General elements of the balance
5.3 Computation of the unconfined ground- water balance
The unconfined ground-water balance over the time interval At is computed for the zone which ranges from the highest level of the capillary fringe to the top of the underlying impervious bed.
Among positive elements of this balance are: infiltration reaching the capillary fringe, IAz; unconfined ground-water inflow in a horizontal direction Q I ; and confined water leakage from the underlying aquifers Qb,1.
The negative elements of the balance are evapotranspiration from the top of the capillary fringe above the water table U A V, including ascending capillary moisture flow in the zone of aeration; unconfined ground-water outflow, Qz, in a horizontal direction;
and unconfined ground-water outflow, Qb,z, downwards as leakage to underlying semi-confined aquifers.
Because the algebraic sum of the infiltration value IAz and evaporation from the water table, uAV, is equal to the value of recharge W4t from above, computation of the un- confined ground-water balance commonly requires one of the following approaches : 1. Hydrodynamic analysis of the unconfined ground-water régime wherein knowledge 2. Experimental determination of all the components of the water balance beginning From Equation 5.2(3) and the above-mentioned components of the unconfined ground- water balance the equation can be written as:
of the individual balance components is not required.
with the recharge value, expressed in its general form by Equation 5.2(8).
At
+
I A Z-
u A V 5.3(1) where p4H is the change in unconfined ground-water storage at the balance plot (for an elemental area F) for the time interval At. The other symbols are the same as in Equations 5.2(3) and 5.2(4).Consider the first method of compiling the unconfined ground-water balance from observations of the ground-water régime. Throughout the catchment area of the basin, flow elements for computation are defined by drawing the mid-lines between adjacent pairs of observation wells installed to penetrate the unconfined ground-water régime.
With unconfined ground-water leakage into a semi-confined aquifer, additional observa- tion wells may need to be installed in the flow elements near any pumped wells tapping the underlying semi-confined (interstratal) aquifer.
From observations on the water levels of the unconfined aquifer and the underlying aquifer the vertical gradient of the flow is determined, from which the rate of unconfined ground-water leakage into or from the underlying semi-confined aquifer is calculated by:
5.3(2)
Kb is the vertical hydraulic conductivity of the semi-confining layer;
A H b is the head difference between water levels in the unconfined and confined parts of the ground-water system, determined from two observation wells in the middle of the flow element;
is thickness of the semi-confining layer;
is the area of the flow element.
m F
Values of unconfined ground-water recharge from above for the given flow element are calculated from observed fluctuations of water levels in water-table wells.
5.3 page I
Ground-water studies
Various equations for analytical and finite-difference methods are given in Sections 6.1 and 6.2. In the following paragraphs the discussion is therefore restricted to the sequence for computing and compiling the elements in the water balance for the unconfined part of the ground-water régime for a year, using the method of finite differences:
1. The annual trend of water-level fluctuations in the unconfined ground-water system, as observed in the middle well (Fig. 5.2.la), is divided into separate intervals of time At within which the level rises or falls approximately at a constant rate.
2. Data on water levels for each interval of time At are entered in Table 5.3a where wells 1, 2 and 3 correspond to the upper, middle and lower cross-sections of the flow respectively.
To account for changes in the thickness of the unconfined ground-water zone in each section as given in Table 5.3a, the corresponding values of h are determined.
3. Observations of water level and of the saturation deficit or specific yield, fi, of soils are used for calculating changes in unconfinedground-water storage, A =fi(AH/At) ; for computing the flow rates QI and Q Z values of the hydraulic conductivity, K, and the distances h, 12 between the wells are used.
4. After determining the recharge rate, W, for each time interval, Af, the unconfined ground-water balance for a year is compiled (Table 5.3b and Fig. 5.3a). Vertical leakage of ground water from one aquifer into another is here considered absent;
if this is not the case additional columns of the table with values Qb and Q b At calculated from Equation 5.3(2) are needed.
After summing the unconfined ground-water balance elements the annual balance is obtained. From such a calculation a number of conclusions can be made: (a) on the sources of local ground-water flow, i.e. the difference between the outflow and the inflow of ground water for the flow element; (b) on losses of precipitation which has infiltrated to the water table, or run off or evaporated; and (c) on the volume and annual changes in subsurface flow.
If there are adequate flow elements in a river basin (for example, not less than 10 for an area of 20-30 kmz), under similar conditions of lithology and relief, then the average values, weighted over the drainage area (IAr)av, and (uAV)a, and (fidH)av per annum can be established from the unconfined ground-water recharge values.
Knowing these weighted average values, Equation 5.2(3) can be used to determine the average annual mean layer of ground-water flow, weighted (over the basin), in the absence of ground-water leakage into the underlying strata:
where QII is the total ground-water outflow from the basin.
This relationship is derived from Equation 5.2(3) and agrees with the condition that the weighted (over the area) average value of the difference At) corresponds to the average value of the ground-water flow because there is no unconfined ground- water contribution in the basin from the adjoining basins, i.e. unconfined ground-water flow to the basin QI = O.
From Equation 5.3(3) the modulus of ground-water flow, (QII/F). can be calculated, and subsequently the magnitude of the unconfined ground-water resource.
If there are few computation flow elements in the basin and appreciable differences in the depths to unconfined ground water are noted, then the correlations between seasonal infiltration IAt and unconfined ground-water evaporation U A V with the depth to water must first be found. Commonly a graphic expression of this relationship is adequate.
Using these relationships and maps of unconfined ground-water depths, values of IAr and ud V over the watershed area can be extrapolated. From such extrapolations a table or a map showing the areas of various depths to water and corresponding values of
(
QzF
av5.3 pogt? 2
Ground-water studies
TABLE 5.3a. Determination of recharge rates for the unconfined ground-water régime at a balance plot in an area near Moscow (U.S.S.R.)
Water-level altitude, H, and flow thickness, h (in m) Water-level Calculation values [eq. 5.2 (3)1
Date altitude, H, and Water-level __-
Defining the water balance
s! 2 E E
Infiltration of precipitation to water table.
Difference between unconfined ground-water inflow and outflow.
Evapotranspiration from unconfined ground water.
Change in ground-water level.
FIG. 5.3a. Dynamics of elements of unconfined ground-water balance for 1951-52 at a balance plot.
unconfined ground-water recharge for seasons can be constructed. These allow the weighted average values of the same elements of the balance to be determined.
W h e n there is unconfined ground-water leakage into interstratal aquifers, representative plots where leakage occurs are selected. For these plots the values [(QI
-
Qz)/F]dt and[(Qb.l - Qb,z)/F]At are determined and these are averaged over the area.
The second method of compiling the water balance for the unconfined ground-water reservoir is based on the experimental determination of balance elements. This method is most commonly used in water-economy practice, for example in irrigation, when it is required to define the water-balance components with a view to controlling the balance.
The quantity of infiltration of precipitatiqn down to the water table is determined commonly from the rate of water-level rise A H caused by this infiltration, by multi- plying the value A H by the specific yield, p. This can be adopted when no canal, river or other hydraulic boundary exists near the observation wells; similar water-level variation in various wells over the same time interval, Ar, may indicate an extensive ground-water flow system with no near-by boundary.
5.3 pufie 5
Ground-water studies
The use of lysimeters (soil monoliths) where different water levels are maintained artificially is more common. The unconfined ground-water loss by evaporation can be determined experimentally using a lysimeter.
Losses of irrigation water by seepage down to the water table are determined by similar methods. For this purposes, a régime of irrigation similar to the one on the surrounding field must be reproduced over the lysimeters.
Water-infiltration losses from canals are calculated by a variety of formulae and from the difference of the water discharges measured simultaneously at the upstream and downstream outlets, taking account of the time lag, evaporation from the water surface and precipitation.
The inflow QI and outflow Qz of unconfined ground water for the given area are determined by Darcy’s equation if the transmissivity of the aquifer and flow gradients are known.
Condensation recharge of unconfined ground water is usually negligible and recorded automatically at the lysimetric observations; the difference u
-
KI can be determined directly.The unconfined ground-water level variation, AH, for the time interval Ar* is determined in wells.
All the water-balance elements mentioned above are determined independently. The water balance is considered to be calculated satisfactorily if the difference between the positive and negative elements of the balance divided by the parameter p does not differ from the weighted average water-level change, A H a v , by more than 15-20 per cent.
Experimental observations of the majority of the elements of the unconfined ground- water balance are usually carried out at experimental balance plots with areas of several tens and hundreds of hectares. O n such plots a dense network of observation wells, lysimeters and hydrometric installations on rivers and canals is set up.
In compiling the unconfined ground-water balance by such a method, a question arises about areal variations over the watershed of such elements as the infiltration, irrigation water and evaporation from the water table and the value of the parameter p. For obtaining reliable average values, observations are carried out not less than three times under various geologic-lithological and hydrogeological conditions, and these values correlated with various natural and water-economic factors.
The unconfined ground-water balance is calculated monthly in order to examine variations in its component parts related to hydrometeorological conditions and various water-economic measures in the area (soil cultivation, irrigation, etc.) throughout the year.
5.3 poge 6
Groicnd-water studies Defining the wafer balance
TABLE 5.3b. Water balance for the unconfined ground-water régime at a plot in an area near Moscow (U.S.S.R.) (data continued from Table 5.3a)
Date (in- days)
Ground-water Rate of Time ueriod At storage change ground-water
recharge from inflow and outflow Subsurface inflow Infiltration
QI - Q? less outflow from above
Release of water from storage
for time t at the expense of
___
Ground-water Control calculation ___-Subsurface outflow Ground-water balance
less inflow evaporation 1000 p A H Water-level Ground-water
Defining the water balance
5.4