La

Mountains snowmelt

Plains snowmelt

Plain snowmelt latitude contrast

R. Arve Switzerland

R. Columbia Canada

R. Volga USSR

Rainfall dependent

Equatorial two maxima j

R. Lobe Cameroun

Intertropical

Intertropical

R. Chari Chad

Temperate oceanic

R. Seine France

Mediterranean

R. Vinalapo Spain

JD Avon (Spey) 543 Km2 Mean 14,49G m3 s-1

JD Rye (Derwent, Ouse) 679 Km2 Mean 9,443 m3 s-1

Avon 324 Km2 Mean 3,455 m3 s-

Exe 422 Km2 -Mean 12,161 m3 s-

Eden 616 Km2 -Mean 13,384 m3 s-1

Fig. 11.4 River regimes for: (a) different types of climatic regime; and (b) different UK rivers expressed as a ratio of mean monthly flow to the annual mean flow.

• Seasonal tropical. Within the tropics, there are usually marked wet and dry seasons that vary in length according to latitude, and the flow ratios vary according to rainfall quantities. The River Chari in Chad is a clear example. Some catchments have double peaks, as in the equatorial region, but only separated by 1 or 2 months rather than 6 months.

• Temperate oceanic. The River Seine in France demonstrates the characteristic regime of these regions. Rainfall occurs all the year round, but the summer evaporation provides the relatively small variation in the seasonal flow pattern, which is however annually irregular.

• Mediterranean. The regime resembles that of the temperate oceanic regions, but is more extreme. The dry summers result in very low flows; along the desert margins, rivers dry up completely. Most of the flow results from the winter rains, but occasional very heavy summer storms may produce flood flows. The river regime is also very variable from one year to another, in parallel with the irregular incidence of rainfall.

The flow regime of a river draining a catchment area within a single climatic region may be readily estimated by considering the features demonstrated by the simple regimes. It must be remembered that away from the equatorial region, the patterns will be reversed in the southern hemisphere. However, the conditions in the high mountains in any of the regions will result in modifications to the expected pattern. Rivers with two or more sources of supply have a mixed regime. For example, a spring maximum may be identified as snowmelt, whereas early winter rains give a second peak.

More complex regimes result from the overlapping of different causes. These are usually characteristic of large rivers, especially those flowing through several climatic zones. The major rivers of the world, the Congo, Nile, Mississippi and the Amazon come into this category. With mixed or complex regimes, the range between the extreme months is usually small, and the annual variability decreases with increase in catchment size.

Examples of river regimes within the UK are given in Fig. 11.4b. The general pattern resembles that for temperate oceanic regions with a relatively small range between the wettest and driest months. The Scottish Avon, a tributary of the Spey, shows the least seasonal variation, the result of persistent rainfall throughout the year. Further south, the effect of summer evaporation losses becomes more apparent, and the Rye in east Yorkshire reflects this tendency. The slight differences in the other four diagrams stem from varying location and catchment characteristics. There are sustained later spring flows above normal from the chalk of the south coast Avon, and the exposure of the Dovey catchment in central Wales causes high flows from the mountains in early winter. These are average conditions calculated from the years of record available for each station, but there are great variations from year to year that result from the irregular incidence of rainfall.

11.3 Mixing models for determining runoff sources

As well as the amount of runoff, the sources of water that make up the stream hydrograph can also sometimes be of interest. In Chapter 1, the idea of separating different sources of water using mixing models was introduced in the discussion of concepts of runoff generation. It was noted there that this has been very important in the development of scientific hydrology since a large number of studies have shown that in many different catchments the hydrograph from a rainfall event is not made up of rainfall falling in that event but of old or pre-event water stored in the catchment prior to that rainfall falling. This should not be expected to be the case everywhere (the hydrograph from an intense rainfall falling on an arid catchment might be expected to be dominated by event water), but such mixing model analyses conflicted with a generally held perception at the time that storm hydrographs were caused by surface runoff made up of rainfall. It is therefore worth considering the nature of mixing model calculations in more detail.

Inevitably some simplification is necessary since in reality there is certainly a whole spectrum of different sources of storage in a catchment that might contribute to the hydrograph. It is also the case that even the simplest separation will not be possible if the potential sources cannot be differentiated by having different chemical characteristics in some way. A problem that then arises is that such chemical characteristics will not be constant over time, but will change as a catchment wets and dries. Thus any such separations will be, at best, approximate.

11.3.1 Two-component mixing

Consider first a simple two-component mixing model with storm rainfall as one source and all other sources from pre-event storage as the second. A number of chemical characteristics have been used in such separations including silica (normally nearly zero in rainfall, but higher in soil and groundwaters), and the stable isotopes of hydrogen and oxygen. The former has the disadvantage that there is evidence that rainwater might increase in silica concentration quite rapidly once in contact with the soil. The latter have the advantage that hydrogen and oxygen are part of the water molecule and will therefore necessarily follow the flow pathways of water, but the disadvantage that the rainfall inputs do not always have a significantly different concentration from the pre-event water sources (and that different pre-event sources may have rather different concentrations). The analysis then requires that concentration measurements are available for both rainfall and for the pre-event water. The latter is usually achieved by sampling the river water prior to an event. This may represent the mix of concentrations from different sources that is then assumed to remain constant throughout the event. That this is not always a good assumption is demonstrated in the next section where three component mixing is considered.

For this two-component mixing, we can then write down mass balance equations for both the water and the chemical constituents as follows:

for water

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