Agricultural Drought Indices - US Department of Agriculture

60
50
40
Error
30
20
Systematic
Error
Total Error
Calibration
Error
10
0
Complexity
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
Figure 2. Relationship between model complexity and errors (systematic and calibration). Adapted
from Zhang et al. (2002).
Water Balance Models in Current Use for Agricultural Purposes
Several water balance models are available in the literature, ranging from very simple models,
based only on rainfall and evapotranspiration balance for a given volume of soil, to very complex
ones, based on detailed weather, crop, and soil data and considering the soil as a multi-layer
compartment where the water moves up and down depending on the different vertical and
horizontal water inputs and outputs.
Among the simpler models, the one proposed by Thornthwaite and Mather (1955) is the most used
around the world for agricultural purposes. Meteorological services of countries like Argentina,
Brazil, China, India, the United States, and Uruguay use Thornthwaite and Mather’s water balance
for monitoring regional soil water conditions for agricultural crops as well as for monitoring drought
conditions.
The model proposed by Thornthwaite and Mather (1955) requires rainfall (R), potential
evapotranspiration (ETP), and soil water holding capacity (SWHC) as inputs. ETP, also called
reference evapotranspiration (ETo), is the evapotranspiration of a short grass crop covering all
surfaces, actively growing, having leaf area index around 3, not suffering from water stress, and
having a fetch area long enough to avoid advection of sensible heat from adjacent areas. ETP can
be estimated by different methods, as for example those proposed by Thornthwaite (1948),
Priestley and Taylor (1972), Hargreaves and Samani (1985), and Penman-Monteith,
parameterized by Allen et al. (1998) and Camargo et al. (1999).
Thornthwaite and Mather’s model assumes water withdrawal as negative exponential function,
while water reposition is linear, based on the balance between R and ETP (Figure 3). When (R -
ETP) < 0, soil moisture will decrease according to the accumulated negative (NAc) values of (R-
ETP). When (R – ETP) > 0, soil moisture will increase proportional to the amount of R above ETP.
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