Water Balances

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The change of moisture in an area equals the difference between (i) the gain (as precipitation and inflow) and (ii) the loss by evaporation and outflow. This equality is the 'water balance' (Section 4.4). It may be considered on any scale of space or time. The 'change of moisture' might involve an alteration of level in a reservoir, or wetter soil, for instance. Runoff occurs once the storage is full (Figure 10.13).

Water-balance estimates are often made in agriculture to check the need for irrigation. For instance, measurements in a ricefield near

Figure 10.13 The bucket model for the water balance in the soil beneath an irrigated crop. The amount of water stored in the soil increases if the inputs (from rain and irrigation) exceed the losses from evaporation into the air and infiltration into the subsoil. There is overflow in the form of surface runoff, in the bucket model, only when the soil from rootbase to the surface is saturated, i.e. its Total Available Water capacity is filled.

Figure 10.13 The bucket model for the water balance in the soil beneath an irrigated crop. The amount of water stored in the soil increases if the inputs (from rain and irrigation) exceed the losses from evaporation into the air and infiltration into the subsoil. There is overflow in the form of surface runoff, in the bucket model, only when the soil from rootbase to the surface is saturated, i.e. its Total Available Water capacity is filled.

Griffith (NSW) showed that the rainfall during a week in February was 13 mm, 86 mm of irrigation water was applied, 10 mm infiltrated into the soil, the water level fell by 23 mm and the flow away of drainage water was equivalent to 1 mm. So the evaporation inferred from the water balance was 65 mm (i.e. 86+13-1-23-10), or 9.3 mm/day, which is relatively high (Section 4.6).

Water Balances on a Large Scale

The average rainfall over all the oceans is estimated to be about 1,140 mm/a, whereas the evaporation rate is about 1,260 mm/a; the difference is made up by riverflow into the sea. For the Indian ocean, the rainfall has been estimated as 1,170 mm/a and evaporation 1,320 mm/a, with one inflow from rivers equivalent to 80 mm/a, and another in currents from other oceans of 70 mm/a. In the case of the world's land surface, the average rainfall is reckoned to be about 730 mm/a, 420 mm/a (i.e. 57 per cent) of which evaporates, the difference being carried away in the rivers.

The precipitation and evaporation rates at various latitudes are shown in Figure 10.6. The climate is wet and there is runoff wherever rainfall exceeds evaporation, at the equator and at latitudes around 55 degrees. On the other hand, most deserts are found at 20-30 degrees latitude (Chapter 16), where the potential evaporation rate exceeds the rainfall (Note

Rainfall averages 1,630 mm/a in South America and evaporation 700 mm/a, and the difference, equivalent to 930 mm/a, is carried away in huge rivers. The Australian figures are 470 mm/a rainfall and 420 mm/a evaporation, so that the rivers here carry merely 50 mm/a equivalent. More specifically, evaporation amounts to 94 per cent of the rainfall in the arid Murray-Darling watershed of Australia. The mean precipitation is only about 160 mm/a in Antarctica, almost all of which is lost in glaciers flowing slowly to the sea (Chapter 16).

Water Balances on a Local Scale

It is instructive to compare a map of rainfall in Australia (Figure 10.3 and Chapter 16) with the pan evaporation Ep (Section 4.5), from which one can infer approximate rates of lake evaporation Eo, i.e. 0.7 E The comparison shows that annual rainfalls tend to be less than Eo at most places in Australia, e.g. the rainfall and Eo at Alice Springs are 250 mm/a and 2,200 mm/a, respectively. Equivalent figures for Hobart are about 600 and 700 mm/a, approximately. But places like Darwin (where the annual rainfall is 1,490 mm and Eo about 1,680 mm/a) should be compared on a monthly basis because of the highly seasonal climate: Eo greatly exceeds precipitation in the dry season but is less than the rainfall from November to April.

Not all the rain from clouds reaches the ground. Some evaporates below cloud base (Section 9.1). There is also interception of some rain by the leaves of vegetation, though most of that is subsequently evaporated. The fraction intercepted is typically 10 per cent in the Amazon basin, 15-40 per cent for conifers, 10-25 per cent for deciduous hardwoods and 14-22 per cent for prairie grass. Measurements in a mature Australian wheat crop showed that about a third of the rain was held on the leaves. The amount held can be 2 mm or so in the case of grass, and 8 mm for a cotton crop. Around 5 mm was intercepted during each storm above a rainforest in north Queensland, depending on the leafiness of the foliage. It follows that deforestation increases runoff, e.g. by 5-10 per cent in northern Queensland.

When rain reaches the ground it tends to pond on the surface, and then either evaporates, flows away as runoff or is absorbed into the ground. All the rain is absorbed if the intensity is less than the maximum rate at which the soil can accept it, which depends on the type of soil and its prior wetness. For unsaturated soils it may be around 50 mm/h in the case of sand, but 4 mm/h for clay, for example. So there is a wide range of infiltration rates within a single drainage basin.

The ratio of the runoff (R) to the precipitation is called the runoff coefficient. It is greater with high rainfall intensities. It is also affected by surface roughness, vegetation, soil type, soil wetness and the slope of the land (Figure 10.14). Values vary widely (Table 10.4).

What is called the effective rainfall (or influential rainfall) is that part which is neither evaporated, intercepted by vegetation nor carried away as runoff. It penetrates into the ground and is mostly taken up by roots, later evaporating from the vegetation's leaves. It is the part of the rainfall involved in growing plants, roughly estimated in various ways. One procedure is to ignore daily rainfalls of less than 5 mm, for instance (which are assumed to evaporate without wetting the ground to root level), and disregard all rainfall falling after 75 mm has fallen on the same day; this is supposed to run off. However, such threshold values are arbitrary, and different in various countries. Another way, used for agriculture in southern Australia, has been to take the ineffective part of each month's rainfall as about equal to a third of the lake evaporation (Section 4.5).

Water Budgeting

An important application of the water-balance concept is in water budgeting. This is a procedure for keeping track of changes of soil-moisture content, using data on the rainfall P and actual evaporation Ea, during each successive period of ten days, for instance. P

rainfall intensity: mm/h

Figure 10.14 Effect of rainfall intensity and kind of surface on the runoff coefficient. Curve 1 refers to impervious roofs, concrete and urban areas generally, 2 to steep rocky slopes, 3 to medium soil on open slopes, 4 to residential suburbs with gardens, 5 to parks, lawns and meadows, 6 to forests and sandy soils, 7 to cultivated fields with good growth.

rainfall intensity: mm/h

Figure 10.14 Effect of rainfall intensity and kind of surface on the runoff coefficient. Curve 1 refers to impervious roofs, concrete and urban areas generally, 2 to steep rocky slopes, 3 to medium soil on open slopes, 4 to residential suburbs with gardens, 5 to parks, lawns and meadows, 6 to forests and sandy soils, 7 to cultivated fields with good growth.

Table 10.4 Values of the run-off coefficient

Runoff coefficient

Table 10.4 Values of the run-off coefficient

Runoff coefficient

Basins:

Murray-Darling rivers

6

Mississippi river

22

Zaire river

23

Clarence river, NSW

27

Amazon river

42

Various surfaces:

Parkland

10-25

25% urbanised suburb

13

Well-engineered catchment in

16

South Australia

50% urbanisation

26

Totally suburban

52

Downtown

70-90

raises the moisture content from a known value at the start of a period, and Ea lowers it, so that the moisture content at the end of that period (and the start of the next) can be calculated by simple book-keeping. Details are given in Note 10.P. The procedure shows when and how much irrigation is needed.

Another reason for keeping a soil's water budget is that the soil-moisture content (M) indicates the eventual crop yield (Note 4.G). Yield correlates more strongly with M than with climatic features such as evaporation, rainfall or temperature. Calculations with climate data for several years show how often a crop's yield would be satisfactory on new land.

Water budgeting also shows the amount of runoff and therefore the expected river flow. For instance, the curves in Figure 10.15 indicate that runoff at Launceston in Tasmania can be expected from June-October, i.e. that is when flooding is most likely.

10.6 FLOODS

Floods are rivers which overflow their banks.

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