1. Topics for 9/6 Annual water balance and the Budyko curve
Project progress

2. Water Balance Ratios can be used to “characterize” watersheds
Q/P, ET/P…
Energy limited vs Water limited systems
Budyko (1974) Climate and Life

3. 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

4. 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

5. 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

6. Two Scenarios Case 2: Wet Climate (humid) P>Ep, p(t) > ep(t)
What happens to the bucket?
E = Ep, Q = P – Ep
Upper limit to e(t) is the evaporation demand
Energy limited
S/Sb = 1
Too wet, adverse to life

7. 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

8. Limits of Budyko Diagram
Whole world can be divided in to “energy limited” and “water limited” areas
Why doesn’t empirical curve match theoretical?