Relationship among different quantities usually changes in the time, spatial, and spectral domains due to the complicated dynamics in the geosystem. In this study, we propose a general statistical modeling approach to address this problem and apply the approach to evaluating the continuous dependence of relationship between sea surface temperature (SST) and turbulent heat flux (TQ relationship) on spatial scales. In the Kuroshio extension region, it is found that the turbulent heat flux (defined positive upward) anomalies are positively correlated to SST anomalies at scales ranging from ~150km to ~4000km. The TQ relationship stays stable at mesoscales (<1000km) with a regression coefficient
of 26W/(m2K). However, its value decreases rapidly as scales further increase. In addition, exhibits a pronounced seasonal cycle with coherent phase at all the scales. The largest and smallest values occur in winter and summer, respectively.