Analysis of expanded NLSST algorithm formulation

1. 1 Analysis of expanded NLSST algorithm formulation Jean-François Cayula Doug May

2. 2 Background • Standard Daytime NLSST algorithm form: • SST = a0 + a1*T11 + a2*Ts0*ΔT + a3*Sθ*ΔT ΔT = T11 – T12 • Ts0 = First Guess Temperature Field in Celsius • Sθ = Secant of satellite zenith angle minus 1 • Previous VIIRS SST algorithm studies have shown: • Daytime NLSST Ts0 term should be in Celsius rather than Kelvin for best accuracy. • Nighttime NLSST Ts0 term should be in Kelvin rather than Celsius or else use MCSST for best accuracy.

3. 3 NLSST Daytime Algorithm Form ΔT = T11 – T12 Ts0 = First Guess Temperature Field in Degrees Celsius Sθ = Secant of satellite zenith angle minus 1 SST = a0 + a1*T11 + a2*Ts0*ΔT + a3*Sθ*ΔT Offsetting Ts0 by x, i.e. , Replacing Ts0 by Ts0 + x generates different accuracy results. - The plot shows that the NLSST equation is more accurate with Ts0 in Celsius (Ts0 + 0⁰) than with Ts0 in Kelvin (Ts0 + 273.15⁰) - The optimal offset to Ts0 is 16.2⁰ and provides the most accurate NLSST results.

4. NLSST Nighttime Algorithm Form ΔT = T37 – T12 Ts0 = First Guess Temperature Field in Degrees Celsius Sθ = Secant of satellite zenith angle minus 1 SST = a₀ + a₁*T11 + a₂*Ts0*ΔT + a₃*Sθ Offsetting Ts0 by x, i.e., Replacing Ts0 by Ts0 + x generates different accuracy results. - The plot shows that the NLSST equation is less accurate with Ts0 in Celsius (Ts0 + 0⁰) than with Ts0 in Kelvin (Ts0 + 273.15⁰) - As a side note, and not obvious from the plot, Ts0 in Fahrenheit results in better NLSST accuracy than either Kelvin or Celsius! - The optimal offset to Ts0 is 43.28⁰ and provides the most accurate NLSST results.

5. Expanded NLSST Algorithm Form Walton’s 1998 NLSST paper demonstrated that the coefficient for the ΔT term in the algorithm (Gamma) should be a function of surface temperature rather than a constant. He proposed that Gamma should be: A* Ts0 Results from the previous slides suggest that Gamma should be expressed as A*(Ts0 +x) or a*x + b* Ts0 which provides a better fit to Gamma in the Figure than A* Ts0 does. The expanded NLSST daytime equation becomes: SST = a₀ + a₁*T11 + a₂*(Ts0 +x)*ΔT + a₃*Sθ*ΔT which expands to: SST = b₀ + b₁* T11 + b₂* Ts0 *ΔT + b₃* ΔT + b₄*Sθ*ΔT with b₀=a₀, b₁=a₁, b₂=a₂, b₃=a₂*x, b₄=a₃. --------------- Similarly the NLSST nighttime equation expands to: SST = b₀ + b₁* T11 + b₂* Ts0 *ΔT + b₃* ΔT + b₄*Sθ

6. 6 June 2012 RMS errors

7. 7 Residual plots show that expanded NLSST form still has warm bias trend at cold SSTs, although not as severe as NLSST form. Perhaps a dry/moist stratified algorithm form could improve this. NLSST Expanded NLSST

8. 8 Summary • Results suggest that expanded NLSST form is more accurate than standard NLSST form • Gamma coefficient should be expressed as (a*x + b* Ts0 ) • For daytime VIIRS and AVHRR – • Expanded NLSST form is more accurate than MCSST • Expanded NLSST is as accurate /more accurate than NLSST • For nighttime VIIRS and AVHRR – • Expanded NLSST is more accurate than NLSST • Expanded NLSST is as accurate /more accurate than MCSST • The accuracy of the expanded NLSST form is independent of the chosen temperature unit