Derived Root Zone Soil Moisture

VanderSat’s soil moisture measurements refers to the top of the soil (up to 10 cm depth, depending on the band used and the moisture conditions). While in many cases this is a good representation of the water availability for plants we can use a simple method to estimate the moisture over a deeper layer, for example the root zone.

The method used by VanderSat to estimate Root Zone Soil Moisture is described in the literature by Wagner et. al. (1999), Alberger et. al (2008) and Paulik et. al. (2014). The method is also used in the Copernicus Global Land Service for the soil water index (SWI).

In this method, the main assumption is that the moisture content in the soil profile is determined solely by the changes in the top of the profile. These changes can be observed by the top soil soil moisture and thus extrapolated to the deeper soil layers.

The formulation describes a simple two-layer water budget model. The first layer represents the layer that is observed directly by the satellite. The second, deeper and thicker, layer represents the root zone and is connected to the atmosphere via the top layer. As a result of the different volumes in the top layer and the bottom layer, the dynamics from the top layer are dampened in the bottom layer. A schematic representation of the model is shown in the figure below.

$L \frac{d\theta(t)}{dt} = C [\theta_{wg} (t) - \theta (t)]$
$T = L/C$
$\theta_{wz} (t_n) = \frac{\sum_{i}^{n} \theta_{wg} e^{-\frac{\Delta t }{T}}}{\sum_{i}^{n} e^{-\frac{\Delta t}{T}}}$