic contaminants (e.g., pesticides) Stock Watering Good water quality is essential for successful livestock production Animal production and fertility can both be impaired by poor-quality water Contaminants in water can result in residues in animal products (e.g., meat, milk, and eggs) that can create human health risks and adversely affect their salability Guidelines for stock water quality generally focus on the physical, chemical, and (micro)biological factors that may affect animal health The tolerance to contaminants varies among animal species (generally decreases in the order sheep, cattle, horses, pigs, and poultry), between different stages of growth and animal condition, and between monogastric and ruminant animals (ANZECC/ARMCANZ, 2000a) Guidelines provide threshold values for ● ● ● Microbiological indicators (e.g., cyanobacteria, pathogens, and parasites) Inorganic ions (e.g., calcium, magnesium, nitrate, sulfate, salinity, and heavy metals) Organic contaminants (e.g., pesticides) Aquaculture Aquaculture is a rapidly growing industry that involves production of food for human consumption, fry for recreational and natural fisheries, and ornamental fish and plants for the aquarium trade Poor water quality can result in loss of production of culture species and also may reduce the quality of the end products Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website WATER QUALITY GUIDELINES 1.8 WATER Few guidelines are available for aquaculture water quality; however, Australia and New Zealand have published such guidelines for the first time (ANZECC/ARMCANZ, 2000a) These focus on the physical, chemical, and microbiological factors that may affect the production or quality of the food for human consumption Guidelines (trigger values) are provided for ● ● ● Microbiological stressors (e.g., cyanobacteria, pathogens, and parasites) Physicochemical stressors (e.g., dissolved oxygen, pH, salinity, and temperature) Inorganic and organic toxicants (e.g., heavy metals and pesticides) Recreational Water Water-based recreational activities are popular in many countries Guidelines have been established to protect these waters for recreational activities, such as swimming and boating, and to preserve the aesthetic appearance of the water bodies Guideline values are provided for the following indicators: ● ● ● Microbiological stressors (e.g., pathogens and viruses) Nuisance organisms (e.g., algae) Physical and chemical stressors (e.g., color, clarity, turbidity, pH, and toxic chemicals) It is the microbiological stressors that normally are the main focus of recreational water quality guidelines More information on recreational water quality guidelines can be found in USEPA (1986b), ANZECC (1992), WHO (1998, 1999), and ANZECC/ARMCANZ (2000a) ECOSYSTEM PROTECTION Existing Water Quality Guidelines Water quality guidelines for ecosystem protection were first introduced in the early 1970s (Hart, 1974; NAS/NAE, 1973) These early guidelines focused primarily on physical and chemical stressors and provided threshold values for two broad water types: fresh and marine waters These threshold values often are interpreted as indicating degradation if they are exceeded and safe conditions if not exceeded; unfortunately, they often become pseudostandards This is so despite the fact that most of the guideline documents stress that the published values are for guidance only and that if conditions in a particular system approach or exceed the guideline value for a particular indicator, more site-specific work should be undertaken (ANZECC, 1992; Hart et al., 1999) The ecosystem protection guidelines in use over the past 10 years are little different from these earlier guidelines in that they still focus heavily on physical and chemical stressors, although some have included biological indicators (USEPA, 1986a; CCREM, 1991; ANZECC, 1992) The physicochemical indicators can be classified into two groups: ● ● Those which have direct toxic effects on the biota (e.g., heavy metals, salinity, pesticides, and temperature) Those which affect ecosystems indirectly (e.g., nutrients, turbidity, and excess organic matter) Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website WATER QUALITY GUIDELINES WATER QUALITY GUIDELINES 1.9 The way in which these guidelines are established is discussed briefly below Then we identify a number of limitations to these guidelines as a lead-in to discussion of the new risk-based approach recently adopted by the Australian government Physicochemical Indicators Threshold values are provided for a range of physicochemical indicators, including ● ● ● ● ● ● ● Color (this can influence primary production) Dissolved oxygen (this can adversely affect fish and invertebrates) Nutrients (in excess, these can result in cyanobacterial (blue-green algae) blooms) pH (low pH can adversely affect aquatic biota directly and also can result in release of heavy metals from sediments) Salinity (high salinity can adversely affect freshwater macrophytes and other aquatic biota) Suspended particulate matter and turbidity (these can influence primary production) Temperature (both high and low temperatures can adversely affect aquatic biota) Different threshold values normally are provided for freshwaters and marine waters Few of the guidelines make any provision for the site differences that can occur between ecosystem types within these two broad categories Toxicants Most of the trigger values for toxicants are derived using data from singlespecies toxicity tests on a range of test species Readers are referred to Chapman (1995), OECD (1995), and Warne (2001) for details on toxicity testing It would be preferable to use data from multispecies toxicity tests because these would better represent the complex interactions that occur in the field However, few such data are available A number of extensive databases containing toxicity data for many inorganic and organic compounds and for many test organisms (e.g., fish, zooplankton, macroinvertebrates, and algae) now exist (USEPA, 1994; Warne et al., 1998, 1999) These generally contain a large amount of data on acute toxicity and a smaller amount on chronic toxicity.* Guideline values for a number of types of toxicants are listed in many of the existing guideline documents (e.g., USEPA, 1986a; ANZECC, 1992): ● ● ● Inorganic compounds (e.g., ammonia, cyanide, and hydrogen sulfide) Heavy metals (e.g., copper, cadmium, mercury, and arsenic) Organic compounds (e.g., pesticides, PCBs, and dioxins) These are derived largely from acute toxicity data using the assessment-factor method This method involves dividing the lowest acute toxicity value by an arbitrary assessment factor to provide a safe level A factor of 0.05 was used for toxicants that are nonpersistent or are not accumulated, and a factor of 0.01 was used for toxicants that are persistent This method is far less rigorous than the statistical methods now in use and is used only as a default when insufficient data were available Further information on the newer statistical methods is provided on page 1.23 (see also Aldenberg and Slob, 1993; Warne, 2001) *Acute toxicity is the rapid death of organisms caused by a toxicant It is normally specified as the concentration of the toxicant that causes death to 50 percent of the test organisms in a set time, often 96 hours—this concentration is referred to as the 96h-LC50 Chronic toxicity is the biological response to the long-term exposure to a toxicant A chronic toxicity test generally attempts to test over several generations of the test organism and can extend from weeks to months Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS 27.2 DATA ANALYSIS SAMPLING AND DATA PREPARATION The first step is to observe a parameter, e.g., the concentration of CO2 at various intervals in time It is important to recognize that the sampling rate must relate to the maximum expected cyclic frequency, as discussed below Frequencies There are various units for frequency, the most common are ● ● Cycles per unit time (often called hertz if time is measured in s) Radians per unit time One cycle equals 2␲ radians Ideally, a time series is sampled at regular intervals Figure 27.1 shows two such series Of course the samples in Fig 27.1 not provide a very detailed picture of the sinewave, and the underlying data form a smoother pattern The time series is said to be sampled sparsely, the underlying data being illustrated in Fig 27.2 There may be entirely legitimate reasons for sampling at this rate; e.g., it may be expensive and time-consuming In addition, the analytical technique may not be very accurate and may require a sample that uses a lot of material; e.g., in a geological core there would be a maximum rate at which the core could be sampled, limiting the feasible frequency Nyquist Frequency Consider the time series of Fig 27.2, each sampling point being indicated If the time series were sampled at half the rate, it will appear that there is no oscillation because every alternative data point will be eliminated (Fig 27.3) Therefore, there is no way to distinguish FIGURE 27.1 Two time series sampled once per unit time at a frequency of (top) 0.25 cycles or 0.5␲ radians per unit time and (bottom) 0.5 cycles or ␲ radians per unit time Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS TIME-SERIES ANALYSIS 27.3 FIGURE 27.2 Sampling a time series such a series from a zero-frequency series The oscillation frequency in Fig 27.2 is called the Nyquist frequency or ␯Nyq Anything that oscillates faster than this frequency will appear to be at a lower frequency, so a frequency of ␯Nyq ϩ ␦ will be indistinguishable from one of ␯Nyq Ϫ ␦ A frequency of 2␯Nyq will appear to be indistinguishable from one of 0, and a frequency of 2␯Nyq ϩ ␦ will appear to oscillate at the rate of ␦, and so on Hence the sampling rate establishes the range of observable frequencies The higher the rate, the greater is the range In order to increase the frequency band, a higher sampling rate is required, and so more data points must be collected per unit time The equation N ϭ 2ST (27.3) links the number of samples obtained (e.g., N ϭ 100), the range of observable frequencies (e.g., S ϭ 10 cycles per year), and total sampling time (e.g., T ϭ years) In other words, in order to reliably observe a process that oscillates at the rate of 10 cycles per year, it is necessary to take at least 100 samples over a 5-year period Higher frequencies are folded over or aliased There are also a number of other factors that distort the apparent rate of oscillation close to the Nyquist frequency, especially in environmental samples that cannot always be obtained evenly in time, so a good rule of thumb is to have a sampling rate at least twice the minimum frequency required to observe a cyclic process Therefore, to monitor a process that is suspected to be of a frequency of cycles per hour, it is advisable to sample 20 times an hour or every minutes, although it is still possible to obtain some information by sampling at a lower rate Interpolation Most mathematical techniques for time-series analysis assume data that are equally spaced in time In many applications, such as electronic circuits or spectroscopy, it is easy to obtain data of this nature However, it is rare to be able to obtain regularly spaced samples in environmental monitoring If the aim is to sample once a month, it is not necessarily possible to sample on exactly the same date each month, and in fact, since months have different lengths, even if this is achieved, the samples will still be unequally spaced in time In order to obtain an evenly spaced data set, it is normal to interpolate the raw data There are a number of methods, but a simple one is as follows Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS 27.4 DATA ANALYSIS FIGURE 27.3 Sampling at twice the Nyquist frequency Establish a desired sampling interval, which normally should be slightly smaller than the average sampling interval for the overall data set If this interval is given by ␦t, then the nth interpolated sample will be at time t ϭ n(␦t Ϫ 1) For each interpolated sampling time, see if a real sample is obtained at exactly that time, and if so, keep it If not, take the real samples immediately before and after the desired interpolated sampling time If these occur at times t1 and t2, then the interpolated measurement is given by (t Ϫ t1) f(t2) ϩ (t2 Ϫ t) f(t1) Interpolated f(t) ϭ ᎏᎏᎏ t2 Ϫ t1 (27.4) A simple numerical example is presented in Table 27.1 For example, the interpolated measurement at t ϭ is (0.3 ϫ 2.112 ϩ 0.5 ϫ 1.854)/0.8 ϭ 1.950 Notice that some measurements will be ignored using this method of interpolation, such as the measurement at t ϭ 5.6 More elaborate approaches that use all the initial information are possible but can distort the underlying time series substantially Preprocessing In environmental chemistry it is quite common to scale the data prior to time-series analysis Instead of raw measurements (e.g., the concentration of a heavy metal), a function of this is used in time-series analysis A common form of scaling is logarithmic, an example being pH, which is the logarithm of [Hϩ] If we want to study the change in acidity of seawater with time, it is usual to use a pH scale This protects against very large values dominating the analysis A problem with logarithmic scaling is that in some circumstances an analyte may be undetected or at a very low concentration Using unscaled data, a value of is entirely acceptable, but the logarithm of is undefined One way around this is to replace all 0s by a number that is slightly less than the smallest positive number in the data set (e.g., half this) and then take the logarithm of this new value For example, if the lowest detected concentration of a compound is mg/ml, replace a value (which often occurs because the real concentration is below detection limits) by 0.5 mg/ml prior to logarithmic scaling Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS 27.5 TIME-SERIES ANALYSIS TABLE 27.1 Interpolation Time 1.7 2.5 3.2 5.1 5.6 Measurement Interpolated time Interpolated measurement 2.261 1.950 1.884 1.401 1.532 0.784 2.261 1.854 2.112 1.793 1.401 1.5456 0.771 0.784 NOISE Imposed on the cyclic processes is noise In fact, sometimes processes modeled by noise can be quite interesting in their own right, but time-series analysis is restricted to determining cyclic trends, and therefore, the techniques usually employed aim to reduce the influence of any noncyclic phenomena, which could be treated as a form of noise In many traditional areas of statistics, although the nature and origin of noise often are unknown, they frequently obey a normal distribution Indeed, many statistical tests such as the t test and F test assume this and are only approximations in the absence of experimental study of such noise distributions In environmental sampling and analysis, there are three fundamental sources of noise or error (all error is noise, but not all noise is error): The first involves sample preparation, e.g., dilution, weighing, and extraction efficiency We will not discuss these errors further in this chapter, but it is important to recognize experimentally that this can distort measurements, especially if different investigators are employed during different phases in a project The second is inherent to a measurement technique No instrument is perfect, so the signal is imposed on noise The observed signal is given by x ϭ ~x ϩ e (27.5) where ~x is the perfect or true signal, and e is a noise function The aim of most signalprocessing techniques is to obtain information on the true underlying signal in the absence of noise, i.e., to separate the signal from the noise The final relates to the underlying process within the environment For example, there may be a seasonal variation in CO2 levels in the air, but other factors affect this, some of which may occur more or less randomly This nondeterministic element of the time series can seriously distort the apparent cyclic patterns In addition, there are two main types of noise Stationary Noise The noise at each successive point in time does not depend on the noise at the previous point The magnitude of the noise at sampling time t is independent of that at the previous sampling time This noise is sometimes also called white noise Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS 27.6 DATA ANALYSIS In turn, there are two major forms of stationary noise: Homoskedastic noise This is the simplest to envision The features of the noise, normally the mean and standard deviation, remain constant over the entire data series The most common type is modeled by a normal distribution with mean and standard deviation dependent on the particular application In most real-world situations, there are several sources of noise, but a combination of different distributions often tends toward a normal distribution (this is called the central limit theorem) Hence this is a good approximation in the absence of more detailed knowledge of a system Heteroskedastic noise This type of noise is dependent on the size of the measurement, often proportional to intensity The noise may still be represented by a normal distribution, but the standard deviation of that distribution is proportional to intensity A form of heteroskedastic noise often appears to arise if the data are transformed prior to processing, a common method being a logarithmic transform used in many types of spectroscopy, such as electronic absorption spectroscopy, or infrared spectroscopy The true noise distribution is imposed on the raw data, but the transformed information distorts this Figure 27.4 illustrates the effect of both types of noise on a time series It is important to recognize that quite detailed models of noise are possible, but in practice, it is not easy to perform sufficient experiments to determine such distributions Indeed, it may be necessary to obtain several hundred or thousand samples to obtain an adequate noise model, which is rarely feasible in environmental science It is not possible to rely too heavily on published studies of noise distribution because each application is different, and the experimental noise distribution is a balance between several sources, which differ in relative importance for any sampling experiment In the absence of certain experimental knowledge, it is best to stick to a fairly straightforward distribution such as a normal distribution FIGURE 27.4 A time series (bottom) plus homoskedastic (middle) and heteroskedastic (top) noise Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS TIME-SERIES ANALYSIS 27.7 Correlated Noise Sometimes the level of noise in each sample of a time series depends on that of the preceding one Consider, for example, a parameter that depends on a cyclic change in temperature Although there will be well-defined cycles over a year, there will be random local variations in temperature that are unlikely to be in the form of sudden blips This type of noise is sometimes also called nonstationary noise Many such sources cannot be understood in great detail, but a generalized approach is that of autoregressive moving average (ARMA) noise The moving average component relates the noise at time i to the values of the noise at previous times A model of order p is given by tϭp ei ϭ Α ciϪteiϪt (27.6) tϭ0 where eiϪt is the noise at time i Ϫ t and ciϪt is a coefficient A simple approach for obtaining this type of noise is to put p ϭ and set the coefficient to Under such circumstances, ei ϭ gi ϩ eiϪ1 (27.7) where gi may be generated using a normal distribution Table 27.2 illustrates a stationary noise distribution and a moving average (MA) distribution generated simply by adding successive values of the noise so that, for example, the noise at time ϭ is given by 0.112 ϭ Ϫ 0.009 ϩ 0.062 TABLE 27.2 Stationary and Moving Average Noise Time Stationary MA 10 11 12 13 14 15 16 17 18 19 20 Ϫ0.128 0.142 Ϫ0.060 0.051 0.062 Ϫ0.144 Ϫ0.106 0.065 0.055 Ϫ0.001 0.044 Ϫ0.084 0.215 Ϫ0.011 Ϫ0.084 Ϫ0.145 0.115 0.008 0.131 0.037 0.015 0.082 Ϫ0.009 0.112 Ϫ0.083 Ϫ0.250 Ϫ0.041 0.120 0.054 0.043 Ϫ0.040 0.131 0.204 Ϫ0.095 Ϫ0.229 Ϫ0.030 0.123 0.139 0.168 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS 27.8 DATA ANALYSIS The autoregressive component relates the noise to the observed value of the response at one or more previous times A model of order p is given by tϭP xi ϭ Α ciϪtxiϪt ϩ ei (27.8) tϭ0 Note that in a full ARMA model, ei itself is dependent on past values of noise There is a huge literature on ARMA processes, which are particularly important in the analysis of long-term trends such as in economics It is quite likely that an underlying factor causing errors in estimates changes with time rather than fluctuating completely randomly There have been developed a battery of specialized techniques to cope with such situations The environmental chemist must be aware of these noise distributions, but there is rarely sufficient experimental evidence to establish highly sophisticated noise models It is well advised, though, when studying a process to determine whether a stationary noise distribution is adequate, especially if the results of simulations are to be relied on, so an appreciation of basic models is important CORRELOGRAMS After obtaining the samples and interpolating and preprocessing the data as required, it is necessary to use statistical techniques to examine the main cyclic trends in the data Autocorrelograms A common approach is to calculate an autocorrelogram Consider the information depicted in Fig 27.3, which represents a process changing with time It appears that there is some cyclicity, but this is buried within the noise The data are presented in Table 27.15 A correlogram involves calculating the correlation coefficient between a time series and itself shifted by a given number of data points called a lag Correlation coefficients have values between ϩ1 and Ϫ1 and are a method of determining the similarity between two series They often are defined as covxy rxy ϭ ᎏ sxsy (27.9) where covxy is the covariance between x and y and sx is the standard deviation of x The higher the magnitude, the more similar the two series are Hence an autocorrelogram compares how similar a time series is with itself shifted by a certain number of points in time If there is cyclicity, high correlation coefficients will be obtained for lags corresponding to cyclic frequencies If there are I datapoints in the original time series, then a correlation coefficient for a lag of l points will consist of I Ϫ l data points Hence, in Table 27.3, there are 30 points in the original time series but only 25 points in the data set for which l ϭ For a lag of 5, point number in the shifted time series is the same as point number in the original one The correlation coefficient for lag l is given by Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS 27.9 TIME-SERIES ANALYSIS TABLE 27.3 Data for Auto-Correlogram i 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 data, /ϭ0 data, /ϭ5 2.768 4.431 Ϫ0.811 0.538 Ϫ0.577 0.262 1.744 5.740 4.832 5.308 3.166 Ϫ0.812 Ϫ0.776 0.379 0.987 2.747 5.480 3.911 10.200 3.601 2.718 2.413 3.008 3.231 4.190 3.167 3.066 0.825 1.338 3.276 0.262 1.744 5.740 4.832 5.308 3.166 Ϫ0.812 Ϫ0.776 0.379 0.987 2.747 5.480 3.911 10.200 3.601 2.718 2.413 3.008 3.231 4.190 3.167 3.066 0.825 1.338 3.276 IϪl IϪl I Α xixiϩp Ϫ ᎏ Α xΑx I Ϫ l iϭ1 iiϭl i iϭ1 rl ϭ (27.10) Ί๶๶๶๶ Ί๶๶๶๶ IϪl IϪl xi2 Ϫ ᎏ Α xi Α I Ϫ l iϭ1 iϭ1 l I Α xi2 Ϫ ᎏ Α xi I Ϫ l iϭl iϭ1 Sometimes a simplified equation is employed: IϪl IϪl ΂Α x x Ϫ ᎏI Ϫ1ᎏl Α x Α x ΃/(I Ϫ l) r ϭ ᎏᎏᎏ ΂Α x Ϫ ᎏ1Iᎏ Α x ΃/I iϭ1 i iϩp iϭ1 I i iϭl l I iϭ1 i (27.11) I i iϭ1 i The latter equation is easier for repetitive computations because the term at the bottom needs only to be calculated once, and such shortcuts were helpful prior to the computer age Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS 27.10 DATA ANALYSIS However, using modern packages, it is not difficult to use the first equation, which will be used in this chapter Notice that the two calculations will provide slightly different answers There are a number of properties of the autocorrelogram: For a lag of 0, the correlation coefficient is It is possible to have negative lags as well as positive lags, but for an autocorrelogram, rl ϭ rϪl, and sometimes only half the correlogram is displayed The closer the correlation coefficient is to 1, the more similar the two series are If a high correlation is observed for a large lag, this indicates cyclicity As the lag increases, the number of data points used to calculate the correlation coefficient (the window) decreases, and so rl becomes less informative and more dependent on noise Large values of l are not advisable; a good compromise is to calculate the correlogram for values of l up to I/2, or half the points in the original series The autocorrelogram for the time series of Fig 27.5 is presented in Fig 27.6 The cyclic pattern is now much clearer than in the original data Note that the graph is symmetric about the origin, as expected, and the maximum lag used is 14 A correlogram emphasizes cyclic features Sometimes noncyclic trends are superimposed over the time series Such situations occur regularly in economics Consider trying to determine the factors relating to expenditures in a seaside resort A cyclic factor undoubtedly will be seasonal, there being more business in the summer However, other factors such as interest rates and exchange rates also will come into play, and the information will be mixed up in the resulting statistics Expenditure also can be divided into food, accommodation, clothes, and so on Each will be influenced to a different extent by seasonality In environmental chemistry, correlograms are most valuable when time-dependent noise interferes with stationary noise, e.g., in a river where there may be specific types of pollutants or changes in chemicals that occur spasmodically but once discharged take time to dissipate A correlogram also can be represented in the form of probabilities, e.g., the chance that there really is a genuine underlying cyclic trend of a given frequency Such calculations, though, make certain definitive assumptions about the underlying noise distributions and experimental error and are not always applicable to a given system FIGURE 27.5 Time series used for calculation of an autocorrelogram Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS 27.11 TIME-SERIES ANALYSIS FIGURE 27.6 Auto-correlogram for data of Fig 27.5 Cross-Correlograms It is possible to extend these principles to the comparison of two independent time series Consider measuring the levels of Ag and Ni in a river over time Although each may show a cyclic trend, are there trends common to both metals? The cross-correlation function between x and y can be calculated for a lag of l, that is, cxy,l rl ϭ ᎏ sxsy (27.12) where cxy,l is the covariance between the functions at lag l, given by cxy,l ϭ IϪl Α (xi Ϫ ෆx ) (yiϩ1 Ϫ ෆy )/(I Ϫ l) iϭ1 for l Ն I Α (xi Ϫ ෆx ) (yiϩ1 Ϫ ෆy )/(I Ϫ l) iϭ1Ϫ1 cxy,l ϭ for l Ͻ and s corresponds to the appropriate standard deviations Note that the average of x and y strictly should be recalculated according to the number of data points in the window, but in practice, provided that the number of data points is not too small, using the overall average is acceptable Notice that it is not necessary that the two time series are of equal length, but regions of equal size must be found for each correlation function It is, of course, essential that the two time series are sampled or interpolated to be equally spaced in time The cross-correlogram is no longer symmetric about 0, a negative lag not giving the same result as a positive lag Table 27.4 presents two time series The raw time series and the corresponding cross-correlogram are illustrated in Fig 27.7 The correlogram suggests that both contain a cyclic trend at around data points, since the correlograms exhibit a strong minimum at l ϭ Ϯ8 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS 27.12 DATA ANALYSIS TABLE 27.4 Two Time Series for Calculation of Cross-Correlogram Series Series 2.768 2.583 0.116 Ϫ0.110 0.278 2.089 1.306 2.743 4.197 5.154 3.015 1.747 0.254 1.196 3.298 3.739 4.192 1.256 2.656 1.564 3.698 2.922 4.136 4.488 5.731 4.559 4.103 2.488 2.588 3.625 1.061 1.876 0.824 1.598 1.985 2.796 0.599 1.036 2.490 4.447 3.722 3.454 1.961 1.903 2.591 2.032 2.485 0.549 3.363 3.271 5.405 3.629 3.429 2.780 4.024 3.852 4.810 4.195 4.295 4.332 Multivariate Correlograms In the real world, there may be a large number of variables that change with time, e.g., the concentration of several polyaromatic hydrocarbons in industrial waste Rather than calculating correlograms for each individual parameter, it is often valuable to calculate the principal compound or similar multivariate function of the raw data and then look at the cyclic trends with time FURTHER METHODS Smoothing Functions Sometimes it is desirable to smooth the data either before or after a correlogram has been calculated A variety of methods can be applied The simplest are linear filters whereby the resulting smoothed data are approximated by a linear function of the raw data Normally, this involves using the surrounding data points in time to recalculate a value for point i Algebraically, such functions are expressed by Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS TIME-SERIES ANALYSIS 27.13 FIGURE 27.7 Example of two time series and their cross-correlogram p xi,new ϭ Α cj xiϩj (27.13) jϭϪp where cj is often called a weight One of the simplest is a three-point moving average (MA) Each point is replaced by the average of itself and the points before and after, so in the preceding equation, ● ● pϭ1 cj ϭ 1/3 for all points The filter can be extended to a five-, seven-, etc.-point MA, the weights being equal to 1/(2p ϩ 1) The effect of a five-point moving average filter is presented in Fig 27.8 The number of points used in the calculation depends on the nature of the data: ● ● The more the points in the filter, the greater is the reduction in noise, but the higher is the chance of blurring the signal This can have a significant effect for oscillations close to the Nyquist frequency The number of points (2p ϩ 1) in the filter is the window Several other MA methods have been proposed in the literature, two of the best known being three-point windows, namely, the Hanning window (named after Julius Von Hann) (weights 0.25, 0.5, and 0.25) and the Hamming window (named after R W Hamming) (weights 0.23, 0.54, and 0.23)—not to be confused but with very similar effects Fourier Analysis A final technique sometimes used is to Fourier transform (FT) a time series There are several excellent texts on Fourier transform techniques, and we will use the discrete Fourier Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS 27.14 DATA ANALYSIS Smoothed data Raw data FIGURE 27.8 Smoothing using a five-point moving average transform (DFT) The method can be applied to time series of any size and is not limited to data sets whose length equals a power of We will not discuss the theory of FTs in this chapter However, by Fourier transforming a correlogram, cyclically repeating features are transformed into peaks, so the frequencies can be presented along the horizontal axis (Fig 27.9) This transform is sometimes called a spectrum, and the procedure of calculating a correlogram followed by Fourier transformation is often called spectral analysis in statistical texts, which must be distinguished from the chemist’s terminology, which has a particular physical connotation It is important to recognize that although it is also possible to FT a raw time series, the clarity of the transform is normally quite poor because it will be dominated by noise, sampling errors, etc., and the procedure for computing a correlogram prior to Fourier transformation improves the quality of the spectrum greatly It is possible to FT a cross-correlogram, in which case the frequencies will be those which are common to two time series The vertical axis relates to the strength or importance of an oscillation Finally, there are a number of methods for smoothing and enhancing the quality of these transforms CONCLUSION Time series are very common in environmental monitoring, and there are a number of wellestablished statistical techniques for handling these types of data There are many potential steps in a full spectral analysis, such as interpolation, preprocessing, smoothing, calculation of correlograms, and Fourier transformation The resulting data are normally presented graphically, usually as a correlogram If a good idea of noise distributions is available, it is sometimes possible to produce a numeric value of the probability of underlying cyclic processes Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS TIME-SERIES ANALYSIS 27.15 FIGURE 27.9 Fourier transform of a correlogram Quite different techniques are necessary for the analysis of noncyclic trends, but these are conventionally not called time-series analysis, and the aim of the techniques introduced in this chapter is to treat these trends as noise and reduce their influence Many methods for time-series analysis have their origins in economics, and some of the most comprehensive software packages are available to econometricians It is easy to perform most straightforward calculations using common spreadsheet software such as Excel, which has functions for correlation coefficients and other simple manipulations, but more elaborate computations are available in most common economics packages or enhancements of statistical software Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website TIME-SERIES ANALYSIS 27.16 DATA ANALYSIS REFERENCES Anderson, T W (1971) The Statistical Analysis of Time Series Wiley, New York Berner, R A (1990) Science 249:1382–1386 Box, G E P., and Jenkins, G M (1970) Time Series Analysis, Forecasting and Control Holden-Day, San Francisco Chatfield, C (1996) The Analysis of Time Series: An Introduction, 5th ed Chapman and Hall, London Davis, J C (1986) Statistics and Data Analysis in Geology, 2d ed Wiley, New York Janacek, G., and Swift, L (1993) Time Series, Forecasting, Simulation, Applications Ellis Horwood, Chichester, U.K Keeling, C D., Whorf, T P., Wahlen, M., and van der Plicht, J (1995) Nature 375:666–670 Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website ... at the website Source: ENVIRONMENTAL MONITORING HANDBOOK CHAPTER DESIGN OF WATER QUALITY MONITORING PROGRAMS William A Maher and Graeme Batley INTRODUCTION Water quality monitoring programs are... rights reserved Any use is subject to the Terms of Use as given at the website Source: ENVIRONMENTAL MONITORING HANDBOOK CHAPTER WATER QUALITY GUIDELINES Barry T Hart INTRODUCTION Most countries...Source: ENVIRONMENTAL MONITORING HANDBOOK P ● A ● R ● T ● WATER Downloaded from Digital Engineering Library @ McGraw-Hill