AN ABSTRACT OF THE THESIS OF Biao Huang for the degree of Master of Science in Agricultural and Resource Economics presented on August 21, 2009. Title: The Value of Short Run In‐stream Temperature Forecasts: An Application to Salmonids in the Klamath and John Day Rivers Abstract approved: __________________________________________________________ Christian Langpap Water temperature is an important measure of water quality, as well as a dominant factor affecting aquatic life within the stream environment. Elevated water temperatures can decrease the survival rate of fish in each life stage. Cold water species, such as salmonids, are particularly susceptible to elevated water temperatures. For example, increased water temperatures are believed to have been the major cause of the large fish kill observed in the Klamath River in September 2002. This thesis examines the economic value of short‐term water temperature forecasts for salmonid management. Forecasts may have value if they allow the water resource manager to make more cost‐effective water allocation decisions. Specifically, this study considers two applications. One is the case of adult Chinook salmon (O. tshawytscha) returning to the Lower Klamath River in California, where cold water could be released upstream from the Lewiston Dam into the Trinity River to lower The Klamath River water temperature. Water releases create opportunity costs because of foregone hydropower production and crop irrigation. The second application is to juvenile summer steelhead (Oncorhynchus mykiss) in the North Fork John Day River, where water could be purchased from agricultural uses to prevent excessive water temperature increases. This generates opportunity costs in the form of lower crop yields. This thesis incorporates bio‐physical models and water temperature distribution data into a Bayesian framework to simulate the potential fish populations after ten generations and the corresponding opportunity cost of water under different forecast accuracies. Simulation results indicate that the marginal cost in the Klamath River decreases from about $80 per fish saved when the forecast standard deviation is 6 to about $40 when the forecast standard deviation is 0(perfect forecast). In the John Day River the marginal cost per fish decreases from $34 for a standard deviation of 6 to $29 for a standard deviation of 0. A key result of the thesis is the pattern of decreasing marginal costs as the forecast accuracy increases, suggesting that provision and use of such stream temperature forecasts would have value to society. The Value of Short Run In‐stream Temperature Forecasts: An Application to Salmonids in the Klamath and John Day Rivers by Biao Huang A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science Presented August 21, 2009 Commencement June 2010 Master of Science thesis of Biao Huang Presented on August 21, 2009. APPROVED: _____________________________________________________________________ Major Professor, representing Agricultural and Resource Economics _____________________________________________________________________ Head of the Department of Agricultural and Resource Economics _____________________________________________________________________ Dean of the Graduate School I understand that my thesis will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my thesis to any reader upon request. _____________________________________________________________________ Biao Huang, Author ACKNOWLEDGEMENTS I would like to express my deepest gratitude to many individuals for their support, encouragement, and guidance during the past two year of study experience in Oregon State University. In particular, I would like to thank the follow people: Dr. Christian Langpap for his endless support and guidance in all the time of this research and the writing of the thesis, the work could not have been finished without his extraordinary supervision and incisive comments; Dr. Richard M. Adams for a multiplicity of innovative ideas and inspirations, superior expertise and stories. His intellectual energy and insight motivate my academic endeavors; Dr. Gregory M. Perry for his open door policy, providing great suggestions; Dr. David Sampson for his supports and advice in the preparation of the bio‐model; Wesley Bignell, Bret Sechris and other students in Agricultural and Resource Economics at Oregon State University for their help, friendship and jokes. Nicholas C. Hayden for his support, encouragement and friendship. NOAA for providing me with the data and project summer funding. CDFG for providing the data. TABLE OF CONTENTS 1. Introduction ........................................................................................................................................... 1 1.1 Background ...................................................................................................................................... 1 1.2 Problem Definition ........................................................................................................................... 3 1.3 Objectives .......................................................................................................................... 6 1.4 study Area and Cope .......................................................................................................... 7 1.4.1 The Klamath River ..................................................................................................................... 7 1.4.2 The John Day River ................................................................................................................. 10 1.5 Thesis Organization.......................................................................................................... 12 2. Literature Review ................................................................................................................................ 14 2.1 Agriculture ..................................................................................................................................... 15 2.2 Energy and Water Management .................................................................................................... 18 2.3 Fisheries management .................................................................................................... 23 2.4 Forestry .......................................................................................................................................... 24 2.5 Transportation ............................................................................................................................... 25 3. Conceptual Issues and Methodology ................................................................................................... 27 3.1 Bayesian Decision Theories ............................................................................................................ 27 3.2 Bayesian Simulation Procedures ................................................................................................... 29 4. Biophysical Relationships and Models ........................................................................................... 34 4.1 Temperature effects on Salmonid ................................................................................................. 34 4.1.1 Chinook Salmon ........................................................................................................................ 37 4.1.2 Juvenile Steelhead ..................................................................................................................... 39 4.2 Biological Modeling ......................................................................................................................... 41 4.2.1 Ricker Model for Chinook Salmon ............................................................................................. 43 4.2.2 Ricker Model for Steelhead ....................................................................................................... 44 5. Water Management Decision Models ................................................................................................... 46 5.1 Temperature Distribution ................................................................................................................. 46 5.2 Decision Models in the Klamath River ............................................................................................. 48 5.3 Decision Models in the John Day River ............................................................................................ 51 TABLE OF CONTENTS Continued)________________________________________________Page 6. Stream‐flow, Water Temperature and Cost Analysis ............................................................................. 54 6.1 Stream‐flow and Water Temperature Relationship in the Klamath River ........................................ 54 6.2 Cost Analysis for the Klamath River .................................................................................... 60 6.3 Stream‐flow and Water Temperature Relationship in the John Day River ........................ 61 6.4 Cost Analysis for the John Day River ................................................................................... 62 7. Results ....................................................................................................................................... 64 7.1 Model Validation .............................................................................................................................. 64 7.2 Comparisons of accuracies and values ........................................................................................... 66 7.2.1 Case in the Klamath River ............................................................................................................ 66 7.2.2 Case in the John Day River ........................................................................................................... 68 7.3 Sensitivity Analysis ............................................................................................................................ 71 8. Conclusion .............................................................................................................................................. 73 8.1 Summary ........................................................................................................................................... 74 8.2 Management Implications ................................................................................................................. 76 8.3 Limitations of this Study ................................................................................................................... 78 8.4 Implication for Future Study ............................................................................................................. 78 BIBLIOGRAPHY ............................................................................................................................................ 80 LIST OF TABLES Table____________________________________________________________________Page Table 7.1 Model Outputs under Different Forecast Accuracies in the Klamath River ............................ 66 Table 7.2 Model Outputs under Various Forecast Accuracies: the John Day River ................................ 69 The Value of Short Run In‐stream Temperature Forecasts: An Application to Salmonids in the Klamath and John Day Rivers 1. INTRODUCTION 1.1 Background Water temperature is an important measure of water quality, as well as a dominant factor affecting aquatic life within the stream environment (Hynes, 1970). In terms of salmonids, elevated temperatures can decrease fecundity, reduce egg‐to‐fry survival rates, inhibit the growth and survival rate of parr and smolts, lower rearing densities, decrease the ability of young fish to compete with other species for food, and reduce their ability to avoid predation (Sullivan et al. 1990, 2000; Spence et al. 1996; McCullough 1999; Beacham and Murray 1990). Water temperature influences the entire life cycle of cold water fishes, with each life stage having its own thermal tolerance limit (Brett 1956; Bisson et al. 1988; Taylor 1988; Konecki 1995; Cech Jr and Myric 1999; Welsh et al. 2001). Exposure to elevated water temperatures for an excessive period of time could also cause thermal stress, weight loss, and increased mortality rates (Sullivan et al. 2000). Higher temperatures can also increase the vulnerability of juveniles to disease. For example, at 20.5 ⁰C, salmonid juveniles exposure to a disease (Ceratomyxa Shasta) results in an 85% mortality (Udey 1975). Another disease, the Myxozoan pathogen, reported by Foot et al. (2004), has a high mortality for salmonids when water 2
temperature reaches 16 ⁰C and above. A well‐known example of this disease effect is the unprecedented fish kill in the Klamath River in 2002. The California Department of Fish and Game (CDFG) (2004) estimates that during September and October of 2002 between 33,000 and 70,000 adult salmon died in the Lower Klamath River during their spawning migration. It was the first major adult salmonid mortality event ever recorded in the Klamath River. The primary cause of the fish‐kill was a disease that occurred under ideal conditions for such pathogens, created by a combination of warm water temperature, an above average number of Chinook salmon, and low river volumes (due to diversions), which created serious overcrowding. Temperature and other weather information forecasts have economic value in resource management because forecasts may be incorporated into management strategies to mitigate the risk related to weather uncertainty. For example, in agriculture farmers use short term weather forecasts to improve harvest strategies (Wilks et al. 1993; Abawi et al. 1995), to develop protective management decisions (Katz and Murphy 1982), improve irrigation strategies (Wilk and Wolfe 1998) and fertilizer application decisions (Hill et al 2000; Mjelde et al. 1997; Mjelde and Penson 2000), and to make land allocation or crop choice decisions (Messina et al. 1999; Mjelde et al. 1996). The value of longer term weather forecasts, such as the El Niño‐Southern Oscillation (ENSO) phenomenon, has also received attention with respect to agriculture and fisheries management (Adams et al. 1995, 1999, 2003; Costello et al. 1998; Barber and Chavez 1983; Solow et al. 1998; Chen et al. 2001, 2002). The value of both weather and climate forecasts has also been studied in the transportation industry (Rhoda and 3
Weber, 1996; Sunderlin and Paull 2001; Paull, 2001), in the field of water resource and energy management (Yeh et al, 1982; Wyse, 2004; Hamlet et al, 2002; Pagano et al, 2001), and in fisheries management (Pearcy and Schoener, 1987; Johnson, 1988; Costello, 1998; Kaje and Huppert, 2007). 1.2 Problem Definition With the use of short –range weather forecasts (such as daily and weekly precipitation, water, air or soil temperature and evaporation), farmers seek to improve management decisions regarding when and how to increase production under weather uncertainty. In the case of fisheries, uncertainty with respect to weather and environmental factors affects variability in fish dynamics, one of the sources of uncertainty in fisheries management (Roughgarden and Smith 1996). According to the Pacific Marine Fishery Council (PFMC) (1996), ocean conditions were not incorporated into salmon management plans before 1995. Since then, the predictor for Coho salmon has included such ocean conditions, but not in terms of forecast of this environmental variable (Costello 1998). With the accumulation of knowledge and technology, the ability to forecast weather (e.g., temperature) and other climate variables is already in place and its accuracy is expected to improve in the coming years (Adams et al. 1995; Katz and Murphy 1997). Given that fish managers typically must commit to various management actions well in advance of harvests or other management actions, incorporating such uncertainty into management strategies seems to have potential value. 4
To date, no systematic analysis has been conducted to explore the value of in‐
stream temperature forecasting for the benefit of fish production. Freshwater fish are more constrained to climate change and multiple human‐induced stresses than many species in that they are slower to adapt to climate change. This leads to an increasing likelihood of ecosystem disruption, thus placing freshwater fish at greater risk compared to marine fish. Moreover, the distribution of freshwater fish subjected to temperature effects is the most accessible evidence for projecting the potential climate change impact (Minns and Moore 1995). Pacific salmon are anadromous fish, part of their lives are spent in freshwater and part in saltwater. They spawn and rear as juvenile in fresh water, grow up as smolts, then migrate to the sea, returning several years later to their natal streams to reproduce, and then die. Unlike other anadromous Pacific salmonids, steelhead may survive spawning and return to the ocean and spawn again in a later year (Moyle 1976). The fish loss in the Klamath River in 2002 has had far‐reaching economic implications. According to the Pacific Coast Federation of Fishermen’s Associations (2005, 2007), a “weak stock” management policy was implemented after this fish kill, and the resulting economic loss for the commercial salmon fishery was estimated to be over $100 million. Fall run Chinook salmon mainly return the Klamath River beginning in late July, peaking in September near the mouth of the Trinity River and continuing into December (Andersson 2003). The fish kill occurred in the Lower Klamath River, downstream of Coon Creek Falls (River Miles 36), and the disease outbreak on the Klamath River occurred over a period of about two weeks. Had in‐stream water 5
temperature forecasts been available one week prior to this period, the water managers within the Klamath River system could have made a decision to release water during this time period. For example, Lewiston Dam on the Trinity River, the biggest tributary of the Klamath upstream of the fish die‐off reach, has a large reservoir of cooler water. Releases of such water could reach the affected stream within 72 hours. However, the water in Lewiston Dam is part of the Central Valley Project. The water is primarily intended to be diverted via Clear Creek Tunnel, through Judge Carr Powerhouse, Spring Creek Powerhouse and the power plant at Keswick Dam, until it reaches the Sacramento River, then flows south to the Delta Region of San Francisco Bay, where it is pumped and used for production of irrigated crops in the San Joaquin Valley (Douglas and Taylor 1999). Another salmonid of high importance in the Pacific Northwest is the steelhead trout (Adams et al. 1993; Li 1994; Wu et al. 2000). High water temperatures can also affect the life cycle of this species. For example, steelhead trout in the John Day River typically spend two years in freshwater as juveniles, two years in the marine environment as adults and one year for migration between each environment (Johnson and Adams 1988). Most of the John Day basin receives less than 7.9 cm of precipitation per year and has a low flow and high temperature period occurring during August (1.7 cubic meters per second, measured at Service Creek River, Kilometer 252). Water temperature measures of 30 ⁰C have been recorded in Rock Creek (Li 1994). The semi‐
arid nature of the basin increases the value of out‐of‐stream water and thus increases 6
conflict between in‐stream uses for steelhead production and water withdrawal for agriculture and pastureland irrigation for livestock production in this area. In summary, the problem faced by the resource manager in this thesis is defined as a water allocation problem between fish, hydroelectric power generation, and agriculture. In this setting, the decision maker must account for the effect of water releases and withdrawals he or she makes today on all future fish populations. This allocation problem is evaluated using a stochastic dynamic simulation model to estimate the effect of changes in management actions in response to water temperature forecasts in both the Klamath and John Day rivers. 1.3 Objectives There are two general objectives of this thesis. The first objective is to develop a framework for assessing the value of short‐term, in‐stream water temperature forecasts using a dynamic biological model with stochastic parameters. The second objective is to apply this framework to fishery management to assess the potential value of improved forecasts for Chinook salmon management in the Klamath River in California, and steelhead trout management in the John Day River in Oregon. In the empirical analyses in the Klamath River and the John Day River, the value of various forecast accuracies will be assessed. In order to assess the value of short term in‐stream water temperature forecasts, a base scenario is necessary. In this case it is the fish production levels and cost corresponding to decisions using historical water temperature information. The forecast time frame is one week (7 days) in advance, which means that a resource 7
manager, after receiving the one‐week water temperature forecast, will incorporate this forecast information into current management strategies to make decisions. 1.4 Study Areas 1.4.1. The Klamath River The Klamath River originates in south‐central Oregon, then flows 263 miles in a general southwesterly direction into California where it is intersected by the Trinity River, then turns northwesterly and continues to the Pacific Ocean. The Klamath River basin includes a diverse ecosystem, ranging from high elevation wilderness areas to irrigated farmland in southern Oregon and northern California. The main stem of the Klamath River drains about 5,000 square mile in Oregon and 10,000 square in California (DFG 2004; NRC 2008), and it is divided into the Upper and Lower Klamath basins, with a generally accepted boundary being Iron Gate Dam (RM, 190). The Upper Klamath River basin supports 18 species of native fish, two of which are listed as endangered under the U.S. Endangered Species Act (ESA), and one is listed as threatened (NRC 2008). There are six dams in the Upper Klamath River that block access for fish upstream migration, and are currently undergoing Federal Energy Regulatory Commission (FERC) relicensing hearings. The Lower Klamath River and its tributaries are home to 19 native and 13 invasive fish species (Mount and Moyle 2003). Important fishes of the Lower Klamath include the coho salmon (Oncorhynchus kisutch), listed as threatened under the Endangered Species Act, the declining steelhead (O. mykiss), and the largest and most abundant salmonid, the Chinook salmon (O. tshawytscha). Chinook salmon stocks 8
include spring run Chinook and fall run Chinook; fall run Chinook are the focus of this study. The difference between these two stocks is that the spring run adults enter the river before they are ready to spawn and reside in deep pools for 2‐4 months before they spawn, whereas the fall run adults spawn shortly after they reach their spawning destination (Moyle 2002). The fish‐kill took place on the lower 36 miles of the Klamath River, with dead fish being observed between at least September 18 and October 1, 2002 within the area from river’s mouth upstream to Coon Creek Falls and the entire Yurok Indian Reservation (Figure 1.1) according to CDFW (2004). Figure 1.1 Map of the Klamath River Basin showing pertinent feature Source: CDFG (2004) 9
Water conditions in the Klamath River show substantial annual variability. For example, the U.S. Geological Survey (USGS) gauge data show that mean monthly temperature in the Lower Klamath River, the only portion currently accessible to anadromous salmonids, generally ranges from 3‐6 ⁰C in January and to 20 ‐22.5 ⁰C in July and August (Bartholow 2005). Summer maximums in the Lower Klamath River basin below the Trinity River Confluence around Weitchpec may reach 26.6 degrees Celsius (Blakey 1996). In contrast, the water temperatures of releases from Lewiston Dam on the Trinity River from April to October are between 8 and 11.6 ⁰C. The contribution of flow from the Trinity River to the Klamath River below the confluence varies across the seasons. For example, it contributes 37% in July, peaking at 50% at the end of August (Zedonis 2005). Lewiston Dam is part of the Trinity River Division (TRD) of the U.S Bureau of Reclamation (USBR) and is a feature of the Central Valley Projects. Since its completion in 1963, Lewiston Dam has changed water use and diversions in the Trinity River. Prior to TRD, summer and early fall flows in the Trinity River near Lewiston ranged from 100 cfs in dry years to 300 cfs in wet years. Currently, the flow is augmented to 450 cfs by court order (DFG 2004). Nonetheless, it is not sufficient in a hot dry year to maintain non‐threatening water temperatures in the Lower Klamath River. Hydrological and fishery management in this basin is complicated because decision makers have to develop potential strategies to address conflicts between fish, dams, and diversions. 10
1.4.2. The John Day River The second study area is the John Day River basin in north‐eastern Oregon (Figure 1.2). It encompasses an area of 8010 square miles and varies in elevation from 150 feet above sea level at the mouth of the John Day River to 9038 feet on Strawberry Mountain (Johnson 1987). The John Day River is the second longest free‐flowing river in the continental United States. Major tributaries flowing into the main stem are the North Fork, Middle Fork and the South Fork John Day River. The John Day River supports entirely wild runs of fall and spring Chinook salmon and summer steelhead. However, in the past 40 years the population of anadromous fish has declined in the John Day River (Adams et al. 1993). Many factors limit the fish productivity in this area including both natural conditions and human activities. The semi‐arid nature of much of the basin results in large seasonal in‐stream flow variation. For example, flow data at Picture Gorge (near Dayville) for the last 40 years show a highest annual flow (1,207 cfs occurred in 1984) that was about 8 times greater than of the lowest annual flow (143 cfs in 1977) (Adams et al. 1993). Human activity, such as over‐grazing on riparian vegetation has increased the insolation reaching the stream, resulting in increases in water temperatures. Such elevations in water temperature close to lethal level may impose high metabolic costs on trout, offset higher food availability and affect the availability of prey and restrict salmon and steelhead productivity (Li et al 1994). 11
Together, the lower summer stream flows due to riparian damage and the basin’s semi‐arid climate exacerbate the potential conflicts between in‐stream uses (fish production) and out‐of‐stream water uses (crop irrigation and pastureland and livestock production). The focus species in the John Day River is steelhead (juvenile) in North Fork located primarily in Grant County. This portion of the drainage is selected because it contains the largest proportion of steelhead, contributing 40% of the entire steelhead population in John Day River (Johnson and Adams 1988). Figure 1.2 The John Day River Basin Oregon Source: Johnson (1988). 12
1.5 Thesis Organization This thesis consists of eight chapters. Chapter 2 provides a literature review on studies addressing the value of weather forecast in terms of agriculture, energy and water management, fisheries management, transportation industry and forestry management. Chapter 3 gives a brief presentation of the methodology used here, which is based on simulations that incorporate Baye’s Theorem. Chapter 4 introduces the biological components of the framework including the link between water temperature, salmonid survival rates, and classic Ricker spawner‐recruit models as they relate to the Klamath River and the John Day River. Chapter 5 begins with the water distribution in the Klamath River and John Day River, and then continues with a discussion on how to update the expected water temperature after receiving a new forecast. Various decision models are discussed here, including the no‐forecast decision model, where the manager only considers the prior water temperature distribution, the case of the imperfect forecast decisions, with small, medium, and large variance, and the perfect forecast scenarios in both the Klamath River and the John Day River. Chapter 6 presents the stream‐flow and water temperature relationship in the Klamath River and the John Day River, and the opportunity costs associated with the water releasing decision and water purchasing decision in the rivers. Results from the different decision models, including the changes in fish numbers and corresponding costs, are discussed in chapter 7. Chapter 7 also contains sensitivity analyses to test the robustness of the estimation of the value of information. Chapter 8 presents a summary and discussion of the finding of 13
the value of information, reviews management implications of the analysis, and concludes with a brief discussion of recommendations for future research. 14
2. LITERATURE REVIEW The potential value of climatology information has long been recognized by climatologists and economists in a variety of different situations. Quantitative assessments of the value of such information have been performed in a number of contexts, including the agricultural industry, fisheries (commercial and recreational), energy, water resource management, the transportation industry, and other resource management settings. These applications are well summarized by Mjelde and Frerich (1987), Katz and Murphy (1997) and Houston, Adams, and Weiher (2004). Assessments cover valuation of both short‐term and long –term forecasts. Short‐
term forecast information such as daily, weekly or monthly weather forecasts require decision makers to take immediate action to increase their production or decrease their damages. Long‐term forecasts (seasonal) would allow a farmer to choose a different crop mix or allow fisheries managers to initiate different management strategies.
However, one problem with long –term evaluation is the choice of an appropriate social discount rate. In particular, when dealing with choice under uncertainty, calculations of present value versus future trade‐off of benefits and costs are difficult (Chavas et al. 1991). Revealed preference, contingent valuation and measures of capitalization (productivity gains from improved information) are three commonly used methods in these information valuation studies. Non‐market sectors such as recreation and the household sector have been studied using the revealed preference and contingent 15
valuation methods. The measure of capitalization is more common in commercial sectors such as agriculture, energy, and transportation, where increased values, gained from improvements in decision making, can be expressed in dollar terms (Houston, Adams, and Weiher 2004). Decision makers in many of these cases have to consider two options: take a protective action or operate at the risk of loss. Upon receiving forecast information, the decision maker is assumed to update the initial probabilities by Bayes’ theorem. Most studies used economic models that embed Bayesian frameworks to evaluate the value of weather forecast information (Conklin et al. 1977; Katz et al 1982; Katz and Murphy 1984; Mjelde et al. 1988; Adams et al. 1995; Costello et al. 1998). The following are selected studies on the value of weather forecast information in different sectors, and collectively they provide guidance on how to infer the economic value for weather forecasts. 2.1 Agriculture Most of the effort so far has focused on studies of agriculture because crops or fruit trees are heavily dependent on weather conditions. Short‐term weather forecast such as daily predictions of precipitation and daily or weekly temperatures are useful for the decision maker in that it could allow the manager to make irrigation, fertilization, and harvesting schedules or, in some cases, frost protection decisions. One of the early studies on the value of weather forecast is by Lave (1963). He evaluated the value of weather forecast for the raisin industry in California in terms of whether and when to produce raisins or to sell grapes for juice. Considering market 16
factors, he found that there was a high value for weather forecast of three weeks in advance for a particular grower who received the forecast information, but the aggregate value of information to the raisin industry as a whole could be negative due to an inelastic demand. Unlike Lave who accounted for the marker factor, Conklin, Baquet and Halter (1977) made various assumptions about human risk attitudes, prior information, and accuracy of forecasts, and estimated the economic value of frost forecasts for pear production during a two month period. They simulated the frost protection decision process with a Bayesian framework to update nightly temperature distribution, and estimated that the imperfect information value per ha per year was $ 798, and perfect information was $1,270. The same problem was also studied by Katz et al (1982) for pears, apples and peaches. Unlike Conklin et al. who used a static model, Katz et al (1982) used dynamic programming and estimated that the value of imperfect information forecast per ha per year was $667 to $1,997 and $1,406 to $3,047 for the perfect information forecast. The value of forecasts has also been estimated for irrigation management. The early studies of value of forecast information on irrigation (Allen and Lambert 1971; Swaney et al. 1983) used a static framework instead of the inherent dynamic process and produced some spurious results, such as the value of a perfect forecast being smaller that the value of an imperfect forecast, and a negative value for forecast information (Wilks 1997). Later studies have focused much more on dynamic situations. 17
For example, using a stochastic dynamic programming algorithm, Wilks and Wolfe (1998) studied the daily weather forecast information for lettuce irrigation in New York. They estimated an additional value of approximately $ 1,000 per hectare per year for an optimal use of weather forecast. Also, Wilks, Pitt and Fick (1993) used a dynamic programming approach to evaluate the value of forecast information in regards to alfalfa harvest, and estimated that the average annual crop value was increased by about 5‐10%. The value of seasonal forecast information with regards to the timing and amount of fertilization in agriculture has also received attention. Byelee and Anderson (1969) evaluated the forecast information value in regards to the amount of fertilizer for wheat. With the same static framework, Doll (1971) examined the forecast information value for fertilizer for corn, and estimated $ 0.17 to $0.54 per ha per year for the imperfect information, and a larger value of $9.93 to $ 17.4 for perfect information. Mjedle et al (1988) not only considered the amount of fertilizer but also the forecast lead time when they estimated the value for corn production in east‐central Illinois. They used a stochastic dynamic programming model to determine the value of forecasts and concluded that a less accurate forecast received earlier in the production process may be more valuable than a more accurate forecast later. Long‐term forecasts are useful for crop choice, crop variety, planting dates, and investments in certain types of infrastructure. The choice of different crops or the allocation of different areas to different crops depends on the decision maker’s weather 18
expectations over a long time scale. For example, Agnew and Anderson (1997) considered wheat acreage in the entire United States for different hypothetical temperature and precipitation forecasts. The value of an imperfect forecast was $10.8 million per year and the value of a perfect forecast $208 million per year. Tice and Clouser (1982) considered the planted acreage allocation between corn and soybeans. Other long term forecast studies have focused on climatic conditions, such as ENSO, and most of these studies were evaluated in a regional or national level. For example, using models from meteorology, plant science, and economics, Adams et al (1995) considered four crops in the southeastern United States, and estimated that the value of improved forecasts was $96 million for imperfect information and approximately $145 million for perfect information. Values for imperfect ENSO forecasts in the United States have been estimated to range from $300 to over $900 million (Chen et al. 2001, 2002; Solow et al. 1998), with a perfect forecast having a value of more than $1.7 billion. Adams et al (2003) also estimated the ENSO forecast for agricultural sector in five states in Mexico, with about $20‐$30 million for imperfect information and up to $79 million for perfect information. 2.2 Energy and Water Management Climate, in particular temperature, plays an important role in energy management, such as consumption and distribution of fuel and electricity. For example, high summer temperatures are positively correlated with increased energy use for air conditioning, and cold winter temperatures with increased energy use for heating. 19
Medium to long range weather forecasts allow water managers to efficiently allocate limited water resources among agricultural irrigation, hydropower generation, municipal use, and endangered or threatened species. Energy producers are concerned with the competing demand for water from different kinds of users, which can create water deficits. Examples include the 1976‐78 droughts in western United States which hampered electricity production, and the 1979‐1980 water shortage which affected the Delaware River Basin area in New York and New Jersey (Greis 1982). Studies in energy and water management were put together because water management often involves the stream flow estimates which may affect hydropower energy production. Greis (1982) incorporated effects of temperature on consumer energy demand and water evaporation in the cooling tower to develop a water demand model for electricity production, and formulated the water demand for energy production as a function of climate, especially temperature. He concluded that the imperfect climate outlook can be useful in energy management since a decision had to be made in one to three months, which was shorter than the time required for the perfect forecast in this particular case. A longer scale forecast makes it possible to produce useful stream flow forecasts for a powerhouse dam manager in that it allows the dam manager to relax the current stream flow constraints in years when a high stream flow is possible. For example, Yeh, Becker and Zettlemoyer (1982) evaluated the value of the long range forecast for the multipurpose Oroville‐Thermalito reservoir operation system of the California State 20
Water Project. The benefit derived from the forecast included hydropower generation, water conservation for agricultural irrigation, decreased seepage damage to crops and flood control. Incremental benefits depend on the forecast lead time and the forecast accuracy. The hydropower benefits were estimated between $0.2 and 0.4 million annually in 1983 dollars, flow releases for crops were estimated to increase by 22‐24 percent, depending on the crop. Georgakakos (1989) evaluated the benefit of stream flow forecasting in the Savannah River system in the state of Georgia, and the High Aswan Dam and the Equatorial Lake system in the Nile basin. The author used a statistic stream flow model of increasing forecasting ability, coupled with stochastic control simulation, and found that the forecast benefits were system specific and may range from quite substantial to fairy minimal. In contrast to Georgakakos, Hamlet et al. (2002) used the improved ENSO and the Pacific Decadal Oscillation (PDO) to derive the stream flow forecast for the Columbia River hydropower. They estimated that annual net revenue was increased by about $40 million per year on average relative to the status quo, and that if a small decrease in the reliability of meeting storage targets in conjunction with firm energy production was permitted, the average annual revenue would rise by $153 million. If weather forecasting is used to predict wind velocity instead of temperature, this forecast information will enable wind energy producers to make better decisions, which can have genuine value in the context of the electricity market. Roulston et al. (2002) simulated the performance of generators using different strategies under a 21
simplified electricity market to examine the value of medium range weather forecasting. They found that the forecasts could improve the performance of generators with lead times up to 6 days. The forecasts using numerical weather prediction provided most of the improvement over climatology (using only historical information), they doubled net income at short times and even at three days income would be raised by 75%, the usage of ensemble prediction forecast system would boost the income by up to 20%. Even in unseasonably calm periods, the 4‐day ensemble forecast user had a higher daily income on 60% of the days and higher net weekly income on 80% of weeks than the historical climatology information user. These medium range forecast users could increase their income by reducing losses resulting from underproduction and/or reducing the opportunity cost related to under‐promising when the actual energy production is unseasonably high. Natural disaster effects have also been studied. Hurricane forecasts are valuable for energy producers offshore in that producers facing hurricanes have to temporarily stop the flow of raw oil from production fields and evacuate drilling rigs. A more accurate hurricane forecast will generate fewer false alarms, therefore preventing unnecessary evacuations and production disruptions. Considine et al. (2004) used a probabilistic cost‐loss model to estimate the incremental value of hurricane information for oil and gas production in the Gulf of Mexico over the past two decades. These authors concluded that the value of hurricane forecast information to the oil and gas industry is $10.5 million and $ 8.1 million for 24 and 48 hours, but with twice the accuracy the incremental annual value is approximately $15 million. 22
As mentioned before, drought management is an important aspect of water management. In some states, the seasonal climate forecast is the primary decision criterion for some programs. For example, policy makers in Georgia have to decide whether or not to implement the Flint River Drought Protection Act, a program aimed at compensating farmers who volunteer to suspend agricultural irrigation acreage during potential drought years. The State began using forecast information in 2001, and it was estimated that the economic benefit was $100‐$300 million in state‐declared years (2001, 2002) and $5‐$30 million in 2003 and 2004 (Steinemann 2006). Another aspect of water management is stream flow management. Pagano et al. (2001) considered the impact of El Niño Southern Oscillation (ENSO) and winter climate on snow pack and summer stream flow. The long‐lead forecast for future rains allowed the managers to avert the expensive contingency plan of pumping groundwater when rain was forecasted. The authors found that, although the climate forecast was a useful tool for managers, to improve the value of the forecast closer cooperation between hydro‐climatic researchers and water managers was necessary. Rayner et al (2005) obtained similar results when they identified the reason why water resource managers were reluctant to incorporate climate forecasting information into their management strategies. Studies in the Metropolitan Water District of Southern California, the Columbia River system in the Pacific Northwest, and the Potomac River Basin and Chesapeake Bay in the Washington D.C metropolitan region showed that institutional reasons affect the use of forecast information by decision makers. These authors concluded that incorporating the forecast information into the organizational 23
practices and routines, and enhanced usability such as a finer spatial resolution of forecasts, would increase the likelihood of acceptance by decision makers. 2.3 Fisheries management Surprisingly, there are few studies that value climate forecasts in the context of fisheries, given the growing recognition of the intricate relationship between climate variability, marine and fresh water environmental conditions and fish population dynamics, and the improvement in lead time and accuracy of climate forecasts. The use of climate forecast information has value in fisheries management because fish managers, knowing the fish stock abundance, could adopt better fish management strategies, or water managers could make better protective decisions during critical phases for fish. For example, low levels of commercial fish stock, attributed in part to El Nino, resulted in a complete closure of the recreational and commercial Coho salmon fisheries off California, Oregon and Washington in 1994, and a closure of the commercial Coho fishery off California and Oregon in 1995 (Pacific Fishery Management Council 1996). Costello et al. (1998) were the first to conduct a systematic analysis of the value of climate forecasts for fisheries. They estimated the value of improved El Niño forecasts in the management of salmon in the Pacific Northwest. El Nino forecasts enable the fish manager to adopt fish management strategies in term of the fish harvest rate and hatchery production. The authors used nonlinear optimization and stochastic dynamic programming to evaluate naïve, improved, and perfect one year forecasts, and found 24
that a perfect El Niño forecast resulted in an annual welfare gain of approximately $1 million, and an imperfect forecast was valued at approximately $0.4 million. They also concluded that increasing the twelve‐to‐eighteen month forecast accuracy would produce a higher gain than that from lengthening the forecast lead time. NOAA (2003) reported that improvements in satellite imagery and sounder will help fish managers to evaluate fish biomass by providing high spatial resolution data and frequent location coverage of temperature boundaries in areas where many species congregate. This biomass estimates in return will enable fish managers to implement catch control policies. Using both commercial and recreational catches in the Atlantic, Gulf, and Pacific coasts, these authors estimated an economic value of nearly $3.2 million increase in commercial catch. Broad et al (2002) considered the forecast dissemination problem in Peruvian fisheries, and tested the claiming that the seasonal‐to‐annual climate predictions yield benefits to society. These authors found potential constrains on the realization of the benefit, such as limited access to the internet and understanding of the information. They also suggested that a detailed definition of societal benefit was necessary to define the value of climate prediction, and provided several choices for forecast dissemination. 2.4 Forestry Climatology information also has value in the forestry sector because weather conditions will determine the allocation of scarce suppression resources among different locations facing different fire risk. For example, researchers at the US Forest 25
Service’s Pacific Northwest Research Station are currently producing maps linking weather conditions and fire occurrence since 1895, and using this information to develop 3‐ to 12‐month fire forecasts (Houston et al. 2004). This kind of information will help the forest manager better prepare for the wildfire. Brown and Murphy (1987) estimated the economic value of weather forecasts in wildfire suppression mobilization decisions in a simple two‐fire situation. Using data derived from the Deschutes National Forest in Oregon, they estimated that ‘state of the art ‘forecasts have an expected economic value of about $6,100, and perfect forecasts have a value of $16,600. Other studies on the value of forecasts related to forestry include Anderson (1973) and Furman (1982). Ecological and economic impacts of future climatic conditions on the forestry sector also have been studied (McCarl et al. 2000; Dale et al. 2001). 2.5 Transportation Another sector that heavily depends on weather conditions is the transportation industry. The air transportation sector is particularly vulnerable to weather in that bad weather could change flight schedules. For example, poor visibility in an airport would cut the flow rate, and thunderstorms force aircraft into a holding pattern. It is not surprising that most of the studies on the value of weather forecast on transportation have focused on the aviation industry. Keith and Leyton (2006) evaluated the value of weather forecast for airports for commercial aviation by studying the decision for fuel carriage. Carriage fuel is the fuel 26
required to carry the extra weight from the additional fuel which is loaded in case of bad weather conditions at the destination. Significant costs can result from unnecessary burning of the carriage fuel when additional fuel is carried but not utilized or from a diversion when additional fuel is not carried but needed. Using a cost‐based decision making model, this study focused on the forecasts of low ceiling and visibility and their impact on flight arrival at three majors airports in the United States. The results are compared between two forecast systems, and the better one, statistic probability forecast, could produce potential annual savings of approximately $50 million in operation costs. Rhoda and Weber (1996) studied the Integrated Wind Shear System of Weather Systems Processor deployment, and estimated a $25 million per year delay benefit, based on expected year 2000 traffic counts at planned WSP airports. Other studies on the benefits from flight delay includes Allan et al. (2001), Evans et al. (1999), NOAA (2002), Sunderlin and Paull (2001). The benefits from reductions in accidents have also been studied, for example, Paull (2001) estimated an annual cost of $106 million, or 0.1% of GDP from air transportation from reducing the risk of in‐flight icing accidents. 27
3. CONCEPTUAL ISSUES AND METHODOLOGY The value of information is derived by comparing the economic outcomes of choices made under different information levels. Decision analysis is defined as a set of concepts and procedures for analyzing decision‐making problems involving uncertainty in a logical, rational manner (Keeney, 1982). The principle is to maximize the total expected value or to minimize the total expected cost over a period of time. Decisions made under environmental uncertainty, as in the cases of water flow management in the Klamath River and the John Day River, must be treated as stochastic. This section presents a brief overview of Bayesian decision theory and how it may be embedded in a simulation model, which provides the general framework for this study. 3.1 Bayesian Decision Theories The key feature of Bayesian decision theory is the updating of prior information upon receiving new information. Bayesian statistical analysis is based on Bayes’ Theorem (named after Rev. Thomas Bayes, 1702‐1761). The theorem relates the conditional and marginal probabilities of two events. For example, given that an event B already occurred, the conditional probability of an event A is equal to: (3.1) P ( A | B) =
P ( A ∩ B) P( A) * P( B | A)
=
, P( B)
P( B)
where P ( A | B) is the posterior probability or the conditional probability of A given B, because it considers the probability information of event B; P( A) is the prior or historical probability because it does not consider the probability of event B; P ( B | A) is 28
the conditional probability of B given A; and P(B ) is the prior or historical probability of B. The corresponding formulation for continuous probability distributions is (3.2) P ( A | B ) =
f ( B | A) * P ( A)
∫
f ( B | A) * P ( A)dA
, where f ( B | A) is the probability density function of B , given A . In this study, we use Bayes’ theorem to update expectations about in‐stream water temperature on the basis of water temperature forecasts. Let T denote the average in‐stream water temperature for the relevant period, with prior probability density function p(t). Let Y be the forecasted water temperature. Then, by Bayes’ theorem, the posterior probability density function of T when Y = y is (3.3) p(t | y) =
f ( y | t) p(t)
∫ f ( y | t) p(t)dt
, where f(y|t) is the probability density function of Y when T = t. Assume that the historical distribution of T is normal with estimated mean μ and variance σ 2 . If the historical record is long enough, then this fitted distribution can be regarded as the prior distribution of T . Suppose that, given T = t, the water temperature forecast is given by Y = t +ε 29
where ε is a normal prediction error with mean 0 and known variance σ Y2 . The forecast is correct on average, and the variance σ Y2 can be interpreted as representing the accuracy of the forecast. For small values of σ Y2 , Y will be close to t, whereas if σ Y2 is large they can differ significantly. For this model the posterior distribution of T given Y = y is also normal with mean (3.4) μ ( y ) = wμ + (1 − w) y , and variance (3.5) where w =
σ 2 ( y ) =
σ 2σ Y2
, σ 2 + σ Y2
σ Y2
σ 2 + σ Y2
The predictive distribution of Y is normal with mean μ and variance σ 2 + σ Y2 . 3.2 Bayesian Simulation Procedures Fish production is a dynamic and continuous process over the entire life cycle of the species and is impacted by a range of factors, both anthropogenic and natural. The purpose of this section is to develop a simulation framework reflecting the role of water management decisions in the Klamath and John Day rivers. The simulations are 30
conducted within a dynamic economic setting to evaluate the effect of stream temperature forecasts on these water management decisions. In the Klamath River, Chinook salmon return from the ocean in the fall, with the number of returning fish peaking in September. Because in‐stream water temperatures would be forecasted seven days ahead, the simulations for the Klamath River correspond to a week in September when the water temperature is very high and the number of Chinook returning is relatively large. Theoretically, the dynamics of water releases for the entire month of September should be considered, but since the available data are seven day forecasts, the decision is to be made up to one week ahead. For the free‐flowing (no dams) John Day River, the water temperature typically peaks in August, and water diversions for agricultural use are the primary cause for elevated water temperature and ultimately for the increased mortality for steelhead. From a decision making point of view, both expected net value (benefits) and cost should be considered here, and each should be taken as an ex ante measure, since they have yet to occur. However, this study only focuses on the maximized fish number instead of the net value of the fish. The net economic value of the fish could be calculated if a marginal value of fish were assigned. However, since some of these stocks are listed as “endangered” or “threatened”, it is deemed inappropriate to assign a value to the fish. Associated with the expectation of the fish number and the corresponding cost is some level of variability around the expected fish numbers or costs. For example, if a 31
decision were repeated many times, such as fish production over many generations, the long run average fish number would be the expected fish production and long run cost would be the corresponding cost for the decisions made during these multiple generations of fish. The impact of management decisions on the expected number of fish in this analysis occurs through the release of cold water from Lewiston Dam, upstream of the Trinity River, to reduce high water temperatures in the Klamath River below the confluence point between the Klamath River and the Trinity River. In the case of the John Day River, fish numbers are affected through purchase or lease of water from agriculture (to remain in‐stream). Theoretically, the highest level of fish survival rate occurs if the fish are never threatened by elevated water temperatures, as would be the case if following a strategy of always releasing water. This is not the case for the Klamath River or the John Day River, where high water temperatures in August and September are common, and water allocation becomes an issue among different users. If a rational water resource manager is risk‐neutral, the best he could do is to utilize experience and subjective judgment to predict an expected water temperature which represents the long‐run average temperature expectation. The expected fish survival rate is unique to the manager because it reflects an individualized expectation of water temperature. However, for a given week the actual or ex post fish survival rate may be greater than, equal to or less than the expected survival rate depending upon 32
the resource manager’s decision. The corresponding cost, viewed ex ante, is discussed in chapter 5. A Bayesian decision framework is used to model and evaluate water release decisions for Lewiston Dam, and water diversion choices in the John Day River. The modeling process includes the following steps: 1) Simulate the water temperature seven days in advance, and, 2) measure the expected change in fish numbers and the accumulated corresponding cost throughout the entire time period of the simulation (ten generations of fish). The following presents a simulation procedure of the Bayesian decision framework for the decision problem in the Klamath River and the John River, indicating how the information used by the model is evaluated. As mentioned above, the analysis covers one week in September in the Klamath River, and one week in August in the John Day River. •
Randomly draw from the prior water temperature distribution and get a prior temperature expectation. •
Randomly draw from the predictive water temperature forecast. •
Update the expected water temperature using Bayes’ Theorem. •
Make a management decision based on the chosen threshold and the expected water temperature according to the threshold •
Randomly draw from the prior water temperature distribution to obtain the realized water temperature •
Set the initial fish number and, based on the management decision and the realized water temperature, calculate the number of fish for the first generation. 33
•
Calculate the opportunity cost corresponding to the decision made for the first generation. These steps are repeated for a total of ten generations, after which the fish numbers reach a steady state. The final number of fish at the end of each generation is used as the starting number for the next generation. The final number of fish corresponds to the tenth generation. The present value of opportunity costs is calculated over the ten generations using a yearly 7% discount rate, which is a common discount rate in fishery literature. In this manner the marginal cost per fish with regard to different information structures can be calculated. The entire process is repeated one thousand times, and the mean number of fish and present value of costs over the thousand repetitions are reported. 34
4. BIOPHYSICAL RELATIONSHIPS AND MODELS Calculation of the value of in‐stream water temperature forecasts requires the development of models reflecting the relationship between physical environments including water temperature, and fishery production models. The previous chapter covers the statistical framework for assessing the value of information. This chapter details the biophysical relationships and models used in this assessment. First, models of temperature effects on salmonids are introduced. This is followed by the fish production models. 4.1 Temperature effects on salmonids Temperature affects virtually every aspect of the salmonid life cycle, from egg‐
to‐fry survival, and smolt migration survival to pre‐spawning survival, with each life stage having different thermal limitations (Sullivan et al. 1990, 2000; Spence et al. 1996; McCullough 1999; Beacham and Murray 1999; Scheurell et al. 2006). The stock‐
recruitment relationship is used by policy‐makers to determine the level of fishing that a stock can support and ultimately to produce guidance on total allowable catch (Planque and Fredou 1999). However, the major biological models, such as the Ricker model and the Beverton‐Holt model, typically do not include environmental variables. According to Cushing (1988), as early as 1958 Rounsefell introduced the idea of analyzing environmental factors as deviations from the logistic form of the Ricker model. Other studies then began to incorporate environmental factors into stock and recruitment models. For example, Stocker et al. (1985) used a multiplicative, environmental‐
35
dependent Ricker spawner‐recruitment model to identify significant environmental components, such as sea temperature, river discharge and sunlight hours when he studied Pacific herring in the Strait of Georgia. The resulting model suggested a significant dome‐shaped relationship between temperature and spawning success. Lawson et al. (2004) examined the influence of seasonal stream flow and air temperature on fresh water Coho salmon survival and smolt production in the Pacific Northwest. They used a general additive model to fit smolt numbers and environmental variables, and found that annual air temperature and the second winter flow are highly correlated with smolt production. Weitheimer el al. (2004) used a linear Ricker model to fit environmental variables to evaluate the effect of hatchery releases on wild stock productivity in Alaska. These authors found that marine survival, Alaska summer sea surface temperature, and zooplankton variables could explain about 80% of the variation in wild‐stock productivity. Scheuerell et al (2006) developed the Shiraz model, which includes anthropogenic effects such as land use, management policies including hatchery operations and harvest management, and environmental factors, such as temperature, and used it to evaluate conservation planning for Chinook salmon in Puget Sound, Washington. Other studies used bioenergetics models to analysis the temperature effect on fish growth rate and predation behavior. For example, Peterson and Kitchell (2001) used the bioenergetics model for northern squawfish to predict their predation on salmonids, 36
and found that the predation rate was 68‐96% higher in the warmest year than in the coldest year. Based on daily temperature, Sullivan et al. (2000) developed a bioenergetics model to predict Coho salmon size difference in Washington. The model included the effect of temperature and food consumption rate to evaluate the growth rate of juvenile Coho during the summer. Water temperature also heightens disease infection rates because increases in metabolic demands caused by higher temperatures can lead to a decrease in resistance to disease and an increase in susceptibility to parasites (Cairns et al. 2005). Many pathogens that Chinook salmon carry are dormant at cooler temperatures, but become virulent when the temperature exceeds 15.6°C. Studies have shown there are greatly increased risks of massive salmonid mortality above this limit (McCullough 1999). Traxler et al. (1998) identified ambient water temperature to be responsible for the outbreak of ichthuophthiriasis that led to the loss of Sockeye salmon in the Babine River during 1994 and 1995. Also, the losses of spring and fall Chinook salmon in the Rogue River in Oregon were the direct result of disease (ODFW, 1992, 2000). Most temperature measures used in the above studies are monthly or annual temperatures. The exception is the bioenergetics model, which use the daily water temperature to evaluate the effect on growth rate, instead of the survival rate, which is the concern of this study. Temperature effects on disease infection rates, though well documented, do not provide quantitative analysis of the relationship between survival rate and temperature. The upper incipient lethal temperature (UILT) is a useful way to 37
measure the relationship between survival rate and temperature. The UILT is the exposure temperature which, when applied to a species with a previous acclimation to a constant temperature, results in a 50% survival rate (Elliott, 1981). This temperature is termed the LT50. Its curve shows a steep‐to‐flat downward trend, which means that as the temperature increases, fish can have a 50% survival rate for a shorter time. Logistic form equations of the temperature effect on the survival rate are employed in some fisheries studies. For example, Baker et al. (1994) used a logistic function to represent the temperature effect on survival when they studied Chinook salmon smolt migrating through the Sacramento‐San Joaquin River Delta of California. A logistic function takes the form: (4.1) S (Ti ) =
1
1+ e
−b1 −b2Ti
, It is a generalized linear model with a canonical link function. The biological explanation behind these two parameters (b1 , b2 ) is ( LT 50, a ) , where LT 50 is the temperature at which the predicted survival rate is 0.50, and a is the slope of the survival function at T = LT 50 . Baker et al. (1994) used the maximum likelihood method to estimate LT 50 = 23.12 and a = −0.1718 . 4.1.1 Chinook Salmon In the Klamath River case, I consider the case of the upstream migration of adult fall run Chinook salmon. Chinook salmon homing peaks in September near the mouth of the Trinity River (Andersson 2003) when the water temperature is typically high, up 38
to 26.3 ⁰C in the Seiad Valley reach of the river (NOAA). In this study, the pre‐spawning survival is considered. Pre‐spawning mortality is assumed to occur as a direct result of incipient lethal temperature, or indirectly through increased metabolic function and environmental stressors which reduce overall fish fitness, and in turn increase the disease infection rate and reduce the reproduction success. Ericksen et al. (2007) used data on pre‐spawning survival of Chinook to predict Coho salmon survival in the Klamath River. Based on Marine (1992) and USEPA (2001), they set a lower temperature threshold of 16 ⁰C having a survival rate of 95%, and declining to 1% at an upper lethal temperature of 26 ⁰C. They then used a logistic function to express the relationship between water temperature and the survival rate: (4.2) S Pr espaw =
1
1+ e
−15.01+ 0.75*T
, This survival function was assumed to account for the disease effect via the temperature survival scalar. In their paper, T is mean water temperature in week I, the warmest week experienced by the cohort. In this study, the in‐stream water temperature is assumed to be predicted seven days ahead. Therefore, the temperature in the above equation is represented by the average temperature over seven days chosen to correspond to the upstream migration of Chinook salmon. The pre‐spawn survival is the survival rate during that week. Figure 4.1 shows the water temperature and survival rate relationship for Chinook salmon. 39
Figure 4.1 Water Temperatures and Survival Rate Relationship for Chinook Salmon 100.00%
Weekly Survival
75.00%
50.00%
25.00%
0.00%
5 6
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Water Temperature (deg.c)
4.1.2 Juvenile Steelhead The lethal water temperature for steelhead is different from that for Chinook. For example, in northern California juvenile steelhead were observed actively feeding in water temperature as high as 24 ⁰C. One explanation is that a big proportion of juvenile steelhead move into adjacent stratified pools during the period of high ambient stream temperatures (Nielsen et al. 1994). Similar results were also drawn by Ebersole et al. (2001) when they studied rainbow trout in an arid‐land stream in northeast Oregon. They found that rainbow trout used thermal refugia where the water temperatures were on average 3‐8 0 C colder, to avoid the high ambient stream temperature. Spina (2007) found that over‐summering juvenile steelhead in southern California were able to withstand a higher body temperature by adjusting their foraging behavior. While the reasons are unknown, they might involve acclimatization or other factors that promote heat tolerance. Steelhead production is dependent upon the survival in the most temperature sensitive growth stage, which may be the parr or pre‐smolt stages, during 40
which steelhead juveniles stay at least two summers in fresh water before they reach maturity (McCullough, 1999). This study in the John Day River focuses on juvenile summer steelhead during the fresh water stage of their life cycle. Railsback and Harvey (2001) also used a logistic function to represent the relationship between water temperature and cutthroat survival rate in northwestern California. Railsback and Harvey adapted studies by Myrick (1998) and Dickerson and Vinyard (1999) to consider low diurnal variation effects and estimated a 90% daily survival rate when the temperature is 25.8 ⁰C, and a 10% daily survival rate when the temperature reaches 30 ⁰C. Since lethal temperatures are similar among trout species (Behnke 1992), and the John Day River shares the same hot summer temperature due to the low flow and high exposure to insolation as the Truckee River system in Dickerson and Vinyard’s study, I adopt their results directly. Specifically, I use a weekly survival rate for juvenile steelhead of 0.4 at 26 ⁰C. Another value used here is derived from Myrick (1998) who, following Railsback and Harvey (2001) found approximately a 60 percent survival rate of golden trout juveniles over a 30‐day period at a constant temperature of 24 ⁰C. However, to be consistent with the seven‐day forecast time periods used here, the 30‐day time scale needs to be converted to a weekly scale. Hence, the scale survival rate is adjusted by the same method used in Railsback and Harvey (2001), who provide an example of how to convert the daily survival rate into the monthly survival rate. Specifically, they use the following equality to convert a daily survival probability of 0.99 into a 30‐day mortality 41
of 26%: 0.99 30 = 0.64 . Following this example, the monthly survival rate can be converted to a weekly survival rate: SWeekly = ( S Monthly ) 7 / 30 , where temperature is the average water temperature over a seven‐day period. Using this method, a weekly survival rate of 0.89 is derived when the water temperature is 24 ⁰C. Using these two temperatures and these two survival rates in equation 4.1, the values of the parameters b1 and b2 could be derived. The logistic function is: (4.3) S =
1
1+ e
−31.734 +1.236T
, Figure 4.2 Water Temperatures and Survival Rate Relationship for Juvenile Steelhead Weekly Survival
100.00%
75.00%
50.00%
25.00%
0.00%
18
19
20
21
22
23
24
25
26
27
28
29
30
Water Temperature (deg.c)
4.2 Biological Modeling Two stock‐recruitment models commonly used in the fish population dynamics literature are the Ricker Model and the Beverton‐Holt model. The Beverton‐Holt Model 42
describes an asymptotic curve with high mean recruitment at high spawner abundance, and the Ricker Model has a dome shape and is based on increasing density‐dependence mortality at high spawner abundance (Jennings et al, 2001). The main difference between these two models is the assumption of density‐independence in the Beverton‐
holt Model and of density‐dependence in the Ricker Model. The stock‐recruitment relationship, shown in figure 4.3, is the Ricker Model which will be used in both cases because of data availability for the two riverine settings being evaluated. Recruits
Figure 4.3 Ricker Stock‐Recruitment Relationships S pa w ning S tock
The Ricker Model (1954) takes the form: (4.4) Rt +1 = aS t e − bSt , where Rt +1 is the recruitment in generation t+1, S t is the spawning stock size, a is the coefficient of density‐independent survival, and b is the coefficient representing the density‐dependence of the mortality between eggs and recruitment. 43
According to Hilborn and Walter (2001), the Ricker Model was built based on the assumption that the mortality rate of the eggs and juveniles is proportional to the initial cohort size: (4.5) dN
= −(q + pS ) N dt
where N is the cohort size at any time prior to recruitment, S is the initial spawning stock size, q+pS is the instantaneous mortality rate for the cohort, and q is the density‐
independent mortality rate. The Ricker model can be derived by solving the differential equation for the cohort size at some specific time t. 4.2.1. Ricker Model for Chinook Salmon The Klamath River fall Chinook salmon stock‐recruitment model developed by the Klamath River Technical Advisory Team (KRTAT 1999) was employed in the case of the Klamath River. They used data provided by CDFG and estimated the Ricker model as: (4.6) R = 8.218S w exp(−0.02329S w ) , The root‐mean‐squared error is 0.997 However, in their analysis S w in equation (4.6) is biomass,, calculated by using the number of fish N a and a weight index, given by Wa = {1.0, 1.548, 1.992} , where a= {3, 4, 5} denotes the age structure of fish. The total biomass equals to the number of fish of a specific age times the corresponding relative weight index: S w = ∑3 Wa N a . The units of R and S w are in thousands of fish, weighted 5
as explained above. In this analysis, the number of fish is the measure of interest. 44
Therefore, I used ordinary least squares with KRTAT data to estimate the relationship between the total fish number ( S n = ∑a =3 N a ) and the total biomass ( S w = ∑3 Wa N a ). 5
5
The estimation yields S w = 1.23 * S n , with adjusted R square being 99.2%, and a highly statistically significant fit (t statistic is 42, p = 0.000). Therefore, the reformatted Ricker Model in terms of fish numbers is: (4.7) R = 10.11S n exp(−0.02865S n ) , The units are thousands of fish. However the model initially estimated by KRTAT used data for the Klamath River fall Chinook run for the period 1979 to 1993, which includes several major El Nino events. So an updated model reflecting more recent data, as well as the Trinity River Chinook run is developed. Since the average fish escapement from the new time series (1994 to 2008) is almost double the initial escapement found in the data used by KRTAT (1999), the density dependence parameter b, is reduced by half to yield a new spawner‐recruitment model: (4.8) R = 10.11S n exp(−0.014325S n ) , 4.2.2. Ricker Model for steelhead As noted earlier, the steelhead life cycle differs from salmon in that a small proportion of steelhead could survive and return to the ocean and spawn again. While the Ricker model is generally applicable only for the semelparous species (Hilborn and Walter 2001), Ricker models have been employed for these steelhead species (Johnson 1989; Carmichael 2006). Specifically, Carmichael (2006) used redds (the spawning nest 45
of salmonid) counts and two data sets when he estimated the stock‐recruitment relationship. One was the unadjusted recruit‐per‐spawner data, the other was smolt‐to‐
adult return rates (SAR) adjusted from recruits‐per‐spawner. The SAR measure is used to reduce the variation resulting from variable smolt outmigration and marine survival. For the North Fork John Day steelhead, Carmichael (2006) estimated a stock‐
recruitment curve fit parameter under these two different data sets. For the purpose of this study, I adopted the result obtained by Charmichael from using a SAR adjusted stock‐recruitment: (4.9) R = 4.32S exp(−0.0007 S ) , 46
5. WATER MANAGEMENT DECISION MODELS To achieve the stated objective of this study, the number of fish in the Klamath River and John Day River is assessed under three different scenarios reflecting in‐stream water temperature predictions of varying accuracy. This chapter begins with a discussion of the water temperature distributions that are the basis for water flow management in the two rivers. The second section of this chapter describes the decision models for fall Chinook salmon in the Klamath River, the last section discusses the decision models for summer steelhead in the John Day River. In both cases, a no‐
forecast decision model, a series of imperfect forecast decision models with varying accuracy, and a perfect forecast decision model are discussed. 5.1 Temperature Distribution Water temperature has been measured sporadically at multiple sites in the Klamath River by CDFG and in the John Day River by NOAA. Air temperature and stream flow are two significant predictors for stream temperature. There is some evidence that on longer time scales (longer than one week) air temperature may be a good index for stream temperature (Mohseni and Stefan 1999). In some cases air temperature has served as a surrogate for water temperature, assuming the both water and air temperature are driven by insolation, in particular for inland gauging stations (Lawson et al. 2004). Since it is common to assume that daily maximum and minimum air temperature are normally distributed (Harmel et al. 2001), the in‐stream water temperature was assumed to follow a normal distribution. 47
A data set containing maximum daily water temperatures during September at Seiad Valley in the Klamath River, covering the years 2001 – 2007, is used to represent the water temperature condition in the Klamath River and to derive the temperature distribution (Figure 5.1), T ~ N (20.32,2.02 2 ) . Figure 5.1 September Water Temperature Distribution in the Klamath River 0.25
Probability
0.2
0.15
0.1
0.05
0
<15
16
17
18
19
20
21
22
23
24
25
>26
Water temperature (Celsius)
In an intermountain area such as the North Fork basin of the John Day River, the highest temperatures arise between late July and the beginning of September. A data set containing daily maximum water temperatures for August, at Monument, the North Fork John Day River (USGS 14046000), provided by NOAA, is used to estimate the water temperature distribution: T ~ N (24.54,1.76 2 ) . The distribution is shown in figure 5.2. 48
Figure 5.2 September Water Temperature Distribution in the North Fork John Day River 0.3
Probability
0.25
0.2
0.15
0.1
0.05
0
<21
21
22
23
24
25
26
>27
Water Temperature (Celsius)
5.2 Decision Models in the Klamath River In the Klamath River case, the following decision rule is employed: release water from Lewiston Dam if the expected water temperature is higher than or equal to 21 ⁰C; do not release water if the expected water temperature is lower than 21 ⁰C. A threshold of 21 0 C is chosen mainly because of the natural conditions of the Klamath River and the objectives of this thesis. As is evident from the temperature distribution, the mean temperature is 20.32 0 C for the time period of data used here. A 21 0 C threshold ensures that the manager will not automatically release water from the Trinity River. This behavior provides the base scenario for the historical information strategies (no water releases), and is believed to be common in current management strategies. The “no forecast” model provides a yardstick against which the value of water temperature forecasts is measured. This subsection begins with a discussion of the no 49
forecast decision model. As the name implies, a no forecast model assumes complete ignorance of future water temperature conditions and is the least accurate model presented here. In a no forecast information scenario, the manager makes decisions regarding the need to release water based solely on prior climatology information. Specifically, the manager assumes that water temperature in the future will behave as it has in the past, and that the water temperature distribution is determined by the prior distribution, T ~ N (20.32,2.02 2 ) . The solution is relatively straightforward. The expected water temperature is always 20.32 0 C (the mean for the time period), which is lower than 21 0 C , the threshold for releasing water. Thus, according to the decision rule specified above, the manager never releases water from the Trinity River. This decision will lead to a fish loss if the actual water temperature is high, but it generates no opportunity costs. For the imperfect information scenario, three different forecast standard deviations are chosen to represent different forecast accuracy where a forecast standard deviation of 1 means an accurate forecast, 4 means a forecast of moderate accuracy, and 6 means a highly inaccurate forecast. I assume that the manager updates the expected water temperature upon receiving the new information by using the Bayesian decision framework discussed in section 3, and then makes decisions according to the decision rule. After receiving water temperature information from a forecast with small variance equal to 1 (an accurate forecast), the predictive water temperature distribution now is T ~ N (20.32, 2.542 ) , and the expected water temperature becomes: 50
1
2.02 2
(5.1) T1 =
* 20.32 +
* T , 1 + 2.02 2
1 + 2.02 2
With a medium variance of 4 2 , the predictive water temperature distribution now is T ~ N (20.32,4.48 2 ) , and the expected water temperature becomes: 42
2.02 2
(5.2) T1 = 2
* 20.32 + 2
* T , 4 + 2.02 2
4 + 2.02 2
With a large variance of 6 2 (low accuracy), the predictive water temperature distribution now is T ~ N (20.32,6.33 2 ) , and the expected water temperature becomes: (6.3) T1 =
62
2.02 2
*
20
.
32
+
* T , 6 2 + 2.02 2
6 2 + 2.02 2
Although the stream flow effect on water temperature is a continuous function, for simplicity it was defined as follows: If T1 and the real water temperature Tr are both higher than or equal to 24 0 C , the correct decision is to release 2300 cfs, which results in water temperature being reduced to 20 0 C . If T1 is higher than or equal to 24 0 C , but Tr is lower than 24 0 C , then a mistaken release of 2300 cfs will result in an ultimate water temperature of 18 0 C , which provides relatively small fish benefits compared to the cost occurred. If T1 is higher than, or equal to 21 0 C , but lower than 24 0 C , and Tr is higher than 24 0 C , a mistaken release of 1900 cfs will decrease the water temperature to 22 0 C . If T1 is higher than, or equal to 21 0 C , but lower than 24 0 C , and 51
Tr is lower than 24 0 C , a correct release of 1900 cfs will lower the water temperature to 20 0 C . Finally, if T1 is lower than 21 0 C , no water is released. The last decision model involves the upper bound of an imperfect forecast, a perfect forecast. For the perfect forecast, there is not forecast error, so the forecasted temperature is always equal to the actual temperature. If the forecast water temperature is higher than or equal to 21 0 C , water is released; otherwise, no water is released. 5.3 Decision Models in the John Day River The John Day River differs from the Klamath River in that there is no dam in the John Day River, and the only way to lower potentially high summer water temperatures is buying or leasing water rights from farmers, thereby reducing water diversions for agriculture. From a management perspective, this situation in the John Day River means that the elevated water temperature can only be reduced by increasing stream flow. As a result, two possible actions are applied in the North Fork of the John Day River: buy/lease water rights if the expected water temperature is greater than, or equal to 25 ⁰C; do not buy/lease any water if the expected water temperature is less than 25 ⁰C. When there is no forecast information available for a manager in the John Day River, the manager expects that water temperature will behave in a historical fashion, and follow the distribution T ~ N (24.54,1.76 2 ) . Since the threshold for withholding water from irrigation in this river is 25 0 C , the manager will never purchase any water 52
rights for in‐stream flow enhancements during September, and farmers would continue to withdraw water for alfalfa use in Grant County. Hence, under this scenario, there will be elevated water temperature events, leading to an increasing mortality rate. As in the Klamath River, three different forecast accuracy levels were considered for the imperfect information cases for steelhead in John Day River: a small forecast variance of 1, a medium forecast variance of 4 2 , and a large variance of 6 2 . As is the case for the Klamath River, upon receiving the new information, a fisheries manager dealing with the John Day River will adjust the expected temperature following Bayesian procedures. For the small variance case, the predictive water temperature distribution now is T ~ N (24.54,2.02 2 ) , and the expected water temperature becomes: (5.4) T1 =
1
1.76 2
*
24
.
54
+
* T , 1 + 1.76 2
1 + 1.76 2
In the case of a medium variance of 4 2 , the predicted water temperature distribution now is T ~ N (24.54,4.37 2 ) , and the expected water temperature becomes: (5.5) T1 =
42
1.76 2
*
24
.
54
+
* T , 4 2 + 1.76 2
4 2 + 1.76 2
With large variance ( 6 2 ), the predicted water temperature distribution now is T ~ N (24.54,6.25 2 ) , and the expected water temperature becomes: (5.6) T1 =
62
1.76 2
*
24
.
54
+
* T , 6.25 2 + 1.76 2
6.25 2 + 1.76 2
53
If T1 is lower than or equal to 25 0 C , then no water rights are purchased and farmers withdraw 50cfs of water, which increases the real water temperature Tr by 1.5 0 C , based on the water temperature and stream flow relationship for the John Day River. Otherwise, the manager purchases 50 cfs and no water is withdrawn for agriculture. 54
6. STREAMFLOW, WATER TEMPERATURE AND COST ANALYSIS In this analysis the water fishery manager’s objective is assumed to be to maximize the expected fish return numbers over the seven day interval covering each forecast, but the manager has to consider the opportunity cost related to the decision made. This section focuses on the stream‐flow and water temperature relationship, and on the costs associated with decisions of releasing or purchasing water. Specifically, on each day, the manager must decide how much stored water to release from Lewiston Dam in the case of the Klamath River, or whether to buy water rights from farmers in Grant County adjacent to the North Fork of the John Day River, and evaluate the corresponding costs of each decision. 6.1 Stream‐flow and water temperature relationship for the Klamath River The volume of water released is dependent upon how much water temperature cooling is required under each high water temperature event. Timing, in addition to water temperature, is another factor to be considered in the decision‐making process. For example, the time required for an initial flow released from Lewiston to affect temperatures downstream varies with distance. For example, Zedonis (2003) reported that increased flow on August 24, 2002 took approximately 20, 30, and 44 hours, respectively, to reach gauging stations at Burnt Ranch, Hoopa, and Terwer. A peak release of 1800 cfs on August 25th, 2002 was estimated to require 18, 27, and 41 hours to reach the Burnt Ranch, Hoopa, and Terwer gages, respectively. Thus, if a high water 55
temperature event is predicted in seven days at any of these locations, the increased flow from Lewiston Dam would have sufficient time to reach the area of concern. Figure 6.1 shows the complex geographical conditions of the Trinity River. Stream flow is released from Lewiston Dam (RK, 178.2), combines with the flow from the North Fork Trinity River (RK, 116.7) before joining the stream flow from the South Fork Trinity River (RK, 50.5), then flows in a southwest direction until it reaches the confluence with the Klamath River at Weitchepec, where it then continues to the Pacific Ocean. 56
Figure 6.1 The Trinity River: Map and Water Diversion Routine Source: Douglas and Taylor, 1999 Most of the flow in the Trinity at Hoopa (RK, 20) is from Lewiston Dam, under mandated flow requirements. USGS data for September 2001 to 2008 show that about 270 cfs was from the tributaries, including the North Fork and the South Fork Trinity River. Monitoring also indicates that the contribution of flow from Lewiston Dam during late August and September is 50% of the total stream flow in the Klamath River (Zedonis 2005). 57
Increased water releases from Lewiston Dam for the period from August to the middle of September have a large influence on the water temperature in both the lower Trinity River and the Lower Klamath River. For example, Zedonis (2003) reported that the increased flow from Lewiston Dam that occurred from August 24 to September 17, 2002 was accompanied by reduced temperatures in both the lower Trinity River and the Klamath River. Before the arrival of the pulse flow at Weitchepec, water temperatures of the Trinity River were 0.8 0 C colder than the Klamath River, but after the arrival at Weitchepec, water temperatures in the Trinity River were from 1.4 to 4 0 C colder than in the Klamath River. There are two steps to estimate how much water needs to be released from Lewiston in order to reduce the water temperature in the Klamath River by a given amount. First, the relationship between the stream flow released from Lewiston Dam and the water temperature at Hoopa in the Trinity River was estimated with the stream flow data at Lewiston and the water temperature data at Hoopa. Then the heat balance model provided by Brown (1969) was used to estimate the cooling effect of the stream flow on the Klamath River. Water temperature data for Hoopa in the Trinity River were provided by CDFG, covering September daily water temperatures in 2002 and 2004 to 2008. September daily stream flow data at Hoopa and Lewiston are from the USGS. The OLS estimate showed the relationship between the stream flow and the water temperature to be: (6.1) WT = 20.31 − 0.0012 F ; R2 = 0.02, p = 0.085 58
where WT is water temperature, and F is stream flow. At the confluence between the Trinity River and the Klamath River, a heat balance model was considered and applied, and was used to calculated the cooling effect of the stream flow from the Trinity River on the Klamath River. Mixing water from smaller streams into larger rivers has been extensively studied (Brown 1969; Fernald et al. 2006; Seedang et al. 2008; Burkhold et al. 2008). Generally, when the cooler or warmer water stream flow enters the larger stream, the proportion of the stream flow over the total stream flow determines the rate of decrease or increase in the receiving stream temperature. The water temperature balance equation is (Brown 1969): (6.2) Tm =
T1Q1 + T2 Q2
, Q1 + Q2
Where T1 is the temperature of the inflow, Q1 is the stream flow of the inflow, T2 is the main stream temperature before the merging or confluence, Q2 is the main stream flow before the confluence, and Tm is the main stream temperature after the confluence. In this study, T1 is the water temperature at Hoopa in the Trinity River, calculated from the stream flow and water temperature relation developed above, and T2 is the water temperature at the Klamath River above the confluence. Using the historical data from USGS from 2001 to 2008, a September stream flow of 270 cfs of the North Fork and the South Fork Trinity River is derived from the difference between the stream flow at Hoopa and Lewiston, so the total stream flow in the Trinity River is 270 cfs plus the 59
water release from Lewiston Dam. The mean September stream flow of the Klamath is 1680 cfs at Orleans (RM, 59.1), 15 river miles above Weitchep, calculated from the USGS data from 2001 to 2008, and is used to represent the stream flow of the Klamath River before the confluence. If the water temperature at the Klamath River is larger than, or equal to 24 0 C , then to obtain a 4 0 C water temperature reduction(to reduce to 20 0 C ), the water release from the Lewiston is 2300 cfs, derived from: (6.3) WT = 20.32 − 0.012* 2300 ≈ 17.52 1680 * 24 + 17.52 * (2300 + 270)
≈ 20 1680 + 2300 + 270
If the Klamath River water temperature is between 21 0 C and 24 0 C , I assume that the water temperature is 22.5 0 C . Using the same procedure, I find that a release of 1900 cfs is needed to reduce the water temperature to 20 0 C . Under an imperfect forecast situation, if the Klamath River temperature is below 24 0 C , but a manager mistakenly releases 2300 cfs, I assume that the water temperature below Weitchepec drops to 18 0 C . If the Klamath River temperature is greater than, or equal to 24 0 C , but again a manager mistakenly releases 1900 cfs, I assume the water temperature drops to 22 0 C . In the first case, the imperfect information leads to added costs but with a relatively small increase in fish because the water temperature is relatively low, but the volume of mistaken water release is large. 60
In the latter case, the imperfect information leads to not enough water being released and a loss of fish. The details of the consequences of decisions in the imperfect forecast scenario will be presented in the next chapter. 6.2 Cost Analysis for the Klamath River The Trinity River and Lewiston Dam, as part of the Central Valley Project, provide significant amounts of outflow to the nearby Sacramento River and the Central Valley Project, with these waters used for hydropower, agricultural production and other purposes (Douglas and Taylor, 1999). In this study, the foregone hydropower benefit and agricultural benefits are considered as the opportunity costs of water released to cool the Klamath River. As shown in Figure 5.1, the water is diverted from Lewiston Dam via Clear Creel tunnel, through Carr Powerhouse down to Whiskeytown Lake, and from there it flows through Spring Creek Powerhouse and Keswick Power plant before joining the Sacramento River. A combination of turbine type, gross head and flow volume determines the hydroelectric power generation. In this study it is assumed that the only variable affected is the flow volume, so energy production foregone is dependent on the amount of additional releases to the Trinity River. The Western Area Power Administration (Western)(1997), and the California Department of Energy(COE) estimated that under normal operating conditions, 1 acre foot of water diverted from Lewiston Dam to the Sacramento River could generate approximately 1,100 Kilowatt hour as water flows through Spring Creek and Carr Powerhouses and the Keswick Power plant. A one cfs water release from Lewiston into the Trinity River to cool the Klamath is 61
equal to 14 acre feet (for one week). Thus, one cfs for one week is equal to $1030 of foregone electricity production. The electricity price used here is the weighted average wholesale price in September 2008, 6.689 cents per kilowatt‐hour. Brown (2004) studied western water markets for agricultural water and observed a mean price of $96 per acre foot per year from 1990 to 2003, which equals approximately $110 in 2008 dollars. Though a high water price will make the farmer more likely to shift from the low value production such as barley, hay and wheat to high value production such as vegetables, and orchards, the conservative value $110 is used in this case for the irrigation water price in the San Joaquin Valley. Since the cost will be summed up for ten generations of fish (approximately 30 years), the discount rate used here is 7%, which is common in the fisheries literature, and can be converted into a 22.5% per fish generation, under the assumption that a fish life cycle is three years. 6.3 Stream‐flow and water temperature relationship for the John Day River Using the daily September water temperature for 2007 at Monument, (provided by NOAA) and the September daily stream flow at the same gauging station (from USGS), the stream flow and water temperature relation is derived by ordinary least squares: (6.4) WT = 27.32 − 0.031F , where the R square equals 12%, and p value equals 0.053. 62
From this relationship, one can infer the effect of changes in flow on the stream temperature. For example, if water temperature is expected to be greater than 25 0 C , then obtaining 50 cfs from agriculture in this area would result in a 1.5 0 C decrease in water temperature. 6.4 Cost Analysis for the John Day River According to the Oregon Department of Agriculture (2002), the North Fork sub‐
basin has an irrigation water right amounting to 291.5 cfs, which are used to irrigate a total of 13,400 acres, mostly by sprinkler. Although most of the water rights in the North Fork are assigned to mining usage, the proportion that is used by agriculture is mainly for hay (ODFW 2000). I assume the affected area is Grant County, which makes up most of the North Fork basin. The irrigation in this county is mainly used for irrigating alfalfa hay and pastureland. Since alfalfa hay takes a major proportion of the hay production in this area, the impact of leasing water from agriculture is calculated in terms of lost revenue from alfalfa. Alfalfa production (yields) under different irrigation application levels has been studied extensively (Bauder et al, 1978; Carter and Sheaffer, 1983; Doorenbos et al, 1988; Bolger et al, 1990; Orloff et al, 2003, 2005). According to Orloff et al (2005), there are typically 3 alfalfa cutttings in intermountain areas such as the North Fork basin. Results from Orloff et al indicate there is an alfalfa yield loss of 0.74 ton per acre if there is no irrigation after the second cut. Eliminating the last seasonal irrigation would save approximately 5.5 acre‐inches of water. These results are used to calculate the alfalfa 63
yield loss for Grant County in the North Fork John Day area. With an average alfalfa price of $125 per ton (acreage price, 2000 to 2008, Oregon State University Extension Service) if 50 cfs of water are withdrawn from alfalfa use for one day, the opportunity cost in terms of lost alfalfa production will be: 50 * 24 * 0.74 *125
≈ 20181 dollars. 5.5
64
7. RESULTS Previous chapters described the components of the assessment framework and detailed how each component is integrated into a framework to derive the value of in‐
stream water temperature forecasts when used in the management of salmonids in the Pacific Northwest. In this chapter, results of the application of this framework are reported. Comparisons of the simulation results with the historical management and physical data in these two rivers are used to validate the model. This is followed by the estimated value of information under varied information structures detailed in the last chapter. Results for the Klamath River and the John Day River are presented and compared among the three scenarios: no‐forecast, improved forecasts, and perfect forecast. 7.1 Model Validation Validation is the comparison of the output provided or estimated by a model with historical data for the system being evaluated. The levels of the control variables in each case, namely water releases or purchases, are selected in the decision model. The levels of water release and the corresponding fish numbers have to be realistic for the value of information estimation to be credible. In reality, fishery management involves more complex interactions than are examined here. Thus, it is expected that the model results will deviate from those arising from historical management practices. However, the values derived here must still be consistent with plausible biological and 65
management realities. This section compares the results from this study with those from current management in the Klamath River and the North Fork John Day River. The results used for comparison are from the imperfect forecast scenario with an assumed 20 percent mortality rate from harvest and other factors. In the Klamath River, the historical average total escapement from 1978‐2008 is 89 thousand fish, while the result of the imperfect forecast model with a forecasting variance of 4 is 119 thousand fish, which is within the variability in the historical data. As to the stream flow, a comparison of the total stream flow after 10 generations with the average stream flow from Lewiston is not relevant since the emphasis here is on incremental releases from the dam. The stream flow released from Lewiston is about 710 cfs under the simulation. This is also well within the water release variability in the historical data and is thus technically feasible. For the North Fork, the results from the imperfect forecast with a 20 percent mortality rate from harvest and other factors (there is no commercial harvest for the steelhead in the ocean, but in the river fish are harvested by native Americans) are chosen as basis for comparison with the historical average. Although the fish number estimated from the forecast simulation (1632) is larger than the historical average for the period (1190), it is within the population variability in the historical data. For the stream flow, the maximum water withdrawal evaluated here is 50 cfs, which is much smaller than the water diversions currently occurring in the North Fork. These results indicate that the outputs from the models developed in this study are plausible. 66
7.2 Comparisons of Accuracies and Values 7.2.1 The Case of the Klamath River The accuracy of water temperature forecasts is characterized by the various forecast errors embedded in each simulation scenario, and is summarized by the standard deviation of the forecast variance. In the case of the Klamath River, the expected cost is given by the opportunity cost of released water in terms of lost hydropower production and lost agricultural production in the Central Valley of California, as shown in Table 7.1. Table 7.1 Model Outputs under Different Forecast Accuracies in the Klamath River. Fish Number (thousands)
107
Fish Number Increase(%)
Impecrfet Forecast(8)
113
5
0.274
Imperfect Forecast(6)
Imperfect Forecast(4)
Imperfect Forecast(1)
Perfect Forecast(0)
115.5
119.3
125.9
137.7
8
11
17
29
0.476
0.757
1.166
1.25
Historical Information
Opportunity Cost Marginal Cost Per (millions of dollars)
Fish (dollars)
80.8
77
69
40
As is evident from the table, the number of fish increases as the water temperature forecast improves, because the improved forecast assists the water manager in determining if and when to release water from the dam to lower fish mortality. This results in an increasing total opportunity cost with increases in water temperature accuracy, because the forecasts lead to additional water releases. Also, as 67
shown in the table, the percentage increase in the number of fish ranges from 8% to about 29%, depending on the forecast accuracy. However, to only consider the fish number is not enough; the opportunity cost should be taken into account. There is no opportunity cost associated with the Klamath River under prior management, given that until 2002 water releases for adult salmon survival were not employed. Therefore, a standard deviation of 6 is selected as a basis for comparison with the results from other information settings. Compared to the low accuracy case, the marginal cost of fish decreases with increasing forecast accuracy, or increases with a growing forecast deviation(Figure 7.1). When the forecast deviation is 4, the marginal cost per fish is 74 dollars. It is 66 dollars for a forecast deviation of 1, and only 35 dollars with a perfect forecast. This figure shows a generally increasing pattern in terms of increasing forecast deviation, but with a moderate fluctuation in the imperfect forecast scenarios, where the forecast error is close and the stochastic effect and randomness of the water temperature simulation dominate the increasing percentage of fish number and opportunity cost. The pink line (real) displays the simulation results, while the blue line corresponds to a fitted line derived from an OLS regression of standard deviation on the corresponding marginal cost per fish, SD=51.93+4.98*MC, where the p value for the estimated coefficient is 0.034. The fitted line also displays the general increasing trend with the larger forecast standard deviation. 68
Figure 7.1 Marginal Costs per Fish as a Function of Forecast Standard Deviation in the Klamath River Marginal Cost per Fish(dollar)
90
80
70
60
50
Fitted
40
Real
30
20
10
0
0
1
2
3
4
5
6
Standard Deviation
7.2.2 Case in the John Day River Unlike in the Klamath River, there is a cost for the historical information scenario for the John Day River because the assumed temperature threshold is sufficiently high to allow agricultural diversions to occur. As Table 7.2 shows, with improved water temperature forecasts, fish numbers increase while agricultural output decreases due to lower availability of water for agricultural withdrawals. By using the forecast deviation of 6 as a proxy for the historical case, the fish numbers increase about 59 percent, while agricultural output drops about 18 percent. If the forecast accuracy could be improved to a level where forecast deviation is only 1, fish numbers could more than double from initial fish numbers. 69
Table 7.2 Model Outputs under Various Forecast Accuracies: the John Day River Historical Information
Imperfect Forecast(8)
Imperfect Forecast(6)
Imperfect Forecast(4)
Imperfect Forecast(1)
Perfect Forecast(0)
Fish Number
868
1185
1377
1649
1980
2158
Fish Number Alfalfa Alfala Output increase (%) Output(dollars) change(%)
95466
11.4
37
84494
18
59
78313
25.4
90
71207
39.1
128
58118
39.3
149
57904
Cost Per Fish(dollars)
34.63
33.72
31.05
33.60
29.12
Table 7.2 also indicates that the percentage change in fish numbers and alfalfa output varies across information structures. The marginal cost exhibits a general declining pattern as the forecast accuracy improves, but with some fluctuation among the imperfect forecast scenarios. The marginal cost ranges from 29 dollars to 33 dollars. Comparisons of this cost and the costs from other information structures are shown in Figure 7.2. The pink line in the figure is the plot from the simulation results, and the blue line corresponds to a fitted line derived from an OLS regression of standard deviation on the corresponding marginal cost per fish, SD=30.83+0.416*MC, where the p value for the estimated coefficient is 0.027. The key feature of these two lines is the upward trend, showing that the marginal cost per fish become larger with decreasing forecast accuracy. 70
Figure 7.2 Marginal Costs per Fish as a Function of Forecast Standard Deviation in the John Day River Marginaal Cost per Fish(dollar)
36
35
34
33
32
Fitted
31
Real
30
29
28
27
26
0
1
2
3
4
5
6
8
Standard Deviation
The marginal costs in the Klamath River and John Day River cases show a general declining trend with an improved forecast. However, the values in these two rivers are different due to three major reasons. First, the analysis is based on different life stages for different fish species. Specifically, the Ricker model for the adult Chinook salmon in the Klamath River has a very different density dependence parameter from that of juvenile steelhead in the John Day River. Second, water temperatures in the rivers are different, with a mean difference of 4 ⁰C, which results in significant fish survival rate differences. The last and most important factor are the differences in decision rules. The free‐flowing nature of the John Day River means that water temperatures can never be lowered, whereas in the Klamath River, there is a large volume of water that could be released from the dam that will cool downstream temperatures. 71
7.3 Sensitivity Analysis Sensitivity analyses were performed to test the robustness of the model outputs to changes in assumptions employed in these assessments. Specifically, simulations were tested in terms of their sensitivity to different mortality, including harvest rates and out‐migration mortality. According to CDFG(2007), in‐river harvest and escapement angling mortality is about 2.04% of harvest, and net mortality is 8.07% of harvest, so here a 10% mortality was used to present the “background” mortality. Figure 7.3 Results of Different Levels of Other Mortality in the Klamath River 10% Other Mortality
20% Other Mortality
40% Other Mortality
90
Marginal Cost per Fish
80
70
60
50
40
30
20
10
0
0
1
4
Standard Deviation
The general patterns of these marginal costs per fish in the Klamath River are similar for these three levels of harvest rate and out‐migration mortality, but differ in magnitude (Figure 7.3). Under an information case with a forecast deviation of 6, the 10% other mortality scenario has the highest marginal cost of fish, and the highest harvest rate produces the lowest marginal cost of fish. The reason is that the Ricker 72
model for Chinook salmon in the Klamath River is very sensitive in terms of the density dependence assumption. This general declining pattern of fish values under mortality or harvest assumptions is also seen in the John Day River (Figure 7.4). However, the fluctuation between the imperfect scenarios is more obvious in this case than for the Klamath River. Also, the Ricker model for the North Fork steelhead is not as sensitive to the density dependence as is that for Chinook salmon, which results in a non‐monotonic ordering of the marginal cost per fish, with the 40% other mortality scenario having the highest marginal cost per fish, and the 20% and 10% other mortality scenarios having about the same marginal cost per fish. This is quite counterintuitive, but a second look will suggest that the combination of a density dependence parameter and a density independence parameter of the 10% and 20% of other mortality does not make a big difference on the effect of the population dynamics. Figure 7.4 Results of Different Levels of Other Mortality in the North Fork John Day River 40% Other Mortality
20% Other Mortality
10% Other Mortality
Marginal Cost per Fish
45
40
35
30
25
20
15
10
5
0
1
2
3
4
Standard Deviation
73
8. CONCLUSIONS Factors inhibiting the growth and survival of Pacific Northwest salmonids have received extensive attention for over fifty years. Despite the attention, many stocks continue to decline. A range of recovery plans have been proposed, such as riparian recovery, restrictions on logging, stream flow modifications, and harvest and hatchery release restrictions. As cold water fish, salmonids are vulnerable to elevated water temperature in the fresh water environment. Thus, many recovery programs include current and future water temperature as a component of fish recovery. Augmentation of stream flow, as a means to lower water temperature, has been incorporated into recovery plans. However, as the demand for water from different competitors grows, information on an efficient allocation of water in terms of timing and amount is particularly important to minimize such conflicts among users. The existence of threatened and endangered species, such as Chinook salmon and summer steelhead, complicates the already difficult water management decision. Currently, water regulations are in place requiring minimum amounts of water to be released to meet spring or summer criteria. However, these minimum flow releases may not meet emergency situations when water temperatures rise unexpectedly due to weather variability. Forecasts for a range of weather phenomena, such as temperature, rain, snow and hail storms have been shown to have economic value for sectors such as agriculture, transportation, and recreation. Short‐term water temperature forecasts 74
may be useful for emergency situations regarding water resource management involving fish. Unlike some other settings, water management frequently must incorporate the interest of other parties into its management strategies or it will accentuate the conflict between users. 8.1 Summary The overall objective of this study is to develop a general modeling framework to determine the value of in‐stream water temperature forecasts in a stochastic dynamic setting. The empirical focus is on two specific cases, one involves fall run Chinook salmon in the Klamath River, and the other focuses on summer steelhead in the North Fork of the John Day River. In the absence of water temperature forecasts, the resource manager has to undertake management in the face of uncertainty concerning future water temperature conditions. The pre‐spawning fish kill in the Klamath River in 2002 triggered many studies and controversies over the allocation of limited water resources stored behind Lewiston dam. However, there are few systematic studies of the timing of releases and the amount of releases from the perspective of using future water temperature forecasts. The water conflicts in this area provided an excellent setting for this purpose. Summer steelhead in the John Day River complements the Klamath River setting in that no dam exists on the John Day River, and the only way to lower the water temperature is to obtain water by leasing it from farmers in the area. These two cases consider the likely actions that water managers could undertake to mitigate for rising water temperatures. 75
The decision models were structured using a Bayesian approach, and were formulated to describe the relationship between the decisions and outcomes under different water temperature forecasts. The decision rule in this decision making process is limited to water releases or to a decision to lease water for in‐stream flows. Each decision leads to a change in fish survival and the corresponding costs. The empirical model constitutes a stochastic simulation decision model. Stochastic factors stemming from future water temperature conditions were incorporated into the biological models, either calibrated or drawn directly from literature to estimate fish numbers. The associated costs were included in the model to identify the costs arising from the decisions. Results concerning the value of water temperature forecasts are presented for the case of Chinook salmon in the Klamath River and steelhead in the John Day River. Specifically, results from five different forecast accuracy scenarios in each river, chosen to represent a plausible information structure available for water managers, were derived. The first scenario is the historical information setting, which assumes normal water temperature conditions for the future. Then three imperfect information scenarios are presented, which assume that the resource manager will update the prior distribution upon receiving the forecast information. Finally, the study also considers a perfect forecast scenario which, although unrealistic, provides an upper bound for the imperfect forecast. Assessment of the value of a forecast improvement involves 76
comparing the results from different information (forecast) structures with an appropriate base case (typically the historical case). Results indicate that improvements in in‐stream water temperature forecast have value. Using the prior climatological record as the base case for comparison, improving water temperature forecasts will lower the marginal cost per fish. The magnitude of the increase in fish depends on the accuracy of the imperfect forecast. The marginal cost per fish in the Klamath River is higher than that for steelhead in the North Fork. For example, when there is no harvest, the marginal cost per fish in the Klamath River ranges from $48 to $87 per fish, compared with a range of $30 to $ 35 per fish in the North Fork. More important is the finding of a declining trend in marginal costs for both rivers, i.e., the more accurate the forecast becomes, the lower the marginal cost per fish. 8.2 Management Implications Accurate assessment of the value of improved in‐stream temperature forecasts requires that the decision‐making framework incorporate plausible components. A closer approximation of these components to reality and a correct solution procedure will enable the resource manager to manipulate the decision‐making model to answer specific question of interest, and provide criterions for the resource management strategy. Results of this study have several implications for resource management strategies. 77
When high water temperature is accurately forecast, increased survival rates could be achieved if the resource manager releases adequate amounts of water. However, this results in foregone benefits from hydropower and agricultural production. Essentially, water releases or purchases can be characterized by a simple trade‐off between fish survival and water opportunity cost. If the forecast is imperfect, the best option for the manager is to update the expected water temperature and make decisions according to the decision rule. As the uncertainty becomes larger, the manager will tend to make decisions according to the long term climatological record. As shown in Chapter 5, there is a large divergence between the water released in current resource management strategies and those obtained from this study for the Klamath River. The difference arises from the fact that water releases from Lewiston Dam do not necessarily achieve efficient allocation with regard to the timing and amount of the release. For the North Fork, the resource manager should buy more water rights from the farmers during high temperature events. Estimates of the value of short‐run in‐stream water temperature forecasts, when viewed in conjunction with the potential negative impacts of water withdrawal for agriculture or hydropower on fish production in the Klamath River and the North Fork John Day River, proves the concept that short‐run in‐stream water temperature forecast is valuable, and that the value depends on the specific setting and location. 78
8.3 Limitations of this study This study is intended as a first step in examining the potential economic value of short‐term stream temperature forecasts. As such, it has limitations that should be noted. First, for tractability a single spot below the confluence of the Klamath River and the Trinity River was used to represent the water temperature feature of the entire Lower Klamath River basin. Second, better temperature data could provide more convincing results. Finally, the water manager in the North Fork makes the water purchase decision from the farmers around Grant County according to water temperature at the gauge station at Monument. The implicit assumption made here is that water temperature at the North Fork is uniformly distributed, which leads to a uniform distribution of steelhead in this area. An explicitly spatial model of water temperature distribution and a well‐defined steelhead distribution in the North Fork are more realistic, but beyond the scope of this study. 8.4 Implication for Future Study Value of information (VOI) is important for policy implementation as policy makers consider the consequences of their decisions. With specific regard to fisheries, the results of this thesis point to several potential research directions. The usefulness of long run climate forecasts has been shown by Costello et al (1998), and incorporated into current management strategies. Short‐run water temperature forecasts, as suggested in this study, could provide assistance in complicated resource management problems. Future research in this setting should focus on how water temperature and 79
other mortality‐related factors lead to the failure of fish production and on a detailed model of Chinook salmon and steelhead. Further refinements of the decision rule and release decision and a spatially explicit water temperature and stream flow model will allow more specific analysis of the appropriate amount of water to be released. Also, incorporating the effects of water diversions on alfalfa yield loss and livestock production from inadequate water diversion for pastureland irrigation will provide a closer approximation of the North Fork John Day River situation, but will not change the general pattern of decreasing marginal cost per fish with improved information structure. In conclusion, these exploratory quantitative analyses of complex decision‐
making processes indicate that a better understanding of both economics and biology is necessary to establish defensible estimates of the economic benefits of water temperature forecasts. This thesis has demonstrated that short term in‐stream water temperature forecasts have value. 80
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