6
Water Cycling

The exchange of water among the oceans, atmosphere, and upper crust of the Earth constitutes the hydrologic cycle. Whereas most of the storage and exchange of water occurs within and above the oceans (Figure 6.1), understanding temporal and spatial variations in water exchange on land is of critical and world wide environmental and economic importance. Measurements of changes in land-based water exchange are of use in long-term weather prediction, global climate modeling, assessment of the health of agricultural lands, and major groundwater supplies. Space-based measurements of the temporal variations in gravity have the ability to quantify variations in storage of continental components of the hydrologic cycle that are not currently known with sufficient accuracy. Satellite gravity measurements cannot, by themselves, discriminate between changes in water on the surface, in the soil, or in the water table. Instead, they provide constraints on changes of the total water in vertical columns, integrated from the Earth's surface down through the base of the water table. In areas undergoing large scale aquifer depletion, this quantity will be dominated by the groundwater signal. In other areas, auxiliary land-based measurements of seasonal changes in groundwater levels offer the potential to separate the groundwater component from the soil water component.

WATER TRANSFER TO THE ATMOSPHERE

The transfer of water to the atmosphere from the land surface is a complex process that is not only a part of the hydrologic cycle but also a key control of energy cycling on the Earth. An SST mission could provide seasonal values of changes in water mass with 10-mm uncertainty over about 550,000 km2 (Figure B.4), and the annually-varying amplitude could be determined at an accuracy of 10 mm over about 250,000 km2 (Figure B.2; see Appendix B for a description of how these errors are estimated). For an SSI mission, the results improve to give a 10-mm monthly value over 150,000 km2 and a 10-mm annually-varying amplitude over 100,000 km2. Measurements of mass and energy exchange at this spatial resolution would be useful for long-term weather forecasting on continental and whole-Earth scales, since this exchange has a significant influence on weather processes. For both missions, conversion of water mass changes to estimates of land/atmosphere mass transfer will require auxiliary land-based measurements. They would also be of significant use to global-climate modelers.

Water transfer to the atmosphere can occur through a number of processes. Evaporation occurs from moist soils, plant surfaces, snow bodies, and lakes and rivers. Sublimation (the direct transfer of water from solid to



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Satellite Gravity and the Geosphere: Contributions to the Study of the Solid Earth and its Fluid Envelope 6 Water Cycling The exchange of water among the oceans, atmosphere, and upper crust of the Earth constitutes the hydrologic cycle. Whereas most of the storage and exchange of water occurs within and above the oceans (Figure 6.1), understanding temporal and spatial variations in water exchange on land is of critical and world wide environmental and economic importance. Measurements of changes in land-based water exchange are of use in long-term weather prediction, global climate modeling, assessment of the health of agricultural lands, and major groundwater supplies. Space-based measurements of the temporal variations in gravity have the ability to quantify variations in storage of continental components of the hydrologic cycle that are not currently known with sufficient accuracy. Satellite gravity measurements cannot, by themselves, discriminate between changes in water on the surface, in the soil, or in the water table. Instead, they provide constraints on changes of the total water in vertical columns, integrated from the Earth's surface down through the base of the water table. In areas undergoing large scale aquifer depletion, this quantity will be dominated by the groundwater signal. In other areas, auxiliary land-based measurements of seasonal changes in groundwater levels offer the potential to separate the groundwater component from the soil water component. WATER TRANSFER TO THE ATMOSPHERE The transfer of water to the atmosphere from the land surface is a complex process that is not only a part of the hydrologic cycle but also a key control of energy cycling on the Earth. An SST mission could provide seasonal values of changes in water mass with 10-mm uncertainty over about 550,000 km2 (Figure B.4), and the annually-varying amplitude could be determined at an accuracy of 10 mm over about 250,000 km2 (Figure B.2; see Appendix B for a description of how these errors are estimated). For an SSI mission, the results improve to give a 10-mm monthly value over 150,000 km2 and a 10-mm annually-varying amplitude over 100,000 km2. Measurements of mass and energy exchange at this spatial resolution would be useful for long-term weather forecasting on continental and whole-Earth scales, since this exchange has a significant influence on weather processes. For both missions, conversion of water mass changes to estimates of land/atmosphere mass transfer will require auxiliary land-based measurements. They would also be of significant use to global-climate modelers. Water transfer to the atmosphere can occur through a number of processes. Evaporation occurs from moist soils, plant surfaces, snow bodies, and lakes and rivers. Sublimation (the direct transfer of water from solid to

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Satellite Gravity and the Geosphere: Contributions to the Study of the Solid Earth and its Fluid Envelope FIGURE 6.1 The global hydrologic cycle, illustrating storages in 106 cubic kilometers (boxed) and fluxes in 106 cubic kilometers per year. Figure from NRC (1986); Berner and Berner (1987). gas form without melting) occurs from snow bodies. Transpiration (the transfer of water from plant matter to the atmosphere primarily through the leaves of plants) is critically important in forested and agricultural lands. Some of these processes are influenced by human activity. Deforestation and agricultural development affect the distribution and amount of biomass on Earth and alter both the storage of water in soils and rivers and the transfer of water to the atmosphere by evaporation and transpiration (evaporation and transpiration are often lumped as evapotranspiration). Irrigation of agricultural lands redistributes surface water, transfers groundwater to the land surface, and accelerates evapotranspiration. While continental-scale averages of this transfer are somewhat well known (Figure 6.1), spatial and temporal changes in these processes are imprecisely known owing to the difficulty of direct measurement. Also, measurements made directly on the land surface are point measurements and, in general, are so widely spaced that it is not possible to derive meaningful estimates of spatial variations. Over spatial scales of several hundred thousand square kilometers, measurements of seasonal changes in water mass with a resolution of 10-30 mm in thickness would be useful for weather forecasting, climate modeling, and soil moisture and aquifer assessments. Measurements of water mass changes at this resolution and spatial scale should be possible with either an SST or SSI mission. The amount of water mass transferred from the land surface to the atmosphere depends strongly upon such factors as soil moisture, biomass, air temperature, and air humidity. The global average annual amount of water transfer from the land surface to the atmosphere is about the equivalent of a column of water of 0.5 m. Because gravity depends directly on mass, variations in this transfer should have a direct impact on gravity. Currently, spatial and temporal variations in this transfer are typically inferred from empirically derived water-balance formulas (such as the Thornthwaite formula, [Dunne and Leopold, 1978]) whose accuracy is questionable. However, these empirical formulas suggest that annual and spatial variations are large. For example, in estimates of the fluctuations in global soil-water mass (Figure 6.2) the seasonal (annual) variations dominate up to degree 10; at higher degrees the contributions from the seasonal and non-

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Satellite Gravity and the Geosphere: Contributions to the Study of the Solid Earth and its Fluid Envelope seasonal terms are approximately equal. Spatial and temporal variations are as large as 0.3 m. This would produce a geoid signal that would vary annually by as much as 6 mm (Figure 6.3). The amplitude of these signals is well above the uncertainties of measurement error for a 5-year SST mission at values of l below 30, and a 5-year SSI mission at values of l below 40 (Figures 4.5 and 4.6). In theory, a five-year SST mission at an altitude of 400 km should allow us to resolve annual changes in water mass in the subsurface equivalent to a 1-mm column of water for an area of 1,500,000 km  and annual changes equivalent to a 10-mm column of water for an area of 250,000 km2 (Figure B.2). For the nominal SSI mission, the 1-mm error could be achieved over about 125,000 km2, and a 10-mm error for an area of about 80,000 km2. As discussed in Chapter 4, these accuracy estimates do not consider the problem of separating the hydrological gravity effects from the effects of other geophysical processes. The effect of changes in oceanic mass could cause problems for hydrological estimates at locations near the shore. Atmospheric pressure could cause problems anywhere, although the gravitational effects of atmospheric pressure could be largely removed using global, gridded pressure data available from meteorological centers. Nevertheless, any error in the pressure data would map directly into an error in the hydrologic estimates for that region. For example, a 0.3-mbar pressure error would correspond to a 3-mm  error in the inferred water storage. The accuracy of future pressure data over continental regions is difficult to predict; it could range upward from a few tenths of a mbar, depending on the location (see Chapter 8). Consequently, detection of changes in water mass of less than a few millimeters must be accompanied by accurate atmospheric pressure measurements. FIGURE 6.2 The rms of the degree variances found from the monthly soil moisture data from 1987-1991, showing the annually- varying and the non-annual contributions. Note that the non-annual contributions are about one-half to two-thirds the size of the annually-varying effects for l<10; but that they are of equal importance at higher degrees (i.e., shorter wavelengths). See Appendix B for a detailed discussion of the accuracy of the generic missions.

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Satellite Gravity and the Geosphere: Contributions to the Study of the Solid Earth and its Fluid Envelope FIGURE 6.3 The annually-varying contributions to the geoid from changes in continental water storage, as estimated from the soil moisture data set for 1987-1991. Top panel: the amplitude of cosine(ωt), where ω = 1 cycle/yr and t = 0 on January 1. Bottom panel: the amplitude of sine(ωt).

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Satellite Gravity and the Geosphere: Contributions to the Study of the Solid Earth and its Fluid Envelope While detection of water-mass changes with a resolution of 10 mm would be extremely valuable for estimating sub-continental energy and water-mass exchange between the Earth's surface and the atmosphere, it should be noted that this signal does not strictly represent land-atmosphere mass and energy exchange. The detected water-mass changes largely reflect the combined changes in water mass in groundwater and soil moisture. Water mass changes in groundwater are generally not directly linked with atmospheric exchange and are strongly influenced by direct transfer and exchange with surface water. Estimates of mass exchange between the land surface and the atmosphere will require the use of existing land-based measurements of soil moisture and groundwater levels. Monitoring groundwater levels over large regional areas would enable separation of the groundwater influence on water mass changes. Since land/ atmosphere mass exchanges are dominated by soil moisture changes, point measurement of soil moisture will provide a partial control on the mass changes inferred from gravity measurements. SOIL MOISTURE INVENTORY Crop abundance in agricultural regions depends on proper levels of soil moisture. About 15 million square kilometers, or 10% of the world's land surface, is used for growing crops (World Resources Institute, 1990). More than four-fifths of these lands and more than nine-tenths of lands outside Asia are not irrigated and depend wholly upon precipitation. Agricultural production is thus highly dependent upon annual and seasonal variations in precipitation. Yearly projections of agricultural production would be greatly improved by measurements of soil moisture on a semi-annual basis. Such information would be highly valuable to commodity futures markets and to those world wide agencies that assess food availability, particularly if we can provide seasonal measurements with a resolution of 10-30 mm over an area of a few hundred thousand square kilometers (Figures 4.5 and 4.6). The seasonal variability in soil moisture ranges widely, depending on the plant cover, soil type, and precipitation. Typical seasonal variations in water thickness are on the order of 150 mm (Dunne and Leopold, 1978). Seasonal variations in soil moisture of one tenth this magnitude should be detectable from a SST mission at 400-km altitude at a spatial resolution of roughly 300,000 km2 (Figure B.2). For a nominal SSI mission, the area that can be resolved is 90,000 km2. The potential exists for space-based gravity measurements to provide a world wide inventory of the ability of agricultural lands to produce high yields in a given year. As in the case of inferring land-atmosphere water exchange from gravity, the use of spaced-based gravity to infer changes in soil moisture levels has an inherent ambiguity due to other water-related influences. Inferences of seasonal changes in soil moisture from gravity would be abetted by land-based measurements of groundwater levels and point measurements of soil moisture. GRAVITY AND THE GEWEX CONTINENTAL-SCALE INTERNATIONAL PROJECT Estimates of evapotranspiration rates and soil moisture levels would be of direct use to the GEWEX (Global Energy and Water Cycle Experiment) Continental-Scale International Project (GCIP). Satellite-based estimates of hydrologic properties at the large scales (such as the Mississippi River basin scale), which can be inferred from a satellite gravity mission, are considered an essential part of GCIP. The overall goal of GCIP, which was formed in 1990, is to improve climate models by bridging the gap between small scales appropriate for modeling discrete processes over land and large scales practical for modeling the global climate system. The primary objectives of GCIP are to determine the variability of the Earth's hydrological cycle and energy-exchange budget over a continental scale; to develop and validate techniques for coupling atmospheric and surficial hydrological processes in climate models; and to provide a basis for translating the effects of future climate change to impacts on regional water resources. The initial focus area of GCIP is the Mississippi River basin, which was selected because of its extensive hydrological and meteorological observation network. Both the SST and SSI missions would be able to provide estimates of changes in water mass at a resolution of 10-30 mm over the spatial scale of the initial GCIP focus area (Figure 4.5). Part of the initial phase of GCIP is to build up the science base and technical expertise on regional and continental-scale processes. The surface-based, model-derived, and satellite-based data will be used to develop models that couple complex atmospheric and surficial hydrological processes on a wide range of spatial scales. A second phase of GCIP will focus on extending this capability to the global scale, using observations that will be forthcoming near the turn

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Satellite Gravity and the Geosphere: Contributions to the Study of the Solid Earth and its Fluid Envelope of the century from the next generation of Earth-observing satellites. SNOWLOAD AND ASSOCIATED RUNOFF Estimates of snowload in mountainous regions are important in assessing the level of potential flood hazard associated with snow melt. Prediction of flood magnitude associated with spring snow melt is highly dependent upon the water content of the snowpack. Currently, the annual snow  load in mountainous regions can be monitored to about 300-mm accuracy (approximately 60 mm water equivalent) using passive-microwave remote sensing. The data are validated using point measurements from surface stations located at wide spatial intervals. These point measurements typically overestimate snow cover because they are often biased to regions of larger-than-mean snow accumulation. Snow  hydrologists would find useful a gravity mission that could estimate integrated water equivalent, thus providing an independent validation of the radiometer data. This is desirable in the Rocky Mountains (500 km × 1,000 km) but is especially needed in the Tien Shan and Pamirs (1,000 km × 2,000 km) of central Asia where validation points are currently very sparse. For the SST case, the accuracies for the Colorado Rockies and the Tien Shan are about 10-20 mm and 2-3 mm, every 90 days, respectively. For SSI, they become about 0.35 mm and 0.25 mm, respectively. Practical flood hazard assessment using space-based gravity would likely require 30 day or more frequent sampling. AQUIFERS In many regions of the world, groundwater is the primary source for irrigation. Groundwater reserves are commonly being used faster than they can be replenished in these regions. In the United States alone, groundwater reserves are being depleted in vast regions of the western U.S. and throughout Georgia and Florida. The most publicized U.S. example of groundwater depletion is the High Plains aquifer (formerly called the Ogallala aquifer) in the Great Plains region (Figure 6.4). In the late 1970s this aquifer supplied over a quarter of the groundwater used for irrigation in the United States (Gleick, 1993). The estimated average area-weighted water-level decline from about 1940 to 1980 was 3.0 m, which represents an average water mass decline in the vertical of 11 mm/yr (Dugan and Cox, 1994). Since 1980, water levels have continued to decline, but at a slower rate. The estimated average area-weighted water-level decline from 1980 to 1993 was 0.6 m, representing an average rate of mass decline of 7 mm/yr. The lower rate of decline since 1980 is associated with above normal precipitation and reductions in irrigation use. By the early 1990s, severe depletion of the aquifer was a significant factor in driving much of the region out of agricultural production. Saudi Arabia, an exporter of wheat, depends upon groundwater reserves that are being depleted. During the latter half of the 1980s, groundwater pumping exceeded estimated recharge in the country by a factor of five. Groundwater overdrafting is also widespread in many regions of India, China, Mexico, northern Africa, and the former Soviet Union. Groundwater levels are falling up to one meter per year in parts of northern China. Heavy pumping in portions of southern India dropped water levels by as much as 25-30 m in the previous decade. Future growth in the agricultural use of arid and semi-arid lands partly fueled by population growth and partly influenced by a desire for self-sufficiency of agriculture and economic diversification will further increase the overdrafting of aquifers world wide. For example, in the near future Libya plans to irrigate some 200,000 hectares with water drawn from aquifers that receive little recharge. Annual space-based gravity surveys offer the potential to measure long-term declines in the world's large aquifers. These declines, the equivalent of tens to hundreds of millimeters of water mass per year, are large enough to be detectable; indeed, in regions of large-scale groundwater withdrawal, the associated gravity change should be the dominant signal in a space-based measurement. Given an SST mission at an altitude of 400 km, secular changes in water mass on the order of 10 mm  per year should be readily detectable in a region the size of the High Plains aquifer (Figure 4.5; Figure B. ). An SSI mission could do more than an order of magnitude better than this, although the interpretation of the data would probably be limited by contamination from the effects of other geophysical processes. CONCLUSIONS Gravity missions can provide centimeter and better accuracies for the changes in the thickness of water stored on continents at spatial scales of several

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Satellite Gravity and the Geosphere: Contributions to the Study of the Solid Earth and its Fluid Envelope FIGURE 6.4 Groundwater overdraft in the High Plains aquifer, predevelopment (approximately 1940) to 1980 (modified from Dugan and Cox, 1994). Center circle represents an area of 250,000 km2 for reference. tens of thousands of kilometers and larger. The amplitude of these signals is well above the uncertainties of measurement error for a 5-year SST mission at values of l below 30, and a 5-year SSI mission at values of l below 40. Estimates would be of direct use to GEWEXGCIP. Gravity measurements of changes in water storage are important to hydrologists for making the connection between hydrological processes at traditional hydrological length scales (tens of kilometers and less) and those of longer scales useful for estimating global water and energy balances. Gravity measurements of changes in water storage are important to meteorologists because of the impact of soil moisture on evapotranspiration. Seasonal variations in soil moisture of 10-30 mm  should be detectable from an SST mission at 400-km altitude at a spatial resolution of roughly 300,000 km2. For an SSI mission, the area that can be resolved is 90,000 km2. Both monitoring and prediction are technologically feasible and hold promise for the mitigation of natural hazards and ongoing evaluation of the state of one of the world's most important renewable resources, its fresh water. Measurements of gravity variations can help monitor aquifer depletion. Gravity results can aid in monitoring snow pack, predicting floods and the runoff available for irrigation, and assessing agricultural productivity on large scales.

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