In equation S3, is the temperature at the depth and time of interest: is the difference in T(z,t) ∆Ti bottom water temperature over time-step is the depth of interest, is the time range from the time of i, z τ interest to the last observed time, and is the TD at the depth of interest. For a series of temperature α changes, TD can be calculated using a stepwise approach: this explains the summation term in equation 3, with each term representing a single temperature step. The number of time steps, is one less than the i n, number of observed data points. Equation 3 allows for downward propagation from the bottom water sensor, resulting in model fits that can be adjusted for a variety of possible TD values. To determine T(z,t) at the three depths of interest, the differences between consecutive points in the bottom water temperature sensor’s data were computed in Matlab version R2011a. This gave a vector with each value ∆Ti corresponding to a 1 minute timestep. The vector was then calculated, with τ (S4) where is the time of the last datapoint in the record and is the time of the current datapoint tn ti corresponding to the beginning of the range. A vector was then generated for a range of TD values ∆Ti centered on an estimate of the expected TD values from Thomson (2010). These vectors were supplied to equation S2, generating a matrix for each sensor depth (5 cm, 10 cm, and 15 cm) where the rows T(z,t) correspond to time steps and the columns correspond to TD values. Each column was then differenced with the observed data from that depth, and the standard deviations of those values were plotted as a function of the column’s TD (Figure 3). Sensitivity Analysis Of the variables in equation S3, the depth of interest (z) was the only parameter where error could be introduced during operation of the probe: if the probe was inserted to a different depth than the ideal, the sensors would be offset from the model depths. The use of a high definition camera during deployment allowed us to mitigate this error by visually inspecting the position of the sediment-bottom water interface along the scale on the probe. Thus we are confident that our deployment depths were
In equation S3, T(z,t) is the temperature at the depth and time of interest: ∆Ti is the difference in bottom water temperature over time-step i, z is the depth of interest, τ is the time range from the time of interest to the last observed time, and α is the TD at the depth of interest. For a series of temperature changes, TD can be calculated using a stepwise approach: this explains the summation term in equation 3, with each i term representing a single temperature step. The number of time steps, n, is one less than the number of observed data points. Equation 3 allows for downward propagation from the bottom water sensor, resulting in model fits that can be adjusted for a variety of possible TD values. To determine T(z,t) at the three depths of interest, the differences between consecutive points in the bottom water temperature sensor’s data were computed in Matlab version R2011a. This gave a ∆Ti vector with each value corresponding to a 1 minute timestep. The τ vector was then calculated, with (S4) where tn is the time of the last datapoint in the record and ti is the time of the current datapoint corresponding to the beginning of the ∆Ti range. A vector was then generated for a range of TD values centered on an estimate of the expected TD values from Thomson (2010). These vectors were supplied to equation S2, generating a T(z,t) matrix for each sensor depth (5 cm, 10 cm, and 15 cm) where the rows correspond to time steps and the columns correspond to TD values. Each column was then differenced with the observed data from that depth, and the standard deviations of those values were plotted as a function of the column’s TD (Figure 3). Sensitivity Analysis Of the variables in equation S3, the depth of interest (z) was the only parameter where error could be introduced during operation of the probe: if the probe was inserted to a different depth than the ideal, the sensors would be offset from the model depths. The use of a high definition camera during deployment allowed us to mitigate this error by visually inspecting the position of the sediment-bottom water interface along the scale on the probe. Thus we are confident that our deployment depths were
elementa.000039.s001.docx