### Key Point: Annual water balance is controlled by climate

```Topics for 9/6
• Annual water balance and the Budyko curve
• Project progress
Water Balance
• Ratios can be used to “characterize”
watersheds
– Q/P, ET/P…
– Energy limited vs Water limited systems
• Budyko (1974) Climate and Life
Physical Controls on Water Balance at
Catchment Scales
• Treat as a lumped system
– Receives rainfall at the rate p(t), loses water through
evapotranspiration e(t), and runoff q(t)
• dS/dt = p(t) – q(t) – e(t)
– Where S is the storage of water at any time (t)
• At the annual scale we assume there is no carry over from
year to year and
– P = Q + E where P, Q, and E are annual totals
– We will investigate the “partitioning” of the water balance at
the annual scale
• Key Point: Annual water balance is controlled by climate
Bucket Model Assumptions
•
•
p and e are uniform through the year
e occurs at potential rate as long as water is
available
•
No runoff if bucket is less than full
Two Scenarios
• Case 1: Dry Climate (arid)
– Ep>P, and ep(t) > p(t)
–…
– Actual E is controlled by the amount of rainfall
• Water limited system
• S/Sb= 0
– No water storage, no vegetation…adverse to life
Two Scenarios
• Case 2: Wet Climate (humid)
– P>Ep, p(t) > ep(t)
• What happens to the bucket?
– E = E p, Q = P – E p
– Upper limit to e(t) is the evaporation demand
• Energy limited
• S/Sb = 1
• Too wet, adverse to life
Budyko Diagram
• Consider the limits
– Plot E/P vs Ep/P
• If E = Ep (wet climate)…
• If E/P = 1 (dry climate) …
– E/P is a measure of actual water balance
– Ep/P is a measure of climate, called dryness index
Limits of Budyko Diagram
• Whole world can be divided in to “energy limited” and “water
limited” areas
• Why doesn’t empirical curve match theoretical?
```