Chapter 6

Runoff and subsurface flow

6.1 Hydrological regime

6.1.1 Definition

Stream hydrological regime is defined by means of flow variations, usually represented by the monthly average flow graphics (calculated for a certain number of years). Monthly flow coefficient is the monthly rapport of the inter-annual, which allows repartition representation, in percents, of the monthly flows during the year.

The hydrological regime of a stream is defined by the flow variations usually represented by the monthly average flow graphic (calculated for a certain number of years and called inter-annual module- rainfall):

(6.1)

It can be defined as the annual flow coefficient:

(6.2)

The curve of monthly flow coefficients shows the systematic character of seasonal variations and compares the streams between them.

Figure 6.1 Examples of average flow curves [Musy, 2001]

Average annual flow can be represented by the following relation:

(6.3)

6.1.2 Classification

A simple classification of hydrological regimes has been done by Pardé (1933), who distinguished three regime types:

• simple regime: characterized by a maximum and generally only one water supply (glacial regime, snow regime, gauging regime)
• mixed regime: characterized by two maximums and two minimums per year, with several ways of water supply (snow-glacial regime, snow-gauging regime)
• complex regime: many extremes and many ways of water supply

In a first step two flow types can be distinguished: "rapid" flows (surface and subsurface flow) and "slow" flows (groundwater flow).

6.1.3 Annual flow balance

The annual flow E_t represents the water quantity that flows every year through a basin. Total flow can be expressed by means of the following relation:

(6.4)

For important rainfall E_s >> E_h. For this reason when it cannot always be distinguished quantitatively on the field, E_s and E_h, is often adopted:

(6.5)

where:
	Cr	surface flow coefficient
	Ces	superficial flow coefficient
	P	rainfall

Figure 6.2 Rain heights repartition during a shower of constant intensity [Musy, 2001]

6.2 Runoff (Overland flow)

Overland flow is a phenomenon that appears when the rain intensity exceeds the soil's maximum capacity to absorb water. This capacity decreases in time until it reaches a constant value. In homogenous soils, with a deep underground layer, this maximum capacity is equal to the hydraulic conductivity at saturation. Natural soils with an increased hydraulic conductivity in temperate and humid climate have an infiltration capacity inferior to the maximum intensity of rain.

Otherwise the flow process is developed in two phases:

1. At the beginning of the shower, the infiltration capacity is generally superior to the rain intensity; water will be completely infiltrated. Rain is retained in the soil until the soil saturation capacity is achieved. The submersion time (t_s), can be defined as the duration between the beginning of rainfall and the instant when the soil achieves saturation capacity. The submersion time also indicates the flow beginning. For soils the submersion time is variable and depends on rainfall intensity and initial soil humidity.

2. The rainfall intensity exceeds the infiltration capacity. The subsurface flow is constituted by the difference between these two terms.

Figure 6.3 Infiltration rate and cumulate infiltration for a uniform
rain and submersion time definition [Musy, 2001]

When the runoff process exceeds the infiltration capacity water flows into another area of the watershed with a superior infiltration capacity. Using mathematical models and site experiments, the resultant runoff process explains the hydrological basin's answer in semi-arid climates and also in conditions of important rainfall intensity.

The flow on saturated surfaces is produced when it exceeds the soil capacity to retain water and the capacity to transmit laterally the water flux. Figure 6.4 shows these two situations: flow on saturated surfaces and flows that exceed the infiltration capacity .

Figure 6.4 Flow process generated through exceeding the infiltration capacity
and through flows on saturated surfaces [Musy, 2001]

Generally the flow is indirectly estimated from the hydrographical network.

6.3 Subsurface flow

Part of the infiltrated effective rainfall circulates more or less horizontally in the superior soil layer and appears at the surface through drain channels. This flow is called subsurface flow (in the past it was called hypodermic flow). The presence of a relatively impermeable shallow layer favours this flow. Subsurface flows in water bearing formations have a drainage capacity slower than superficial flows, but faster than groundwater flows. The essential condition for the appearance of the subsurface flows is: the hydraulic lateral conductivity of the environment has to be superior to the vertical conductivity. The subsurface flow in unsaturated regimes can be the base flow in the area with large slopes, and it is dominant in humid regions with vegetal covering and well-drained soils.

Figure 6.5 Different flow types [Musy, 2001]

6.3.1 Piston effect

Piston effect permits analysis of the subsurface flow. The existence was assumed of a mechanism to transmit a quasi-instantaneous pressure wave. This mechanism, called "the piston effect" assumes that water that falls on a slope is transmitted downstream with a pressure wave and causes a sudden exfiltration on the watershed.

This phenomena principle can be explained by analogy with a saturated soil column to which known quantity of water is added. Due to the gravitation effect water moves to the bottom of the column.

6.3.2 Flow through macro pores

Macro pores are pores in which the capillarity phenomena are inexistent.

The origin of macro pores

We can distinguish:

• pores formed due to soil micro fauna: with dimension of 1-50 mm. In general they are located in the superior soil layer (0-100 cm).
• pores formed due to vegetation roots. These pores become free when the plants die. The structure of macro pores network will depend on vegetation type and also on the growing state.
• natural macro pores: appears when the initial hydraulic conductivity is large.
• cracks.

Subsurface flow is carried through macro pores. Which lead the water to unsaturated areas.

6.3.3 Pipe flow

Pipe flow emphasizes soil drainage and water flow. It is difficult to establish the exact difference between pipes and macro pores. Pipes are considered to be larger than macro pores. Also pipes present a higher connectivity degree than pores, without saying that the pipes are forming a continuous network. Pipes lead the water to an unsaturated environment.

6.4 Groundwater flow

Since the aeration zone has enough humidity to allow deep-water infiltration a part of the rainfall penetrates into the phreatic layer. The amount of water depends on the underground structure and geology and also on the water volume that comes from rainfall. The water flow passes through the aquifer with a speed of several meters per day before it returns to the stream. This flow, wich comes from the phreatic layer, is called base flow or groundwater flow. The groundwater flows generally maintain stream discharge in the absence of rainfall.

Figure 6.6 Two distinct situations in which the underground layer can contribute
to stream discharge or drain the stream [Musy, 2001]

Darcy's Law and the continuity principle govern the non-steady state movement of water in the ground. For the difference between inflow and outflow, the following equation can be written:

Inflow = Outflow +/- Variation in Storage

6.5 Flow resulting from ice and snow melting

The flow resulting from ice and snow melting dominates generally in glaciers and mountain regions, where the climate is cold. The snow melting process reloads the water layer and also saturates the soil. In some cases it can contribute to the surface flow. The increase in the surface flow will depend on water equivalent to snow or ice layer, on the melting regime, and finally on the snow's characteristics.

6.6 Sediment transport

Alluviums are particles of different shapes and dimensions transported by the stream current. They come from the soil layers, from the slopes and also from the ground of the streambed. The alluviums from slopes are gravel and small boulders disintegrated by the hitting of raindrops or other atmospheric agents and they are carried to the streambed by overland flow.

The solid transport is the sediment quantity (or solid discharge) transported by the stream. This phenomenon is regulated by two stream properties:

• its competence - it is measured using the maximum diameter of rocks that can be transported by the stream. This characteristic depends on water speed.

Figure 6.7. Hjulstrom diagram shows the competence
depending on water speed [Musy, 2001]

• its capacity - it represents the maximum quantity of materials that can be transported to a given point and instant of the water stream. Capacity depends on the water speed, on the flow and on the section characteristics (shape, roughness)

These two properties are not directly connected. The silt transport of a water stream is determined by the particle characteristics (shape, size, concentration, the drop speed and particles density). These allow us to determine:

• The suspended load is composed of those materials whose size and density allow them to move without touching the stream bottom. Suspended load transport is generally made up of silts, clays, and colloidal substances. This solid discharge can be measured and extrapolated in certain conditions for the entire sector. In many cases the suspension load represents a high percentage of the total transport. These particles make the water turbid. The particles have a prismatic shape, sharp edges and the smaller ones reach several microns.
• The bed load is composed of gross matter that cannot be found in suspension because of its weight and of the speed of flow. These particles move by rolling. They have round edges and flattened shapes due to friction and collision of the particles.

Notions about specific transport and mechanical erosion on watershed

The notion of specific transport and mechanical erosion on watershed regroups two different processes. These two notions show the difference between the processes of alluvium detachment and transport, before going back into the stream, and also the transport into the stream.

The first notion concerns erosion agents, which are rain, wind, flow and also factors that condition the quantity of dragged particles: rain characteristics, soils, vegetation, topography and human activity. The quantity of dragged particles will be also determined by a number of factors like water speed, streambed characteristics, aggregate grading. Bank erosion can contribute to the suspension load measured in streams, and the presence of lakes and reservoirs leads to particle sedimentation. The sedimentation of solid matters transported by a stream is introduced into the reservoir. And to the downstream of dams erosion of the streambed takes place.

The following aspects emerge out from the second notion:

• the stream bed is the transit way for alluviums in their movement from upstream to downstream
• the alluvium quantity grows when the water flow is over a critical value
• the alluvium movement within the stream takes place intermittently, being influenced by the flow.

Figure 6.8. Classification of different types of riverbed sediments [Musy, 2001]

Bibliography

Musy, A. 1998. Hydrologie appliquée, Cours polycopié d'hydrologie générale, Lausanne, Suisse.

Musy, A. 2001. e-drologie. Ecole Polytechnique Fédérale, Lausanne, Suisse.

Shaw, E. M. 1988. Hydrology in practice. Van Nostrand Reinhold International, London, United Kingdom.

Vladimirescu, I. 1984. Bazele hidrologiei tehnice. Ed. Tehnica, Bucuresti, Romania.