The Global Water Budget
The hydrological cycle can be described quantitatively by applying the principle of conservation of mass，w hich often is referred to as a water balance or water budget w hen used in this w ay. A simple statement of conservation of mass for any particular compartment ( usually referred to as a control volume) is that the time rate of change of mass stored within the compartment is equal to the difference betw een the inflow rate and the outflow rate. For example，if w e are adding tw o grams of w ater to a bucket every minute and one gram of w ater is leaking out each minute，then the mass stored w ithin the bucket is increasing at the rate of one gram per minute. Symbolically，w e can w rite this as:
w here M is mass w ithin the control volume ［M ］; t is time ［T ］; I' is mass inflow rate［MT－ 1］; O' is mass outflow rate ［MT－ 1］. The expressions in square brackets are the mass- length-time dimensions associated w ith the defined quantity; for example，the dimensions of I' are mass per time or ［MT－ 1］.
In many instances，the density of w ater can be taken as approximately constant and the conservation law expressed in terms of volume. The terms involving mass in Equation ( 1. 1) can be expressed in terms of density times volume and density can be canceled from both sides of the equation. Thus，Equation ( 1. 1) can be rew ritten as:
Where V is volume of w ater w ithin the control volume ［L3］; I is volume inflow rate ［L3T－ 1］; O is volume outflow rate ［L3T－ 1］.
We can construct a global w ater budget by applying the principle of mass conservation ［Equation ( 1. 2) ］，using the continents as our control volume. The quantity V is then the volume of w ater stored on or w ithin the continental land masses. Inflow is precipitation and outflow consists of evapotranspiration ( evaporation and transpiration combined ) and runoff ( both surface water and groundwater) . Note that in addition to ignoring density variations we must express the rate of evaporation or transpiration — outflow s of w ater vapor from the continents to the atmosphere — in“liquid w ater equivalent”or LWE units. Otherw ise，density is varying ( w ater vapor is much less dense than liquid w ater) ，and mass，rather than volume， is the conserved quantity.
If w e consider only average annual conditions for our w ater budget，the dV / dt term in Equation ( 1. 2) becomes negligible. That is，over a period of years the average amount of w ater stored as ice ( icecaps and glaciers ) ，as surface w ater ( rivers and lakes ) and as subsurface w ater ( groundw ater) does not change significantly. Over much longer time periods such as centuries or millennia this may not be true if there is a dramatic shift in climatic conditions. If there is no change in storage over time，w e say that the system is at steady state. For any given control volume at steady state，a completely general w ater budget equation can be w ritten ( using bars over the terms to indicate that they are annual average quantities) :
w here
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is average volume of w ater stored，and assumed to be constant;水文地质专业英语
is average precipitation rate;水文地质专业英语
is average surface w ater inflow rate;水文地质专业英语
is average groundw ater inflowrate;水文地质专业英语
is average surface w ater outflow rate;水文地质专业英语
is average groundw ater outflow rate; et isaverage evapotranspiration rate. All terms in the equation have dimensions of volume per time［L3T－ 1］. For the continents，we will simplify Equation ( 1. 3) by neglecting the inflows and outflow s of groundw ater，because they tend to be very small. We also w ill neglect surface w ater inflow s，because surface w ater flow s from the continents to the oceans，and w ill refer to surface w ater outflow s as runoff，rs. With these simplifications，Equation ( 1. 3) becomes:or
w here
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s average precipitation rate ［L3T－ 1］;水文地质专业英语
is average surface runoff rate ［L3T－ 1］;水文地质专业英语
isaverage evapotranspiration rate ［L3T－ 1］.To quantify the global hydrological cycle w e can examine the relative sizes of the various storage compartments and the magnitudes of the various flow s to and from these compartments ( Figure 1. 2) . Nearly 97% of all water on the Earth is stored in the oceans，while only about 0. 001% is stored in the atmosphere ( Table 1. 1 ) . Considering only freshw ater ( defined as having a concentration of total dissolved solids less than 0. 5 parts per thousand and considered potable ) ，w hich accounts for about 2. 5% of the total storage，69. 6% is contained in the polar icecaps and glaciers w hile 30. 1% is contained in groundw ater. The freshw ater contained in lakes，streams，rivers，and marshes represents only 0. 296% of all freshw ater and 0. 008% ( 80 drops in a million! ) of all w ater on the Earth. Another useful concept for thinking about the size of the various reservoirs in relation to the flow s of w ater into and out of them is the residence time. The residence time，tr［T］，is a measure of how long，on average，a molecule of w ater spends in that reservoir before moving on to another reservoir of the hydrological cycle. The residence time is easily calculated for systems at steady state，w hen the inflow and outflow rates are identical:
The residence time has dimensions of time，because volume divided by volume per time is time. The residence time provides an indication of the time scales for flushing a solute out of that particular reservoir. Water in the oceans has a residence time approaching 3000 years， w hile w ater in the atmosphere has a residence time of only 0. 02 years or about 8 days; the residence time of w ater in rivers is 0. 05 years or about 18 days ( Table 1. 1) .
Figure 1. 2 Flows within the hydrological cycle Units are relative to the annual precipitation on the land surface ( 100 = 119 × 1012m3/ a) . Upward arrows depict flows to the atmosphere，downward arrows depict flows to land or oceans，and horizontal arrows indicate lateral flows
Table 1. 1 Sizes and residence times for major reservoirs in the hydrological cycle
The w ater budget for all the land areas of the w orld is:
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= 800 mm，水文地质专业英语
= 310 mm，and水文地质专业英语
= 490 mm ( Figure 1. 2) ( Note that w e now are referring to the volumes divided by the areas being considered. It is sometimes more convenient to use depth rather than total volume， because the volumes can be quite large; also， w e are probably more familiar w ith the statement，“20 mm of precipitation w as recorded at Smith Airport ” than “Smith Airport received 20000 m3of w ater”) . On average，39% of precipitation to the continents runs off and 61% is returned to the atmosphere through evapotranspiration. In other w ords，the runoff ratio水文地质专业英语
is equal to 0. 39. The balance is，of course，affected by many topographic and climaticfactors and the budgets for individual continents can be quite different from the average ( Table1. 2) . The budget for North America is水文地质专业英语
= 670 mm，水文地质专业英语
= 290 mm，and水文地质专业英语
= 380 mm. Thus，inNorth America 43% of precipitation runs off and 57% evapotranspires on average.Table 1. 2 Average annual water budget for the continents excluding Antarctica*
* Values for average annual precipitation，runoff，and evapotranspiration are reported as depths of water over each land area. The total volume may be calculated by converting the depths to km and multiplying by the land areas. Note that several estimates of these quantities exist，all of which are uncertain to some degree. ( Source: Hornberger et al. ，1998)
水文地质专业英语