General elements of the balance
5.2 Determining the total water balance
5.2.1 Computing parameters of water balance und ground-water flow
Water-balance studies in various land areas are useful for purposes of agriculture, irrigation, reclamation, hydraulic engineering, and water supply.
1. Determination of separate balance elements on the land surface and in the zones of 2. Hydrodynamic analysis of the ground-water régime.
3. Genetic separation of river hydrographs.
Analogue simulation of ground-water dynamics and hydrological processes has been widely used during the last two decades and complex studies of the dynamics of moisture and heat movement in the unsaturated zone have been made.
Much literature is available on water balances studies, including original research and methods and results of study, the soil water régime and the surface and ground-water balance, as for example: Dokuchaev (1892), Ismailsky (1894) Lebedev, A. F. (1936), Velikanov (1940), Tkachuk (1951), Rode (1952), Thornthwaite and Mather (1955), Favorin (1959), Schoeller (1959), Holmes (1960), Kiselev (1961), Kats (1963), Chapman (1964), Downes (1964), Kohler (1964), Lebedev, A. V. (1963), Phillip (1964, 1969), Ubell (1965), Hagan et al. (1967), Childs (1969), and Ritjema and Wassink (1969).
Studies of surface and ground-water resources ensure thorough definition of the man- ner in which water régimes are formed in river basins and the interrelationships between surface and ground waters. These studies are made with due reference to the analysis of water-balance equations, which reflect the general variations in water storage in the river basins and in the zones of aeration and saturation.
Investigation of the water régime in the zone of aeration is made to show how shallow ground-water bodies are formed, to assess their balance and magnitude, and to resolve a number of practical problems including estimates of moisture available to agricultural crops, design of irrigation systems, and analysis of ground-water recharge.
1. Determination of moisture storage in the soils.
2. Compilation of moisture balance in the zone and ascertaining its relation with the water balance of the unconfined ground-water reservoir and with hydrometeorological factors.
3. Assessment of recharge, evaporation, and discharge of ground water and the moisture migration in the zone.
The following equation can be adopted for the moisture balance in the zone of aeration in a volume element of horizontal cross-section area F square metres (Fig. 5.2.la) bounded by the vertical plane surfaces NI and Nz, by the land surface above, and by the water table below:
Principal items of such a study are:
aeration and saturation.
Studies of the zone of aeration include:
W a A t
+
1000-
Q z At = Cz-
CI+
NAHF 5.2(1)
where :
W u is the rate of infiltration at the land surface (or evaporation if negative), in
"/day ;
QI, Q2 are respectively the rates of ground-water inflow and outflow at the surfaces NI and Nz, in msjday;
F is the area of the flow element for one-dimensional water movement, in m2;
At is the computation interval of time, in days;
5.2 page 1
Ground-water stirdies
Cl, CZ are moisture reserves in the zone of aeration between the land surface and the water table at the beginning and the end of the computation interval of time, respectively, in mm of an equivalent layer of water (Fig. 5.2.lbj;
is the maximum moisture capacity of the soil expressed as a fraction of the volume of soil ;
is the rise or fall of the water table, in mm, in the flow element during the time interval At.
N AH
2 3
-
-. -
+ Observation well.
Initial position of water table.
Subsequent position of water table.
Flow element.
FIG. 5.2.la. Diagram of flow element for observation of soil moisture in the zone of aeration.
If a quantity of confined water E A t flows at a rate of E "/day through a semi-confining layer into the flow element from beneath, then this component is to be considered in the left part of Equation 5.2 (1).
The equation of the water balance at the land surface is:
5.2(2j Y1
-
Y2W a A t = X
-
Z+
KI+
1000 F At-
W1where:
X is precipitation, excluding condensation of atmospheric vapour for the time interval At, in mm;
2 is evapotranspiration from the land surface, in mm;
Ki is value of water-vapour condensation on the land surface and in the zone of aeration, in mm;
YI, YZ are inflow and outflow of surface water (m3/dayj over a land-surface area, F, in m2;
Wi is increase in surface-water storage, in mm.
The remaining symbols are as previously defined.
5.2 page 2
Defining the wafer balance
TI T2
A. Moisture storage during a water-table rise.
7-1 T2
B. Moisture depletion
during a water-table decline.
-
1'- --
-x-x-
Initial water-table position at time T Subsequent water-table position at time T 2' Schematic representation of the water-table change from TI to T2.
FIG. 5.2.lb. Diagram of moisture changes in the soil prism during the time interval from 17' to Tz.
The water balance for the unconfined ground-water régime in the same element of flow, in the absence of leakage through a semi-confining bed (Fig. 5.2.la), is described by the equation
p A H = 1000
" - "
At+
W A t 5.2(3) Fwhere :
p is the specific yield of the soil, expressed as the yield of ground-water in mm of an equivalent surface layer of water per m m decline in the water table, or the recharge per unit rise of water table;
W is the rate of free ground-water recharge from above, in "/day.
The remaining symbols are as defined previously.
In the case of leakage at a rate E, into the flow element NINZ from an underlying aquifer, the term EAt is added to the right-hand side of Equation 5.2 (3).
Adopting the method of finite differences for the calculation of W , short intervals of time At are selected for computation during which either recharge, I (nim/day), to the ground-water reservoir from infiltration, or discharge, IL ("/day), from the ground- water reservoir through evaporation, prevails.
Under such conditions, water-level fluctuation analysis provides values of recharge IAz to the ground-water reservoir, or discharge, u n V, from the reservoir as evaporation (or moisture flux, ascending into the zone of aeration).
The value of free ground-water recharge from above over a time period At
=
A Z+
A V is therefore:
5.2(4) W A t = IAt
-
u A V5.2 pugc 3
Groimd-water studies
The increase, B, of moisture stored in the zone between the land surface and the minimum position of the water table over the given interval of time At (between the land surface and the line 1-1 in Figure 5.2.lb. A) may be expressed as follows:
B = Ca
-
CI+
uAH 5.2(5)If the naturally retained moisture content or specific retention, &,u, where O is porosity and ,u is specific yield, is written V,, then the increase in non-drainable moisture, WZ, during the time interval At in the element is:
5.2(6) From Equations 5.2(1) and 5.2(2) the total water-balance equation may be derived for the zone bounded by the land surface and the first aquiclude:
AtS.1000
-
At 5.2(7)Y1
-
Y2~ / x A H + WI+ W Z = X-Z-tK1+1000 ~ F
In case of leakage from deep-seated strata through a semi-confining bed, the term E A t The quantity of free ground-water recharge from above during the time interval At js added to the right-hand side of Equation 5.2(7).
is found from the expression:
From observations of soil moisture in the range from the land surface to the water The moisture storage (hm, in mm) in the zone of aeration is calculated from the table the curve for the distribution of moisture is constructed (Fig. 5.2.1~).
formula:
5.2(9) where :
Vo is specific retention as a fraction of the unit of soil volume;
Ahi is depth interval (cm).
Average soil moisture in a multilayered formation is calculated as a weighted average value taking account of the thicknesses and volume weights of separate soil layers through the vertical section. Knowing moisture storages from Equation 5.2(9) at the beginning and end of the observation period, W Z is calculated from their difference. The technique for determining soil moisture throughout the zone of aeration is discussed in Section 7.4.5.
The following installations are required at water-balance sites to study the elements of the unconfined ground-water balance factors influencing such a balance:
1. Observation wells located along a line of single-dimensional flow (Fig. 5.2.la) or distributed in a square in the case of two-dimensional flow.
2. Points of soil sampling for moisture determination if the drying/weighing method is used.
3. Moisture meters based on the use of radioactive isotopes (the gamma method or neutron method).
4. A meteorological station comprising rain gauges or in winter snow-gauging stakes at which snow density is measured regularly; soil-moisture instruments; evaporation pans for comparison of the evapotranspiration with the potential evaporation.
If a water balance site has been selected on a slope, simple run-off gauges must be installed for studying the overland flow.
5.2 page 4
Defining the water balance
Section
A A A A A A A A A A A
Shading denotes moisture- calculation intervals, Ah,
- I
Moisture content
0 Sampling points.
l m
L o a m with soil.Sandy loam.
Sand with gravel.
Sand, homogeneous, fine, Sand, heterogeneous.
Z
FIG. 5.2.1~. Soil-moisture profile in the zone of aeration.
Thermometric observations within soils in the zone of aeration are essential for the analysis of the moisture régime. From the observed data relating to the elements of the water balance at the land surface, the monthly value of moisture exchange, WaAt, between the zone of aeration and the atmosphere is calculated from Equation 5.2(2) and the value of free ground-water recharge from above for the same month from Equation 5.2( 8).
The value of the recharge of free ground water for control can be calculated on the basis of the hydrodynamical analysis of free ground-water-level fluctuations, if data are available for traverses across the water-balance site (Fig. 5.2.la).
The negative value of free ground-water recharge (-WAt) obtained for a short interval of time At will correspond to the discharge of ground water into the zone of aeration by evapotranspiration.
Knowing the variation of free ground-water level AHfor the interval of time At and the
5.2 page 5
Ground-water stirdies
value of recharge WAt, the difference between inflow and outflow for the same time is found from Equation 5.2(3), the difference being equal to [(QI
-
Qz)/F]At.If [(QI
-
Qz)/F]At < O, recharge of ground-water flow is taking place in the given element of flow. Since the weighted average value of the difference [(QI - Qz)/F]At over the catchment area corresponds to the average layer of ground-water flow and charac- terizes natural ground-water conditions, therefore, a knowledge of this difference at or near each water-level observation well is of practical and scientific interest.The value of recharge from above, WAt, can be determined from the experimental observations in the selected flow element (Fig. 5.2.la). This in turn leads to the value WoAt of moisture exchange between the zone of aeration and the atmosphere from Equa- tion 5.2(8). A knowledge of this value assists in the interpretation of vertical moisture migration in the zone of aeration, the determination of the quantity of moisture pene- trating upwards or downwards through the bottom of the root-holding layer of soil, or the estimation of evapotranspiration (Lebedev, 1963).
For the solution of these problems, auxiliary moisture balances are recommended either for the genetic soil horizons or at depths of moisture sampling. Penetration of moisture WoAt from above, initial and final moisture storages derived from moisture observation records are the known elements of such balances. Moisture discharge through the bottom of each balance layer is the unknown element of a balance.
The total water balance of a soil prism expressed by Equation 5.2(7) is made up of three water balances: one for the land surface from Equation 5.2(2); one for the zone of aeration from Equation 5.2(8), and one for the saturated zone from Equation 5.2(3).
Determination of the difference between the inflow and outflow of free ground water [(QI - Qz)/F]At presents the greatest problem in all balance calculations.
If the water-balance site is geologically uniform and has been studied hydrogeologically, determination of QI and Qz from ground-water equations may not prove difficult, but, in the more common case where the site has not been studied adequately, it is advisable to determine hydrogeological parameters (the diffusivity in particular) using records of water-level fluctuations in observation wells. Then, knowing this parameter and using subsequent water-level fluctuations in observation wells, the recharge value WAt can be determined (see Section 6.2).
From records of recharge (Wdt)i and variation of free ground-water storage (pAH)r the value [(QI
-
Qzj/F]At can be determined for a well by means of Equation 5.2.(3).W h e n only data on water-level fluctuations in wells and experimental data on water- balance elements at the land surface and in the zone of aeration are available, then the value WAt is determined first from Equation 5.2(8) and then the value [(QI
-
Qz)/F]Atfrom Equation 5.2(3).
Statistical analysis is adapted for determining the required number of soil sampling points for moisture analysis or the points for installation of moisture meters with the aim of obtaining average values of a specified accuracy and probability.