The net storage heat flux is not only a large part of the urban surface energy balance (SEB) but its determination remains a significant challenge. The diurnal hysteresis behaviour found between the net storage heat flux (Δ<i>Q<sub>S</sub></i>) and net all-wave radiation (<i>Q</i>*) has been captured in the Objective Hysteresis Model (OHM) parametrization of Δ<i>Q<sub>S</sub></i>. Although, successfully used in urban areas, the limited availability of coefficients for OHM hampers application. To facilitate use, and enhance physical interpretations of the OHM coefficients, an analytical solution of the 1-dimensional advection-diffusion equation of coupled heat and liquid water transport in conjunction with the SEB is conducted, allowing development of AnOHM (Analytical Objective Hysteresis Model). A sensitivity test of AnOHM to surface properties and hydrometeorological forcing is undertaken using a stochastic approach (the Subset Simulation). From this albedo, Bowen ratio and bulk transfer coefficient, solar radiation and wind speed are identified as being critical. AnOHM, driven by local meteorological conditions at five different land use areas, is shown to simulate the Δ<i>Q<sub>S</sub></i> flux well (RMSE values of ~30 W m<sup>−2</sup>). The intra-annual dynamics of OHM coefficients to are explored which offers significant potential to enhance modelling of the surface energy balance over a wider range of conditions.