It looks like PyNIO (and hence xarray) can open this file if you rename it to have a ".h4" extension:
In [5]: mv /Users/Stephan/Downloads/A2003001.L3m_DAY_NSST_4/Users/Stephan/Downloads/A2003001.L3m_DAY_NSST_4.h4
In [6]: xr.open_dataset('/Users/Stephan/Downloads/A2003001.L3m_DAY_NSST_4.h4', engine='pynio')
Out[6]:
<xarray.Dataset>
Dimensions: (fakeDim0: 4320, fakeDim1: 8640, fakeDim2: 4320, fakeDim3: 8640)
Coordinates:
* fakeDim0 (fakeDim0) int64 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ...
* fakeDim1 (fakeDim1) int64 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ...
* fakeDim2 (fakeDim2) int64 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ...
* fakeDim3 (fakeDim3) int64 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 ...
Data variables:
l3m_qual (fakeDim2, fakeDim3) uint8 255 255 255 255 255 255 255 255 255 ...
l3m_data (fakeDim0, fakeDim1) uint16 65535 65535 65535 65535 65535 ...
Attributes:
Latitude_Step: [ 0.04166667]
Start_Year: [2002]
Map_Projection: Equidistant Cylindrical
Title: MODISA Level-3 Standard Mapped Image
SW_Point_Latitude: [-89.97916412]
Start_Time: 2002365123005000
Start_Day: [365]
Mission:
Easternmost_Longitude: [ 180.]
Longitude_Units: degrees East
Units: deg-C
Scaled_Data_Maximum: [ 45.]
Station_Name:
Sensor:
Input_Files: A2003001.L3b_DAY_NSST.main
Period_Start_Day: [1]
Number_of_Lines: [4320]
Sensor_Name: MODISA
Period_End_Year: [2003]
Scaled_Data_Minimum: [-2.]
End_Year: [2003]
Longitude_Step: [ 0.04166667]
L2_Flag_Names: LAND,~HISOLZ
End_Millisec: [8704000]
Processing_Time: 2006068023708000
Intercept: [-2.]
Product_Name: A2003001.L3m_DAY_NSST_4
Scaling: linear
Software_Name: smigen
Software_Version: 3.30
Processing_Control: smigen par=A2003001.L3m_DAY_NSST_4.param
Period_End_Day: [1]
Parameter: Sea Surface Temperature
Orbit: [0]
Mission_Characteristics:
SW_Point_Longitude: [-179.97917175]
Start_Orbit: [0]
Station_Latitude: [ 0.]
Data_Bins: [4241743]
Data_Center:
Product_Type: D
Scaling_Equation: (Slope*l3m_data) + Intercept = Parameter value
Input_Parameters: IFILE = /data1/vdc/sdpsoper/vpu0/workbuf/A2003001.L3b_DAY_NSST.main|OFILE = A2003001.L3m_DAY_NSST_4|PFILE = |PROD = sst|PALFILE = DEFAULT|RFLAG = ORIGINAL|MEAS = 1|STYPE = 0|DATAMIN = 0.000000|DATAMAX = 0.000000|LONWEST = -180.000000|LONEAST = 180.000000|LATSOUTH = -90.000000|LATNORTH = 90.000000|RESOLUTION = 4km|PROJECTION = RECT|GAP_FILL = 0|SEAM_LON = -180.000000|PRECISION = |
Start_Millisec: [45005000]
Slope: [ 0.00071718]
Southernmost_Latitude: [-90.]
End_Orbit: [0]
Period_Start_Year: [2003]
Replacement_Flag: ORIGINAL
Data_Maximum: [ 34.93000031]
Number_of_Columns: [8640]
Latitude_Units: degrees North
Station_Longitude: [ 0.]
Data_Minimum: [-1.99999905]
Northernmost_Latitude: [ 90.]
Westernmost_Longitude: [-180.]
End_Time: 2003002022504000
Measure: Mean
End_Day: [2]
Sensor_Characteristics: