NOAA KLM User's Guide

Section 7.6

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7.6 Microwave Humidity Sounder (MHS)

The Microwave Humidity Sounder (MHS) has nominal and redundant Platinum Resistance Thermometers (PRTs) built into the instrument. One set each of five PRTs and three calibration resistors is routed to the telemetry acquisition circuit of the Processor and Interface Electronics A (PIE-A) and PIE-B, respectively. MHS also has nominal and redundant local oscillators, Side-A and Side-B. One of the sets will be used for nominal and the other will serve as backup. A more thorough description of the MHS instrument can be found in Section 3.9.

7.6.1 Computation of PRT Temperatures

The PRT temperatures are derived in a two-step process. First the PRT counts in the MHS data packets are converted to resistance R (in ohms) using three reference resistor values which are in the data packets (in counts). Subsequent conversion of PRT resistance R into PRT temperature is accomplished using a cubic polynomial of the form,

T sub k = sum from j=0 to 3 of F sub {kj} times {R sub k}^j (7.6.1-1)

where Tk and Rk represent the temperature and resistance of the PRT k , respectively. The coefficients fkj will be provided for each PRT. MHS has five PRTs (per PIE) mounted on the underside of the onboard calibration target (OBCT). Each PRT is sampled once per scan and these PRT counts are output in the science data packet. The PRT count must be converted into resistance Rk which appears in Equation 7.6.1-1. The process of converting the PRT counts into resistance is described in the next section.

7.6.2 Three PRT Calibration Channels

MHS has three PRT calibration channels which provide data for a linear count-to-resistance conversion that is updated in each scan. These are precision resistors whose values are known to high precision over their operating temperatures and life. Their values are chosen to lie at the upper, middle, and lower resistance ranges expected of the OBCT PRTs throughout mission life. These three resistors are referred to as the PRT Calibration channels 1, 2, and 3 (PRT CALn,where n=1, 2, and 3), respectively. Their values in counts are measured once per scan and are output in the science data packet. The resistance of the PRT CALn is assumed to be a linear function of the PRT CALn counts,

R sub CALn = alpha + beta times C sub CALn

where RCALn and CCALn represent the resistance and count of the PRT CALn, (with n=1, 2, and 3) respectively. The α and β are the offset and slope, respectively. For each scan, the CCALnvalues are measured and the RCALn values, which remain constant, are provided for each MHS flight model. Therefore, the α and β can be obtained by a least-square fit from Equation 7.6.2-1. The results are,

alpha = {{sum from n=1 to 3 of R sub CALn} times {sum from n=1 to 
3 of {C sub CALn}^2} - {sum from n=1 to 3 of C sub CALn} times {sum from n=1 to 3 of C sub CALn times R sub CALn}} over {3 times {sum from n=1 to 3
of {C sub CALn}^2} - {sum from n=1 to 3 of C sub CALn}^2}
beta = 3 times {{sum from n=1 to 3 of C sub CALn times R sub CALn} -
{sum from n=1 to 3 of R sub CALn} times {sum from n=1 to 3 of C sub CALn}} over {3 times {sum from n=1 to 3 of {C sub CALn}^2} - {sum from n=1 to 3 of C sub

7.6.3 Conversion of PRT Counts into Resistance

For each scan, these α and β values are computed and then applied to each OBCT PRT to convert the OBCT PRT count Ck into resistance Rk as follows,

R sub k = alpha + {beta times C sub k}

where Rk and Ck are the resistance and count, respectively, of the PRT k with k=1 to 5. The Rk will be used in Equation 7.6.1-1 for calculation of the OBCT PRT temperatures, Tk, values of which are output to the MHS Level 1b data.

7.6.4 Blackbody Temperature

The mean OBCT temperature, TW , is calculated from the individual PRT temperatures,

T sub w = {sum from k=1 to m of {W sub k times T sub k}} over 
{sum from k=1 to m of W sub k}+ Delta T sub W

where m=5 represents the number of OBCT PRTs (as listed in Table and Wk is a weight assigned to each PRT k. The quantity ΔTW represents a warm load correction factor, which is derived for each channel from the pre-launch test data at three instrument temperatures (low, nominal, and high). The procedure for determining the ΔTW values is described in Mo (1996). The Wk value, equals 1 (0) if the PRT k is determined good (bad) before or after launch. For the central PRT, Wk=2 will be assigned.

Similarly, a cold space temperature correction, ΔTC , may be required. This is due to the fact that the space view may be contaminated by radiation which originates from the spacecraft and the Earth's limb. Thus, the effective cold space temperature is given by:

T sub C = 2.73 + Delta T sub C

where 2.73K is the cosmic background brightness temperature and ΔTC will be determined from pre- or post-launch data analysis. The ΔTC values of individual channels and each of the possible space viewing directions will be provided for each MHS flight model in Appendix D.

7.6.5 MHS Housekeeping Thermistors and Current Monitors Standard Thermistors

There are 24 Housekeeping (HK) thermistors which monitor the temperatures at various MHS telemetry points, such as amplifiers, and local oscillators. These data, which are primarily for instrument health and safety monitoring, are not used in the radiometric retrieval algorithm of science data. The accuracy of these HK temperatures is less rigorous than that of the PRT temperatures. The 24 HK thermistors use a common set of conversion coefficients. The two-step process of converting counts to resistance and resistance to temperature can be compressed into a single step with negligible errors. This single step process computes the thermistor temperatures directly from the thermistor counts, using a polynomial of the form,

T sub th = {sum from n=0 to 4 of {g sub n} times {C sub th}^n

where Tth and Cth represent the temperature and count of the thermistors, respectively. The Cth is also referred to as the 8-bit code from the Thermistor Telemetry. The coefficients gn, which are valid for -40o C to 60o C (i.e., 243 K to 333 K), will be provided for each MHS flight model in Appendix D. Current Monitors

There are six current monitors that measure the current consumption of various power lines in the MHS instrument. The measured output in count CI is converted to current, I (in amperes) by a linear relationship as follows,

I = I sub 0 + {m times C sub I}

where I0 is the intercept and m denotes the slope, respectively. Values of I0 and m will be provided for each monitor in Appendix D. Survival Thermistors

In the MHS analog telemetry, there are three survival thermistors which monitor the temperatures of the Receiver, Electronics Equipment, and Scan Mechanism. These survival thermistors are powered to provide measurements even when the instrument power is off.

The conversion of the survival thermistor counts into temperatures is accomplished by a polynomial of the form,

T sub SUR = sum from m=0 to 5 of {h sub m} times {V^m}

where V = 0.02 x Count represents the measured output in volts. One set of coefficients hm applies to all three survival thermistors.

7.6.6 Calibration Algorithm

The calibration algorithm from Mo (1996) that converts the Earth scene counts CS to radiance, RS , is given as follows,

R sub S = R sub W + {R sub W - R sub C} times {{C sub S - mean C sub W} over
{mean C sub W - mean C sub C}} + Q

where RW and RC are the radiance computed from the OBCT temperature TW and the effective cold space temperature TC , respectively, using the Planck function. The CS is the radiometric count from the Earth scenes. The mean C sub W and mean C sub C are the convoluted blackbody count and space counts, respectively, as defined in Equation 7.6.6-3 below. The quantity Q, which represents the nonlinear contribution, is given by,

Q = u times {R sub W - R sub C}^2 times {{C sub S - mean C sub W} times
{C sub S - mean C sub C}} over {mean C sub W - mean C sub C}^2

where u is a free parameter, values of which are determined at three instrument temperatures (low, nominal, and high) from the pre-launch calibration data. After the launch of MHS, the u value at an actual on-orbit instrument temperature will be interpolated from these three pre-launch values.

For each scan, CW represents the mean blackbody radiometric count of the four samples of the blackbody target. Similarly, CC represents the mean space radiometric count of the four samples of space viewing. To reduce noise in the calibrations, the CX (where X=W or C) for each scan line were convoluted over several neighboring scan lines according to a weight function,

{mean C sub x} = sum from i=-n to n of {w sub i times C sub x (t sub i)} over
sum from i=-n to n of w sub i}
where ti (when i ≠ 0) represents the time of the scan lines just before or after the current scan line and t0 is the time of the current scan line. The variable ti can be written as: ti = t0 + iΔt, where Δt = 8/3 seconds for MHS. The 2n+1 values are equally distributed about the scan line to be calibrated. Following the NOAA KLM operational preprocessor software, the value of n=3 is chosen for MHS. A set of triangular weights, 1, 2, 3, 4, 3, 2, and 1 are chosen for the weight factor wi that appears in Equation 7.6.6-3 for the seven scans at i = -3, -2, -1, 0, 1, 2, and 3, respectively.

For MHS channel 19, the monochromatic assumption breaks down and a band correction with two coefficients has to be applied. These coefficients modify TW to give an effective temperature t sub w prime:

T sub W prime = b + c times T sub W

which is then used in the Planck function to give an accurate radiance. The application of Equation 7.6.6-4 is not necessary for the space temperature since the errors in the monochromatic assumption are negligible for such low radiance.

7.6.7 Calibration Quality Control

Quality control (QC) in the MHS calibration is very important for producing accurate calibration coefficients in the NESDIS operational calibration process. A scan-by-scan QC process can detect bad data which are flagged in the Level 1b data sets. All of the QC processes that have been built into the NESDIS operational AMSU-B preprocessor are to be included in this MHS algorithm. These and additional QC items are listed as follows,

7.6.8 NOAA Level 1b Data

The NOAA Polar Orbiter Level 1b data are raw data that have been quality controlled and assembled into discrete data sets, to which Earth location and calibration information are appended but not applied. For simplification of application, Equation 7.6.6-1 can be rewritten as,

R sub S = a sub 0 + {a sub 1 times C sub S} + {a sub 2 times {C sub S}^2}

where the calibration coefficients ai (where i = 0, 1, and 2) can be expressed in terms of RW , G, mean C sub W and mean C sub C. This is accomplished by rewriting the right-hand side of Equation 7.6.6-1 in powers of CS and equating the ai's to the coefficients of the same powers of CS. The results are,

a sub 0 = R sub W - {{C sub W bar} over G} + u times {{
C sub W bar times C sub C bar} over G^2}
a sub 1 = {1 over G} - u times {{C sub C bar} + {C sub W bar}}
over G^2


a sub 2 = u times {1 over G^2}

where G represents the channel gain and is defined as

G = {{C sub W bar}-{C sub C bar}} over {R sub W - R sub C}

These calibration coefficients will be calculated at each scan line for all channels and appended to the Level 1b data. With these coefficients, one can simply apply Equation 7.6.8-1 to obtain the scene radiance RS. Users, who prefer brightness temperature instead of radiance, can make the simple conversion,

 T sub S = B ^{-1} (R sub S)

where B-1 (RS) is the inverse of the Planck function for radiance RS . The TS is the converted brightness temperature.

For MHS channel 19, the band correction must be taken into consideration in the inverse process as follows,

T sub S = {B^{-1} (R sub S) - b} over c}

Amended February 23, 2004

Amended March 17, 2006

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