Chapter 1 · Unit 1-2
Every watershed keeps a water account
Textbook p. 6–8
Goals
In one sentence
Water in − water out = change in water stored
Treat the watershed as a system
Hydrology treats a watershed or basin as a system of its own. A watershed is usually small; a basin is a large watershed.
Mass conservation, Eq. (1-1)
I − O = dSdt
I: input O: output dS/dt: change in storage per unit time
Like a bank account: income − spending = change in savings.
Earn more than you spend, and savings grow.
The easiest system to see
River water from upstream is the inflow I, water released by the dam is the outflow O, and the lake holds the storage S.
Inflow > outflow: the surplus is stored and the level rises, dS/dt > 0.
Inflow < outflow: storage is drawn down and the level falls, dS/dt < 0.
A watershed works the same way, but its storage hides on the surface, in the soil and in groundwater, with no level to watch.
Split the watershed into two layers
Above the surface, Eq. (1-2)
P − (E + T + INF + Q) = ΔSsΔt
Precipitation in; evaporation, transpiration, infiltration and surface runoff out
Below the surface, Eq. (1-3)
INF − (INT + G) = ΔSgΔt
Infiltration in; interflow and groundwater flow out
Two budgets become one
Add Eqs. (1-2) and (1-3):
P − (E + T + INF + Q) + INF − (INT + G)
Infiltration only moves water from the upper layer to the lower one. For the whole watershed it is an internal transfer: one out, one in, so it cancels.
Whole watershed, Eq. (1-4)
P − (E + T + Q + INT + G) = ΔSΔt
Streamflow is surface runoff plus interflow plus groundwater flow, so Q + INT + G is the streamflow measured at the outlet. Every hydrologic method builds on this equation.
The hydrologist's unit of account
Rain gauges measure depth (mm); stream gauges give volume (m³). To keep both in one budget, spread the volume evenly over the whole watershed:
depth = volumearea
Example 1.1
Annual rainfall is 2200 mm. A river crosses the land: mean monthly inflow 300,000 m³, monthly outflow 250,000 m³. Storage rises by 6.5 hm³ per year on average. Find the annual evapotranspiration E (mm).
Practice: month by month
Start of year Storage 60
Each month: storage at month end = last month's end + inflow − outflow
Practice: storage and water level
Inflow is a steady 2.8 cms; surface area and outflow vary with level (see textbook table). Key: change in storage = surface area × change in level, ΔS = A·Δh.
Interactive lab
A flood flows into the reservoir. On the right, set the flood peak, release and spillway, and watch the water level and outflow respond. Try to:
Inflow, outflow and storage
Inflow IOutflow OStorage S
Self-check
01Over a period, a reservoir's inflow stays greater than its outflow. What happens to storage?
02Combining the above-surface (1-2) and below-surface (1-3) equations into (1-4), which term drops out?
03A reservoir starts the year with 60 units. From January to August, inflow totals 74 units and outflow 78 units. How many units are stored at the end of August?
Summary
Next unit
1-3 Modeling, Applications & Taiwan
How are hydrologic models classified? What makes Taiwan's mountains and rivers special? And how a mass curve sizes a reservoir.