(1) Department of Ocean Sciences, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, Florida, USA (2) Jet Propulsion Laboratory, NASA, Pasadena, California, USA Yang Liu(1), Toshio Chin(2), Peter Minnett(1) The Parameterization of Sampling Errors in Infrared Sea Surface Temperatures Clouds and inter-swath gaps are the primary reasons for incomplete coverage of satellite infrared (IR) measurements of the Earth’s surface, and yield sampling errors in averaged IR Sea-surface Temperature (SST) fields. In a recent paper (Liu & Minnett. 2016; hereafter referred to as LM16) we found that the MODIS (Moderate Resolution Imaging Spectroradiometer (Esaias et al. 1998)) monthly SST sampling error referenced to MUR SSTs (Multi-scale Ultrahigh Resolution (Chin et al. 2010), is up to O(1 K), which far exceeds the error threshold needed for climate research. The next question to ask is, can the sampling errors be predicted? In reality, when assessing sampling errors in satellite-derived IR SST fields we do not have an appropriate reference field at the various temporal and spatial averaging intervals. However, we do have access to a number of relevant variables that can be used with the results of LM16 to estimate the sampling errors, for example in terms of the local SST difference from a reference, gap fraction, cloud persistence (the number of consecutive days during which a location is detected to be cloudy), or season and region. Introduction Figure 3. Global seasonal sampling errors quantified using MUR SSTs (red) and MUR SST anomalies (blue). Figure 2. Sampling errors generated using OISST climatology. Upper: temporal averaging of [0.25º, mon]; lower: spatial averaging of [5, 1d]. Boreal seasons are denoted on the Asian continent. As a preliminary exploration, we assume the error function can take the form: 𝜀𝜀𝑚𝑚= 𝛼𝛼0𝜀𝜀𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐+ (𝛼𝛼1𝑓𝑓𝑎𝑎2 + 𝛼𝛼3 ො𝑝𝑝𝑎𝑎4)𝜎𝜎+ 𝛼𝛼5 where 𝛼𝛼0, 𝛼𝛼1, 𝛼𝛼2, 𝛼𝛼3, 𝛼𝛼4, 𝛼𝛼5, are coefficients found by a Levenberg-Marquardt algorithm to reach a non-linear least squares fit; 𝛼𝛼3 = 0 in spatial sampling error estimates, 𝑓𝑓is the gap fraction (0 < 𝑓𝑓< 1), ො𝑝𝑝is the normalized cloud persistence (0 < ො𝑝𝑝< 1), and 𝜎𝜎is the standard deviation of the SSTs in the averaging grid cell from MUR (𝜎𝜎𝑀𝑀𝑀𝑀𝑀𝑀). We also test the model using SST standard deviation of the climatology (𝜎𝜎𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐). When 𝜎𝜎𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐is applied, the model computes the sampling error estimates 𝜀𝜀𝑚𝑚′ without any inputs from a Level 4 reference field and thus is predictive. Error Parameterization Figure 1. Sampling errors generated using MUR SST. Upper: temporal averaging of [0.25, mon]; lower: spatial averaging of [5, 1d]. Boreal seasons are denoted on the Asian continent. The sampling errors quantified using MUR SST anomalies calculated using the OISST climatology (Banzon et al, 2014) as the reference are smaller, especially in spatial averages that both mean error and RMSE are substantially (>90% mean ERR and >50% RMSE) reduced after the seasonal signals are removed. However, the RMSE and the mean error barely change magnitudes after the removal of the climatology. Banzon, V.F., Reynolds, R.W., Stokes, D., & Xue, Y. (2014). A 1/4°-Spatial-Resolution Daily Sea Surface Temperature Climatology Based on a Blended Satellite and in situ Analysis. Journal of Climate, 27, 8221- 8228 Chin, T.M., Jorge, V., & Armstrong, E. (2010). Algorithm Theoretic Basis Document: Multi-scale, motion- compensated analysis of sea surface temperature Version 1.1. Liu, Y., & Minnett, P.J. (2016). Sampling errors in satellite-derived infrared sea-surface temperatures. Part I: Global and regional MODIS fields. Remote Sensing of Environment, 177, 48-64 SST Sampling Errors The Climatology Component Figure 4. The 60ºN-80ºN summer month error estimates using 𝜀𝜀𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 (first column), 𝜀𝜀𝑚𝑚′ (second column), and 𝜀𝜀𝑚𝑚(third column). r denotes the correlation coefficients; N is the total number of grids at the resolution [0.25º, mon]; RMSE and the fitting line are de