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Effects of a Carbon Dioxide-Induced Climatic Change on Water Supplies in 7 the Western United States Roger R. Revelle and Paul E. Waggoner In this chapter we show that warmer air temperatures and a slight decrease in precipitation would probably severely reduce both the quantity and the quality of water resources in the western United States. Similar effects can be expected in many water-short regions elsewhere in the world. We have not attempted to estimate these, primarily because we do not know enough to be able to do so. But we hope that hydrologists of other countries will be stimulated by our calculations to investigate the probable consequences of a CO2-induced climate change on water resources in their own countries. In all coun- tries, planning and construction of large-scale water-resource systems takes many decades. The time involved is of the same order of magnitude as the time over which a significant change in climate from increase of carbon dioxide and other greenhouse gases can be expected. Thus, we believe that planners and managers of water systems throughout the world should be able to make good use of forecasts of the hydrologic conse- quences of a warmer climate and of possible changes in precipitation. 7.l EMPIRICAL RELATIONSHIPS AMONG PRECIPITATION, TEMPERATURE, AND STREAM RUNOFF To assess the effects on the United States' water resources of probable climatic change we used the empirical relationship found by Langbein et al. (l949) among mean annual precipitation, temperature, and runoff. This was based on representative data from 22 drainage basins in the conterminous United States. Their relation in Table 7.l gives the estimated annual runoff for different values of mean annual precipi- tations and weighted mean annual temperatures. The latter were computed for each catchment basin by dividing the sum of the products of average monthly temperature and precipitation by the mean annual precipitation. In this way, the average temperature during each month is weighted by the precipitation during that month. The catchments studied by Langbein and his colleagues were distri- buted over climates from warm to cold and from humid to arid, but in Table 7.l we have shown the relations among runoff, temperature, and precipitation only for relatively arid areas. In these arid areas, the value of actual evapotranspiration is less than the potential evapo- 4l9
420 TABLE 7.l Runoff (nun yr-l) as a Function of Precipitation and Temperature3. Weighted Average Precipitation (mm yr-l) Temperature (Â°C) 200 300 400 500 600 700 - 2 54 92 l54 230 330 440 0 40 74 l24 l90 275 380 2 28 57 95 l54 225 320 4 l7 40 78 l25 l90 265 6 9 25 60 l00 l55 220 8 0 l7 42 82 l28 l85 l0 8 29 64 l03 l55 l2 0 l9 47 80 l30 l4 l0 32 65 l05 l6 0 20 50 85 ^Source: W. B. Langbein et al. (l949). transpiration that would occur if sufficient water were present and evapotranspiration was controlled mainly by temperature. For example, at a temperature of 4Â°C, potential evapotranspiration is about 450 mm yr"l. Yet Langbein's data show that even when annual precipitation is only 300 mm, there is still significant runoff, about l3% of the precipitation. Correspondingly, average actual evapotranspiration must be only 260 mm yr-l. From Table 7.l we observe that for any given annual precipitation, runoff diminishes rapidly with increasing temperature. Similarly, for any given temperature, the proportion of runoff to precipitation increases rapidly with increasing precipitation. For example, at a weighted mean annual temperature of 4Â°C and annual precipitation of 200 mm, runoff is only 8.5% of precipitation, whereas for the same temperature and an annual precipitation of 700 mm, runoff is 38% of precipitation. At an annual temperature of 8Â°C, runoff is zero when precipitation is 200 mm or less and is l85 mmâor 26.4% of precipitationâwhen the average annual precipitation is 700 mm. For any particular region, the relations shown in Table 7.l are rather crude approximations because many physical factors, including geology, topography, size of drainage basin, and vegetation, may alter the effect of climate on runoff. We believe, nevertheless, that these relationships can be used without serious error to describe the effects of relatively small changes in average temperature and precipitation on mean annual runoff. In Table 7.2, we have used the data in Table 7.l to compute the approximate percentage decrease in runoff for a 2Â°C increase in tem- perature. Climate models (e.g., Manabe and Wetherald, l980) indicate that a temperature change of this magnitude or greater is likely as a result of the doubling of carbon dioxide and increased concentration of "greenhouse gases" expected during the next century. We see that for a
42l TABLE 7.2 Approximate Percent Decrease in Runoff for a 2Â°C Increase in Temperature3. Initial Temperature Precipitation (mm yr-l) (Â°C) 200 300 400 500 600 700 - 2 26 20 l9 l7 l7 l4 0 30 23 23 l9 l7 l6 2 39 30 24 l9 l7 l6 4 47 35 25 20 l7 l6 6 l00 35 30 21 l7 l6 8 53 3l 22 20 l6 l0 l00 34 22 22 l6 l2 47 32 22 l9 l4 l00 38 23 l9 Computed from Table 7.l. present weighted mean annual temperature of 4Â°C and annual precipita- tion of 300 mm, a 35% diminution in runoff would follow a 2Â°C warming. The percentage decrease in runoff from a warming diminishes with increasing precipitation and becomes greater for successively higher values of the initial temperature. Table 7.3 shows the approximate percentage decreases in runoff for a l0% decrease in precipitation. According to the results of climate models (see Chapter 4), such a diminution in precipitation is likely, at least in certain regions of the United States, with a doubling of atmospheric C02. Again we see that the effect becomes larger with higher average annual temperatures. There is a relatively small dif- ference in the percentage decrease in runoff at a given temperature over the range of initial precipitation values shown in the table. Comparison of Tables 7.2 and 7.3 shows that below an initial mean annual precipitation of 500 mm, the effects of a 2Â°C warming are larger than those caused by a l0% decrease in precipitation. The reverse is true when mean annual precipitation is 500 mm or more. 7.2 EFFECTS OF CLIMATE CHANGE IN SEVEN WESTERN U.S. WATER REGIONS Stockton and Boggess (l979) have used Langbein's empirical relation to estimate the effects of a climatic change on water in the l8 water regions of the conterminous United States defined by the U.S. Water Resources Council (l978). They find that a 2Â°C warming and a l0% reduction in precipitation would not have serious effects in the humid regions east of the l00th meridian. In the West, however, the impact would be severe on seven water regions: the drainage basins of the Missouri, Arkansas-White-Red, Rio Grande, and Colorado rivers; the river basins draining into the Gulf of Mexico from the northern two thirds of Texas; and the rivers of California. The only western water
422 TABLE 7.3 Approximate Percentage Decrease in Runoff for a l0% Decrease in Precipitation! Temperature Initial Precipitation (mm yr-l) (i>C) 300 400 500 600 700 - 2 12 l6 l7 l8 l8 0 l4 l6 l7 l9 l9 2 l5 16 l9 l9 20 4 l7 l9 l9 2l 21 6 23 23 2l 2l 2l 8 30 24 24 22 22 l0 24 27 23 23 l2 40 30 25 25 l4 34 30 27 l6 50 36 29 ^Computed from Table 7.l. regions that would not be severely affected are the water-rich Pacific Northwest and the Great Basin (parts of Nevada, Utah, and Idaho), where demand is relatively small and groundwater reserves are large. In estimating the impact of climate change, Stockton and Boggess assumed: l. The region-by-region variation in annual runoff is predomi- nantly influenced by climate, although other factors such as geology, topography, vegetation, and many other variables may be important, especially in smaller drainages. 2. The empirical curves associating total annual precipitation and total annual runoff with weighted mean annual temperature are appropriate for all l8 regions although derived from a relatively small (22 drainage basin) sample. 3. Changes in land use have relatively small influences on regionwide annual runoff. 4. Annual runoff is not greatly affected by large-scale ground- water overdraft. 5. Evapotranspiration is controlled solely by temperature. 6. The postulated climatic change does not modify the present monthly distribution of temperature and precipitation; only the amplitude of the present distribution is increased or decreased. 7. Selection of a few meteorological stations for each region adequately establishes the relation of the weighted mean temperature and annual precipitation to annual runoff. In Table 7.4 we have summarized the estimates by Stockton and Boggess of the effects of a 2Â°C increase in temperature and a l0% reduction in precipitation in the seven water regions of the western United States in which climate change would have the most serious
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424 impact. These regions cover about half the area of the conterminous United States, but they produce only about l5% of the mean annual stream runoff. The table shows the present mean annual water supply for each region, not including mined groundwater, in millions of hectare meters (l0l0 m3 yr-l) and the estimated mean annual requirement in the year 2000. The mean annual requirements listed in Table 7.4 represent "consumptive" use of water plus evaporation from reservoirs, that is, the total quantity of water that is evapotrans- pired in the course of beneficial human use. Although actual with- drawals from streams and underground aquifers are considerably larger, portions of these withdrawals are returned to the streams or back into the ground where the water may be reused. In the present climate the ratio of estimated requirements to supplies is less than one for all regions except the Lower Colorado River. In this region today, the deficit of supply is presently made up by extensive mining of groundwater. For the postulated climatic change, supplies would greatly diminish in all regions, ranging from almost a 76% reduction in the Rio Grande region to nearly 40% in the Upper Colorado, with the result that estimated requirements would exceed supplies in the Missouri, Rio Grande, and Upper and Lower Colorado regions. Mean annual requirements would still be less than future mean annual supplies in the Arkansas- White-Red, Texas Gulf, and California regions. But requirements would almost certainly exceed supplies in the Texas Gulf and California regions during future prolonged droughts. Conditions are highly vari- able in different parts of the Arkansas-White-Red region, with the western part tending to be deficient in water supplies and the eastern part having a surplus. To maintain the present pattern of water use, large-scale transfers between basins might be necessary here even under average conditions, let alone to meet water requirements during pro- longed droughts. A serious deterioration in water quality would follow from climatic change in all seven regions. The ratio of future requirements to supply would probably be even less favorable than indicated in Table 7.4 because evapotranspiration from irrigated farms and reservoirs would undoubtedly increase with a rise in temperature. On a global basis this would be compensated for by an increase in precipitation, but this might or might not occur in the regions we are considering. At present, California depends for about l5% of its water on imports from the Colorado River. These imports might be eliminated entirely with the postulated climatic change, in which case the ratio of mean annual requirements to mean annual runoff would increase to 0.83, more than double the present ratio. In all seven regions, irrigation is by far the largest user. Its share of water withdrawals ranges from 68% in the Texas Gulf region to 95% in the Rio Grande region. Total water withdrawals for agriculture are now l3.2 million hectare meters, and in the seven regions the irrigated area is (very approximately) l3 million hectares (Rogers, l983) so that, on the average, the annual depth of irrigation is about l m. Consumptive water use in irrigation is much smaller; a large share of the water that is not consumed reappears as return flows that
425 can be used downstream. Reduction in the irrigated area and an increase in the efficiency of water use in irrigation would significantly lower the overall water requirements in the seven western regions. A l5% increase in water-use efficiency is probably feasible (Jensen, l982) . Reduction in the irrigated area might come about automatically if an interstate economic market for water were to develop, because economic returns to irrigation are relatively low in large parts of the seven western regions. On the other hand, potentially very large Indian claims for irrigation water for their reserved lands must eventually be settled, and this could result in a major reallocation of water rights (Back and Taylor, l980). The effects of future droughts in the Arkansas-White-Red, Texas Gulf, and California regions from the assumed climatic change could be significantly mitigated by construction of additional reservoirs for water storage, but increases in storage would help little in the Missouri, Rio Grande, or Upper and Lower Colorado regions because their storage reservoirs are already so large compared to the annual runoff. In these regions strict water conservation would be essential. The mean annual requirements listed in Table 7.4 represent "con- sumptive" use of water plus evaporation from reservoirs, that is, the total quantity of water that is evapotranspired in the course of beneficial human use. Although actual withdrawals from streams and underground aquifers are considerably larger, portions of these with- drawals are returned to the streams or back into the ground where the water may be reused. As Stockton and Boggess show, the one western region where a large surplus would still exist after their postulated climatic change would be the Pacific Northwest. Their estimated ratio of requirements to supplies following a 2Â°C warming and a l0% reduction in precipitation would be 0.l0. The annual supply would then be 23.7 million hectare meters. Transfer of 20% of this total supply to water-short regions through large, long-distance conveyance could increase future supplies in the seven western regions shown in Table 7.4 by nearly 30%, thereby compensating for much of the estimated shortages from climatic change. The ratio of requirements to supplies in the Pacific Northwest region would still be a comfortable 0.l8. From an economic standpoint, however, such a transfer would probably not be desirable. The value of the hydroelectric energy that could be generated from a hectare meter of water in the Pacific Northwest, assuming a total head of 500 m and a price of 5# per kilowatt-hour, would be over $600, considerably in excess of the value of a hectare meter of water for irrigating the fodder and cereal crops grown in most of the western regions (Rogers, l983). 7.3 THE COLORADO RIVER Except for the Rio Grande, the waters of the Colorado River are more intensively used than those of any other major stream in the United States. Half the estimated "normal" flow of l8,500 million cubic meters per year at Lee Ferry in Arizona has been allocated by inter-
426 state compact, confirmed by federal law, to the lower basin states of California and Arizona, with minor amounts going to Nevada. Nearly all of the runoff originates from snow in the high-mountain area of western Colorado, southwestern Wyoming, and eastern Utah.* (As defined, the Upper Basin also includes northwestern New Mexico.) To check the probable effect of a climatic change on the flow of-the Colorado River, we calculated a multiple regression of the relation between annual averages of precipitation and temperature and the "virgin flow" of the Colorado at Lee Ferry, Arizona, which is the southernmost point on the river in the Upper Colorado Basin. The "virgin flow" is the measured flow at Lee Ferry plus estimated depletions within the upper basin, evaporation from reservoirs, and changes in reservoir storage. Estimates for the annual virgin flows were furnished to us by Myron B. Holbert, chief engineer of the Colorado River Board of California. The flow for each water yearâOctober l to September 30âfrom l93l to l976 is tabulated in Table 7.5. It ranges from 9,450 to 25,490 million cubic meters. The average for the 46-year period is l6,430 million cubic meters (l3.5 million acre feet). This average value is 2065 million cubic meters, or ll% less than the assumed "normal flow" on which the Colorado River Compact is based, but it agrees well with Langbein's relationship, shown in Table 7.l, among temperature, precipitation, and runoff. Interpolating between the values given in the table for temperatures of 4 and 6Â°C and precipita- tion of 300 and 400 mm yr"l, we arrive at a runoff of 53 mm, cor- responding to an annual river flow for the 296,000 kin2 in the Upper Colorado drainage of l5,700 million m3. The flow of the Colorado is mainly collected in five catchments corresponding to the five climatic divisions in the Upper Colorado Basin outlined in Figure 7.l. Mean annual precipitation and temper- ature for each drainage area and water-year from l93l to l976 were provided to us by Daniel Cayan of the Scripps Institution of Ocean- ography, who obtained the original data from the National Climate Center, Asheville, North Carolina. The annual data for each division are the areally weighted averages of the records of individual weather stations. As Cayan has pointed out, the number of weather stations was not constant but gradually increased from l93l to l976. Between l95l and l980, continuous records were obtained from 45 stations in the western Colorado division, l0 stations in the Green and Bear drainages in Wyoming, and l0 in the three drainage basins of eastern Utah (North Mountains, Uinta Basin, and Southeast Utah). By l980, there were 65 stations in western Colorado, 26 in the three Utah divisions, and l6 in southwestern Wyoming. We weighted the data from these five drainage basins in proportion to their areas: Colorado drainage in western Colorado, 0.430; Green and Bear drainages in Wyoming, 0.l84; North Mountains in Utah, 0.ll0; *See Dracup (l977) and Howe and Murphy (l98l) for useful discussions of the economic, social, political, and international problems of the Colorado River compact.
427 FIGURE 7.l Basins or drainages of the western United States.
428 Uinta Basin, 0.053; and southeast Utah, 0.223. The weighted sum of the precipitation in millimeters for the five drainages is called PRECIP in the following equation. It varies from 262 to 439 mm yr"l, with an average for the 46 years of 332 mm yr"l. Weighted annual average temperatures obtained in the same manner are called CELSIUS. They range from 2.52 to 6.75Â°C and average 4.l8Â°C. The weighted annual averages for l93l to l976 are tabulated in Table 7.5. The relation of the virgin flow to PRECIP and CELSIUS is assumed to fit the equation: FLOW = b + (b x PRECIP) + (b2 x CELSIUS). The regression coefficients, b^, and their standard errors relating the virgin flow at Lee Ferry to the mean annual precipitation and the mean annual temperature in the watershed from l93l to l976 are as follows: bQ in millions of cubic meters = 9274 Â± 3838, b^ in millions of cubic meters/mm = 52 + 7, b2 in millions of cubic meters/Â°C = -2400 _+ 507. The fit of the equations to the data is represented by the square of the correlation coefficient, R2, which is 0.73. About 75% of the variation of the flow about the mean is explained by the equations. We see that a 2Â°C rise in temperature would decrease the virgin flow by 4800 +. l0l5 million cubic meters yr"l, or about 29% +. 6%. A l0% decrease in precipitation would reduce the flow by l730 _+ 230 cubic meters, or an additional ll% +_ l.4%. The combined effect would be a reduction in flow by 40% _+ 7.4%, very close to the estimate of 44% given by Stockton and Boggess. Estimates of the virgin flow between l900 and l930 were also provided by Holbert, and we attempted a similar analysis for these years, using data published in the Weather Bureau publication, The Climates of the States. Unfortunately, the data for these earlier years are sparse. Only l0 stations recorded precipitation more or less continuously during this period in western Colorado and even fewer in Utah and Wyoming. Temperature data were available from only Garnett, Colorado; Lander, Wyoming; and Modena, Utah, and none of these is in the high-mountain regions of heavy snowpack that contribute most of the runoff to the Colorado River. The data for l900 to l930, Table 7.6, indicate that the average runoff was about 20% greater than between l93l and l976, while the average precipitation was about 7% less and the average temperatures for the three available stations were about 2Â°C higher. The low estimate of average precipitation may reflect a deficiency in estimating the quantities of water precipitated as snow. These estimates were very uncertain before the advent of the "snow courses" initiated by the U.S. Soil Conservation Service in the l930s. The extreme variations in average annual temperature for the three stations were only 2.45Â°C, in contrast to the range of 4.23Â°C for the average of the much larger number of stations in l93l-l976.
429 TABLE 7.5 Annual Averages of Precipitation, Temperature, and Virgin Flow of the Colorado River at Lee Ferry, Upper Colorado Region, l93l-l976 Year Precipitation (mm yr"l) Temperature (eC) Flow (l06 m3 yr-l) l93l 268 4.95 9583 l932 355 3.23 2l270 l933 283 3.5l l4009 l934 228 6.75 6958 l935 3l6 5.l4 l4247 l936 349 4.62 l7023 l937 378 3.80 l6948 l938 392 5.04 2l643 l939 30l 4.22 l3666 l940 323 5.7l 10609 l94l 45l 4.ll 22386 l942 357 3.5l 23592 l943 362 4.68 l6l64 l944 334 3.99 l8693 l945 355 3.97 l6542 l946 305 4.08 l2860 l947 4l8 4.39 l9083 l948 346 4.l3 l9258 l949 385 3.32 20l99 l950 320 3.68 l5904 l95l 298 4.60 l4366 l952 424 3.20 25490 l953 273 4.63 l3ll9 l954 308 5.64 9450 l955 29l 3.57 ll333 l956 255 4.3l l3259 l957 429 4.25 24787 l958 323 4.28 20339 l959 294 4.75 l06l9 l960 262 4.49 l3893 l96l 340 4.82 l0432 l962 300 3.38 2l338 l963 305 5.44 l0423 l964 286 3.61 l2527 l965 439 3.30 23329 l966 282 4.06 l3825 l967 350 4.20 l4687 l968 326 3.45 l6854 l969 36l 3.84 l7745 l970 352 4.05 l9002 l97l 302 3.78 l8645 l972 303 3.46 l502l l973 435 2.52 23893 l974 254 4.22 l6355 l975 347 3.51 20447 l976 300 4.27 l4064 Mean 333 4.l8 l6432
430 TABLE 7.6 Annual Averages of Precipitation, Temperature, and Virgin Flow of the Colorado River at Lee Ferry, Upper Colorado Region, l90l-l930 Year Precipitation (mm yr-l) Temperature (Â°C) Annual Sum (m/sec) l90l 229 6.56 l6753 l902 l95 6.7l ll586 l903 285 5.35 l8264 l904 240 6.55 l9297 l905 3l4 6.l0 l9769 l906 370 5.86 23585 l907 350 6.78 28865 l908 274 6.49 l5857 l909 364 6.05 28709 l9l0 233 6.57 l7574 l9ll 327 7.49 l9770 l9l2 3l3 5.05 253ll l9l3 269 5.7l l7852 l9l4 355 6.68 26l76 l9l5 308 6.47 l7303 l9l6 304 7.08 23684 l9l7 346 5.04 29650 l9l8 263 7.32 l895l l9l9 253 6.43 l5372 l920 33l 5.58 27076 l92l 355 6.57 28389 l922 300 6.60 22580 l923 336 6.04 22535 l924 252 5.63 l75l7 l925 338 6.4l l6077 l926 303 6.28 l9554 l927 404 6.88 22963 l928 253 6.58 2l3l4 l929 392 5.46 26432 l930 309 6.44 l836l Mean 306 6.29 2l098 The multiple regression for the earlier period showed a smaller effect of temperature and a somewhat larger effect of precipitation than during l93l-l976. But during the earlier period the standard deviations for the effects of both temperature and precipitation were almost twice as great, and the square of the correlation coefficient was only 0.57.
43l We conclude tentatively that the weakness of the correlation and the relatively larger standard errors from l90l to l930 resulted from the paucity of precipitation and temperature data, the probable inaccuracy of estimates of the quantity of water precipitated as snow, and the probably unrepresentative character of the stations used for average temperatures. In both the earlier and the later periods, variations in precipitation were reflected almost linearly in variations in runoff without the amplification that might be expected from the results obtained on smaller watersheds (Schaake and Kaczmarek, l979) or from Table 7.3. After the postulated climatic change, the mean annual flows at Lee Ferry computed from our multiple regression equation for l93l to l976 would be only 9900 million cubic meters. This last amount is 2060 million cubic meters, or l7%, less than the historically lowest l0-year average annual flow of ll,960 million cubic meters, calculated by Stockton from tree-ring records for the decade from A.D. l584 to A.D. l593 (Dracup, l977). A similar prolonged drought in the middle of the twenty-first century with the same percentage decrease in runoff as in l584-l593 could bring the l0-year annual average flow down to 7200 million cubic meters, or about 44% of the annual average virgin flow from l93l to l976. Although a 2Â°C warming is probably a conservative estimate of the effect over the next hundred years of increase of greenhouse gases for the northern United States, the magnitude and even the sign of possible changes in precipitation are uncertain. According to our regression equation, a l0% increase in average annual precipitation combined with a 2Â°C rise in average temperature would result in an l8% decrease in runoff. To counteract the effects of a 2Â°C warming completely, a 28% increase in precipitation would be required. Clearly, higher spatial resolution in climate models is needed for more credible forecasts of the effects of increasing atmospheric carbon dioxide and other green- house gases on the quantity of water supplies. Possibly, also, seasonal variations from year to year in precipitation and temperature may be more critical in determining Colorado River runoff than annual averaged variations. This possibility could be investigated by statistical analysis of monthly averages of temperature and precipitation for each year against the annual "virgin flow" at Lee Ferry. 7.4 CLIMATE CHANGE AND WATER-RESOURCE SYSTEMS Planning and construction of major water-resource systems have a time constant of 30 to 50 years. In the past, these activities have been based on the explicit assumption of unchanging climate. The probably serious economic and social consequences of a carbon dioxide-induced climatic change within the next 50 to l00 years warrant careful consideration by planners of ways to create more robust and resilient water-resource systems that will, insofar as possible, mitigate these effects.
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