# Topics for 9/6 Annual water balance and the Budyko curve

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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 = Ep, Q = P – Ep 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?

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