Agricultural Drought Indices - US Department of Agriculture

Depending on the objective of the study and data availability, water balance modeling can have
different levels of complexity, although the model is a simplification of the real world, no matter how
complex it may be (Zhang et al. 2002).
Simple models normally are based on the balance between R and ET and are used for longer time
scales (ten-day and monthly). These models when well adjusted for a given region can be as
accurate as complex ones, which require multiple inputs not always readily available or estimated
with enough precision. These models normally require as input rainfall, potential
evapotranspiration, and soil water holding capacity. An example of such a model is the one
presented by Thornthwaite and Mather (1955).
On the other hand, complex models, which deal with soil water dynamics as a function of the
interaction among soil-plant-atmosphere systems, can be more accurate, mainly for short time
scales (daily). These models simulate more complex interactions between soil, plant, and
atmosphere. Examples of complex models are presented by Ritchie (1972), Faria and
Madramootoo (1996), Zhang et al. (2005), and Ji et al. (2009).
However, independent of the complexity, all models inevitably have to be simple enough, and
parameters can be estimated from known climate and system characteristics (Zhang et al. 2005).
In other words, users should avoid unnecessary complexity but at the same time choose the best
option to achieve a level of detail consistent with the importance of the process for the application
in question. This is usually to improve the understanding of the influence of soil water storage on
crop growth, development, yield, and quality.
Several aspects must be considered when choosing between simple and complex water balance
models for monitoring soil moisture. The main limitation in using more complex models is the
number and complexity of the input variables, which sometimes are not available. Another aspect
related to the use of a complex model is how understandable it is for users. Using a complex
model without understanding its structure, parameters, coefficients, and input variables can lead to
numerical and interpretation errors. On the other hand, when simple models are used, the errors
are related to lack of details to describe all the processes involved. Under these conditions, such a
model is not universal, requiring adjustments and calibration for each new application in different
locations and conditions.
When choosing a water balance model, users should be aware of two types of modeling errors:
systematic and calibration (Zhang et al. 2002). Figure 2 presents these errors, which are
associated with the type of the model used. The “systematic error” tends to be greater with simpler
assumptions considered. This error tends to diminish when more processes are added to the
model, which implies increasing its complexity. When the model becomes very complex,
considering all the factors and processes involved with the modeled phenomena, the “systematic
error” tends to zero, but on the other hand, under this condition, “calibration error” increases,
associated with the greater risk of parameterization error resulting from lack of knowledge of the
parameters that are required by the model. According to Figure 2, the best situation occurs when
both errors are balanced, generating the minimum total error. However, it is not easy to define
exactly the best balance between simplicity and complexity. Users should avoid unnecessary
complexity but at the same time choose the best option to achieve a level of process detail
consistent with the importance of the process for the application in question.
The main factor that is crucial for choosing a water balance model is the availability of weather, soil,
and plant data. Under limited availability of data, a relatively simple model is likely to be required.
When weather, soil, and plant data are not limited, complex models can be used. However,
complexity in this case is not a guarantee of accurate results. If it is not properly parameterized for
the specific conditions of interest, a complex water balance model can give poor results as easily
as a simple model can. (Zhang et al. 2002).
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