The MODIS SST hypercube is a multi-dimensional look up table of SST retrieval uncertainty, bias and standard deviation, determined from comprehensive analysis of the MODIS Match-up Data Base (MDB). The MDB includes contemporaneous, co-located satellite brightness temperature, in-situ buoy and radiometer SST, environmental ‘observations’ from analyzed model or satellite observed fields, satellite viewing geometry, time and location. A series of quality tests is applied to each pixel during processing of the MDB data to identify cloud and dust aerosol contaminated retrievals and assign each pixel to one of several quality levels (0-3).

After grouping MDB records by quality level the dataset is partitioned into a multi-dimensional array with the following 7 dimensions:  time by season (4)  latitude bands (5 steps in 20 degree from 60S to 60N)  surface temperature (8 increments in 5 degree steps)  satellite zenith angle (4 increments)  brightness temperature difference as a proxy for water vapor (4 intervals for 4 um and 3 intervals for mm SST)  retrieved satellite SST quality level (2 intervals ql==0 and 1)  day/night selection (2 intervals).

The bias (satellite-in situ) and standard deviation are then computed for each element. This hypercube look up table is then used during processing to predict the uncertainty bias and standard deviation of the retrieval. Requires a large MDB sufficient geographic, seasonal, and viewing geometry to capture statistical performance of both algorithm and sensor. –TERRA 7+ years 2.6 million records –AQUA 5+ years 2.4 million records –Unlike your stockbroker,the hypercube approach assumes that the past does predict future performance and that the types of errors can be classified and these characteristics remain relatively stable.

Determining partitions in a hyper cube  Requires understanding of what drives retrieval performance and a good reference fields for exploring the relationships.  The MMDB contains 130 satellite, in situ and ancillary fields that are used to explore the SSES by recursive partitioning. Understanding algorithm strengths and weaknesses  Water vapor, aerosol, clouds  Measurement understanding skin,bulk, reference  Sensor characteristics  viewing geometry,mirrors, detectors, calibrations

Through recursive partitioning the dataset is split into smaller bins along the 7 dimensions while still retaining a sufficient number of records within a bin to produce stable and meaningful statistics (>50 records/bin). Some regions of the hypercube will always remain unpopulated generally when the bin is non-physical eg. It’s never 30 60N. Bins that contain insufficient records due to a lack of in situ buoy measurements (generally at high latitudes during winter months) are filled with the global SSES average as the default.

The MODIS SSES are referenced to in situ bulk measurements but the MODIS instrument measures skin temperature. Diurnal heating effects means that the measurement of the error will behave differently at night versus day- - a natural split in the cube. Water vapor and aerosols can impact the uncertainty estimates for MODIS this is captured by proxy in the channel BT differences (dBT). The quantity and distribution of water vapor, type of aerosol change as a function of latitude and time of year. The relationship between dBT the SSES also changes as a function of scan angle and surface temperature.