ARM TR-057

> New Microwave Radiometer Profiler (MWRP) Handbook
>
> January 2005
>
> J.C. Liljegren
>
> Work supported by the U.S. Department of Energy,
>
> Office of Science, Office of Biological and Environmental Research

# Contents {#contents .Heading-Front}

[1. General Overview 1](#general-overview)

[2. Contacts 1](#contacts)

[3. Deployment Locations and History
1](#deployment-locations-and-history)

[4. Near-Real-Time Data Plots 1](#near-real-time-data-plots)

[5. Data Description and Examples 1](#data-description-and-examples)

[6. Data Quality 2](#data-quality)

[7. Instrument Details 3](#instrument-details)

# General Overview

The microwave radiometer profiler (MWRP) provides vertical profiles of
temperature, humidity, and cloud liquid water content as a function of
height or pressure at approximately 5-minute intervals for nearly all
weather conditions. The profiles are derived from measurements of
absolute microwave radiances (expressed as "brightness temperatures")
obtained at twelve frequencies in the range of 22-30 GHz and 51-59 GHz.
The data are useful for input to numerical weather forecast models and
others that require continuous, high temporal resolution profiles. The
microwave radiance measurements are useful for testing models of
microwave radiation transfer used to derive the profiles.

# Contacts

## Mentor

Jim Liljegren

Decision and Information Sciences Division

Argonne National Laboratory, Bldg. 900

Argonne, IL 60439

Phone: 630-252-0540

E-mail: <jcliljegren@pnl.gov>

## Instrument Developer

# Deployment Locations and History 

# Near-Real-Time Data Plots

# Data Description and Examples

This section is not applicable to this instrument.

## Data File Contents

### Primary Variables and Expected Uncertainty

#### Definition of Uncertainty

### Secondary/Underlying Variables

### Diagnostic Variables

### Data Quality Flags

### Dimension Variables

## Annotated Examples

## User Notes and Known Problems

## Frequently Asked Questions

# Data Quality

## Data Quality Health and Status

## Data Reviews by Instrument Mentor

## Data Assessments by Site Scientist/Data Quality Office

## Value-Added Procedures and Quality Measurement Experiments

# Instrument Details

## Detailed Description

### List of Components

### System Configuration and Measurement Methods

### Specifications

## Theory of Operation

The frequency-dependent microwave radiance, reported as a brightness
temperature TB is the fundamental quantity measured by the radiometer.
The accuracy of the brightness temperature measurements is critical to
obtaining accurate retrievals of atmospheric state parameters. The
measurement accuracy depends on the quality and stability of the
hardware as well as on the accuracy and precision of the calibration,
which can be difficult to separate. In this section the measurement
accuracy is evaluated by analysis of the calibration data and through
direct and indirect comparisons with other instruments. A detailed
investigation of the calibration procedures and algorithms is beyond the
scope of this study.

At each frequency the signal voltage ~Vsky~ resulting from a sky
measurement is transformed to a brightness temperature according to the
expression

> *T~B~ = ~Tref\ ~*^-*G*-1^ *Vref -Vsky*
>
> *( )*
>
> \(1\)
>
> where *~Tref~* is the (near ambient) temperature of an internal
> blackbody reference target, *~Vref~* is the
>
> †
>
> signal voltage resulting from a measurement of the reference target,
> and *G* is the radiometer gain
>
> given by
>
> *G = Vhi -Vlo*
>
> *(* )/ *Thi -Tlo*
>
> *( )*
>
> \(2\)
>
> where *~Thi~* ^and^ *~Vhi~* are the temperature and signal voltage
> associated with a high temperature
>
> †

reference and *~Tlo~* ^and^ *~Vlo~* are associated with a low
temperature reference. In the case of the

MWRP, the low temperature reference is provided by the internal
blackbody target such that *Tlo=Tref.* The high temperature reference is
achieved by adding a noise injection temperature *Tnd* from a calibrated
noise diode such that *~Thi~ = ~Tref~ + ~Tnd~*~.~ The gain is then
calculated as

> *G = Vref +nd -Vref*
>
> *( )*/*Tnd*
>
> *G = Vref -Vcold*
>
> *(* )/ *Tref -Tcold*
>
> *( )*

where *~Vref+nd~ -- ~Vref\ ~*is the difference in signal voltages
recorded when viewing the internal target

> †

with and without the noise diode switched on. The value of *~Tnd~* is
calibrated as follows. First the

gain is determined using

where *~Tcold~* ^and^ *~Vcold~* correspond to the temperature and signal
voltage of a cold external reference.

> †

Then (3) and (4) are combined to yield

> ***Ê ˆ***
>
> ***( )** [Vref +nd -Vref]{.underline}*
>
> *.*
>
> *Tnd = Tref -Tcold Á ˜*
>
> *Ë Vref -Vcold ¯*

Because the K-band (22-30 GHz) and V-band (51-59 GHz) receivers operate
over different

> †

ranges of brightness temperature, different methods of providing the
cold external reference

temperature are utilized.

**K-band channels (22-30 GHz)**

The water vapor resonance centered at 22.235 GHz is weakly absorbing so
the optical thickness increases linearly with increasing water vapor
amount. Consequently, the tipping curve method is used to provide the
cold reference temperatures in the 10-90 K range necessary to calibrate
the K-band channels. The tipping curve method exploits the linear
relationship between optical thickness and atmospheric path length that
holds when the sky is free of liquid water clouds and strong horizontal
water vapor gradients to derive the zenith brightness temperature, which
serves as *~Tcold~* in (5), from which *~Tnd~* is determined.

The MWRP acquires tipping curve measurements continuously, at about
15-minute intervals. These are screened for valid sky conditions based
on the linearity of the regression of optical thickness on path length
("air mass") by requiring that the correlation coefficient exceed 0.99.
Since the MWRP was redeployed to the SGP in June 2001, over 26,000 valid
tipping curves have been acquired. A statistical summary of the values
of *~Tnd~* derived from these tipping curves is graphically depicted in
Figure 5. The filled circles indicate the monthly means for 2001 (black)
and 2002 (grey); the error bars indicate twice the standard deviation,
which represents about 96% of the range of values.

The statistics depicted in Figure 5 address the issue of the long-term
stability of the K­band receiver and the calibration. The inter-annual
variation in the monthly means is generally very small (\<1%) and in no
case exceeds the spread for the month. It is also apparent that the
values of *~Tnd~* vary seasonally, which reflects a weak dependence on
temperature. To account for this, temperature correction coefficients
have been determined for each channel based on a linear fit of *~Tnd~*
^to^ ~*Tref*.~ The corrections are used to adjust the individual values
of *~Tnd~* to a nominal reference temperature (290 K). The adjusted
values are low-pass filtered: *yi = axi + (1^--^a)yi--1* where a = 0.1.
The most recent low-pass filtered values of *~Tnd~* are then adjusted to
the current value of *~Tref~* prior to being used in (3) to calculate
the gain.

\\.![](media/image1.png){width="4.279861111111111in"
height="7.793055555555555in"}

Figure 5. Monthly mean noise injection temperatures *~Tnd~* derived from
tipping curves for 2001 (black circles) and 2002 (grey circles). The
error bars indicate twice the standard deviation or 96% of the range of
values. Individual values of *~Tnd~* derived from liquid nitrogen
calibrations are indicated by crosses.

The small crosses on days 122, 179, and 340 in Figure 5 indicate values
of *~Tnd~* determined using a liquid nitrogen-filled external target to
provide the cold temperature reference in (5). For the most part these
values are consistent with the results of the tipping curve
calibrations. However, the results for the 23.035 GHz channel on day 179
in 2001 are more than two standard deviations away from the mean of the
tipping curve-derived values for that channel; the results for the
22.235 and 23.835 GHz channels on this day are more than one standard
deviation from the mean. This upward bias could have resulted from
condensation forming on the bottom of the liquid nitrogen target, which
would have caused the effective target temperature to be greater than
that used to compute ~*Tnd*;~ however, no such errors were observed in
the calibration data for the V-band (temperature sensing) channels.
Also, the spread of the liquid nitrogen-derived results is relatively
large, comparable to the monthly standard deviation of the tipping
curve­derived results in most cases. Although this suggests that the
liquid nitrogen-filled target is inferior to the tipping curve procedure
for providing a cold temperature calibration reference for the K-band
channels, the number of liquid nitrogen-derived values is insufficient
to draw a firm conclusion in this regard.

> To assess the accuracy of the brightness temperatures measured by the
> MWRP, the measurements at 23.835 and 30.0 GHz were compared with
> brightness temperatures measured by a two-channel microwave radiometer
> (MWR) at 23.8 and 31.4 GHz. The calibration of the MWR is described by
> Liljegren (2000). The differences between the MWRP and MWR brightness
> temperatures are presented as functions of the MWR brightness
> temperature in Figures 6 and 7. Because these comparisons are not at
> exactly the same frequencies, the predicted differences based on the
> Rosenkranz (1998) absorption models for oxygen and water vapor are
> also indicated. The statistics are summarized in Table 4.

Table 4 . Brightness temperature difference \~TB statistics for the
comparison of MWRP and

MWR during 2000-2002 under liquid-water-free sky conditions.

+-------------------------------+---------+---------+---------+-------+
|                               | *       | *       | > *     | **    |
|                               | *2000** | *2001** | *2002** | Model |
|                               |         |         |         | ^†^** |
+-------------------------------+---------+---------+---------+-------+
| > Number of samples           | > 8650  | 7202    | >       |       |
|                               |         |         |  13,711 |       |
+-------------------------------+---------+---------+---------+-------+
| > *23.835 -- 23.8 GHz*        |         |         |         |       |
+-------------------------------+---------+---------+---------+-------+
| > Slope of \~TB vs TB         | > 0.005 | 0.036   | > 0.030 | > -   |
| > regression, K/K             |         |         |         | 0.009 |
+-------------------------------+---------+---------+---------+-------+
| > Regression root-mean-square | > 1.03  | 0.70    | > 0.67  |       |
| > error, K                    |         |         |         |       |
+-------------------------------+---------+---------+---------+-------+
| > Mean \~TB (bias), K         | > 0.14  | 0.59    | > 0.48  |       |
+-------------------------------+---------+---------+---------+-------+
| > Standard deviation \~TB, K  | > 1.03  | 0.93    | > 0.82  |       |
+-------------------------------+---------+---------+---------+-------+
| > *30.0 -- 31.4 GHz*          |         |         |         |       |
+-------------------------------+---------+---------+---------+-------+
| > Slope of \~TB vs TB         | >       | 0.089   | > 0.070 | >     |
| > regression, K/K             |  -0.016 |         |         | 0.048 |
+-------------------------------+---------+---------+---------+-------+
| > Regression root-mean-square | > 0.79  | 0.51    | > 0.51  |       |
| > error, K                    |         |         |         |       |
+-------------------------------+---------+---------+---------+-------+
| > Mean \~TB (bias), K         | > 0.08  | 0.43    | > 0.32  |       |
+-------------------------------+---------+---------+---------+-------+
| > Standard deviation \~TB, K  | > 0.79  | 0.73    | > 0.66  |       |
+-------------------------------+---------+---------+---------+-------+

> ^†^Rosenkranz, 1998.
>
> ![](media/image2.png){width="4.733333333333333in"
> height="8.027083333333334in"}

Figure 6. Differences in measured brightness temperature between the
MWRP at 23.835 GHz and the collocated two-channel MWR at 23.8 GHz at the
SGP. The heavy black line indicates the differences between
model-calculated brightness temperatures at these frequencies.

> ![](media/image3.png){width="4.746527777777778in"
> height="7.979861111111111in"}

Figure 7. Differences in measured brightness temperature between the
MWRP at 30.0 GHz and the collocated two-channel MWR at 31.4 GHz at the
SGP. The heavy black line indicates the differences between
model-calculated brightness temperatures at these frequencies.

The results do not appear to be entirely consistent over all three
years: for both the 23.8 and 31.4 GHz comparisons, the mean difference
is near zero over the range of brightness temperatures in 2000 whereas
for 2001 and 2002 the mean difference is near zero for the lower end of
the brightness temperature range but shows increasing bias (MWRP higher)
with increasing brightness temperature. The latter behavior appears to
agree with the model-predicted trend at 31.4 GHz; however, the
correlation with the trend at 23.8 GHz suggests this may also be a
coincidence. The difference in behavior between 2000 and 2001-2002 may
be due to modifications made to the radiometer by Radiometrics after it
was returned from Barrow, Alaska in the spring of 2001. The explanation
of the observed trends in the measured brightness temperature
differences between the MWRP and MWR is not clear and will require a
detailed analysis of the tipping curve reduction algorithms implemented
in the MWRP to determine. Despite this, the mean brightness temperature
difference is generally less than the claimed 0.5 K accuracy of the MWRP
and the regression root-mean-square (due to variations in both the MWR
and MWRP) is only slightly larger than #2 times the claimed
repeatability of 0.25 K.

To assess the accuracy of all five K-band channels, comparisons were
carried out with model-calculated brightness temperatures. Of course,
such a comparison depends on the accuracy of the model as well as the
accuracy of the profiles of pressure, temperature, and water vapor used
to drive the model. The Rosenkranz (1998) absorption models were used in
the brightness temperature calculations. To overcome the known dry bias
of the radiosonde relative humidity sensors as well as to reduce the
variability in their calibration, the ARM linearly scaled sounding
product (sgplssondeC1.c1) was used to drive the model. In this product
the measured radiosonde relative humidity is linearly scaled by the
ratio of the integrated water vapor amount from a collocated two-channel
MWR to that of the original sounding. Ratios of measured-to modeled
brightness temperatures are presented in Figure 8 for the 2001-2002
deployment at the SGP. The blue circles indicate the case where the
collision-broadened width parameter *gC* of the 22.235 GHZ water vapor
line used in the model calculations was the original value supplied by
Rosenkranz; the red circles indicate the case where the width was
reduced to 95% of the original value (per conversation with S. A.
Clough). Statistics corresponding to the results in Figure 8 are
presented in Table 5.

Although the trend of increasing ratio with increasing brightness
temperature reflects the earlier trend of the MWRP--MWR comparison,
nevertheless the results clearly show that reducing the line width
substantially improves the agreement between the measurements and the
model. Not only is this an important result in its own right, but it
also demonstrates the consistency of the measured brightness
temperatures across the five K-band channels.

The scatter in these comparisons reflected in the standard deviation of
the ratios is not affected by the reduction in line width. This scatter
results from variations in the sounding data and the MWR data used to
scale the soundings as well as the MWRP measurements. This suggests that
the accuracy of the MWRP K-band channels is better than 2.5-3.0%,
consistent with the MWRP--MWR comparisons summarized in Table 4.

![](media/image4.png){width="5.229861111111111in"
height="7.273611111111111in"}

Figure 8. Ratios of measured and modeled brightness temperatures at the
K-band frequencies for both the original value of the width parameter
(blue) provided with the Rosenkranz (1998) water vapor absorption model
and 95% of the original value (red).

Table 5. Statistics of the ratio *TB, MWRP/TB, Model* at the five K-band
frequencies using the original and reduced collision-broadened line
width parameter *gC* for 719 clear-sky comparisons at the SGP during
2001-2002.

+----------------------+-----------+------------+-----------+--------+
|                      | **Mean**  |            | > **Std.  |        |
|                      |           |            | > Dev.**  |        |
+----------------------+-----------+------------+-----------+--------+
| > **Frequency, GHz** | **1.0     | **0.95     | **1.0     | **0.95 |
|                      | *gC***    | *gC***     | *gC***    | *gC*** |
+----------------------+-----------+------------+-----------+--------+
| > 22.235             | 1.040     | 1.003      | 0.026     | 0.025  |
+----------------------+-----------+------------+-----------+--------+
| > 23.035             | 1.026     | 0.998      | 0.029     | 0.028  |
+----------------------+-----------+------------+-----------+--------+
| > 23.835             | 1.013     | 1.001      | 0.026     | 0.025  |
+----------------------+-----------+------------+-----------+--------+
| > 26.235             | 0.984     | 0.996      | 0.026     | 0.026  |
+----------------------+-----------+------------+-----------+--------+
| > 30.000             | 0.997     | 1.009      | 0.032     | 0.032  |
+----------------------+-----------+------------+-----------+--------+

**V-band channels (51-59 GHz)**

The strongly absorbing oxygen resonances in the 51-59 GHz range cause
the relationship between optical thickness and absorber amount or
atmospheric path length to be non-linear, which precludes the use of the
tipping curve method for calibration. Instead, because the lowest
brightness temperature measured at the least absorbing frequency (51.25
GHz) is about 100 K, a liquid nitrogen-filled external target is used to
provide the \~77 K cold temperature reference needed to determine
*~Tnd~* in (5). As shown in Figure 9, the external target is comprised
of a very low absorption thick-walled Styrofoam^™^ container with a
blackbody target placed inside on the bottom and filled with 25-30
liters of LN2. Alternating measurements of the near ambient internal and
cold external targets are performed for up to an hour, or until
condensation forms on the bottom of the Styrofoam container. The heated
blower normally used to prevent dew from condensing on the polycarbonate
foam window of the radiometer is manually cycled on and off to delay the
formation of condensation on the bottom of the container.

The brightness temperature measured by the MWRP when viewing the LN2
target is elevated \~2K above the boiling point of LN2, which depends on
atmospheric pressure, due to a number of effects, principally reflection
at the interface between the Styrofoam and LN2 (\~1.7 K), the absorption
of the Styrofoam (\~0.2K), and the elevation of the boiling point of LN2
due to the hydrostatic pressure of the 20 cm column of LN2 above the
bottom of the container (\~0.2K) as discussed by Solheim (1993).
Corrections for these effects are included in the calibration process.
No attempt has been made in this evaluation to verify these corrections.

Since the V-band receiver was upgraded in the spring of 2001, four LN2
calibrations have been performed. The results of these calibrations are
summarized in Table 6. The standard deviations of the LN2-derived values
of *~Tnd~* over the 11-month period shown have generally been less than
1% of the mean, except for the 52.85 GHz channel, which was slightly
above 1%. This demonstrates good calibration stability.

![](media/image5.png){width="6.529166666666667in"
height="4.861805555555556in"}

Figure 9. The Microwave Radiometer Profiler (MWRP) at Barrow, Alaska
with the LN~2~-filled Styrofoam target in place during calibration of
the V-band channels in September 2000.

Table 6. Statistics of temperature-corrected *~Tnd~* at the seven V-band
measurement frequencies

> for the LN2 calibrations performed at the Radiometrics facility in
> Boulder, CO and at the SGP\
> during 2001-2002.

+-------+------+-------+-------+-------+-------+------+-------+-------+
| > **  | >    | > **  | **    | > **  | **    | **5  | > **  | > **  |
| Locat | **Da | 51.25 | 52.28 | 53.85 | 54.94 | 6.66 | 57.29 | 58.80 |
| ion** | te** | >     | GHz** | >     | GHz** | G    | >     | >     |
|       |      | GHz** |       | GHz** |       | Hz** | GHz** | GHz** |
+-------+------+-------+-------+-------+-------+------+-------+-------+
| > Bo  | Jun  | 2     | 2     | 2     | 1     | 19   | 2     | 2     |
| ulder | 2001 | 42.65 | 31.05 | 10.10 | 94.26 | 6.76 | 02.81 | 17.23 |
+-------+------+-------+-------+-------+-------+------+-------+-------+
| > SGP | Jun  | 2     | 2     | 2     | 1     | 19   | 2     | 2     |
|       | 2001 | 43.68 | 29.87 | 09.42 | 94.67 | 6.79 | 03.44 | 16.76 |
+-------+------+-------+-------+-------+-------+------+-------+-------+
| > SGP | Dec  | 2     | 2     | 2     | 1     | 19   | 2     | 2     |
|       | 2001 | 44.29 | 35.66 | 12.91 | 96.58 | 6.87 | 04.18 | 17.60 |
+-------+------+-------+-------+-------+-------+------+-------+-------+
| > SGP | May  | 2     | 2     | 2     | 1     | 19   | 2     | 2     |
|       | 2002 | 43.83 | 34.87 | 10.52 | 94.71 | 7.61 | 05.24 | 18.47 |
+-------+------+-------+-------+-------+-------+------+-------+-------+
| >     |      | 2     | 2     | 2     | 1     | 19   | 2     | 2     |
|  Mean |      | 43.61 | 32.86 | 10.74 | 95.05 | 7.01 | 03.92 | 17.51 |
+-------+------+-------+-------+-------+-------+------+-------+-------+

+--------------------+------+------+------+------+------+------+----+
| > Standard         | 0.69 | 2.83 | 1.52 | 1.04 | 0.41 | 1.04 | 0. |
| > Deviation        |      |      |      |      |      |      | 73 |
+--------------------+------+------+------+------+------+------+----+
| > Std Dev/Mean (%) | 0.29 | 1.22 | 0.72 | 0.53 | 0.21 | 0.51 | 0. |
|                    |      |      |      |      |      |      | 33 |
+--------------------+------+------+------+------+------+------+----+

Because a direct comparison of measured brightness temperatures with
another instrument was not possible, a comparison with model-calculated
brightness temperatures was performed. Again the Rosenkranz (1998)
absorption models were used with input profiles of pressure,
temperature, and water vapor supplied by radiosondes. MWRP--Model
brightness temperature differences are presented in Figure 10 as a
function of the day of the year. The colors indicate the calibration in
effect at the time of the measurement, including the deployment at
Barrow, Alaska. Summary statistics are provided in Table 7.

Several features are evident in the comparison results. First, the
measured *TB* values generally agree 1-2 K with the model-calculated
values. These biases could be due to shortcomings in the model or may
reflect the limit of the liquid nitrogen calibration procedure. Also,
the results are generally very consistent over time. The exceptions are
at 51.25 GHz for the SGP 2000 calibration and at 52.28 GHz for the SGP
2001A calibration, where substantial drift in the calibration is
evident. In both of these instances, it appears that the drift did not
continue after the instrument was recalibrated. Radiometrics recommends
monthly calibrations; however, this may not be practical at remote
locations. The data indicate that semi-annual calibrations are
sufficient, but regular calibration checks by comparison against
model-calculated values would be helpful to detect drifts that may
require a recalibration to be performed.

> ![](media/image6.png){width="5.663888888888889in"
> height="8.073611111111111in"}

Figure 10. Brightness temperature differences (measured -- modeled) for
the V-band channels under clear-sky conditions during 2000-2002. The
colors indicate the calibration in effect at the time.

Table 7. Brightness temperature difference \~TB statistics (MWRP--Model)
at the seven V-band

frequencies for 719 clear-sky comparisons at the SGP during 2000-2002.

+------------+-----------+---------------+--------+---------+--------+
|            |           | ***\~TB,* K** | *      |         | *      |
|            |           |               | **TB,* |         | **\~TB |
|            |           |               | K**    |         | /TB*** |
+------------+-----------+---------------+--------+---------+--------+
| > **       | **Mean**  | **Std. Dev.** | **     | **Std.  | **Std. |
| Frequency, |           |               | Mean** | Dev.**  | Dev.** |
| > GHz**    |           |               |        |         |        |
+------------+-----------+---------------+--------+---------+--------+
| > 51.25    | 1.11      | 1.72          | 111    | > 6.70  | 0.015  |
+------------+-----------+---------------+--------+---------+--------+
| > 52.28    | -0.86     | 1.36          | 153    | > 6.12  | 0.009  |
+------------+-----------+---------------+--------+---------+--------+
| > 53.85    | 0.62      | 0.65          | 257    | > 5.88  | 0.003  |
+------------+-----------+---------------+--------+---------+--------+
| > 54.95    | -0.07     | 1.18          | 287    | > 5.68  | 0.004  |
+------------+-----------+---------------+--------+---------+--------+
| > 56.66    | 0.77      | 0.45          | 294    | > 6.47  | 0.002  |
+------------+-----------+---------------+--------+---------+--------+
| > 57.29    | 1.06      | 0.47          | 294    | > 6.51  | 0.002  |
+------------+-----------+---------------+--------+---------+--------+
| > 58.80    | 0.86      | 0.79          | 295    | > 6.67  | 0.003  |
+------------+-----------+---------------+--------+---------+--------+

Although the standard deviation of the differences is generally small --
mostly less than 1 K and considerably less than 1% of the mean -- the
51.25 GHz channel appears to be noisy relative to the other channels,
and the 54.94 and 58.80 GHz channels appear to have become considerably
noisier in July 2002. This aspect of radiometer performance is
quantified by the noise figure *F* in decibels, defined by Solheim
(1993) as

> Ê *[Tr +]{.underline} [T]{.underline}*[0]{.underline} ˆ
>
> *F* =10log Á ˜ . (6)
>
> Ë ^*T*0^ *¯*

*T0* is a reference temperature set to 290 K by convention. *T~r~* is
the effective noise temperature of

> †

the receiver such that the brightness temperature *TB* corresponding to
a signal voltage *V* measured by the radiometer is given by

> *T~B~ = ^G^*^-1^ *V -V*~0~
>
> *( )*
>
> \(7\)

and *V0* is the voltage offset due to the receiver temperature (i.e.,
*T~r~ = G^-1^V0). †*

Substituting (2) for the gain into (7), *T~r~* can be calculated as

> [*Thi* ^-*Y*^]{.underline} *[Tlo]{.underline}*
>
> *T~r~ = ,* (8)
>
> *Y* -1

where *Y = ~Vhi/Vlo~*~.~ In the case of the MWRP for *~Tlo~ =
~Tref\ ~*^and^ *~Thi~ = ~Tref~ + Tnd,*

> *[Tnd]{.underline}*
>
> *T~r~ = -Tref*
>
> \(9\)
>
> *Y* -1

and *Y = ~Vref+nd~ / Vref.*

> †

Weekly averaged values of *F* are presented in Figure 11 for the 7
V-band channels during the SGP deployment in 2001-2002. The error bars
indicate twice the standard deviation or 96% of the range of values. The
dashed line indicates the value of *F* (5.55 dB) corresponding to *T~r~*
= 750K, a typical value for a radiometer of this design. It is clearly
evident that the noise figure significantly exceeds 5.55 dB for the
51.25 GHz channel whereas all of others have noise figures at or below
5.55 dB until week 29 (mid-July) of 2002. The relatively greater scatter
in the MWRP--Model comparison at 51.25 GHz in Figure 10 and Table 7
reflects the elevated noise figure for this channel. At week 29 the
average value of *F* jumps above 5.55 dB at 54.94 GHz, and the spread of
the weekly averages increases markedly at 51.25, 54.49, and 58.80 GHz.
Radiometrics diagnosed this as a failing synthesizer.

**Infrared Thermometer (IRT)**

The accuracy of the IRT measurements was evaluated by comparison with a
similar instrument mounted on the collocated MWR at the SGP, and by
comparison with the Atmospherically Emitted Radiance Interferometer
(AERI) spectrometer at both the SGP and NSA. The comparison with AERI
was accomplished by first integrating the AERI spectral radiance *L(n)*
over the IRT pass band *f(n)*

> u2

*L = L(u) f (u)du Ú*

> \(10\)
>
> *v*1

then integrating the Planck radiance *B(n, T)* over this pass band

> u2
>
> *L*\* *= B(u,T) f (u)du Ú*
>
> *v*1

and iteratively adjusting the temperature until *^L\*^ = L.* The results
of these comparisons are

> †

presented in Figure 12 and summarized in Table 8.

> ![](media/image7.png){width="3.0965277777777778in"
> height="7.136805555555555in"}

Figure 11. Weekly average values of noise figure for the V-band channels
during 2001-2002 at the SGP. The error bars indicate twice the weekly
standard deviation. The dotted line corresponds to an effective receiver
noise temperature of 750 K.

![](media/image8.png){width="3.3868055555555556in" height="8.23125in"}

Figure 12. Comparison of IRT on MWRP with (a) IRT on MWR at SGP for
2002-2001; (b) AERI at SGP during June 2001; (c) AERI at NSA during
February 2001.

Table 8. Statistical summary of IR temperature comparison (MWRP -- MWR)
for 2001-2002 at\
SGP for all sky conditions.

  -----------------------------------------------------------------------
  Number of comparisons 19,367 Mean difference (bias) -0.11

  K Median difference -0.56 K Standard deviation 4.5 K
  -----------------------------------------------------------------------

The agreement between the IRT on the MWRP and the IRT on the MWR shows
negligible bias. However, the large scatter and corresponding large
standard deviation is primarily due to the differences in field of view.
The IRT on the MWRP has a 30° field of view whereas the field of view of
the IRT on the MWR is less than 3°. Although the larger field of view
permits greater sensitivity, it also causes the IRT to respond to clouds
that are not within the field of view of the MWRP (Table 1). The
agreement with AERI is also good, but shows increasing bias at low sky
temperatures. This is consistent with the expected decrease in accuracy
as the difference between the IRT housing temperature and the target
temperature increases (Table 1).

**Surface Meteorological Sensors**

The comparison of the barometric pressure, temperature, and relative
humidity sensors in the MWRP to the surface values of the radiosondes is
summarized in Table 9.

Table 9. Statistical summary of surface meteorological sensor comparison
(MWRP -- sonde) for\
719 soundings at SGP, 2001-2002.

+-----------------------+--------------+---------------+--------------+
|                       | **\~P, mb**  | **\~T, K**    | **\~RH, %**  |
+-----------------------+--------------+---------------+--------------+
| > Mean (bias)         | -0.14        | 0.12          | -0.48        |
+-----------------------+--------------+---------------+--------------+
| > Standard deviation  | 0.66         | 0.71          | 3.5          |
+-----------------------+--------------+---------------+--------------+

These results are consistent with the combined uncertainty in the MWRP
sensors and the radiosonde sensors.

## Calibration

### Theory

### Procedures

### History

## Operation and Maintenance

### User Manual

### Routine and Corrective Maintenance Documentation

### Software Documentation

### Additional Documentation

## Glossary

See the [ARM Glossary](http://www.arm.gov/about/glossary.stm).

## Acronyms

See the [ARM Acronyms and
Abbreviations](http://www.arm.gov/about/acronyms.stm).

## Citable References