There are many factors that can shape a hydrograph. If there is more runoff, if means that there will be more discharge. More runoff also means that there will be a shorter lag time as more water will arrive at the river in a shorter space of time.
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Factors that affect the shape of a hydrograph:
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Temperature
Hot and dry conditions, or cold and freezing conditions lead to hard, impermeable ground and much more runoff - lag time is therefore decreased.
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Amount/type of rainfall
Lots of short, heavy rainfall means that there will be more run off. Therefore, lag time is decreased and river discharged is increased.
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Land use
Urban areas have drainage systems to take away a lot of rainwater. However, around some tivers, they can be covered in impermeable materials, such as concrete, which increases runoff.
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Previous weather
If there's been a lot of rain recently, the soil can become saturated. This can increase runoff, therefore decreasing lag time and increasing river discharge.
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Rock type
Water infiltrates through pore spaces in permeable rocks and flows along cracks in pervious rocks. This decreases runoff, which means that lag time increases, and discharge decreases. If the rock is impermeable, the water can't infiltrate it, therefore increasing runoff, shortening lag time and there is also an increase in discharge.
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Relief
There's a lot more runoff on steep slopes. This decreases lag time and increases discharge.
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Definitions
Relief -> how the height of the land changes
Saturated soil -> soil that can't absorb any more water