12. Storage Heat Flux¶

The storage heat flux \(\Delta Q_S\) is the net energy stored or released by changes in sensible heat within the canopy air layer, roughness elements (e.g. vegetation, buildings in an urban environment), and the ground. Knowledge of \(\Delta Q_S\) is crucial to a wide range of processes and applications: from modelling turbulent heat transfer and boundary layer development to predicting soil thermal fields.

In rural sites, or simple bare soil sites, the flux may be a small fraction of the net all-wave radiation (Oliphant et al.,2004). However, in areas where there is more mass, such as cities, the term becomes much more significant (Kotthaus and Grimmond, 2014a) and a key element of the SEB and well-known effects such as the urban heat island.

12.1. Objective Hysteresis Model¶

The objective hysteresis model (OHM) is a simple model to calculate storage heat flux using net all-wave radiation \(Q^*\) following the hysteresis relation (Camuffo and Bernardi, 1982).

The OHM is forced by \(Q^∗\) and accounts for the diversity of the surface materials (sub-facets) in the measurement source area of interest with weightings (\(f\)) for their two- or three-dimensional extent (Grimmond et al., 1991):

(12.1)¶\[\Delta Q_{\mathrm{S}}=\sum_{i} f_{i}\left(a_{1, i} Q_{i}^{*}+a_{2, i} \frac{\partial Q_{i}^{*}}{\partial t}+a_{3, i}\right)\]

where the \(a_1\), \(a_2\), and \(a_3\) coefficients are for individual facets determined by least-square regression between \(\Delta Q_S\) and \(Q^*\) using results from observations.

These coefficients capture the net behaviour of a facet type in a typical setting, rather than being required to identify the component materials within a facet (e.g. multiple materials making up a roof, wall, with varying thermal connectivity and individual properties). A set of example OHM coefficients can be found here.