A method for estimating the diffuse attenuation coefficient (Kd) from paired thermistors

A new method for estimating the diffuse attenuation coefficient (Kd) from paired thermistors was derived using a simplified representation of thermal gains from the attenuation of penetrating shortwave radiation. We show that during cases where radiative gains dominate daily temperature changes, time series measurements of water temperatures at multiple depths (z1 and z2) are related to one another by a scaling factor (α). Kd can then be estimated by the simple equation Kd = ln(α)/(z2-z1). A suggested work flow was created which outlines the procedures for calculating Kd according to the paired thermistor (PT) method, and the detection of cases that violate the assumptions of the method. The PT method is best suited for lakes where radiative temperature gains are large relative to physical noise (i.e., small dark lakes), but can be employed for other lake types during certain conditions, such as low wind speeds and/or where spatially redundant measurements of temperatures are available. The optimal vertical placement of thermistors according to a priori knowledge of Kd is also described. This information can be used to inform the design of future deployments using the PT method, or for campaigns where characterizing sub-daily changes in temperatures is important. The PT method is a better physical representation of water column transparency compared to Secchi depth, and can be a useful alternative to expensive and labor intensive radiometer profiles.