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Overview and Reco~enciations I NTRO D U CTI ON The earth's climate is changing, and associated predictions of future floods and droughts reverberate throughout the news media. Coupled with forecasts of climatic change, one can often find associated predictions of social unrest, wars, and famines, but these possible derivative issues are not addressed in this volume. The papers consider only the simpler problems of water shortages, which may or may not be severe enough to be ciassifiecI as droughts and which may or may not have resulted from climatic change, as well as make an assessment of the probable effects of climatic variability and climatic change on the nation's water supply needs, policy, and design. Lack of water hampers population and economic growth in some areas of the world, but even in such areas it is common to think of water as a resource that is renewable within the bounds imposed by a stationary regional climate. Unex- pected, prolonged, and widespread shortages of water resulting from climatic change could have an unsettling and depressing effect on regional ant! possibly even on the national economy. In spite of the foregoing, it is now the opinion of this pane] that there is small probability of a change in regional climate so abrupt, widespreacI, severe, and statistically unambiguous that current water- resource design practices need or should be radically altered. However, the 1

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Overview and Recommendations probability of such a change is not zero, ant! there is a great deal that could be done now that would allow for mitigation of the effects of possible climatic changes on future water supplies. The papers in this volume c30 not call for sudden, massive inputs of new federal, state, and local funds to builds reservoirs, canals, ancl other water- resource structures to alleviate droughts caused by climatic changes. To advo- cate such action programs without making comparative analyses of the other long-term hazardous shortages facing the nation would not be particularly productive, while to make such complete analyses was clearly beyond the mission of this panel. What has been attempted in this volume is to evaluate the interactions between hydrology, water supply, climate, ant! climatic change and to highlight areas where deficiences in knowledge and data make rational water-resource decision-making more difficult than it needs to be. Solving even the limiter! objectives outliner! above is complicated. The evaluations embrace not only the geophysical disciplines of meteorology and hydrology but also societal, legal, engineering, ant! economic questions that are quite difficult to resolve in their own right. A further complication to a rational study of climatic change and water supply is the aura of uncertainty that hovers over all who try to predict the future on the basis of limited data and understand- ing. The disciplines of probability and statistics ant] the fields of computer modeling and decision theory all impinge on the evaluations that are offered. With such a complex subject, a single person has difficulty encompassing all the neeclec! specialties. Hence, the papers in this volume are from authors from diverse disciplines, each paper reflecting the inclivic3ual author's background in one or more of the disciplines relevant to the overall issue of future climate ant! water supply. There is little overlap among the papers and little that should be omitted, although, as might be expected, common themes en cl recommendations do appear in many of them from time to time. CONCLUSIONS AND RECOMMENDATIONS 1. Barring totally unforeseen circumstances, the United States can expect to experience periodic, local, severe water shortages. 2. Very little information is available on the sociological anti economic impli- cations of droughts. Are the solutions imposed permanent or temporary, and what would the optimum strategy be for a community facing a water shortage? A series of studies that focus on the adequacy of future water supplies ant! water-transfer systems relative to demand under adverse conditions should be initiated. That is, research on the resilency of water-resource systems is needed. 3. The transfer functions from climatic forecast to water-supply values are still embryonic and neecI to be improved greatly. 4. The transfer functions and the cTimatic-index variables to get from climatic forecast to crop yield are not yet known for many crops anti localities. Interactive research between climatological forecasters and crop specialists is needed. 5. The conflicts resulting from future water shortages, whether from natural climatic variability or climatic change, couIcl be alleviated by adjusting water law along the lines suggested in the 1973 National Water Commission report, Water Policies for the Future. In particular, fecleral reserved rights shouIcl be eliminated, and Indian water rights should be iclentified and quantified. 2

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Overview and Recommendations 6. In order to project future water demands in a comprehensive fashion for a region, a series of regions, and ultimately the nation, a multisector economic framework shouIcI be established for some base year. Within this framework a consistent set of economic activity levels should be developed; ant! water-use data, disaggregated by encI-use, should be organized to include information relating to self-supplie~1 and publicly supplied water, demand elasticities for those sectors as applicable, and technological considerations. The need for such a data base becomes particularly great when we wish to consider probable changes in water demand] associated with future climatic changes, the expansion of irrigated agriculture and supplemental irrigation water supplies in the ciry farming areas of the United States, or both. 7. PaTeoclimatic research offers a promising approach to better estimates of past climatic variability and drought probabilities. This type of research can be justified on the grounds that it may help in producing more robust water- resource systems. 8. Future water shortages may be exacerbated by climatic change, but unfor- tunately the climatologist's current forecast ability is insufficient to air! the water-resource planner or hydrologic designer. To be useful to water-resource planning, climatic-change forecasts would need to be specific by area and be ~ - A, ~ accurate over the 50 to 100 year clesign-life of the water-resource system, otiset bv Me adclitional 10 to 30 Years that are needled to Stan and build the system. There is no evidence that such a forecast ability either exists or will appear within the immediate future. Research on deterministic physics-based climatologic modeling and climatic change shouicI continue, as it may eventually help to provide the necessary scientific justification for proposed snow- augmentation programs. HYDROLOGY AND WATER-RESOURCE DESIGN There is undoubtedly a definite relation between the storage provided by an impounding reservoir on any stream and the quantity of water which can be supplied continuously by it. The relation, however, is a complex one, and our knowledge of its character is limited. Allen Hazen, 1913 There are very few certainties in water-resource design and even fewer studies in which the effect of various uncertainties on the water-resource design process have been evaluated. A pioneering study that used a four-way analysis of variance to partition the total variance between four planning variables" con- cluded that uncertainties in the economic projection were of prime importance and hydrologic uncertainties were of the least relative importance to the water- resource planning process. Unfortunately, there has been little or no follow-up work of a similar nature, and the case for the relative unimportance of hydrology should not necessarily be extended to situations of heavier demand or areas of more uncertain supply. The uncertainty of hydrology in water-resource design arises because hy- drologists are unable to forecast the future sequence of flows that any proposed water-resource structure will encounter during its design life. However, this is of little concern as Tong as the natural supply is large and stable and We demand relatively low. Under such favorable conditions, the chance of shortages occur- ring within the lifetime of a proposed water supply system are minimal and may be safely ignored. Critical water shortages arise when the regional demand increases to an appreciable portion of the long-term expected mean supply, for then seasonal and longer period variability in the natural flows causes shortages to appear. Prolonged periods of water shortage are popularly referred to as 3

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Overview and Recommendations "droughts," droughts. The basic phflosophy used by all water-resource planners has been that the and it is the duty of the water-resource planner to circumvent recent past is the key to the near future. The near future is easily defined as the design life of the proposed structure, while the techniques for clefining the recent past have not been widely agreed upon and have even been the subject of some controversy. These specializes] arguments will not be cliscussec! here, but the interested reader can learn much from the papers by Stockton, Matalas and Fiering, Schwarz, ant] Dracup, and from their cited references. As an overview of the issues, it is necessary that this introduction be over- simplified; hence the discussion that follows is restricted] to annual flows ant! a set of hydrologic or climatologic properties that are believer] to be related to most hydrologic designs. An attempt is made to show how these properties may be relatecI to a set of hydrologic statistics whose values may be estimated and usec] in the design process. From a set of annual streamflows x I, X2, X3, . . . XT-], XT, the mean flow, X, and its variability, S. caller! the standard! deviation of the flows, may be estimated.2 While it is obvious that these statistics must be relater] to water-resource system performance, they are in themselves insufficient because it is also necessary to consider the order of occurrence of the flows, that is, the tendency or lack of tendency for high flows or low flows to cluster. More specifically, the capacity of the smallest reservoir that couicl be built, R *, that would yield uniform outflow and become full only once and empty only once when subjected to a given sequence of inflows can be visualizer] as the absolute sum of the maximum negative, R-, ant! positive, R+, accumulative departures from the accumulative mean flow, as shown in Figure 1. Experience has shown that R* is usually much too large to be used as the design variable for reservoir sizing, but shorter periods of critical Tow flow, Cf. selected from the sequence xi have been used as design variables. R* and Cf are statistically related and positively correlatecI. Hydrologists have always realized that Of was itself a random variable, but it was not until the Harvard Water Program of the early 1950's that the importance of this concept was formalized. The Harvard Water Program used very Tong hydrologic sequences dividect into many se- quences of length equal to the proposed design life of the water-resource sys- tems to arrive at designs that performed "better" with a variety of sequences and hence for a variety of Ci's. As sequences of the require(1 length clid not exist, the Harvard group use .' . . ~ ~ ~ ~ ~ ~ ~ ~ . ~ synthetic lag-one Markov sequences Xi = Plxi-1 + Ei, where the ci are independent random variables scaled to preserve the observed means, variances, and lag-one correlations, pi. Subsequently, it was foun(1 that these synthetic sequences, generate(l so as to be "equally likely to occur as the observed," actually tendecl to yield Cf values lower than those of the observed sequences; and a search was initiated for alternative generating mechanisms that wouIcl not clisplay this unclesirable property. The search for alternative synthetic hydrologic generating mechanisms has three aspects: First, incremental changes to the basic lag-one Markov mode! such as correcting for biases in the parameter estimating proceclures, or going to multilag moclels. Much of this work has been sound, as well as useful, but the basic problem has not been conquered by this approach. Second, the climatic change approach under which the basic lag-one Markov moclel is retained, but the parameters are changed according to the dictates of a master Tong-term 4 . it ~

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Overview and Recommendations FIGURE 1 Definition of R * = R + + | R- | . in it: > Hi, Cal 1+~ K Al I.Al,, ATI\/F UFAhI FLOW _ ~ ~ ~U[WU~^I I v c richly i' CUMULATIVE DEPARTURES FROM THE MEAN FLOW o YEARS T cTimatic-change moclel. The overall result of this second approach is a nonlinear, nonstationary, synthetic hydrology that has not yet been made operationally useful and that will remain stat~st~ca~y suspect until the models of climatic . . . .. .. . ~ ~ ~ .. . change are based more closely on the laws ot physics. The third approach to generation of more realistic synthetic hyctrologic se- quences has been to use a radically different set of stochastic processes, namely, Manclelbrot's fractional noises3 anct approximations thereof, basect on engineer- ing judgment.4 Fractional noises have the unusual property R*ls ~nh where n is the sequence length and h is a parameter of the fractional noise that can take any value between O and 1 except for 0.5. The usefulness of the exponent h is that most geophysical records and some laboratory experimental noises5 have h > 0.5, while all stationary independent and short memory stochas- tic processes have h = 0.5. Fractional noises and their more cleveloped approxi- mations have been found to yield Cf values that are statistically inclistinguish- able from observed Cf's. Water-resource system design is a complex ant! time-consuming process, and alternative designs, if prepared, represent discrete rather than continuous dif- ferences in design. The Harvard Water Program and its predecessors implicitly assumed constant climate and searched among alternative system designs for the "best" clesign, where best (resign was specified as that which maximizes the net benefits or minimizes the economic regrets. In this volume, Matalas and Fiering discuss the calculus of economic regrets in water-resource design in the light of possible procedural changes that could result from considering forecasts of climatic changes. In particular, they emphasize that unless the exact sequence of future flows can be precticted with certainty there may be little benefit to hydrologic system design of even an exact forecast of a change in one or more of the parameter values of the hydrologic input. As previously mentioned, alternative system designs are discrete, with each design being the operational choice over a certain range of climatic parameters; hence the same design may still be the best choice under a changed climate. To allow explicitly for climatic change in the design process, Matalas and Fiering introduce and define the concept of "robustness." A robust design may not be the optimal choice in the classical sense defined above, but it will be a design that performs reasonably well under a variety of possible climates. Further, Matalas and Fiering point out that the resilience of an existing well-buffered water-resource system can be enhanced by changes in insurance, subsidies, zoning, water law, and price structures, as well as by additional structural measures such as reservoirs, pipelines, and well fields. Resilience then is the property that allows a system designed for one climate and set of conditions to be modified in response to persistent new climates or other conditions. System

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Overview and Recommendations resilience is probably quite variable, and to assess fully the consequences of climatic shifts, the tradeoffs among all the above resilience strategies would have to be evaluated and articulated. Certainly, prolongecI droughts caused by persistent demonstrable climatic changes couIc! enhance the conflicts of interest between groups of water users. It is hoped that the resolution of such conflicts wouIc! be rational, with the resulting tradeoffs being acceptable to allin other words, along what Matalas and Fiering have referred to as the Paretian frontier. CLI MATI C VARIAB I LITY . . . The early part of the century (1907-1932) was one of anomalously high persistent runofffrom Me upper Colorado River Basin, apparently the greatest and longest in the last 450 years. This wet period was preceded by a long persistent low flow period during 186~1892. Stockton and Jacoby, 1975 . ~ - Hydrologists have Tong appreciated that cTimate is highly variable over all time scales, ant! the sequences of observed river flow are unlikely to be repeated in future periods. It has been the evident uncertainty of future flows that has led U.S. hydrologists to appreciate long, accurate records and to design water- resource systems that are as robust as possible to the vagaries of climate. Further, U.S. water-resource systems, when finally built, have tencled to be operated to maximize the inclividual system's resilience to climatic or other insults that the heavens or man impose. While river flow is the primary symptom of climate that concerns the water- resource planner or the hydrologic scientist, it is not the variable that climatologists consider when they talk about climate, climatic variability, and climatic change. But even precipitation, a more "normal" index of climate than streamflow, has proved to be inexplicably variable; for instance, consider Figure 2, which shows the extreme differences in the Tong-term accumulative precipita- tion that have been recordecI at four Canadian weather stations situated only a few miles apart in a topographically homogeneous region of ostensibly uniform climate. For the 30 or so years of record, annual precipitation in this region has varied from 7 to 27 inches. Total precipitation amounts for 10-year periods have varied by over 40 inches at fixed sites, while similar differences between adjacent sites for iclentical periods have also been observed. While it is known that persistent differences in the catch of two rain\gauges situated only 10 feet apart can be as high as 50 percent because of differences in gauge exposure,6 the meteorologists who have analyzed the data base of Figure 2 have been unable to detect any such biasing. The conclusion remains that point rainfall data in an aria! region can be disconcertingly different for long periods of time, even at gauges that are spaced quite close to each other. Global average temperature is probably the most studied and written about ~ , variable of climate. Over the last 1000 years, global temperature has fluctuated on the order of 1~/2C; and as Schneider and Temkin note in their paper, changes of this magnitude can be expected to influence global food production. But greater global temperature changes have occurred] in the geologic past, and smaller changes in the more recent past. For instance, consider the Mohonk Lake mean annual temperature u~sp~ay~c~ in Figure 3. Mohonk Lake is situated amic! 5000 acres of largely unspoiled forested land owned by the Mohonk Trust of New Paltz, New York. The lake obtains its water from groundwater flow, and there are no surface streams.7 From 1896 to 1950, there has been an increasing trend in the mean annual temperature 6 ~ . _ 11 _ _ 1 _ _ _ 11

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Overview and Recommendations it. Walburg l The Pas .~ Prince Albert ~ MVasecQ// Al TO I ASaskatoon FIGURE 2 Cumulative departure from av- erage precipitation for four Canadian weather stations. The figure illustrates that prolonged wet and dry periods can be observed for localities that are quite close to each other. When dealing with natural long-term climatic variability of this magnitude, it may be dif- f~cult for the water-resource planner to dis- tinguish the effects of the climatic change reported by climatologists to have occurred during the late 1960's. Figure redrawn from a paper by G. A. McKay that appeared in the proceedings of the Saskatoon Water and Cli- mate Symposium, November 1964 (Water Studies Institute Report No. 2, October 1965, Saskatoon, Sask., Canada). MAN _eA ) ~ l LOCATION ) ~ MAP SASK. \w | 21 Oo ~ ,~ A MA >0 ~ ~ r -10 ~ IJ ~\.~` I -20 ~ \- / '` rat Prince Albert 3oo ~ \/ `, ~ ~ / The Pas 1890 1900 19 1 0 1920 ~30 1940 1950 1960 ACCUMULATED DEPARTURE FROM AVERAGE PRECIPITATION ~ '~N he Pnc 20 0,10 O0 -10 -20 ~30 -40 1910 19 20 19 30 1 9 40 19 50 1 9 60 ACCUMULATED DEPARTURE FROM AVERAGE PRECIPITATION . / \ ,^~_~^v ^v~ / ' a' ~ ^~ ~ _. , " Are\ v v ~ . AA \ I,~~ r/ Woseca \~\ :~ St. Walburg \ ret 1 . 1 .\~. I observed at Mohonk Lake, and from 1950 onward a decreasing trend. Similar trencis have been observed for most other weather stations in the United States and Canada. The importance to water-resource design and operation of long-term time- depenclent temperature changes of the magnitude shown in Figure 3 are not satisfactorily known.. Further, as shown in the paper by Lofting and Davis, it may be quite difficult to make the necessary economic analyses without some reforms in the way that water-use data are currently collected ant! preserved, not to mention the acIditional difficulties associated with the climate-to-hydrology transfer functions (see later sections). The prime hydrologic variable, water available for impoundment in a reservoir, can also be as variable as the usual climatological variables (precipita- tion, temperature, wind speed, cloud cover, etc.~. In particular, long periods of high average flow and long periods of Tow average flow are the rule for rivers in aria] environments. Further, as population and water use increase so does the likelihood! of water shortages that are both more intense and more widespread than previously experienced. Nowhere in the United States is the future collision between avaflable supply and projected use more apparent than in the upper Colorado River Basin, the subject of John Dracup's paper in this volume. Two estimates of the adjustecI-to-"virgin"-flow condition (that is, without upstream diversions and Tosses) have been macle for the Colorado River at the Lee Ferry compact point for the period! 1914-1965. The two estimates differ in details, but they are both in accord that the 52-year sequence of annual flows was much wetter in the period 1914-1933 t17.0 million acre-feet (maf)] than in the period 1946-1965 (13.3 maf). If we are to regard the hydrologic generating mechanism giving rise to these Colorado River flows as a stationary-independent 7

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Overview and Recommendations ,_ 50 46 ' 44 MOHONK LAKE ANNUAL TEM~URE 1896-1973 1900 1910 1920 1930 1940 1950 1960 1970 YEARS FIGURE 3 Annual temperature in F for Mohonk Lake, 189~1973, with a moving aver- age trendline. The 189~1950 upward-sloping trendline is statistically significantly different from zero trend at the 95 percent confidence level based on the assumption that the indi- vidual data points are independent of each other. Figure has been redrawn from the Mohonk Trust Newsletter, November 23, 1974. The Mohonk Trust is headquartered at Mohonk Lake, New Paltz, New York. or stationary short memory (say lag-one Markov) process, observed differences of this magnitude are very rare occurrences. For instance, consider the statistic Z = AX ~ - X2 ~ /~(S i2 + S 22~/n~ Y2 where n is the period length and X and S are the respective period means and standard deviations and for which the above data yield Z = 2.88. If the two 20-year sequences are considered to have no cross correlation and to be sample functions from a normal independent process, then a value of Z as high as 2.88 could be expected to occur less than 1.0 percent of the time. Note that it is known that the Z statistic is insensitive to differences in the coefficient of skewness for a two-parameter log normal generating process and that considering the generat- ing process to be lag-one Markov with low p, would not appreciably change the probability of observing such a high Z. A similar conclusion can be reached by considering the resealed range, R*IS, for the period 1914-1965 and comparing the observed value, 13.08, with density functions for R*/S. In other words, low flow probabilities for the Colorado River Basin should not be assessed on the assumption that the annual events have been generated by an independent or short memory generating process. In fact, to do so would result in an underesti- mation of the regional drought hazard. When a set of data sampled over time has statistical properties similar to the Lee Ferry adjusted virgin flow data, it is improbable that an accurate determina- tion of the true long-term mean can be made by considering a record of only 25 observations. If the series is considered stationary, then the sample mean, X, will indeed approach the long-term mean, ,u, as the length of record increases; however, the rate of convergence will be much slower than that expected for sequences taken from independent or simple Markov processes. Under the above circumstances, the techniques of geochronology as outlined by Stockton should give a better estimate of ,u than does X. Based on tree-ring indices and regression, a 450-year-long record of estimated annual flows for the Colorado River has been prepared, and for this record the estimated long-term mean flow, A, was 13.5 maf. Had this estimate of,u been available during the deliberations leading to the Colorado compact,8 it is probable that little credence would have ~ , been attached to the estimate given the much higher known flow of the preceding 25 years. However, subsequent flows have averaged close to 13.5 maf, and the possible argument for ignoring the long-term estimate based on the magnitude of the previously mentioned Z statistic is no longer tenable. Geochronology is a useful tool for relating climatology and hydrology, espe- cially when estimates of the long-term mean are needed. However, the estimates of climatic variability derived from regressions are biased (see the Matalas and Fiering paper), and the uncertainties attached to extreme drought frequencies derived from geochronology are as yet unknown. Still, it is interesting to note that the 450-year reconstructed record shows that multiyear periods of low flow 8

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Overview and Recommendations have probably occurred on all the subbasins of the upper Coloraclo in the fairly recent past and that these periods of Tow flow have not necessarily been in phase for the different subregions a result reminiscent of Figure 2. While the problems of future water shortages in the arid southwest are obvious ant] imminent, this is not the only area of the country where future water shortages are predictable. The paper by Schwarz considers the humid industrial northeast region and finds very low storage capacities for water. Rainfall tennis to be comparatively evenly clistributec! throughout the year in the northeast, but occasionally successive years of low late-summer and early-fall rainfall occur; the most recent of these ciry periods was the 1963-1967 New England drought. However, other severe ciry periods of similar length have occurred] on at least four different occasions in the last 230 years,9 and it would be quite surprising if we dicI not experience similar shortages in the future. In summary, available hydrologic and meteorologic records show that climate has been extremely variable in both space and time in the immediate past. Unless climatologists produce evidence to show that this past climate instability has lessened, it would be only prudent for resource planners to expect such variability to continue in the future. It is against this background] of immense, often inexplicable, climatic variability that climatologists distill their signals of climatic change and develop their models for forecasting future climatic change. It is not an easy task. LON G-RAN G E F ORE CAS TS OF C LI MATI C VARIAB LE S . . . when somebody asks me what I think about the future climate, I usually say that the best way of showing that you are not a capable climatologist is to try to make a forecast. Bert Bolin, 1976 Not all meteorologists agree with Professor Bolin's view of climatic predict- abilities, but his view floes coincide rather closely with the official position of the American Meteorological Societyi and also with the rather well- documented and carefully thought-out view expressed by the ad hoc Panel on the Present Interglacial.~i However, this conservative view of climatic predict- ability has not been so well publicized as that of those who prophesy imminent climatic cloom, and it appears likely that hydrologists and water-resource plan- ners may not be aware of the tenuous scientific underpinnings of most climatic forecasts that are often based on what Cant has referred to as "poor foundations, apparent similarities, parallel-Iooking curves and analogous trends." Intrinsically, there are two approaches available for Tong-range climatic forecasting. The preferable method is to unclerstand the climatic system and all its relevant feedback mechanisms so thoroughly that it becomes possible to make a deterministic, physics-base`] mode! that reproduces the important fea- tures of different regional climates with sufficient accuracy to produce forecasts of future climatic events that are correct in both time and space. Moclels that inclucle the key interactions between the elements of the atmosphere-ocean- polar ice cap system responsible for climatic change on various scales of time clo not yet exist. Even when the models do exist, their reliability will be largely unknown and may hinge on factors that are totally external to the moclel, such as solar changes or explosive volcanic eruptions. In summation, physics-based, deterministic climatic forecastability does not yet exist at the detailed level that would be needed if a water-resource planner or manager wished to incorporate such forecasts into the decision process. The seconc! method of forecasting future climates is statistical. For instance, using a long paleocTimatic record (see the paper by Stockton), we could assign 9

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Overview and Recommendations probabilities of going from the current climate to a different one baser! on certain assumptions about the distribution of intervals between transitions. This ap- proach has not been used in water-resource design, probably because of the unreliability of transfer functions that would get the planner from the paleo- cTimatic index to the water-resource design variable, Cf. Another statistical approach is to take observer! climatic records and Took for past trends or cycles and then to use these as a basis for forecasting future events. However. as aficionados of the stock market have found, a chartist philosophy, basing fore- casts on past trends and cycles without a solid unclerstanding of the mechanisms that have given rise to the apparent trenc! or cycle, often leads to erroneous forecasts. As an illustration of possible climatic forecasts that couch be made based on trends, consider the previously presented temperature data of Figure 3. Climatologists have not yet agreed on the physical mechanism causing these trencis, and it is doubtful that the existing data base is sufficient to support a mathematical mocleling of the phenomena even if all the possible mechanisms were totally understoocl. It is obvious from Figure 3 that projecting in the late 1940's from the then-existing trenc! in temperature would have yielded an erroneous forecast, and hence projecting the present trenc] into a near-future mini ice age may not prove any more reliable. Further, we should point out that to the panel's knowledge the effect of these past Tong-term temperature trends on U.S. water supply and clamant] has not yet been either noticed or evaTuatecI. How severe a global average-temperature change wouic] have to be before a specific water-resource design would neec! to be altered] is a subject for future research (see the papers by Matalas and Fiering, and Lofting and Davis). Cycle analysis is also user! as a basis for long-term climatic forecasts. The procedures use more sophisticated techniques than trend analysis to Took for "significant" cycles in weather or other data ant] then to use these cycles as a forecasting algorithm for predicting future climatic anomalies. The tests of significance used are usually baser! on the implicit assumption of noncycTic inciepenclence in the data an unlikely assumption for climatic ciata.~3 Further, it is experimentally verifiable that stochastic processes with low-frequency com- ponents can yield! sample functions with numerous "significant" spurious cy- cles.~4 In addition, it is widely known that "significant" cycles are often intro- cluced into the analysis by moving average manipulations to smooth what are otherwise noisy data.~5 In spite of those defects to cycle analysis, it is still a popular occupation among a portion of the forecasting community and even supports its own specialty journals, which contain discussions of cycle syn- chronies observed for almost all wavelengths and phenomena. As an example, consider: . . . the clustering of phenomena around for example: 4.0, 6.0, 8.0, 9.0, 9.2, 9.5, 9.9, 11.2, 12.0, 12.6, 162/3, 17~/3, 17.7, 18.2, 22.0, 54.0, and 164 years, are substantiated by so many well established cycles that it seems improbable to explain these by statistical freaks only. More specifically, one may consider the long-range climatic forecasts made several years ago for the various locations in the United States.~7-~9 A compli- catec! algorithm was clevelopeclbased on solar cycles of 91, 46, and23 years and 91, 68, 55, 44~/4, 39~2, 34, 30~/3, 25~/2, 21, 11.87, 11.29, 9.79, and 8.12 months. Subsequently, the algorithm was used to forecast monthly precipitation amounts for 10 years in advance of publication of the articles,~7 i8 for 32 U.S. locations. An apparently similar algorithm was developed to predict monthly temperatures six years in advance of publication for 10 U.S. Tocations.~9 An analysis of the correctness of these Tong-range forecasts based on Spear- 10

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Overview arid Recommendations man's rank correlation coefficient20 shows that about one half of the 384 correla- tions are positive, while one half are negative, leading one to believe that overall the forecasts are no better than random. While overall these forecasts may be random, the possibility does exist that the extremal forecasts might be more reliable than random. Accordingly, the years of highest and lowest precipitation were noted for each station and month, and the ranks observed for these maximal years were averaged. The observed ranks corresponding to the forecast minimums had a mean of 5.68 and a standard deviation of 2.93, while the observed ranks for the forecast maximums had a mean rank of 5.36 and a standard deviation of 2.87. Note that a random assignment of ranks wouIc] yield! an average value of 5.5. A similar analysis for the six years of forecast temperatures provider! 120 rank correlations, 53 of which were negative and 67 of which were positive. The average ranks of the observed temperatures corresponding to the forecast minimum and maximums were both close to expected random value of 3.5. It wouIcI appear that these Tong-term forecasts of extreme events were not signifi- cantly correlated with reality. Shorter-range forecasts than the preceding study are routinely published in U.S. newspapers, and examples can be found in Figure 4. The Weather Service long-range prediction group believes that these 30-day forecasts are useful ant! that they show some skill and have shown improvement over the years, with the caveat that these forecasts are not primarily intenclec! for specific points, espe- cially those that have local peculiarities of climate. However, the Weather Service does believe that these forecasts are suitable and useful for use on large geographical areas.2t The current 30-clay forecasts classify temperature into three groups (upper 30 percent, middle 40 percent, ant] Tower 30 percent), and precipitation into two groups (above or below the median). Prior to 1974 more numerous groupings were used, with temperatures being classified into five groups (~/8, i/4, l/4, l/4, {/8), and precipitation into three groups (~/3, l/3, lea. Weather Service 30-day forecasts are referred to a 30-year base period! callecl the "normal," and the base period is intermittently updated to reflect a more recent "normal." It is instructive to consider these forecasts as they might be viewed by water-resource managers. On the Mohonk Trust lancis are two small reservoirs used for water supply and irrigation, and it is conceivable that these reservoirs might be managed using the publishe(1 30-day forecasts for precipitation and temperature. For the period 19S4 1973, the 30-clay forecasts of precipitation were correct 39 percent of the time compared with the 36 percent correct that would have resulted! from forecasting normal for each month. For the period lanuary 1974 to April 1976, there were 28 monthly precipitation forecasts made on the basis of above or below the median. Twelve of these forecasts matched reality, that is, the later period precipitation forecasts were correct 42 percent of the time. For 30-day temperature forecasts during the period 1954 1973, the comparable values were 27 ancI 23 percent, while for the later-period temperatures 12 of 28 percent were correct, compared with the 11 of 28 percent that wouIc] have resulted! from forecasting normal. There was no strong evidence for any seasonal or time bias in these results. Larger-area evaluations of current monthly forecasts tend to be much more subjective and to yielcl results of even more (lubious value to water-resource planners or managers. For example, consi(ler that from October 1975 to February 1976 northern California experiences! its worst drought since 1924, with many streams generating only 50 percent or less of their normal runoff.22 The five monthly precipitation forecasts (Figure 4) for this region were, respectively, 11

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Overview and Recommendations ~ ~~;~.~ ~ ~~ ~ ~ ~ ~~ .~ :~ ~ ~ ~~ ~ ~ ~ ~ ~ ~~ ~ ~ ~ ~ ~: : :: ::::: :~ :~:: :::::: rs^~ ::: ::: :: ~ ~ ~ :~::~ :~:: : : ::: :?: DILL ::::: ~ ~~ ~~:~ ~ :: it: :::::; JANUARY limo 12 ~ :~ ~ -- OCTOBER ~ 975 ~ ~ ;. ~ ~ T. ~ A: ~ ~ ~ ~ ~~ i; ~1~9~:5 . .~. : ~~ NOVEMBER 1 975 FIGURE 4 National Weather Service 30- day forecast of precipitation: (a) for Oc- tober 1975; (b) for November 1975; (c) for December 1975; (d) for January 1976; (e) for February 1976. ~ FEBRUARY 1976

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Overview and Recommendations above the meclian; above the median; some above, some below the median; below the median; below the median. It is difficult to see how such uncliscern- ing statements could be operationally useful to hydrologic managers or planners. In acIdition, even if the transfer functions to variables of hydrologic interest were known and error-free, the forecasts for even large areas by water- resource standards could be very much in error. In a recent issue of Western Water, G. F. Snow reporter! that in February substantial rains fell in the area of California south of MercecI, with parts of the San Joaquin valley receiving 200 percent of its normal February rainfall and parts of Southern California receiving up to 294 percent of the normal expecter! rainfall.22 From Figure 4(e) the comparable forecast for this location ant! period is seen to be "below the . ,, met fan. Other analyses of long-range forecasts, not reporter! here, support the general conclusion that past climatic forecasts have not been useful to the water-resource planning process. It wouicI be an act of faith to assume that current long-range climatic forecasts are likely to be any more useful to water-resource planners than have past forecasts. In summation, current long-range weather forecasts are optimistically only a little better than random. There is little or no verifiable scientific evidence to indicate that current Tong-range cTimatological forecasting is accurate ant! reli- able to the point of being usable on the watershed! or irrigation district basis that would be neeclecI by those concerned! with the operational management of water-resource systems. Further, given normal climatic variability and the customary 30-year lag between planning and operation of large water-resource systems, it appears unlikely that forecasts of climatic change will be relevant to the water-resource systems designer within the foreseeable future. CLIMATIC CHANGE, DELIBERATE AND INADVERTENT Leaders in climatology and economics are in agreement that a climatic change is taking place, and that it has already caused major economic problems throughout the world. COLA, 1974 The CiA report from which the above quote was extracted must surely rank as one of the most wiclely publicizes! and cliscussed documents in the history of climatology. That climatic change is taking place is almost tautological, for climatic change has been a property of the earth's atmosphere as long as the earth has had an atmosphere, and it seems probable that climatic change will continue even after mankind is no longer available to record the changes. What appears to separate this age from its precursors is that for the first time in history mankind has sufficient power to upset the worId's climate or, at least, to trigger changes that might have occurred at a later date without mankinc3's mo(lifica- tions. In this brief review only one inadvertent and one deliberate climatic modifca- tion will be discussed. Further details and possibilities are discussed in the paper by Schneider and Temkin and in the previously mentioned report of the ad hoc Pane! on the Current Interglacial. The increasing use of fossil fuels in recent years has resulted in a global atmospheric CO2 increase of about 0.7 percent per year.23 CO2 molecules are very strong absorbers of long-wave thermal radiation at wavelengths at which the earth's atmosphere is otherwise transparent. The increased absorption tends to insulate the earth's surface from infrared heat losses to outer space, leading to higher surface temperatures (the greenhouse effect). It has been estimated that a 10-percent increase in atmo- 13

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Overvieu' and Recommendations spheric CO2 is likely to warm the entire lower atmosphere by an average of about 0.3Can inadvertent climatic change. Possible mechanisms for reconciling the apparent discrepancy between the decreasing temperature shown in Figure 3 and the expecter! increasing temperature of the greenhouse effect are to be found in the Schneider and Tempkin paper. Discussion of the probable impor- tance of a climatic change of this magnitude to water-resource design can be found elsewhere in this report. The one aspect of deliberate weather modification that concerns this pane! is the suggestion that impregnating winter clouds with silver iodicle crystals is a viable mechanism to augment the snowpack in the mountains of the arid West. It is evident that there are those with unshakable convictions who believe that the future water-supply shortages prognosticates! by Dracup for the Upper Colorado River Basin can be avoiclect by the generation of extra snow whenever ancl wherever needled (note that integrated over time this wouicI amount to deliberate climatic change). This group believes that existing technology and understanding are adequate for management purposes and that further research is either unnecessary or, if neeclecI, shouIc! not be allowecI to interfere with ongo- ing management programs the public cannot continue to afford the luxury of further randomized tests. It is evident that there are others, just as determiner! in their beliefs, who conclude that snow augmentation is a most important area for an expancled program of carefully consiclered scientific research but that the existing knowledge ant! technology are inadequate to guarantee success and may even have effects contrary to those that are desired. In an interesting program of ongoing research Farhar and her associates at the University of Colorado24 have studied the sociology of those who favor manage- ment programs as opposer! to those who favor further research into weather modification. Representatives of these two groups tend to come from quite different occupational and technical backgrounds, and it is easy to infer that our pane] is unlikely to have container! representatives of either extremal group. It is true, however, that too many of our pane] members have hack experience in simulation and numerical analysis for the group as a whole to be regarcled as a random sample. It was not the duty of this pane! to analyze and reanalyze weather-modification experiments, but we die] conduct a literature review. The U.S. House of Repre- sentatives Subcommittee on the Environment and the Atmosphere has recently concluder! hearings and published more than 1300 pages of testimony,25 much of which is relevant to this subject and which in summation tends to support the view that more research is needecl before seeding cloucls on an operational basis with intent to increase snowfalls. A prerequisite for any management program designed to modify a geophysical process, be it snow augmentation, earthquake attenuation, or the subsidence of Venice, is accurate forecasts of the relevant phenomena and all major side effects, based on three-dimensional, time-varying, physics-basecI, computer models. The snow augmentation movement is not supported in this manner, ant! scientific cre~libility for a management program is lost. Further, the statistical justification for snow-augmentation management programs is weak because the statistically randomized portions of snow- augmentation experiments have not shown consistent results (positive, nega- tive, and inconclusive results abound). Claims for success have been baser! on post hoc analyses in which certain storms ant! measurement stations have been removed from the analysesa procedure that is perfectly honest and permissi- ble providing the objective is increaser! understanding of the phenomena being stuclied, better simulation models, or more carefully designee! future experi- 14

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Overview and Recommendations meets. Post hoc statistical analyses clo not, however, amount to controlled, unbiased statistical tests26 of the phenomena being studier! and are not a justification for management programs, only for further research. It is the opinion of this panel that weather-modification technology has the . ~ , . . ~ . . ~ . . .. ... ~ potential to be a useful tool tor increasing the resilience ot water-resource systems, although more research will be needled before this hypothesis is proven (see the following section on Climatic Transfer Functions). Furthermore, to justify future water-resource projects on the grounds that current weather- moclification technology will procluce the water as needed appears somewhat unreasonable. CLIMATIC TRANSFER FUNCTIONS Before the forecast values of future changed climates become useful to hy- drologists and water-resource planners, the variables of the climatic forecast have to be converted into the variables of water supply and projected water use. Water-resource designers customarily work with seasonal water-supply values, where the number of seasons varies from 2 to 12 per year. However, for some situations, annual flow estimates are sufficient, while for other situations very-short-period (dafly) estimates are required. Hydrologists have generated hundreds of models for converting climatic variables into estimates of streamflow, but it is only recently that hydrologists have started to make the necessary sensitivity tests27 on the physics-based moclels, and only one attempt at an unbiased statistical evaluation of mode! forum tic hats haven reporteCi.28 This latter study, conducted! by the World Meteorological Organization (WMO) from 1968 to 1974, evaluates! the perfor- mance of ten models on up to six watersheds for a two-year forecast period. The results were scarcely encouraging to the mo(lel builders. Even with the actual daily rainfall and temperature measurements recorded within the incliviclual basins for the forecast periods, the forecast flows were often greatly in error. Errors in the sum of the forecast flows for the complete two-year forecast periods ranged in excess of 40 percent (see Figure 5 for an example). Furthermore, as shown in Figure 6, incliviclual events sometimes showed little or no correlation between the observed and forecast values. It is possible to conclude from the WMO Study that existing hydrologic moclels may be poorly adapter! to the job of mapping forecast values of climatic variables into water-supply forecasts. In addition, snowmelt routines Mat could be used to convert augmenter! snow- LU I: I C FIGURE 5 Plot of cumulative forecast for a c: two-year period against cumulative observed flow for the Nam Mune River. Figure redrawn from WMO Hydrology Report No. 7, 1974. In m o w 15 LINE OF PERFECT / f ORECAST \/ / I' ~ ~ , / SSARR MODEL FORECAST DISCHARGE

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Overview and Recommendations FIGURE 6 Plot of the highest daily flow per month forecast for a two-year period against the comparable observed flows. Appreciable rainfall occurred in only 7 of the 24 months (SRFCH model, Wollombi Brook data). Figure redrawn from WMO Hydrology Report No. 7, 1974. In - o at C) > LU In CD o X X XX /- PERFECT FORECAST / x FORECAST RUNOFF (ems) pack figures to water behind the dam were not included in the WMO analysis. Clearly, such a relationship is nonlinear in both time ant! space, ant] the models used to estimate this transfer function need! to be evaluated in an unbiased and careful manner before the water results of snow augmentation can be known. The WMO study has shown that our existing cTimate-water transfer functions are inaccurate, but Matalas and Fiering point out that further general uncertain- ties will accrue when these moclels are used to forecast uncler a new uncali- brated climatic regime. Changes in temperature and precipitation regimes cause changes in cloucI cover and racliation transfer, which can initiate changes in the patterns of human settlement, cropping, and development. In turn, these changes can cause changes in streamflow patterns, which can cause further geomorphological changes. These latter changes are themselves affected by the extent to which regional flora and fauna become adapter] to the new climatic regimes. In summation, transfer functions to get from a climatic forecast to water-resource design variable, Cf. are in a very primitive stage of development and need to be greatly strengthener! before they achieve statistical reliability. In a(lclition, it is possible that the specific forecasts of climatic variables may themselves be in error and that the combination of errors in the initial forecasts, combined with the errors in the cTimate-to-water-supply conversion, may lead to the transfer of negative information.29 That is, the water-resource designer might be able to obtain a better design by considering only the existing record and its variability while ignoring the forecast values. Much careful research will be neecled before such questions are satisfactorily resolved. Besides the climate-to-water-supply conversion discussed above, the water- resource planner may want to consider that the demands for water uncler a forecast climate may be different from the currently observed one. For instance, how much water for energy or irrigation will be needed under the new climate regime? What crops shouIcl be grown an(1 where? How will the cropping patterns an(1 irrigation demands vary in the future? In their paper, Lofting an(1 Davis discuss the difficulties that economists have in defining, projecting, and estimating water clemand. THE ECONOMIC PROBLEM OF PREDICTING FUTURE WATER DE MAN D Economic uncertainties have been shown under certain circumstances to be more important to water-resource clesign than uncertainties that arise from 16

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Overview and Recommendations hydrologic causes. Lofting and Davis document the problems facing those who must estimate water "clemand," ant] they point out that the uncertainties in'the economics (hence, the economic benefits accruing to a possible water-resource design) appear to be increasing rather than decreasing. Further, they note that those who wish to apply classical market economics find many special problems attached to estimating future water demand. For instance, demand! for water does not exist in a conventional sense until after the supply has been assured, then "use" expands in the area up to the limits of the available supply but not beyond. Thus, present use is a self-fulfi~ling prophecy of a previous estimate of a potential clemanc! and may be misleading as a basis for estimating future "requirements." There are also problems associated with the concept of water use as an elastic property of price, a concept that, for water, may or may not be true. In acldition, there are special diffic0Ities attacher] to the manner in which the statistics and basic data of water use are estimated and recorclec3. The Lofting and Davis paper makes interesting reading for those who are concerned with future water requirements anti our ability to estimate them. Their paper also includes practical proposals for research, which if conclucted would go a Tong way toward reducing these more obvious uncertainties in the economics of estimating future water use. But, as Lofting and Davis note, there are at least three new sources of economic uncertainty that make forecasts of future water demands particularly . am. lo. ~ . . . .. . ~ .. ,~ . . uncertain. l he first cause ot mayor new uncertainties in forecasting tuture water clemancis is the enactment of Public Law 92-500, which has legisTatecI the elimination of the discharge of all pollutants by 1985 and the regulation of all irrigation to assure minimal water use and minimal return discharge. A major present use of water is pollution abatement by dilution, and if the law and its timetable are enforced, there will be revolutionary changes in future water demands. Water economists are only just beginning to assess all the implica- tions and ramifications of Public Law 92-500. The second source of new uncertainty in the forecast of future water clemancis is less certain of execution but couIc! also cause large changes in future water usage, namely, a large increase in irrigates! agriculture. The Malthusian day of reckoning appears to be rapi(lly approaching, with worI(1 food supplies low and worIc} population still increasing at a much greater rate than worIc! foot! supplies. It has been suggested that the food deficits of "Thirc! World" countries could be met by expansion of the agricultural production of the United States. To meet this goal might entail, among other things, an increase in irrigated agriculture and perhaps the resurrection of some dormant plans for the interbasin transfer of water. Whether the Uniter! States has the political cohesion or the economic power to succeed in such a policy was not a subject of investigation for this panel, but the possibility of such a national goal increases uncertainties in estimates of water demand. The third new cause of increased economic uncertainty in the estimates of future water supply is the threat of climatic change, real or imaginecl, which can alter what farmers will plant, as well as what economists think they will plant. At present, we do not know whether climatic change will result in more or less water available for storage behind! a proposed dam. Further, we do not know what the net effect of a postulated average annual global temperature change may be on the future water requirements within an actual specific project area. It wouIcT appear that rather than global averages, the climatic-change estimates that might actually influence projections of water use are estimates of changes in frequency and severity of extremal periocls. Climatologists may find reliable, nonstationary, extreme value forecasting beyond their abillity.30 17

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Overview and Recommendations THE SOCIETAL IMPACT OF WATER SHORTAGES A good rain is the only quick solution to problem of drought.... Unfortunately, a good rain washes away more than the drought, it washes away much of man's interest in providing for the next one, and it washes the supports from under those who know that another cirv r~vr~lf~ is r~r~mina and ~vh`~ Army Weir fellows to make ready for it. W. P. Webb, 1954 From reacting Meier's contribution to this volume, one can find that what was true in Texas in 1954 is still true over most of the United States in 1977. Nearly all the thousands of indiviclual water-resource source systems currently operat- ing in this country are susceptible to shortages of various severity and duration. Shortages can come from inadequate supplies, structural failures, increased demand, or poor operating policies. The one common denominator to link all of these future failures as they occur is that their effects will be macle more noticeable by a lack of advanced "contingency planning" and by the slowness with which the responsible officials can be expected to act. As Matalas and Fiering note, system resiliency is a fertile field for further water research, and Meier's "societal impacts" are an aspect of resiliency that shouIc! not be overlooked. Resiliency research can be expecter! to air! greatly in the production of sound contingency plans and even to contribute to better estimates of water demand. If climatic change were sudden and pronouncer] and in a direction that greatly reduced supply or increaser] demand, then the need for such research wouIc] become immecliately obvious, but the need exists even without considering possible climatic changes. WATER LAW AND CLI MATIC CHANGE If our climate should change for the worse, our water laws should change for the better. Trelease, 1976 The one area of the climatic change-water supply problem that has not yet been mentioned in this introduction is the matter of water law. Elsewhere in this volume Trelease uses an eloquent broad brush to discuss He major aspects of U.S. water law from the point of view of climatic change. He stresses that water law can and does change as a result of man's perception of his aqueous en- vironment and that legal changes can be expecter} to accelerate uncler the stress of climatically induced change. Trelease believes that future legal changes will tend to generate increased flexibility in rights and institutions, and, optimisti- cally, all of this wil lead to the greater good for the greater number an encour- aging prospect. However, water law is complicated and varies widely from state to state, as well as from river to river. In the eastern states, vestiges of English common law, in the form of "riparian" rights, still remain, although often overlain by regulatory statutes and federal controls. Litigation is still a major method used to allocate water supplies in the east, and this approach to conflict resolution would appear to be unnecessarily costly, slow, and clumsy. Trelease has many practical suggestions for making water law more responsive to human needs and desires, but he also places "prior appropriation," "interstate compacts," "reserved rights," and "environmental water law" in their appropriate context, both historically and with regard to future climatic change. CONTRASTING PROBLEM AREAS THE NORTHEAST AND THE SOUTHWEST Early in the panel's deliberations it was decided that the exercise should not be wholly academic and that the panel should try to assess the climatic change- 18

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Overview and Recommendations water supply function for at least two sample areas. Schwarz agreed to consider the metropolitan industrial northeast, and John Dracup volunteered to make one more assessment of the much studied Colorado River Basin. The northeast contains about 5 percent of the nation's land area, but it holds about 25 percent of its population and produces nearly 30 percent of its wealth. Some 1200 water suppliers in the region currently furnish an average 241 m3/sec of water, with 70 percent of this supply being used in the three metropolitan areas of Washington, New York, and southeastern New England. Depending on which projection of growth is realized, the region is likely to require 416~78 m3/sec of assured supply by the year 2000. Given that all major water-supply projects in the northeast have been stalled for more than 10 years over uncertainties in the incliviclual demand forecasts, as well as because of fiscal and environmental constraints, it would appear that water shortages in the northeast are going to be prevalent in the near future. The alternatives to severe water shortages in the northeast appear to be either climatic changes that prevent shortages in supply in a consistent beneficial manner or a much slower regional growth rate than has been projected. The first of the above alternatives is questionable, and the second may be politically undesirable. Schwarz suggests detailed measures that could alleviate some of these threatened water shortages, but it would appear that without major new regional cooperation, and federal commitment, the northeast will soon suffer water shortages. Dracup discusses the Colorado compact that divides the 1924 estimate of long-term flow equally between the Upper and Lower Basin states. He notes that legal constraints require specified releases from the upper to the lower basin states, that the existing water-storage configuration favors the lower basin states, and that extensive energy developments projected! for the Upper Basin states entail extensive water requirements. His conclusion is that the results of any period of extended low flow would oppress the Upper Basin states more than the Lower Basin states and that water shortages in the Upper Basin states can be expected after 1985, if not sooner. When consumptive use in the Upper Basin states becomes hampered by the Colorado compact allocation of flow, it seems probable that the Upper Basin states will attempt to renegotiate the contract. At that juncture, the courts or Congress will have to clarify whether the intent of the compact was to divicle the long-term flow equally between upper and lower basin states or to guarantee 75 maf of water per decacle to the Lower Basin states. Current estimates of the long-term flow inclicate that these two interpretations of the compact are con- flicting. However, given that approximately four years of average flow can be stored near the compact point, it would be possible to adjudicate future dry- period releases based on the previous year's adjusted virgin flow and hence to bypass further consideration of climatic change or the unknowable true long- term mean flow of the river a flexible solution to match a variable climate. SUMMARY The nation as a whole can expect to experience severe local and even regional water shortages. Future water shortages may be exacerbated by climatic change, but current and foreseeable climatologic forecast ability is not likely to be accurate or specific enough in either time or space to be useful to the water- resource planner. However, there are many useful measures that could be implemented now that would help to mitigate the undesirable effects of future water shortages. 19

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Overview and Recommendations REFERENCES AND NOTES 1. I. C. James, B. T. Bower, and N. C. Matalas (1969~. Relative importance of variables in water resources planning, Water Resources Res. 5, 1165. 2. For a set of streamflows A, x2, x3 . . . XT-l, XT, the mean,X, and standard deviation, S. are defined as X = ~ taxi; S =:~ xi2- X2. i=1 i=1 3. B. B. Mandelbrot (1965). Une classe de processes stochastiques homothetiques a sol; application a la loi climatologique de H. E. Hurst, Compt. Rend. Acad. Sci. Paris 260, 3274. 4. Mandelbrot's original paper has spawned a vast literature. At present, Box and Jenkins' autore- gressive models, ARMA ~ 1, 1), appear to be the easiest to use approximations to fractional noise, and they appear to be sufficiently flexible for most hydrologic situations. See P. E. O'Connell, in Mathematical Models for Surface Water Hydrology, John Wiley and Sons, Inc., New York, 1977. 5. J. A. Brophy (1970). Statistical randomness and 1/f noise, Naval Res. Rev., pp.8-21, October. 6. A. Court (1960~. Reliability of hourly precipitation data,J. Geophys. Res. 65, 4017. 7. D. C. Smiley, personal communication. Mr. Smiley is a trustee of the Mohonk Trust and has been largely responsible for the maintenance and preservation of the weather records on the Mohonk Trust lands and for the publication of the Mohonk Trust Newsletter. See especially No. 23, Winter 1974, from which issue Figure 3 has been redrawn. 8. For a full discussion of the Colorado compact see the papers by Trelease (Chapter4) and by Draeup (Chapter 8) in this volume. 9. H. E. Landsberg, C. S. Yu, and L. Huang ( 1968). Preliminary reconstruction of a long time series of climate data for the eastern United States, U. of Maryland Tech. Note BN-571. 10. Policy statement of the American Meteorological Society on weather forecasting (1973). Bull. Am. Meteorol. Soc. 54, 1. 11. Report of the Ad Hoc Panel on the Present Interglacial (1974). Federal Council for Science and Technology, National Science Foundation, Washington, D.C. 12. J. Gani (1975). The use of statistics in climatological research, Search 6, Nos. 11-12. Dr. Gani is a statistician who believes that climatology would benefit from increased communication with the statistical community. 13. B. B. Mandelbrot and J. R. Wallis ( 19691. Some long-run properties of geophysical records, Water Resources Res. 5. Mention of this point is also made in the discussion of "red" and "white" noises contained in the above-mentioned report of the Ad Hoc Panel on the Present Interglacial (Ref. 11). 14. For an example of an apparently significant spurious cycle see Figure 8 of I. R. Wallis and N. C. Matalas (1971~. Correlogram analysis revisited, Water Resources Res. 7, 1448. 15. E. Slutzky (1927). The summation of random causes as the source of cyclic processes, Economet- rika 5, 105. 16. S. W. Tromp (1975). Possible extra-terrestrial triggers of interdisciplinary cycles on earth, J. Interdisciplinary Cycle Res. 6, 303. 17. C. G. Abbot (1960~. A long-range forecast of United States precipitation, Smithsonian Misc. Collections 139(9). 18. C. G. Abbot and L. Hill (1967). Supplement to a long-range forecast of United States precipita- tion, Smithsonian Misc. Collections 152~5~. 19. C. G. Abbot (1961). A long-range temperature forecast, Smithsonian Misc. Collections 143~5). 20. The Spearman rank correlation coefficient is defined as N 6 ~ df2 i = 1 1- N3-N ' where N is the number of values to be ranked and d is the difference in the individual rankings. For January precipitation at Montgomery, Ala., from 1961 to 1970 the values and ranks of the 10 forecasts and 10 observed precipitation amounts were: 1961 1962 1963 1964 1965 +52 -9 +3 +12 +8 10 5 6 8 7 2.18 5.20 7.14 6.49 6.10 2 6 10 9 7 Year Forecast Ranked Forecast Observed Ranked Observation yielding d and d2 values of d d2 20 8 -1 64 1 -4 -1 16 1 o o 1966 1967 1968 1969 1970 +40 -10 -41 -37 -48 9 4 2 3 1 6.20 2.77 2.78 1.85 2.83 8 3 4 1 5 1 1 1 1 -2 2 4 4 -4 16

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Overview and Recommendations and a Spearman rank correlation coefficient of +0.35. A value of +1.0 would signify perfect agreement between forecast and observed ranks, while a value of -1.0 would signify a complete disagreement. Equal values in the observations on values in the forecasts were treated follow- ing Siegel's Non-Parametric Statistics, McGraw-Hill Book Co., New York, 1956. Data for the complete analysis are presented in Tables R.1 and R.2. TABLE R.1 Rank Correlations between Forecast and Observed Precipitation for the Period 1961-1970 City Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Montgomery, Ala. 0.35 0.67 0.51 0.07 - 0.50 -0.49 -0.41 0.34 - 0.31 0.51 -0.19 0.26 Natural Bridge, Ariz. -0.36 -03.5 0.35 0.59 0.44 0.07 -0.06 0.18 0.27 -0.22 -0.05 0.15 Little Rock, Ark. 0.25 -0.05 -0.16 0.03 0.22 -0.27 0.31 0.02 0.05 0.52 0.26 0.01 Sacramento, Calif. -0.55 - 0.40 - 0.30 -0.14 -0.37 0.25 0.12 0.20 0.00 0.28 0.27 -0.01 San Bernardino, Calif. -0.61 -0.57 0.03 0.62 0.05 -0.11 0.28 0.48 -0.35 -0.32 -0.18 0.19 Denver, Colo. - 0.34 0.32 0.08 -0.25 0.13 0.26 0.25 -0.36 - 0.17 0.60 0.07 0.15 Augusta, Ga. -0.24 0.37 0.14 -0.63 -0.03 -0.25 0.30 0.02 0.15 -0.18 0.08 0.05 Thomasville, Ga. -0.34 -0.38 0.09 0.15 -0.37 0.62 0.25 -0.20 -0.45 0.09 0.21 0.16 Peoria, Ill. -0.25 0.12 -0.19 -0.25 -0.02 0.29 -0.16 -0.36 -0.61 0.22 -0.16 -0.41 Independence, Kan. -0.13 -0.25 -0.41 0.54 0.70 -0.14 -0.32 0.33 -0.48 0.09 -0.32 -0.19 Washington, D.C. -0.15 0.48 0.00 -0.83 0.19 0.04 0.24 0.36 -0.05 -0.23 -0.20 -0.25 Detroit, Mich. - 0.07 0.18 -0.60 -0.07 -0.20 -0.32 -0.13 -0.17 -0.45 0.20 0.39 0.20 St. Paul, Minn. 0.20 0.05 0.31 0.28 0.60 - 0.35 -0.26 -0.26 -0.09 -0.15 -0.08 0.24 Port Gibson, Miss. 0.52 -0.08 -0.04 -0.58 -0.25 0.05 0.06 -0.34 -0.59 0.34 -0.04 0.18 St. Louis, Mo. - 0.10 0.50 - 0.44 0.03 0.17 0.22 0.12 -0.49 - 0.16 0.25 0.17 0.37 Helena, Mont. 0.56 -0.03 0.41 0.55 0.28 0.43 0.45 0.58 -0.22 0.05 0.00 0.44 Omaha, Neb. -0.22 -0.31 -0.03 0.38 0.31 0.33 -0.13 -0.05 0.19 -0.25 0.12 0.10 Eastport, Maine 0.33 - 0.31 0.52 0.10 0.15 0.14 0.23 -0.22 0.09 -0.11 0.16 0.13 Santa Fe, N.M. -0.33 0.26 0.29 -0.10 0.18 0.56 -0.37 0.45 -0.24 -0.12 0.43 0.42 Albany, N.Y. -0.22 - 0.08 - 0.53 0.69 0.27 0.55 0.54 0.17 0.12 0.01 -0.34 0.00 Rochester, N.Y. 0.09 0.25 0.18 -0.24 -0.08 -0.13 -0.13 -0.11 -0.04 0.19 -0.05 -0.42 Salisbury, N.C. -0.18 -0.14 -0.04 -0.35 0.45 0.05 0.12 -0.08 -0.52 -0.01 -0.02 0.03 Bismarck, N.D. -0.11 -0.59 0.02 0.29 -0.28 -0.36 0.19 0.08 0.05 -0.49 -0.25 0.29 Cincinnati, Ohio 0.25 0.11 -0.29 -0.22 0.02 -0.09 0.21 0.08 0.14 -0.44 0.17 0.13 Albany, Ore. 0.05 -0.36 0.07 0.03 -0.25 -0.23 -0.28 -0.23 - 0.04 0.04 0.17 0.31 Charleston, S.C. -0.07 0.31 -0.04 0.38 0.28 -0.31 0.15 0.15 -0.06 -0.08 -0.35 -0.43 Nashville, Tenn. 0.12 0.21 0.15 0.21 0.38 -0.74 -0.17 -0.47 -0.41 0.49 0.85 -0.14 Abilene, Tex. -0.24 -0.43 -0.68 0.27 0.14 -0.15 -0.27 -0.24 0.11 -0.41 -0.07 -0.20 E1 Paso, Tex. -0.46 -0.35 -0.02 -0.70 0.65 -0.56 -0.58 -0.01 0.53 -0.04 -0.03 0.16 Salt Lake City, Utah 0.22 -0.14 -0.08 0.47 -0.03 -0.30 0.14 0.27 0.01 0.19 -0.48 0.01 Spokane, Wash. 0.64 -0.61 -0.36 -0.38 -0.19 0.54 -0.42 -0.12 0.29 -0.21 0.34 -0.13 Madison, Wisc. -0.30 -0.07 -0.54 -0.12 - 0.52 0.02 0.20 -0.07 0.20 0.15 0.33 - 0.38 TABLE R.2 Rank Correlation between Forecast and Observed Temperature for the Period 1962-1967 City Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. St. Louis, Mo. 0.70 0.83 -0.04 0.20 0.26 - 0.04 0.60 0.03 - 0.03 0.66 0.11 - 0.56 Los Angeles, Calif. 0.66 0.83 0.36 -0.54 -0.43 -0.03 -0.53 -0.54 -0.10 0.07 -0.26 0.60 Atlanta, Ga. 0.20 0.09 -0.43 -0.36 0.77 -0.09 -0.14 0.26 0.14 -0.76 0.26 0.66 Washington, D.C. 0.13 0.71 -0.71 -0.71 0.09 0.26 0.39 -0.30 -0.37 -0.49 -0.03 0.03 Detroit, Mich. 0.43 0.43 -0.37 0.31 0.53 -0.54 0.53 0.01 -0.30 0.20 0.37 -0.03 St. Paul, Minn. 0.26 0.20 -0.18 0.54 0.27 0.61 -0.14 0.01 0.54 - 0.39 -0.13 - 0.09 Omaha, Neb. 0.14 -0.49 0.20 0.04 -0.50 0.14 0.49 0.07 0.54 -0.61 -0.37 -0.60 New York, N.Y. 0.39 0.49 -0.36 0.40 0.66 -0.13 -0.49 0.04 -0.37 -0.49 -0.16 0.07 Abilene, Tex. 0.36 -0.54 0.37 0.76 0.33 -0.09 -0.81 -0.54 -0.61 -0.03 0.20 0.77 Salt Lake City, Utah -0.26 0.77 0.41 0.31 0.49 -0.13 0.60 -0.31 0.07 0.66 -0.21 0.59 21. U.S. Department of Commerce (1961~. Verification of the Weather Bureau's 30-day outlooks, Tech. Paper No. 39. It should be noted that the issuers of these forecasts prefer to refer to them as outlooks a semantic difference not a functional one. The analysis of the Mohonk data presented here tends to give a lower estimate of forecast reliability than did the in-house evaluation because different criteria and periods were used in the evaluations. A more interest- 21

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Overview and Recommendations ing criterion than used in either of these evaluations would be one based on the initial 5-day period forecast. Five days is the limit for skillful synoptic weather forecasting, and what is of interest is the forecast skill that exists beyond this initial period. 22. Western Water (March-April 1976). Published by the Association of California Water Agencies. 23. C. D. Keeling, J. A. Adams, C. A. Ekdahl, and P. R. Guenther (1976). Atmospheric carbon dioxide variations at the South Pole, Tellus 28, 552. 24. B. C. Farhar, Human Ecology Research Services, 855 Broadway, Boulder, Colo. 80302. 25. Publications Nos. 78 and 79, Committee on Science and Technology, U.S. House of Representa- tives, Ninety-fourth Congress, Second Session, 1976. 26. Even before statistical tests and statisticians were in vogue, the dangers of post hoc data analysis with a single hypothesis in mind (silver iodide increases snowpacks) were appreciated by some. In this regard, see H. C. Chamberlin (1890). Science 15, 92, reprinted in Science 148 (1965), from which the following quote was gleaned: There is an unconscious selection and magnifying of Me phenomena that fall into harmony with the theory and support it, and an unconscious neglect of those that fail of coincidence. The mind lingers with pleasure upon the facts that fall happily into the embrace of We theory, and feels a natural coldness toward those that seem refractory. Instinctively there is a special searchinsr-out of phenomena that support it. for ~ ~ ~ O ~ ~ ~ ~ the mind is led by its desires. There springs up, also, an unconscious pressing of He theory to make it fit the facts, and a pressing of the facts to make them fit the theory. The panel has not determined whether such unconscious biasing exists in the post hoc snow augmentation analyses, but it does wish to point out that the danger exists and that indepen- dent scientific corroboration of any post hoc analysis is desirable from a research standpoint and absolutely necessary before implementing a management program. 27. R. A. Freeze (1975). A stochastic-conceptual analysis of one-dimensional groundwater flow in non-uniform homogeneous media, Water Resources Res. 11, 5. 28. Intercomparison of Conceptual Models Used in Operational Hydrological Forecasting, World Meteorological Organization, Operational Hydrology Rep. No. 7 (1974). The project involved the testing of ten operational conceptual hydrologic models submitted by seven countries on six standard river catchment data sets from climatologically and geo- graphically varied conditions in six countries. Each data set consisted of two distinct periods: a calibration period (six years) and a verification period (the next two years). For each data set, the model owners were supplied with the necessary concurrent observed input data (precipita- tion, evaporation, and other meteorological data) and observed output data (streamflow) for the six-year calibration period and only the observed input data for the two-year verification period. The observed output data for the two-year verification period were retained by the WMO Secretariat. For each data set, the model owners used the concurrent observed input and output data for the six-year calibration period to calibrate and develop the parameters of their models and employed the additional two years of observed input data in the verification period to produce a simulated discharge (computed output). The simulated discharges produced by the tested models for both the calibration and verification periods in each data set were then centrally evaluated and compared by WMO using several graphical and numerical verification criteria agreed upon by all modelers. 29. J. R. Wallis and N. C. Matalas (1972). Information Transfer via Regression in Markovian Worlds, IBM Research, Yorktown Heights, N.Y., RC 4207. 30. In this regard consider the much quoted statement, " . . . the probability of getting fifteen consecutive years that good is about one in 10,000" (referring to the unusually good weather for agriculture in the United States from 1957 to 1972). The uncertainties that should be attached to a transfer function that converts a paleoclimatic index variable to a prairie wheat yield are totally unknown. However, they may be sufficiently large that the above authoritative sounding proba- bility statement may well be just another example of a type II imaginary number (see Time, Aug. 2, 1971, for other examples of this phenomenon). 22