SMAP Radiometer Performance Model Derek Hudson, GSFC 8 January 2009

1. SMAP Radiometer Performance Model Derek Hudson, GSFC 8 January 2009

2. General Method • Estimate of Th = f( dozens of measurements, mi) • Uncertainty2 in Th = Σi (δf / δ mi)2 (uncertainty in mi)2 + additional terms where uncertainties in mi are correlated

3. Internal calibration ΔT (w/o bias) Antenna pattern correction ΔT Main beam instability Cross-pol instabilities Sidelobe instability Sidelobe Earth, Sun, and Space scene uncertainty Thermal ΔT Reflector losses Feed losses Front-end losses Thermal fluctuations Noise diode calibration Reference load calibration Residual Faraday rotation ΔT Radio-Frequency Interference Residual error after RFI removal Guess of undetectable RFI (or count as data loss???) Uncertainties (ΔT) to include in L2-SR-45

4. Uncertainties NOT includedin Level 2 Science Requirement 2.1.9 • Uncertainty of absolute calibration standards (see sketch) • Assume post-launch calibration / validation will ascertain scale error and offset • Earth sidelobes inside main beam • Atmospheric uncertainties

5. Radiometer error budget

6. Assumptions/notes common to all cases • NEΔT: • Nominal 285 µsec PRI • Nominal 230 µsec tau per PRI (output ≡ “snapshot”) • Binning of snapshots into 30 km x 30 km grid in swath coordinates) • Yields minimum net integration time = 32 ms (fore looks only) • 280 K antenna temperature and 35.4 K (0.5 dB) LNA noise temp (figure) • Ant. pattern: CBE of 0.3 K is driven by large assumptions: MBE stability of 0.1%, ESL stability of 3%, and corr. coeff. of -0.5 between them. • Calibration: CBE is 0.2 K but depends on immature operations concept and thermal stability • RFI: residual error unknown – highly dependent on RFI trade decision, RFI data loss requirement, and urban etc. masks • Faraday rotation: residual error unknown – depends on calibration biases and may differ for AM vs PM data.

7. Assumptions in “CBE” • NEΔT: • Bandwidth = 20 MHz. • Pre-LNA loss = 3.4 dB (add cross-over switch=.1 & cable=.22; old (Aquarius) internal coupler=.9) • Ant. pattern: stability assumptions are accurate • Calibration: optimal interleaving of cal and scene snapshots; no surprise effects

11. Major APC assumptions • Land north of 70 deg and south of S. America is excluded (affected in eclipse season) • 0.1% of pixels are written off as data loss (rather than affecting error budget) since AP G_sun is highest for them. • MBE HAS A 1-SIGMA STABILITY OF 0.1% ( 0.3 K error) • Unmodeled boom & feed back radiation lower MBE by 3% • MB cross-pol efficiency (fraction) HAS A 1-SIGMA STABILITY OF 1% ( 0.01 K error) • EARTH SIDELOBE FRACTION HAS A 1-SIGMA STABILITY OF 3% ( 0.1 K error) • A constant nominal G_sun is used to correct for solar contribution for the whole mission (the simplest correction). ( 0.1 K error) • MBE fluctuations and ESL fraction fluctuations have a corr. coeff. of -0.5 • MBE fluctuations and Gsun error have a corr. coeff. of 0.1 • Gsun error and ESL fraction fluctuations have a corr. coeff. of 0.2

12. Error due to mesh emissions • - Assume emissivity of 0.0040 (worst case from 2001 OSIRIS testing) • Assume 30 deg C 1-σ error in knowledge of mesh temp. (see plot above, provided by E. Y. Kwack) • Resulting error due to mean emissivity is 0.12 K. • Assume 22 K 1-σ variability in mesh temperature (excluding eclipse, see plot above) • Resulting error is 0.05 K. • Worst case total error (sum of above): 0.17 K, which satisfies 0.2 K allocation.

14. Questions & Requests on L2 Science Requirements • Must undetected (but expected) error be booked in the 1.5 K error budget, not written off as data loss? • Example: suppose we expect small solar flares to add 2 K to the data 0.1% of the time. Two options to deal with this: • (1) Do not detect or correct for it in processing, but allocate 0.1% of Data Loss to it. • (2) Detect and correct for it (using ancillary data) and budget the residual as part of the 1.5 K error budget. • RFI data loss requirement is needed – and expect it to be met with zero margin, since that minimizes residual RFI (accomplished by tuning detection threshold). • Faraday rotation needs no allocation in my budget since 1.5 K only applies to AM data (can that be stated in L2-SR-45?) and is adequately booked in Science error budget • Add to L2-SR-45 that 1.5 K (1-sigma) applies to each pixel separately, not on a regional or global basis? • Define urban mask (or threshold “urban” population density) and other masks • 30% along-scan overlap has no effect on 1.5 K reqmt! Is that acceptable? • Whether analog backend meets requirements depends on requirements…

15. Backup slides

19. Assumptions in “Best Case” • NEΔT: • Bandwidth = 25 MHz. • Pre-LNA loss = 2.4 dB (no BPF, no cross-over switch, new internal coupler = 0.3 dB) • Ant. pattern: stability assumptions are over conservative • Calibration: optimal interleaving of cal and scene snapshots; no surprise effects • RFI: larger undetected RFI ≡ data loss and/or much urban masking and/or hardware upgrade for subbanding (+kurtosis?) • Faraday: small cal biases and/or AM data only (possibly with ancillary ionospheric data)

20. Assumptions in “Worst Case” • NEΔT: • Bandwidth = 20 MHz. • Pre-LNA loss = 3.9 dB (add BPF=.2, cable=.24, cross-over switch=.1, & cable=.24; old (Aquarius) internal coupler=.9; worst of Aquarius OMT etc.) • Ant. pattern: stability assumptions are underestimates • Calibration: sub-optimal (but simple) scheduling of cal snapshots; effects unaccounted for • RFI: larger undetected RFI ≡ error and/or little urban masking and/or Aquarius-like hardware • Faraday: medium cal biases; budget for PM data; error adds to total rather than RSSing

21. Derivation of mesh emissions error • True emissions = (Tave + Tvar) * e. Tvar captures variation over each scan, orbit, and year. Worst case Tave + Tvar varies from about 80+273 to 210+273 K (see Mr. Kwack’s plots), so Tave is 145+273 while Tvar ranges from -65 to +65 K, which I model as a zero mean Gaussian random variable with standard deviation of 22 K. • Define our best estimate of mesh emissions as (Tave + Tvar +ΔT)*(e+Δe). • ΔT: Is difficult to know error in model of mesh temperature. Assume 30 K, 1-sigma. Ask Mr. Kwack for better info • e: Combining the two 20 opi estimates in Table 6.3-1 of 2001 OSIRIS report gives a CBE of 0.0023. • Δe: Combining the two 20 opi standard deviations inTable 6.3-1 of 2001 OSIRIS report gives a standard deviation of 0.00057. But we need 3-sigma for Δe since Δe will not fluctuate. Therefore, use Δe=0.00172. Assume Δe is constant over the mission (if it weren’t, antenna gain would probably change). • There are two different corrections which we might implement: • 1) A constant correction -- subtract our best constant estimate, (Tave +ΔT)*(e+Δe),from the radiometer measurents • Resulting error = -Tave*Δe + Tvar*e - ΔT*(e+Δe). • The -Tave*Δe term is a constant bias which we assume to be removed along with other biases via post-launch cal/val.’ • The Tvar*e term has a 1-sigma value of 22*0.0023 = 0.051 K. This residual error will vary quickly (period of one scan) for smallest beta angles. Assuming ground coverage is NOT exact repeat, this residual for a given pixel will vary in a quasi-Gaussian manner over the course of half a year. (Ask Mr. Kwack to generate T over half a year to get better idea. Perhaps could be reduced by a careful analysis to determine Δe during first 90 days in orbit.) • -ΔT*(e+Δe) term: Its worst case size = 30*(0.0023+0.00172)= 0.121 K. • We do not know how correlated ΔT is with Tvar. Assume worst case (-100% correlation) so that the Tvar*e and -ΔT*(e+Δe) terms add rather than RSSing. Then total mesh emissions error is 0.051+0.121 = 0.171 K, which is less than our 0.2 K allocation. • 2) A more sophisticated correction – subtract best estimate of (Tave + Tvar +ΔT)*(e+Δe) from the radiometer measurents. • Resulting error = -Tave*Δe - Tvar*Δe - ΔT*(e+Δe), which is same as above except that second term is reduced to a magnitude of 22*0.00172=0.038 K. • Total error therefore is reduced to 0.159 K. Not a significant improvement.

23. Derivation of RFE thermal rate requirement • Aquarius’s three RF amplifiers have a gain sensitivity of 0.02 dB/°C each, for a total of 0.06 dB/°C. Similar sensitivity expected for SMAP. • Allocation for gain uncertainty is 0.1% (has been all along) • Assume full calibration every 4 s (conservative -- one edge only) • Allocate 1/10th of gain uncertainty to non-zero thermal rate – i.e., 10^(0.06*R*4 sec / 10) < 1.0001 • Thermal requirement is therefore R < 0.11 °C/minute • Current requirement (R < 0.05 TBR °C/minute) satisfies this with factor-of-two margin

24. Thermal stability of uncalibrated components • L3-Instr-474 reads, “Uncertainty (one-sigma, not including removeable bias) in knowledge of the combined loss of the feedhorn through the OMT-side half of the CNS coupler, over the radiometer passband, shall be less than 0.01 (TBR) dB.” • An over-conservative, draft translation of this requirement into thermal requirements is the following. The components referred to, in order from the feedhorn, are feedhorn, thermal isolator, OMT, cable, and CNS coupler. Define the standard deviation of their respective temperatures (from unspecified mean values) as ΔT1, ΔT2, ΔT3, ΔT4, and ΔT5, in degrees Celsius. The thermal design must be such that these standard deviations satisfy the following inequality: • -10*log10 { (1 - ΔT1/13e4) (1 - ΔT2/11e4) (1 – ΔT3/1.4e4) (1 - ΔT4/7e4) (1 - ΔT5/19e4) } ≤ 0.01 dB . (1) • CBE is that the left hand side is about 0.001 dB (based on EY Kwack simulations of mesh, horn, isolator, & OMT)