Efficient estimation of temperature distribution, heat storage, thermocline migration and vertical eddy conductivities in stratified lakes

SUMMARY 1. Factorial designs were used to investigate the spatial and temporal components of temperature sampling error in two medium‐sized (maximum fetch = 9 and 11 km; maximum depth = 24 and 70m) Wisconsin lakes (Mendota and Green). Sampling designs were then optimized for estimating temperature distributions, thermocline migration, lake heat content, and vertical eddy conductivities in these and similar stratified lakes. 2. Errors were at a minimum for: (i) isotherms positioned 1 / 3 ‐ 1 / 2 of the way down through the seasonal thermocline; (ii) at lake stations located near the node of the principal internal seiche; (iii) after an extended interval of low windpower. If seven spatially distributed lake stations were sampled n 1 , n 2 times during the two low‐power intervals bracketing a weather front, and the rime delay between revisits was randomized with respect to the period of the uninodal temperature seiches, the resulting standard error (cm) in ΔZ̄ 17 (depth of 17° isotherm; an unbiased, minimum‐variance estimator for main thermocline migration) was (144/ n 1 + 144/ n 2 ) 1/2 . If n 1 = n 2 = 2 ‘revisits’, the resulting CV (coefficient of variation) was 5–10% for ΔZ̄ 17 accompanying major individual cold fronts in early summer. 3. When estimating K z , the vertical eddy conductivity, the most important component of error relates to Δ H z , the change in heat content below depth z . The error in Δ H z is minimized in the same manner as for lake‐mean isotherm depth. Using the Mendota sampling design described above, the RMS error in Δ H z decreases from ∼90 cal cm −2 in the upper metalimnion to ∼35calcm −2 near the base of the metalimnion. For seven take stations, and n 1 = n 2 = 2, K z can be estimated with a CV ∼10% bracketing a single major cold front. The CV decreases approximately as Δ H z −1 , hence is roughly proportional to Δ t −1 or to (cumuiative windpower) −1 .