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Published byArmando Kenderdine Modified over 2 years ago

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

Project progress

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**Water Balance Ratios can be used to “characterize” watersheds**

Q/P, ET/P… Energy limited vs Water limited systems Budyko (1974) Climate and Life

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**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

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**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

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**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

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**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

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**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

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**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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